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begins to increase from zero. However, t here is no meaningful change in the physics or discernable signal 
in the transient when pressure is equal to  Shmin. Because  there is not a signal in the data when pressure 
reaches Shmin, the difference between contact pressure  and Shmin  is a source of uncertainty  when 
estimating Shmin . 
Craig and Blasingame (200 6) and Craig et al. (2017) define the total storage in a piece -wise fashion – 
neglecting different parts of the storage at different points during the test. In their definition, th e 𝐴
𝑆𝑓 term is 
negligible after ‘closure, ’ implying that Sf is infinite. This assumption does not appear to be well -founded. 
With realistic values in Equation 4, the 𝐴
𝑆𝑓 term is not negligible until pressure is hundreds or thousands of 
psi below Shmin.  
A.3 G -function analysis  
The G -function (also called G -time) is a monotonic transformation of Δ𝑡 (shut-in time ). Nolte (1979)


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derived the G -function (also call ed G-time) such that, under reasonable assumptions, the cumulative leakoff 
after shut -in is linearly proportional to G -time. A related function, the g -function, is derived to be linearly 
proportional to the cumulative leakoff from the start of injection (C astillo, 1987; Gulrajani and Nolte, 2000) : 
𝑉𝐿(Δ𝑡)=2𝐴𝐶𝐿√𝑡𝑒𝑔(Δ𝑡).          (13) 
The G -function is defined as:  
𝐺(Δ𝑡)=4
𝜋(𝑔(Δ𝑡)−𝑔(Δ𝑡=0)).        (14) 
The cumulative leakoff after shut -in is defined as:  
𝑉𝐿𝑠(Δ𝑡)=2𝐴𝐶𝐿√𝑡𝑒(𝑔(Δ𝑡)−𝑔(0))=𝜋
2𝐴𝐶𝐿√𝑡𝑒𝐺(Δ𝑡).      (15) 
The exact form of the G and g functions depend on assumptions about fracture growth. However, there is 
little practical difference between the different forms of the g and G -functions. For example, within 
reasonable ranges, the cumulative leakoff at shut -in can be bounded with 𝑔0=𝑔(Δ𝑡=0) is a number in 
the narrow range between 4/3 and 𝜋
2 (Equation 30 of the appendix from Gulrajani and Nolte, 2001). The 
most common form of the g -function is:  
𝑔(Δ𝑡)=4


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most common form of the g -function is:  
𝑔(Δ𝑡)=4
3[(1+Δt
te)1.5
−(Δt
te)1.5
].        (16) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   31 
Because cumulative leakoff after shut -in is proportional to G -time, the derivative of cumulative leakoff 
with respect to G -time is equal to a constant. In the ideal case, f racture stiffness is constant prior to contact , 
and so the total system storage (and  stiffness) are also constant prior to contact.  Therefore, from Equation  
3, a plot of pressure versus G -time should form a straight line  (Castillo, 1987) : 
𝑑𝑃
𝑑𝐺=1
𝐶𝑡𝑑𝑉
𝑑𝐺=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 .          (17) 
If fracture geometry and mechanical properties of the rock are known, then Equation 17 can be solved for 
the leakoff coefficient  (Nolte, 1979; Castillo, 1987; Gulrajani and Nolte, 2000) .  
If the fracture formed instantaneously during injection, then the G -function would be equivalent  the square 
root of time . The square root s caling aris es because the G -function assumes  Carter leakoff. The G-function 
is not exactly equal to the square root of time because accounts for the progressive growth of the fracture


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during injection. As a result, t he duration of leakoff is a function of position along the fracture area. 
Equation 24 from  McClure (2017) provide s a succinct derivation of the G -function for the special case that 
the fracture grows linearly with respect to time during injection.  
A.4 Deviation from Carter leakoff  
The G -function  is derived based on the assumption of Carter leakoff (Nolte, 1979; Howard and Fast, 1957 ). 
For the simple case with no filtrate zone or filtercake, Carter leakoff can be derived as the solution the 1D 
diffusivity equation with a Dirichlet  (constant pressure)  boundary condition  (Bird et al., 2007) : 
𝑉𝐿𝑠=4𝐴√Δ𝑡(𝑃−𝑃𝑟𝑒𝑠)√𝜙𝑐𝑡𝑘
𝜋𝜇=4𝐴𝐶𝐿√Δ𝑡.       (18) 
The leakoff coefficient is defined from Equation 18 as: 
𝐶𝐿=(𝑃−𝑃𝑟𝑒𝑠)√𝜙𝑐𝑡𝑘
𝜋𝜇.          (19) 
The leakoff coefficient can be generalized to include the effect of filtrate invasion and filtercake formation. 
Filtercake does not form during a DFIT becaus e the injection is performed with water. Filtrate invasion is


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minor in DFIT’s because of the low permeability and relatively large fracture surface area.  
The G-function assumption of Carter leakoff  is violated during a DFIT because pressure decreases over  
time (Castillo, 1987). As long as the change in the fracture pressure is relatively small relative to the 
difference between ISIP (initial shut -in pressure) and the formation fluid pressure, then the leakoff rate is 
reasonably described by Carter leakoff.  But e ventually, the fluid pressure drops sufficiently far that there is 
significant deviation from Carter leakoff (Castillo, 1987) . The leakoff rate reduces relative to the rate that 
would have occurred if Carter leakoff had continued. Because  𝑑𝑉
𝑑𝐺 is constant during  Carter leakoff , the 
deviation causes  𝑑𝑉
𝑑𝐺 to decrease  (because leakoff occurs more slowly than if Carter leakoff had continued),  
and so the derivative of pressure with respect to G -time begins to decrease.  This causes dP/dG  to decrease


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and G*dP/dG to bend downward. The peaking of G*dP/dG and t*dP/dt occurs during the progressive 
transition from Carter leakoff  to late -time impulse behavior (McClure, 2017).  
A.5 The effect of closure  
Equation  3 provides a conceptual framework f or understanding the effect contact between the fracture 
walls. When the fracture walls come into contact, stiffness begins to increase (Equation 7). Increasing 
stiffness c auses dP/dG to increase. Based on this insight, contact can be identified as occurring when dP/dG 
begins to increase (McClure et al., 2016).  
Equation  3 depends on the assumption that pressure in the fracture can be described with a single parameter, 
P. This is valid if the fracture is approximately infinite conductivity. The dimensionless fracture 
conductivity is defined as:  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   32 
𝐶𝑓𝐷=𝐶𝑓
0.5𝑘𝐿𝑓,           (20) 
where 𝐶𝑓 is fracture conductivity and Lf is fracture length. Fractures are ‘infinit e conductivity’ when 𝐶𝑓𝐷 is 
above approximately 300 (some authors use a lower threshold). From the cubic law, fracture conductivity 
is equal to (Witherspoon et al., 1980):  
𝐶𝑓=𝑊3
12.           (21) 
For a fracture with half -length of 150 ft and matrix permeability of 100 nanodarcies, the fracture will be 
infinite conductivity as long as fracture aperture is greater than just 2 5 microns  (equivalent to conductivity 
around 1 md -ft). Zhang et al. (2013) measured the conductivity of unpropped fra ctures in the Barnett Shale 
and found that conductivity remained above 1 md -ft until effective normal stress exceeded 1000s of psi. 
For unaligned fractures, the conductivity was even higher, and in -situ, fractures are probably rougher than 
in small -scale f ractures induced in the lab.


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in small -scale f ractures induced in the lab.  
For permeability on the order of microdarcies or millidarcies, it becomes less likely that the fracture will 
remain infinitely conductive after contact. If dimensionless fracture conductivity drops sufficiently rapidly 
with co ntact, then it is conceivable that nonnegligible pressure gradient could develop in the fracture. If this 
occurs, then contact would cause an apparent reduction in the ‘leakoff rate,’ 𝑑𝑉
𝑑𝐺, and this could potentially 
cause the pressure derivative to de crease, rather than increase, with contact.  
In the worst case, stiffness and leakoff rate could change in approximately equal amounts and result in no 
change in 𝑑𝑃
𝑑𝐺 with contact. This scenario is probably uncommon because it requires coincidental equ ality 
of two opposing effects, but probably occurs occasionally. Decreasing 𝑑𝑃
𝑑𝐺 with contact (due to decreased 
dimensionless fracture conductivity) has been confirmed by numerical simulation (McClure et al., 2016).


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If this occurred, 𝑑𝑃
𝑑𝐺 may decre ase monotonically after contact. If the fracture begins to become finite 
conductivity, it is possible that the conductivity could be spatially variable along the fracture area.  
A.6. Impulse flow  
Craig and Blasingame (2006) pointed out that the late time be havior of a DFIT can be described with 
impulse flow solutions from conventional well test analysis. The impulse flow solution can be found by 
taking the dimensionless time derivative of the nondimensionalized solution for constant -rate injection 
(Houze et al, 1988; Ayoub et al., 1988; Gu et al, 1993). For example, constant rate injection into an infinite 
conductivity fracture yields a scaling of Δ𝑃∝(Δ𝑡)1
2 (Gringarten et al., 1974) . Therefore, the impulse 
solution for an infinite conductivity fracture is Δ𝑃∝(Δ𝑡)−1
2. Late-time impulse transients can be used to 
infer permeability and fluid pressure (Sections A.10.iii and 3.1.6). 
A.7 Near -wellbore pressure drop


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A.7 Near -wellbore pressure drop  
In field DFIT’s in horizontal wells , there is usually always  a period of rapid pressure drop immediate ly after 
shut-in. At very early time, this pressure drop is due to the end of wellbore and perforation friction  (if the 
well is perforated) . But subsequently, there can be  a period of rapid pressure drop  that may last tens of 
minutes or longer. During this  time, pressure commonly drops  by 1000s of psi. This behavior  is apparent  
in most of the field data reviewed in this study.  
Near -wellbore pressure drop can be modeled as a pressure difference between the wellbore and the fracture 
(Wright, 2000):  
Δ𝑃𝑛𝑤=𝐶𝑛𝑤𝑄𝛽,          (22) 
where 𝐶𝑛𝑤 is a constant, Q is the volumetric flow rate from the well into the fractur e, and 𝛽 is an exponent 
(typically equal to 0.5).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   33 
After shut -in, flow at the wellhead is zero, but fluid continues to flow into the formation because of wellbore 
storage. The flow rate Q can be estimated as:  
𝑄=𝐶𝑤𝑑𝑃
𝑑𝑡.            (23) 
Δ𝑃𝑛𝑤 can be estimated from the equation:  
Δ𝑃𝑛𝑤~𝑃−𝑃𝑒𝑓𝑓,           (24) 
where P is the bottomhole pressure of the well and Peff is the ‘effective’ pressure estimated by extrapolating 
back to G -time equal to zero from the point of minimum dP/dG ( Section 3.1 .1). Peff is an estimate for the 
fluid pressure in the fracture, on the ‘other side’ of the near -wellbore pressure drop from the wellbore.  
These relations make it possible to plot the difference between well pressure and fracture pressure versus 
volumetric flow rate and directly infer 𝐶𝑛𝑤.    
A.8 The h -function  
Nolte (1979) derived the G -function to be proportional to the cumulative leakoff volume after shut -in and 
derived the g -function to be proportional to the total volume of fluid leaked off after the start of injection.


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Both functions are derived assuming Carter leakoff.  Following a similar approach, it is convenient to define 
an ‘h’ function that is proportional to the cumulative leakoff volume  from the start of injection , but unlike 
the g -function, accounts  for deviation fro m Carter leakoff caused by pressure change over time . This is 
accomplished using  a time -convolution integral of the  one-dimensional  constant pressure solution  (given 
by Equation 18). This approach is related to the method described by Mayerhofer and Economides (1993) 
and Mayerhofer et al. (1995) , who proposed a procedure  for estimating permeability using  an 
approximation to the leakoff rate and the n a convolution integral of the constant rate solution  (Section 
A.3.vii) , and is also related to the relative stiffness relations developed by Wang and Sharma (2018) .  
The cumulative leakoff from the start of pumping can be estimated as: 
𝑉𝐿=4𝐴√𝑘𝜙𝑐𝑡
𝜋𝜇 ∫(𝑃(𝜏)−𝑃𝑟𝑒𝑠)
𝑑𝜏√Δ𝑡+𝑡𝑒/2−𝜏𝑑𝜏Δ𝑡+𝑡𝑒/2
0=4𝐴ℎ(Δ𝑡)√𝑘𝜙𝑐𝑡
𝜋𝜇 .   (25)


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𝑑𝜏√Δ𝑡+𝑡𝑒/2−𝜏𝑑𝜏Δ𝑡+𝑡𝑒/2
0=4𝐴ℎ(Δ𝑡)√𝑘𝜙𝑐𝑡
𝜋𝜇 .   (25) 
Thus, the h -function is defined as:  
ℎ(Δ𝑡)=∫(𝑃(𝜏)−𝑃𝑟𝑒𝑠)
𝑑𝜏√Δ𝑡+𝑡𝑒/2−𝜏𝑑𝜏Δ𝑡+𝑡𝑒/2
0.       (26) 
If pressure versus time  is known , cumulative leakoff can be calculated  as: 
𝑉𝐿(Δ𝑡𝑘)≈4𝐴√𝑘𝜙𝑐𝑡
𝜋𝜇 [(𝑃0−𝑃𝑟𝑒𝑠)√Δ𝑡𝑘+𝑡𝑒
2+∑ (𝑃𝑖−𝑃𝑖−1)𝑘
𝑖=1 √Δ𝑡𝑘−Δ𝑡𝑖].   (27) 
The h -function is calculated  as: 
ℎ(Δ𝑡𝑘)≈(𝑃0−𝑃𝑟𝑒𝑠)√Δ𝑡𝑘+𝑡𝑒
2+∑ (𝑃𝑖−𝑃𝑖−1)𝑘
𝑖=1 √Δ𝑡𝑘−Δ𝑡𝑖.     (28) 
Analogous to the G -function, an H -function can be defined that is proportional to the volume of fluid leaked 
off since shut -in: 
𝐻(Δ𝑡)=∫(𝑃(𝜏)−𝑃𝑟𝑒𝑠)
𝑑𝜏√Δ𝑡+𝑡𝑒/2−𝜏𝑑𝜏Δ𝑡+𝑡𝑒/2
𝑡𝑒/2.       (29) 
The H-function is calculated as:  
𝐻(Δ𝑡𝑘)≈(𝑃0−𝑃𝑟𝑒𝑠)(√Δ𝑡𝑘+𝑡𝑒
2−√𝑡𝑒
2)+∑ (𝑃𝑖−𝑃𝑖−1)𝑘
𝑖=1 √Δ𝑡𝑘−Δ𝑡𝑖.    (30) 
Cumulative leakoff after shut -in can be written as:  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   34 
𝑉𝐿𝑠(Δ𝑡𝑘)≈4𝐴𝐻(Δ𝑡𝑘)√𝑘𝜙𝑐𝑡
𝜋𝜇 .         (31) 
The h -function can be calculated directly from pressure versus time data  and an  estimate of the reservoir 
pressure, 𝑃𝑟𝑒𝑠. Estimation of reservoir pressure is discussed in Section 3.1 .6. 
Unlike the G -function, Equation 25 does not rigorously account for the effect of the propagation of the 
fracture over time. Instead, leakoff during injection is approximated by assuming the fracture formed 
instantaneously after a duration of injection of te/2. Although simple, this is a rea sonably accurate 
approximation. Equation 25 implies that the volume of fluid leaked off at shut -in is equal to:  
𝑉𝐿(Δ𝑡=0)≈4𝐴√𝑘𝜙𝑐𝑡
𝜋𝜇 [(𝑃0−𝑃𝑟𝑒𝑠)√𝑡𝑒
2]=2𝐴𝐶𝐿√𝑡𝑒 √2.     (32) 
The factor √2 in Equation 32 is analogous to 𝑔(Δ𝑡=0)=𝑔0 in Equation 13 (which is taken from the 
more d etailed derivations of Nolte, 1979, and Gulrajani and Nolte, 2000). 𝑔0 is bounded within the range 
4/3 and 𝜋
2, and √2 lies within this range .   
A.9 Relative stiffness


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2, and √2 lies within this range .   
A.9 Relative stiffness  
Using Equation  3 and Equation 25, it is possible to derive a ‘relative stiffness’ value ( Srel) that is linearly 
proportional to fracture stiffness:  
𝑑𝑃
𝑑𝑡=(1
𝐶𝑡 𝑑𝑉
𝑑𝑡)∝1
𝐶𝑡𝑑ℎ
𝑑𝑡.          (33) 
1
𝐶𝑡∝𝑑𝑃
𝑑𝑡
𝑑ℎ
𝑑𝑡=𝑆𝑟𝑒𝑙.           (34) 
Using tabular data of pressure versus time and an estimate for formation fluid pressure, it is possible to 
directly calculate the relative stiffness:  
𝑆𝑟𝑒𝑙(𝑡𝑘)=𝑑𝑃
𝑑𝑡(𝑡𝑘)
𝑑ℎ
𝑑𝑡(𝑡𝑘)=𝑑𝑃(𝑡𝑘)
𝑑ℎ(𝑡𝑘).         (35) 
A plot of relative stiffness versus pressure can be used to identify contact . When the relative stiffne ss 
increases, this indicates that the fracture walls have come into contact (Wang and Sharma, 2018) .  
Because of near -wellbore pressure drop, the measured wellbore pressure after shut -in is typically higher 
than the actual pressure in the far -field fractur e. To address this problem, the relative stiffness and the h -


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function can be calculated using an ‘effective pressure,’ Peff, that represents a best estimate for the true 
pressure in the fracture (Section 3.1 .1).  
A.10 Methods of estimating permeability  
The following sections describe methods for estimating permeability and leakoff coefficient. We 
recommend estimating permeability from multiple techniques: the G -function technique, the h -function 
technique, impulse linear, and/or impulse radial. These estima tes use different parts of the data and can be 
compared for consistency. At the end of this section, we review several common methods that are not 
recommended.  
A.10.i G -function technique  
Combining with Equations 4 and 17: 
𝑑𝑃
𝑑𝐺=1
𝐶𝑡 𝑑𝑉
𝑑𝐺=−𝜋
2 𝐴𝐶𝐿𝑆𝑡√𝑡𝑒=−𝜋
2𝐴𝐶𝐿√𝑡𝑒
𝐶𝑤+𝐴
𝑆𝑓+𝑉𝑓𝑐𝑓𝑙.       (36) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   35 
𝑑𝑃
𝑑𝐺 can be directly estimated from the data. 𝑉𝑓𝑐𝑓𝑙 is negligibly small and is omitted from the following 
equations. Assuming a radial crack, the leakoff coefficient can be calculated as:  
𝐶𝐿(𝑟𝑎𝑑𝑖𝑎𝑙 )=−𝑑𝑃
𝑑𝐺 𝐶𝑤+16𝑅𝑓3
3𝐸′
𝜋2
2𝑅𝑓2√𝑡𝑒=−𝑑𝑃
𝑑𝑔 𝐶𝑤+16𝑅𝑓3
3𝐸′
2𝜋𝑅𝑓2√𝑡𝑒.       (37) 
Assuming a fixed -height (PKN) crack, the leakoff coefficient can be calculated as:  
𝐶𝐿(𝑃𝐾𝑁 )=−𝑑𝑃
𝑑𝐺 2𝐶𝑤
𝜋+𝐿𝑓ℎ𝑓2
𝐸′
𝐿𝑓ℎ𝑓√𝑡𝑒=−𝑑𝑃
𝑑𝑔 2𝐶𝑤+𝐿𝑓ℎ𝑓2𝜋
𝐸′
4𝐿𝑓ℎ𝑓√𝑡𝑒.       (38) 
Equations 37 and 38 cannot be solved direct ly because they require estimation of the fracture size, either 
radius or length. In addition, the PKN calculation requires an assumption of fracture height. It is not possible 
to estimate height solely from the DFIT. It needs to be estimated from ancillar y information, such as 
knowledge of a stress contrast creating height confinement. If wellbore storage is neglected and height is 
assumed, Equation 38 reduces to an equation that can  be solved directly for leakoff coefficient (Marongiu -


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Porcu et al., 2011).  
Radius and length in Equations 37 and 38 can be estimated by writing a mass balance equation for the entire 
system:  
𝑉𝑖𝑛𝑗=𝐶𝑤(𝑃(Δ𝑡)−𝑃𝑤,𝑖𝑛𝑖𝑡)+𝐴
𝑆𝑓(𝑃(Δ𝑡)−𝑆ℎ𝑚𝑖𝑛 )+2𝐴𝐶𝐿√𝑡𝑒𝑔(Δ𝑡).    (39) 
Equation 39 states that the volume of fluid injected is equal to wellbore storage, fluid store d in the fracture, 
and leakoff. Equation 39 forms a system of two equations (with Equation 37 or 38) and two unknowns ( 𝐶𝐿 
and Rf or Lf). These equations can be solved to estimate leakoff coefficient and fracture extent. 𝑃𝑤,𝑖𝑛𝑖𝑡 is the 
measured pressure at the beginning of inje ction. The term 𝐶𝑤(𝑃(Δ𝑡)−𝑃𝑤,𝑖𝑛𝑖𝑡) accounts for the net flow 
due to wellbore stora ge. 
Equations 37, 38, and 39 must be evaluated at a particular point in time. We recommend evaluating dP/dG  
at the minimum point in dP/dG . Because dP/dG is never constant, this point is probably distorted by both  
near-wellbore pressure drop and contact. As a result , it is an upper bound  on the true value of dP/dG and


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may lead to an overestimate of leakoff coefficient. Nevertheless, it is the best  available point in  time to 
estimate dP/dG.  
We recommend evaluating Equation 39 at the effective ISIP ( Section 3.1 .1) in order to minimize the relative 
impact of the Shmin uncertainty on the calculation of net pressure. Eq uation 39 is evaluated from the 
estimate of the effective ISIP, rather than the literal ISIP, because near -wellbore pressure drop elevates the 
literal I SIP far above the actual pressure in the fracture at shut -in. 
Once leakoff coefficient has been calculated, permeability can be calculated from Equation 19. 
A.10.ii h -function technique  
The assumption of Carter leakoff is a limitation of the G -function method. This limitation can be overcome 
using the h -function method. Similar to Equation 39, we can write a mass balance on the system using the 
h-function to calculate leakoff:  
𝑉𝑖𝑛𝑗=𝐶𝑤(𝑃(Δ𝑡)−𝑃𝑤,𝑖𝑛𝑖𝑡)+𝐴
𝑆𝑓 (𝑃(Δ𝑡)−𝑆ℎ𝑚𝑖𝑛 )+4𝐴ℎ(Δ𝑡)√𝑘𝜙𝑐𝑡
𝜋𝜇 .    (40)


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𝑆𝑓 (𝑃(Δ𝑡)−𝑆ℎ𝑚𝑖𝑛 )+4𝐴ℎ(Δ𝑡)√𝑘𝜙𝑐𝑡
𝜋𝜇 .    (40) 
After selecting appropriate values for A and Sf (for either rad ial or PKN geometry), Equation 40 contains 
two unknowns: permeability and fracture radius (or length). The problem is solved by evaluating the 
equation at two different points in time: at shut -in (using the effective I SIP) and at the point of maximum 
G*dP/dG. The point of maximum G*dP/dG is reached a significant period of time after  the fracture walls Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   36 
come into contact . The fracture still retains some aperture, but it is reasonable to assume that the great 
majority of f luid has leaked off from the system. Specifically, we assume that 10% of the total injection 
volume remains stored in the fracture at this point in time (the calculation is not strongly dependent on the 
precise percentage that is assumed). This assumption yields:  
0.9𝑉𝑖𝑛𝑗=𝐶𝑤(𝑃𝑝𝑒𝑎𝑘 −𝑃𝑤,𝑖𝑛𝑖𝑡)+4𝐴ℎ(Δ𝑡𝑝𝑒𝑎𝑘 )√𝑘𝜙𝑐𝑡
𝜋𝜇 .      (41) 
Rearrangement yields an equation for 𝐴√𝑘:  
𝐴√𝑘=0.9𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃𝑝𝑒𝑎𝑘 −𝑃𝑤,𝑖𝑛𝑖𝑡)
4ℎ(𝛥𝑡𝑝𝑒𝑎𝑘 )√𝜙𝑐𝑡
𝜋𝜇 .         (42) 
Equation 40 can be solved for area:  
𝐴=(𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃(Δ𝑡)−𝑃𝑤,𝑖𝑛𝑖𝑡)−𝐴√𝑘(4ℎ(Δ𝑡)√𝜙𝑐𝑡
𝜋𝜇 ))𝑆𝑓
𝑃−𝑆ℎ𝑚𝑖𝑛.    (43) 
𝐴√𝑘 can be calculated from Equation 42 and plugged into Equation 43. Appropriate r elations for A and Sf 
are plugged into Equation 43, assuming either radial or PKN geometry , and  the equation can be  solved for 
either radius or fracture length. Then, it is trivial to calculate area and permeability.


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We recommend evaluating Equation 40 at Δ𝑡 equal to zero (using the effective ISIP) in order to minimize 
the relative effect of uncertainty in the estimate of Shmin. For the case of Δ𝑡=0, Equation 40 reduces to:  
𝑉𝑖𝑛𝑗=𝐶𝑤(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑤,𝑖𝑛𝑖𝑡)+4(𝐴√𝑘)(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑟𝑒𝑠)√𝑡𝑒
2√𝜙𝑐𝑡
𝜋𝜇 +𝐴
𝑆𝑓 (𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑆ℎ𝑚𝑖𝑛 ). (44) 
For radial geometry, the radius is calculated as:  
𝑅𝑓=√3𝐸′[𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑤,𝑖𝑛𝑖𝑡)−4(𝐴√𝑘)(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑟𝑒𝑠)√𝑡𝑒
2√𝜙𝑐𝑡
𝜋𝜇 ]
16(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑆ℎ𝑚𝑖𝑛 ) 3
     (45) 
For PKN geometry, the fracture length is calculated as:  
𝐿𝑓=2𝐸′[𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑤,𝑖𝑛𝑖𝑡)−4(𝐴√𝑘)(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑟𝑒𝑠)√𝑡𝑒
2√𝜙𝑐𝑡
𝜋𝜇 ]
ℎ𝑓2𝜋(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑆ℎ𝑚𝑖𝑛 ).     (46) 
A.10.iii Impulse linear  
The late time behavior of a DFIT can be interpreted like an impulse test from classical well test analysis 
(Craig and Blasingame, 2006). The late -time analytical solution for linear flow with constant rate injection 
is (Gringarten et al., 1974):  
𝑃=𝑃𝑟𝑒𝑠+𝑄
𝐴√𝜇
𝜋𝑘𝑐𝑡𝜙√Δ𝑡,         (47)


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𝑃=𝑃𝑟𝑒𝑠+𝑄
𝐴√𝜇
𝜋𝑘𝑐𝑡𝜙√Δ𝑡,         (47) 
where Q is the volumetric injection rate. Taking the derivative of the nondimensionalized form of th e 
equation, we can find the solution for injection of a volume of fluid Vslug into the system  (Houze et al, 1 988; 
Ayoub et al., 1988; Gu et al, 1993 ). 𝑉𝑠𝑙𝑢𝑔 should take wellbore storage into account:   
𝑃=𝑃𝑟𝑒𝑠+𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃𝑟𝑒𝑠−𝑃𝑤,𝑖𝑛𝑖𝑡)
2𝐴√𝜇
𝜋𝑘𝑐𝑡𝜙1
√Δ𝑡.       (48) 
Equation 48 can be rearranged to calculate 𝐴√𝑘 from the slope of a plot of pressure versus 1
Δ𝑡1/2. Once 𝐴√𝑘 
has been estimated, radius (or length) and permeability can be estimated from Equations 45 and 46.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   37 
A.10.iv Impulse radial  
The late -time analytical solution for radial flow with constant rate injection is (Theis, 193 5; Horne, 1995):  
𝑃−𝑃𝑟𝑒𝑠=𝑄𝜇
2𝜋𝑘ℎ[0.5(𝑙𝑛(𝑘Δ𝑡
𝜙𝜇𝑐𝑡𝑟𝑤2)+0.80907 )+𝑠].      (49) 
Therefore, impulse radial is the derivative of the constant rat e solution ( Houze et al, 1988; Ayoub et al., 
1988; Gu et al, 1993 ): 
𝑃−𝑃𝑟𝑒𝑠=(𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃𝑟𝑒𝑠−𝑃𝑤,𝑖𝑛𝑖𝑡))𝜇
4𝜋𝑘ℎ1
Δ𝑡.        (50) 
Equation 50 can be rearranged to show that the permeability -thickness product , 𝑘ℎ, can be calculated from 
the slope of a plot of pressure versus 1
Δ𝑡. To calculate permeability, it is necessary to m ake an estimate for 
h, the height of the permeable formation. If well logs indicate that there is a clear ‘pay’ zone with higher 
permeability than surrounding formations, then the thickness of this zone can be used for h. Alternatively, 
if well logs indica te strong height confinement, then the fracture can be assumed to have known height, and 
this value can be used for h.


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this value can be used for h.  
If there is not clear indication of height confinement and there is a not a single ‘high permeability’ pay 
zone, we recommend using a ra dial fracture geometry and setting h equal to 2 Rf. For known kh (estimated 
from Equation 50), then k is approximately equal to (𝑘ℎ)𝑒𝑠𝑡
2𝑅𝑓. Equation 44 becomes:  
𝑉𝑖𝑛𝑗=𝐶𝑤(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑤,𝑖𝑛𝑖𝑡)+4(𝜋𝑅𝑓2√(𝑘ℎ)𝑒𝑠𝑡
2𝑅𝑓)(𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑃𝑟𝑒𝑠)√𝑡𝑒
2√𝜙𝑐𝑡
𝜋𝜇 + 16𝑅𝑓3
3𝐸′  (𝑃𝐼𝑆𝐼𝑃 ,𝑒𝑓𝑓−𝑆ℎ𝑚𝑖𝑛 ) 
            (51) 
Equation 51 is a cubic equation for Rf. It can be solved with a nonlinear solver and then used to estimate h 
and k.  
A.11 The linear flow time function  
Sometimes, impulse interpretations are performed with the ‘linear flow time function’ defined by Gulrajani 
and Nolte (2000) as:  
𝐹𝐿=2
𝜋sin−1√𝑡𝑐
Δ𝑡,          (52) 
where tc is the shut -in time to ‘closure.’ 𝐹𝐿 is only defined for  Δ𝑡≥𝑡𝑐. 𝐴√𝑘 is estimated from impulse 
linear flow using a plot of pressure versus 𝐹𝐿 or 𝐹𝐿−1. 𝑘ℎ is estimated from impulse radial flow using a plot


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of pressure versus 𝐹𝐿2 or 𝐹𝐿−2.  
Equation 52 can be understood by considering the behavior of the arcsine function as its argument 
approaches zero:  
lim
𝑥→0sin−1𝑥=𝑥.          (53) 
Therefore, once 𝑡𝑐+Δ𝑡 is substantially larger than tc, 𝐹𝐿 can be approximated as:  
𝐹𝐿≈2
𝜋√𝑡𝑐
Δ𝑡.           (54) 
For Δ𝑡 equal to 2𝑡𝑐, the approximation is accurate within 11%. For Δ𝑡 equal to 10𝑡𝑐, the approximation is 
accurate within 2%.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   38 
Thus, for most practical purposes, a plot of pressure ve rsus 𝐹𝐿 is equivalent to a plot of pressure versus 
reciprocal square root of time, and a plot of pressure versus 𝐹𝐿2 is equivalent to a plot of pressure versus 
reciprocal time. A plot of 𝐹𝐿−2 is equivalent to a plot of pressure versus time.  
The FL function is significantly different from 2
𝜋√𝑡𝑐
𝛥𝑡 in the period from Δ𝑡=𝑡𝑐 to Δ𝑡=2𝑡𝑐 (it is not defined 
prior to tc). Should FL be used if data is not available for Δ𝑡 greater than 2𝑡𝑐? Possibly, but interpreters 
should keep in mind the assump tions underlying FL. It is derived assuming that Carter leakoff occurs until 
closure, and then there is zero leakoff after closure (Nolte et al., 1997; page 76 from Carslaw and Jaeger, 
1959). But in reality, leakoff rate gradually deviates from Carter leak off as pressure decreases in a system 
coupled with nonlinear evolution of system storage (Section A.13). Because of this simplification, the


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period from Δ𝑡=𝑡𝑐 to Δ𝑡=2𝑡𝑐 is the period when the assumptions underlying FL are least reliable. After 
this p eriod, FL is similar to the impulse solution.  
A.12 Estimating efficiency  
Fracture efficiency, 𝜂, is defined as the volume of fluid remaining  in the fracture at shut -in divided by the 
volume of fluid injected into the fracture (the total injection volume minus wellbore storage). A classical 
equation for estimating efficiency is (Equation 9 -60 from Gulrajani and Nolte, 2001):  
𝜂=𝐺𝑐
2+𝐺𝑐,           (55) 
where 𝐺𝑐 is G-time at ‘closure.’  
Equation 55 is derived assuming the same assumptions discussed in Section A.11 : Carter leakof f occurs 
until ‘closure,’ at which point there is zero fluid remaining in the fracture. Conventionally, Equation 55 
would be applied with the tangent m ethod for picking closure. But there has been substantial deviation from 
Carter leakoff by the time of the tangent closure pick. As discussed in Section 3.1 .9, due to fracture


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roughness, there is likely to be significant fluid remaining the fracture at the  point of contact, and even 
when pressure is equal to or less than Shmin. Because of the offsetting effect of different approximations, 
Equation 55 often yields a reasonable approximation  of efficiency in many cases if applied with the tangent 
method of picking closure.  
Alternatively, efficiency can be estimated after estimating leakoff coefficient and/or permeability using the 
techniques in Section A.10. Then, cumulative leakoff at shut -in can be estimated from Equation 13, and 
efficiency  can be calculated  directly by applying mass balance (including the effect of wellbore storage):  
𝜂=𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃−𝑃𝑤,𝑖𝑛𝑖𝑡)−𝑉𝐿(Δ𝑡=0)
𝑉𝑖𝑛𝑗−𝐶𝑤(𝑃−𝑃𝑤,𝑖𝑛𝑖𝑡).         (56) 
A.13 Estimating pore pressure with a short shut -in 
Sometimes, DFIT’s are not performed with sufficient shut -in duration to reach impulse linear or radial. A 
simple numerical simulation and history match can be used to provide a rou gh estimate for fluid pressure.


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1. Assume W0 and Pres. 
2. Use the h -function method to integrate the measured pressure data (after conversion to Peff) and use 
the method in Section A.10.ii to infer leakoff coefficient and fracture surface area. Use the 
estimated  area and assumed fracture geometry to calculate Sf,o. 
3. Numerically solve the following equation for a DFIT pressure transient (derived from Equation 3): 
𝑑𝑃
𝑑𝑡(𝐴
𝑆𝑓+𝐶𝑤)=𝑑𝑉𝐿
𝑑𝑡.         (57) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 123   39 
𝑑𝑉𝐿
𝑑𝑡 is the leakoff rate, calculated from Equation 25. When the calculated aperture reaches Wo, the 
fracture stiffness is increased to account for the c ontribution of Sf,c, as discussed in Section A.1.ii. The 
integration can be solved numerically with explicit Euler:  
𝑃𝑘=𝑃𝑘−1+(𝑑𝑃
𝑑𝑡)
𝑘Δ𝑡,         (58) 
where (𝑑𝑃
𝑑𝑡)
𝑘 is calculated from Equation 57. 
4. Check to see if the timing and value of the peak in t*dP /dt has been accurately predicted. If not, go 
back to Step 1 and select new values for W0 and Pres. Iterate until convergence.  
A.14 Generating plots of aperture versus effective normal stress  
Wang and Sharma (2018) propose  a method for estimating aperture versus pressure. The technique in this 
section is conceptually similar. From Equation 35, the derivative of P with respect to h is proport ional to 
system stiffness. Therefore, neglecting wellbore storage, we can write:  
𝑑𝑃
𝑑ℎ
(𝑑𝑃
𝑑ℎ)𝑚𝑖𝑛𝑆𝑓
𝐴=𝑑𝑃
𝑑𝑉.           (59)


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𝑑𝑃
𝑑ℎ
(𝑑𝑃
𝑑ℎ)𝑚𝑖𝑛𝑆𝑓
𝐴=𝑑𝑃
𝑑𝑉.           (59) 
The permeability estimation methods in Section A.10 yield estimates of fracture area and stiffness prior to 
contact, Sfo. Next, estimate the derivative of pressure with respect to aperture:  
𝑑𝑃
𝑑𝑊=𝐴𝑑𝑃
𝑑𝑉.           (60) 
If we assume that aperture at the peak of G*dP/dG  is an arbitrary, small value, 3.28e -5 ft, then we can 
perform an integral to  roughly approximate  average fracture aperture as a function of pressure:  
𝑊(𝑃)=3.28∗10−5 +∫1
𝑑𝑃
𝑑𝑊𝑑𝑃𝑃
𝑃𝑝𝐺,        (61) 
where 𝑃𝑝𝐺 is the pressure at the peak G* dP/dG. Figure 7 shows a result from this procedure.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC: 3717105 
 
Improvement in the Characterization of Vaca Muerta With DFIT Type 
Curves Analysis 
 
Cristian F. González* and Ignacio Arhancet †, YPF S.A. 
† Now with TotalEnergies 
 
Copyright 2022, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/urtec-2022-3717105 
 
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 
20-22 June 2022. 
The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted 
by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, 
or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any 
person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not


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necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by anyone other than the 
author without the written consent of URTeC is prohibited.   
 
Abstract 
Natural decline of conventional fields and the good results in the development of USA shale plays motivated 
YPF, Argentina’s National Oil Company, to start in 2010 the exploitation of unconventional resources. 
Vaca Muerta Formation in Neuquén Basin was selected among others because of its excellent petrophysical 
and geomechanical properties. Since then, more than 1000 wells have been drilled and completed across 
the basin proving that Vaca Muerta is a world-class unconventional play. 
Identification of sweet spots, optimization in drilling and completion of shale wells and a proper field 
development plan require a good dynamic characterization of the reservoir. In conventional reservoirs this


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was traditionally performed by a series of tools in which well tests were a key part to get reservoir pressure 
and permeability. Because of the extremely low permeability of shale reservoirs, classical well testing is no 
longer a practical tool to estimate these parameters. Diagnostic Fracture Injection Tests (DFITs) are one of 
the few methodologies that allows estimation of reservoir transmissibility and pore pressure in 
unconventional reservoirs. DFITs are also useful to obtain closure pressure, a geomechanical parameter 
necessary to define the stress state. 
However, DFITs interpretation by conventional methodology, also known as holistic approach, is not 
always successful because it requires specific flow regimes during decline time to correctly estimate 
reservoir parameters. Additionally, as DFIT tests are generally pumped through horizontal well’s toe prior 
to completion stage, they must compete against fracture bundle efficiency given its high costs of standby.


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All of this, results in short shut-in times leading to a poor DFIT interpretation efficiency [i.e., low 
percentage of tests with confident reservoir data (closure pressure, reservoir pressure and transmissibility)]. 
This paper describes how using type-curves methodology, YPF increased the number of valid results from 
DFITs improving the characterization of Vaca Muerta. Better mapping of pore pressure and knowledge of 
typical ranges of permeability were possible after reanalyzing more than 100 DFITs. 
Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 3717105  2 
 
Introduction 
The focus towards development of low permeability reservoirs during recent years has changed the way to 
get reservoir parameters from a well testing perspective. Diagnostic Fracture Injection Test (DFIT) has 
emerged as one of the few tools that allows to estimate pore pressure and permeability in unconventional 
reservoirs. Because of this, data acquisition plans usually include DFITs in wells of different locations and 
landing zones.  
YPF has led exploration, appraisal, and early development stages of Vaca Muerta shale in Argentina during 
the first ten years (2010-2020). In that period, 135 DFITs were executed across the Neuquén basin to capture 
key information (stress state, pore pressure and reservoir permeability) necessary to characterize the 
reservoir and identify sweet spots. Fig. 1 shows the location of DFITs in a map of Vaca Muerta’s area.  
 
Fig. 1- Location of DFITs in Vaca Muerta during 2010-2020.


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Fig. 1- Location of DFITs in Vaca Muerta during 2010-2020. 
Those tests were interpreted following the classical best practices for DFIT analysis known as holistic 
approach (Barree et al, 2007). Analysis of results indicated that almost 90% of tests had a closure pressure 
estimation but only half of them presented a reservoir pressure calculation. Transmissibility values were 
only present in around 10% of tests. That poor outcome in reservoir parameters can be explained by the 
limitations of the traditional approach that are described in the following section.  
Considering the previous situation and with the objective of improving those numbers and extracting more 
value from DFITs, reservoir and stimulation engineering teams evaluated new interpretation techniques. 
Dr. David Craig’s work in type curves applied to DFITs (Craig, 2014) was considered a good alternative 
because it removes the main limitation of after closure analysis (ACA).


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Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 3717105  3 
 
Limitations of Traditional Approach in Unconventionals 
Current most common procedure of DFITs interpretation is mainly based on Ken Nolte’s works and it is 
well described in Barree et al (2007). This approach, known as holistic, relies on proper flow regime 
identification using different diagnostic graphs and special mathematical functions of time (e.g., G-function 
time, Squared linear flow time, etc.) 
Leak-off type and closure pressure are not always simple to determine in before closure analysis (BCA) of 
unconventional wells using the holistic approach. Horizontal wells promote complex fracture growth 
geometries that result in early events that disturb the G-Function plot’s curves and can lead to different 
interpretations generating uncertainty in in-situ minimum stress estimation. 
In after closure analysis (ACA), correct estimation of pore pressure requires reaching specific flow regimes:


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pseudolinear or pseudoradial. On the other hand, transmissibility or permeability calculation is only 
possible in pseudoradial flow. 
Pseudolinear flow is expected to be developed in DFITs pumped in unconventional reservoirs after several 
hours of pressure decline while pseudoradial flow would be extremely rare due to its low permeability. 
Because of this, DFITs in unconventionals are considered a good tool for initial pressure estimation but not 
so much for transmissibility or permeability calculation.  
In practice, pseudolinear flow is not always present in unconventional reservoirs DFITs due to lack of 
sufficient shut-in time or because of fracture-rock system complexities that result in non-ideal reservoir 
signatures. Regarding interpretation, the use of auxiliary lines with characteristic slopes in flow regime 
identification graphs sometimes promotes that the analysts see that specific flow regime even when it is not


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present or it is not fully developed yet, leading to wrong estimations in reservoir parameters.  
On the operational side, as DFITs are generally pumped through horizontal well’s toe prior to completion 
event, shut-in times are limited by fracture set’s schedule and its high cost of standby. Consequently, fall 
off registration time is usually lower than desirable for low permeability rocks. 
All of this, results in many tests with poor interpretation outcomes and it has led some operators to stop 
pumping DFITs in horizontal wells and question its validity.  
Type-Curves Methodology in DFITs 
David Craig (2014) presented a new method for DFIT analysis based on type curves whose main advantage 
is that no specific flow regime is needed to estimate reservoir pressure and permeability overcoming the 
principal problem of the holistic approach. This new methodology also provides an alternative way to 
estimate closure pressure which is particularly useful in horizontal wells where classic technique is


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sometimes ambiguous. 
DFIT type-curves analysis is analogous to classic well testing, i.e., it uses special derivatives to aid the 
matching process between field data and different theoretical models (type curves) and, in contrast to the 
traditional method, integrates all data in a unique analytical solution. Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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As DFITs consist of a small injection of fluid followed by a long shut-in time, it could be practically 
considered as a slug test or short-flow transient test. Craig and Blasingame (2006) demonstrated that DFITs 
could be modeled with a variable-storage slug test solution. Additionally, slug tests pressure response could 
be transformed into an equivalent constant-rate drawdown by deconvolution (Peres et al, 1989). This allows 
the use of conventional constant-rate type curves for DFIT analysis. 
 
Fig. 2- Schematic of DFIT transformation into an equivalent constant-rate drawdown. 
The problem is that cited transformation requires knowing the initial pressure which it is one of DFIT’s 
objectives. In 2008, David Craig found out, after differentiating the slug test solution, that the same semi-
log derivative used in the log-log plot of holistic approach can be matched to a special derivative of


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constant-rate type curves (Eq. 1). This was the missing part that made possible to calculate the initial 
pressure and completed the matching process. 
 
𝑡஽ௗ௣ೢವ
ௗ௧ವᇣᇧᇤᇧᇥ
஽ிூ் ௦௘௠௜ି୪୭୥ௗ௘௥௜௩௔௧௜௩௘= −𝑝௪௦஽(଴) × 𝐶 ௦஽ต
௦௧௢௥௔௚௘
௖௢௘௙௙௜௖௜௘௡௧ × 𝑡 ஽ௗమ௣ೢ೎ವ
ௗ௧ವమᇣᇧᇧᇤᇧᇧᇥ
௖௢௡௦௧௔௡௧ି௥௔௧௘  ௗ௥௔௪ௗ௢௪௡
ଶ௡ௗ ௢௥ௗ௘௥ ௗ௘௥௜௩௔௧௜௩௘ (Eq. 1) 
Another important conclusion of Craig’s work is that fracture closure is a storage phenomenon. Storage 
effects are recognized by unit-slope and superposition of pressure and first derivative curves in well testing 
diagnostic plots.  Hence, fracture closure pressure could be identified as the point where both curves 
separate from each other and deviates from unit slope. This provides an alternative to tangent method 
(holistic technique), and it is especially useful in horizontal wells where complex signatures during closure 
are common. 
The procedure for analyzing DFITs with type curves can be resumed as: 
1. Match semi-log derivative of DFIT data with a constant-rate second order derivative type


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curve. Different constant storage coefficients can be used to construct the set of type curves. 
2. Calculate initial pressure from a matching point (MP) using the following equation: 
𝑝௜= 𝑝௪(௧೐)−ଵ
௣ೢೞವ(బ)஼ೞವ቎௧೏೛ೢ(೟)
೏೟
ି௧ವ೏మ೛ೢ೎ವ(೟ವ)
೏೟ವమ቏
ெ௉(Eq. 2) 
3. Once initial pressure has been estimated, constant-rate pressure and first derivative can be 
calculated. The slug test (DFIT) has been transformed into an equivalent constant-rate 
drawdown. 
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4. Overlap preceding curves with type curves. Perhaps, it could be necessary to slightly adjust 
initial pressure to refine matching. 
5. Transmissibility can be calculated from a matching point over the pressure curve.  
௞௛
ఓ= (141.2)(24) 𝑝௪௦஽(଴)𝐶௦஽(𝑝଴−𝑝௜)ቈ௣ೢ೎ವ(೟ವ)
∫൫௣ೢ(೟)ି௣೔൯ௗ௧೟
బ቉
ெ௉(Eq. 3) 
6. Fracture closure pressure is determined from the point where pressure and first derivative 
deviate from unit slope and separate from each other. 
Previous workflow considers a constant storage coefficient. In cases when variable storage is evident (e.g., 
non-ideal leak-offs during fracture closure), the effect could be incorporated in type curves and equations 
(Craig, 2014). 
Examples of Application 
In this section, two examples of application to Vaca Muerta’s wells are presented and compared with the 
holistic approach. Detailed discussion about how well compared both methodologies for each parameter is 
presented in the following section adding more wells to the analysis.


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Well A is an exploratory vertical well where a 3 barrel-DFIT was pumped in the lower section of Vaca 
Muerta and pressure decline was registered for 64 hours. Fig. 4 groups the set of graphs that are normally 
used for DFIT holistic interpretation. ACA shows a long pseudolinear flow period; hence, initial pressure 
can be estimated with confidence using traditional technique and can be compared with type-curve method. 
Additionally, a pump-in flowback rebound test (PIFBRT) was executed in well A after the DFIT providing 
an alternative estimation of closure pressure for comparison.  
Fig. 3 shows the type-curve match using Craig’s methodology and Table 1 resumes the results of 
interpretation by both methods. Pore pressure estimation is consistent between methods, being slightly 
greater (+1%) for type-curve analysis. Regarding closure pressure, the tangent-line technique (holistic 
approach) does not provide an easy way to determine closure in this case because of a tip extension leak-


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off signature (no local maximum in dP/dG derivative and tangent line on GdP/dG does not pass through 
the origin). The interpreted value is slightly lower (-2%) than the PIFBRT estimation but it has a high 
degree of uncertainty. Type-curve closure pressure is in contrast a little bit greater (+1%). Despite the small 
difference, the type-curve analysis yielded an acceptable estimation of closure pressure, and it is a simple 
alternative when the classical approach is ambiguous.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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Fig. 3- DFIT type-curve match for well A. 
 
Fig. 4- Conventional DFIT analysis of well A. Upper left: Log-log diagnostic plot. Upper right: G-function plot. Lower left: ACA diagnostic plot. 
Lower right: Linear flow function plot. 
 
Method Closure Pressure 
[psi] Closure Gradient 
[psi/ft] Initial Pressure 
[psi] Pressure Gradient 
[psi/ft] Transmissibility 
[mD.ft/cP]  
Holistic 9118 0.978 8258 0.887 - 
Type Curve 9378 1.006 8348 0.895 1.4 
PIFBRT 9278 0.995 - - - 
Table 1- DFIT interpretation results for well A. 
Well A 
Well A Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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Second example corresponds to Well B, a horizontal well landed in a high TOC section of Vaca Muerta. 
36 barrels of fresh water were injected at 6 barrels per minute and shut-in lasted around 120 hours.  Fig. 6 
shows the different specialized plots that were used for analyzing that DFIT under traditional workflow. A 
clear and long-lasting pseudoradial flow could be observed after fracture closure, then transmissibility and 
initial pressure were estimated with a high degree of confidence (Table 2). 
 
Fig. 5- DFIT type-curve match for well B. 
 
Fig. 6- Conventional DFIT analysis of well B. Upper left: Log-log diagnostic plot. Upper right: G-function plot. Lower left: ACA diagnostic plot. 
Lower right: Radial flow function plot. 
 
Well B 
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Fig. 5 is the plot of DFIT type-curve analysis for well B and results are presented in Table 2. Initial pressure 
estimation is almost identical in both methods and transmissibility is very similar, being slightly greater for 
type-curve analysis but consistent with traditional estimation. Closure pressure was also determined with 
both techniques. In this case, the closure point is very clear on the G-function plot hence its value is a good 
reference for comparison. Type-curve estimated a closure pressure 2% greater than the tangent line method. 
 
Method Closure Pressure  
[psi] Closure Gradient 
[psi/ft] Initial Pressure  
[psi] Pressure Gradient 
[psi/ft] Transmissibility 
[mD.ft/cP]  
Holistic 8146 0.851 7496 0.783 12.83 
Type Curve 8341 0.871 7507 0.784 14.21 
Table 2- DFIT interpretation results for well B. 
Validation 
DFIT type-curve methodology was validated by comparison with holistic method results before further


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application. DFITs with clear pseudolinear or pseudoradial flow regimes were selected for this purpose so 
its results were reliable for validation. The comparison was divided considering the main parameters of 
DFITs interpretation: initial pressure, transmissibility, and closure pressure.     
●  Initial Pressure 
Initial pressure estimations from 35 DFITs with pseudolinear flow and 7 with pseudoradial flow were 
compared and plotted in Fig. 7. As it can be seen, linear regression gives practically unit slope and R2=1 
indicating that both methods estimate almost identical values.   
 
Fig. 7- Crossplot and linear regression of initial pressure estimations with both methods. 
 
 
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●  Transmissibility  
Due to few tests with pseudoradial flow in Vaca Muerta, 8 DFITs from tight sands were included in the 
comparison. Fig. 8 shows the crossplot and linear regression. R-squared is 0.9972 and slope of the line is 
around 1.02. In general, type-curve transmissibilities are slightly greater than holistic’s but are very close 
since data practically lies in the 45º line. Considering the uncertainty in this parameter, these differences 
are totally acceptable for engineering use.   
 
Fig. 8- Crossplot and linear regression of transmissibility estimations with both methods. 
●  Closure Pressure 
Closure pressure estimations of 87 DFITs from both methods are plotted in Fig. 9. R-squared is 0.9998 and 
slope of the line is around 1.01 indicating that values for type-curves are on average slightly greater (+70-
100 psi).  
Closure pressure estimation from DFITs has generated a lot of debate in the industry since the fracture-


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compliance method was presented by McClure et al (2016). This method results in closure pressures 
significantly greater (500 psi or more in some cases) than the tangent-line technique (holistic approach).  
Results from Fig. 9 would preliminarily indicate intermediate values but closer to the tangent-line method 
since differences are small. Nevertheless, application of fracture-compliance method to this dataset must 
be performed to correctly compare between all these methods. Comparison with other techniques like 
PIFBRT, whenever it is available, would be desirable. 
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Fig. 9- Crossplot and linear regression of closure pressure estimations with both methods. 
Analysis of Type Curves Non-uniqueness  
As it is well known in well testing interpretation, type-curve matching is usually non-unique (i.e., data could 
be matched with several type curves). This is also true for DFIT type curves, therefore, the impact of curve 
selection in pressure and transmissibility estimation was evaluated. 
A DFIT with a not fully developed post-closure flow regime (Fig. 10) was selected to evaluate a case of 
high uncertainty. Flow regime identification after fracture closure shows a slope of -0.15 in semi-log 
derivative after 80 hours that could be interpreted as a slow transition to pseudolinear flow. Conventional 
ACA cannot be applied because pseudolinear flow is not developed.   
Two extreme type curves were selected to test sensitivity. Dimensionless storage coefficient of 0.09 (Fig.


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10) implies transition to a long pseudolinear flow regime (realistic case) and dimensionless storage 
coefficient of 0.36 (Fig. 11) means short pseudolinear flow followed by pseudoradial flow (unlikely case). 
In both cases, an acceptable match can be performed.  
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Fig. 10- Type-curve match with lower storage coefficient. 
 
Fig. 11- Type-curve match with higher storage coefficient. 
Table 3 resumes the results of both interpretations. Closure pressure and initial pressure are independent of 
the type curve selected for analysis since estimations are practically identical. This proves that type-curve 
methodology is an excellent tool for closure and initial pressures estimations.  
 
Dimensionless 
Storage 
Coefficient  Closure 
Presure  
[psi] Closure Gradient 
[psi/ft] Initial Pressure  
[psi] Pressure Gradient 
[psi/ft] Transmissibility 
[mDft/cP]  
0.09 8339 0.913 7474 0.818 1.22 
0.36 8339 0.913 7489 0.820 3.38 
Table 3- Results of different type curves interpretations. 
Transmissibility estimation, in contrast, does depend on what curve is used. For this example, a factor of 3 
was obtained between cases. This sensitivity can be seen as a weakness of the method but must be


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considered that there are not many other alternatives to estimate transmissibility from DFITs, especially in 
CSD=0.09 
-tDd2pwcD/dtD2 CSD=0.09 
pwcD 
tDdpwcD/dtD 
-tDd2pwcD/dtD2 
Closure 
CSD=0.36 
-tDd2pwcD/dtD2 CSD=0.36 
pwcD 
tDdpwcD/dtD 
-tDd2pwcD/dtD2 
Closure Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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unconventional reservoirs where pseudoradial flow is extremely rare. In any case, transmissibility 
estimations from different type curves will result in the same order of magnitude.  
Results 
Fig. 12 shows the improvement in the percentage of DFITs with valid estimates for different parameters 
after applying the type-curve methodology to over 100 tests in Vaca Muerta.   
Closure pressure percentages were slightly improved from 87% to 91%. Type curves allowed reinterpreting 
a few tests where closure was not clear or impossible to estimate with the tangent-line method.  
Before type-curve application only half of tests had an estimation of initial pressure. Type-curves rise the 
percentage to 80%, adding tests where no pseudolinear or pseudoradial flow were seen. 
Since transmissibility is only possible to be calculated in pseudoradial flow using the traditional approach, 
the percentage of test was too low (roughly 1 of 10) before type curves implementation. That number


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improved to 6 of 10 because of type-curves methodology. 
 
Fig. 12- Comparison of percentage of DFITs with closure pressure, initial pressure, and transmissibility estimations before and after type-curves 
application. 
Applications 
The results presented in the previous section increased the data available for Vaca Muerta characterization. 
Better areal coverage of closure and initial pressures across Neuquén basin resulted in better mapping of 
stress state and pore pressure. For pore pressure mapping, more data availability allowed to construct maps 
for the different landing zones. All of this is key information for sweet spots identification. 
Another example of application is knowledge of permeability ranges for Vaca Muerta. Permeability that 
contributes to production in unconventionals [i.e., system permeability (matrix + fissures)] is impossible to 
estimate from classical tools such as well testing. Rock cores offer an alternative to knowing permeability,


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but they are not very representative because of its small volume of investigation. DFIT type-curves analysis 
is an excellent tool for permeability estimation in unconventional reservoirs. 
Fig. 13 shows a S-curve of DFIT’s permeabilities for Vaca Muerta calculated from type-curves 
transmissibilities. Error bars have been included in the graph to indicate the estimated uncertainty of 
calculated permeabilities. 
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URTeC 3717105  13 
 
 
Fig. 13- S-curve of Vaca Muerta DFIT permeability. 
 
Conclusions 
 Application of type-curves analysis allowed YPF S.A. to improve DFITs’ interpretation 
efficiency resulting in better characterization of Vaca Muerta. 
 Type-curves methodology was validated by comparing results with classic approach in DFITs 
of reference (clear pseudolinear and pseudoradial flow). 
 Closure and initial pressure estimations are practically insensitive to the selected type curve. 
This puts the type-curves method as one of the best ways to estimate reservoir pressure in 
unconventional reservoirs.    
 Transmissibility estimation does depend on the type curve used in the analysis. Different 
interpretations can differ as much as a factor of 3. Being one of the few methods to get 
transmissibility in unconventional reservoirs, the authors consider it acceptable despite the 
range of uncertainty.  
 Type-curves method provides an alternative way to estimate closure pressure which is


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particularly useful in horizontal wells where complex pressure signatures are common. 
 Type curves are an excellent tool for improving the analysis of DFITs in unconventional 
reservoirs like Vaca Muerta. 
Acknowledgments 
The authors would like to thank YPF S.A. for the permission to publish this paper and Dr. David Craig for 
creating and sharing this powerful tool for DFITs analysis. 
Nomenclature 
ACA After Closure Analysis  
BCA Before Closure Analysis  
DFIT Diagnostic Fracture Injection Test  
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MP Matching Point  
PIFBRT Pump-In Flowback Rebound Test  
TOC Total Organic Carbon  
USA United States of America  
  
𝐶௦஽ Dimensionless storage coefficient 
𝐺 G-function time 
ℎ Height 
𝑘 Permeability 
𝜇 Viscosity 
𝑝௜ Initial pressure 
𝑝଴ Pressure at end of injection 
𝑝௪ Wellbore pressure 
𝑝௪஽ Dimensionless wellbore pressure  
𝑝௪௖஽ Dimensionless constant-rate wellbore pressure  
𝑝௪௦஽ Dimensionless slug-test wellbore pressure  
𝑡 Time 
𝑡஽ Dimensionless time 
𝑡௘ Time at end of injection 
 
References 
Barree, Robert David, Barree, Valencia L., and David Craig. "Holistic Fracture Diagnostics." Paper 
presented at the Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, U.S.A., April 
2007. doi: https://doi.org/10.2118/107877-MS  
Craig, David P. "New Type Curve Analysis Removes Limitations of Conventional After-Closure Analysis 
of DFIT Data." Paper presented at the SPE Unconventional Resources Conference, The Woodlands, Texas,


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USA, April 2014. doi: https://doi.org/10.2118/168988-MS  
Craig, David P., and Thomas Alwin Blasingame. "Application of a New Fracture-Injection/Falloff Model 
Accounting for Propagating, Dilated, and Closing Hydraulic Fractures." Paper presented at the SPE Gas 
Technology Symposium, Calgary, Alberta, Canada, May 2006. doi: https://doi.org/10.2118/100578-MS  
Craig, David P., and Robert A. Jackson. "Calculating the Volume of Reservoir Investigated During a 
Fracture-Injection/Falloff Test DFIT." Paper presented at the SPE Hydraulic Fracturing Technology 
Conference and Exhibition, The Woodlands, Texas, USA, January 2017. doi: 
https://doi.org/10.2118/184820-MS  
McClure, Mark W., Jung, Hojung, Cramer, Dave D., and Mukul M. Sharma. "The Fracture-Compliance 
Method for Picking Closure Pressure From Diagnostic Fracture-Injection Tests." SPE J. 21 (2016): 1321–
1339. doi: https://doi.org/10.2118/179725-PA  
Nolte, Kenneth G., and Michael B. Smith. "Interpretation of Fracturing Pressures." Paper presented at the


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SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979. doi: 
https://doi.org/10.2118/8297-MS  
Nolte, Kenneth G. "Determination Of Fracture Parameters From Fracturing Pressure Decline." Paper 
presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979. 
doi: https://doi.org/10.2118/8341-MS  
Nolte, Kenneth G.. "Fracturing-Pressure Analysis for Nonideal Behavior." J Pet Technol 43 (1991): 210–
218. doi: https://doi.org/10.2118/20704-PA  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023


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URTeC 3717105  15 
 
Nolte, K.G., Mack, M.G., and W.L. Lie. "A Systematic Method for Applying Fracturing Pressure Decline: 
Part I." Paper presented at the Low Permeability Reservoirs Symposium, Denver, Colorado, April 1993. 
doi: https://doi.org/10.2118/25845-MS  
Nolte, K.G., Maniere, J.L., and K.A. Owens. "After-Closure Analysis of Fracture Calibration Tests." Paper 
presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 1997. doi: 
https://doi.org/10.2118/38676-MS  
Peres, A. M. M., Onur, M., and A. C. Reynolds. "A New General Pressure Analysis Procedure for Slug 
Tests." Paper presented at the SPE California Regional Meeting, Bakersfield, California, April 1989. doi: 
https://doi.org/10.2118/18801-MS  
Talley, G.R., Swindell, T.M., Waters, G.A., and K.G. Nolte. "Field Application of After-Closure Analysis 
of Fracture Calibration Tests." Paper presented at the SPE Mid-Continent Operations Symposium,


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Oklahoma City, Oklahoma, March 1999. doi: https://doi.org/10.2118/52220-MS  
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SPE-201413-MS
DFIT Analysis and Simulation: A Utica Shale Field Study
Jeffery Hildebrand, Jr. and Yu Liang , The University of Texas at Austin
Copyright 2020, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Annual Technical Conference & Exhibition originally scheduled to be held in Denver, Colorado, USA, 5 – 7
October 2020. Due to COVID-19 the physical event was postponed until 26 – 29 October 2020 and was changed to a virtual event. The official proceedings were
published online on 21 October 2020.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect


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any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written
consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
Since 2010, hydrocarbon production from long horizontal wells targeting shales has become the norm for
industry leaders. Because of the steep decline rates, it is vital to understand the reservoir and its properties
before going through with a full-scale fracture stimulation. Through the application of Diagnostic Fracture
Injection Tests (DFIT), one can determine accurate estimates of closure pressure, net pressure, pore pressure,
formation permeability, and induced fracture geometry. The Utica shale is among the most promising


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reservoirs of the future, but there is limited information available discussing its properties. In SPE-196149-
MS, we analyzed a DFIT from one horizontal well targeting the Utica. However, in order to fully understand
the Utica shale at scale, further analysis is required. In this study, we will present three additional horizontal
wells targeting the Utica, and analyze the pressure and its derivative to accurately estimate the properties
mentioned above.
DFIT analysis is an advanced technique to accurately predict stress regimes and reservoir properties.
However, interpretation of DFIT data is challenging, especially in shale formations. In this study, we
overview the geologic properties of the Utica shale, discuss the development of DFIT analysis and its
governing equations, then present the three data sets and resulting conclusions. We specifically discuss
the Tangent Line Method, the Compliance Method, and the Variable Compliance method in detail, while


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comparing their underlying equations and assumptions to determine closure pressure. After-Closure analysis
is then performed in order to verify fracture closure and identify flow regimes. Through linear regression
of this data, pore pressure from a linear flow regime is extrapolated, and through numerical simulation, key
reservoir properties, such as permeability and fracture geometry, are estimated for the Utica shale.
The DFIT interpretation and simulation results from this study are very insightful. Interpreting the GdP/
dG function, the closure pressure ranges from 4,943 psi to 6,141 psi, contributing to a closure pressure
gradient of 0.797 to 0.891 psi/ft for the Utica shale. Based on the pressure transient analysis, the pore
pressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient of 0.486 to 0.616
psi/ft for the Utica shale. Additionally, field wide ranges of reservoirs properties are presented, allowing


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industry to further optimize their drilling and fracing techniques in the Utica shale. Two of the wells in this
study are close in proximity and show very similar results both in After-Closure analysis and in pressure
response curves. The third well displays a different GdP/dG response, leak off characteristics, pressureDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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2 SPE-201413-MS
transient behaviors, formation permeability, and fracture geometry. This variance in results can be attributed
to regional differences in geology, stresses, and pressures. Therefore, operators need to consider regional
differences in reservoir properties in order to enhance the development of Utica shale and unlock all potential
recoverable hydrocarbons.
Introduction
Since 2010, hydrocarbon production from long horizontal wells targeting shales has become the norm for
industry leaders. Because of the steep decline rates, it is vital to understand the reservoir and its properties
before going through with a full-scale fracture stimulation. Through the application of Diagnostic Fracture
Injection Tests (DFIT), one can determine accurate estimates of closure pressure, net pressure, pore pressure,
formation permeability, and induced fracture geometry. The Utica shale is among the most promising


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reservoirs of the future, but there is limited information available discussing its properties. In SPE-196149-
MS, we analyzed a DFIT from one horizontal well targeting the Utica. However, in order to fully understand
the Utica shale at scale, further analysis is required. In this study, we will present three additional horizontal
wells targeting the Utica, and analyze the pressure and its derivative to accurately estimate the properties
mentioned above.
Geological Overview of Utica Shale
Underlying many parts of the Northeast United States lies a vast, organic rich laminated shale that spans an
approximate 115 square miles. Upper Ordovician in age, the Utica shale was deposited in the Appalachian
basin around 450 million years ago. The play has thickness ranging from less than 100 feet to over 500 feet
and depths ranging from 14,000 feet to just 2,000 feet below sea level. Outcrops of the Utica can even be


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observed in Quebec; however, this area is far outside of the producing zone. All of the major rock units in
the Appalachian basin follow the same basic trend: thickness and depth to the southeast, while progressively
thinning and uplifting with northwestward progression.
Created by some 1,182 wells logs, Figure 1 illustrates the stratigraphic nature of the Utica shale. The
majority of drilling activity has occurred in eastern Ohio for two main reasons: the Utica is at optimal depth
ranging from 6,000 ft - 9,000 ft and it's home to the wet gas/condensate region. Additionally, the Marcellus
overlies the Utica in this area and the existing wellbores can serve as a re-entry point to the shallower target
after the Utica wells become uneconomic. The oil window resides to the west of the production wells in
Figure 1  and corresponds with GOR's of less than 10,000 scf/bbl. Conversely, the gas window resides to
the east of the production wells and corresponds with GOR's greater than 10,000 scf/bbl. The three defined


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hydrocarbon windows in the Utica can be defined by vitrinite reflectance (Ro), which is directly related
to thermal maturity. The oil window has Ro values between 0.6% and 1.1% while the dry gas window
has values between 1.4% and 3.2%. A Ro value above or below these ranges suggests that no producible
hydrocarbons exist in that interval. Because the Utica is Ordovician in age, the vitrinite reflectance is
calculated from bitumen and conodont reflectance data (U.S. Energy Information Administration, 2017 ).
Conodonts are microfossils of small marine animals that lived from the Cambrian through Triassic periods.
These tiny, eel like animals are most frequently found in marine sedimentary rocks. When the surrounding
rock is heated, the color of the conodonts change from light to dark. This is known as the conodont alteration
index or CAI. Because the change in color is irreversible, studying conodonts is a great way to determine


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the maximum temperature a rock has endured. Oil generation is associated with a CAI range from 1 to 2
and anything greater is likely to be gas dominated. Similar to vitrinite reflectance, the western Utica has
CAI values between 1 and 2 while the eastern portion has values greater than 2.5.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 3
Figure 1—Structure map of the Utica formation ( U.S. Energy Information Administration, 2017).
The Utica was deposited on a carbonate shelf in a shallow marine environment, experiencing frequent
algal blooms and storms. Fossils suggest that the depositional environment was shallow, well oxygenated,
and exposed to sunlight (West Virginia Geological and Economic Survey, 2020). However, due to the
dominant presence of amorphinite in Utica cores, the region must have gone through seasonal anoxic periods
in which dissolved oxygen in the sea plummeted and marine algae flourished. Interestingly enough, areas
with high organic material deposition had similar water depths to areas with low organic material deposition.
This was likely due to small moving currents and erosional surfaces created by storms throughout the region
(U.S. Energy Information Administration, 2017 ).
The Utica has an average total organic content (TOC) of about 3.5% and an average carbonate content


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of 25%. Due to the low carbonate content and high clay content, fracturing the Utica proves difficult. In
reality, the majority of wells drilled in eastern Ohio are actually targeting the underlying Point Pleasant
formation. The Lower Point Pleasant has an average TOC around 4.5% and has a much higher carbonate
content of 40%-60%, making it a more productive and much easier rock to induce fractures (West Virginia
Geological and Economic Survey, 2020 ).
Generally speaking, Gamma Ray (GR) and TOC are directly related when plotted against each other.
Ordovician shales are unique in the sense that they do not follow this trend. The gamma ray values from these
shales correlate almost exactly with carbonate content instead of TOC, unlike the overlying Marcellus shale.
The implications of this unique characteristic can be hugely beneficial to operators in the region if analyzed
correctly. Because carbonate rich rocks are more brittle, they respond better to hydraulic fracturing. From


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Figure 2 , it seems that the Lexington/Trenton Formation may be the best target in this organic rich interval
due to the high carbonate and TOC content. However, the presence of clay particles creates matrix porosity,
so the optimal target here is the lower organic rich member of the Point Pleasant Formation. In general, there
is an increasing carbonate content and a decreasing clay content with depth in this organic rich interval.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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4 SPE-201413-MS
Figure 2—GR log, carbonate content and TOC from the Eichelberger No. 1,
Ashland County, Ohio ( West Virginia Geological and Economic Survey, 2020).
High in both calcite and clay content, the Utica shale is an extremely tight reservoir. With an average
permeability range of 0.00008 to 0.003 mD and an average porosity range of 3.7% to 6%, data analyzation is
paramount in the pursuit to unlock untapped reserves in the Utica shale. Through the utilization of diagnostic
fracture injection tests, this goal can be achieved.
DFIT Theory and Methods
Diagnostic fracture injection tests (DFITs) have been referred to as a number of different names including
fracture calibration tests, mini-frac tests, and injection fall-off tests. The test involves pumping a small
amount of fluid down a cased and perforated wellbore at a constant rate to induce a small fracture in the
near wellbore region. The well is then shut in and the pressure transient data is analyzed to obtain reservoir


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properties and in situ stresses. Historically, DFITs were conducted to estimate frac design parameters such as
leak off coefficient, fluid efficiencies, and minimum principal stress. In recent years, it has become possible
to predict reservoir pore pressure, permeability, and fracture geometry through numerical simulation. DFITs
lend countless advantages, which allow the industry to have a more comprehensive understanding of the
reservoir before continuing with a full-scale frac stimulation.
Figure 3  illustrates an idealized version of what a typical DFIT pressure as a function of injection rate
would look like. The bottom hole pressure increases linearly until the leak off pressure (LOP) and is usually
associated with a slope change, meaning a small fracture has been induced in the near wellbore rock matrix.
The formation fully fractures at the formation breakdown pressure and the fractures propagate at the fracture


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propagation pressure until injection ceases. The well is then shut in and the pressure drops to the ISIP due
to the loss of friction in the wellbore and in the newly induced fractures. The bottom hole pressure will then
decline into a linear and then into a radial flow regime. The closure pressure, which is defined by whenDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 5
the planes of the newly induced fracture come into contact, is a proxy for minimum in situ stress and is
estimated by the variable compliance method on a GdP/dG vs. G-time graph. It should be noted that it could
take months after a DFIT test for a well to exhibit a radial flow regime, which makes estimation of reservoir
pore pressure difficult.
Figure 3—Typical DFIT test data plotted with pressure vs. time ( Wang and Sharma, 2017).
DFIT pressure data is generally split into two distinct groups: Before-Closure data (BC) and After-
Closure data (AC), separated by the fracture closure pressure. Before-Closure data is used to estimate leak
off and fracture geometry, assuming normal leak off behavior according to Carter's leak off. However,
Carter's leak off oversimplifies leak off behavior and generally leads to severe over or underestimation
of the minimum in situ stress. After-Closure data is mainly used to predict formation pore pressure and


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permeability. Because only half of the data is being used in each case, the results can be misleading. Attempts
have been made in the past to bridge the gap between the two sets of data but the models were based on
the fundamentally flawed G-function assumptions. Up until the development of the variable compliance
method, which assumes variable fracture stiffness and pressure dependent leak off, no mathematical model
was able to seamlessly integrate both regions of data.
The basic mathematical model underlying DFIT analysis contains two important components. The first
component assumes that the pressure derivative is constant with time throughout the induced entire fracture
network and is based on the material balance ( Hildebrand and Liang, 2019). Through derivation, it is found
that the leak off rate is proportional to the pressure derivative with respect to time. The second component,
which is in a similar form to 1D diffusivity equation with constant pressure boundaries, is the Carter Leak


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Off Theory (Hildebrand and Liang, 2019). The Carter Leak Off Theory suggests that the leak off rate is
proportional to the inverse of the square root of time, and assumes that the single-phase fluid in the fracture
and in the formation are identical (Howard and Fast, 1957). Carter Leak Off Theory also assumes that fluid
pressure in the fracture is constant over time and that spurt loss is neglected ( Hildebrand and Liang, 2019).
With the integration of these two components, the basic mathematical model underlying DFIT analysis can
be written asDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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6 SPE-201413-MS
(1)
where Δ P is the change in pressure after shut-in time, C is a constant that relates to comprehensive
compressibility and the leak off coefficient, Δt is the change in time after shut-in, A is the fracture surface
area and Sf is the fracture stiffness/compliance. The basic mathematical model assumes that the fracture is
formed at the time of shut-in and that the fracture stiffness Sf stays constant before fracture closure, varying
once the fracture walls initially come into contact. Consequently, the closure pressure is picked at the point
on the plot where pressure as a function of the square root of Δt first deviates from linearity. However,
because of the underlying assumptions in the basic mathematical model, correct identification of closure
pressure by this method is not feasible.
In the following years, Nolte (1986a, 1986b , 1979 ) modified the leak off equation by assuming the


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fractures form over a period of time instead of instantaneously at the time of shut in. Still used today for
analysis, the model is known as the G-function. Assuming power law fracture growth, negligible spurt loss,
constant fracture stiffness, constant fracture surface after shut in, and Carter Leak Off Theory, Nolte was
able to provide an equation for fracture pressure as a function of dimensionless time and can be written as
(2)
where P is the pressure in the fracture, ISIP is the instantaneous shut-in pressure, CL is Carter's leak
off coefficient that is a constant, te is the shut-in time, and G (ΔtD) is the G-function as a function of a
dimensionless time Δ tD. The dimensionless time Δ tD is defined as
(3)
Then G-function is defined as the following
(4)
Fluid efficiency is defined as the ratio of the pumped fluid that is stored in fractures to the total fluid that
is pumped into the well. High fluid efficiency indicates that more fluid is stored in the fracture due to the


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low leak off rate, and vice versa.
For high fluid efficiency, g (Δ tD) is defined by
(5)
For low fluid efficiency, g (Δ tD) is defined by
(6)
Not long after the development of the G-function, Castillo (1987) began analyzing Nolte's pressure versus
G-function plot under the assumption of normal leak off behavior (constant Carter leak off coefficient, leak
off area, and stiffness). Similar to the basic mathematical model, Castillo determined that fracture pressure
should scale with G-function linearly before the fracture closure ( Hildebrand and Liang, 2019). As a result,
he interpreted the closure pressure should be picked at the point where the pressure first deviates from
linearity, and the slope of the line is used to calculate the leak off coefficient CL (Hildebrand and Liang,
2019 ).
However, when interpreting plots of pressure versus G-function, initial linearity is highly uncommon.
Usually, these plots contain many points of inflection due to a multitude of factors and identifying a linear


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trend is generally not clear. Due to the ambiguous nature of the straight-line method, correct identification
of closure pressure is also not feasible. Recognizing the straight line method was unreliable, Barree et al.
(2009 , 1996 ) developed a new way to estimate closure pressure by the Tangent Line Method. In this method,Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 7
Barree plotted GdP/dG versus G time and determined the closure pressure was the line tangent to the GdP/
dG curve that also passed through the origin. Integrating this method with Castillo's pressure versus G time
graph, estimating the closure pressure became much more consistent. The tangent line method is still a
widely accepted method today, however the method has not been scientifically proven, which makes for an
interesting research topic (Wang and Sharma, 2017). By taking the derivative of pressure with respect to
the G-function of Equation 2, the equation of GdP/dG can be written as
(7)
Non-ideal transient behaviors are commonly observed when using the G-function to process field DFIT
data, including pressure dependent leak off, fracture tip extension, and height recession/transverse storage
behaviors, as depicted in Figure 4 .
Figure 4—Signatures of non-ideal leak off behaviors (a,b,c) on the G-function plots ( Barree et al., 2009 ).


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Advancing this topic, McClure et al. (2016 , 2014 ) developed the Compliance method to estimate the
fracture closure pressure at the point on the G-function plot where the trend starts to deviate from its original
linearity. Based on the Compliance method, Wang and Sharma (2019, 2018a, 2018b , 2017 ) suggest the
Variable Compliance method to estimate the fracture closure pressure by addressing that fracture stiffness
gradually increases as the fracture walls come into contact. As a result, the Variable Compliance method
identifies closure pressure at the average G-function time of the Tangent Line and Compliance methods.
DFIT numerical simulation is an advanced method to estimate matrix permeability and fracture geometry,
which are important to the development of unconventional assets. The DFIT numerical simulation of this
manuscript is based on the algorithm by Wang and Sharma (2019, 2018a , 2018b , 2017 ).


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The differential form of mass balance, with the assumption of 1D leak-off into a semi-infinite formation,
can be presented as
(8)
Where Ct is the total compressibility, k is the formation permeability and ø is the formation porosity. The
boundary condition of Equation 8 can be written as
(9)
The initial conditions of Equation 8 are written as
(10)
(11)
Where ISIP is the instantaneous shut-in pressure, Po is the initial reservoir pressure and Sf is the fracture
stiffness. The net pressure is written asDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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8 SPE-201413-MS
(12)
Where Shmin is the minimum principal stress and wf is the average fracture width. The minimum principal
stress is assumed to be the closure pressure, and ISIP is estimated by extrapolation in this paper. Pnet and Sf
are used to evaluate the induced fracture geometry based on expressions in Table 1 , as shown below.
Table 1—Fracture stiffness by different fracture geometry models (Wang and Sharma, 2017).
Fracture Geometry PKN KGD Radial
Fracture Stiffness
The pressure decline and GdP/dG behaviors during DFITs are simulated by Equation 8 with Equation
9 constraining as the boundary condition; Equation 10 and 11 are governing Equation 8 as the initial
conditions. One essential feature of this numerical simulation algorithm, which is based on the Variable
Compliance method, is that this model is able to capture variable fracture stiffness and pressure-dependent
leak-off during the progressive fracture closure process. The fracture geometry is estimated by Equation
12 and Table 1 .


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12 and Table 1 .
Three DFIT Cases Targeting Utica Shale
Accurate estimations of closure pressure, pore pressure, and permeability are essential to the successful
development of a shale play. However, permeability of shale formations are low, thus interpretation of DFIT
data targeting shale formations is challenging. The Utica shale is one of the most promising unconventional
plays in the United States, but there are not many publications discussing its closure pressure, pore pressure,
and permeability. In SPE 196149-MS, we presented one set of DFIT data and its related interpretation. Here,
three additional DFIT cases are presented to give a comprehensive, field wide estimation of stress regimes
and reservoir properties of the Utica shale.
DFITs are performed on Well-A, Well-B, and Well-C with the locations of these three wells shown in
Figure 5 . They are all horizontal wells with their horizontal intervals all being stimulated by hydraulic


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fracturing into multiple stages. The TVD and MD for the wells are as follows: 6,600 feet and 12,500 feet
for Well-A, 6,200 feet and 9,300 feet for Well-B, and 6,900 feet and 12,600 feet for Well-C. During each
DFIT, water is injected into the targeted wellbore for approximately 15 minutes at a constant rate of around
3.5 bbl/min. Figures 6  through 8 display the wellhead pressure and pump rate vs. time for Well-A, Well-
B, and Well-C, respectively.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 9
Figure 5—DFITs targeting the Utica shale were carried out on Well-A, Well-B and Well-C.
Figure 6—WHP and pump rate vs. time for the DFIT on Well-A.
From Figure 6 , it can be determined that the leak off pressure (LOP), the fracture breakdown pressure
(FBP), and the fracture propagation pressure (FPP) of Well-A are estimated to be 8,467, 9,126 and 8,938 psi.
When the pump is shut down and the pump rate reads zero, the instantaneous shut-in pressure (ISIP) after
adding hydrostatic reads 8,206 psi and quickly drops to 7,657 psi after one minute. This significant drop in
ISIP indicates that the friction and the tortuosity inside the wellbore are high and the fracture complexity near
the wellbore is significant, therefore the true ISIP is estimated by extrapolation to calculate net pressure andDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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10 SPE-201413-MS
analyze the G-function. At end of the DFIT, the pressure of Well-A drops to 4,762 psi, which is magnified
in the inserted image. Similarly, Figures 7 and 8 show wellhead pressure and pump rate vs. time for wells B
and C. Based on the plots, LOP, FBP, FPP, and ISIP are estimated to be 8,121, 8,629, 8,480, and 7,744 psi for
Well-B, and 7,854, 8,668, 8,642, and 7,926 psi for Well-C. It should be noted that high wellbore tortuosity
and significant fracture complexity are also observed in Well-B and Well-C due to the significant drop in
pressure after shut-in, therefore the extrapolated ISIPs are applied to the following analysis and simulation.
Figure 7—WHP and pump rate vs. time for the DFIT on Well-B.
Figure 8—WHP and pump rate vs. time for the DFIT on Well-C.
Based on the field DFIT data from three wells, a plot of pressure and GdP/dG vs. G-function can be
seen in Figure 9 . There is quite a bit of noise in GdP/dG response after the closure time, represented by


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the blue line, which is commonly observed in DFIT analysis. The noise in the data is smoothed by the
Butterworth filter with a smoothing coefficient of 0.11, and the filtered data is represented by the red line.
The G-functions of wells A and C experience a similar trend, while well B does not. Further analysis on
these trends is explained with the simulation results.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 11
Figure 9—G-function plots for Wells A, B, and C, respectively.
Figures 10  through 12 show closure pressure determination by the Tangent Line method, the Compliance
method, and the Variable Compliance method for the three wells, as depicted by red, blue and turquoise
dotes, respectively. The Compliance method suggests that fracture closure pressure is determined when
GdP/dG response starts to deviate from expected linearity, and the Variable Compliance method is an
average result of the Tangent Line method and the Compliance method. Therefore, the Compliance method
shows an upper bound while the Tangent Line method suggests a lower bound of closure pressure estimation.
As shown in Figure 10 , the closure pressure by the Tangent Line method for Well-A is estimated to be
5,690 psi, contributing to a stress gradient of 0.862 psi/ft; 6,125 psi with 0.928 psi/ft by the Compliance
method, and 5,973 psi with 0.905 psi/ft by the Variable Compliance method. As shown above, the true ISIP


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is extrapolated to 6,300 psi when the square root of time reaches to zero, compared to the estimated ISIP
of 8,206 psi from the pump schedule presented above. A net pressure of 327 psi is determined and applied
to the fracture geometry estimation, which is discussed in the following simulation section. As a result, the
Well-A DFIT analysis estimates that the closure pressure ranges from 5,690 psi to 6,125 psi, contributing
to the stress gradient of 0.862 – 0.928 psi/ft in this area.
Figure 10—Closure pressure determination by the Tangent, the Compliance
and the Variable Compliance methods using the filtered Well-A DFIT data.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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12 SPE-201413-MS
Figure 11—Closure pressure determination by the Tangent, the Compliance
and the Variable Compliance methods using the filtered Well-B DFIT data.
Figure 12—Closure pressure determination by the Tangent, the Compliance
and the Variable Compliance methods using the filtered Well-C DFIT data.
Figure 11  demonstrates the closure pressure by the Tangent Line method for Well-B is estimated to be
4,692 psi, contributing to a stress gradient of 0.757 psi/ft; 5,154 psi with 0.831 psi/ft by the Compliance
method, and 4,943 psi with 0.797 psi/ft by the Variable Compliance method. The true ISIP is extrapolated
to 5,700 psi when the square root of time reaches to zero, compared to the estimated ISIP of 7,744 psi from
the pump schedule. A net pressure of 757 psi is determined and applied to the fracture geometry estimation.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 13
As a result, the Well-B DFIT analysis estimates that the closure pressure ranges from 4,692 psi to 5,154 psi,
contributing to the stress gradient of 0.757 – 0.831 psi/ft in this area.
Figure 12  presents the closure pressure by the Tangent Line method for Well-C is estimated to be 5,662
psi, contributing to a stress gradient of 0.821 psi/ft; 6,416 psi with 0.929 psi/ft by the Compliance method,
and 6,141 psi with 0.891 psi/ft by the Variable Compliance method. The true ISIP is extrapolated to 6,250
psi when the square root of time reaches to zero, compared to the estimated ISIP of 7,926 psi from the
pump schedule. A net pressure of 109 psi is determined and applied to the fracture geometry estimation. As
a result, the Well-C DFIT analysis estimates that the closure pressure ranges from 5,662 psi to 6,416 psi,
contributing to the stress gradient of 0.821 – 0.929 psi/ft in this area. Overall, the closure pressure ranges


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from 4,943 psi to 6,141 psi in the Utica shale, contributing to the closure pressure gradient of 0.797 to 0.891
psi/ft by the Variable Compliance method.
A log-log pressure derivative plot vs. shut in time is used in this analysis to verify fracture closure and
estimate the pore pressure, as shown in Figure 13 . Well-A, Well-B, and Well-C all experience similar after
closure-flow patterns: after the pump is shut down, the afterflow rate is greater than the leak-off rate in the
fracture, causing the fracture to propagate in all directions. This signature is marked by a unit slope in the
figures. Once the injected fluid reaches the fracture tip, the fracture is propagating only into its longitude
direction and fracture length is increased, signaled by a zero slope. Following that, leak-off phenomenon
starts to govern the process, and fractures starts to close progressively. The peaks of the pressure derivative


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in the figures clearly indicate that the induced fracture is mechanically closed, verifying the fracture closure
determination in the analysis above. After fracture closure time, reservoir flow starts to dominate the process
and the pore pressure is estimated by pressure transient analysis. The adjacent reservoir fluid first flows in
the induced fracture by a 1D flowing pattern, resulting in a linear flow regime and implied by a slope of
−0.5 on the pressure derivative plot, as shown by the red line in Figure 13. Well-B is a bit unique in the sense
that the pressure derivative experiences a significant drop after the peak pressure, and then reaches a linear
flow regime marked by a −0.5 slope, where Well-A and Well-C reach linear flow immediately after the
derivative peak. This observed signature could indicate that there are natural or secondary fractures existing
near Well-B, which is consistent with observations from its G-Function plot.


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Figure 13—Before-Closure (BC) and After-Closure (AC) analyses by pressure derivative log-log plots for
Well-A, Well-B and Well-C. Signature of linear flow regime is slope of −0.5 after the fracture closure time.
To estimate pore pressure, the pressure data in a linear flow regime is regressed linearly in a log-log
plot of pressure vs. the inverse of square root of time, as shown in Figures 14 through 16. In general, pore
pressure by radial flow regime gives an upper bound estimation while linear flow gives a lower bound.
Figure 14  demonstrates that the pore pressure of Well-A by linear flow regime is estimated to be 28.03 MPa
or 4,064 psi, contributing to a pore pressure gradient of 0.616 psi/ft. Similarly, Figure 15  shows that the
pore pressure of Well-B by linear flow regime is estimated to be 22.33 MPa or 3,238 psi, contributing to a
pore pressure gradient of 0.522 psi/ft. Figure 16 indicates that the pore pressure of Well-C by linear flow


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regime is estimated to be 23.1 MPa or 3,351 psi, contributing to a pore pressure gradient of 0.486 psi/ft.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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14 SPE-201413-MS
As a result, the pore pressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient
of 0.486 to 0.616 psi/ft for the Utica shale.
Figure 14—Pore pressure of Well-A is estimated by pressure transient analysis.
Figure 15—Pore pressure of Well-B is estimated by pressure transient analysis.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 15
Figure 16—Pore pressure of Well-C is estimated by pressure transient analysis.
By inputting the rock properties and fracture parameters into the simulator developed by Wang and
Sharma (2019 , 2018a , 2018b, 2017 ), DFIT numerical simulations are performed to match the historical
pressure and GdP/dG data for DFITs from Well-A, Well-B, and Well-C. The input parameters include
porosity, viscosity, Poisson's ratio, injection volume, total compressibility, Young's modulus, and wellbore
storage coefficient. Figures 17 to 19 demonstrate that the simulated pressures and derivatives match with the
field DFIT data well. It should be noted that although the shape of the simulated results may not be exactly
the same, the most important aspect is making sure that the peaks of the GdP/dG (blue) and simulated
results (red) agree. This will validate that the closure pressure and permeability are accurate estimates. The


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simulated reservoir permeability for Well-A is 0.000041 mD, 0.002 mD for Well-B, and 0.000025 mD
for Well-C. The fracture geometry simulation is performed based on the material balance, the net pressure
calculation by Equation 12, and the fracture geometry calculation from Table 1 . With an assumption of a 50-
foot fracture height, the simulation results of fracture geometry are summarized in Table 2 . It should be noted
that the simulation results are consistent with the estimations from our reservoir and petrophysics studies.
Figure 17—Numerical simulation and history match of pressure and pressure derivative for Well-A DFIT data.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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16 SPE-201413-MS
Figure 18—Numerical simulation and history match of pressure and pressure derivative for Well-B DFIT data.
Figure 19—Numerical simulation and history match of pressure and pressure derivative for Well-C DFIT data.
Table 2—Fracture length and width with different fracture geometries.
Well A Well B Well C
Fracture Geometry Radial PKN Radial PKN Radial PKN
Estimated Frac
Length (ft)72.95 263.62 50.87 89.39 82.43 380.3
Fracture
Average Width
at Shut-in (ft)0.01406 0.00891 0.02165 0.01969 0.00736 0.00413Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 17
The G-function signatures of these DFITs, as depicted in Figure 9, are insightful. At the very beginning
of the shut-in time, a minor hump in GdP/dG in Well-A and Well-C is seen, corresponding to an accelerated
and considerable pressure drop. As discussed above, these wells are long horizontal wells and this minor
GdP/dG hump results from wellbore tortuosity and fracture complexity. Therefore, it should be excluded
from the closure pressure determination. After that, a major hump in GdP/dG appears and follows a
classic concave-up trend, which is a characteristic signature of pressure-loss-acceleration. Indicating that
the induced fracture is closed progressively and, thus closure pressure can be determined by the Compliance
method. Height recession and transverse storage are the two main mechanisms contributing to the pressure-
loss-acceleration signature. However, they are two different mechanisms from the perspective of physics.


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Height recession occurs when the induced fracture grows into overlying and/or underlying formations
during a DFIT, causing increasing stiffness and thus accelerating pressure drop rate. Transverse storage takes
place when fluid, expelled from transverse fractures due to fracture closure, enters into the induced fracture,
and contributes to the increasing leak-off rate and accelerated GdP/dG. Besides these two mechanisms,
McClure (2016 , 2014 ) states that fracture closure is a dynamic process, and the concave upward trend is
actually an indication that two fracture planes come into contact and stiffness is therefore increased. It is
difficult to confirm which mechanism is dominating without further supporting data, but the methodology to
determine the closure pressure of a concave-up trend is consistent. On the contrary, Well-B does not display
a hump at the beginning of shit in time. Instead, we observe a consistent concave down trend throughout the


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test. This is a typical signature of pressure dependent leak off in a naturally fractured formation and generally
occurs in a dual porosity system when the fluid loss rate varies with the pressure dependent permeability. The
potential existence of secondary fractures near Well-B is also verified by the pressure derivative analysis, as
shown in Figure 13 . It is common to observe a signature of tip extension in DFIT targeting shale formations,
which usually leads to a questionable estimation of closure pressure. However, the DFIT results presented
in this paper do not show characteristics of tip-extension, which is an indication of productive shale quality.
As seen from the simulated fracture geometries in Table 2 , we again see similarities between wells A
and C. In both radial and PKN geometry, the fractures exhibit the similar lengths and widths. These two
wells are very close in proximity to each other and share similar depths, so it's physically meaningful that


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these two wells experience similar results. Well-B is located further north on the trend and the results from
this study show that the differences in DFIT behaviors and simulation, including GdP/dG response, leak off
characteristics, pressure transient behaviors, formation permeability, and frac geometries, can be attributed
to regional geology, stresses, and pressures. Therefore, operators need to consider regional differences in
reservoir properties in order to enhance the development of the Utica and unlock all potential producible
hydrocarbons.
Conclusion
The objective of this study was to continue analysis on the Utica shale and its properties through multiple
DFITs across the extent of the play. In this study, we presented three additional wells to perform analysis
and determined field wide ranges of closure pressure, pore pressure, net pressure, formation permeability,
and fracture geometry. In this study, we first gave a geological overview of the Utica shale, then explained


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the theories and methods behind DFITs, and finally presented a field wide range of reservoir characteristics
and properties. The results from this study are encouraging and insightful, showing that there are regional
differences across the shale and can be identified through the application of DFITs. The knowledge resulting
from this study indefinitely creates value for the industry in the pursuit of unlocking hydrocarbons in the
Utica shale. The analysis and results from this study provide the following conclusions:
•As observed by all three wells, the sharp breakdown of pressure after shut in indicates that the
friction and the tortuosity inside the wellbores are high, and the fracture complexity near the
wellbore is significant for horizontal wells and the Utica shale.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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18 SPE-201413-MS
•Interpreting the GdP/dG data by the Variable Compliance Method, the closure pressure ranges
from 4,943 psi to 6,141 psi in the Utica shale, contributing to a closure pressure gradient of 0.797
to 0.891 psi/ft.
•Calculating based on the closure stress and ISIP, the net pressure in the fractures from wells A, B,
and C are 327, 757, and 109 psi, respectively.
•Based on G-function analysis, Wells A and C follow a classic concave-up trend, which is a
characteristic signature of pressure-loss-acceleration, indicating that the induced fracture is closed
progressively. Well-B displays a consistent concave down trend, which is a typical signature of
pressure dependent leak off in a naturally fractured formation and generally occurs in a dual
porosity system when the fluid loss rate varies with the pressure dependent permeability. This
observation is consistent with the pressure derivative analysis.
•On the log-log plots of pressure derivative, Well-A, Well-B, and Well-C experience similar After-


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Closure flow patterns in general. The sharp decline in pressure derivative on the log-log plot after
its peak indicate that there are natural and secondary fractures near Well-B. This observation is
consistent with the G-function analysis.
•From the linearly regressed log-log plot of pressure vs. the inverse of square root of time, the pore
pressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient of 0.486 to
0.616 psi/ft for the Utica shale.
•Through numerical simulation, the formation permeability for Well-A is 0.000041 mD and
0.000025 mD for Well-C. The numerical simulation shows that the formation permeability for
Well-B is 0.002 mD, which is higher than Well-A and Well-C.
•Wells A and C show similar fracture geometries with an average frac length of 77.69 feet and width
of 0.01071 feet in radial geometry, and an average frac length of 321.96 feet and width of 0.01304
feet in PKN geometry. For Well-B, the frac length is estimated 50.87 feet in radial geometry and


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89.39 feet in PKN geometry. The difference in fracture geometry indicates that Wells A and C are
located in an area where induced fractures tend to propagate into longitude direction.
•As shown above, Wells A and C are very close in proximity and thus they display similar DFIT
results and reservoir properties. Well-B is well north of wells A and C, and it shows different
GdP/dG response, leak off characteristics, pressure transient behaviors, formation permeability,
and frac geometries. This variance can be attributed to regional differences in geology, stresses,
and pressures.
Acknowledgment
The authors wish to thank Dr. Mukul Sharma and Dr. Hanyi Wang for their continued support and guidance.
Nomenclature
ASurface area of fracture
CA constant relevant to leak off coefficient and comprehensive compressibility
CAI Conodont alteration index
CLCarter's leak off coefficient
CtTotal compressibility
E’Plane strain for Young's Modulus
GR Gamma ray
GOR Gas Oil Ratio
hfFracture height


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GR Gamma ray
GOR Gas Oil Ratio
hfFracture height
ISIP Instantaneous shut-in pressure
kFormation permeabilityDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-201413-MS 19
LOP Leak off pressure
PPressure in fracture
PoInitial reservoir pressure
PnetNet pressure
RfFracture radius
RoVitrinite reflectance
SfFracture stiffness
ShminMinimum principal stress
teShut-in time
TOC Total organic content
wfAverage fracture width
xfFracture half-length
ΔPPressure difference after shut-in
ΔtTime difference after shut-in
∆tDDimensionless time that is discussed in Equation 3
ϕFormation porosity
Reference
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SPE-199690-MS
DFIT Analysis and Interpretation in Layered Rocks
Shuang Zheng, Ripudaman Manchanda, HanYi Wang, and Mukul Sharma, The University of Texas at Austin
Copyright 2020, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The Woodlands, Texas, USA, 4-6 February
2020.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written


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consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
Diagnostic fracture injection tests (DFITs) are often used to estimate formation properties such as closure
stress, pore pressure, and matrix permeability. These estimations are typically based on analysis of pressure
data assuming the closure of simple planar fractures in homogeneous reservoirs. These interpretations
are incorrect when dealing with complex reservoir environments such as layered reservoirs with different
properties and stresses. This paper investigates the impact of such complex environments on DFIT
interpretation and presents a systematic method to analyze the data.
A 3-D implicitly integrated poroelastic fracture-reservoir-wellbore model is used to simulate DFITs.


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DFIT fracture propagation and well shut-in are simulated with implicitly computed fluid leak-off and
fracture closure. The model is validated by simulating a DFIT for a homogeneous reservoir and the implicitly
calculated surface pressure is interpreted to obtain the simulation inputs (stress, pore pressure, permeability,
etc.). A multi-layer reservoir model is then built in the numerical simulation domain and a DFIT is simulated
in the target layer. The properties and thickness of the layers are varied to analyze their impact on the
observed DFIT signature.
We analyze the impact of layer thicknesses, layer stresses, pressure and permeability of each layer, stress
contrast between the layers, fracture interaction with bedding planes and the rock roughness and hardness
of each layer on the DFIT pressure signature. We show that the layer property variations can cause different
but characteristic DFIT pressure responses. Fracture propagation into layers with different stresses induces


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multiple closure events in the observed pressure signature, which provides a quantitative representation of
the fracture height growth. The emergence of these closure events in the pressure signature are found to be
dependent on the hardness and modulus of the rock layers and the fluid communication between the closing
parts of the fracture. The DFIT signature patterns are also found to correlate with the interaction of the
fracture with bedding planes (cross/arrest/divert) and provide valuable insights into fracture containment.
In this work we present best practices for performing DFIT analysis in layered reservoirs. Results from
simulated DFITs in layered reservoirs clearly show the effect of key heterogeneity parameters on DFIT
responses. The results from this work can be used to more accurately determine reservoir closure stress,
pore pressure, reservoir permeability, fracture compliance, fracture conductivity, and fracture containment


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in heterogeneous reservoirs.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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2 SPE-199690-MS
Introduction
The technology of multi-stage hydraulic fracturing in horizontal wells plays a key role in creating highly
conductive flow channels connecting the wellbore with ultra-tight formations and this has led to the shale
revolution in North America. Diagonostic Fracture Injection Test (DFIT) has been an efficient method for
determining formation properties, for example, fracture closure stress and pore pressure. A DFIT is usually
performed on a vertical data well or after the horizontal well is drilled and cemented and before the main
hydraulic fracturing treatments start. A small amount of water is injected at low rate aiming to create a
fracture and then the well is shut-in for several days while the pressure is recorded. During the shut-in, water
gradually leaks into the reservoir and the fracture gradually closes. The fracture closure stress and pore
pressure can then be inferred from the closure and post-closure pressure data. Both analytical approaches


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(summarized in the Appendix) and numerical approaches (e.g., Zheng et al., 2019b; Zheng et al., 2019g; Ji
et al., 2019 ; Kamali and Ghassemi, 2019 ) have been developed for DFIT data interpretation.
Previous researchers have mainly focused on DFIT interpretations and simulations assuming a planar
fracture geometry in a homogeneous reservoir, however, it is not uncommon for the fracture that is
created to intersect several layers with different stress and mechanical/flow properties. This can have a
big impact on the DFIT signature since the mechanical properties (rock Young's modulus, Poisson's ratio,
fracture touchness, rock surface roughness, stress state) and the flow properties (permeability, porosity, pore
pressure) may vary a lot between different layers. Bedding planes are commonly seen in shale formations.
During a DFIT, bedding planes may be connected and opened by the hydraulic frcature and the hydraulic


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fracture may be arrested by the bedding planes or cross them and propagate further ( Tang and Wu, 2018).
DFIT fractures interacting with bedding planes will significantly impact the final fracture geometry and
leakoff rate during shut-in, and thus influence the pressure response (Wang and Sharma, 2019b). Very
complicated DFIT pressure signals are commonly observed in field data. For example, a field example of
a G-function plot of the pressure and pressure derivative ( Figure 1) shows multiple humps. However, most
DFIT interpretations in the past did not take the layer effect into consideration. The traditional analytical
interpretation approaches (as summarized in the Appendix) are inadequate in these complicated but real
scenarios. Other numerical models (e.g. Ji et al., 2019 ; Kamali and Ghassemi, 2019) also fail to capture
these complex behaviors due to their inability to model rock heterogeneity.
Figure 1—Field example case of complex DFIT pressure response ( Zheng et al., 2019g ).


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In this paper, we apply our fully integrated reservoir-fracture-wellbore simulator to DFIT simulations.
Through the fully integrated fracturing and reservoir simulation, we can for the first time, study the behavior
of the DFIT pressure response in layered formations. To fully understand the impact of the layer properties
we vary different layer properties with the ultimate aim of identifying the key parameters that affect the
DFIT interpretation. The effect of layer stress contrast, layer permeability, layer thickness, rock asperity
roughness, rock hardness, bedding planes on the closure stress and pore pressure estimation are clearly
shown. Many of these factors are found to have a significant impact on the DFIT analysis. The paper isDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 3
structured as follows: First, we provide a brief summary to our fully integrated simulator in the Model
Description section with the model domains, model physics and solution algorithms. Sensitivity studies
and discussions of the effect of different layer properties on the DFIT response and interpretation are then
provided in the Results and Discussions section. A Conclusion section summarizing the key findings of this
paper is included at the end of this paper.
Model Description
A fully integrated hydraulic fracturing and reservoir simulator is used in this paper to simulate a DFIT:
hydraulic fracture propagation and shut-in. This simulator has been developed for designing and evaluating
pad scale fracturing treatments previously ( Zheng et al., 2019a; 2019b ; 2019c; Manchanda et al., 2019a;
2019b ). It was then extended from a single-phase flow model to multi-phase black-oil flow model and from


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single well fracturing simulator to an integrated fracturing and reservoir simulator. An energy balance model
was inporporated into the simulator to consider temperature changes ( Zheng et al., 2019d). The fully implicit
geomechanical hydraulic fracturing simulator was also extended to an integrated Equation-of-State based
compositional fracturing and reservoir simulator in recent work (Zheng et al., 2019e ; Zheng et al., 2019f).
This simulator couples the reservoir-fracture-wellbore system ( Figure 2) and has the capability to
simulate the lifecycle of wells: hydraulic fraturing, shut-in, flowback, primary production, and improved
oil recovery. Multiple physics in each domain are tightly coupled. Solid deformation, flow in the rock
matrix and the fracture, and temperature are modeled and solved in the reservoir domain. Fracture fluid
and proppant flow, and fracture width change are solved in the fracture domain. Slurry and proppant


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distribution, wellbore storage, hydrostatic and friction pressure drops are considered in the wellbore domain.
The coupled, non-linear system of equations is solved using the Newton-Raphson method. An Implicit
pressure, explicit saturation/concentration based (IMPES/IMPEC) solution algorithm is shown in Figure
3. After the solutions to the coupled system of equations are obtained, mesh topology change (fracture
propagation, dynamic mesh refinement) is checked and looped until no more mesh topology changes are
needed. Then the fluid mass conservation equations and temperature equations in the reservoir and fracture
domain as well as the the proppant volume equations in the fracture domain are solved. The simulation enters
the next time step after the phase behavior analysis (using correlations if black-oil model and using Equation-
of-State if using a compositional model) is performed. Although only the IMPES/IMPEC algorithm is


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shown here, different sets of equation for different physics can be chosen to be coupled into the main Newton
iteration block or removed from the block with great flexibility. For example, the fluid mass conservation
equations can be coupled into the main Newton iteration block, making the simulation fully implicit and
the solid deformation equation can be removed from the iteration block, making it a non-geomechanical
reservoir simulator. A detailed formulation of the simulator can be found in the references cited above.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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4 SPE-199690-MS
Figure 2—The coupled domains and physics of the fully integrated simulator ( Zheng et al., 2019d ).
Figure 3—The IMPES/IMPEC solution algorithm of the fully integrated simulator.
This simulator was first applied to fracture closure and DFIT modeling in Zheng et al., 2019b in which
the Barton-Bandis contact correction was incorporated to model fracture closure on asperities/proppants.
This simulator was successfully validated for DFIT simulation and applied to study the effect of depletionDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 5
induced stress and pore pressure heterogeneity on DFIT closure stress and pore pressure estimation ( Zheng
et al., 2019g ). Readers are encouraged to read Zheng et al., 2019g for more details on the model validation.
Base Case
In the Base Case, a small amount of fluid (2 m3) is injected into the wellbore in 5 minutes and then the well
is shut-in for 10 days to mimic a DFIT job. The simulation domain is 400 × 400 m2 in the horizontal plane
and 200 m in the height direction (Figure 4). The perforation clusters are placed in the middle of the domain.
Other reservoir properties and completion design parameters are summarized in Table 3. The bottom hole
pressure versus time is computed and plotted in this simulation. The simulation involves propagation of a
single vertical fracture from a horizontal wellbore drilled in a formation with layered stress heterogeneity.
The stress distribution with the DFIT fracture initiation point is shown in Figure 5. The initial mesh size is 40


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× 10 × 10 m3 and is dynamically refined as can be seen from Figure 6. Grid convergence analysis (Zheng et
al., 2019g ) is performed to determine the correct mesh size for a grid converged solution and it is found that
when the smallest grid size reached 0.625 × 1.25 × 1.25 m3 by three levels of static refinement perpendicular
to the wellbore direction and three levels dynamic refinement in all directions, the results will not change
with further mesh refinement. A plot of the fracture geometry with width distribution and pore pressure
distribution at the end of shut-in (t  = 10 days) is shown in Figure 6. In this figure, each fracture segment
has an area of 1.25 × 1.25 m2 and the length of the smallest grid perpendicular to the wellbore direction is
0.625 m. During fracture propagation and shut-in, fracturing fluid in the fracture leaks into the reservoir,
causing a pressure increase in the reservoir matrix adjacent to the fracture. The fracture width shows good


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agreement with the input layer stresses, with smaller widths being computed in the high stress layers.
Figure 4—Illustration of simulation domain, well location, and cluster locationDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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6 SPE-199690-MS
Figure 5—Stress distribution in a vertical slice of the reservoir
Figure 6—Fracture geometry with width distribution and pore pressure distribution at the end of shut-inDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 7
Table 1—Reservoir properties and completion design in the Base Case
Parameter Value Unit Parameter Value Unit
Length of the domain in the x-direction 400 m Initial stress in the x-direction ( Shmin) 35/36 MPa
Length of the domain in the y-direction 400 m Initial stress in the y-direction ( Shmax) 51 MPa
Length of the domain in the z-direction 200 m Initial stress in the z-direction ( Sv) 70 MPa
Permeability 2e-19 m2 Vertical stress gradient 0.02262 MPa /m
Porosity 0.08 Young's modulus of the rock 20 GPa
Critical energy release rate 1000 Pa ∙ m Poisson's ratio of the rock 0.25
Contact width 2e-4 m Fluid viscosity 0.001 Pa ∙ s
Asperity initial stiffness 5e8 Pa/m Total injection time 300 s
Wellbore volume 55 m3 Total injection volume 2 m3
Well diameter 0.1397 m Number of perforations per cluster 2
Shut-in time 10 days Perforation diameter 0.0127 m
Figure 7  shows the fracture contact area and fracture width distribution when shut-in time equals to


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57, 67, 77, 87, 97, and 107 hours, respectively. As can be seen from Figure 7, the fracture maintains the
largest width in the middle low stress region and the two low stress regions below and above the middle
low stress region also have a large width as compared to the fracture tip regions and the high stress regions.
The fracture surfaces first fall in contact around the tips of the high stress regions followed by the internal
fracture surface area in the high stress region. At about 97 h, all the fracture surfaces in the high stress region
come into contact on the rough asperities. During fracture closure, fracture width decreases, however, the
fracture width in the low stress region is always higher than in the high stress region. Between time 97 h
and 107 h, the fracture in the upper and lower low stress region closes first. The fracture in the middle low


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stress region closes last.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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8 SPE-199690-MS
Figure 7—Fracture contact area and fracture width at selected times during shut-in.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 9
The resulting pressure and G-function plot is shown in Figure 8. Since the stress contrast in the case is
not significantly large (1 MPa ), the fracture closure sequence in the high stress and low stress regions is
not very different. No double humps are observed in the G-function plot (they are not visually obvious).
However, one can still observe that there is a small change in the pressure derivative between a G-time of 80
and 100, which is caused by the non-uniform fracture closure event in different stress layers. By applying
the variable compliance method, the estimated closure stress value is about 35.6 MPa, which is an averaged
value of the high stress value (36 MPa) and the low stress value (35 MPa ) input into the simulation.
Figure 8—G-function plot for the Base Case.
Results and Discussion
In this section, we apply our numerical DFIT model to study the effect of different layer properties on the


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DFIT signature and its interpretation. Based on the Base Case setup, we vary the layer properties including
layer stress contrast, layer permeability, layer thickness, layer rock stiffness and simulate DFIT fracture
propagation during injection and fracture closure during shut-in. Bottom hole pressure is obtained and
analyzed. We also study the effect of bedding planes on the DFIT signature. From the simulation results, it
is found that most of the layer properties have a very big impact on the DFIT signature and interpretation.
1. Effect of layer stress contrast
In this subsection, we show two sets of simulations to investigate the effect of layer stress contrast on DFIT
signature and interpretation. In the first set of simulations, we modify the base case, in which the low stress
is fixed at 35 MPa  and the stress contrast is varied. Figure 9 shows the DFIT fracture geometry at the end
of injection with a stress contrast of 1 MPa in Case (a) (Base Case), 3 MPa in Case (b), and 5 MPa in Case


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(c). The color scale depicts the fracture width distribution. It is observed that the magnitude of the stress
contrast significantly affects the DFIT fracture geometry and fracture width. In Case (a), the stress contrast
is the smallest and it does not have a very big influence on fracture containment. The fracture grows in both
length and height in Case (a). By comparison, Case (b) has an intermediate stress contrast which limits the
fracture height growth. Case (c) has the highest stress contrast, resulting in mainly length propagation of
the fracture in the low stress region. In the central low stress layer, Case (a) shows the largest fracture width
whereas Case (c) shows the smallest fracture width.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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10 SPE-199690-MS
Figure 9—Fracture geometry with color scale showing the fracture width distribution for
stress contrast comparison. The stress contrasts are 1MPa in (a), 3MPa in (b), and 5MPa
in (c), respectively. The middle layer where the fracture is initiated is a low stress layer.
After injection, the well is shut-in for 20 days leaving the fracture to close gradually. The G-function plots
of pressure and pressure derivative for each case are shown in Figure 10 . From the pressure plot, one can
observe different Instantaneous Shut-in Pressure (ISIP) for these three cases: the larger stress contrast case
gives a large ISIP and vice versa, which is reasonable since more energy is needed to open the rocks under
larger compressive stress. One can also observe that cases with larger stress contrast close faster than the
cases with low stress contrast. Double humps are observed in the pressure derivative plots in Case (b) and


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Case (c) because of the lag time between fracture closure in the different stress layers are distinguishable
while in Case (a) this time is not distinguishable and the two peaks merge into a single peak. Through DFIT
interpretation, the closure stresses correspond to the first and second humps in Case (b) are determined to be
35.9 MPa  and 34.6 MPa , and the closure stresses correspond to the first and second humps in Case (c) are
determined to be 36.7 MPa and 34.7 MPa using the tangent line method. In Case (b) and Case (c), the lower
closure stresses are almost same, but lower than the input low stress value (35 MPa). The higher closure
stresses are 35.9 MPa  and 36.7 MPa , which are also lower than their input values (38 MPa and 40 MPa). As
expected, the tangent line method underestimates the closure stress. When the variable compliance method
is used to estimate the layer closure stresses, better agreement with the input stresses is obtained: The closure


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stress in Case (b) and Case (c) are 37.4 MPa and 35.1 MPa, 38 MPa and 35.1 MPa, respectively. A very
good estimation to the lower stress is obtained and the estimation to the higher stress is improved. Table
2 summarizes these results.
Figure 10—G-function plots of stress contrast comparison. The
middle layer where the fracture is initiated is a low stress layer.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 11
Table 2—Estimated closure stress corresponding to cases shown in Figure 9
Tangent
line methodCompliance
methodVariable
compliance
method
Case (b)35.9 MPa
34.6 MPa38.4 MPa
35.5 MPa37.4 MPa
35.1 MPa
Case (c)36.7 MPa
34.7 MPa38.5 MPa
35.4 MPa38 MPa
35.1 MPa
In the second set of simulations, we inverse the stress in the first set of simulations, while all other things
remain the same. This means that the old high stress layers become the low stress layers and the old low
stress layers become the high stress layers. In this set of simulations, the fracture is initiated in the high
stress layer. The fracture geometries for different stress contrasts are shown in Figure 11 . Similarly, since
the stress contrast in Case (a) is only 1 MPa, it does not have a big restriction on the fracture geometry and
fracture height growth, but one can still observe the the low width value in the central high stress layer.


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From Case (b) and (c), one can see that the DFIT fracture breaks through into the upper and lower low stress
layers and grows preferentially in the two low stress layers. Case (c) shows a better fracture containment
and longer fracture length than Case (b) because of its higher layer stress contrast.
Figure 11—Fracture geometry with color scale showing the fracture width distribution for
stress contrast comparison. The stress contrasts are 1MPa in (a), 3MPa in (b), and 5MPa
in (c), respectively. The middle layer where the fracture is initiated is a high stress layer.
The G-function plots for the second set of simulations are shown in Figure 12 . It is observed that larger
stress contrast gives early fracture closure. However, in this case, the fracture in the high stress layer closes,
and consequently the wellbore will lose its hydraulic connection to the fracture. Compared to the previous
set of simulations, in the current simulation set, the time lag between the two closure events is larger. This


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is because of the bottleneck in the fracture geometry which makes it easier to isolate the fracture portions
in different stress layers. The closure stresses using tangent line method, the compliance method and the
variable compliance method are shown in Table 3. The tangent line method gives the best estimation of the
lower closure stress. The closure stresses estimated from the variable compliance method area is overall
closer to the input layer stresses. In these three cases in Figure 12 , the fracture closes first in the high stress
layers, including the middle high stress layer where the wellbore goes through. This limits the hydraulic
connectivity between the fracture in other layers and the wellbore and leads to a slow fracture closure, which
can be seen in Figure 12 where the stiffness keeps increasing slowly even at late G time. This "slowly rising


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tail" is comparable to the similar "slowly rising tail" as shown in Figure 1.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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12 SPE-199690-MS
Figure 12—G-function plots of stress contrast comparison. The
middle layer where the fracture is initiated is a high stress layer.
Table 3—Estimated closure stress corresponding to cases shown in Figure 11
Tangent
line methodCompliance
methodVariable
compliance
method
Case (b)36.2 MPa
35.3 MPa37.9 MPa
35.7 MPa37.3 MPa
35.5 MPa
Case (c)37.2 MPa
35.1 MPa38.4 MPa
36.5 MPa38 MPa
36.3 MPa
2. Effect of layer thickness
In this subsection, we vary the layer thickness from the the Base Case. The stress contrast is fixed at 3 MPa
(35 MPa  for low stress and 38 MPa for high stress). Different layer thickness has been tested: 5 m in Case
(a), 10 m in Case (b), and 15 m in Case (c) as shown in Figure 13 . The fracture is initiated in the low stress
layer and it can be summarized that smaller layer thickness gives larger fracture surface area, longer fracture
length, smaller fracture height and smaller fracture width. The ratio of the area of the fracture portion in the


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low stress layer to the total fracture area are 46.7%, 72.8%, and 87.7%, respectively.
Figure 13—Fracture geometry with color scale showing the fracture width distribution for layer
thickness comparison. The stress contrast is 3MPa. The layer thicknesses are (a) 5m, (b) 10m,
and (c) 15m, respectively. The middle layer where the fracture is initiated is a low stress layer.
The DFIT plots of the first set of simulations are shown in Figure 14. We observe that double humps
are more likely to occur if more of the fracture area is in the high stress layer. In Figure 12, Case (a) hasDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 13
the largest proportion of fracture area in high stress layer whereas Case (c) has the smallest proportion of
fracture area in the high stress layer. Case (b) lies between Case (a) and Case (c). As observed from Figure
13 and Figure 14 , the time when fracture starts to closure follows the sequence Case (a) < Case (b) < Case
(c), which is caused by the fact that under the same condition, the fracture width of Case (a) is the smallest
while the width of Case (c) is the largest. More fracture propagates into high stress layer in Case (a), making
the signal from the high stress closure more pronounced and comparable to the low stress layer fracture
closure signal. This results in two humps in the pressure derivative plot. Comparatively speaking, most of
the fracture stays in the low stress layer in Case (b) and Case (c). For this reason, the ISIP also follows Case
(a) > Case (b) > Case (c). The closure of the high stress layer fracture does not give a large enough fracture


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stiffness increase and there is not a large enough gap between the different fracture areas, which leads to
only one hump in the pressure derivative plot for Case (b) and Case (c).
Figure 14—G-function plots of layer thickness comparison. The
middle layer where the fracture is initiated is a low stress layer.
In the second simulation (Figure 15), the high stress layers and low stress layers are reversed, which
means the fracture is initiated in the high stress layer. It can be observed the DFIT fracture tends to break out
of the high stress layer and preferentially propagate in the low stress layer. The proportions of the fracture
in the low stress layer are 54.1%, 75.1%, and 75.9%, respectively.
Figure 15—Fracture geometry with color scale showing the fracture width distribution for layer
thickness comparison. The stress contrast is 3MPa. The layer thicknesses are (a) 5m, (b) 10m,


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and (c) 15m, respectively. The middle layer where the fracture is initiated is a high stress layer.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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14 SPE-199690-MS
All the three cases show two humps in the pressure derivative plots in Figure 16. In all the three cases,
the first hump corresponds to the closure of the fracture in the high stress layer whereas the second hump
corresponds to the closure of the fracture in the low stress layer. A larger proportion of fracture surface in
the high stress layer leads to a larger stiffness increase in the first closure event (fracture in high stress layer
closes). The magnitudes of the first hump are: Case (a) > Case (b) = Case (c), which agrees well with the
fracture surface area ratio under high stress layer in the three cases. The fracture starts to close earliest in
Case (c) and lastest in Case (a), as observed in Figure 15 . In these three cases in Figure 15 , the fracture
closes first in the high stress layers, including the middle high stress layer where the wellbore goes through.
This limits the hydraulic connectivity between the fracture in other layers and the wellbore and leads to a


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slow fracture closure, which can be seen from Figure 15 where the stiffness keeps increasing slowly even
at late G time.
Figure 16—G-function plots showing the effect of layer thickness.
The middle layer where the fracture is initiated is a high stress layer.
3. Effect of rock stiffness and hardness
In this subsection, we study the effects of rock asperity stiffness on DFIT interpretation. The stress is uniform
in all the layers. The rock asperity stiffness is varied by varying the initial normal stiffness parameter in
the Barton-Bandis contact correlation. Three cases have been run. In the small and large stiffness cases,
the initial normal stiffnesses are fixed at uniform values of 100 MPa/m and 500 MPa/m, respectively. In
the mixed stiffness case (Figure 17 ), the initial normal stiffness value varies between 100 MPa/m and 500
MPa /m in different layers. The DFIT G-function plot is shown in Figure 18 , from which one can see that the


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asperity stiffness has no impact on the fracture propagation but greatly affects the fracture closure period.
The DFIT fracture is found to close much faster in the small stiffness case than in the large stiffness case and
the mixed stiffness case lies in between the two uniform cases. From the Barton-Bandis correlation, one can
see that smaller initial normal stiffness will result in a smaller contact force. The contact force applied on
each other's rough surface by the soft rock is much smaller than the hard rock, which lead to a fast fracture
closure in the soft rock. This is also obvious from Figure 17: The fracture residual width is much larger in
the high asperity stiffness layers than that in the low asperitiy stiffness layers.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 15
Figure 17—Fracture geometry showing the effect of rock asperity stiffness. The
color scale shows (a) rock asperity initial normal stiffness and (b) fracture width.
Figure 18—G-function plots of asperity stiffness comparison.
The effect of rock stiffness (Young's modulus) is also studied. Two cases using Young's modulus values
of 20 GPa and 10 GPa are studied, but it not found to have a big impact on fracture propagation and fracture
closure if the Young's modulus is not significantly different. So, the effect of rock stiffness will not be
discussed in detail in the paper.
4. Effect of Bedding plane
In this subsection, we study the effects of bedding planes and their relationship (arrest/cross) to the
DFIT signature and interpretation. In this DFIT simulation with a bedding plane, we do not simulate the
propagation of the fracture but rather assume a fracture and bedding plane geometry and open the fracture


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and bedding plane using a uniform fracture pressure value and then perform the shut-in and fracture closure
simulation. Two simulations have been setup as shown in Figure 19 . In Case (a), the propagating DFIT
fracture is arrested by the bedding planes. In Case (b), the DFIT fracture interacts with the bedding planes
and finally crosses the two bedding planes. In both cases, the minimum horizontal stress is set to 35 MPa
whereas the vertical stress is set to be 36 MPa. The simulation results show large fracture width in the vertical
fracture section and small width in its connected bedding plane. On the fracture-bedding plane intersection
point, the fracture width is low because of the shear displacement of the bedding plane ( Tang and Wu, 2018).Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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16 SPE-199690-MS
Figure 19—Fracture geometry with bedding plane. The color scale shows the fracture width distribution.
(a) DFIT fracture is arrested by the bedding planes. (b) DFIT fracture crosses the bedding planes.
The G-function plots of the DFIT simulation with the bedding plane are shown in Figure 20. It can be
seen that the crossing DFIT fracture and the arrested DFIT fracture give very different DFIT signatures. In
both cases, the opened bedding planes close first followed by the DFIT fracture. In the case in which the
the fracture was arrested by the bedding plane, the corners of the bedding plane close first followed by the
inner side of the bedding plane and the DFIT fracture. Thus, there is an initial sharp increase in its pressure
derivative, which depicts the closure of the bedding plane. Then a sharp drop is observed which means the
complete closure of the bedding plane, which is further interrupted by a reincrease which infers the closing


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of the main DFIT fracture starts to happen. In the case in which the fracture crosses the bedding plane,
the intersection points of the bedding plane and fracture close first due to its small width, which cutoff the
hydraulic connectivity between the DFIT fracture and the bedding planes. This explains the slow increase
of the system stiffness in the first hump in the pressure derivative curve. The closure in the rest part of the
bedding planes has been successfully blocked by the conductivity cutoff. The system stiffness restarts to
increase in the second hump, when the DFIT fracture starts to close.
Figure 20—G-function plots in the presence of of bedding planes (fracture crossing or dilating the bedding plane).Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 17
5. Effect of layer permeability and pore pressure estimation
In this subsection, we study the effect of layer permeabilities on DFIT interpretation. As shown in Figure
21, in Case (a), the permeability is uniform 0.2 μD where as in Case (b) and Case (c), the background
permeability is fixed at 0.2 μD and the interlayer permeability is 0.5 μD and 0.8 μD, respectively. The stress
is uniform 35 MPa everywhere. By applying the variable compliance method, the closure stress obtained
from the G-function plots are the same as the input minimum horizontal stress value. The G-function plots
for the three cases are collected and plotted on the same figure shown in Figure 21(d) . It can be concluded
that the fracture closes earlier and faster in high permeability cases, but the closure stress estimation is not
affected by the rate of fracture closure.
Figure 21—G-function plots with permeability layer heterogeneity. (a) Layer perm=0.2μD,


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(b) Layer perm=0.5μD, (c) Layer perm=0.8μD, (d) Overall plot for the three cases.
We then analyze the initial pore pressure using the pressure response from Case (b) and Case (c) in Figure
21 to investigate the effect of permeability layers on pore pressure estimation. The plot of the pressure
derivative versus time in a log-log scale for the two cases are shown in Figure 22. Before-closure and after-
closure linear flow regimes are observed in both casese, which happen earlier in the high permeability
case because of the high leakoff rate. The pressure data in the post-closure linear flow period are picked
and plotted against one over square root of time in Figure 23. The straight lines are fitted using the linear
regression and intercept pressure values of 24.574 MPa and 24.631 MPa are obtained. The deviations from
the initial pore pressure (25 MPa) are 1.704% and 1.476%, respectively. The results indicate that formation


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layer permeability may not have a big impact on the pore pressure estimation, as long as the post-closure
linear flow regime is clearly observed. However, it is also shown that if the layer permeability is too low,
it will take a very long time for the fracture to close completely and the post-closure linear flow to occur.
Operators or service companies may not want to wait for such a long time to obtain the data for pore pressure
estimation. The novel Rapid Injection Flowback Test (RFIT) (Wang 2019) can be a fast way to obtain a
quicker estimation of both closure stress and pore pressure.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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18 SPE-199690-MS
Figure 22—Identifying the linear flow regime before and after fracture closure.
Figure 23—Initial pore pressure estimation.
Conclusions
This paper presents results that clearly show the impact of layer properties on the response of a DFIT. The
effect of key heterogeneity parameters on the DFIT plots including layer stress contrast, layer thickness,
layer rock stiffness and hardness, bedding plane, and layer permeability are demonstrated. The main
conclusions are:
1.The complex fracture closure behavior as indicated by the G-function plot is a combined result of the
DFIT fracture geomery and layer properties.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 19
2.The number of humps shown in the pressure derivative curve depends on the the relative difference in
magnitude between the closure stress in different layers. If only one peak is observed in the pressure
derivative, the estimated closure stress corresponds to an averaged stress value in layers that the
fracture penetrates. If multiple peaks are observed, then the estimated closure stress values correspond
to the minimum horitontal stress in different layers.
3.Early near wellbore fracture closure leads to a shadow effect and long-time fracture closure which is
indicated by a slow increase in the pressure derivative plot.
4.Rock stiffness plays an important role in fracture closure. Hard asperities on the fracture surface result
in gradual fracture closure whereas softer asperities result in fast fracture closure. Simply varying the
Young's modulus of the rock matrix does not play a significant role in controlling the pressure fall-


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off behavior. However, it should be noted that the stiffness of the fracture asperities is closely related
to the Young's modulus of the rock.
5.Higher layer peameability leads to earlier and faster fracture. Hoever, permeability heterogeneity does
not substantially affect the closure stress estimation.
6.Post-closure pore pressure estimation may not be affected by the layer permeability heterogeneity as
long as the post-closure linear flow period is observed. However, it may take a very long time for
the linear flow regime to be observed from the field if the rock matrix is very tight. Rapid Injection
and Flowback Tests (RIFT) can be a much faster method to estimate closure stress and pore pressure
simultaneously.
7.Pre-existing bedding planes interacting with a DFIT fracture significantly alters the final fracture
geometry and leakoff rate during shut-in and results in very different DFIT responses and
interpretation. Hydraulic connectivity in this complex geometry also significantly affects the pressure


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response.
Acknowledgements
We would like to thank the Hydraulic Fracturing and Sand Control Industrial Affiliates Project at the
University of Texas at Austin for the financially supporting this research.
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Zheng, S. , Manchanda, R.  and Sharma, M.M. , 2019b. Efficient incorporation of a contact model into a fully
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Zheng, S. , Kumar, A. , Gala, D.P. , Shrivastava, K. and Sharma, M.M., 2019f. Simulating Production from Complex
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Zheng, S., Manchanda, R., Wang, H. and Sharma, M.M., 2019g . Fully 3D Simulation of Diagnostic Fracture Injection Tests
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Denver, Colorado. https://doi.org/10.15530/urtec-2019-314Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-199690-MS 21
Appendix
The traditional DFIT analysis approach employs the G-function model and uses the tangent line method to
estimate closure stress (Nolte, 1979 ; Barree and Mukherjee, 1996). A G-function is calculated to represent
the shut-in time. The G-function is defined by Eq. (1), (2) and (3).
(1)
(2)
(3)
where α is assumed to be 1.0, ∆ tD = ∆t/te, ∆t is the time since shut-in and te is the shut-in time.
The pressure ( P) versus G and the pressure derivative GdP/dG versus G are plotted on the same chart.
In the tangent line method, the closure point is picked by drawing a tangent line from the origin to the
pressure derivative curve. The pressure corresponding to the G-time of the tangent point is identified as the
closure pressure. McClure et al. (2016) proposed the "compliance method" in which they suggest picking
fracture closure at the initial deflection point from the linear portion on the pressure derivative curve. Wang


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and Sharma (2017) proposed the "variable compliance method" which further refines the analytical DFIT
method by averaging the G-time (or the square root of time) of the closure point given by the tangent line
method and the compliance method and uses the extrapolated value at the averaged G-time (the square
root of time) to identify the fracture closure stress. They clearly showed that the tangent line method
underestimates the closure stress, the compliance method overestimates the closure stress while the variable
compliance method consistently provides the lowest error in this estimate. An example G-function plot is
shown in Figure 24 to illustrate these three methods.
Figure 24—Illustration of three analytical methods in identifying closure stress from a G-function plot.
Wang and Sharma (2019a)  also demonstrated that both the G-function model and square root of time
model are just special cases of their general time-convolution solutions. After closure analysis focuses on the


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post-closure linear and pseudo-radial flow to estimate the reservoir initial pore pressure, matrix permeability,
leakoff coefficient and fracture compliance (Wang and Sharma, 2019a). For example, a log-log plot of the
pressure derivatives versus shut-in time clearly distinguishes the different flow regimes in the reservoir,
before and after fracture closure. The intercept of pressure versus the inverse of the square-root of shut-Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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22 SPE-199690-MS
in time straight line in the post-closure linear flow regime gives the initial pore pressure in the reservoir
(Figure 25 ).
Figure 25—Initial pore pressure estimation using post-closure linear flow data.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS
DFIT Analysis in Low Leakoff Formations: A Duvernay Case Study
Behnam Zanganeh, Mason K. MacKay, and Christopher R. Clarkson, University of Calgary; Jack R. Jones, NSI
Fracturing LLC
Copyright 2018, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Canada Unconventional Resources Conference held in Calgary, Alberta, Canada, 13-14 March 2018.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written


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consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
Diagnostic Fracture Injection Test (DFIT) responses in some shale reservoirs, such as the Duvernay shale
in western Canada, are not consistent with those interpreted through traditional analysis methods. Indeed,
interpretation with traditional techniques may result in significantly incorrect estimates of closure pressure,
pore pressure and formation permeability. The goal of this paper is to explain the observed DFIT behaviours
for selected Duvernay shale wells in terms of low leakoff of fracturing fluid to the formation, activation of
pre-existing fractures, and tip extension during the test.
DFIT data in the Duvernay shale are analyzed using pressure transient analysis methods. Two scenarios


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are presented to explain the overall falloff behavior; moving-hinge closure with tip extension, and activation
of secondary natural fractures. The validity of each scenario is examined using rigorous coupled flow-
geomechanical simulation, geological information and geomechanical settings in the Duvernay Formation.
Due to extremely low leakoff, the main mechanism affecting pressure falloff during the DFIT is pressure
dissipation through the primary fracture created during injection. This results in significant tip extension or
activation of secondary fractures. The fluctuations and spikes observed on G-function or pressure derivative
plots are explained in the context of these scenarios. The leakoff rate varies with the pressure change, and
the enhanced fracture surface area, during tip extension. Therefore, the assumption of Carter leakoff, and
the traditional closure picks based on a straight-line tangent to the semi-log derivative on a G-function plot


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or 3/2 slope on Bourdet-derivative plot are not valid. Due to very low matrix permeability and the additional
fracture length created through tip extension, it is unlikely that formation radial flow is established during
the test, compromising the ability to obtain a valid pore pressure or formation permeability.
Introduction
A Diagnostic Fracture Injection Test (DFIT), also known as a minifrac or fracture calibration test, has
become the standard pre-stimulation method for determining fracturing treatment properties, effective
reservoir permeability and initial reservoir pressure in unconventional reservoirs. A DFIT is an injection-
falloff test conducted before the main hydraulic fracturing treatment. The DFIT procedure involves
breakdown of the rock and creation of a short fracture during the injection of high pressure fluid (usuallyDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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2 SPE-189826-MS
water), and recording of the pressure response for long enough that the created fracture closes, and the
transient associated with this closure event is dissipated before the onset of reservoir flow regimes.
In the following, a brief overview of the Duvernay Formation geological and geomechanical
characteristics is provided, with a focus on those characteristics favoring episodic fracture growth. A
hydraulic fracturing treatment example with microseismic observations is presented to illustrate this
concept. A Theory and Methods section is then provided, including a brief review of DFIT interpretation
methods. The appropriateness of interpreting Duvernay DFITs with the conventional interpretation methods
is then examined. Two simulation models are built to generate synthetic DFIT responses. Finally, in the
Results and Discussion section, field data are interpreted in the context of simulation results.
Geological Overview
Duvernay Formation


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Geological Overview
Duvernay Formation
The Duvernay Formation is a Devonian aged shale exploited for hydrocarbons within the Western Canadian
Sedimentary Basin (WCSB). Depositional conditions within shales results in marked vertical heterogeneity,
which leads to mechanical complexity (Harris et al. 2011). Within the Duvernay Formation, at least ten
microfacies are identified, each with their own natural fracture fabrics and elastic properties (Knapp et al.
2017 ). This vertical mechanical heterogeneity favors the creation of bed-contained, sub-vertical fracture
systems (Cooke and Underwood 2010). Natural fractures within the Duvernay are observed and inferred
over a variety of scales from microfractures (Ghanizadeh et al. 2015) to larger fractures (Fox 2015) and
even fault systems ( Chopra et al. 2017 ).
The in-situ stress conditions are interpreted in terms of the orientation and magnitude of the effective


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stress. Through basin scale modelling work, the stress regime is thought to be in a strike slip regime in
much of the basin with thrust fault regimes encountered proximal to the Rocky Mountain deformation zone
(Reiter and Heidbach 2014). The regional stress in much of the sedimentary basin trends with an azimuth
of 047 as indicated through borehole breakout directions and other geologic indicators ( Reiter et al. 2014).
The Duvernay Formation has a characteristically high organic content with TOC values ranging from 0.1
up to 11 percent ( Rivard et al. 2014 ) which suggests significant potential for hydrocarbon generation. In fact,
it is the source rock for most of the hydrocarbons trapped within the upper Devonian section of the WCSB
(Creaney and Allan 1990). Hydrocarbon generation can raise fluid pressures and may be the underlying
cause of significant overpressure conditions observed within the Duvernay (Fox and Soltanzadeh 2015,


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Davis and Karlen 2014 ). The highly overpressured conditions create a geomechanical sensitivity that brings
discontinuities to a state of incipient failure. This phenomenon is directly observed through reported cases
of induced seismicity arising from treatment operations within the Duvernay Formation (Bao and Eaton
2016 ; Schultz et al. 2017 ).
The Duvernay Formation is primarily composed of mudstones and thus is associated with low matrix
permeability in the range of 3.7 × 10−7 to 1.2 mD ( Ghanizadeh et al. 2015). This low permeability
suggests that significant leak-off into the matrix is unlikely over the timescale of a DFIT. Instead, fracture
fluid volume may be accommodated through crack tip extension of the hydraulic fractures as well as
accommodation through secondary natural fractures. This process of rupture of the rock and subsequent
flow of fluid into the fracture is theorised to occur in temporally intermittent periods. Evidence of sporadic


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spatial-temporal evolution of fluid flow is supported through various case studies of microseismicity in
shales. For example, Goertz-Allman et al. (2017)  provide a case study where microseismicity occurs due to
punctual activation of faults which controlled fluid movement in the subsurface.
Evidence for Episodic Fracture Growth in the Duvernay
Evidence of temporally-intermittent fracture behaviour is gleaned from microseismic observations during
the main hydraulic treatment of a nearby well within the Duvernay Formation. The microseismic temporalDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 3
evolution shows that the hydraulic fracture does not grow in a simple, steady and continuous way, but rather
the fracture expands to new areas of the reservoir over time. This occurs episodically through growth phases
followed by relative calm. In Fig. 1b, four major microseismic clusters are identified during a hydraulic
fracturing treatment stage, each following a growth front envelope. While there is a trend to follow these
pressure diffusion fronts (Shapiro and Dinske 2009), microseismicity may jump ahead of the theoretical
curve or fall behind, indicating that fracture growth is not continuous and steady. Furthermore, multiple
microseismic clusters form within a single treatment stage, suggesting that rock deformation processes
follow an episodic behavior as well. Fig. 1b also illustrates how the hydraulic fracture accesses different
parts of the reservoir throughout the treatment. The first hydraulic growth cluster produces a large half


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length towards the northwest. Subsequently, active deformation occurs closer to the wellbore before finally
moving towards the southeast. Even though continual pumping occurred, the fracture did not continually
grow in length, but rather accessed different areas of the reservoir at different times.
Figure 1—Microseismic clusters showing episodic fracture propagation. (a) Treatment parameters showing
consistent injection (top), yet nonconsistent growth phases (bottom); (b) microseismic events plotted
in plan view and colored by time illustrating episodic spatial temporal growth throughout the reservoir.
This intermittent behavior may be a response to the mechanical layering found within the Duvernay
Formation. Brenner and Gudmundsson (2004) described how hydrofractures become arrested at mechanical
contrasts between layers especially when propagating from a stiff layer into a soft layer. This arresting
behavior would mean that as a fracture grows, it may encounter a difficult layer to propagate into; thus, a


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new area of the reservoir will be accessed instead. Additionally, the aperture of the hydraulic fracture varies
depending on the Young's modulus of the surrounding rock matrix and the fluid pressure within the fracture.
Therefore, the hydraulic fracture likely has a non-uniform aperture distribution resulting from the complex
mechanical heterogeneity. The heterogeneous mechanical contrast suggests that a hydraulic fracture will
undergo a period of dilation and extension as it extends in length. This transition between dilation and
rupture likely contributes to episodic fracture growth. Furthermore, soft elastic rock will be able to store
elastic potential from dilation of the fracture during injection. This mechanical potential energy can be a
driving mechanism for growth after the injection has ceased if the pressure was not able to leak off due to low
matrix permeability. This effect has been observed through the generation of Krauklis waves, where fracture


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wall deformation coupled to fluid flow creates resonances within the hydraulically connected fluid network
(Krauklis 1962 ). In this case, the dilation and subsequent collapse of fracture aperture is coupled to fluid
movement within the fracture (Liang 2017 ). The time scale that this process occurs on is partially dependent
on the elasticity of the surrounding rock mass, where low shear modulus values of the rock mass producesDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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4 SPE-189826-MS
larger time period fluid movement events (Tary et al. 2014). This is because the rock can accommodate
more elastic deformation and thus larger apertures may be reached before the fracture constricts.
Abundant vertical natural fractures are observed in image logs taken from a horizontal leg within the
Duvernay Formation (Fig. 2a ). These natural fractures occur in specific orientations called sets. The first set
is an extension fracture and follows the orientation of maximum horizontal stress. The second set is a shear
fracture and occurs at an angle to the main set. The third set is a cross joint perpendicular to the maximum
horizontal stress. To calculate the resolved normal and shear stress on the natural fractures, an understanding
of the in-situ effective stress field is required. In this case, we use a vertical stress based on 24 KPa/m and
a pressure gradient of 20 KPa/m located at 3 km depth. We choose the minimum horizontal stress to be 0.8


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times the vertical while the maximum horizontal stress is 1.5 times the vertical stress. Using tensor rotations,
the normal and shear stresses are resolved for each fracture set and shown on a Mohr's circle (Fig. 2b).
Figure 2—(a) Stereonet representation of natural fracture orientations observed from image logs in the horizontal leg
within the Duvernay Formation. Fracture planes are shown as great circles while the poles to the fractures are plotted
as points. (b) Mohr's circle representation of normal and shear stresses resolved onto fractures under the estimated
in-situ stress conditions. A Mohr-Coulomb envelope with no cohesion and 20 degree friction angle is plotted to show
how close to failure the fracture system is. (c) Natural fracture system within the Duvernay Formation as exposed in
outcrop. Fluid alteration (steel blue) follows the fracture network with some leakoff occurring into the rock matrix.


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As fluid pressure is increased during injection, the normal effective stress in the fracture system decreases
within the fluid front. The extension fracture will accept fluid most easily as it has the least resolved normal
stress; however, when the linking cross joint or shear joint are encountered, they will transmit fluid from one
fracture to another. Before they can transmit the fluid, there must be a buildup of fluid pressure because they
require a higher normal stress to open. Once the fluid builds up to sufficient level to overcome the normal
stress, fluid may be transmitted to another extension fracture which in turn will release the pressure to a
lower state. Thus, flow through the fracture system itself leads to episodic buildup and release of pressure
as different fracture systems are accessed. Fig. 2c  illustrates this effect in a Duvernay Formation equivalent
outcrop exposure at Roche Miette in Jasper National Park, Alberta. The natural fracture system is comprised


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of multiple connecting fracture sets in which fluid flow pathways are established. The low permeability ofDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 5
the matrix concentrates fluid into the fracture system as observed from the mineralogical alteration front
following the natural fracture system.
From the above summary, it is concluded that the Duvernay possesses several properties that may
complicate DFIT analysis: low matrix permeability, limiting leakoff from fractures; an extensive natural
fracture system; and fine-scale mechanical layering, the latter two properties increasing the propensity
for intermittent fracture growth that could affect the DFIT signature. Direct observations of this behavior
are illustrated through episodic spatial-temporal clustering behavior of microseismicity during a hydraulic
fracture treatment.
Theory and Methods
DFIT Interpretation Methods
DFIT analysis was pioneered by Nolte (1979), who introduced the Gfunction, based on material balance
and the Carter leakoff model (Howard and Fast 1957) for before closure analysis. Gu et al. (1993) and Nolte


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et al. (1997) demonstrated the possibility of observing afterclosure reservoir linear and pseudo-radial flow
and their application in estimation of fracture geometry and reservoir properties.
Barree and Mukherjee (1996)  and Barree (1998) recommended using the G-function and its diagnostic
derivatives 
  to identify fracture closure. Barree (1998) and Barree et al. (2009) also presented
signatures for non-ideal leakoff behaviors such as tip extension, pressure-dependent leakoff (PDL) and
height recession/transverse storage based on G-function, square-root of shut-in time, and log-log plot of
pressure change with shut-in time plots. Fig. 3 summarizes normal leakoff and nonideal leakoff signatures
on G-function combination plots based on the Barree at al. (2009) interpretation methodology.
Figure 3—(a) Normal leakoff; (b) PDL; (c) tip extension; (d) storage/height


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recession signatures on G-function combination plots ( Barree et al. 2009 ).Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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6 SPE-189826-MS
Mohamed et al. (2011) and Marongiu-Porcu et al. (2011) presented a model to predict the falloff pressure
trend of an idealized DFIT (normal leakoff) using standard pressure transient (PTA) log-log diagnostic plots.
A log-log diagnostic plot of the basic falloff response shape predicted by their model is shown in Fig. 4 .
They identified normal leakoff as a 3/2 slope on the Bourdet-derivative (with respect to superposition time),
and picked fracture closure as the deviation from the 3/2 slope.
Figure 4—Log-log diagnostic plot for an idealized fracture-injection/falloff test (Marongiu-Porcu et al. 2011).
Bachman et al. (2012) presented a combination of conventional diagnostic PTA plots to identify various
flow regimes before and after fracture closure, summarized in Table 1. They demonstrated that a 3/2 on
Bourdet-derivative corresponds to a straight line trend on G-function derivatives, representing Carter leakoff
(Nolte flow).


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(Nolte flow).
Table 1—Identification of flow regimes using derivative slope on log-log plot
of pressure difference versus equivalent time functions (Bachman et al. 2012)
Log-Log Flow Regime!
Carter Linear Bilinear
Equivalent Time
Derivative
FunctionEarly
Time
Slope
-------
Ends
tD=0.08Late
Time
Slope
-------
Starts
tD=5.0Early
Time
Slope
-------
Ends
tD=0.04Late
Time
Slope
-------
Starts
tD=4.0Early
Time
Slope
-------
Ends
tD=0.13Late
Time
Slope
-------
Starts
/n=8.0
terdΔP/dter
(Radial)1/1 3/2 1/2 1/2 1/4 1/4
ΔtdΔP/dtec
(Carter)1/1 1/1 1/2 0 1/4 -1/4
Δt0.5dΔP/dtel
(Linear)1/1 3/2 1/2 1/2 1/4 1/4
Δt0.25dΔP/dteb
(Bilinear)1/1 3/2 1/2 1/2 1/4 1/4Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 7
Recently, Zanganeh et al. (2018)  explained the spectrum of flow patterns and signatures observed before
and after closure during DFITs. Their interpretation was based on rigorous numerical simulation which
included the dynamic nature of fracture geometry (i.e. fracture expansion, tip extension, hinge closure,
progressive closure), variable leakoff rate (as a function of fracture surface area, fracture pressure, and
falloff time) and relative magnitude of afterflow with respect to total leakoff rate. They showed that with
DFITs, unlike conventional buildup/falloff tests, afterflow caused by wellbore storage can last for a much
longer period of time, affecting pressure transient in various time periods during the pressure falloff.
Problems with Application of Conventional DFIT Analysis Methods to the Duvernay
Some DFIT responses in shale reservoirs, such as the Duvernay shale, are not consistent with those


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interpreted through traditional analysis methods. Fig. 5  provides pressure profiles during injection for two
DFITs conducted in the Duvernay Formation. There is no clear breakdown, or a sharp pressure drop after
the breakdown, as expected in more conventional reservoirs. In fact, in some cases there is an increasing
pressure trend after the breakdown even though the injection rate is constant or decreasing (see Field
Example 2, Fig. 5b ). Another common signature observed in Duvernay DFITs is a large pressure drop at the
time of shut-in, e.g. 20 MPa and 25 MPa for Field Example 1 and 2, respectively. This significant pressure
drop is likely caused by another mechanism other than friction in the wellbore or tortuosity.
Figure 5—Pressure profile during injection for (a) Field Example 1; (b) Field Example 2.
PTA and G-function diagnostic plots for Field Example 1 are provided in Fig. 6 . The trend of 
curve is not similar to any of the signatures proposed by Barree et al. (2009). Except for the early time


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unit slope, no other straight line trend with a specific slope is observed on any of the derivative plots.
According to Zanganeh et al. (2018), the long transition after unit slope, with no sharp characteristic hump,
indicates that leakoff from fracture to surrounding formation is not dominant. This is probably due to very
low matrix permeability of the formation coupled with small fracture surface area of the created fracture.
Several fluctuations are observed on all of the derivative plots, each lasting for a considerable period of
time. In this case, there is no signature of fracture closure based on any of the identification methods.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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8 SPE-189826-MS
Figure 6—G-function and PTA diagnostic plots for Field Example 1.
Based on the geological information, geomechanical settings and evidence for episodic hydraulic fracture
growth in the Duvernay Formation provided in the previous section, combined with the anomalous DFIT
observations just illustrated, two hypotheses are presented to explain the DFIT behavior in the Duvernay
formation; moving-hinge closure with tip extension, and propagation through activation of secondary
fractures. As will be discussed below, model-generated synthetic results are compared with field data, and
necessary modifications are made to calibrate the model. The observations from the calibrated model are
then used to explain field behaviors.
Model Description and Setup
A customized fully-coupled stress-pore pressure simulator (Abaqus Analysis User's Guide 2016) is used
herein to generate synthetic DFIT responses. The customized model is capable of simulating all the physical


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processes involved in a typical DFIT including: porous media deformation; fluid flow inside the reservoir;
hydraulic fracture initiation, propagation and closure (based on the cohesive zone method); compliance
change before and after closure; residual fracture aperture and conductivity; and fluid flow inside the fracture
and fluid interaction between the fracture and reservoir (leakoff).
The modeling procedure is described in detail in Zanganeh et al. (2017) and Zanganeh et al. (2018).
The cohesive zone method (CZM) is used to model hydraulic fracture initiation, propagation and closure.
With the CZM, the fracture is modeled as a gradual separation between two material (rock) surfaces. This
separation is modeled as a progressive degradation of cohesive strength along the cohesive layer, which
is a pre-defined surface embedded in the rock and follows a traction-separation law. Model 1 assumes
propagation of a single planar primary fracture (HF; Fig. 7a). However, in Model 2, there is a pre-existing


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network of natural fractures (NF; Fig. 7b ), similar to the system observed in the Duvernay outcrop (Fig.
2c). The cohesive elements are embedded in the formation rock - they are assumed to be non-existent in the
model until fracture initiation and propagation criteria are reached, at which time these elements act as the
potential pathway for fracture growth. In both simulation models, a matrix permeability of 25 nd was used.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 9
Figure 7—Simplified schematics of (a) Model 1; (b) Model 2.
In the previous simulation models of Zanganeh et al. (2017 and 2018 ), tangential fluid flow inside the
fracture is calculated using Poiseuille's law:
(1)
where w is the fracture opening, μ is the fluid viscosity and Pf is the fluid pressure along the fracture length
(x direction). For an injection fluid with low viscosity (i.e. water), even a small fracture aperture of 0.1
mm, results in a fracture with large tangential permeability (conductivity) without any significant pressure
gradient inside the fracture. To achieve synthetic pressure responses similar to the presented field examples
in the Duvernay Formation, especially during pumping and early shut-in time, the β coefficient is introduced
into Poiseuille's formula ( Eq. 1 ). After several sensitivity simulation runs, a β value of 1000 was selected
as the optimum value.
Results and Discussion
Model 1: Tip Extension


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Results and Discussion
Model 1: Tip Extension
Fig. 8a  provides the simulated pressure profile, G-function semi-log derivative and PTA plots during
pressure falloff for Model 1. The overall trends of the curves are similar to the Field Example 1 ( Fig. 6).
At the time of breakdown, the created fracture has finite conductivity with a considerable pressure gradient
inside the fracture. This results in the sudden pressure drop at the time of shut-in.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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10 SPE-189826-MS
Figure 8—(a) PTA diagnostic plots; (b) pressure profile and G dP/
dG curves. Tip extension phases are shown with the dotted squares.
As shown by Zanganeh et al. (2018), moving hinge closure occurs during the transition from afterflow
dominance (caused by wellbore storage) to leakoff dominance. Due to low matrix permeability and the
pressure gradient inside the fracture in the Model 1, coupled with the presence of afterflow, the pressure
front moves to the tip of fracture and causes tip extension of the primary fracture. Pressurization and
depressurization during tip extension can be repeated several times (Fig. 9) during the transition period
before leakoff dominates the falloff process. Tip extension phases are shown as fluctuations on pressure
derivative plots. It must be noted that in the simulation models, the magnitude and duration of these
fluctuations are controlled by the size of fracture elements which is uniform throughout the length of


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fracture. However, in reality, the magnitude and duration of each tip extension phase can be different.
Figure 9—Plan view of a single wing of the fracture showing pressure gradient inside the
fracture and tip extension phases during falloff. The fracture aperture is magnified 1000 times.
In Model 1, leakoff dominance starts after 4.5 log-cycles and fracture closure does not occur.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 11
Model 2: Pre-existing Fractures and Tip Extension
As mentioned in the model description and setup section, Model 2 uses a pre-existing network of natural
fractures (NF), similar to the system observed in the Duvernay outcrop. Pre-existing natural fractures can
be activated during injection and falloff and affect propagation direction and pressure response. Fig. 10a
illustrates the pressure profile during injection and early shut-in period. There is no significant pressure
drop at the time of breakdown due to the low conductivity of the primary fracture. As the primary fracture
hits the pre-existing fracture, propagation temporarily stops (upward trend on pressure profile) until the pre-
existing fracture is activated. Then, the propagation continues in the original direction perpendicular to the
minimum horizontal stress ( Fig. 10b ).
Figure 10—(a) Pressure profile during injection and early shut-in time for Model 2; (b) Propagation as the


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primary fracture hits and activates a preexisting fracture (fracture apertures are magnified 1000 times).
The falloff behavior is similar to Model 1. Given the low matrix permeability and leakoff, reactivation
of secondary fractures can happen during the falloff period, too. The response on pressure derivative plots
will be similar to tip extension phases as illustrated in Model 1.
Field Example 1
The observed trends of Field Example 1 in Fig. 6  can be explained based on the simulation Model 1. The
absence of a clear breakdown and the significant pressure drop at the time of shut-in ( Fig. 5a) is caused by
low conductivity and the large pressure gradient inside the created fracture.
The PTA plots for this dataset are revisited in Fig. 11. The long transition after the early time unit slope,
with no sharp characteristic hump, indicates that leakoff from the fracture to surrounding formation is
not dominant. This is due to low matrix permeability of the formation coupled with low conductivity and


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pressure gradient inside the fracture. Three major extension cycles are observed during the falloff period
demonstrated by the fluctuations and inflection points. The pressure changes at the end of fall period are
very small as the leakoff is low and no additional extension occurs. As a result, the end of falloff period
is highly affected by ambient temperature changes. No signature of fracture closure is observed after 200
hours. Therefore, no reliable estimate of closure pressure and formation permeability can be made in this
example.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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12 SPE-189826-MS
Figure 11—PTA plots for Field Example 1 showing the interpretation based on tip extension cycles.
Field Example 2
In this DFIT, a total volume of 6.8 m3 of fresh water was injected during 3 minutes of pumping. The pressure
values were recorded using surface gauges. The increasing trend after breakdown while the injection rate
is kept constant ( Fig. 5b ) indicates the activation of secondary fractures in addition to the primary fracture
during the injection. Again, there is a long transition of about 2 log-cycles after the early unit slope. There are
two major opening cycles during this transition, caused by activation of secondary fractures or extension of
primary fracture during falloff, which creates additional fracture surface area for fluid leakoff from fracture
system to the formation. As a result, leakoff dominance starts after about 2.2 hours. The slope of 
  and
 plots during leakoff dominance is smaller than 3/2 and 1/2, respectively; and there is no evidence of


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Carter leakoff. The closure is picked at the inflection point on 
  curve that corresponds to change of
slope on PPD and 
  curves, with closure pressure of 32.1 MPa and closure time of 51.4 hours. Formation
linear or radial flow are not observed after 300 hours of shut-in time, and no reliable estimate of formation
permeability or initial pressure can be made.
Figure 12—PTA plots for Field Example 2.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/18URC/1-18URC/D011S002R001/1236476/spe-189826-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE-189826-MS 13
Conclusions
DFIT responses in the Duvernay Formation for the cases studied are controlled by the following
mechanisms:
•Episodic fracture growth during injection and falloff. The hydraulic fracture does not grow in a
simple, steady and continuous way. Growth occurs episodically through growth phases followed
by relative calm.
•Low permeability of the matrix. This property delays the transition to leakoff dominance in the
falloff period, and results in long fracture closure times. Also, low leakoff favors the episodic
fracture growth (moving hinge-closure and tip extension) as it provides a mechanism to release
pressure and create additional fracture surface area.
•Long lasting afterflow (caused by wellbore storage) and transition period due to limited leakoff.
•Low conductivity fractures. The fractures, both primary and pre-existing, have a low conductivity
resulting in pressure gradient within the fractures. This explains the unclear breakdown point and


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pressure responses after the breakdown.
The above mechanisms result in complex leakoff and pressure behavior. Therefore, the assumption of
Carter leakoff, and the traditional fracture closure picks based on a straight-line tangent to the semi-log
derivative on a G-function semi-log derivative plot or 3/2 slope on Bourdet-derivative plot are not reliable.
Finally, it is very unlikely for the formation radial flow to occur during short falloff periods of days or weeks.
Nomenclature
Field Variables
GG-function time, dimensionless
mSlope of straight line, dimensionless
PPressure, Pa
PfFracture pressure (fluid pressure in the cohesive element), Pa
qfracGap flow rate within the cohesive element, m3/sec
ShmaxMaximum horizontal stress, Pa
ShminMinimum horizontal stress, Pa
taAgarwal's time, dimensionless
tpPumping time, sec
wFracture opening (aperture), m
Greek Variables
βCoefficient in the Poiseuille's formula, dimensionless
ΔtShut-in time, sec
μFracturing fluid viscosity, cp
References


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ΔtShut-in time, sec
μFracturing fluid viscosity, cp
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SPE 167074  
Application of Open-hole Diagnostic Fracture Injection Test Results to 
Regional Stress Interpretation in Bowen Basin Coals  
Scott, M, Mazumder, S, Gibson, M, Probst, P, Arrow Energy  
Copyright 2013, Society of Petroleum Engineers  
 
This paper was prepared for presentation at the SPE  Unconventional Resources Conference and Exhibition -Asia Pacific held in Brisbane, Australia, 11– 13 November 2013.  
 
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract  submitted by t he author(s). Contents of the paper have not been 
reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessar ily reflect any position of the Society of Petroleum Engineers, its


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officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Socie ty of Petroleum Engineers is prohibited. Permission to 
reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.  
 
 
Abstract  
Diagnostic fracture injection testing (DFIT) has become an established method of well testing in low permeability 
unconventional reservoirs –  particularly in shales and coal seam gas  (CSG) . As well as providing in -situ measurements of 
permeability and reservoir pressure, the test allows estimation of the closure pressure (and fluid loss characteristics) for the 
formation under investigation , which is assumed to be a measure of minimum horizontal stress ( σh).  
 
Arrow Energy is currently conducting a wide -scale exploration and well testing programme in the Bowen Basin region of


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Queensland, Australia, in support of its plan ned CSG to liquefied natural gas (LNG)  project. This programme is mainly 
focussed on evaluation of formations within the Moranbah and Rangal Coal Measures; these are typically present as thick, low 
permeability zones.   
Traditional Drill Stem Test (DST) and Injection Fall- Off Test (IFOT) results have proven unreliable within such low 
permeability and under -pressured reservoirs. The limited drawdown generated by DSTs in such formations has historically 
been an issue for th ese, and other, reservoirs. Similarly, difficulties have been encountered with regard to the appropriate 
management of IFOT injection rates in the Bowen Basin coals, which can fracture at very low rates; the resultant diagnostic 
typecurves needed for analysis of such a “failed” test have tended to introduce an u nnecessary level of uncertainty in the 
results.


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results.  
 At present, the preferred exploitation method for these formations is extended -reach, open -hole, horizontal in -seam wells. As 
such, very few instances of cased -hole completions are available. Whilst the DFI T technique has previously been widely 
applied in cased -hole completions, largely due to its prevalence as part of hydraulic fracture stimulation treatment in North 
America, its application has been extended successfully to open -hole testing as part o f this programme. Arrow has to date 
completed over 140 open -hole DFITs in this region, with an approximately 80% success rate in interpreted parameters with 
reasonable confidence.  
 
The results of this programme have been incorporated into a basin -wide interpre tation of regional stresses and subsurface 
properties. These results have been used , in combination with Mechanical Earth Models (MEM) , to evaluate optimal  lateral


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well orientation , hydraulic fracture treatment design , as well as the mapping of variable st ress gradients in an effort to better 
understand the distribution of permeability trends across different geo -domains . 
  
Introduction  
Arrow Energy’s Bowen Basin operations are located in an area characterised by thick, continuous coal seams, with low 
formation permeability. Typical values of permeability are in the order of 0.1 -10mD. Production experience within the basin 
has already pro vided sufficient information to frame the development concept around exploitation of the low -deliverability 
reservoir; identified well types include concepts such as horizontal in -seam or hydraulically stimulated wells . 
 
The focus of any large -scale, value -driven data acquisition programme is to better understand:  
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2  SPE 167074  
• Regional Permeability Trends:  Well concepts and development options may be identified based on regional trends 
in permeability; areas of high er, or lo wer, than expected permeabilities may also pla y a role in development decision -
making processes.  
• Implications for Well Construction:  A number of subsurface elements , over and above permeability , are critical 
components in refining well layout and detailed construction designs.  For example, cleat orien tation is also a material 
consideration in planning the azimuth of horizontal well with respect to this system: a higher productivity is 
theoretically achieved by intersecting as many face cleats as possible.  
 
Both the estimation of probability of success for drilling execution and production forecasting in a given region require an 
integrated and comprehensive assessment  of the subsurface environment; such a n analysis should be focused on identify ing


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which variables will prove the li miting factor in any development scenario.  
 In the Bowen Basin, for example, the traditional response to encountering thick, low -permeability coal seams has been to 
propose a horizontal well development. In highly faulted areas, or regions where geological  control suggests frequent splitting 
and merging of individual seams, this concept becomes less viable; this is especially true when attempting to minimise surfac e 
footprint through the use of extended- reach drilling techniques, as geology may prove a greater constraint than the technical 
limitations of the available rig -fleet.  
 
Bowen Basin  
Thick, continuous formations with a high net -to-gross ratio are present across the majority of the Bowen Basin. In gener al, 
there is a trend for permeability to decrease with depth  within these formations . This is compounded by increased complexity


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and low net -to-gross figures in certain regions and sequences, which are likely to impede in -seam drilling via geo -steering. 
These  features have a material impact on well type selection and spacing.  
 
A suitable data acquisition programme comprising petrophysical (i.e. dipole sonic and geochemical) logs and core analyses, coupled with mechanical earth models (MEM), is necessary to identify the optimum well design  per region , as a function of 
local stress fields and property contrasts.  
 
Geology  
The Late Permian Blackwater Group is the primary target formation for coal seam gas development in the northern Bowen 
Basin. This group was deposited within extensive fluvial and lacustrine environments that prograded into the basin initially 
from the we st (German Creek Coal Measures , GCCM ); later, the Moranbah, Rangal and Fort Cooper Coal Measures ( MCM, 
RCM, and FCCM) were deposited from the west, north and east  (Fielding et al.,  1995) . The latter three coal measures form the


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basis of Arrow Energy’s development focus within its current acreage in the Bowen Basin . 
 
Coal  Permeability  
Coal is a poro- elastic medium, in which the primary permeability is due to the naturally fractured structure of the cleat system. 
Natur al, orthogonal fractures, known as “cleats”, are the primary source of permeability in coal; these are categorised as  “face” 
and “butt” cleats . 
 
Face and butt cleats create a tortuous flow path, with two transport types  during production , whereby t ransport from matrix to 
fractures (gas only) is diffusive , and f racture transport is characterised by continuum flow (water and gas) .  
 Very little consideration is given to  the impact of such a cleat system on fluid transport in coal ; it is generally assumed to be 
similar to o ther fractured / dual porosity reservoirs, or even clastics . In reality, horizontal anisotropy, as well as randomly 
distributed “bundles” of cleats, may have a significant impact on the permeability measured by well tests.


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Depending upon the stress magnitude and orientation, depletion of the (incompressible) fracture fluids may have a dr astic 
impact on permeability ; higher stresses perpendicular to the face cleat orientation may result in “closure”, or compaction, of 
the cleat system, reducing permeability. This thus impacts the magnitude of resistance in the horizontal plane, resulting i n 
closure  of the cleat network perpendicular to the maximum horizontal stress.  As such, q uantification of the orientations of face 
cleats and horizontal stresses may assist in assessing the extent to which pressure -dependent permeability is likely to impac t 
long-term production.  
 This compaction effect may be accelerated by the production process, whereby depletion of the reservoir fluids changes the 
effective  stress (
σ’), defined as:  
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SPE 167074   3 
𝝈′=𝝈−𝑷𝒑 ( 1 ) 
 
In coal formations, the critical component of this total stress model is the effective horizontal stress, as  the principal horizontal 
stresses often act pe rpendicular to the cleat system, at least at the time of cleat formation (Laubach et al.,  1997) . A numbe r of 
models exist which predict the impact of this changing net stress on permeabilit y (Shi & Duruc an, 2004,  Cui & Bustin, 2005 ); 
one such model is as follows : 
 
𝑘=𝑘0𝑒�−3�𝐶𝑓�𝜎′−𝜎0′��� ( 2 ) 
 
Note that t he basic geo -mechanical models propose a second, competing phenomenon, “matrix shrinkage”, which occurs when 
gas desorbs  from the surface of the coal micropores, reducing the matrix volume.  This has been illustrated through field 
analysis of production wells in the Bowen Basin (Mazumder  et al. , 2012).   
 
The brevity of well tests is likely to preclude the observation of such phenomena, but the parameters required to estimate th e


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long-term implications are critical; this can be achieved through the application of suitable test types.  Arrow  has undertaken a 
number field and core -based studies in order to quantify these key parameters (Mazumder et al., 2012, Conn ell et al., 2013), 
and their incorporation into improved reservoir forecasting practices is currently ongoing ( Feng et al ., 2012) . 
 
 
Coal Formation Stresses  
Measurements from a variety of Bowen Basin coal formations are included in Figure 1, illustrating the regional trends in 
maxi mum and minimum horizont al, as well as vertic al, stresses.  Based on these data, it is common for the vertical stress to be 
greater than the maximum horizontal stress (i.e. a n ormal stress regime) at shallow depth s. This typically transitions to a 
Strike -Slip stress system at approximately 1000- 1300ft , the actual transition point between stress sys tems varies within each 
region.


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region.   
 
This transition has been confirmed in a number of Mechanical Earth Modelling studies currently underway in Arrow Energy’s 
Bowen Basin tenements; these models are currently being utilised  in appraisal programmes to better define the characteristics 
of each area as part of the stimulation planning and design process.   
The Strike -Slip (
σH > σh > σv) system is preferred for the purposes of hydraulic fracturing, as it provides the best chance of 
developing vertic al, full-height fractures orthogonal to the wellbore. Conversely, the Extensional (Normal ) or Compressional 
(Reverse) systems are not p referred from the perspective of fracture success.  
 
The local stress orientations may change between the interburden and coal formations at a given depth; this poses certain 
issues from a number of perspectives:  
 
• Horizontal Drilling:  Drilling upwards throu gh such an interbedded zone exposes the lateral well to a number of


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different principal stress orientations, which may affect the stability of open -hole wellbores.  A sub -optimal stress 
balance may impede the drilling process, resulting in borehole management becoming problematic in a given 
azimuth. This may, in turn, limit the potential length of any horizontal wells which may be drilled.  
• Hydraulic Fracturing:  Hydraulic fracture confinement within a coal formation is critical to the success of any 
stimulation treatment, and depends heavily on the magnitude and direction of stress (and mechanical strength) contrasts between adjacent formations. The geometry of any hydraulic fracture may change significantly upon 
escaping such confinement; this will affect the  treatment, and resultant production, performance.  The near -region 
stress regimes and contrasts may be used to estimate the likelihood of successfully stimulating coal formations (i.e. 
with respect to fracture containment), and thus be used to discern a per -well probability of success (POS) factor for


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such a development scenario.  
 
Data Acquisition  Strategy  & Formation Stress Mapping  
The well testing workflow  adopted by Arrow Energy to evaluate and effectively utilise the key subsurface parameters is 
outlined in  Figure 2. This paper outlines the testing strategy adopted by Arrow Energy in support of this process. The 
Mechanical Earth Modelling (MEM) stage, as it applies to the Bowen Basin, is outlined in a separate paper (Mazumder et al.,  
2013).  
 
A major focus of this process is on the relative merits of each type of well test at a development planning level. For example, 
in a high permeability (high porosity) formation, high injection rates and large volumes may be required to achieve formation 
breakdown , rendering a destructive injection test unviable. Furthermore, at higher poroperm values, stimulated completions or


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horizontal wells may be unnecessary, negati ng the requirement for additional geo -mechanical data.  Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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4  SPE 167074  
 
As a result, Diagnostic Fracture Injection Testing (DFIT) has been employed for this purpose of identify ing in-situ stress 
parameters in regions generally considered to be of low permeability . Previous data acquisition work undertaken by  Arrow 
Energy , supplemented by data from various mining companies , has been sufficient to provide an understanding of the 
permeability trends in the region  and focus activities . 
 
Visualisation is a key element of all in terpretation and decision -making, especially at a cross -discipline level. A geologist can 
look at a map and identify one critical subsurface element, whilst an engineer may see another –  all of these are relevant to 
informed decision making. Stress data can be used in the following:  
 
• Estimation of permeability versus stress trends;  
• Assessment of pressure -dependent permeability effects;  and, 
• Estimation of effectiveness of well design (i.e. hydraulic fracture containment, wellbore stability).


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Diagnostic Fracture Injection Testing  
Traditional Drill Stem Test (DST) and Injection Fall- Off Test (IFOT) results have proven unreliable within such low 
permeability and under -pressured reservoirs. The limited drawdown generated by DSTs in such formations has histor ically 
been an issue for these, and other, reservoirs. Similarly, difficulties have been encountered with regard to the appropriate 
management of IFOT injection rates in the Bowen Basin coals, which can fracture at very low rates; the resultant diagnostic 
typecurves needed for analysis of such a “failed” test have tended to introduce an unnecessary level of uncertainty in the 
results.  
 
Whilst DSTs and IFOTs involve a relatively lower equipment cost, a DFIT provides a wider array of valuable data, which can  
be used to inform project -level decisions, i.e. well layouts and, potentially, stress -related sweet -spots, as opposed to simply


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providing the basis for well productivity estimation . The chief value of the DFIT, therefore, lies in the ability to acquire 
additional (potentially more critical) data, as part of the testing process.  
 
Arrow Energy is conducting a large -scale data acquisition programme across the Bowen Basin in support of its Upstream LNG 
Project planning. This includes the coring, logging and te sting of 43 boreholes in the main target formations. In addition, a few 
cased and perforated frac wells have been drilled as part of this programme for production testing purposes; however, the large 
majority of these tests (97%) have been conducted open -hole. 
 
Theory  
A small volume of  low-viscosity fluid is pumped at  a low rate to achieve formation breakdown ; the use of formation water 
wherever possible is beneficial,  both in ter ms of leak -off characteristics as well as fluid compatibilities with any clay minerals


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present in the formation . The intentional creation of this fracture is the key difference between the DFIT and IFOT test types; 
formation breakdown during IFOTs has traditio nally resulted in additional uncertainties in the interpreted reservoir pr operties.  
 
Once a fracture has been developed, the pressure is allowed to ‘fall -off’, or equalise with the reservoir, to identify key events 
and flow periods . The rate of pressure fall -off is proportional to the exposed surface area of the formation –  once  a step -change 
in equalisation rate is observed, it is assume d that the fracture has closed; this occurs at the point at which fluid in the fracture 
is no longer able to offset the stress acting orthogonally ( σh).  
 Post-fracture closure, the reservoir is moving towards radial flow . This period can then be assessed for traditional reservoir 
proper ties, specifically permeability and reservoir pressure, in accordance with the standard after -closure analysis methods . An


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extensive discussion of the  theory is available in the literature ; particularly in that published by Ramurthy  et al. (2002, 2003, 
and 2009) . 
 
Equipment  & Procedure  
The tests have been conducted across the basin in core / chip holes using a straddle packer configuration ; an illustration of a 
typical testing string is included in Figure 4. The equipment utilised in the testing programme includes:  
 
• 4-stage, dual -packer in jection tool : The tool includes a by-pass for avoidance of pressure spikes during the inflation 
sequence.  The tool configuration f acilitates downhole shut -in (DHSI) , which has been observed to reduce wellbore 
storage effect s and shut-in time . 
• Injection string : A 2 3/8” injection string has proven suitable  in the majority of cases , given the relatively low


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injection rates  required as a result of the low -permeability formtion s (generally ≤2bbl/min) . Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE 167074   5 
• Downhole g auges:  High- fidelity gauges are r un as part of the testing assembly to ensure any final test interpretation 
is based on reliable data; this reduces the need to account for hydrostatic or frictional effects  which may  introduce 
uncertainty during analysis . 
• Surface g auges:  Gauges  are used for preliminary analysis  when operating with surface shut -in; this allows real -time 
identification of the required  test events and flow periods . The test duration can thus be extended (or reduced), 
depending on the desired outcomes . These gauges  are connected between the wellhead and the pump discharge.  
• Pumping unit : The current  HP 3 3/8” fluid end pump (or similar) provides wide range of injection rates , with good 
control at lower volumes. Early tests were conducted using a less fit -for-purpose system, but the use of larger 
plungers resulted in difficulties with delivering low -rate. 
 
An outline of the open -hole testing procedure is as follows:


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• The testing assembly is run -in-hole, and pulled back up to the required testing depth.  
• Pressure testing  of the surface lines (between the pumping unit and injection head) is conducted . 
• The downhole test tool is adjusted to the “inflate”  setting and the packers are inflated.  
• Once the packers are set, the downhole valve is closed and the injection string is pressure -tested.  
• With a successful pressure test to 3000psi, the tool is opened to the zone and fluid is injected.  
• A low- viscosity injection flu id is pumped at a constant rate to generate (and propagate) a fracture.  
• The well is shut -in using a  surface or downhole valve (or combination of both). Surface gauge data can be used to 
analyse test progress . 
• Once radial flow (or closure pressure, depending upon the test requirements) is achieved, the testing valves may be opened and the pressure bled  down into the surface tanks .


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Of particular note is the difference in test performance between surface and downhole shut -in. There are a number of 
differences between the two testing mechanisms : 
 
• Surface:  The test interval is exposed to the tubing hydrosta tic in addition to the surface injection pressure. Real -time 
monitoring is available via gauges installe d in the surface surface lines (and adjusted for hydrostatic pressures).  
• Downhole:  The test zone is not influenced by the tubing hydrostatic pressure.  The progress of the test is monitored 
using 30 -second pressure data set via real -time telemetry to the surface. This downhole gauge pressure data is 
measured from within test interval.  
 
The advantage of open -hole testing is that any complications due to the cementing or perfor ation scheme are avoided, such as 
geomet ric skin effects d ue to limited -entry phenomena or limited perforation effectiveness. It does, however, require that


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borehole conditions  are amenable to packer setting , as washouts, etc, may prevent successful zonal isolation, resulting in a 
failed test.  Hitherto , the bounding formations have proven sufficiently competent for the packer isolation process to be 
successful in the majority of cases.  
 
Programme Results 
To-date, Arrow  energy has conducted  more than 140 DFIT s, 76% of which have targeted coal formations . The success rating 
of the tests in coal estimating formation parameters is as follows:  
 
• Closure Pressure:   94% 
• Permeability Estimates:  64% 
• Reservoir Pressure:  59% 
 
Note that the number of permeability estimates reported here represents only those values which may be considered with a 
reasonably high degree of confidence. Any tests which have provided an upper estim ate but not a definitive value,  due to an 
incomplete profile , are not included in this summary . 
 
By contrast, a comparison with 144 DST / IFOT results in the company’s database shows that only 57% of such tests


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facilitated the estimation of a permeability value with a moderate to high confidence. This is largely attributable to:  
 
• The recent i nclusion of real-time monitoring, which has facilitated impro ved decision -making around testing 
timeframes;  
• An improved equipment reliability in more recent testing programmes; and,  
• A greater appreciation for the limitations  of DST / IFOT in low -permeability coal formations.  
 
The type and quality information acquired as part of Arrow Energy’s DFIT programme is outlined in the following section.  Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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6  SPE 167074  
Formation Responses  
Typical  formation responses , approximating “DFIT type-curves ”, have previously been identified in the literature (Ramurthy 
et al., 2002) ; these are invaluable in interpretation of the general formation properties , as well as confirmation of the near -
wellbore geological setting  such as the identification of the presence of baffling formations . The following have been observed 
as part of Arrow Energy’s testing programme:  
 
• Pressure Dependent Leak -off (PDL): The PDL  response is the most common reservoir behaviour observed as part 
of the testing programme . 
• Fracture Height Recession (FHR) : FHR has been observed when testing thin, interbedded formations such as the 
FCCM; the presence of this effect can be forecast by pressure fluctuations  observed during the constant -rate pumping 
schedule.  
• Fracture Tip E xtension (FT E): Observed in a number of very low -permeability formations , the occurrence of this


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effect has helped to identify suitable (and unsuitable) well testing target zones.  
 
Reliability of Permeability Measurements  
Concerns have previously been raised over the reliability of DFIT permeability results in comparison with DST or IFOT test 
types ; the relative merits of each test type has been the subject  of some discussion within the literature  (Gelber et al., 2012 ; 
Tan et al., 2013 ). DFIT permeability estimates for four different geo -domains within the Bowen Basin are plotted in Figure 6, 
alongsid e the average permeability trend calculated from the previously -acquired DST / IFOT results within Arrow Energy’s 
database.   
 
Comparison between the two data sets suggests that permeability estimates generated by the DFIT programme demonstrate a 
similar correlation , both between tests types, and with respect to depth.  Of particular interest is that the trend in DFIT results


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tends to illustrate a more  favourable permeability  compared to DST / IFOT  estimates at greater depths . A number of elements 
contribut e to this:  
 
• DST / IFOT “low” side bias: The DST / IFOT permeability -depth trend in Figure 6 has been generated using results 
in which there is “high” confidence only, i.e. excluding those estimates where the quality of the radial flow (or otherwise) interpretation is unreliable , potentially resulting in low -side bias in the trend . There is , in general,  greater 
confidence in the quality of the DFIT data, and thus the resultant interpretation, as a result of improved operational 
practices, leading a reduced discrediting of high er-perme ability outcomes in deeper zones . 
• DFIT “high -side” bias: Occasionally, “upper estimates” of permeability , based on forecasts of pressure data in the 
interpretation software, may be introduced to the dataset, creating a “high -side” bias in the DFIT results.  It should be


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noted that this practice is not restricted to DFIT interpretation, and the same issue may arise in the DST / IFOT trends.  
 Nevertheless, the DFIT dataset sits well within the range of scatter observed in the DST / IFOT programme, and the esti mated 
permeability values are considered valid as the basis for subsurface uncertainty modelling.  
Breakdown & Closure Pressures  
One of the critical features of Arrow Energy’s DFIT programme is the nature of the formation breakdown response during 
treatment. In very few instances are the classical high -energy “hump” observed prior to fracture propagation  (Figur e 3). This is 
currently interpreted to be the result of the  treatment method stimulating the existing cleat system, rather than creating a new 
fracture.  
 
The response to this uncertainty is  the avoidance of “stepping ” the injection rate during the pumping process. For a constant


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injection rate, the treatment plot is visually equivalent to a pressu re versus cumulative volume curve. As with standard leak- off 
tests in permeable formation s, identification of two distinct slopes in such a scenario allows an approximation of the formation 
breakdown pressure . This method has been used to generate an estimate of formation breakdown pressure (Figure 7); the same 
four geo -domains as above are represented for continuity . 
 
As discussed above, fracture closure pressure is assumed to provide an estimate of the magnitude of the minimum horizontal 
stress. Closure pressures versus formation depth, as measured in Arrow Energy’s DFIT programme, are illustrated in Figure 8. 
The majority of data has been coll ected between 750ft and 2000ft; t he convergence in closure pressures between 
approximately 700ft and 1000ft indicates that at this depth, th e stress contrasts between target and bounding zones are


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minimal; fracture confinement at such a depth is heavily reliant on the density differences.  
Fracture Reopening Pressure  
Performing a fracture “re -opening” test at the completion of the typical DFIT  cycle has previously been proposed as a method 
for estimating the hydraulic fracture tensile strength  (Bjarnason et al., 1989, Hickman & Zoback, 1983) . Haimson & Fairhurst Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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SPE 167074   7 
(1967) derived the following equation for estimating formation tensile strength, T : 
 
𝑃𝑏−𝑇=3𝜎ℎ−𝜎𝐻−𝑃𝑜 ( 3 ) 
 
More recently, application of the technique has been concerned with estimating maximum horizontal stress in low 
permeability formation; if the tensile stre ngth of the rock is assumed to represent the full  difference between the break -down 
and re -opening pressures , the maximum horizontal stress, σ H, can be estimated via the method proposed by Bredehoeft et al . 
(1976) : 
 
𝜎𝐻=3𝜎ℎ−𝑃𝑏−𝑃𝑟𝑒 ( 4 ) 
 
It has  been suggested that the results  of such a procedure are somewhat uncertain (Rutqvist et al., 2000; Ito et al., 1999) , and 
an investigation into the validity of this approach is ongoing within Arrow Energy.  An area of particular note is the nature of 
the typical breakdown profile  (Figure 3); the lack of a definitive breakdown pressure value greater than the propagation


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pressure implies that the tensile strength  is very low (according to the assumption above) , but alternative explanations may be 
found in the nature of the reservoir itself . 
Test Parameters  
Prescribed s hut-in times versus depth ( for surface shut -in tests) are plotted in Figure 9, along with injection volume s versus the 
ratio of depth to formation thickness ; these have been calculated based on the time required to achieve a 90% success rate.  As 
permeability decreases (typically, with depth), a smaller injection volume is required to achieve a permeability estimate in a 
suitable timef rame.  
 
Reducing the injection volume  has the obvious impact of limiting the radius of investigation , which in turn limits the scale of 
heterogeneity captured in the average permeability  estimated through interpretation . Direct application of permeability values 
which may represent “false” positives can result in erroneous simulation results. However, given the scale of heterogeneity


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obser ved in Bowen Basin coals, which can demonstrate changes in cleat properties over distances less than tens of metres, the 
question is to what extent a  large radius of investigation is  representative of the formation properties . As a result , it is possible, 
and from a cost perspective, preferable, to account for this heterogeneity via a suitable uncertainty management process  in the 
reservoir simulation workflow . 
 
 
Stress Mapping Case Study: “Red Hill”  
The Red Hill area is situated in the north -west central portion of ATP 1103 on the western flank of the Bowen Basin due north 
of the MGP. Arrow’s tenement in Red Hill work -pack covers an area of approximately 225sq mi . The t opography across the 
area is rel atively benign with a relief of approx imately  330ft . To the east of the work -pack area a sharp increase in height is 
experienced attributed to the Burton Fault.  The MCM  sub-crop to west of the area, and d ip to approx 3300ft  in the east; the


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package is greater than 800ft  thick across the region.   
 
The region is part of the Collinsville Shelf , which is c haracterised by s tructurally low disturbance , with gently easterly -dipping 
strata (approximately 3 -5°); it is bounded to the east by the Burton Jellinbah Fault Zone . Key geological features of interest in 
the region are d iscrete areas of coked coal , and s urface basalts . The main MCM target formations in Red Hill are  the 
Goonyella Upper (GU) , Goonyella Middle (GM)  and Goonyella Lower (GL)  seams.  
 The Red H ill region has been assess ed in accordance with the data acquisition workflow outlined in Figure 2, with a view to 
developing a better understanding of the interactio n between formation evaluation and reservoir performance results.   
 
Input Data  
The data available within Arrow Energy for the purposes of regional -scale stress mapping includes the following:


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• Acoustic Scanner Log s: Structural dip, possible faults / microfaults, natural fractures,  coal cleat orientation  
• Coal Quality Information : Cleat o rientation , permeability  
• Geological and Structural Models : Structure and c ontours , deformation zones, tectonic stress, joints / f aults / folds, 
intrusion s / magnetic anomalies  
• Micro -seismic : Fracture stimulation  performance  
• Rock Mechanics Core Test Results : Unconfined Compressive Strength , Young’s Modulus , Poisson’s Ratio  
 A large majority of the data are available through mining activities in the area; Arrow Energy has undertaken a more targetted 
data acquisition programme in areas identified as requiring additional design support.  Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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8  SPE 167074  
 
The above methodology was applied to the Red Hill region of the Bown Basi n, utlising the following data:  
 
• Stress measurements : Three  DFITs were conducted on target coal and boundary formations  to identify 
instantaneous shut -in pressure (ISIP) , breakdown and closure pressure s. This dataset was later added to with four 
more tests  in the nearby region  to confirm mode lled properties . 
• Rock mechanics results : Core tests were conducted on two coal and two boundary formation samples . 
• Sonic / image logs : Mono- and di -pole sonic logs were recorded across the three wells in question , along with 
magnetic imaging lo gs. 
• Petrophysical logs : A suite of petrophysical logs, including density, resistivity, porosity, SP and gamma ray were run 
on all wells in the sample set.  
• Static geological model:  A full-field geological model, based on previously acquired well logs , seismic  and drilling


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data was available for depth correlation and identification of relevant structural features . 
 
The process employed to combine these data into  a One-Dimensional  (1D)  MEM is outlined in a separate piece of literature 
(Mazumder et al.,  2013) . 
 
Mechanical Earth Modelling  
All of the above data are combined to generate MEM  for a given region; these models are then used as an input to  horizontal 
and hydraulic fracture well design. A key aspect of this process is the calibration of the model with rock mechanics test results 
and σh values estimated from DFIT results. The horizontal stresses in the formations may then be calculated via the following 
equations ( Thiercelin  & Plumb, 1994):  
 
(𝜎ℎ−𝛼𝑃)=𝑣
1−𝑣(𝜎𝑣−𝛼𝑃)+𝐸
1−𝑣2𝜀ℎ+𝑣𝐸
1−𝑣2𝜀𝐻 ( 5 ) 
 
(𝜎𝐻−𝛼𝑃)=𝑣
1−𝑣(𝜎𝑣−𝛼𝑃)+𝐸
1−𝑣2𝜀𝐻+𝑣𝐸
1−𝑣2𝜀ℎ ( 6 ) 
 
The orientation of maximum horizontal stress can be estimated from the borehole breakouts observed in the magnetic 
formation imaging logs acq uired as part of the MEM work.  
 
Modelling Results


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Modelling Results  
The resultant 1D MEM output for Red Hill, compared with pilot wells in the region, is included i n Figure 10.  
 
• Cleat Orientation: Intrinsic anisotropy is identified in the target c oal seams  using dipole sonic logs . The direction of 
“Fast Shear” provides the direction of the f ace cleats in the c oal intervals.  
• Stress Orientation : The strike direction of borehole breakout s observed in the formation magnetic imaging logs  is 
approximately WNW -ESE, suggesting that the azimuth of principal horizontal stress is approximately N30 °E. 
• Stress Magnitude: The magnitude of σh is calculated from the DFIT results, and used to calculate the magnitude of 
SH using the method outlined above.  
 
The outcomes of the modelling process , including their implications for the development well concepts,  are: 
 
• The s tress regime at the evaluated depths is mostly strike -slip, suggesting that any fractures generated are likely to be 
of a vertic al, full-height  nature .


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of a vertic al, full-height  nature . 
• Coal fractures are nearly perpendicular to the orientation of σH within the analysed region.  However, th is also 
suggests that the natural fracture system will be highly susceptible to pressure -dependent permeability effects as fluid 
is removed from the cleats during primary depletion . 
• Bounding formation fractures are predominantly parallel to σH. The o rientation of natural fractures in sand/shale may 
represent a preferential flowpath for hydraulic fracturing fluids . 
• Coals are of lower stress than boundary formations ; however, the stress differential across the formations is relatively 
low (150- 400psi), suggesting the the likelihood of containment is low.  
 
These results have correlated well with observed  data during execution of the drilling and stimulation  programmes , including 
later-stage micro -seismic conducted as part of the hydraulic fracturing programme.


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SPE 167074   9 
Conclusions  
Open -Hole  DFITs have proven a successful, high- reliability method for assessing a number of geo- mechanical properties in 
low-permeability coal  formations . The testing procedure has allowed the estimation of formation breakdown and closure 
pressure data, along with permeability and reservoir pressures.  These permeability estimates have demonstrated similar 
conformity to regional trends as more well -established test types, suggesting that the open -hole DFIT methodology employed 
is a suitable appraisal method.  
 
Coupling these results with special logging suites to generate 1D -MEMs has allowed the quantification of stress properties and 
trends throughout a specific area.  The ability to successfully calibrate geomechanical models with the  observed stress data has 
proven a valuable element in the justification of open -hole DFITs as a method for acquiring in -situ subsurface data.


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When tested against a proposed development region, t he inclusion of the closure pressure dataset in the 1DMEM p rocess has 
provided valuable insights into the nature of the subsurface environment, as well as its likely impact on future development 
and production planning exercises.  
 
 
Nomenclature  
Note:  The subscript zero ( 0) denotes a ny of the below properties  as defined at the initial reservoir conditions.  
 
Cf Cleat volume compressibility  (psi-1) 
E Young’s modulus  (psi) 
h Net pay  (ft) 
k Absolute p ermeability  (mD)  
Pb Formation breakdown pressure  (psi) 
Pp Pore pressure  (psi) 
Pre Fracture re -opening pressure  (psi) 
T Formation tensile strength  (psi) 
α Biot’s coefficient  (psi-1) 
εh Tectonic strain coefficient (direction  of σh) (-) 
εH Tectonic strain coefficient ( direction  of σH) (-) 
v Poisson’s ratio  (-) 
σ Total stress  (psi) 
σv Vertical stress  (psi) 
σh Minimum  horizontal stress  (psi) 
σH Maximum  horizontal stress  (psi) 
 References


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σH Maximum  horizontal stress  (psi) 
 References  
Bjarnason, B, Ljunggren, C, Stephansson, O. ‘New developments in hydrofracturing stress measurements at Luleå University 
of technology’. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts , Volume 
26, Issue 6 , December 1989, Pages 579- 586. 
 
Cui, X. and Bustin, M. 2005. ‘ Volumetric strain associated with methane desorption and its impact on coalbed gas production 
from deep coal seams ’. AAPG Bulletin , 89(9): 1181- 1202.  
 
Feng, Q, Shi, H, Zhang, X, Zhang, J. 2012. ‘ New Inflow Performance Relationship for Coalbed Methane ’. SPE/EAGE 
European Unconventional Resources Conference & Exhibition , 20 March 2012. SPE 152163.  
 
Fielding, C, Steph ens, C, Kassan, J, Holcombe, R. 1995.  ‘Revised palaeogeographic maps for the Bowen Basin , Central 
Queensland ’. Bowen Basin Symposium , 1-3 October, 1995.


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Queensland ’. Bowen Basin Symposium , 1-3 October, 1995.  
 
Gelber, T, Kamenar,  A, Edgoose , J. 2012 . ‘Comparison of DFIT, DST and IFT P ermeabilities in Coal Sea m Reservoirs 
Subject to Stress ’. Paper Presented at the S PE Asia Pacific Oil and  Gas Conference and Exhibition, Perth, Australia  
(SPE 158297- MS). 
 
Hickman , S, Zoback,  M. 1983 . ‘The interpretation of hydraulic fracturing pressure -time data for in -situ stress determination ’. 
Hydraulic Fracturing Measurements , National Academy Press, 44- 54. 
 
Ito, T, Evans,  K, Kawai,  K, Hayashi,  K. 1999. ‘ Hydraulic fracture reopening pressure and the estimation of maximum 
horizontal stress ’. International Journal of Rock Mechanics and Mining Sciences , 36 (6), 1999, pp. 811- 826. Downloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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10  SPE 167074  
 
Laubach, S, Mar ett, R, Olson, J, Scott, A. 1998 . ‘Characteristics and origins of coal cleat: A review ’. International Journal of 
Coal Geology , 35, 175–207. 
 Mazumd er, S, Scott, M, Jiang, J. 2012. ‘Permeability increase in Bowen Basin coal as a result of matrix shrinkage during 
primary depletion ’. International  Journal of Coal Geology , 96-97, pp. 109- 119. 
 Palmer, I. 2009. ‘ Permeability changes in coal: analytical mo delling ’. International Journal of Coal Geology , 77, pp. 119 -126. 
 
Ramurthy, M, Marjerisson, DM, Daves, SB. 2002. ‘Diagnostic Fracture Injection Test in Coals to Determine Pore Pressure 
and Permeability ’. SPE Gas Technology Symposium , April -May 2002.  
 
Ramu rthy, M, Young, GBC, Daves, SB, Witsell, F. 2003. ‘Case History: Reservoir Analysis of the Fruitland Coals Results in 
Optimizing Coalbed Methane Completions in the Tiffany Area of the San Juan Basin ’. SPE Annual Technical 
Conference and Exhibition, October  2003.


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Conference and Exhibition, October  2003.  
 
Ramurthy, M, Lyons, B, Hendrickson, RB, Barree, RD, and Magill, DP . 2009.  ‘Effects of High Pressure -Dependent Leakoff 
and High Process -Zone Stress in Coal -Stimulation Treatments ’. SPE Prod uction  & Oper ations ,24 (3), pp. 407- 414 
(SPE -107971- PA). 
 
Rutqvist, J , Tsang, C, Stephansson, O. 2000. ‘Uncertainty in the maximum principal stress estimated from hydraulic 
fracturing measurements due to the p resence of the induced fracture’.  International Journal of Rock Mechanics and 
Mining Sciences , 37 ( 1–2), pp. 107-120. 
 
Shi, JQ, Durucan, S. 2005.  ‘A model for changes in coalbed permeability during primary and enhanced methane recovery ’. 
SPE Reservoir Evaluation & Engineering, 8 ( 4), pp. 291 -299. 
 Tan, CH , Demircan , G, Satyagraha , M. 2013. ‘CSG well testing –  our experience in Queensland’.  Paper presented at the  
APPEA Conference and Exhibition, Brisbane, Australia .


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APPEA Conference and Exhibition, Brisbane, Australia . 
 
Thiercelin, M, Plumb , R. 1994 . ‘Core -based prediction of lithologic stress contrasts in East Texas formations ’. SPE Formation 
Evaluation (2510258).  
 
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SPE 167074   11 
Figures & Tables  
 
 
Figure 1: Bowen Basin Stress Data (Arrow Energy Internal)  
 
 
Figure 2: Data Acquisition Strategy  
 
WELLCONCEPT
PLANNING
Appraisal Programme
(Field)
DEVELOPMENT
CONCEPT
•Permeability
•Closure Pressure
•Pore Pressure
•Breakdown 
Pressure
RESERVOIR
SIMULATION
•Drawdown Regime
•EUR
LOG
ACQUISITION
•Dipole Sonic
•Formation Imaging 
(Breakouts, 
Washouts) 
GEO-
MECHANICAL
MODELLING
•Single / Multi -Lateral
•Inclination / Azimuth
•Solids Control 
Technologies
DFIT RESULTSLab / Desktop Studies Field Development Planning
RESERVOIR
QUALITY
•Regional Trends
(Stress, Permeability, 
etc.)
•Compaction•In-situ Stresses
•Sanding Models
•Poro -elastic 
Properties
•Mechanical 
Strength Properties
COREDATA
RecycleDownloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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12  SPE 167074  
 
  
(a) Classical b reakdown profile  (b) Observed coal breakdown pattern  
Figure 3: Observed f racture initiation in open- hole DFITs  
 
 
Figure 4: Testing string configuration  
 TimeTreating Pressure, 
Injection RateInjection Rate
Treating Pressure
TimeTreating Pressure, 
Injection RateInjection Rate
Treating Pressure
P
P
PP
P
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SPE 167074   13 
 
(a) Before Closure  
 
(b) After Closure  
Figure 5: Before - and a fter-closure  analyses of typical open -hole test  
 
 
Figure 6: Perme ability versus depth trend (MCM and  RCM formations)  
 
0
500
1000
1500
2000
2500
30000.01 0.10 1.00 10.00 100.00
Formation Midpoint [ft]Permeability [mD]
Geo-Domain 1
Geo-Domain 2
Geo-Domain 3
Geo-Domain 4
DST / IFOT TrendDownloaded from http://onepetro.org/SPEURCE/proceedings-pdf/13URCE/All-13URCE/SPE-167074-MS/1593465/spe-167074-ms.pdf/1 by University of Houston user on 27 October 2023


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14  SPE 167074  
  
(a) Coal  Formations  (b) Boundary  Formations  
 
Figure 7: Formation breakdown pressures 
 
  
(c) Coal  Formations  (d) Boundary  Formations  
Figure 8: Closure Pressures in Coal and Boundary formations  
 
  
(a) Shut -in Time  (b) Injection Volumes  
Figure 9: Prescribed shut -in times  and injection volumes  for 90% success rates (coal formations  only) 
 0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000Formation Midpoint [ft]Breakdown Pressure [psi]
Geo-Domain 1
Geo-Domain 2
Geo-Domain 3
Geo-Domain 40
500
1000
1500
2000
2500
3000
35000 500 1000 1500 2000 2500 3000 3500 4000Formation Midpoint [ft]Breakdown Pressure [psi]
Geo-Domain 1
Geo-Domain 2
Geo-Domain 3
Geo-Domain 4
0
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000Formation Midpoint [ft]Closure Pressure [psi]
Geo-Domain 1
Geo-Domain 2
Geo-Domain 3
Geo-Domain 40
500
1000
1500
2000
2500
30000 500 1000 1500 2000 2500 3000Formation Midpoint [ft]Closure Pressure [psi]
Geo-Domain 1
Geo-Domain 2
Geo-Domain 3


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Geo-Domain 1
Geo-Domain 2
Geo-Domain 3
Geo-Domain 4
0
500
1000
1500
2000
2500
30000 5 10 15 20 25 30 35 40 45Formation Midpoitn [ft]Shut -in time [hrs]
Low Confidence
High Confidence
Mid Confidene
Prescribed SIT
0.002.004.006.008.0010.0012.0014.00
0 50 100 150 200 250 300 350 400Formation Midpoitn [ft]
Depth / Thicness [ft/ft]Volume
Prescribed 
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SPE 167074   15 
 
 
Figure 10: Stress / Cleat contrast for permeability trending  
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1. INTRODUCTION 
Hydraulic fracturing is a proven technology for the in-
situ rock stress measurement. The magnitude and orientation of the minimum horizontal stress S
h and the 
maximum horizontal stress SH can be estimated by 
controlling the fracturing and shut-in processes of test intervals in a borehole. Hydraulic fracturing is widely 
used in rock engineering,  oil drilling, and seismic 
research fields, with the bene fits of great measure depth, 
simple calculation without rock mechanics parameter, 
reliable result, and almost in any rock formation. 
Although hydraulic fracturing method has been well 
developed in measuring technique and measurement 
equipment, further studies of its measurement principle and rock failure mechanism are necessary 
[1]. For 
complex conditions in the field test, the actual result is 
not as simple as conventional theory. For example, the measured reopening pressure, which is very important to estimate the maximum horizontal stress, is affected not


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only by in-situ stress, but also injection rate, pore 
pressure, system compliance, etc. In the conventional theory, the pore pressure is generally substituted by 
hydrostatic pressure, and the system compliance is 
ignored. As a result, a non-ignorable error may exist in 
the estimation of the maximum horizontal stress. 
In this paper, the effect of residual aperture and system 
compliance on reopening pressure is studied. A novel 
analysis is presented to explain the phenomena observed in the comparing experiments which were carried out by 
hydraulic fracturing method in Beijing Wenquan Station. 2. CONVENTIONAL THEORY  
The information related to in-situ stress estimation can 
be obtained from the borehole pressure P curve with 
time t. A typical borehole pressure record is shown in 
Fig.1. In the hydraulic fracturing field test, a short 
interval in a borehole is sealed off by inflatable packers, 
and pressurized by fluid injection from a pump on the ground (stage 2 in Fig.1). When the fluid pressure


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exceeds the tensile strength of the rock around the seal-off section, fracture occurs on the borehole wall, and 
propagates perpendicular to the least principal in-situ stress (stage 3 in Fig.1). To define the pressure of the 
fracture walls, several reopening and draining repeated 
cycles are needed (stage 6-9 in Fig.1). 
 
Fig. 1. Typical curve of pressure-time by hydraulic fracturing.              
ARMA 12-169                                                                
 
Study on effect of residual aperture and system compliance in in-situ stress 
measurement by hydraulic fracturing method 
 
Dong, Y.K., Li, H. and Wang, H.Z.  
Key Laboratory of Crustal Dynamics, Institute  of Crustal Dynamics, CEA, Beijing, China 
ABSTRACT:  Residual aperture causes pressure penetration into the fract ure prior to its reopening, and system compliance makes 
the measured reopening pressure unequal to the real value. Both of the two fact ors are ignored in the conventional theory. Taki ng


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account of residual aperture and system compliance effects, we  analyzed the phenomenon that  measured reopening pressure Pr(a) 
decreases with the repeated test  cycles, and considered that Pr(a) gradually approaches to the real value Pr0 due to the increased 
dVc/dP and residual aperture effect. Furthermore, we present two critical values, critical crack length Lc and critical crack capacity 
Cc, to explain the phenomenon that Pr(a) is less than Ps. It is concluded that Pr(a) is between Pr0 and Ps when Cc appears earlier than 
Lc. Comparing experiments by hydraulic fracturing in 3 borehole s of about 5 m away from each other were carried out. For the 
phenomenon Pr(a) is less than Ps at 2 test sections, that is different from others at  the same depth, we concluded that it’s not caused 
by high stress difference, and modified the 2 abnormal data to average lever based on  residual aperture and system compliance 
theory.


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theory. 
 
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Two important parameters, reopening pressure Pr and 
shut-in pressure Ps, can be obtained from the P-t curve. 
When the fracture propagates sufficiently away from the 
borehole, normal stress on the fracture wall is the 
minimum horizontal stress Sh, which can be estimated by 
the shut-in pressure Ps. At the beginning of the fracture, 
the stress concentration by the borehole is a function of 
SH and Sh. Thus the borehole pressure while the induced 
fracture begins to reopen, i.e. the reopening pressure Pr, 
can be used to estimate SH [2]. In the conventional theory 
of hydraulic fracturing, SH and Sh are estimated from the 
following two equations: 
  r0 3HhSS P P=− −                          (1) 
                  hsSP=                                (2) 
where P0 is pore pressure inside the fracture before 
opening. 
3. EFFECTS OF RESIDUAL APERTURE AND 
SYSTEM COMPLIANCE  
Based on the conventional theory, Pr generally is larger 
than Ps, except that there is a big difference between SH


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than Ps, except that there is a big difference between SH 
and Sh (e.g. SH/Sh >2). However, the statistic data of field 
tests indicate that the measured reopening pressure lies 
so close to the shut-in pressure  that it is far beyond our 
expectations, i.e. Pr=Ps. In order to explain such a 
paradox, Ito et al. took into account of the residual aperture of the fracture and the hydraulic compliance of 
fracturing system, which are entirely ignored in the 
conventional theory 
[3]. 
3.1. Residual aperture 
Although the fracture is shut-in under the action of 
crustal stress after draining pr ocess, it can’t return to the 
state prior to the fracturing. The residual aperture exists between two surfaces of the fracture since the net area of contact of the two surfaces is usually a small fraction of 
their nominal area, as Fig.2 shows. 
 
(a)  First fracturing cycle          (b) Reopening cycle 
Fig. 2. Effect of residual aperture.  In the first fracturing cycle, it is appropriate to replace


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pore pressure P0 by hydrostatic pressure. However, in 
the following reopening cycles, the residual aperture 
causes pressure penetration into the fracture prior to its 
reopening. Consequently, the last component in equation 
(1) should be borehole pressure rather than P0, and the 
maximum horizontal stress can be expressed as follows 
[4]: 
r 32HhSS P=−                          (3) 
3.2. System compliance 
With the comparison of Eq. (1) and Eq. (3), it is found 
that Pr from Eq. (3) does not exceed Sh regardless of SH 
value, and be about half of the value from Eq. (1). Ito et 
al. explained the difference by system compliance. 
System compliance C is generally used to indicate 
storage characteristic of the measurement system (fluid 
volume change per unit pressure). It consists of flow 
tube deformation, borehole deformation, and fluid 
compressibility. Assuming negligible fluid leakage into surrounding rock, the effect of the fracture opening on


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the borehole pressure variation can be expressed as follows 
[5]: 
cdP Q
dV dtCdP=
+                           (4)  
where d Vc is the change of pressurized fluid volume due 
to the fracture opening. Q is the flow rate, and P is the 
borehole pressure, as shown in Fig.3. 
 
Fig. 3. Illustration of hydraulic fracturing system.  
We usually determine reopening pressure Pr by choosing 
the point at which the slop of P-t curve begins to sharply 
decrease. Since the flow rate Q and the system 
compliance C are constant, Eq. (4) indicates that the Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA12/All-ARMA12/ARMA-2012-169/1597153/arma-2012-169.pdf/1 by University of Houston user on 30 October 2023


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deviation of the P-t curve depends on the relative value 
of dVc/dP and C. As shown in Fig.4, the reopening 
process can be divided into 4 stages according as the 
deviation. The fracture begins to reopen at stage 2. The 
P-t curve will deviate from linearity to some degree. 
However, since the system compliance C is far larger 
than the value of d Vc/dP at the early stage of fracture 
reopening, no detectable change occurs on the P-t curve. 
Hence, it is difficult to identify the real reopening 
pressure on the P-t curve. When borehole pressure P 
reaches the level of Sh, the stress acting normally on the 
fracture surfaces goes into a critical state. The deviation 
of the P-t curve from linearity gets visible, where the 
measured pressure is common ly considered as the real 
reopening pressure by mistake. To distinguish the two reopening pressure, Ito et al. denote the real reopening 
pressure as P
r0, and the measured reopening pressure as 
Pr(a).


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r0, and the measured reopening pressure as 
Pr(a). 
 
Fig. 4. Relationship of measured reopening pressure Pr(a) and 
real reopening pressure Pr0. 
4. EXPERIMENT RESULTS ANALYSIS 
To study the effects of residual aperture and system 
compliance on reopening pressure Pr, we carried out a 
comparing experiment in Wenquan Station, Beijing. 
Three boreholes of 150 m in depth, 130 mm in diameter, 
and about 5 m away from each other were drilled. The boreholes penetrated into granite, and quaternary deposits 10-20 m. The in-situ stress tests of hydraulic fracturing were carried out in each of 3 boreholes. 
4.1. Pr(a) decreases with repeated cycles  
Fig. 5 shows the recorded hydraulic fracturing P-t curve 
of ZK2 borehole at a depth of  112 m. It indicates that the 
measured reopening pressure decreases with the 
following repeated test cycles, even be less than Sh in the 
last cycle, which can also be observed in most hydraulic 
fracturing measurements. This phenomenon was simply


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fracturing measurements. This phenomenon was simply 
explained in some literature. On the one hand, sometimes the fracturing process in the first cycle is not 
sufficient if we shut down the pump shortly after the 
breakdown pressure is reach. Continuous fracturing will 
be happen in the following one or two repeated cycles 
(the second cycle shown in Fig. 6), which should be 
avoided in the reopening pressure obtaining. On the 
other hand, as the repeated test progresses, pressurized 
fluid will permeate into wall rock and can’t back flow immediately, which results in an increase of pore pressure around the test interval 
[6]. 
012345024681012
 
Fig. 5. Recorded P-t curve at 112m depth in ZK2 borehole.  
Taking account of residual aperture and system 
compliance effects, we give another explanation to the phenomenon. The real reopening pressure P
r0 has no 
change as the reopening and draining cycle repeats, because it changes only with in-situ stress (as Eq. 3 
shows). The measured reopening pressure P


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shows). The measured reopening pressure P
r(a) lies on 
not only in-situ stress but also relative value of d Vc/dP  
and C (as Eq. 4 shows). As the Fracturing continues in 
repeated cycles, Pr(a) will continually decrease and 
approach to Pr0, due to the increased d Vc/dP and the 
effect of residual aperture. 
4.2. Pr(a) is less than P s 
Fig. 6 shows the recorded hydraulic fracturing P-t curve 
of ZK5 borehole at a depth of 67 m. It is shown that the 
reopening pressure Pr(a) is less than Ps in almost all 
repeated cycles. In most cases, it is generally recognized 
that there is a comparative difference between SH and Sh 
in the test area, i.e. ( SH+P0)/Sh≥2, whereas our 
comparing measurement indicates that this phenomenon 
is not caused by high stress difference. 
 
Fig. 6. Recorded P-t curve at 67m depth in ZK5 borehole.  
Since the 3 boreholes are so close to each others, we can 
ignore the differences caused by topography, fault, and rock character, and assume that the results of 3 boreholes


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should be similar within experimental error range. Fig. 7 Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA12/All-ARMA12/ARMA-2012-169/1597153/arma-2012-169.pdf/1 by University of Houston user on 30 October 2023


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shows the stress ratio SH/Sh of each test interval in 3 
boreholes (ZK1, ZK2, and ZK5), where SH and Sh were 
estimated by eq.(1) and eq.(2). All of the SH/Sh values 
distribute around 1.7, except for 2 abnormal points, 
which are marked as solid triangle symbol. The SH/Sh 
values of the 2 abnormal points are larger than 2, while 
the other points at the same depth are about 1.7. So it is 
concluded that the abnormal phenomenon is not caused by high stress difference in the test area, but maybe well 
leakage, pressure relief of packers, large fracturing 
height, etc. 
40
50
60
70
80
90
100
110
120
1301.0 1.5 2.0 2.5 3.0SH / ShDepth /mzk1
zk2
zk5
1.72.22.1
 
Fig. 7. Distribution of SH/Sh values with depth.  
Based on Ito’s theory of residual aperture and system 
compliance, we present two critical values to analyse the phenomenon that P
r(a) is less than Ps. 
• Critical crack length Lc 
The normal stress on fracture is a function of SH and Sh 
due to the effect of stress concentration by the borehole,


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due to the effect of stress concentration by the borehole, 
which weakens rapidly away from the borehole. At a sufficient distance from the borehole, the normal stress 
on fracture becomes almost equal to the value of S
h, as 
shown in Fig. 8. When the fluid pressure reaches to the 
level of Sh, the crack length will greatly increase with 
small increment  of fluid pressure. The reopening crack 
length L at this balance stress condition is defined as 
critical crack length Lc. The fluid pressure is considered 
as Pr0 as the fracture begin to reopen, and equals to Sh at 
critical crack length Lc. 
 
Fig. 8. Sketch of critical crack length Lc. 
• Critical crack capacity Cc 
The parameter of d Vc/dP indicates the crack capacity due 
to the fracture opening, which is related to crack length L, 
crack height H, and borehole radius a. The relative value 
of dVc/dP and C dominates the deviation of P-t curve. 
When d Vc/dP becomes considerably large compared


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When d Vc/dP becomes considerably large compared 
with C, P-t curve begins to deviate from its initial trend. 
The value of d Vc/dP at this moment is defined as critical 
crack capacity Cc, and the measured reopening pressure 
Pr(a) can be located on the P-t curve.  
In most conditions, the two critical states occur not at the 
same time. Fig. 9 is the sketch of d Vc/dP vs open crack 
length L. For some reason, such as larger crack height H, 
the critical value Cc will be achieved earlier than Lc, as 
the solid line shows in Fig. 9. Contrarily, Lc will be 
achieved earlier due to smaller H, as the dashed line 
shows. On the P-t curve, critical value Lc corresponds to 
the point that borehole pressure is equal to Sh, and 
critical Cc corresponds to Pr(a). The appearance order of 
the two critical values determines the relative magnitude 
of Pr(a) and Sh (Ps), and corresponds to two typical 
patterns of the P-t curve. When Cc appears earlier than 
Lc, the measured reopening pressure Pr(a) is less than Sh,


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Lc, the measured reopening pressure Pr(a) is less than Sh, 
and close to the real reopening pressure Pr0 (solid line in 
Fig. 10), as the above comparing experiment result shows.  When L
c appears earlier, Pr(a) is larger than Sh 
(dashed line in Fig. 10). 
 
Fig. 9. Sketch of d Vc/dP vs open crack length L. Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA12/All-ARMA12/ARMA-2012-169/1597153/arma-2012-169.pdf/1 by University of Houston user on 30 October 2023


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Fig. 10. Sketch of relationship of Pr(a) and Sh. 
4.3. Modification 
With consideration of residual aperture and system 
compliance, we try to modify the two abnormal data in 
Fig. 7, whose SH/Sh value is larger than 2. Based on the 
above analysis, we concluded that (1) the measured reopening pressure P
r(a) will gradually approach to the 
real value Pr0 in the repeated test cycles, (2) Pr(a) is close 
to Pr0 when Cc appears earlier than Lc, and (3) the tiny 
deviation of P-t curve at stage 2 (Fig. 4) can be observed 
in a smaller time scale. So we modified the two 
abnormal data by determining Pr(a) in the last test cycle, 
in a smaller time scale, and using Eq.(3) to calculate SH. 
Fig. 11 shows the modified result that the SH/Sh values of 
the two abnormal data are reduced to the average level. 
40
506070
80
90
100110
120
1301.0 1.5 2.0 2.5 3.0
SH / ShDepth /mzk1
zk2
zk5
modified
1.7
 
Fig. 11. Modification of the 2 abnormal data based on residual 
aperture and system compliance theory.  5. CONCLUSIONS


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aperture and system compliance theory.  5. CONCLUSIONS 
In the conventional theory, residual aperture and system 
compliance are entirely ignored. The existence of 
residual aperture prior to the fracture reopening causes 
pressure penetration into the fracture. System 
compliance is the primary factor for the difference 
between Pr(a) and Pr0. 
Taking account of residual aperture and system 
compliance effects, we analyzed the phenomenon that 
measured reopening pressure Pr(a) decreases with the 
repeated test cycles, and considered that Pr(a) gradually 
approaches to the real value Pr0 due to the increased 
dVc/dP and residual aperture effect. Furthermore, we 
present two critical values, critical crack length Lc and 
critical crack capacity Cc, to explain the phenomenon 
that Pr(a) is less than Ps. It is concluded that the 
appearance order of the two critical values determines the relative magnitude of P
r(a) and Sh (Ps), and 
corresponds to two typical patterns of the P-t curve.


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corresponds to two typical patterns of the P-t curve. 
When Cc appears earlier than Lc, Pr(a) will be between Sh 
and Pr0. 
Comparing experiments by hydraulic fracturing were 
carried out to study the effects of residual aperture and 
system compliance. For the phenomenon Pr(a) is less than 
Ps at 2 test sections, that is different from others at the 
same depth, we concluded that it’s not caused by high stress difference, and modified the 2 abnormal data to 
average lever by determining P
r(a) in the last test cycle in 
a smaller time scale, and using Ito’s theory to calculate 
SH. 
REFERENCES 
1. You, M.Q. 2005. Study on the geo-stresses 
measurement with hydro-fracture of borehole. Chinese 
Journal of Geotechnical Engineering, 27(3): 350-353. 
2. LI F.Q., B.C. Zhang, and K.Z. Su. 1993. Reservoir 
Induced Earthquake Risk in Yangtze Gorges Dam Area. 
Beijing: Seismological Press. 
3. Ito, T., T. Satoh, and H. Kato. 2010. Deep rock stress 
measurement by hydraulic fracturing method taking


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measurement by hydraulic fracturing method taking 
account of system compliance effect. In Proceedings of 
the 5th International Symposium on In-situ Rock Stress, 
Beijing, China, 25-27 August 2010 , ed. F.R. Xie, 43-49. 
Leiden: CRC Press/Balkema.  
4. Ito, T., K. Evans, K. Kawai, et al. 1999. Hydraulic 
fracture reopening pressure and the estimation of 
maximum horizontal stress. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 36: 811-826.  
5. Ito, T., A. Igarashi, H. Ito, et al. 2006. Crucial effect of 
system compliance on the maximum stress estimation 
in hydro fracturing method: Theoretical consideration and field test verification. Earth Planet and Space, 58: 
963-971. Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA12/All-ARMA12/ARMA-2012-169/1597153/arma-2012-169.pdf/1 by University of Houston user on 30 October 2023


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6. Guo Q.L., Q.M. An, S.G. Zh ao, and H.Z. Wang. 1996. 
The analysis and interpretation of the data of hydraulic fracturing stress measurement. In Crustal Tectonics and 
Crustal Stress(8). Beijing: Seismological Press, 103- 
113. Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA12/All-ARMA12/ARMA-2012-169/1597153/arma-2012-169.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS
DFIT: An Interdisciplinary Validation of Fracture Closure Pressure
Interpretation Across Multiple Basins
Hernán Buijs , Wintershall Dea GmbH
Copyright 2021, Society of Petroleum Engineers
This paper was prepared for presentation at the 2021 SPE Annual Technical Conference and Exhibition held in Dubai, UAE, 21 - 23 September 2021.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written
consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may


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not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
Recent papers on pre-frac tests have proposed fracture closure pressure interpretation methodologies that
lead to an earlier, higher stress estimation than the ones estimated from well-established practices. These
early time estimations based on the fracture compliance method lead the practitioner to utilize unrealistic
permeability, stress, and fracture pressure models. This, in turn, has a severe impact on the modeled fracture
geometries which hinders the hydraulic fracture optimization process. A multi-basin analysis of pre-frac
tests from the North Sea, Europe, Russia, North Africa and South America is presented to support traditional
closure estimation techniques. The validity of traditional minimum stress interpretation techniques will be
reinforced through multiple case histories by comparing permeability estimates from the time required for


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the fracture to achieve closure during diagnostic injections, after-closure analysis, core, pressure build up
and rate transient analysis. Results will be supported further by fiber optics and production logging tool
(PLT) driven flow allocation, fracture geometry assessment through micro seismic and sonic anisotropy,
and diagnostic injections numerical inversions.
Introduction
Injection pressure has been measured for safety considerations since the inception of hydraulic fracturing.
Its importance for characterizing fractures was recognized as early as 1954 by Harrison et al., who developed
a relation between pressure and the fracture volume. In 1958, the potential importance of understanding the
fracturing pressure response to recognize the type of created fracture was noted by Godbey and Hodges
(Nolte and Gulrajani, 2000).
The art of fracture pressure decline analysis is largely based on Ken Nolte's work (Nolte, 1979 ). His


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innovative postulations allowed our industry to determine the expected frac geometry, its conductivity, the
formation flow capacity, and the optimum hydraulic fracture design as well as the means necessary to place
the treatment (Nolte, 2007 ). Our industry has utilized this knowledge for several decades to optimize fracture
treatments, bringing value to their completions and consistently improve well economics.
Nolte's idealized fracture pressure decline assumptions lead to the development of the G-function,
through which a plot of pressure versus the dimensionless Gtime will yield a straight-line during the fractureDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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2 SPE-206239-MS
closure process. This latter represents a constant leak off condition; where fracture closure pressure is
identified when a deviation of such a linear trend becomes evident.
Regretfully, Nolte's postulations are seldom met in routine field practice; having early time deviations
from the proposed G-function straight line until constant leak off conditions are achieved. Nolte and others
continued to address such non-ideal conditions and provided techniques to diagnose the related pressure
responses ( Nolte, 1991 ; Nolte et al., 1993; Barree and Miskimins, 2016). Independently of the mentioned
non-linearities and the reasons of their occurrence, one of the mainstays of Nolte's work was that fracture
closure can be realized at the end of a fracture linear leak off period.
In order to make a better assessment of the fracture closure pressure, extensions of the original analysis
were made by introducing the utilization of the derivative of pressure with respect to the G-function (dp/


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dG; Castillo, 1987 ) and the superposition derivative (Gdp/dG; Barree and Mukherjee, 1996). This workflow
changed the equation for the whole industry by providing a consistent method for establishing fracture
closure pressure when utilizing in concert the G-function, the log-log plot of pressure change after shut-in
and their respective derivatives (Barree, et al., 2009 ).
Traditional fracture closure estimates were further supported by field and laboratory experiments of
hydraulic fracture closure evaluation. Physical measurements of fracture dimensions during pressure fall
off have been examined and their results proved to be consistent to traditional estimations of fracture
closure pressure. Evidence from downhole tiltmeters, finely instrumented laboratory experiments of fracture
propagation and closure estimates demonstrate that a residual fracture width is retained after closure.
Consequently, closure is a misnomer, and if a "closed" fracture remains open, the relationship between what


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one interprets as fracture closure and the minimum horizontal stress needs to be clearly defined based on
the measurement (Craig, et al., 2017). This supports the definition of fracture closure as the pressure within
the fracture that equals the contacted minimum horizontal stress, representing a neutral stress state (zero
"net pressure" in the fracture).
In 2007, a relationship between wells initial production (IP) and the G-time value at traditional fracture
closure was discovered by Conway et al. Their field-tested observation proved there is an intrinsic
relationship between the time it takes for the fracture faces to close on each other and the host rock
permeability (fast closure times equals more permeability). Additionally, over 3,000 analyzed DFIT's from
the Rocky Mountain region supported that reservoirs with Process Zone Stress (PZS) gradients greater than
0.2 psi/ft were economically poor producers (Ramurthy et al., 2013). A larger PZS, representing a larger


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difference between fracture and minimum stress, could be related to an increase time to reach fracture
closure pressure that stands for lower reservoir permeabilities. Similar approaches were implemented by
several companies when utilizing correlations between the time required for the fracture to close or constant
leak off magnitudes through pressure derivatives to predict the production of multi-fractured completions
(Ponce, 2010 ).
Therefore, if a relationship between the G-function and flow rate exists, then it is reasonable to expect a
correlation between permeability and the G-function. This led to the development of an empirical correlation
to estimate permeability based on fracture closure time during a Diagnostic Fracture Injection Test (DFIT)
when after-closure radial-flow data are not available (Barree, et al., 2009).
Recent papers have proposed fracture closure pressure interpretations based on the fracture compliance


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method, interpreting an earlier, higher stress estimation than the ones estimated from well-established
methodologies ( McClure et al., 2014; 2016  and 2019 ; Jung et al.,2016; Wang and Sharma, 2017 and
2018 ). Regretfully, this not only opposes Nolte's pioneering work but also proves to be inconsistent with
detailed laboratory work, reservoir characterization, fracture geometry assessment technologies, and wells
production performance.
This paper presents a multi-basin interdisciplinary study that seeks to support traditional closure
estimation techniques by DFIT tests numerical inversion further supported by the comparison ofDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 3
permeability estimates based on the time required for the fracture to achieve closure, DFIT after-closure
analysis, core, pressure build up (PBU) and production rate transient analysis (RTA).
As a secondary objective, the case histories presented in this paper prove how the same hydraulic fracture
learning cycle (workflow) can be applied to bring value to multi-fractured completions in any type of
reservoir under a wide range of permeability, pore pressure and state of stress conditions.
Well Selection Criteria
The wells selected for this multi-basin case study have comprehensive and diverse data sets including
complete open hole logging suites, core, PBU, detailed fracture treatment information and long-term
production histories. All analyzed wells are vertical, have permanent downhole gauges and represent a
wide range of permeabilities under different pore pressure and state-of-stress conditions. Produced reservoir
fluids include oil, gas, and gas and condensate.


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fluids include oil, gas, and gas and condensate.
The information utilized for the analysis presented in this paper represents actual conditions encountered
in wells where uncertainty needs to be collapsed through integrated workflows capable of explaining well
production performance consistently. This allows to properly characterize each reservoir and understand
the performance of the fracture treatment placed, providing key information to further optimize hydraulic
fracture design and bring additional value to the completions.
Methodology
Introduction
Since the main parameter utilized to assess the validity of traditional fracture closure estimates presented in
these case histories is permeability, it is pertinent to shortly describe its meaning and how the concept was
established. The development of Darcy's Law started in 1830 with the Saint-Michel well test when Henry
Darcy proved that the obtained water rates could not be the explained by just pressure differentials and pipe


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friction. At this point in time, Darcy deduced an unknown process was occurring, i.e., resistance to flow in
the aquifer. It took almost 30 years of knowledge exchange with practicing engineers, direct observations
of geology and laboratory work to describe the concept of permeability as a means to describe pressure lose
due to fluid flow in porous media (Brown, 2002). This is, in essence, the workflow that is applied to the
presented case histories where a single permeability estimate from multiple processes will be utilized to
describe the reservoir flow capacity. This, in turn, will be utilized to support traditional estimates of fracture
closure pressure based on the time required for the fracture faces to close upon each other during diagnostic
injections.
Workflow
Permeability, net pressure (PZS) and, among others, 1D mechanical earth models (1DMEM) are created
for history-matching the DFIT observed rate and treating pressures. For such purpose, a grid-oriented


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planar 3D fracture simulator with shear decoupling capable of managing pressure dependent leak off
(PDL) and transverse fracture storage is employed (Barree, 1983). DFITs are analyzed utilizing traditional
methodologies ( Barree and Mukherjee, 1996; Barree, et al., 1998 and 2009 ; Talley, et al., 1999). Interpreted
parameters are used to build numerical inversions of such tests based on an iterative process to fine tune the
fracture simulation model (Gulrajani, et al., 1996; Piggott, et al., 1992; Buijs and Ponce, 2018; Buijs, et al.,
2019  and 2020 ). A relationship between the host rock permeability and the time required to reach fracture
closure is validated through a pressure-match model and its numerical inversion. The fracture closure-based
permeability estimates (Gperm) are supported by multidisciplinary estimations obtained from DFIT after


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closure analysis, core, PBU and RTA.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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4 SPE-206239-MS
The correctness of the estimated minimum stress is further validated by evaluating the predictive
capabilities of lithology-based 1DMEM, fiber optic and PLT based production back allocation, near
wellbore and far field assessment of fracture geometries.
Diagnostic Fracture Injection Tests Numerical Inversion and Gperm Calculation
One of the few ways to start a conversation with a reservoir is by pumping completion fluid at fracturing
rates and analyzing how the pressure fall off with time after the injection is stopped. The language for
such a reservoir dialogue and information exchange is formed by the dimensionless time function called
"G-function" introduced by Nolte (1979) . Barree et al. (1996 , 1998  and 2009 ) refined the meaning of the
different type curves to clearly identify the minimum stress and further infer additional information about the
contacted rock. This work also included the development of an empirical correlation to establish reservoir


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permeability based on the time needed for the fracture to close during this type of test as shown by Eq 1:
(Eq. 1)
Gperm= effective permeability (mD); μ = viscosity (cp); P z= process zone stress; φ = effective porosity;
Ct= total compressibility (1/psi); G c= Gtime at closure; E = Young Modulus (MM psi); r p= leak off height
to gross frac height ratio
The dimensionless time-to-closure is a function of the volumetric efficiency of the fluid and the volume
to surface area ratio of the created frac. The viscosity used in this analysis approximates the injected fluid
viscosity corrected for relative permeability effects in the invaded region around the fracture. Leak off until
closure is dominated by the mobility of the injected fluid more than the far-field reservoir properties. The
reservoir effects are handled through the compressive storage term made up of porosity and total reservoir
compressibility ( Barree, 2020 ).


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compressibility ( Barree, 2020 ).
Multiple DFITs pumped with completion fluid are used to characterize the reservoir by utilizing
traditional type curve matching techniques to analyze the pressure transient. Depending on the DFIT
interpretation or how one further refines the input to build the computational grid model, several possible
solutions can provide an identical pressure match of the fall off data. Most of the functions used to describe
processes within the models have no unique inverse solution and therefore can be replicated in various ways.
In order to reduce uncertainty, the analysis was further validated by computing numerical models of such
pre-frac tests in a grid-oriented planar 3D fracture simulator with shear decoupling. The applied workflow
was the same as the one utilized to develop the different type curves used by the industry to infer fracture
closure pressure ( Barree et al., 1996  and 1998):
1.The instantaneous shut in pressure (ISIP) is identified.


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1.The instantaneous shut in pressure (ISIP) is identified.
2.The minimum stress is estimated by type curve matching.
3.A permeability estimate based on fracture closure time is calculated.
4.Traditional after closure analysis is utilized to estimate the reservoir pore pressure and, whenever
possible, permeability.
5.The fracture grid is calibrated, the model is run, and the fall-off data pressure-matched.
6.The modelled pressure is used as it was the actual measured pressure data and analyzed in the same
manner.
7.The fracture model is recalibrated and run again until the pressure match model provides a converging
solution capable of reproducing the same minimum stress, time required to reach closure, fracture
closure mechanisms and after closure pressure transient seen in the measured pressure data.
Real data may offer interpretation challenges by having different fracture closure mechanisms in place,


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making it troublesome to identify the correct minimum stress and the time required to reach it (amongDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 5
other variables). When implementing such interpretation cycles, it is possible to numerically model the
measured pressure data and further validate or update the original interpretations, bringing additional value
to characterize the host rock and the created fracture geometry.
DFIT based reservoir characterization (i.e: permeability and pore pressure) is further compared to
independent measurements such as core, PBU, modular formation tester (MDT) and RTA, showing a high
degree of correspondence. Mini-fracs using gels were not utilized to estimate the flowing capacity of the
host rock since the relationship between closure time and permeability is decoupled by the presence of
polymer accumulating in the fracture faces during leak off.
Fracture Geometry and Production Performance Evaluation
The fracture treating-pressure history for pre-frac tests and main treatments analyzed are modeled using
a commercial grid-oriented planar 3D fracture simulator with shear decoupling. Digital treatment data


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is utilized as the input pumping schedule for fracture geometry simulation in this study. Rock physics
principles are utilized to derive lithology-based minimum stress models (1DMEMs) while pore pressure
and permeability estimates are obtained from multiple and diverse measurements (Barree, et al., 2009; Buijs
and Ponce, 2018 ; Buijs, et al., 2020 ).
A combination of numerical and analytical solutions is utilized to model production from the selected
wells. Initially, RTA is used to assess the contacted net pay ("kh"), the reservoir volume and the drainage
shape that defines the reservoir architecture. The methodology consists of an iterative analysis that honors
the flowing material balance, variable reservoir fluid properties and reservoir energy through depletion
(Cox, S.A. et al., 2002  and 2007 ).
As a second step, a fracture production model is utilized to confirm RTA results and to effectively evaluate


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the combined dynamic interactions of reservoir transient flow, gel clean-up, multiphase and non-Darcy
flow. This latter is a production simulator that combines reservoir transient production forecasting for an
arbitrary shape, rectangular, bounded reservoir with a damaged hydraulic fracture. Its simulations accounts
for effects of closure stress, embedment, spalling, filter-cake deposition and erosion, bulk gel damage, and
non-Darcy multiphase flow on proppant packs (Duenckel, et al., 2019; Barree, et al; 2003). An iterative
process between the modelled fracture geometry, RTA and a production model that accounts for proppant
pack physical behaviours is implemented till a converging solution is found.
Case 1: Shale Oil
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical inversion
that will be reinforced by the integration of permeability modelling, core measurements, stress modelling,
fiber optics, micro seismic and RTA.


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fiber optics, micro seismic and RTA.
This is a vertical cased and cemented technology well in the Vaca Muerta Shale that was completed with
four limited entry fracture stages. In terms of hydraulic fracturing design, the length of individual clusters,
spacing between clusters, number of holes and hole size were done using most recent understanding of
cluster dynamics plus proprietary considerations, following a reservoir and completion quality assessment
(Buijs and Ponce, 2018 ). A hybrid fracture design consisting of slick water and x-linked gel (25 #/1,000
gal) was utilized to pump two different frac job sizes based on preliminary simulations (200 and 300 tons
of proppant).
The attached G-Function, linear flow time function and Talley-Nolte plots (Fig. 1.A and Fig. 1.B )
correspond to a DFIT pumped above the Vaca Muerta's hot section called "The Kitchen". The type curve
identified in the Gplot is described as a "Tip Extension" closure mechanism that accounts for an early-


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time pressure dependent leak-off (PDL) followed by a linear leak-off profile across the created surface till
fracture closure is achieved.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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6 SPE-206239-MS
Figure 1.A— Diagnostic injection G-plot for well A, stage 1.  Blue curve is bottom hole pressure, green is
first derivative curve (Dp/DG), red curve is (G*Dp*/DG). G*Dp*/DG: The semilog or superposition derivative curve
Figure 1.B— Linear Flow Time and Talley-Nolte Plots interpretation for well A, stage 1. Linear time flow function:
Blue curve is bottom hole pressure. Talley-Nolte Plots: Blue curve is delta pressure; green is the log derivative curve.
The pressure fall off analysis provides an interpreted minimum stress of 9,123 psi, a pore pressure of
8,550 psi and a late time fracture closure related to the low permeability of the contacted rock. In that respect,
fracture closure is achieved at a Gtime of ~45, taking approximately 10 hours for the fracture to reach such
condition. An additional confirmation of the validity of the pore pressure estimate is given by the Talley-
Nolte plot that confirms the presence of a linear flow period by the identified half slope of the pressure


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derivative. When the estimated pore pressure is correct, the pressure difference curve will also fall on a half
slope and be 2x higher in magnitude than the derivative as shown in Fig 1.B (Talley, et al., 1999).
From these graphs it is difficult to understand how the fracture geometry develops and how to further
calibrate the leak-off profiles that are utilized in the fracture model. For such purpose, the interpreted
minimum stress and pseudo-linear pore pressure were utilized to calibrate a litho-based 1DMEM that was
able to predict multiple closure points measured on this well under a single tectonic boundary condition
as shown in Fig. 2.A (calibration point is marked with a black arrow, predicted stresses are indicated by
blue arrows).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 7
Figure 2.A—Traditional closure litho-based 1DMEM for well A, stage 1.
The pressure-match model was then run with reduced time steps to better understand how the geometry
developed through time (Fig. 2.B). It proved that, due to the low permeability of this interval, there was
enough remaining energy within the fracture body to keep on propagating the fracture after the pumps
have stopped as presented on Fig. 2.C  (shifting the linear trends of a normal leak-off profile and inducing
a pressure dependent signature related to the additional area created). Under this condition, the Gperm
equation cannot be used directly to estimate the reservoir flowing capacity since the fracture continues
to propagate after the pumps are stopped at surface. In that respect, a DFIT numerical inversion was
implemented to assess the contacted reservoir permeability (Buijs and Ponce, 2018 ; Buijs, et al., 2019).
Figure 2.B—Diagnostic injection pressure-match for well A, stage 1. Green Curve:


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Measured well head pressure Blue Curve: Modeled well head pressure Red curve: Frac rate.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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8 SPE-206239-MS
Figure 2.C—Net pressure plot vs Time for well A, stage 1 (Three-time instants are here illustrated).
The DFIT pressure-match was achieved by implementing an iterative pressure match process until the
modelled pressure converge to provide the same fracture closure mechanism, minimum stress, time to reach
closure and after-closure pressure transient dissipation that allowed to estimate a host rock permeability (as
shown in Fig. 3.A  and Fig. 3.B).
Figure 3.A—DFIT vs simulated DFIT Gplot for well A, stage 1. Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 9
Figure 3.B— DFIT vs simulated DFIT after-closure analysis for well A, stage 1 . Linear time flow function:
Blue curve is bottom hole pressure. Talley-Nolte Plots: Blue curve is delta pressure; green is the log derivative curve.
This interpretation technique was utilized in all the diagnostic injection tests pumped during the
technology phase development across multiple vertical wells. It proved to be an extremely powerful
technique to build a thorough understanding of the pore pressure, permeability and state-of-stress conditions
across different units of the Vaca Muerta shale in this field.
When utilizing the compliance methodology to interpret the minimum stress, fracture closure happens at
a Gtime of ~10 in less than 1 hour, with an interpreted minimum stress of 9,352 psi which is ~200 psi larger
than the one estimated by traditional closure techniques as presented on Fig. 4.A .
Figure 4.A— Compliance DFIT closure analysis for well A, stage 1. Blue curve is


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bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
When implementing this magnitude to calibrate the litho-based 1DMEM (marked as red cross on track 2
in Fig. 4.B ), the stress model not only cannot predict multiple closure points on this well but rather matched
the fracture pressure (ISIPs) measured consistently during multiple injections (marked as blue points onDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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10 SPE-206239-MS
track 2 in Fig. 4.A ). This, in turn, makes the calibrated stress model through the fracture compliance method
invalid, inconsistent and lacking predictive capabilities since it does not allow to properly understand the
state-of-stress in the host rock. Consequently, this will not allow to match any of the near wellbore and
micro seismic measurements of fracture height in this well (unless the concept of stress is decoupled from
the fracture modelling process), stopping the fracturing learning cycle and any meaningful optimization
opportunity that will allow for improving the well economics.
Figure 4.B—Compliance 1DMEM for well A, stage 1.
Ten diagnostic injections pumped across three vertical wells in strategic positions, allow understanding
the permeability and the state-of-stress of this reservoir in a more profound way. When integrating
information from multiple diagnostic injections, it was noticed that DFIT's pumped in zones with low


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resistivity have very limited permeability when compared to high resistivity intervals where fracture
closured happened much faster and, at the same time, have two distinct G-function plot responses as seen
in Fig. 5.A  (i.e. closure mechanisms).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 11
Figure 5.A— Resistivity vs DFIT "G" and log-log plots for well A, stage 1. Log-log plot: Blue curve is
Delta Pressure, green is first derivative curve (dDP/dDT), red curve is (DT* dDP/dDT). DP: fall off pressure
minus the Instantaneous Shut-In Pressure (ISIP), DT* dDP/dDT: The semilog or superposition derivative curve
Taking these observations into account, a permeability function was built by using effective porosity
(PHIE), resistivity, differences between deep-shallow resistivity measurements and the rock mechanics
synthetic travel time curves, which were further constrained by DFIT closure time permeability estimates
(Gperm) called "GRES_Perm" in track 2 of Fig. 5.B  (Buijs and Ponce, 2018; Buijs, et al., 2019 ).
Figure 5.B—GRES-Perm vs TOC and slowness for well A, stage 1 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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12 SPE-206239-MS
As shown in track 3 of Fig. 5.B, there is a strong correlation with the suggested permeability model and
the travel time slowness used to model the Total Organic Carbon or TOC (Passey et al 1990a and 1990b ;
Caniggia and Ferguson, 2014), as it is when plotting the mentioned function against core measured TOC
as presented in track 5.
This phenomenon would indicate that the fissures present in the analyzed wells are related to the
maturation and sourcing of hydrocarbons rather than to macro fissures related to structural deformations.
It is worth mentioning that core permeabilities in multi-fractured tight reservoirs cannot be utilized to
calibrate their flowing capacity models since hydraulic fracturing will induce shear failure in the contacted
rock and alter the overall system permeability (Cluff, et al., 2007; Barree and Miskimins, 2016). In this
case, assuming pulse decay permeabilities can describe the shale matrix permeability, production behaviour


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and DFIT numerical inversion supports that the flowing capacity should be at least one order of magnitude
higher than core-based permeabilities. Simply put, core permeability is a point measurement that cannot
describe the flowing capacity of a naturally fractured or fracture enhance permeability rock since it carries
no information from these high flowing capacity channels. This is further supported by over 30 years of
research on proppant pack fracturing fluid clean up studies that clearly shows that the limited effective
flowing fracture lengths established in a nano-Darcy matrix rock cannot explain the production performance
of these wells, reinforcing the presence of a larger contacted flowing capacity ( Duenckel, et al., 2019).
Additionally, matrix permeabilities cannot explain why the cumulative production from unconventional
wells can be improved by implementing drawdown managment strategies. This latter allows to delay


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the onset of matrix dominated permeabilities and take advantage of the mentioned early time enhanced
permeability to maximize hydrocarbon recovery in such pressure dependent flowing capacity systems.
When the fracture compliance closure is utilized, not only is the 1DMEM incorrect making it impossible
to make a precise assessment of the fracture geometry created by the different treatments pumped on this
well but, additionally, the relationship between the time it takes for the fracture to close and the contacted
reservoir permeability is decoupled. If we assume the fracture closure from the compliance method is
correct, the fracture closure time becomes similar to the ones achieved by the PDL closure mechanism
associated with natural fractures (Gtime of ~10 as presented in Fig 4.B vs Gtime of ~6 as shown in Fig.
5.A). This suggests that the contacted reservoir flowing capacity by both diagnostic injections is comparable


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since fracture closure is achieved on both tests in less than 1 hr. Regretfully, this becomes questionable
since the flowing capacity of a naturally fractured formation is not comparable with one that is dominated
by nano-Darcy matrix permeabilities.
When fractures are initiated within the slowness-brittleness anomaly shown on the second track in Fig.
6.A, fractures can grow excessively in height and production changed drastically. Fiber production data from
the stage placed in the upper Vaca Muerta produced almost 60% of the production of this well. Rare enough,
production came from the upper two perforation clusters instead of the seven clusters utilized to pump the
fracture treatment, suggesting a large flowing capacity unit has been contacted above them ( Fig. 6.B).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 13
Figure 6.A—Sonic anisotropy measured frac height vs slowing-brittleness anomaly
Figure 6.B—Fiber optic production back allocation.
Nevertheless, a discrepancy can be seen between the near wellbore sonic anisotropy fracture height
showing that the fracture stays contained within the upper Vaca Muerta (Fig. 6.A ) and the measured microDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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14 SPE-206239-MS
seismic cloud suggesting that the fracture was able to reach the overlaying Quintuco formation ( Fig. 6.C).
The main question to answer at that time was if the hydraulic fracture grew into Quintuco or if the micro
seismic events were caused by rock shear stress energy release because of the hydraulic fracture (dry events).
Figure 6.C—Micro seismic frac geometry assessment
As seen in Fig 6.D  blue curve, when combining the near wellbore measurement of fracture height with
the GRES-Perm flowing capacity model, the early time well production performance cannot be matched.
To match the early time performance and the produced volumes based on RTA, it is required to have a
larger kh (at least, 2 times higher) which further supports fracture height growth into the Quintuco formation
as shown by the micro seismic fracture geometry assessment. At this stage, it is difficult to judge if the
connection with this higher permeability interval is a partial or a lasting one but is something that cannot


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be avoided in the upper Vaca Muerta and rather capitalized on by landing wells in the right position.
Figure 6.D— RTA – Sonic anisotropy vs micro seismic frac height Red curve: Microseismic kh. Blue curve: Sonic anisotrophy kh.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 15
Focal mechanism analysis performed on the micro seismic events provided a clue to understanding
fracture geometry, showing that most of the events detected in the Quintuco are fluid connected (wet events),
but most likely not propped. In addition, dip-slip has the same radiation pattern as that of horizontal slip on
a horizontal surface slipping orthogonally to the strike of the dip-slip solution suggesting the development
of horizontal fractures.
In this regard, the litho-based stress model calibrated based on traditional interpretation techniques was
utilized to understand the complexity seen on the micro seismic data in the Quintuco formation and why all
events stop drastically at a predefined depth. As can be seen in Fig. 7.A  and 7.B, the high complexity zone
seen in the micro seismic recorded during fracture placement coincides with a zone where the minimum
stress (red curve) and the overburden (black curve) tend to overlap. Under this condition, the fracture


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will not have a clear path to develop growth and the fracture orientation will change from vertical to
horizontal, explaining the development of horizontal fractures interpreted based on micro seismic events.
Additionally, all micro seismic events stop at the same depth where the minimum stress becomes higher than
the overburden stress. At this position, the fractures will stop propagating upwards since the maximum stress
plane will be parallel to the bedding of the rock (fractures will grow in the direction of the bedding planes).
In turn, this proves that the litho-based 1DMEM is not only consistent with a large number of diagnostic
injections but also with the independent assessment of fracture geometry provided by micro seismic events.
Figure 7—Traditional vs Compliance based 1DMEM, micro seismic and proppant convection frac geometry.
When modelling the fracture geometry under the mentioned conditions, the simulation illustrates that


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mostly fluid can grow into the Quintuco ( Fig 7.C ), travelling further than proppant that is held back in
Vaca Muerta due to gravitational/frac wall effects. The modelled fracture geometry is consistent with the
independent interpretation of fracture geometry provided by the micro seismic events and, at the same time,
the near wellbore fracture height measurements when modelling proppant convection as presented in Fig.
7.A (Buijs and Ponce, 2018 ).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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16 SPE-206239-MS
Information from several diagnostic injections, rock physics, litho-based 1DMEM, fracture geometry
assessment technologies, fiber optics, RTA and fracture geometry models were used to understand the
production performance of this well. Among many learnings, integrated modelling clearly shows that the
production from this well can only be explained by having a fracture treatment growing into the Quintuco
formation.
If the compliance closure pressure is utilized to calibrate the 1DMEM, the model becomes inconsistent
with the previous integrated evaluation since the fracture will not be able to grow in height towards the
Quintuco due to having the minimum stress becoming larger than the overburden at a shallower position
as marked with a red arrow on track 2 in Fig. 7.A . This stress model then becomes inconsistent with
the independent assessment of fracture geometry provided by micro seismic supporting events related to


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horizontal fracture development and fracturing fluid rather than proppant. This, in turn, does not allow for
explaining the fiber optic production allocation showing that almost 60% of the production came from the
upper 2 clusters of the fracture stage placed in the upper Vaca Muerta suggesting fracture growth into a
higher deliverability interval.
As proven by the integration of multiple diagnostic technologies, without a clear understanding of
the state-of-stress, how the rock will deform to create fracture width and, among others, the host rock
permeability it is impossible to understand anything useful about fracture geometry. If one fails to properly
interpret a fracture injection test, the created fracture geometry will be incorrect, i.e. 1) the leak-off will be
off, 2) the way the rock fails in shear will not be right, 3) the stress profile will be unsuitable and 4) the flow
capacities of the host rock drastically reduced (affecting production and reserves).


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The main problem is that, depending on the workflow and software applied to describe the system,
fracture geometries and production can be matched by following various alternative assumptions due to not
having enough information to properly constrain the solution. To put things in perspective, in this case it took
ten DFITs, tracers, PLT, fiber optics, micro seismic and near wellbore assessments of fracture geometries
to prove the lack of physical meaning of the fracture compliance closure estimates. It also demonstrates
that the host rock might easily be described in completely different ways, leading the engineer to follow an
inappropriate completion optimization strategy.
Case 2: Tight Gas Sandstone
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical
inversion constrained by triaxial elastic measurements and rock physics modelling, proving there is a direct


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relationship between the estimated permeability based on the time it takes to reach fracture closure and core
permeability measurements.
This is a tight gas reservoir that was fracture stimulated by pumping the treatment through a large
perforation interval in a cased and cemented vertical well. After each perforation run, treated completion
fluid was pumped at low rates to evaluate injection at perf level and to promote better diversion across the
perforated interval.
During the DFIT, treated completion fluid was pumped at 19 bpm for 5 minutes. The pressure fall off
analysis shows a transverse storage closure mechanism supporting the presence of secondary porosity leak
off (either by contacting a natural fracture system or created by the fracturing process). The interpreted


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minimum stress is 9,313 psi with a net pressure of 199 psi (PZS) and a Gperm of 0.046 mD (shown in Fig. 8).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 17
Figure 8—DFIT Gplot interpretation and Gperm calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
The after-closure pressure transient goes into pseudo-radial flow giving an estimate of pore pressure of
~9,100 psi that is consistent with the Talley-Nolte plot since the pressure difference and its derivative fall
on the same unit slope as shown in Fig. 9  (Talley, et al., 1999). An additional confirmation of the validity
of the pore pressure estimate is given by the MDT pore pressure independent measurements (marked with
a blue arrow on track 4 in Fig. 10).
Figure 9— DFIT After closure pseudo-radial flow function and Talley-Nolte plot. Linear time flow function:


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Blue curve is bottom hole pressure. Talley-Nolte Plots: Blue curve is delta pressure (b), green is the log derivative curve.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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18 SPE-206239-MS
Figure 10—Core vs Logging-based models: Perm, PHIE, Static Young Modulus, Poisson's Ratio, Pore Pressure and 1DMEM
The pressure-match model shown in Fig. 11  suggests a fracture height of 16 meters that is incorporated
in the calculated after-closure transmissibility giving a permeability estimate of 0.16 mD.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 19
Figure 11—DFIT Pressure-match model – Net pressure plot Purple Curve: Measured
well head pressure Black Curve: Modeled well head pressure Red curve: Frac rate.
The calibrated litho-based 1DMEM (marked with a black arrow on track 4 in Fig. 10). was able to predict
the minimum stress in the upper stimulated interval supporting the predictive capabilities of the workflow
implemented to describe elastic properties and the distribution of stress across the reservoir (marked with
a red arrow on the same track).
The DFIT was pressure-match with a fracture model that was calibrated with a large amount of triaxial
mechanical tests (as shown by green arrows on track 3 in Fig. 10) and the interpreted DFIT information
in the area indicated by a black arrow on track 1-4 in Fig 10  (interpreted pore pressure, minimum stress
and Gperm estimates).
The difference in magnitude between the Gperm (0.046mD) and pseudo radial (0.16 mD) permeability


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estimates is probably related to the pressure transient dissipation of a complex, non-planar fracture system
developed during injection. The early onset of pseudo radial flow is established due to the fracturing fluid
leaking off through multiple fracture faces and not through a linear PKN fracture as utilized to resolve
the diffusivity equation. If we follow the assumptions of a PKN fracture geometry, and assume that linear
transient flow governs fracture leak off up until closure, then the time required for the induced pressure
transient to establish a pseudo-radial flow regime can be computed from the definition of Tdxf. A minimum
dimensional time (Tdxf) value of one is required to reach pseudo-radial flow during the fall off period
(Barree, et al., 2014 ). The time required to reach pseudo-radial transient flow (Eq. 2 ) for a single planar
bi-wing fracture is in the order of ~70 hours assuming permeability of 0.047 mD, an average fracture


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half-length of 70 meters, a far field fluid viscosity of 0.0315 cp, a 15% effective porosity and reservoir
compressibility of 3.87x10-5 1/psi.
(Eq. 2)
Tpr= time to reach pseudo-radial flow (hours); φ= porosity (fraction); μ=fluid viscosity (cp); Ct=total
reservoir compressibility (1/psi); xf=fracture half-length (ft); k= permeability (md)
When utilizing the pseudo-radial flow function under this condition, the pore pressure estimates will not
be affected, but there will be a significant effect in the calculated permeability due to the complex leak off
conditions in place, making the calculated permeability invalid since it lacks of physical meaning (Barree,
et al., 2014 ; Barree, 2020 ).
The DFIT numerical inversion gives out the same closure mechanism, time to reach closure and minimum
stress as the actual measured data when utilizing the Gperm and modelling the leak off into the secondary
porosity system, further supporting the test interpretation (Fig. 8). This permeability estimate is further


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reinforced by a large number of core permeability tests performed across this interval as seen in Fig. 12,Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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20 SPE-206239-MS
where the effective flowing phase permeability calculations are close to absolute values measured at the
laboratory (flowing phase permeability should be ~75-80% of the core absolute permeability at a irreducible
water saturation of 25%). Regretfully, in this diagnostic injection, the measured DFIT and the numerical
after closure pressure transient cannot be compared directly due to the presence of a false pseudo-radial
regime.
Figure 12—Actual DFIT vs simulated DFIT gplot – Gperm model vs core permeability (mD)
Gplot: Blue curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .
This proves the validity of the interpretation, supporting the relationship between traditional estimates
of minimum stress and closure time estimates of permeability that is consistent with core data ( Fig. 12).
At the same time, when combining core permeability data and the early onset of pseudo radial flow, one


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can affirm that the transverse storage closure mechanism is related to induced natural fractures that provide
pressure support to the main fracture body during closure. The fissure dominated leak off will delay the
time it takes for the fracture faces to close on each other and, at the same time, reduce the time needed to
reach a false after closure pseudo-radial flow regime.
It is worth noting that there is a matrix permeability threshold hold on top of which the enhanced
permeability provided by the shear failure of the rock obtained during fracturing won't be enough to change
the overall system permeability. As supported by this case history, for matrix permeabilities greater than
about 0.05 mD the enhancement generated by induced shear cracks is usually negligible. Nevertheless,
induced or in-situ natural fractures will drastically increase leak off during fracturing operations and should
be accounted for since this may induce premature screen outs.


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be accounted for since this may induce premature screen outs.
When the fracture compliance method is utilized to interpret the DFIT, a minimum stress of 9,455 psi,
a net pressure of 64 psi and a Gperm of 0.087 mD are estimated as shown in Fig. 13.A. For the Gperm
calculation, a Rp of 1 was assumed since the compliance closure considers leak off conditions related to
matrix permeability without the presence of natural fractures. The permeability model constrained with the
compliance Gperm becomes larger than the core permeability tests, making this fracture closure assessment
inconsistent with independent assessments of reservoir flowing capacity.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 21
Figure 13.A— DFIT compliance closure and Gperm calculation – Core vs compliance perm
model  Blue curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
At the same time, the interpreted low net pressures will have an effect in the modelled fracture height
and, specially, in the fracture width since only 64 psi can be applied to deform the rock and develop fracture
aperture. Considering one is dealing with an almost 4 MM psi static young modulus rock and that the low
permeability will not allow the fracture to develop a proper tip-screen out behavior to develop additional
width, a treatment screen out is to be expected under these conditions.
In order to illustrate the effect of a low net pressure on fracture width, we may consider as an example
the maximum width in a linear elastic media for a planar fracture given by the Sneddon and Elliot equation
(1946)  as shown in Eq. 3 :
(Eq. 3)


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(1946)  as shown in Eq. 3 :
(Eq. 3)
W= max frac width (inch); H= fracture height (ft); μ=poisson's ratio; Pnet= PZS (psi); E= Young modulus
(psi)
Taking into consideration a typical 54 meters fracture height coverage for this interval (as presented in
Fig. 13.B ), a 0.068" fracture width is calculated for the fracture compliance closure considering a PR of 0.35
(Fig. 10 ), a PZS of 64 psi ( Fig. 13.A ) and a YMES of 3.5 MM psi (Fig. 10). In that respect, with a 0.068"
frac width, all treatments pumped in this field would have screen out. Nevertheless, over fifty 300-tons 12
ppag (pound per added gallon) fracture treatments were placed without a single screen out, proving that
the developed fracture width should have been much larger. This is only possible when having a higher net
pressure to deform the rock and create fracture aperture that will allow to pump large proppant concentration


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slurries without screen outs, proving the lack of validity of the fracture compliance minimum stress estimate.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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22 SPE-206239-MS
Figure 13.B—Typical fracture height growth in this interval
The analysis described in the previous paragraphs supports a consistent relationship between the
permeability estimates from traditional DFIT fracture closure time, DFIT numerical inversions and core.
This in turn proves that the interpreted time to reach fracture closure during the DFIT test occurs after its
linear leak off period as stated by traditional interpretation techniques. The fracture compliance closure-
based permeabilities are larger than the ones described by core and the interpreted low net pressures will not
allow to place the treatments pumped on this reservoir without inducing a screenout, which further supports
the lack of physical meaning of this methodology.
Case 3: Tight Gas Sandstone
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical inversion
built on permeability estimates based on fracture closure time that will be reinforced by anchoring the


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pseudo-linear estimated pore pressure in a pseudo-radial flow function analysis. This proves that there is a
direct relationship between the estimated permeability and the time it takes to reach fracture closure after
the linear leak off period of the DFIT.
This is a cased and cemented vertical technology well where a DFIT was pumped through a 4.5"
monobore completion at 6.5 bpm through a 3-meter perforation interval. The test took place several months
after well construction was finished, allowing the completion fluid to heat up to reservoir temperatures of
160ºC. A change in temperature of this magnitude will result in a change of viscosity from 1 to 0.19 cp
for a 2% KCl completion fluid (Marc Laliberte, 2007 ). The pressure fall off analysis shows a PDL closure
mechanism with an estimated minimum stress of 9,844 psi, a PZS of 763 psi and a Gperm of 0.012 mD


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and a as presented in Fig. 14.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 23
Figure 14— DFIT Gplot interpretation and Gperm calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
The after-closure pressure transient goes into pseudo-linear flow giving an estimate of pore pressure of
7,130 psi. The Talley-Nolte plot confirms the correct estimation of pore pressure by the identified half slope
of the pressure derivative and the pressure difference curves that are separated by a difference of 2x in
magnitude as shown in Fig 15 .
Figure 15— Pseudo-linear flow function and Talley-Nolte plots. Linear time flow function: Blue curve
is bottom hole pressure. Talley-Nolte Plots: Blue curve is delta pressure, green is the log derivative curve .
After the DFIT was finished, the well was closed for more than twelve months to evaluate the evolution
of bottom and well head pressures. As shown in Fig. 16 , thermal effects can be seen clearly on both gauges,


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still an average reservoir pore pressure of 7,030 psi (485 Bar) can be realized (~ 1% difference with the
ACA estimation that is within the measuring error).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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24 SPE-206239-MS
Figure 16—Bottom hole and surface pressure measurements (Bar).
Scratch tests were utilized to optimize the number of plugs and the regions to be analyzed to get a
representative elastic behavior of the reservoir. The fracture model was calibrated with a mineralogical
model constrained with XRD measurements (Track 1 and 2 in Fig. 17.A ), triaxial mechanical tests (Track
3 in Fig. 17.A ) and the interpreted DFIT information in the area indicated by a black arrow on track 4
in Fig 17.A . The pressure-match model suggests a fracture height development between 2 to 3 meters as
presented in Fig. 17.B .
Figure 17.A—Mineralogy, Rock Physics, Pore Pressure and 1DMEMDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 25
Figure 17.B— Pressure match geometry and net pressure plot. Blue Curve: Measured
well bottom hole pressure Black Curve: Modeled well bottom hole pressure Red curve: Frac rate .
If one utilizes the estimated fracture height from the pressure match model and anchor the estimated pore
pressure in a pseudo-radial flow function, an upper bound on the contacted permeability between 0.025 to
0.037 mD can be estimated (Fig. 18 ). This upper bound on the contacted permeability is consistent with the
Gperm estimated 0.012 mD that was implemented in the pressure-match model related to the time required
to reach fracture closure.
Figure 18—Pseudo-radial flow function permeability sensitivity (anchored pore pressure).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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26 SPE-206239-MS
The pressure match shown in Fig. 17.B  was achieved by implementing an iterative process until the
modelled pressure converged to provide the same fracture closure mechanism, minimum stress, time to
reach closure and after-closure pressure transient dissipation in the host rock as shown in the original DFIT
(as shown in Fig. 19.A  and Fig 19.B).
Figure 19.A—DFIT vs simulated DFIT Gplot . Blue curve is bottom hole
pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 27
Figure 19.B— DFIT vs simulated DFIT after closure analysis . Linear time flow function: Blue curve
is bottom hole pressure. Talley-Nolte Plots: Blue curve is delta pressure, green is the log derivative curve .
The analysis described in the previous paragraphs supports a consistent relationship between the
permeability estimates from traditional DFIT fracture closure time, numerical inversions and after-closure
analysis. This in turn proves that the interpreted time to reach fracture closure during the DFIT test occurs
after its linear leak off period as stated by traditional interpretation techniques.
Case 4: Moderate Permeability, Gas and Condensate Sandstone
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical inversion
built on permeability estimates based on fracture closure time that is consistent with after closure analysis,
PBU and RTA assesments. The fracture closure pressure will be validated through multiple injections fall


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off analysis, proving that there is a direct relationship between the estimated permeability and the time it
takes to reach fracture closure after the linear leak off period of the DFIT.
This well was treated down a 2 7/8" tubing and a large perforated interval, through which a DFIT, mini-
frac and 230 tons treatment was pumped at an average rate of 23 bpm. The DFIT pumped on this well shows
a PDL closure mechanism with an estimated minimum stress of 9,196 psi, a PZS of 333 psi and a Gperm
of 1.42 mD as presented in Fig. 20.A. The change in slope in the log-log plot was utilized to support the
interpreted Gplot minimum stress values (marked with a black arrow in Fig. 20.B).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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28 SPE-206239-MS
Figure 20.A—DFIT Gplot interpretation and Gperm calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
Figure 20.B— DFIT log-log plot  Blue curve is Delta Pressure, green is first derivative curve (dDP/dDT), red curve is (DT* dDP/dDT).
The DFIT estimated minimum stress was additionally confirmed by a mini-frac injection that changed the
closure mechanism from PDL to transverse storage due to the additional energy transferred to the rock by
the crosslinked fracturing fluid (presented in Fig. 21.A). The analysis shows one is dealing with a stiffening
system where the net pressure (PZS) changes with continuous injection, having a PZS difference of almost
600 psi between the DFIT and mini-frac injections. It is worth mentioning that when utilizing traditional
fracture pressure interpretation techniques, the interpreted stress can be identified in a consistent manner


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across multiple injections. If the fracture compliance method is utilized to select the minimum stress, no
consistent interpretation can be made by having almost 700 psi difference between the DFIT (9,196 psi) andDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 29
mini-frac estimates (9,884 psi) (shown in Fig. 21.B). In this case the compliance closure becomes higher
than the fracture pressure (ISIP) of the DFIT, making this minimum stress estimation unrealistic.
Figure 21.A— Mini-frac Gplot interpretation – Traditional fracture closure estimate . Blue
curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .
Figure 21.B—Mini-frac Gplot interpretation–Compliance closure estimate. Blue
curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
The after-closure pressure transient goes into pseudo radial flow giving an estimated pore pressure of ~
8,400 psi ( Fig. 22 ). The Talley-Nolte plot shows that the pressure difference between the fall off pressure
and the estimated pore pressure from the analysis has a negative unit slope that coincides with its logarithmic
derivative during the identified pseudo-radial flow period, supporting the validity of the analysis. The


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pressure match model suggests a fracture height of 16 meters (Fig. 23) that is incorporated in the calculated
after-closure transmissibility giving a permeability estimate of 2 mD.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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30 SPE-206239-MS
Figure 22— DFIT After closure pseudo-radial flow function and Talley-Nolte plots. Linear time flow function:
Blue curve is bottom hole pressure. Talley-Nolte Plot: Blue curve is delta pressure, green is the log derivative curve.
Figure 23— DFIT pressure-match model – Net pressure plot Blue Curve: Measured well
bottom hole pressure. Black Curve: Modeled well bottom hole pressure. Red Curve: Frac rate.
The fracture model was calibrated with DFIT data and, while accounting for the natural fractures leak
off, a reasonable pressure-match obtained by slightly increasing the permeability to 1.65 mD ( Fig. 23 ). The
difference between the Gperm (1.4 mD), pressure match (1.65 mD) and after closure permeability estimates
(2 mD) are within acceptable measurement accuracy.
The DFIT numerical inversion yields the same closure mechanism, time to reach closure, minimum stress


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and after-closure pressure transients as the actual measured data (as shown in Fig. 24 ).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 31
Figure 24.A—DFIT vs simulated DFIT Gplot . Blue curve is bottom hole
pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .
Figure 24.B— DFIT vs simulated DFIT Gplot and after closure analysis . Linear time flow function: Blue
curve is bottom hole pressure. Talley-Nolte Plot: Blue curve is delta pressure, green is the log derivative curve.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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32 SPE-206239-MS
A 230-ton 35# xlinked fracture treatment pumped at an average of 23 bpm was pressure-match, obtaining
a propped fracture length of 230 meters and height of 43 meters as shown in Fig 25.
Figure 25— Main fracture treatment pressure-match fracture geometry – Proppant concentration plot Blue curve: Measured well
bottom hole pressure Black curve: Modeled well bottom hole pressure Red curve: Frac Rate Brown-green curves: Slurry proppant concentration
After the cleanup phase of the main fracture treatment, a PBU test was performed providing a contacted
permeability of 1.27 mD, a pore pressure of 8,340 psi and an estimated fracture flowing length of 55 meters.
For this analysis, the fracture height was assumed to be 50 meters in comparison to the pressure match
fracture contacted net pay of 43 meters. If this latter is utilized to calculate the contacted permeability
through the estimated 63.5 mD*meters kh, an estimated flowing capacity of 1.47 mD is obtained (as shown
in Fig. 26 ).


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in Fig. 26 ).
Figure 26—Main fracture treatment - Pressure build up interpretation
A RTA analysis was performed based on a 12-month production history gathered after the main fracture
treatment took place (presented in Fig 27). The main treatment pressure-match fracture height of 43 meters
was utilized in the analysis, providing a contacted average permeability of 1.33 mD (57.8 mD*meters) and
an infinite flowing fracture half length dimension of 0.04 meters (0.13 feet).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 33
Figure 27—Main fracture treatment-Rate transient analysis interpretation
Information about the reservoir architecture obtained from the RTA was incorporated into the production
model of the fracture geometry simulator software that accounts for the modelled fracture geometry,
proppant packs physical behaviours and the reservoir properties described in the DFIT calibrated fracture
grid. The early clean up phase is not matched by both models since the water injected during the treatment
is not accounted for in the analysis. The modelled fracture geometry contacted an average of 1.4 mD and
was able to match the production history of the well, suggesting flowing fracture lengths between 49 and
56 meters that can be translated into an infinite fracture length of ~0.3 meters (as presented in Fig. 28).
The estimated infinite flowing dimension from the frac production model of 0.2-0.3 meters is consistent


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with the RTA estimated infinite fracture flowing dimension of 0.04 meters (0.13 ft), sustaining the large
pressure drop in the proppant pack is related to non-Darcy flow. During the early production period, the frac
production model estimates a frac length of 49 meters while the PBU suggests a flowing length in the order
of 55 meters. The PBU and production based flowing dimensions are consistent with each other, since the
PBU estimated length should be larger than the ones estimated during production due to not accounting for
turbulent pressure drops ( Barree, et al., 2005 ).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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34 SPE-206239-MS
Figure 28—Frac geometry production model
The analysis described in the previous paragraphs provided a converging solution that is consistent
with multiple tests utilized to calibrate and understand the production performance of this well. The
analysis supports a consistent relationship between the permeability estimates from traditional DFIT fracture
closure time, DFIT numerical inversions, after-closure analysis, PBU and RTA. This in turn proves that the
interpreted time to reach fracture closure during the DFIT test occurs after its linear leak off period as stated
by traditional interpretation techniques.
Comparison of DFIT and mini-frac pressure transients shows how traditional closure interpretation
techniques can be utilized to properly assess the minimum stress when having different closure mechanisms.
Instead, if the fracture compliance methodology is employed, differences of up to 700 psi can be assessed
between different tests minimum stress estimations.


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between different tests minimum stress estimations.
Case 5: Low Permeability, Gas Sandstone – Drained Reservoir
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical inversion
built on permeability estimates based on fracture closure time that is consistent with PBU and RTA
assesments. The fracture closure pressure will be validated through multiple injections fall off analysis,
proving that there is a direct relationship between the estimated permeability and the time it takes to reach
fracture closure after the linear leak off period of the DFIT.
This is a vertical gas well with a 30º inclination produced for several months through a single perforated
interval before fracture stimulating it. PBU data was used to assess the original pore pressure and flowing
capacity of this interval. As it is often the case with complicated test behaviors, various interpretation


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models could match the pressure and rate data. From the possible heterogeneity arrangements investigated,Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 35
a constant permeability model of 0.55 mD was interpreted (shown in Fig 29). The analysis also supported
the possibility of having improved reservoir properties far away from the well.
Figure 29—Pressure build analysis
Historical production and downhole gauge pressures were utilized to build an RTA model. As shown
in Fig. 30 , the analysis supports a developing asymmetric drainage area with an average permeability of
0.52 mD which is further supported by the latest geological and dynamic modelling performed by the field
Reservoir Engineering Team ( Veccia, 2016).
Figure 30—Pre-frac rate transient analysisDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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36 SPE-206239-MS
The dynamic model forecasted production was compared to the predictions of the RTA model, showing
a high degree of correspondence. Slight differences in the late time forecasted production are related to the
drainage defined within geological model used within the dynamic simulation and an extended drainage
that was not able to be predicted by RTA since no boundary influenced flow was reached at the time
the analysis was performed (as presented in Fig. 31.D). Due to not having an understanding of the stress
conditions on this interval, the forecasted pore pressure at the time the fracture treatment should take
place was combined with litho-based rock mechanical properties to create multiple 1DMEMs within an
expected range of tectonic boundaries. Multiple fracture geometries were evaluated under a wide range of
possible state-of-stress conditions, several fracture designs were optimized, and their associated production


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performance modelled to assess possible economic outcomes of the operation ( Fig. 31.A., Fig. 31.B , Fig.
31.C  and Fig. 31.D ).
Figure 31.A—Litho-based rock mechanical properties Fig 31.B: Fracture optimization analysis Fig 31.C: Litho-
based 1DMEM sensitivity analysis Fig 31.D: Production forecasts – with and without fracture treatment.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 37
The estimated pore pressure at the time of fracturing provided by dynamic and RTA solutions is ~ 4,100
psi. The validity of the prediction was assessed through an updated RTA analysis performed based on newly
acquired production data. The analysis supports an average reservoir pressure of 4,080 psi and the presence
of an increased permeability in the late time data supported by the presence of improved reservoir properties
far away from the well as suggested by PBU tests (marked with a black circle in Fig. 32). This latter
represents an upper bound estimate on the average reservoir pressure considering the last production period
cannot be properly matched (the actual average reservoir pressure should be lower than this estimate).
Figure 32—Updated rate transient analysis and Linear flow analysis plot
The DFIT pseudo-linear flow plot indicates a pore pressure of 4,019 psi which is consistent with the


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updated RTA model shown in Fig. 32 and within the expected range of the original predictions of the
production models.
The DFIT analysis provided a minimum stress range between 5,312 and 5,412 psi. As shown in Fig. 33,
the fast fracture closure makes the calculation of the area above the linear leak off conditions and fissure
leak off coefficient difficult to estimate since the data is affected by the water hammer effect.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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38 SPE-206239-MS
Figure 33— DFIT ISIP and G plots – Fracture pressure and minimum stress estimation ISIP Plot: Blue curve is well head
pressure; green is fracturing rate. Gplot: Blue curve is bottom hole pressure; green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
A Gperm sensitivity analysis was performed and the Rp value changed within a range of 1 to 1.3 that
represents the transition from a linear to pressure depend leak off closure mechanism conditions. The
analysis gives an estimated average Gperm of 0.281 mD for the range of minimum stresses evaluated as
shown in Fig. 34 :Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 39
Figure 34—Gperm flowing capacity evaluation
The DFIT minimum stress range was verified by a mini-frac injection that changed the closure mechanism
from pressure dependent leak off (PDL) to transverse storage. The analysis also supports a change in the
fracture pressure with injection that might be related to a stiffening system with continued injection with
a thicker fracturing fluid. In this case, a range is presented since both closure pressures may be estimated
depending on how the gauge pressure is smoothed out.
Figure 35— Minifrac Gplot – Minimum stress evaluation Blue curve is bottom
hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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40 SPE-206239-MS
The average Gperm value is within acceptable measurement accuracy and considered consistent when
compared to PBU and RTA estimations. What is important to notice is that by utilizing traditional
interpretation techniques, independent of the fracture closure mechanism present, the interpreted minimum
stress is exactly the same. As shown in Fig. 36 , if the fracture compliance method is utilized to select the
minimum stress, no consistent interpretation can be made by having almost 900 psi difference between the
DFIT (5,312 psi) and mini-frac estimates (6,191 psi). In this case the compliance closure becomes higher
than the fracture closure pressure of the DFIT, making this minimum stress estimation unrealistic.
Figure 36— Minifrac ISIP and G plots – Fracture compliance closure ISIP Plot: Blue curve is well head pressure; green
is fracturing rate. Gplot: Blue curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).


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The DFIT log-log plot shows a consistent pseudo-linear and an invalid pseudo radial flow pattern that has
been affected by the well annulus pressure (marked with a black circle in Fig. 37 annulus pressure trends).
The annulus pressure affects the surface pressure and bottom hole gauge in different manners. The log-log
plot made from surface data shows a negative slope larger than -1 (physically impossible) while the log-
log plot from bottom hole pressure measurements is flattened out (marked with a black circle on Fig. 37
log-log plots).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 41
Figure 37— Annulus pressure affecting pressure transient  Treating pressure in orange: Annulus pressure (psi).
Log-log plots: Blue curve is Delta Pressure, green is first derivative curve (dDP/dDT), red curve is (DT* dDP/dDT).
The pseudo-linear flow function gives an estimated pore pressure of 4,019 psi, supported by a consistent
Talley-Nolte Plot. This latter confirms the presence of a linear flow period by the identified half slope of
the pressure derivative. When estimated pore pressure is correct, the pressure difference curve will also fall
on a half slope and be 2x higher in magnitude than the derivative as shown in Fig. 38.
Figure 38— After-closure analysis  Linear time flow function: Blue curve is bottom hole
pressure. Talley-Nolte Plot: Blue curve is delta pressure; green is the log derivative curve .
The simulation grid is updated based on the DFIT interpretation and the test is pressure-match assuming


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a minimum stress of 5,313 psi. Fig. 39 shows the measured vs the modelled pressure, where the minimum
stress and the late time pressure transient is relative consistent with the measured data but the early time
after closure transient is difficult to match.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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42 SPE-206239-MS
Figure 39— Pressure match vs fracture geometry net pressure plot Blue curve: Measured
well bottom hole pressure Black curve: Modeled well bottom hole pressure Red curve: Frac rate .
In order to properly calibrate the fracture model and assess its validity, a numerical inversion was
performed through the pressure-match model. The numerical model provides the same fracture pressure,
minimum stress and pore pressure estimates as the measured fall off data. The only difference is a slight miss
match in the time required to reach closure within the model, having the fracture closed within 3 minutes
instead of almost 2 minutes (Fig. 40.A and Fig. 40.B). This indicates that the permeability might be slightly
higher than 0.281 mD as suggested by PBU and RTA.
Figure 40.A—DFIT vs simulated DFIT Gplot . Blue curve is bottom hole


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pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 43
Figure 40.B— DFIT vs simulated after closure analysis . Linear time flow function: Blue curve is
bottom hole pressure. Talley-Nolte Plot: Blue curve is delta pressure; green is the log derivative curve .
Furthermore, even with an increased permeability, the early time fall of pressure is difficult to match.
This seems to be due of the relative position of the well and the grid that is cut at 30º, affecting the near-
wellbore leak off calculations or due to actual crossflow between different perforated layers. Independent
of this, when combining different measurements of permeability, pore pressure and stress one realizes that
the differences are negligible.
The pressure-match DFIT shows that the created fracture has a fracture length in the order of 100 meters
(investigated reservoir volume), giving permeability estimates within the range of the early time PBU and
RTA estimates. The late time RTA suggest production contributions from an improved permeability region


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as discussed in previous paragraphs. Production history after fracture stimulating this interval was gathered
for eight months and analyzed, showing an RTA average permeability of 0.75 mD as shown in Fig. 41 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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44 SPE-206239-MS
Figure 41—Post-frac rate transient analysis
The analysis described in the previous paragraphs supports a consistent relationship between the
permeability estimates from DFIT fracture closure time, DFIT numerical inversions, PBU and RTA. This in
turn proves that the interpreted time to reach fracture closure during the DFIT test occurs after its linear leak
off period as stated by traditional interpretation techniques. Comparison of DFIT and mini-frac pressure
transients shows how traditional closure interpretation techniques can be utilized to properly assess the
minimum stress when having different closure mechanisms. Instead, if the fracture compliance methodology
is employed, differences of up to 900 psi can be realized between minimum stress estimations which makes
this methodology unrealistic.
Case 6: Low Permeability, Gas Sandstone
In this case history, traditional minimum stress interpretations are supported by a DFIT numerical inversion


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built on permeability estimates based on fracture closure time that is consistent with after closure analysis,
core, production modelling estimates and PLT data.
This well was treated down a 4.5" monobore completion, through which a set of DFIT, mini-frac and two
~200-tons treatments were pumped at an average rate of 35 bpm. The Gplot of the first diagnostic injection
pumped on this well accounts for a possible early time PDL, followed by a transverse storage signature
(sometimes called "height recession") and a linear leak-off profile across the created surface before fracture
closure is attained. The test interpretation provided an estimated minimum stress of 9,312, PZS of 1,002 psi
and a Gperm of 0.69 mD as presented in Fig. 42 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 45
Figure 42— DFIT Gplot interpretation and Gperm calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
The early time period does not seem to be related to a PDL signature related to a certain type of natural
fractures, instead this shape of the derivative is affected by fluid decompression due to the high tortuosity
the system has in place at the time this test was pumped. It is important to mention that one may or may
not have a PDL mechanism in place but is not possible to assess it due to fluid decompression affecting the
early time pressure transient. The transverse storage portion of the fall off pressure is most likely due to the
presence of secondary fractures (joints) that can provide pressure support to the main fracture body during
the fracture closure process and not to height recession.
Fig. 43 presents a log-log plot of the fall off pressure minus the Instantaneous Shut-In Pressure (ISIP)


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and its derivatives. There is a clear break of the delta pressure superposition curve that is consistent with
the identified closure and a pseudo radial flow period in the late portion of the pressure transient identified
by a negative slope of 1.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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46 SPE-206239-MS
Figure 43—Diagnostic injection log-log plot . Blue curve is Delta Pressure,
green is first derivative curve (dDP/dDT), red curve is (DT* dDP/dDT).
Fig. shows the pseudo-radial plot utilized to estimate the pore pressure and the permeability of the
contacted reservoir by employing traditional after closure techniques (Talley et al., 1999). The analysis
produced an estimated pore pressure of 6,269 psi that was consistent with MDT pressure measurements
and a contacted permeability between 0.66 to 0.55 mD depending if the assumed fracture height is 4 or 5
meters as suggested by the pressure-match model.
Figure 44— Diagnostic injection after closure analysis pseudo-
radial plot. Radial flow time function: Blue curve is bottom hole pressure.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 47
The permeability calculated based on the time required for the fracture to close on its faces provides the
same estimate as the one obtained when utilizing traditional after closure techniques. The Talley-Nolte plot
was constructed to verify the validity of the pseudo-radial flow period and the calculated pore pressure. Fig.
45 shows that the pressure difference between the fall off pressure and the estimated pore pressure from the
analysis has a negative unit slope that coincides with its logarithmic derivative during the identified pseudo-
radial flow period, supporting the validity of the analysis.
Figure 45— Diagnostic injection Talley-Nolte plot Talley-Nolte Plot: Blue curve is delta pressure, green is the log derivative curve.
The fracture model was calibrated with triaxial mechanical tests and the interpreted DFIT information
that allowed to consistently pressure-match the test as shown in Fig. 46.
Figure 46— Diagnostic injection pressure fall off match . Blue curve: Measured


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well head pressure. Black curve: Modeled well head pressure. Red curve: Frac rate.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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48 SPE-206239-MS
The DFIT was modelled in an iterative manner until the pressure-match model could reproduce a pressure
response that has the same G-function signature/shape, closure pressure, closing time and after-closure
pressure transient through the implementation of a properly calibrated grid (Buijs, et al., 2020). Fig. 47
shows consistent DFIT and numerical DFIT Gplots.
Figure 47— DFIT vs simulated DFIT Gplot. Blue curve is bottom hole
pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG) .
The permeability function utilized to simulate the created fracture geometries was built based on estimates
from fracture closure time and after closure analysis of pre-frac tests. The permeability model was then
superposed over the core based flowing phase permeability model showing that the function is consistent
with an independent estimate of the flowing capacity of this reservoir based on laboratory data (track 2,


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Fig. 48.A )Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 49
Figure 48.A—PHIE vs DFIT-flowing phase core perm.
When calibrating the permeability model on stage 1 (marked with a green "x" on track 2 in Fig. 48.A), the
same function was able to predict the contacted permeability by the pre-frac tests of stage 2. The predictive
power of the function developed supports that both intervals went through the same diagenetic processes
affecting the evolution of permeability through geological times.
Fig. 48.B  shows a comparison of the rock mechanical properties and 1D litho-based stress model with the
3D property cube output generated at this well position. The after-closure pressure estimations from both
pre-frac tests (marked as red points on track 2 in Fig. 48.B) were consistent with the multiple open-hole MDT
measurements (marked as black circles). The lithology constrained 1DMEM of the Well (Stress_Total_G4)
was calibrated with the interpreted data from the pre-frac tests of stage 1 and could predict the interpreted


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closure points measured at stage 2 (marked with black squares on track 2 in Fig. 48.B).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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50 SPE-206239-MS
Figure 48.B—1D-3D litho-based 1DMEM and pore pressure model -
An iterative process within the modelled fracture geometries, RTA and a production model that accounts
for the physical behaviours of proppant packs allowed to estimate the end of well life and EUR within 5%
of the P50 case provided by dynamic simulations performed by the reservoir engineering team ( Fig. 49.A).
The model was also instrumental in predicting the PLT back allocated production that was not provided
for the analysis and was utilized by the operating unit to test the predictive capabilities of the implemented
workflow. Fig. 49.B  shows the production percentage modelled for each stage next to the PLT results,
showing a perfect match (80% of the overall production comes from stage 2 and 20% from stage 1).
Figure 49.A—RTA vs Frac geometry production models.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 51
Figure 49.B—Frac geometry back allocated production vs PLT.
When utilizing the fracture compliance method, a fast closure is achieved, providing an estimated
minimum stress of 10,094 psi, a PZS of 222 psi and a Gperm of ~4 mD as shown in Fig. 50.
Figure 50— DFIT Gplot interpretation and Gperm calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
A low net pressure or PZS, in the range of 20% of the traditional techniques’ estimates ( Fig. 42), is
translated into being able to apply just ~200 psi to deform the rock and create fracture width. At the same
time, when modelling the associated fracture geometry, the simulated fracture height will tend to be much
larger than the estimates presented in this analysis since the rock becomes easier to break (presented in Fig.
46). If we utilize this large fracture height in the pseudo-radial after-closure analysis, the estimated contacted


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permeability will be much lower than 0.55 mD (as shown in Fig. 44) becoming smaller than the flowingDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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52 SPE-206239-MS
phase estimated permeabilities based on core and inconsistent with the compliance Gperm estimates of ~4
mD ( Fig. 50 ).
The analysis described in the previous paragraphs provided a converging solution that is consistent with
multiple tests utilized to calibrate and understand the production performance of this well. The analysis
supports a consistent relationship between the permeability estimates from DFIT fracture closure time, after-
closure analysis, DFIT numerical inversions, core and RTA (Buijs, et al., 2020). This in turn proves that
the interpreted time to reach fracture closure during the DFIT test occurs after its linear leak off period as
stated by traditional interpretation techniques.
On the other hand, the compliance-based fracture closure technique has proven to be inconsistent with
multiple assessments of permeability, will have a clear effect in the contacted net pay and the conductivity of


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the simulated fracture geometry upsetting the predictive capabilities of any modelling workflow. Without a
clear understanding on the permeability, fracture pressure and minimum stress, it is not possible to properly
model the associated fracture geometry of the treatments pumped on this well and, regretfully, implement
any meaningful completion optimization.
Case 7: Low Permeability, Gas and Condensate Sandstone
In this case history, traditional minimum stress interpretations are supported by fracture models built on
permeability estimates based on DFIT fracture closure time that is consistent with PBU and production
modelling estimates. This well was treated down a 2 7/8" tubing and a large perforated interval, through
which a DFIT, mini-frac and 335 tons treatment was pumped at an average rate of 24 bpm.
The DFIT pumped in this well shows a transverse storage closure mechanism with an estimated minimum
stress of 9,487, a PZS of 354 psi and a Gperm of 0.364 mD as shown in Fig. 51 .


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Figure 51— DFIT Gplot Interpretation and Gperm Calculation Blue curve is
bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 53
The pseudo-linear flow function provides an estimated pore pressure of 8,568 psi which is consistent
with the Talley-Nolte plot presented in Fig. 52 . The onset of a pseudo-radial flow regime was affected by the
annulus pressure fluctuations and could not be utilized to assess the reservoir flowing capacity (indicated
with a black arrow in Fig 52).
Figure 52— DFIT after closure pseudo-linear flow function and Talley-Nolte plots . Radial flow time function:
Blue curve is bottom hole pressure. Talley-Nolte Plot: Blue curve is delta pressure, green is the log derivative curve.
The DFIT pressure match was achieved with an average permeability of 0.55 mD that accounts for the
natural fractures pressure dependent leak off (as presented in Fig. 53).
Figure 53—DFIT pressure-match model – Net pressure plot . Blue curve:


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Measured well bottom hole pressure Black curve: Modeled well bottom hole pressureDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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54 SPE-206239-MS
A 335-tons treatment pumped with a 35# crosslinked fluid is pressure-match, obtaining a propped fracture
length of 250 meters and height of 45 meters as indicated in Fig. 54 . The model suggests that almost 40% of
the perforations did not accepted proppant which was consistent with the PLT spinner data that supported
flow from this exact same interval.
Figure 54— Main fracture treatment pressure-match – Proppant concentration plot. Blue curve: Measured well bottom hole
pressure Black curve: Modeled well bottom hole pressure Red Curve: Frac rate Brown-green curves: Slurry proppant concentration.
After 3 months of production, a PBU test was performed providing a contacted permeability of 0.492
mD, a pore pressure of 8,120 psi and an estimated fracture flowing length of 48 meters. For this analysis,
the fracture height was assumed to be 50 meters in comparison to the pressure match fracture contacted net


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pay of 45 meters. If this latter is utilized to calculate the contacted permeability through the estimated 24.6
mD*meters kh, an estimated flowing capacity of 0.54 mD is obtained (Fig. 55).
Figure 55—Main fracture treatment - Pressure build up interpretationDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 55
A RTA analysis is performed based on an 8-month production history gathered after the main fracture
treatment took place (Fig. 56 ). The main treatment pressure-match fracture height of 45 meters was
utilized in the analysis, providing a contacted average permeability of 0.62 mD (28.36 mD*m) and an
infinite flowing fracture half length dimension of 0.004 meters (0.016 feet). This well is produced through
a production manifold connected to 4 additional wells, slight variations between actual and estimated
production are to be expected.
Figure 56—Main fracture treatment - Rate transient analysis interpretation
Information about the reservoir architecture obtained from the RTA is incorporated into a production
model that accounts for the modelled fracture geometry, physical behaviours of proppant packs and
the reservoir properties described in the DFIT calibrated fracture grid. The simulated fracture geometry


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contacted an average of 0.5 mD based on a DFIT-calibrated model and is able to match the production
history of the well, suggesting a flowing fracture in the order of 36 meters that can be translated into an
infinite fracture length of 1 meter (Fig. 57).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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56 SPE-206239-MS
Figure 57—Frac geometry production model.
The estimated infinite flowing dimension from the frac production model of 1 meter is consistent with
the RTA estimated infinite fracture flowing dimension of 0.004 meters, sustaining the large pressure drop
in the proppant pack is related to non-Darcy flow. During the early production period, the production model
estimates a frac length of 36 meters that is consistent with a PBU estimated flowing length in the order
of 48 meters.
When utilizing the fracture compliance method, a minimum stress of 9,775 psi, a PZS of 66.8 psi and a
Gperm of ~0.8 mD can be interpreted as presented in Fig. 58 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 57
Figure 58— DFIT Gplot fracture compliance interpretation and Gperm calculation  Blue
curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
Among other inconsistencies, as mentioned in previous case histories, the compliance based low PZS (net
pressure) will tend promote a larger fracture height growth on this well. To illustrate this, the 1DMEM and
PZS grids from the fracture model are presented, defining the fracture pressure (ISIP) as the minimum stress
plus the PZS or net pressure of the DFIT test interpreted with traditional techniques (shown in Fig. 59).
Figure 59—Traditional closure: Litho-based 1DMEM and PZS models.
Under the modeled state-of-stress conditions, fracture height growth is dominated by the PZS model.


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As indicated by the red arrows in Fig. 59, fracture is contained within layers accounting for a PZS of 800Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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58 SPE-206239-MS
to 1,000 psi (marked with red boxes in Fig. 59 ). When the mentioned PZS magnitudes are added to the
minimum stress at the same depth, this is translated into a fracture pressure of 10,900 psi that the fracture
treatment cannot break through (marked with yellow boxes in Fig. 59). The lower perforated area cannot
be fractured due to the large PZS between 1,000 to 1,300 psi that are translated into fracture pressures in
the order of 11,000 to 11,300 psi (marked with white arrows in Fig 59 ).
When utilizing the compliance based PZS to constrain this model, the mentioned PZS values will decrease
to 150 and 180 psi respectably (~18% of traditional PZS value). In turn, to match the interpreted fracture
pressure, the increased minimum stress model will tend to have a similar stress distribution to the traditional
closure 1DMEM. When reducing the PZS to such low values (~66 psi), the fracture treatment will be allowed


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to grow more in height and contact additional net pay. When this additional fracture height growth of the
main treatment is combined with the high compliance based Gperm, the contacted kh by the fracture model
will be too large to explain the production behavior of this well and become inconsistent with the PBU
results. This example also explains why it is so important to properly interpret DFITs since not being able
to pick the right fracture closure pressure will tend to have a considerable effect on the modelled fracture
geometries, hydraulic fracture design and completion optimization.
The traditional fracture closure analysis described in the previous paragraphs provided a converging
solution that is consistent with multiple tests utilized to calibrate and understand the production performance
of this well. The analysis supports a consistent relationship between the permeability estimates from DFIT


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fracture closure time, PBU and RTA. This in turn proves that the interpreted time to reach fracture closure
during the DFIT test occurs after its linear leak off period as stated by traditional interpretation techniques.
Case 8: High Permeability, Gas Sandstone – Drained Reservoir
This is a high permeability vertical gas well that had a large skin of in the order of ~10 based on its PBU
interpretation. A flowing capacity model was build based on an effective porosity correlation to permeability
that is consistent with the PBU flowing capacity, averaging ~22 mD (Fig. 60.A and Fig. 60.B). This is a
special case where damage was difficult to remove through acidizing based on previous experiences, making
fracturing the most convenient solution to increase well economics.
Figure 60.A—Pressure build up analysis.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 59
Figure 60.B—PBU Permeability model.
During the DFIT, completion fluid was pumped for 12 minutes obtaining a minimum stress of 7,230 psi,
a PZS of 1,271 and a Gperm of 0.538 mD psi ( Fig. 61 ).
Figure 61—DFIT Gplot – Gperm calculation.
The prefrac test had surface and bottom hole gauges that were utilized to track the evolution of the
pressure transient, showing a stabilized late time bottom-hole pressure that is consistent with the PBU
interpretation.
When doing the pressure match of the test, the Gperm estimate of 0.538 mD shown in Fig. 59  could not
be utilized to explain the way pressure was behaving. In that respect, as shown in Fig. 62, the DFIT was
pressure-match by utilizing the PBU reservoir pressure and permeability model shown in Fig. 60.B.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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60 SPE-206239-MS
Figure 62— DFIT Pressure match – Fracture geometry net pressure plot . Red curve: Measured well head pressure Black
curve: Modeled well head pressure Brown curve: Measured well bottom hole pressure Blue curve: Modeled well bottom hole pressure
The DFIT and the pressure-match numerical inversion provide the same closure mechanism, net pressure,
minimum stress and after closure pressure transients (Fig. 63).
Figure 63—DFIT vs Simulated DFIT Gplot.
Nevertheless, the estimated permeability based on closure time is not consistent with the PBU estimate
of ~22 mD utilized to model the fall off pressure. The reason for this inconsistency is related to the Gperm
function becoming insensitive to infer large permeabilities since it becomes nearly vertical on a log scale at


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fast closure times as shown by the marked orange area in Fig. 64 (Barree, 2020 ).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 61
Figure 64—Gperm vs Gtime@closure permeability estimates for a specific DFIT condition.
For reservoirs that require hydraulic fracturing to increase its production performance and become
economical, the relationship of the Gperm to Core, DFIT ACA, PBU and RTA estimates is remarkable.
Conclusions
This multi-basin study from the North Sea, Europe, Russia, North Africa and South America regions
demonstrated how a well-defined workflow can be implemented to reduce uncertainty to properly explain
fracture geometries and their associated production performance by integrating petrophysics, geomechanics,
DFIT, PBU, RTA and fracture geometry modelling.
Correct interpretation of pre-frac tests becomes critical to design effective hydraulic fracture treatments,
tap reservoir potential and maximize revenue. If the minimum stress is not estimated properly, fracture
geometry modelling results in unrealistic fracture height growth, proppant lateral coverage and proppant


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pack conductivities that will negatively affect any fracture optimization approach.
One of the key observations made since the inception of fracture diagnostic injections is that the pressure
decline after injection can be correlated to reservoir flow capacity. Multidisciplinary evaluation of reservoir
flowing capacities from DFIT after-closure analysis, core, PBU, and rate transient analysis show a consistent
range that correlates with permeabilities estimated based on time required to reach well established fracture
closure interpretations (Gperm). Consequently, this proves that the interpreted time to reach fracture closure
during any diagnostic injection occurs after its linear leak off period as stated by traditional interpretation
techniques.
Numerical inversions of DFIT can reproduce the same minimum stress, closure mechanism, time to reach
fracture closure and after-closure pressure transients further supporting the validity of the interpretation.


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Their assoacited litho-based 1DMEM and fracture geometry assessments provide consistent results with the
information delivered by multiple injections on different geomechanical benches, PLT, fiber optics, micro
seismic data, PBU and wells production performance.
The early-time fracture closure identification supported by the fracture compliance method was severely
tested against information provided by dozens of wells across multiple basins under a wide range
of permeability, pore pressure and state-of-stress conditions. Modelling the compliance-based fracture
geometries was avoided, instead its lack of validity was explained in detail by utilizing well observations,Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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62 SPE-206239-MS
consistent interpretations of fracture fall off tests, PBU, core data, litho-based 1DMEM predictive
capabilities, logging data, fiber optics, micro seismic data and simple fracture width calculations. The
supporting theory of the compliance closure methodology might be mathematically consistent with the way
fracture closure is described but is a physical process that cannot be reproduced in real fractures. Simply put,
verifying theoretical results by utilizing fracture models built on physics that assume the described theory
is real, does not constitute validation.
The fracture compliance methodology decouples the closure time and permeability relationship, leading
to utilize inconsistent estimations of the host rock flowing capacity and its state-of-stress which has a severe
impact in the modelled fracture geometries. The compliance-based permeability estimates related to the
time required for the fracture to close tends to be between 2 to 6 times larger than the one obtained when


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following traditional closure estimates. The estimated low net pressures cannot develop enough fracture
width to place fracture treatments without screening out and establishes limited fracture conductivities that
cannot be utilized to explain the production performance of multiple wells presented on this paper. This
latter also has a negative consequence in the modelled fracture heights that, when combined with large
frac closure based permeabilities, results in a large contacted net pay that becomes inconsistent with core
data, fiber optics, PLT, PBU and wells overall production performance. An additional proof of the lack
of physical meaning of the compliance closure can be realized when analyzing multiple injections where
traditional closure techniques can be employed to consistently interpret the minimum stress (even when
fracture closure mechanisms change) but, if the fracture compliance closure theory is utilized instead, large


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differences between the estimated stresses become visible. Regretfully, this theory is not only disagreeing
with Nolte's innovative work, but also has also proven to be incapable of explaining the production behavior
of multi-fractured wells in a consistent manner when integrating numerous fracture diagnostic technologies.
The best proof that exists about the validity of traditional closure estimates lies in our wells, having the oil
and gas industry utilizing this knowledge for decades to consistently improve the production performance
of multi-fractured wells. This would not have been attainable if one fails to understand the state-of-stress
and flowing capacity of the host rock that has a first-order dominant control on the success or failure of
a stimulation treatment.
Acknowledgements
The authors would like to thank Wintershall Dea GmbH and their respective operating units for their
support and permission to publish this paper. Special thanks are given to Antonio Bencic, Matthias


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Stollenwerk, Gunter Harms, Camiel van Soest, Tibor Toth, Jorge Ponce, Dr Barree and Dr Miskimins for
their contribution and large support given towards the publication of this paper.
Nomenclature
1DMEM : 1-dimensional Mechanical Earth Model
DFIT : Diagnostic Fracture Injection Test
DTC : Compressional travel time
DTC_RESIST : Resistivity based synthetic travel time
DTC_GR : Spectral Gamma Ray based synthetic travel time
TOC : Total Organic Carbon
G-function ≈ 2 × ((Time - Pumping Time)/Pumping Time) ^ 0.5
PHIE : Total Average Neutron-Density Porosity – Vlcay
PBU : Pressure Build Up Test
RTA : Rate Transient Analysis
YMES : Static Young Modulus
PR : Poisson's RatioDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/21ATCE/2-21ATCE/D021S036R006/2489405/spe-206239-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-206239-MS 63
ISIP : Instantaneous shut in pressure
bpm : Barrels per minute.
ppag : poung per added gallon.
Infinite
flowing
fracture half
length: Mathematical representation of a frac half length of infinite conductivity.
Flowing
fracture half
length: Maximum physical frac half length available to flow fluids.
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