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pressure as P
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


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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 
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


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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
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.


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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 
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


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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, 
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


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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 
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


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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, 
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


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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 
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


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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. 
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.


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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 
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:


key: chroma:document
string_value:
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


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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
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


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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
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


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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
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,


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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


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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/
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


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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
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


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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
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 ).


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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
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


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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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Darcy proved that the obtained water rates could not be the explained by just pressure differentials and pipe
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


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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
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


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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
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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contacted rock. This work also included the development of an empirical correlation to establish reservoir
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


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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 ).
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


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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.
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


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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,
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


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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
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


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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
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


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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.
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).


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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-
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-


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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
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


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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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Figure 2.B—Diagnostic injection pressure-match for well A, stage 1. Green Curve:
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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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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Figure 4.A— Compliance DFIT closure analysis for well A, stage 1. Blue curve is
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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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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information from multiple diagnostic injections, it was noticed that DFIT's pumped in zones with low
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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case, assuming pulse decay permeabilities can describe the shale matrix permeability, production behaviour
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


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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
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


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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
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


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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


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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
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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stress (red curve) and the overburden (black curve) tend to overlap. Under this condition, the fracture
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.


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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
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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the independent assessment of fracture geometry provided by micro seismic supporting events related to
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


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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).
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


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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
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


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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
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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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:
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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and Gperm estimates).
The difference in magnitude between the Gperm (0.046mD) and pseudo radial (0.16 mD) permeability
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


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(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
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 ).


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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
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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At the same time, when combining core permeability data and the early onset of pseudo radial flow, one
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,


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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.
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


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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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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)
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


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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
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


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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
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


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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
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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of bottom and well head pressures. As shown in Fig. 16 , thermal effects can be seen clearly on both gauges,
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,


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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
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


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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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fracture pressure interpretation techniques, the interpreted stress can be identified in a consistent manner
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


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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
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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The DFIT numerical inversion yields the same closure mechanism, time to reach closure, minimum stress
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


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through the estimated 63.5 mD*meters kh, an estimated flowing capacity of 1.47 mD is obtained (as shown
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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The estimated infinite flowing dimension from the frac production model of 0.2-0.3 meters is consistent
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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capacity of this interval. As it is often the case with complicated test behaviors, various interpretation
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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possible state-of-stress conditions, several fracture designs were optimized, and their associated production
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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The DFIT pseudo-linear flow plot indicates a pore pressure of 4,019 psi which is consistent with the
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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is fracturing rate. Gplot: Blue curve is bottom hole pressure, green is first derivative curve (Dp/DG), red curve is (G*Dp*/DG).
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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The simulation grid is updated based on the DFIT interpretation and the test is pressure-match assuming
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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higher than 0.281 mD as suggested by PBU and RTA.
Figure 40.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 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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RTA estimates. The late time RTA suggest production contributions from an improved permeability region
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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Case 6: Low Permeability, 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 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


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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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Fig. 43 presents a log-log plot of the fall off pressure minus the Instantaneous Shut-In Pressure (ISIP)
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.


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that allowed to consistently pressure-match the test as shown in Fig. 46.
Figure 46— Diagnostic injection pressure fall off match . Blue curve: Measured
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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with an independent estimate of the flowing capacity of this reservoir based on laboratory data (track 2,
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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was calibrated with the interpreted data from the pre-frac tests of stage 1 and could predict the interpreted
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).


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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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46). If we utilize this large fracture height in the pseudo-radial after-closure analysis, the estimated contacted
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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multiple assessments of permeability, will have a clear effect in the contacted net pay and the conductivity of
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.


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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 .
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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natural fractures pressure dependent leak off (as presented in Fig. 53).
Figure 53—DFIT pressure-match model – Net pressure plot . Blue curve:
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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the fracture height was assumed to be 50 meters in comparison to the pressure match fracture contacted net
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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the reservoir properties described in the DFIT calibrated fracture grid. The simulated fracture geometry
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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Under the modeled state-of-stress conditions, fracture height growth is dominated by the PZS model.
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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closure 1DMEM. When reducing the PZS to such low values (~66 psi), the fracture treatment will be allowed
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


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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, 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.


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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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function becoming insensitive to infer large permeabilities since it becomes nearly vertical on a log scale at
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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geometry modelling results in unrealistic fracture height growth, proppant lateral coverage and proppant
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


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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.
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


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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


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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
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


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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
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


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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
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


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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.
References
Barree, R. D. ( 1983 ). A Practical Numerical Simulator for Three-Dimensional Fracture Propagation in Heterogeneous
Media, SPE 12273 . Paper presented at the SPE Reservoir Simulation Symposium, San Francisco, California.
Barree, R.D.  and Mukherjee, H.  1996 . Determination of Pressure Dependent Leak Off and Its Effects on Fracture
Geometry. Presented at the SPE Annual Technical Conference and Exhibition. Denver, Colorado, 6-9 October.
SPE-36424-MS. http://dx.doi.org/10.2118/36424-MS .
Barree, R.D.  1998 . Applications of Pre-frac Tests in Fissured Reservoirs – Field Examples . Presented at the SPE Rocky


key: chroma:document
string_value:
Barree, R.D.  1998 . Applications of Pre-frac Tests in Fissured Reservoirs – Field Examples . Presented at the SPE Rocky
Mountain Regional/Low Permeability Reservoirs Symposium. Denver, Colorado, 5-8 April. SPE-39932-MS. http://
dx.doi.org/10.2118/39932-MS.
Barree, R.D.  and P. Ph. Winterfeld. 1998 . Effects of Shear P lanes and Interfacial Slippage on Fracture Growth and Treating
Pressures . Presented at the SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, 27-30 October.
SPE-48926-MS. http://dx.doi.org/10.2118/48926-MS .
Barree, R. D.; Cox, S.A. ; Barree, V . L., and Conway, M.W.. 2003 . Realistic Assessment of Proppant Pack Conductivity
for Material Selection. SPE-84306-PA presented at the SPE Annual Techn ical Conference and Exhibition. Denver,
CO. http://dx.doi: 10.2118/84306-PA.
Barree, R.D. , Cox, S.A. , Gilbert, J.V .  and Dobson, M. 2005 . Closing the Gap: Fracture Half Length from Design,


key: chroma:document
string_value:
Barree, R.D. , Cox, S.A. , Gilbert, J.V .  and Dobson, M. 2005 . Closing the Gap: Fracture Half Length from Design,
Buildup and Production Analysis. SPE Journal Production & Facilities, November 2005. SPE-84491-MS. http://
dx.doi: 10.2118/84491-MS .
Barree, R.D. ; Barree, V .L. and Craig, D.p.. 2009 . Holistic Fracture Diagnostics: Consistent Interpretation of Pre-frac
Injection Tests Using Multiple Analysis Methods. SPE Production & Operations 24(3):396-406. SPE 107877-PA.
http://dx.doi.org/10.2118/107877-PA .
Barree, R. D., Barree, V . L., and Craig, D.  2009 . Holistic Fracture Diagnostics: Consistent Interpretation of Pre-frac
Injection Tests Using Multiple Analysis Methods. SPE Production & Operations Journal. SPE-107877-PA. http://
dx.doi: 10.2118/107877-PA .
Barree, R. D., Gilbert, J. V . , and Conway, M.W. 2009 . Stress and Rock Property Profiling for Unconventional Reservoir


key: chroma:document
string_value:
dx.doi: 10.2118/107877-PA .
Barree, R. D., Gilbert, J. V . , and Conway, M.W. 2009 . Stress and Rock Property Profiling for Unconventional Reservoir
Stimulation. Presented at the SPE Hydraulic Fracturing Technology Conference held in The Woodlands, TX, 19-21
Jan. 2009. SPE-118703-MS. http://dx.doi: 10.2118/118703-MS.
Barree, R.D. , Conway, M.W., and Miskimins, J.L.  2014 . Use of Conventional Well Logs in Selective Completion Designs
for Unconventional Reservoirs . Presented at the SPE Western North American and Rocky Mountain Joint Regional
Meeting held in Denver, CO, 16-18 Apr. 2014. SPE-169565-MS. http://dx.doi: 10.2118/169565-MS.
Barree, R.D. , Miskimins, J.L. , and Gilbert, J.V .  2014 . Diagnostic Fracture Injection Tests: Common Mistakes, Misfires
and Misdiagnostics . SPE Western North American and Rocky Mountain Joint Regional Meeting. Denver, Colorado.
SPE 169539-MS. http://dx.doi: 10.2118/169539-MS.


key: chroma:document
string_value:
SPE 169539-MS. http://dx.doi: 10.2118/169539-MS.
Barree, R.D. , Cox, S.A. , Miskimins, J.L., and Gilbert, J.V . 2014 . Economic Optimization of Horizontal Well Completions
in Unconventional Reservoirs. SPE Hydraulic Fracturing Technology Conference. Woodlands, Texas. SPE 168612-
MS. http://dx.doi: 10.2118/168612-MS.
Barree, R. D. , 2009-2015 . Principles of Hydraulic Fracturing Course.
Barree, R.D.  and. Miskimins, J.L. , 2016 , Physical Explanation of non-linear derivatives in diagnostic fracture injection test
analysis : SPE Hydraulic Fracturing Technology Conference held in the Woodlands, SPE 179134-MS. http://dx.doi:
10.2118/179134-MS .
Barree, R.D.  Practical Fundamentals of DFIT Execution and Interpretation. December 8, 2020
Brown, G. O. Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078,


key: chroma:document
string_value:
Brown, G. O. Department of Biosystems and Agricultural Engineering, Oklahoma State University, Stillwater, OK 74078,
USA . Article in Water Resources Research July 2002 . DOI: 10.1029/2001WR000727Downloaded 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


key: chroma:document
string_value:
64 SPE-206239-MS
Buijs, H.  and Ponce, J. , 2018  An Engineered Approach to Hydraulically Fracture the Vaca Muerta Shale . Presented at the
SPE Hydraulic Fracturing Technology Conference held at the Woodlands, TX, 23-25 Jan. SPE-189866-MS. https://
doi.org/10.2118/189866-MS .
Buijs, H. ; Ponce, J.; and P. Veeken. Validation of flow capacity and state-of-stress models in unconventional reservoirs
by implementation of numerical mo dels of diagnostic fracture injection tests Published on The Leading Edge, June
2019 . https://doi.org/10.1190/tle38060306.1 .
Buijs, H.  An Engineered Approach to Hydraulic Fracture the Vaca Muerta Shale , 2018 . https://webevents.spe.org/
products/an-engineered-approach-to-hydraulic-fracture-the-vaca-muerta-shale
Buijs, H. , Guerra, C. ; Sonwa, R. ; Nami, P; Vecchia, L. ; and Ishmuratov, R. , 2020  Building Multifrac Completion Strategies
in Tight Gas Reservoirs: A North Sea Case . Presented at the Abu Dhabi International Petroleum Exhibition &


key: chroma:document
string_value:
in Tight Gas Reservoirs: A North Sea Case . Presented at the Abu Dhabi International Petroleum Exhibition &
Conference, Abu Dhabi, 9th Nov. SPE-202713-MS. https://doi.org/10.2118/202713-MS.
Carter, R.D. : Derivation of the General Equation for Estimating the Extend of Fracture Area. Appendix 1 of "Optimum
Fluid Characteristics for Fracture Extension" Drilling and Production Practice, Howard, C.R. and Fast, C.R. , API,
New York ( 1957 ), 261-269.
Castillo, J.L.  1987 . Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff. SPE 16417.
SPE/DOE Low Permeability Reservoirs Symposium held in Denver, Colorado, May 18-19, 1987.
Conway, M. W.; Lindeman, S. W. and Barree, R.D. Selection of Stimulation Fluids and Treatment Design for Low -
Permeability Reservoirs: SPE Hydraulic Fracturing Technology Conference held College Station, TX. SPE 106085-
MS. http://dx.doi: 10.2118/106085-MS .


key: chroma:document
string_value:
Permeability Reservoirs: SPE Hydraulic Fracturing Technology Conference held College Station, TX. SPE 106085-
MS. http://dx.doi: 10.2118/106085-MS .
Cox, S.A. ; Gilbert, J.V .; Sutton, R.P. and Stoltz, P. 2002 . Reserve Analysis for Tight Gas . SPE 78695. Paper presented at
the SPE Eastern Regional Meeting. Lexington, KC. http://dx.doi.org/10.2118/78695-MS .
Cox, S.A. ; Sutton, R.P. ; Stoltz, P. ; Barree R. D. and Conway, M.W. 2007 . Evaluation of Complex Reservoir Geometries and
Completion Practices on Production Analysis. SPE 111285 MS Paper presented at the SPE Easter Regional Meeting.
Lexington, KC http://dx.doi.org/10.2118/111285-MS .
Craig, D. P.; Barree, R. D. ; Warpinsiki, N. R.  and Blasingame, T. A., 2017  Fracture >Closure Stress: Reexamining
Field and Laboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies. Presented at the
SPE Annual Technical Conference & Exhibition held at San Antonio, TX, 9-11 October. SPE-187038-MS. https://


key: chroma:document
string_value:
SPE Annual Technical Conference & Exhibition held at San Antonio, TX, 9-11 October. SPE-187038-MS. https://
doi.org/10.2118/187038-MS.
Cluff, R.M. ; Shanley, K.W. and Miller, M.A. Three things we thought we understood about shale gas, but were afraid
to ask, AAPG  (2007).
Duenckel, R. J.; Barree, R.D., Drylie, S.; O'connell, L.G. and Abney, K.L. Proppants – What 30 Years of Study have
Taught Us, SPE 187451 . SPE Production & Operations. May 2019. http://dx.doi.org/10.2118/187451-MS.
Eissa, A. , Kazi, A. , Relation Between Static and Dynamic Young's Moduli of Rocks . Int. J. Rock Mech. Min. Sci. Geomech.
Abstr . V olume 25, Number 6, Pages 479-482, 1988.
Geerstma J.  and de Klerk F.A.  Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures. SPE
Journal of Petroleum Technology . December 1969, 1571-81.
Godbey, J.K. and Hodges, H.D. : "Pressure Measurements During Formation Fracturing Operations, ". Trans., AIME
(1958) 213, 65–69.


key: chroma:document
string_value:
Godbey, J.K. and Hodges, H.D. : "Pressure Measurements During Formation Fracturing Operations, ". Trans., AIME
(1958) 213, 65–69.
Gulrajani, S.N. , Mack, M.G.  and Elbel, J.L.: "Pressure History Inversion for Interpretation o f Fracture Treatments," paper
SPE 36439, presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA (October 6–
9,1996);
Harrison, E., Kieschnick, W.F. Jr. and McGuire, W.J.: "The Mechanics of Fracture Induction and Extension,". Trans.,
AIME  (1954 ) 201, 252–263.
Johnson, R.L. , You, Z. , Riberiro, A. , Mukherjee, S., Salomao de Santiago, V . and Leonardi, C.. 2020 . Integrating Reservoir
Characterization, Diagnostic Fracture Injection Testing, Hydraulic Fracturing and Post-Frac Well Production Data to
Define Pressure Dependent Permeability Behavior in Coal. Presented at the SPE Asia Pacific Oil & Gas Conference.
Perth, Australia, 20-22 October, 2020. SPE-202281-MS. http://dx.doi.org/10.2118/202281-MS .


key: chroma:document
string_value:
Perth, Australia, 20-22 October, 2020. SPE-202281-MS. http://dx.doi.org/10.2118/202281-MS .
Jung, H. , M. M. Sharma , D. D. Cramer, S. Oakes, and M. W. McClure. 2016 . Re-examining interpretations of non-ideal
behavior during diagnostic fracture injection tests. Journal of Petroleum Science and Engineering 145: 114-136, doi:
10.1016/j.petrol.2016.03.016.
Khristianovic, A.A. and Zheltov, Y .P.. 1955 . Formation of Vertical Fractures by Means of Highly Viscous Liquid. Paper
6132 presented at the 4 th World Petroleum Congress, Rome, 6-15 June.
Lai, C.Y . , Zheng, Z. , Dressaire, E. , Ramon, G.Z., Huppert, H.E and Stone, H.A 2006 . Elastic Relaxation of Fluid - Driven
Cracks and Resulting Backflow . Physical Review Letters, 117, 268001 , December, 2016. Phys. Rev. Lett. 117, 268001
(2016) - Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow (aps.org)


key: chroma:document
string_value:
(2016) - Elastic Relaxation of Fluid-Driven Cracks and the Resulting Backflow (aps.org)
Marc Laliberte , "Model for Calculating the Viscosity of Aqueous Solutions,"  J. Chem. Eng. Data, 52, 321- 335, 2007Downloaded 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


key: chroma:document
string_value:
SPE-206239-MS 65
Marc Laliberte , "Model for Calculating the Viscosity of Aqueous Solutions," J. Chem. Eng. Data, 52, 1507 -1508, 2007
(Correction and update)
McClure, Mark W. , Christopher A. J. Blyton, Hojung Jung, and Mukul M. Sharma. 2014 . The Effect of Changing Fracture
Compliance on Pressure Transi ent Behavior During Diagnostic Fracture Injection Tests . SPE 170956. Paper presented
at the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands.
McClure, Mark W. , Hojung Jung , Dave D. Cramer, and Mukul M. Sharma . 2016 . The fracture compliance method for
picking closure pressure from diagnostic fracture injection tests. SPE Journal 21(4): 1321 -1339, doi: 10.2118/179725-
PA.
McClure, M. ; Bammidi, V .; Cipolla, C. ; Cramer, D.; Martin, L., Savitski, A. ; Sobernheim and V oller, K. 2019 . A
Collaborative Study on DFIT Interpretation: Integrating Modeling Field Data, and Analytical Techniques . URTeC:


key: chroma:document
string_value:
Collaborative Study on DFIT Interpretation: Integrating Modeling Field Data, and Analytical Techniques . URTeC:
123. Paper presented at the Unconventional Resources Technology Conference, Denver, CO. DOI 10.15530/
urtec-2019-123 .
Nolte, K.G.  1979 . Determination of Fracture Parameters from Fracturing Pressure Decline. Presented at the SPE
Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23-24 September. SPE 8341-MS. http://
dx.doi.org/10.2118/8341-MS.
Nolte, K.G. : "Fracturing Pressure Analysis for Non-Ideal Behavior," paper SPE 20704, presented at the SPE Annual
Technical Conference and Exhibition, New Orleans, Louisiana, USA (September 23–26, 1990); also in Journal of
Petroleum Technology  (February 1991 ) 43, No. 2, 210–218.
Nolte, K.G. , Mack, M.G.  and Lie, W.L. : "A Systematic Method for Applying Fracturing Pressure Decline: Part 1," paper
SPE 25845, presented at the SPE Rocky Mountain Regional Meeting and Low Permeability Reservoirs Symposium,


key: chroma:document
string_value:
SPE 25845, presented at the SPE Rocky Mountain Regional Meeting and Low Permeability Reservoirs Symposium,
Denver, Colorado, USA (April 12–14, 1993).
Nolte, K.G. , Maniere, J.L. and Owens, K.A. : "After-Closure Analysis of Fracture Calibration Tests," paper SPE 38676,
presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA (October 5–8, 1997).
Nolte, K.G.  and Gulrajani, S.N.  Fracture Evaluation Using Pressure Diagnostics Reservoir Stimulation, 3rd Edition, 2000
Nolte, K. G. , 2007 . Keynote Speech at the Hydraulic Fracturing Technology Conference. College Station, TX 2007.
Passey, Q. , Creaney S , Kulla J, Moretti F. and Stroud J. , 1990a. Source rock analysis from well logs – ΔLogR Technique.
Based on information in the following reference: Passey, Q.R., S. Creaney, J.B. Kulla, F.J. Moretti, J.D Stroud (1990)
A practical model for organic richness from porosity and resistivity logs , AAPG Bulletin, V ol. 74, No. 12 (December


key: chroma:document
string_value:
A practical model for organic richness from porosity and resistivity logs , AAPG Bulletin, V ol. 74, No. 12 (December
1990), page 1777  – 1794 .
Passey, Q.R.  Creaney S. , Kulla J., Moretti F.  and Stroud J. , 1990b . A practical model for organic richness from porosity
and resistivity logs , AAPG Bulletin , V ol. 74, No. 12 (December 1990), Page 1777 – 1794.
Perkins T.K.  and Kern L.R.  Widths of Hydraulic Fractures. SPE Journal of Petroleum Technology. September 1961 ,
937-49; Trans. AIME 222, September 1961.
Piggott, A.R. , Brady, B.H.  and Gu, H.: "Reservoir Formation Characterization from Hydraulic Fracturing Records,"  Proc.,
Eurock'92 Symposium, London, UK ( 1992 ), 360–365.
Ponce, J. E.  Personal communications  (2010 ).
Ramurthy, M. ; Towler, B. ; Harris, G.H  and Barree, R.D. , 2013 . Effects of High Pressure-Dependent Leak-Off and
High Process-Zone Stress (PZS) on Stimulation Treatment and Production. Presented at the SPE Unconventional


key: chroma:document
string_value:
High Process-Zone Stress (PZS) on Stimulation Treatment and Production. Presented at the SPE Unconventional
Resources Conference and Exhibition Asia-Pacific. Brisbane, Australia. 11-13 November, 2013. SPE-167038-MS.
http://dx.doi.org/10.2118/167038-MS .
Sneddon, I.N.  and Elliot, A.A. : "The Opening of a Griffith Crack Under Internal Pressure," Quarterly of Appl. Math.
(1946 ) 4, 262–267.
Talley, G. D., Swindell, T.M., Water, G.A., and Nolte, K.G. 1999 . Field Application of After Closure Analysis of Fracture
Calibration Test . Paper SPE 52220. Presented at the SPE Mid-Continent Operations Symposium, Oklahoma City,
USA, 28-31 March. http://dx.doi: 10.2118/52220-MS.
Veccia, L. . Personal communications  (2016 )
Wang, HanYi and Mukul M. Sharma. 2017 . New variable compliance method for estimating in-situ stress and leak-off
from DFIT data . SPE 187348. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio,
TX.


key: chroma:document
string_value:
from DFIT data . SPE 187348. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio,
TX.
Wang, HanYi and Mukul M. Sharma . 2018 . Estimating unpropped fracture conductivity and compliance from diagnostic
fracture injection tests. SPE 189844. Paper presented at the SPE Hydraulic Fracturing Technology Conference &
Exhibition. The Woodlands, TX.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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1. INTRODUCTION  
Diagnostic fracture injection tests ( DFIT) involve 
pumping a fluid (typically water), at a constant rate for a 
short period of time, creating a relatively small hydraulic 
fracture before the well is shut in. The pressure transient 
data after shut -in is analyzed to obtain in -situ stresses 
and reservoir properties. In addition, the net pressure 
trends in a DFIT can be also used to infer the induced 
fracture complexity in different geological settings 
(Potocki 2012) and stress -dependent un -propped fracture 
conductivity can be estimated through forward  modeling 
or inverse calculation ( Wang and Sharma 2018 ). This 
valuable information  obtained from DFITs provides key 
input parameters for modeling hydraulic fracture 
propagation ( Wang 2015; Wang 2016; Wang et al. 2016 ), 
stimulation design (Ramurthy et al. 2011), development 
of reservoir models  (Mirani et al. 2017; Loughry et al. 
2015 ; Wang 2017 ) and post -fracture analysis (Fu et al. 
2017) .


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of reservoir models  (Mirani et al. 2017; Loughry et al. 
2015 ; Wang 2017 ) and post -fracture analysis (Fu et al. 
2017) . 
The advent of fracturing pressure decline analysis was 
pioneered by the work of Nolte (1979 and1986). With 
the assumptions of power -law fracture growth, 
negligible spurt loss, constant fracture compliance (or 
stiffness), constant fracture surface area afte r shut -in and 
Carter’s leak -off (a constant pressure boundary 
condition), a remarkably simple and useful equation for the pressure decline can be obtained based on a G -
function approach. Wang and Sharma (2017b) showed  
that that the traditional “tangent lin e method ( Barree et al. 
2009 ) ” undere stimate s the closure stress while the  
“compliance method ” (McClure et al. 2016 ) estimates 
the onset of closure rather than the  closure stress. Based 
on their analysis, a new “varia ble compliance method” 
was proposed to  estimate the closure stress. Wang and


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on their analysis, a new “varia ble compliance method” 
was proposed to  estimate the closure stress. Wang and 
Sharma (2018) further confirmed that fracture 
compliance is pressure -dependent during closure , and 
the mechanical ly closed fracture is still subject to leak -
off. The stress -dependent un -propped fracture 
conductivity c an be estimated by analysis of DFIT data.  
Previous papers  have been mainly focused on planar 
fracture s in homogen eous reservoirs, and relatively little 
work has been done to interpret DFIT data in naturally 
fractured reservoirs with fracture pressure depe ndent 
leak-off (FPDL) and variable fracture compliance. In 
this study, we extend our previous work to investigate 
pressure transient behavior in naturally fractured 
reservoir s.  
2. THE GOVERNING EQUATI ONS  
2.1. 1D Fracture Pressure Dependent Leak -off 
with Variable Compliance              
ARMA 1 8–225


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with Variable Compliance              
ARMA 1 8–225                                                                
 
Estimating Fracture Closure Stress in Naturally Fractured  
Reservoirs with Diagnostic Fracture Injection Test s 
 
HanYi Wang  
The University of Texas at Austin, Austin, Texas, USA  
Mukul M. Sharma  
The University of Texas at Austin, Austin, Texas, USA  
 
Copyright 20 18 ARMA, American Rock Mechanics Association  
This paper was prepared for presentation at the 52nd US Rock Mechanics / Geomechanics Symposium held in Seattle , Washington , USA, 17–20 
June  2018. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and 
critical review of the paper by a minimum of two technical reviewers. The material, as pres ented, does not necessarily reflect any position of


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critical review of the paper by a minimum of two technical reviewers. The material, as pres ented, does not necessarily reflect any position of 
ARMA, its officers, or m embers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the 
written consent of ARMA is prohibited. Permission to reprodu ce in print is restricted to an abstract of not more than 200 words; illus trations may 
not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.   
 
 
 ABSTRACT:  Diagnostic Fracture Injection Tests (DF IT), which have also been referred to as Injection -Falloff Tests, Fracture 
Calibration Tests  or Mini -Frac Tests in the literature, have evolved into a commonly used technique to obtain in -situ stress. 
Simplifying  assumption s used  in traditional G -function model often lead to an underestimation of the  closure stress, even for a


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Simplifying  assumption s used  in traditional G -function model often lead to an underestimation of the  closure stress, even for a  
planar fracture geometry. When a DFIT  is conducted  in naturally fractured reservoirs, the stimulated natural fractures can either 
alter the effective reservoir permeability within the distance of investigation or interact with  the hydraulic fracture to form a 
complex fracture geometry. In this study, we p resent a new pressure transient model for DFIT analysis in naturally fractured 
reservoirs, and it is shown that using established methods to pick closure stress often lead to significant over or underesti mates, 
regardless of whether the reservoir is heavil y fractured or sparsely fractured. Our proposed “variable compliance method” gives a 
much more accurate and reliable estimation of closure stress in both homogenous and naturally fractured reservoirs.


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much more accurate and reliable estimation of closure stress in both homogenous and naturally fractured reservoirs.  
 
 
 
 
  
 
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The transient pressure response during fracture closure is 
derived using the following assumptions:  
1. Reservoir  is isotropic and homogeneous and contains 
a single slightly compressible fluid.  
2. The fluid viscosity, formation porosity and total 
compressibility are independent of pressure.  
3. Reservoir permeability is low so that poroelastic 
effects caused by fluid leak -off are negligible  
4. Gravity effects are negligible and pressure gradients 
are small thorough out the reservoir.  
5. Mechanical ly closed fracture has residual fracture 
width so it is still subject to leak -off (Wang and 
Sharma 2018) and the fracture leak -off surface area 
remains unchanged.  
6. Fracture pressure is uniformly distributed inside the 
fracture.  
7. The pore pressure disturbance c aused by fracture 
propagation is negligible. This means that fluid leak -
off during pumping is very small and the duration of 
injection is very short (typically 3 -5 minutes) while


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off during pumping is very small and the duration of 
injection is very short (typically 3 -5 minutes) while 
the total shut -in time can be hours, days or even 
weeks.  
8. Leak -off is linear  and perpendicular to the fracture 
surface and pressure interference among fractures and 
late time radial flow has not been developed yet.  
Assuming 1D linear Darcy flow and a slightly 
compressible, single -phase fluid in the reservoir, the 
differential form of the mass balance can be written as:  
∂P
∂t=1
𝜇𝑓𝜙𝑐𝑡∂
∂x(k∂P
∂x)                                  (1) 
where P is the pressure, k is formation permeability, 
which can be a function of P. μf is fluid viscosity, ϕ is 
formation porosity and ct is total formation 
compressibility. From a material balance perspective 
(fluid compressibility is negligible compared to that of 
the fracture), the total rate of fluid leak -off into the 
formation,  qf , after shut -in equals the rate of shrinkage


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the fracture), the total rate of fluid leak -off into the 
formation,  qf , after shut -in equals the rate of shrinkage 
of total f racture volume,  Vf, as pressure declines:  
𝑞𝑓=− 𝑑𝑉𝑓
𝑑𝑡                                      (2) 
Fracture stiffness, which is the reciprocal of fracture 
compliance, is defined as (Wang and Sharma 2017a; 
Wang et al. 2018):  
𝑆𝑓=𝐴𝑓𝑑𝑃𝑓
𝑑𝑉𝑓                                              (3) 
where 𝑃𝑓 is pressure inside fracture and 𝐴𝑓 is  half of the 
total fracture surface area (only account for 1 wall). 
Substituting  Eq.(3) into Eq.(2), we have  
𝑞𝑓=− 𝐴𝑓𝑑𝑃𝑓
𝑆𝑓𝑑𝑡                                      (4) 
At the boundary of the fracture surface, both Darcy’s 
law and material balance have to be honored:  𝑞𝑓=− 2𝐴𝑓𝑘
𝜇𝑓 𝑑𝑃
𝑑𝑥=−  𝐴𝑓𝑑𝑃𝑓
𝑆𝑓𝑑𝑡 at x=0        (5) 
Rearranging Eq. (5), we get the boundary condition at 
the fracture surface:  
𝑘
𝜇𝑓 𝑑𝑃
𝑑𝑥=1
2𝑆𝑓𝑑𝑃𝑓
𝑑𝑡 at x=0                     (6) 
With initial condition (disregarding the pressure


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the fracture surface:  
𝑘
𝜇𝑓 𝑑𝑃
𝑑𝑥=1
2𝑆𝑓𝑑𝑃𝑓
𝑑𝑡 at x=0                     (6) 
With initial condition (disregarding the pressure 
disturbance during the short injection period)  
  𝑃=𝑃0 at t=0,x>0                              (7) 
  𝑃=ISIP  at t=0,x=0                           (8) 
where 𝑃0 is the initial pore pressure and ISIP  is the 
instant shut -in pressure. The governing equation  Eq.(1), 
plus the initial condition Eq. (7) -(8) and boundary 
condition Eq.(6) uniquely describe the pressure transient 
behavior during DFITs. To account for wellbore storage 
effects, the fracture stiffness 𝑆𝑓 needs to be replaced by 
the fracture -wellbore system stiffness, which is defined 
as: 
𝑆𝑠=    𝑆𝑓𝐴𝑓
𝐴𝑓+𝑆𝑓𝑉𝑤 𝑐𝑤                                   (9) 
where 𝑉𝑤 is the wellbore volume and 𝑐𝑤 is the water 
(injection fluid in the wellbore) compressibility.   
2.2. Fracture Stiffness of Complex Frac ture 
Geometry  
Because fracture stiffness (or compliance) represents


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2.2. Fracture Stiffness of Complex Frac ture 
Geometry  
Because fracture stiffness (or compliance) represents 
surface normalized compressibility, for a fracture with 
complex fracture geometry, the total fracture stiffness is 
controlled by the stiffness of multiple individual fracture 
segments, as illustrated in Figure.1.  
 
Fig. 1 Illustration of complex fracture geometry . 
The complex fracture is formed by individual segments 
with different orientations and fracture surface area. Let 
the ith fracture surface area of one wall denoted as Af,i 
and its pressure -dependent stiffness denoted as Sf,i, the 
total fracture stiffness  can be determined from the 
stiffness of each individual fracture segment (analogous 
to capacitors in  parallel s): 
𝑆𝑓=𝐴𝑓
𝐴𝑓,1
𝑆𝑓,1+𝐴𝑓,2
𝑆𝑓,2+⋯+𝐴𝑓,𝑛
𝑆𝑓,𝑛                       (10) 
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Where,  
𝐴𝑓=𝐴𝑓,1+𝐴𝑓,2+⋯+𝐴𝑓,𝑛                    (11) 
2.3. Pressure Dependent Permeability  
In previous literature (Barree et al. 2009), the 
phenomenon of pressure -dependent permeability is often 
called as pressure -dependent leak -off ( PDL), however, 
this is not a n appropriate term, because leak -off is 
always pressure -dependent, even  if the permeability is 
constant (Wang and Sharma 2017b). There are many 
equations  that can be used to express the  formation 
effective permeability as a function of pressure, such as 
a linear, power law or hyperbolic relationship. To make 
a general case and use as few  free parameters as 
possible, we can use a general formula to relate 
formation permeability and pressure:  
k(P)=(𝑘𝑒−𝑘0)𝑒𝑐−𝑒𝐼𝑆𝐼𝑃 −𝑃
𝐼𝑆𝐼𝑃 −𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙𝑐
𝑒𝑐−1+𝑘0      (12) 
where 𝑘𝑒 is the effective reservoir  permeability at the 
end of pumping and 𝑘0 is the original reservoir 
permeability. 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙  is the pressure where reservoir


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end of pumping and 𝑘0 is the original reservoir 
permeability. 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙  is the pressure where reservoir 
permeability drops to its original value a nd c a free 
parameter controls the evolution of permeability. 𝑘𝑒 is 
larger than 𝑘0 because the surrounding permeability is 
enhanced by stimulated fracture networks during 
pumping. After the pressure drops to or below 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 , 
the stimulated f racture networks close back to the 
original in -situ state and the effective permeability 
return s to its original value.  Figure.2 demonstrates the 
pressure -dependent permeability for different values of c.  
 
Fig. 2 Illustration of pressure -dependent permeab ility with 
different values of c  
2.4. Pressure Dependent Fracture Compliance  
Fracture closure is a gradual process with increasing 
fracture stiffness (or decreasing fracture compliance) as 
fracture closes from tip to wellbore or closes from higher 
stress region  to lower stress region in layered formations.


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fracture closes from tip to wellbore or closes from higher 
stress region  to lower stress region in layered formations. 
A method t o obtain a pressure -dependent fracture 
compliance based on fracture geometry, rock properties 
and surface roughness has been well discussed by Wang 
and Sharma (2017a) and Wang et al. (2018). The 
influence of surface roughness on fracture compliance is described by a contact law relat ing the  fracture width to 
the net closure stress for fractured rocks (Willis -Richards 
et al. 1996):  
  σc=σref
9(w0
wf−1)for  wf≤w0     (17) 
where wf is the fracture aperture and, w0 is the contact 
width, which represents the fracture aperture when the 
contact normal stress is equal to zero, σc is the contact 
normal stress on the fracture, and σref is a contact 
reference stress, which denotes the effective normal 
stress at which the aperture is reduced by 90%.  
3. DFIT IN NATURALLY FR ACTURED 
RESERVOIRS


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reference stress, which denotes the effective normal 
stress at which the aperture is reduced by 90%.  
3. DFIT IN NATURALLY FR ACTURED 
RESERVOIRS  
All reservoirs are fractured to some degree. D epending 
on the density  and dimension s of natural fractures and 
the location where the DFIT is done, the natural 
fractures can impact hydraulic fracture propagation and 
the adjacent flow capacity. If the reservoir is heavily 
fractured and these natural fra ctures are well -connected, 
as shown in Figure 3, then the formation can be 
considered as homogenous within the distance of 
investigation and the effective permeability is controlled 
by both fracture and matrix. High -pressure  fluid 
injection  during the pump ing period enhance s the local 
effective permeability because it widens the natural 
fractures. However, as pressure declines during shut -in, 
the effective permeability will gradually decline until it 
reaches the original value. The original effective


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the effective permeability will gradually decline until it 
reaches the original value. The original effective 
permea bility does not necessar ily represent the matrix 
permeability, because the existence of natural fractures 
may already have enhanced the permeability.  
 
Fig. 3 Heavily fractured reservoir with well -connected natural 
fractures  
 
If the reservoir is sparsely or moderately fractured, and 
the stimulated natural fractures are discrete and not well -
connected, then these natural fractures or isolated 
fracture networks will not change the overall flow 
capacity in the reservoir  (Wang 2017) , but they can 
interact with  hydraulic fractures, and generate  a complex 
fracture geometry, as shown in Figure  4. Under this 
scenario, the fracture compliance and leak -off surface 
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area are impacted by the sequential closure of individual 
fracture segment s or branch es, where the branc hes with 
the highest normal stress perpendicular to local fracture 
orientation will close first, and the fracture segments that 
open against the minimum principal stress will be the 
last to close. If  the hydraulic fracture does not initiate 
along the maxim um principal stress direction because of 
the local hoop stress around perforations, non -planar 
fracture s can also be formed. In this section, we are 
going to investigate the pressure transient behavior 
under these scenarios and discuss the implications of 
estimating closure stress using  different methods . 
 
Fig. 4 Low to Moderate Fractured Reservoir with Discrete 
Natural Fractures  
3.1. Base Case  
Before we embark on investigating the pressure transient 
behavior with closing  fracture in fractured reservoirs, 
we’ll first examine pressure decline behavior for a planar


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behavior with closing  fracture in fractured reservoirs, 
we’ll first examine pressure decline behavior for a planar 
fracture and discuss the causes for the discrepancy for 
estimated closure stress using  established methods. 
Table 1  shows the input parameters for the Base Case 
Scenario . 
Table 1. Input parameters for the Base Case scenario  
Fracture type  PKN 
Fracture height  12 m  
Fracture half -length  50 m  
Pumping time  5 min  
ISIP 40 MPa  
Minimum in -situ stress  35 MPa  
Initial pore pressure  20 MPa  
Young's modulus  20 GPa 
Total compressibility  6.3e -4 MPa-1 
In-Situ fluid viscosity  0.3 cP  
Formation original permeability  0.0005 md 
Poisson's Ratio  0.25  
Initial porosity  0.03  
Contact width  of asperities  2 mm  
Contact reference stress  of asperities  5 MPa  
 
With the known fracture geometry, rock modulus, 
minimum in -situ stress and surface roughness 
(represented by two contact parameters 𝑤0 and 𝜎𝑟𝑒𝑓),


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With the known fracture geometry, rock modulus, 
minimum in -situ stress and surface roughness 
(represented by two contact parameters 𝑤0 and 𝜎𝑟𝑒𝑓), 
the fracture stiffness and volume evolution can be 
uniquely determined at different fluid pressure s (Wang  
and Sharma 2017a; Wang et al. 2018), the results are shown in Figure 5. As can be seen, when the fluid 
pressure inside the fracture is relatively high, the fracture 
volume declines linearly with pressure under constant 
fracture stiffness (or compliance). However, as the 
pressure declines to a certain level the fracture volume 
and pressure depart from a linear relationship, and 
fracture stiffness start s to increase noticeably. In the end, 
when the fluid pressure drops to a sufficient low level, 
the residual  fracture volume (supported by asperities) 
becomes more or less insensitive to pressure drop with 
extremely high fracture stiffness (low compliance). This 
is because when the pressure inside the fracture is


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extremely high fracture stiffness (low compliance). This 
is because when the pressure inside the fracture is 
relatively high, it is still wide open and its st iffness is a 
constant . However, as pressure continues to drop, the 
fracture will gradually close from its edges to its center, 
which increase s the fracture stiffness gradually.  
 
Fig. 5 Illustration of the fracture stiffness and volume 
evolution from modeling  
Figure.6 shows  the normalized tiltmeter response (its 
slope is proportional to fracture compliance or the 
reciprocal of fracture stiffness) plotted against wellbore 
pressure during the shut -in period of 2B well at three 
different stations from the  GRI/DOE M -site. The 
tiltmeter demonstrates that soon after shut -in, the 
measured displacement declines linearly with pressure 
(roughly constant fracture stiffness). After the pressure 
declines to a certain level, the measured displacement vs 
pressure depa rts from a linear relationship. As pressure


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declines to a certain level, the measured displacement vs 
pressure depa rts from a linear relationship. As pressure 
continues declining, more and more fracture surface area 
comes into contact with the rough fracture surfaces and 
asperities, and the fracture stiffness increases gradually. 
This field measurement is consistent wi th the general 
trend from out modeling results shown in Figure.5. It is 
challenging to estimate closure stress based on 
mechanical closure from tiltmeter measurement. If we 
pick the closure stress using  the “tangent line method” 
on tiltmeter measurement (C raig et al. 2017), the closure 
stress is 15 MPa, and if we pick the closure stress using  
the “compliance method”, the closure stress is 21 MPa. 
There is a 6 MPa discrepancy between these two 
methods. As discussed by Wang and Sharma (2017b), 
the “tangent li ne method” only marks the end of fracture 
storage dominated flow, so it always underestimate s


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the “tangent li ne method” only marks the end of fracture 
storage dominated flow, so it always underestimate s 
closure stress while the “compliance method” can 
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overestimate closure stress,  because it only marks the 
beginning fracture closure on edges or tips. The 
“variable  compliance method” proposed by Wang and 
Sharma (2017b) provides an alternative way to estimate 
closure stress that not only accounts for the difference 
between two endpoints  (fracture compliance start to 
change and fracture compliance become small enough to 
be considered as negligible), but also compensates for 
the impact of leak -off, which  is reflected on G -function 
time or the square root of time.  
 
Fig. 6 Tiltmeter measurement from 2B well of GRI/DOE M -
site project  
To illustrate the benefit  of the “variable compliance 
method” and compare the estimated closure stress from 
different methods, the pressure -dependent fracture 
stiffness from Figure.  5 is used as a boundary condition 
for Eq.(6) to simulate the pressure decline response, all 
other parameter s are provided in Table 1. Figure.7 shows


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for Eq.(6) to simulate the pressure decline response, all 
other parameter s are provided in Table 1. Figure.7 shows 
the pressure decline and its derivatives on the G -function 
and square root of time plots. Compared to the input 
closure stress of 35 MPa, the estimated closure stress by  
the “tangent line method” is 32.2 MPa ( -2.8 MPa error), 
the estimated closure stress by the “compliance method” 
is 36.8 MPa (1.8 MPa error), and the estimated closure 
stress by  the “variable compliance method” is 35.2 MPa 
(0.2 MPa error). It is clear that the closure stress 
estimated by the “variabl e compliance method” is more 
reliable. Detailed comparisons with different fracture 
geometry , surface roughness  and reservoir properties 
have been presented by Wang and Sharma (2017b), and 
hence will not be discussed further.  
Figure.8 show s the pressure profiles in the formation 
away from the fracture surface at different shut -in times.


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Figure.8 show s the pressure profiles in the formation 
away from the fracture surface at different shut -in times. 
Together with Fig.6, we can notice that the closure time 
is around 8.85 hr when fluid pressure drops to the close 
stress, and the corresponding distance of i nvestigation is 
less than 7 m at the time of closure. This is very typical 
in low permeability formations.   
Fig. 7 Pressure decline and its derivatives of Base Case 
scenario  
 
Fig. 8 Pressure profile and distance of investigation for Base 
Case Scenario . 
Now the question remains: what unique features will 
emerge from  DFIT data in naturally fractured reservoirs 
and how do we reliably estimate closure stress under 
these contexts? Are these established methods are 
reliable ways to estimate closure stress?  In  the 
following sections, we’ll examine these cases and 
discuss the associated challenges in identify ing closure 
stress in naturally  fractured reservoir.


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discuss the associated challenges in identify ing closure 
stress in naturally  fractured reservoir.  
3.2. Heavily Fractured Reservoir with Pressure 
Dependent Permeability  
First, let’s investigate the case wher e the reservoir is 
heavily fractured and all the stimulated fractures form 
well-connected networks that alter the effective 
permeability around the hydraulic fracture. The effective 
permeability is highest at the end of pumping and 
gradually declines as pr essure drops and fluid leak-offs 
into formation . Assumes the effective permeability 
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follows Eq.(12), with c=3 and 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙  is 4.5 MPa 
below the ISIP, all the other input parameters are the 
same as the base case. Figure.9  shows the pressure 
decline and its derivatives with different values of 
enhanced effective permeability 𝑘𝑒 at the end of 
pumping. From the results, we can clearly observe that 
there exists a “bump” on the pressure derivative during 
fracture closure befor e it reaches its final peak. And in 
all cases, the pressure derivatives “bump” end at a 
fracturing pressure that is 4.5 MPa below the ISIP, 
which is the exactly value of 𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 . So the values of 
𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙  can be readily obtained from f ield DFIT data if 
it exhibits this pressure -dependent permeability 
signature. We can also observe that the higher the 𝑘𝑒, the 
large the initial slope of pressure derivatives.  
 
 
Fig. 9 Pressure decline and its derivatives with pressure -
dependent permeab ility 
Because the effect of pressure -dependent permeability


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Fig. 9 Pressure decline and its derivatives with pressure -
dependent permeab ility 
Because the effect of pressure -dependent permeability 
masks the initial phase of fracture closure, so the 
moment when the fracture stiffness start s to change 
cannot be identified. In such cases , the “compliance 
method” is hard to apply . We can, howev er, modify our 
“variable compliance method” approach  as follows : first, 
we identify the dimensionless G -time or the square root 
of time at the end of the first pressure derivative “bump” 
(i.e., end of pressure -dependent permeability) and at the 
intersectio n of pressure derivative and a tangent line 
passing through the origin (i.e., the closure point picked 
by the “tangent line method”). Then average the values 
of these two dimensionless G -time or the square root of 
time, finally extrapolate back to the pressure curve that


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of these two dimensionless G -time or the square root of 
time, finally extrapolate back to the pressure curve that 
corresponds to the averaged G -time or the square root of time. Table 2 shows the estimated closures by “tangent 
line method” and “variable compliance method”. As can 
be seen, the “tangent line method” consistently 
underestimates the closure stress. This stems from the 
fact that the “tangent line method” assumes constant 
fracture stiffness and Carter’s leak -off during closure , 
but these two assumptions are not valid (Wang and 
Sharma 2017b). The closure stress estimated by 
“variable compliance method” gives significantly lower 
errors and is a more reliable approach to estimate closure 
stress.  
Table 2. Comparison of estimated closure stress from different 
methods with pressure -depe ndent permeability  
Scenarios  Tangent Line Method  Variable Compliance Method  
Estimated  
 𝝈𝒉𝒎𝒊𝒏   Absolute 
Error  Estimated  
𝝈𝒉𝒎𝒊𝒏   Absolute 
Error


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Scenarios  Tangent Line Method  Variable Compliance Method  
Estimated  
 𝝈𝒉𝒎𝒊𝒏   Absolute 
Error  Estimated  
𝝈𝒉𝒎𝒊𝒏   Absolute 
Error  
𝑘𝑒=𝑘0 32.2 MPa  -2.8 MPa  35.2 MPa  0.2 MPa  
𝑘𝑒=5𝑘0 32.3 MPa  -2.7 MPa  34.4 MPa  0.4 MPa  
𝑘𝑒=10𝑘0 32.1 MPa  -2.9 MPa  34.5 MPa  0.5 MPa  
𝑘𝑒=20𝑘0 32.2 MPa  -2.8 MPa  34.4 MPa  0.4 MPa  
 
3.3. Discrete Natural Fractures  
In the case of sparsely or moderately fractured reservoirs,  
even though  the stimulated natural fractures are d iscrete 
and not well -connected, they can interact with 
propagating hydraulic fracture and generate complex 
fracture geometry. To make modeling and analysis 
trackable, we’ll first investigate a simplified version of 
complex fracture geometry that only consist two sets of 
fractures with di fferent orientations, as shown in 
Figure.10, then more general scenarios will be discussed 
at the end. In Figure.10, we can see that the main 
hydraulic fracture (i.e., fracture set 1) is perpendicular to


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at the end. In Figure.10, we can see that the main 
hydraulic fracture (i.e., fracture set 1) is perpendicular to 
the minimum principal stress, while the natural frac tures 
(i.e., fracture set 2) are perpendicular to the maximum 
principal stress. As pressure declines inside fracture after 
shut-in, the natural fracture that open s against the 
maximum principal stress will close first, and the 
hydraulic fracture that open s against the minimum 
principal stress will be the last to closure. Here, there are 
two possible scenarios are likely to happen during this 
sequential closure process: 1) the closed natural fracture 
remain hydraulic connectivity with the main hydraulic 
fracture. 2) the closed natural fracture lost the hydraulic 
connectivity with the main hydraulic fracture. We’ll 
discuss these two scenarios and their implications in 
interpreting DFIT data separately.  
3.3.1.  Closed Fracture Remain Hydraulic 
Connectivity


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discuss these two scenarios and their implications in 
interpreting DFIT data separately.  
3.3.1.  Closed Fracture Remain Hydraulic 
Connectivity  
If the inter section of fractures are well aligned (not 
skewed) and supported by asperities and tortuous walls, 
then it is likely that the closed natural fractures can 
maintain  hydraulic connectivity to the open fracture.  
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Fig. 10 Top view  of complex fracture geometry with two sets 
of fracture s. 
In this case, the sequential closure natural fractures or 
branches of a complex fracture will not alter the total 
leak-off surface area,  but will change the overall fracture 
stiffness evolution. Ass ume a complex fracture that 
consists of two sets of fracture, as shown in Figure.10. 
The total surface areas are 𝐴𝑓1 and  𝐴𝑓2 for fracture set 
1 and fracture set 2, respectively. The maximum 
principal stress is 38 MPa and the minimum principal 
stress is 33 MPa. We further assume that all fracture 
closes like a PKN fracture. Figure.11 shows the fracture 
stiffness evolution with different surface area ratio. As 
can be seen, if we only have fracture set 2 (i.e., natural 
fracture), the fracture stiffness w ill increase at 39.5 MPa, 
and if we only have fracture set 1 (i.e., hydraulic 
fracture), the fracture stiffness will increase around 34.5 
MPa. The overall fracture stiffness evolution is


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fracture), the fracture stiffness will increase around 34.5 
MPa. The overall fracture stiffness evolution is 
calculated using Eq.(10) with different surface area ratio. 
Because f or complex fracture geometry, the overall 
fracture stiffness is like a parallel system of capacitors, 
so the changes in fracture stiffness is not directly 
proportional to the surface area ratio, but is mostly 
influenced by the fracture set that has the highest ratio of 
surface area to stiffness.  
 
Fig. 11 Fracture stiffness evolution for a  complex fracture 
geometry (hydraulic connectivity remains after closure)  
Figure.12 shows the pressure decline and its derivatives 
of complex fracture geometry when closed  natural 
fractures remain their hydraulic connectivity to the main hydraulic fracture. Because the fracture stiffness 
evolution is smooth and gradual, so the closure of 
natural fracture is undetectable on G -function or the 
square root of time plot. But fro m the pressure


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natural fracture is undetectable on G -function or the 
square root of time plot. But fro m the pressure 
derivatives, we can notice that the larger the surface area 
of natural  fracture, the sooner the pressure derivatives 
curve upward  and the faster the pressure decline during 
closure . 
 
 
Fig. 12 Pressure decline and its derivatives of complex  
fracture geometry (remain hydraulic connectivity after 
closure)  
Table 3 summarizes the estimated closure stress 
(minimum principal stress) by different methods. As 
always, the “tangent line method” underestimates the 
closure stress, while “compliance method” overestimates 
closure stress. The “compliance method” gives a much 
larger error if the surface area of natural fracture is large. 
This is because “compliance method” picks the pressure 
when natural fracture edges or tips start to closure, 
which can  be much higher than the minimum principal 
stress. The “variable compliance method” yields the 
least error.


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which can  be much higher than the minimum principal 
stress. The “variable compliance method” yields the 
least error.  
Table 3. Comparison of estimated closure stress of complex 
fracture geometry (hydraulic connectivity remains after 
closure)  
𝑨𝒇𝟐
𝑨𝒇𝟏 Tangent Lin e 
Method  Compliance 
Method  Variable Compliance 
Method  
𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  
0.5 31  -2  34.8  1.8  33.4  0.4  
1 31.1   -1.9  35.4  2.4  33.6  0.6  
5 31.6   -1.4  37.8  4.8  33.3   0.3  
10 32  -1  39.2  6.2  33.5   0.5  
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In fact, the information on fracture complexity can’t be 
detected under such cases, and compared to a single 
hydraulic fracture scenario (i.e., only fracture set 1 on 
Fig.10), the impact of natural fractures on overall 
fractures stiffness evolution can be substituted by a 
“rougher” fracture walls with larger contact width and 
higher contact reference stress (Wang and Sharma 
2017b) to obtain earlier and steeper increase in fracture 
stiffness as pressure declines. So based on before -closure 
DFIT data alone, w e may not be able to distinguish the 
causes  to the increase of fracture stiffness from fracture 
complexity or surface roughness or recession in barrier 
layers. Nevertheless, as discussed by Wang and Sharma 
(2017b), the “variable compliance method” is insen sitive 
to fracture geometry, surface roughness and reservoir 
properties, and from the above results, we see that it is 
also much less sensitive to the existence of natural


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properties, and from the above results, we see that it is 
also much less sensitive to the existence of natural 
fractures, so the “variable compliance method” is more 
reliable way of estimate clos ure stress, especially when 
we are not sure whether the create d fracture geometry is 
complex or planar.  
3.3.2.  Closed Fracture Lost Hydraulic 
Connectivity  
If the intersections of fractures are skewed and not well -
aligned (such as T-shaped  fracture), then it is likely that 
the closed fracture will lose its hydraulic connectivity to 
the open fracture. In such case, the sequential closure 
natural fractures or branches of a complex fracture will 
alter both the total leak -off surface area and t he overall 
fracture stiffness evolution. Assume the same complex 
fracture as discussed in the previous section. The 
maximum principal stress is 37 MPa and the minimum 
principal stress is 33 MPa. We further assume the natural


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maximum principal stress is 37 MPa and the minimum 
principal stress is 33 MPa. We further assume the natural 
fractures will gradually lose t heir hydraulic connectivity 
to the open hydraulic fracture when fluid pressure drops 
around 37 MPa.  Figure.13 shows the fracture stiffness 
evolution with different surface area ratio when natural 
fractures lose their hydraulic connectivity after closure. 
Compared to Figure.11, we can notice that the overall 
fracture stiffness evolution is not monotonically 
increasing with declining pressure anymore . The surface 
area ratio will shape the fracture stiffness evolution 
before the closure of natural fractures, b ut once the 
pressure drops to a certain level and disconnect the 
natural fractures, the overall fracture stiffness becomes 
the fracture stiffness of the remaining hydraulic fracture.  
Figure.14 shows the pressure decline and its derivatives 
of complex fract ure geometry when closed fractures lose


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Figure.14 shows the pressure decline and its derivatives 
of complex fract ure geometry when closed fractures lose 
hydraulic connectivity. It can be clearly observed that 
there are two peaks on pressure derivatives curve, the 
first one is associated with the closure process of natural 
fractures, and the second one is associated w ith the 
closure process of the hydraulic fracture.  
  
Fig. 13 Pressure decline and its derivatives of complex 
fracture geometry (lose hydraulic connectivity after closure)  
 
 
Fig. 14 Pressure decline and its derivatives of complex 
fracture geometry (lose hydraulic connectivity after closure)  
Table 4. Comparison of estimated closure stress of complex 
fracture geometry (lose hydraulic connectivity after closure)  
𝑨𝒇𝟐
𝑨𝒇𝟏 Tangent Line 
Method  Compliance 
Method  Variable Compliance 
Method  
𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  
0.5 30.5  -2.5 35.4  2.4 33.4  0.4


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Method  
𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  𝝈𝒉𝒎𝒊𝒏  
(MPa)  Error 
(MPa)  
0.5 30.5  -2.5 35.4  2.4 33.4  0.4 
1 30.6  -2.4 35.5  2.5 33.4  0.4 
5 30.7  -2.3 35. 2.7 33.6  0.6 
10 30.9  -2.1 35.8  2.8 33.6  0.6 
 
If we only analyzed the portion of data after the first 
peak of pressure derivatives and use it to estimate the 
closure stress associated with the closure of the 
hydraulic fracture, we can compare the results from 
different methods, as shown in Table 4. Ag ain, we can 
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notice that “tangent line method” underestimates closure 
stress while “compliance method” overestimates closure 
stress. The “variable compliance method” is more 
reliable and gives the least errors.  
In reality, a complex fracture can consist of many 
fracture sets with different orientations and surface area . 
The approach and analysis presented for our simplified 
cases are still valid for these more general scenarios. 
Assum ing that  a complex fracture has four sets of 
fractures with equal surface area, but open against 
different in -situ stresses (37 MPa, 35 MPa, 33MPa and 
31 MPa, where 31 MPa is the minimum principal stress) 
because of their orientations, Figure.15 shows the 
evolutio n of fracture stiffness as a function of fracturing 
pressure. As can be seen, if natural fractures gradually 
lose their hydraulic connectivity around the normal 
stress that is perpendicular to that fracture surface, the 
overall fracture stiffness will exhi bit three peaks before


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stress that is perpendicular to that fracture surface, the 
overall fracture stiffness will exhi bit three peaks before 
it finally reflects the fracture stiffness of the last open 
fracture.  
 
Fig. 15 Fracture stiffness evolution of complex fracture 
geometry with four sets of fracture  
Figure.16 shows the corresponding pressure decline and 
its derivatives. As expected, four peaks emerge on the 
pressure derivatives and if we only analyze the portion 
of data after the third peak to estimate closure stress, the 
“tangent line method” underes timate s the closure stress 
by around 1 MPa. The “variable compliance method” 
gives a close r value. In general, estimated closure stress 
by the “tangent line method” can be regarded as the 
lower bound of closure stress and the closure stress  
estimated  by th e “compliance method” can be viewed as 
the upper bound of closure stress.  
4. COMPARISON WITH EXPERIMENT  
Craig et al. (2017) compared and discussed fracture


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the upper bound of closure stress.  
4. COMPARISON WITH EXPERIMENT  
Craig et al. (2017) compared and discussed fracture 
closure stress estimated by “Compliance Method” and 
“Tangent Line Method” using tiltmeter measurement 
and laboratory experiments.   
 
Fig. 16 Pressure decline and its derivatives of complex 
fracture geometry with four sets of fracture  
Figure.17 shows the G -function plots using data 
extracted from laboratory experiments from their study. 
As expected  the pressure decline is affected by tip 
extension and fluid transient behavior along the fracture 
soon after shut -in, so a brief pressure derivative spike 
often immediately follows shut -in. In many cases, this 
pressure derivative spike may mask the “open fract ure 
period ” (with constant stiffness) and make it difficult to 
locate the moment when the fracture stiffness starts to 
increase. If the closure time is not long enough, this 
early time abnormal pressure (large pressure drop during


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increase. If the closure time is not long enough, this 
early time abnormal pressure (large pressure drop during 
a short time interval) c an’t be distingu ished from the 
signature of pressure -dependent permeability, which is 
normally the case in laboratory experiments where the 
fracture closes in less than 1 minute. In the soft rock case 
of Figure.17, the imposed closure stress is 7 MPa, but 
the closure stress estimated by the “Tangent Line 
Method” is only 3 MPa, which is significantly lower. 
Because the early -time pressure derivative spike masks a 
large portion of before closure data, the “compliance 
method” and “variable compliance method” a re not 
applicable. In the moderately hard rock case of 
Figure.17, the imposed closure stress is 16 MPa, the 
closure stress estimated by  “Tangent Line Method” is 
14.32 MPa and the closure stress estimated by  
“compliance method” is 20.16 MPa. The closure s tress 
estimated by “variable compliance method” is 17.1 MPa


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“compliance method” is 20.16 MPa. The closure s tress 
estimated by “variable compliance method” is 17.1 MPa 
at the averaged G -function time of 1.745. This result is 
consistent to our simulated synthetic cases presented in 
this study and previous  study (Wang and Sharma 
2017b) . Laboratory experiments also  show that  the 
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“variable compliance method” gives the least error and 
“Tangent Line Method” normally underestimates closure 
stress.  
 
 
Fig. 17 Laboratory fracture closure experiment for soft (upper 
figure) and moderately hard rock (lower figure) (Craig et  al. 
2017)  
5. DISCUSSION  
Examining Eq.(1)~Eq.(9) closely, it is evident that the 
pressure decline is governed by a linear Partial 
Differential Equation (PDE) system in the formation that 
is coupled with an Ordinary Differential Equation 
(ODE) at the fracture surface. The minimum in -situ 
stress is just one of many implicit factors that shape the 
evolution of the fracture pressure  in the boundary ODE. 
The causes for the error associated with “tangent line 
method” stems from the traditional G -function plot 
analys is, where the assumptions of Carter’s leak -off and 
constant fracture stiffness during closure (changes 
abruptly to infinite at closure stress) are invalid. The


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constant fracture stiffness during closure (changes 
abruptly to infinite at closure stress) are invalid. The 
causes for the error associated with “ compliance method” is due to the fact that the increase of  fracture 
stiffness can happen even before fracturing pressure 
drops to minimum in -situ stress.  
For a planar fracture geometry, the fracture closes 
progressively from its edges to the center with a gradual 
increase in stiffness, if both numerical modeling (as 
shown in Fig. 5) and tiltmeter measurement s (as shown 
in Fig.6) only shows  smooth curves without a clear 
indication of closure  stress, then the pressure decline 
signature that reflects the combined effects of pressure -
dependent leak -off and fractures  stiffness evolution is 
not going to yield additional information on closure 
stress. The “variable compliance method”, provides an 
alternative way to estimate the minimum in -situ stress. 
By history matching the DFIT data, using properties of


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alternative way to estimate the minimum in -situ stress. 
By history matching the DFIT data, using properties of 
fracture surfa ce roughness and formation flow capacity, 
the ranges of un -propped fracture conductivity and 
formation permeability can be obtained for various 
fracture dimension s (Wang and Sharma 2018).  
In naturally fractured reservoirs, it is difficult to quantify 
such information through a history match. In the case of 
pressure -dependent permeability, the pressure response 
is affected by the declining effective permeability and 
the increase of fracture stiffness. Those two independent 
mechanisms are intertwined and can not be separated 
from the before -closure data, especially in the case 
where the period of pressure -dependent permeability 
spans a large portion of before -closure data. In other 
words, the information on the individual evolution of 
fracture stiffness and ef fective permeability is lost and


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words, the information on the individual evolution of 
fracture stiffness and ef fective permeability is lost and 
cannot be recovered quantitatively from DFIT data. In 
the case of complex fracture s, if the closed fracture 
segments retain their hydraulic connectivity to the main 
hydraulic fracture, we will get a smooth pressure decline 
response. In such case s, we do not know what the 
topology of the complex fracture is and we will not be 
able to constrain the fracture dimension using  a simple 
material balance calculation. Without a good estimation 
of the initial fracture geometry to star t with, a 
meaningful history match and uncertainty analysis are 
not possible. If the closed fracture segments lose 
hydraulic connectivity to the main hydraulic fracture, we 
will observe multiple pressure derivative peaks on G -
function or square  root of tim e plots. In such case s, we 
can discern, at least, how many sets of fractures (with


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function or square  root of tim e plots. In such case s, we 
can discern, at least, how many sets of fractures (with 
different orientations) exist. However, we still have no 
knowledge of the fracture t opology, because the 
information on the individual fracture surface area and 
their stiffn ess are smeared together and can’t be 
separated. The situation can get more complicated if 
some of the closed fracture segments retain their 
hydraulic connectivity to the main fracture while other s 
do not. Nevertheless, our proposed “variable compliance 
method” provides an alternative way to estimate in -situ 
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stress, which can be more reliable than established 
methods, even in naturally fractured reservoirs.  
6. CONCLUSIONS  
In this study, we  present a new pressure transient model 
for DFIT analysis in naturally fractured reservoirs, 
which not only preserves the physics of unsteady -state 
reservoir flow behavior, elastic fracture mechanics , 
material balance, varia ble fracture compliance during 
fracture closure,  but also incorporates pressure -
dependent effective permeability and sequential closure 
of complex fracture branches. Conclusions reached from 
the analysis presented in this paper include the following:  
1) Fracture closure stress (i.e., minimum in -situ stress) 
can’t be pinpointed from DFIT data because of the 
natur e of progressive fracture closure behav ior. 
2) Heavily fractured reservoirs that exhibit pressure -
dependent effective permeability can partly mask 
some information on fracture stiffness (or 
compl iance) evolution and the associated mechanical


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dependent effective permeability can partly mask 
some information on fracture stiffness (or 
compl iance) evolution and the associated mechanical 
closure process . 
3) In sparsely  or more moderately fractured reservoir s 
with complex fracture geometry, if the closed fracture 
maintains  its hydraulic connectivity to the open 
fracture, then fracture complexity cannot be detected 
from before -closure data and the pressure decline 
response resembles a  fracture with  “rougher” fracture 
walls . However, if the closed fracture lose s its 
hydraulic connectivity to the open fracture, then 
fracture complexity can be detected qualitatively by 
the existence of multiple peaks on the pressure 
derivative  plot. 
4) The c onventional “tangent line method” consistently 
underestimates closure stress w hile “compliance 
method” tends to only reflect  the onset of fracture 
closure . Our proposed “variable compliance method” 
gives a much more accurate and reliable estimation of


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closure . Our proposed “variable compliance method” 
gives a much more accurate and reliable estimation of 
closure stress in both homogenous and naturally 
fractured reservoirs.  
 
REFERENCES  
1. Barree, R.D., Barree, V.L. and Craig, D., 2009. Holistic 
fracture diagnostics: consistent interpretation of prefrac  
injection tests using multiple analysis methods.  SPE 
Production & Operations,  24(03), pp.396 -406. 
http://dx.doi.org/ 10.2118/107877 -PA 
2. Craig , D. P., Barree, R. D., Warpinski, N. R., and 
Blasingame, T. A. 2017. Fracture Closure Stress: 
Reexamining Field and Laboratory Experiments of 
Fracture Closure Using Modern Interpretation 
Methodologies. Paper presented at the SPE Annual 
Technical Conferenc e and Exhibition, 9 -11 October, 
San Antonio, Texas, USA.  https://doi.org/10.2118/187038 -MS 
3. Fu, Y., Dehghanpour, H., Ezulike, D. O., and Jones, R. 
S. 2017. Estimating Effective Fracture Pore Volume 
From Flowback Data and Evaluating Its Relationship to


key: chroma:document
string_value:
S. 2017. Estimating Effective Fracture Pore Volume 
From Flowback Data and Evaluating Its Relationship to 
Design Parameters of Multistage -Fracture Completion. 
SPE Production & Operations, Vol  (32)04:423 -439.  
https://doi.org/10.2118/175892 -PA 
4. Loughry, D., Epps, D. and Forrest, J., 2015. Using Pad 
ISIP, DFIT, and ES P Data to Generate a Pore Pressure 
Model for the Midland Basin. Paper presented at the 
Unconventional Resources Technology Conference, 
San Antonio, Texas, USA, 20 -22 July. 
https://doi.org/10.15530/URTEC -2015 -2162973  
5. McClure, M.W., Jung, H., Cramer, D.D. an d Sharma, 
M.M., 2016. The Fracture Compliance Method for 
Picking Closure Pressure from Diagnostic Fracture -
Injection Tests.  SPE Journal 21(04):1321 -1339. 
http://dx.doi.org/10.2118/179725 -PA 
6. Mirani, A., Ma rongiu -Porcu, M., Wang, H., Philippe, 
E. Production -Pressure -Drawdown Management for 
Fractured Horizontal Wells in Shale -Gas Formations.


key: chroma:document
string_value:
E. Production -Pressure -Drawdown Management for 
Fractured Horizontal Wells in Shale -Gas Formations. 
2017. SPE Reservoir Evaluation & Engineering 
(Preprint ). http://dx.doi.org/10.2118/181365 -PA 
7. Nolte, K. G. 1979. Determi nation of Fracture 
Parameters from Fracturing Pressure Decline.  Paper 
8341 presented at the SPE Annual Technical 
Conference and Exhibition, Las Vegas, Nevada, 23 -26 
September. http://dx.doi.org/10.2118/8341 -MS 
8. Nolte, K. G. 1986. A General Analysis of Fract uring 
Pressure Decline with Application to Three Models. 
SPE Formation Evaluation. Vol (1) 06:571 -583. 
http://dx.doi.org/10.2118/12941 -PA 
9. Potocki , D. J. 2012. Understanding Induced Fracture 
Complexity in Different Geological Settings Using 
DFIT Net Fracture Pressure. Paper SPE 162814 
presented at the SPE Canadian Unconventional 
Resources Conference, Calgary, Alberta, Canada, 30 
October -1 November.  
http://dx.doi.org/10.2118/162814 -MS


key: chroma:document
string_value:
Resources Conference, Calgary, Alberta, Canada, 30 
October -1 November.  
http://dx.doi.org/10.2118/162814 -MS 
10. Ramurthy , M., Barree, R.D., Kundert, D.P., Petre, J.E. 
and Mullen, M.J., 2011. Surface -area vs. conductivity -
type fracture treatments in shale reservoirs.  SPE 
Production & Operations,  26(04), pp.357 -367. 
https://doi.org/10.2118/140169 -PA 
11. Wang, H and Sharma, M.M. 2017a. A Non -Local 
Model for Fracture Closure on Rough Fracture Faces 
and Asperities. Journal of Petroleum Science and 
Engineering, Vol  (154):425 -437. http://dx.doi.org/ 
10.1016/j.petrol.2017.04.024  
12. Wang, H and Sharma, M.M. 2017b. New Variable 
Compliance Method for Estimating Closure Stress and 
Fracture Compliance from DFIT data. Paper SPE 
187348 presented at the SPE Annual Technical 
Conference and Exhi bition held in San Antonio, TX, 
USA, 09 – 11 October. http://dx.doi.org/10.2118/


key: chroma:document
string_value:
187348 presented at the SPE Annual Technical 
Conference and Exhi bition held in San Antonio, TX, 
USA, 09 – 11 October. http://dx.doi.org/10.2118/ 
187348 -MS Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA18/All-ARMA18/ARMA-2018-225/1190432/arma-2018-225.pdf/1 by University of Houston user on 30 October 2023


key: chroma:document
string_value:
13. Wang, H. 2015. Numerical Modeling of Non -Planar 
Hydraulic Fracture Propagation in Brittle and Ductile 
Rocks using XFEM with Cohesive Zone Method. 
Journal of Petroleum Science and Engineering , Vol 
(135):127-140. 
http://dx.doi.org/10.1016/j.petrol.2015.08.010  
14. Wang, H. 2016. Numerical Investigation of Fracture 
Spacing and Sequencing Effects on Multiple Hydraulic 
Fracture Interference and Coalescence in Brittle an d 
Ductile Reservoir Rocks. Engineering Fracture 
Mechanics, Vol (157): 107 -124.  
http://dx.doi.org/10.1016/j.engfracmech.2016.02.025  
15. Wang, H. 2017. What Factors Control Shale Gas 
Production and Production Decline Trend in Fractured 
Systems: A Comprehensive Analysis and Investigation. 
SPE Journal, Vol 22(02): 562 -581.  
http://dx.doi.org/10.2118/179967 -PA 
16. Wang, H. and Sharma, M.M. 2018. Estimating Un -
propped Fracture Conductivity and Fracture 
Compliance from Diagnostic Fracture Injection Tests. 
SPE Journal (Pr eprint).


key: chroma:document
string_value:
propped Fracture Conductivity and Fracture 
Compliance from Diagnostic Fracture Injection Tests. 
SPE Journal (Pr eprint).  
http://dx.doi.org/10.2118/189844 -PA  
17. Wang, H., Marongiu -Porcu, M., and Economides, M. J. 
2016. Poroelastic and Poroplastic Modeling of 
Hydraulic Fracturing in Brittle and Ductile Formations, 
Journal of SPE Production & Operations , 31(01): 47 –
59. http://dx.doi.org/10.2118/168600 -PA 
18. Wang, H. , Yi ,S., and Sharma, M.M.  2018. A 
Computationally Efficient Approach to Modeling 
Contact Problems  and   Fracture  Closure  Using  
Superposition  Method.  Theoretical and  Applied  
Fracture Mechanics, Vol(93): 27 6-287. 
https://doi.org/10.1016/j.tafmec.2017.09.009  
19. Willis -Richards, J., K. Watanabe, H. Takahashi. 1996. 
Progress toward a stochastic rock mechanics model of 
engineered geothermal systems. Journal of Geophysical 
Research 101 (B8): 17481 -17496 . 
http://dx.doi.org/10.1029/96JB00882.


key: chroma:document
string_value:
Research 101 (B8): 17481 -17496 . 
http://dx.doi.org/10.1029/96JB00882.  
 
 
 
 
 
 
 
 
 
 
 
 
 Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA18/All-ARMA18/ARMA-2018-225/1190432/arma-2018-225.pdf/1 by University of Houston user on 30 October 2023


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1. INTRODUCTION  
Diagnostic fracture injection tests (DFIT), also referred to 
as a minifrac  test, have been a standard stimulation 
technique in unconventional reservoirs to determine the 
reservoir characteristics. DFIT analysis can estimate key 
reservoir parameters such as reservoir permeability and 
initial reservoir pressure to aid in future frac ture designs. 
A typical DFIT test consists of pumping small amounts of 
fluid, usually water, down the wellbore to initiate the 
stimulation test in the reservoir. Enough water is pumped 
down hole to initiate a small fracture to breakdown the 
formation. The fracture  will continue to propagate until 
pumping is completed and the well is shut in. Once shut -
in occurs, the pressure falloff  response is recorded over a 
long period of time which can be from a few days to 
weeks. An analysis on the pressure data recorded is do ne 
to estimate several reservoir characteristics.  
The pressure response from a DFIT analysis can be


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to estimate several reservoir characteristics.  
The pressure response from a DFIT analysis can be 
separated into two parts: before -closure analysis (BCA) 
and after -closure analysis (ACA). The BCA region of a DFIT test is considered the period when water is injected 
into the wellbore to create a small fracture  until the 
created fracture is mechanically closed. Key parameters 
that can be determined from BCA are fracture closure 
pressure, instantaneous shut -in pressure (ISP), closure 
gradient, net fracture p ressure, fluid efficiency and leak -
off coefficient. The ACA region of the DFIT test is the 
time after the fracture is closed to the end of the shut -in 
period.  Fig. 1 shows a typical pressure response during a 
DFIT test.  
Key parameters that can be determined from ACA are 
flow regime, permeability, and transmissibility. Several 
numerical and analytical models are available to analyze 
the pressure response recorded during BCA and ACA.


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numerical and analytical models are available to analyze 
the pressure response recorded during BCA and ACA.  
Traditional DFIT before closure  analysi s does not 
consider natural fractures. The Perkins -Kern -Nordgren 
(PKN) fracture geometry model created by Perkins and 
Kern and later improved by Nordgren ( Nordgren , 1972; 
Nolte , 1979; Perkins and Kern , 1961 ) derived several key 
parameters: fluid loss coeff icient, fluid efficiency,             
ARMA 21–1387                                                                 
 
New Diagnostic Fracture Injection Test Model with  
Complex Natural Fractures using Embedded Discrete Fracture Model  
 
Bruno , Jonathan and Sun, He 
The University of Texas at Austin, Austin, TX, USA  
Yu, Wei  
Sim Tech LLC, Houston, Texas, USA  
Sepehrnoori, Kamy  
The University of Texas at Austin, Austin, TX, USA  
 
Copyright 20 21 ARMA, American Rock Mechanics Association


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Sepehrnoori, Kamy  
The University of Texas at Austin, Austin, TX, USA  
 
Copyright 20 21 ARMA, American Rock Mechanics Association  
This paper was prepared for presentation at the 55th US Rock Mechanics/Geomechanics Symposium held in Houston, Texas, USA, 20-23 June  
2021. This paper was selected for presentation at the symposium by an ARMA Tech nical Program Committee based on a technical and critical 
review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any pos ition of ARMA, its 
officers, or m embers. Electronic reproduction, distrib ution, or storage of any part of this paper for commercial purposes without the written consent 
of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illus trations may not be copied. The 
abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.


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abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.   
 
 
 ABSTRACT:  Application of diagnostic fracture injection tests (DFIT) are used in unconventional reservoirs to determine rese rvoir 
characteristics for future fracture design and production. The presence of natural fractures can heavily influence the pre - and post -
shut-in pressure data obtained from DFIT. Traditional DFIT models do not capture the complexity of hydraulic and natu ral fracture 
networks into an integrated workflow. This work uses an embedded discrete fracture model (EDFM) to add natural fracture 
complexity into a new DFIT model in conjunction with any reservoir simulator to simulate the pressure response. Incorporati ng 
fracture modeling tools will enhance the existing reservoir model by creating a more accurate representation of an unconventi onal


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fracture modeling tools will enhance the existing reservoir model by creating a more accurate representation of an unconventi onal 
reservoir for future development strategies. EDFM can easily incorporate complex fractures and accurately be embedded in st ructed 
matrix block. Pressure data from the DFIT analysis can be separated into two parts: before -closure analysis (BCA) and after -closure 
analysis (ACA). Past models have analyzed BCA and ACA independently, which can lead to misinterpretation. The new DFI T model 
combines the BCA and ACA while including complex natural fractures into a single workflow. Data from the Lower Eagle Ford 
Formation was used to validate the model by accurately matching the same field data with the new workflow. The workflow consi sts 
of identifying random natural factures connected to the generated small fracture  to observe the true pressure response during DFIT.


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of identifying random natural factures connected to the generated small fracture  to observe the true pressure response during DFIT. 
The workflow in this study can be applied to any DFIT data. Understanding the impact complex natural fractures have on pr essure 
response through an integrated DFIT model with EDFM is important to determine reservoir characteristic and geomechanics for 
future fracture designs.  
 
 
  
 
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fracture closure pressure, fracture length, and fracture 
width. Nolte, in his G -function model, was able to easily 
distinguish the closure pressure using a plot of a derived 
G-function and pressure.  Nolte’s derivation did not 
consider the complexity of natural fractures. His work 
only considered a simple planar fracture  with no natural 
fractures. The effects of natural fractures cannot be 
characterized or evaluated.  
 
Fig. 1. Typical DFIT test pressure response diagram  (Wang 
and Sharma, 2017) . 
Traditional DFIT A fter closure analysis also does not 
consider natural fractures. Soliman ( Soliman et al. , 2005 ) 
has worked on the pressure fall off analysis to estimate 
the formation permeability and pressure. From the 
pressure r esponse, each flow regime can be identified. 
Formation permeability can be estimated based on the 
transient pressure behavior.  ACA analysis fails to 
consider the fracture complexity.


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Formation permeability can be estimated based on the 
transient pressure behavior.  ACA analysis fails to 
consider the fracture complexity.  
In this work, n atural fractures can heavily influence the 
before closure  and after closure pressure response during 
a DFIT test. Traditional BCA and ACA DFIT models do 
not capture the complexity of the natural fracture network 
connected to a small fracture . The pressure transient 
behavior will be influenced by the geometry and density 
of the natural fractures. Implementing natural fractures 
would give a more accurate representation of 
unconventional reservoirs. The pressure data during a 
DFIT test can be co herently interpreted using a single 
workflow.  This work will show the new workflow 
considering complex natural fractures coherently with a 
case study. The objective of this work is to understand and 
implement a new DFIT workflow with natural fractures. 
This work is important to understand the impact of natural


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implement a new DFIT workflow with natural fractures. 
This work is important to understand the impact of natural 
fracturs on reservoir pressure and permeability.  
2. THEORY AND MODEL DEVELOPMENT  
Several analytical models have been developed by Nolte 
that are available for DFIT analysis (Nolte , 1979, 1990; Nolte et al., 1993; Nolte et al. , 1997). Nolte pioneered the 
G-function technique for BCA and ACA analysis based 
off the Carter leak -off model (Nolte , 1979).  In 2014, 
McClure developed a fracture -compliance method for 
estimating the closure pressure for DFIT test a ssuming a 
variable fracture compliance (McClure et al. , 2014). The 
G-function derivative plot was analyzed with a changing 
fracture compliance during closure (McClure et al. , 
2014). The variable compliance method was created by 
Wang et al. (2017) where the  fracture closure point is 
determined to be average of the fracture closure points 
picked using the fracture -compliance method and tangent


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determined to be average of the fracture closure points 
picked using the fracture -compliance method and tangent 
line method. The tangent line method is considered the 
upper bound while the fracture -compliance method is 
considered  the lower bound for the fracture closure point.  
In this study, the G -function technique was used  to 
determine the closure point . 
The application of G -function technique across multiple 
leak-off factors validated Nolte’s model. The original G -
function mode l from Nolte is based on the following 
assumptions:  
(i) constant fracture compliance  
(ii) constant fracture height  
(iii) constant closure pressure  
(iv) constant fracture surface after shut -in 
(v) leak-off coefficient independent of pressure 
change  
(vi) material balance between leak -off fluid volume 
and fracture volume  
The analytical solution for Nolte’s G -function time is the 
following:  
 
𝑔(∆𝑡𝐷)=
{(1+∆𝑡𝐷)sin−1(1+∆𝑡𝐷)−1
2+∆𝑡𝐷1
2    𝛼=1
2
4
3((1+∆𝑡𝐷)3
2−∆𝑡𝐷3


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The analytical solution for Nolte’s G -function time is the 
following:  
 
𝑔(∆𝑡𝐷)=
{(1+∆𝑡𝐷)sin−1(1+∆𝑡𝐷)−1
2+∆𝑡𝐷1
2    𝛼=1
2
4
3((1+∆𝑡𝐷)3
2−∆𝑡𝐷3
2)                             𝛼=1          (1) 
𝐺(∆𝑡𝐷)=4
𝜋[𝑔(∆𝑡𝐷)−𝑔0]   (2) 
𝑔0=𝑔(∆𝑡𝐷=0)    (3) 
∆𝑡𝐷=𝑡−𝑡𝑝
𝑡𝑝    (4) 
 
 
where t is the shut -in time and t p is the total pump time. A 
α value of 1/2 refers to a formation with low fluid leak -
off. A α value of 1 refers to a formation with high fluid 
leak-off. The G -function time solution starts at the shut -
in or when the instantaneous shut -in pressure (ISIP) is 
zero. From Nolte’s G -function time model, Barree used a 
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diagnostic approach to identify the fracture closure 
pressure (Barree , 1998; Barree et al. , 2009). The 
composite derivative of G -function, G *dp/dG, is used to 
show where the pressure change occurs. A s traight line 
can be drawn from the origin from the plot of G *dp/dG 
against G -function time. The deviation point from the 
G*dp/dG curve from the straight line is used as the 
fracture closure point. The closure point was estimated to 
be 25.30 G -function time . Fig. 2 shows the of G *dp/dG 
against G -function time.  
 
 
Fig. 2. Closure point selection using G*dp/dG versus G time . 
The closure point is important to estimate the closure 
stress of the formation from the DFIT data. Using Nolte’s 
G-function time model, the closure pressure is estimated 
to be 7100 psi. Fig . 3 shows the corresponding pressure 
profile using Nolte’s analytic al solution for G -function 
time.  
 
 
Fig. 3. Closure pressure corresponding to the previously 
established closure point.


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time.  
 
 
Fig. 3. Closure pressure corresponding to the previously 
established closure point.  
Once the fracture closure point is found, the simulation 
model can be developed. Fig . 4 shows the steps of the new 
DFIT workflow used in this case study.  
  
Fig. 4. New DFIT workflow . 
The new workflow consists of starting with a single 
fracture to represent the small fracture  created  in a DFIT 
test. With our new DFIT model fracture height , half -
length, conductivity  and closure pressure can be 
manipulated to satisfy your model setup. The new DFIT 
workflow allows the user more flexibility when setting up 
a DFIT model which previous workflows do not allow 
for. The base case model in thi s paper was set up using 
the following parameters in Table 1.  
 
Table 1. Base case parameters for DFIT reservoir model  
Base Case  
Generated  Fracture  Height (ft)  50 
Generated  Fracture  Half-length (ft)  200 
Generated  Fracture  Conductivity (mD -ft) 10


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Base Case  
Generated  Fracture  Height (ft)  50 
Generated  Fracture  Half-length (ft)  200 
Generated  Fracture  Conductivity (mD -ft) 10 
Number of Natural Fractures  60 
Natural Fracture Height (ft)  30-50 
Natural Fracture Half -length (ft)  30-70 
Natural Fracture Conductivity (mD -ft) 2.4-5.6 
Matrix Permeability (mD)  0.001  
 
An embedded discrete fracture model (EDFM) is used to 
implement a small fracture  in the reservoir model .  ED FM 
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can represent fractures with a grid outside normal models 
and uses special connections to model fluid and pressure 
transport.  This method is easy  and efficient to model any 
complex fracture geometries using structured gridding 
(Moinfar et al. , 2014; Xu , 2015; Xu et al. , 2017a, 2017b). 
The complex fractures are discretized into fracture 
segments based on the interaction between the fracture 
geometry  and the structured matrix grid boundary. The 
fluid flow between the matrix and fractures can be 
simulated using a commercial reservoir simulator such as 
CMG by using non -neighboring connections (NNCs) ( Yu 
et al, 2018).  Fig. 5 shows a visualization of the EDFM 
methodology.  
 
 
Fig. 5. Explanation of EDFM method with commercial 
reservoir simulato rs to handle 3D complex fractures (Xu et al., 
2017a)  
There are four types of NNCs: fluid flow between matrix 
and fractures, between fracture segments within a single 
fracture, between intersecting fracture segments within


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and fractures, between fracture segments within a single 
fracture, between intersecting fracture segments within 
different fractures, and between fractures and wellbores. 
More information on the EDFM methodology is available 
in the work by Xu et al. (2017a, 12017b).  This paper 
introduces the use of EDFM  to implement random  natural 
fractures  into a DFIT model . The model flexibility is 
demonstrated by characterizing d ifferent complex natural 
fracture cas es.  
Validation of the DFIT model is shown through a DFIT 
case study.  The pressure transient behavior is captured 
throughout the fracture network. The new DFIT model 
can predict the pressure decline response. Evaluation of 
the natural fractures and a gener ated small fracture  is done to show the effects of changing characterization with 
varying geometry, density, half-length , and conductivity. 
The new DFIT model can increase and decrease the 
density of natural fractures with ease.


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The new DFIT model can increase and decrease the 
density of natural fractures with ease.   
Once a small fracture  is generated, random natural 
fractures are implemented into the model using EDGS. 
EDGS allows you to generate random natural fractures 
with various geometries and density. Fig . 6 shows the 
generated  small fracture  along with the random natural 
fractures.  
 
 
Fig. 6. Generated base case for the new DFIT workflow with 
complex natural fractures.  
The pressure response is initialized in the generated a 
small fracture  using a natural fracture connectivity code. 
The connectivity code can identify the natural fractures 
that are connected to the generated small fracture . Fig. 7 
shows the DFIT model  after running the connectivity 
code. The areas in red are the natural frac tures that have 
been identified that are not connected to the generated  
small fracture . 
 
 
Fig. 7. Connectivity code evaluation of natural fractures not


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been identified that are not connected to the generated  
small fracture . 
 
 
Fig. 7. Connectivity code evaluation of natural fractures not 
connected to the  generated  small fracture . 
A closer look at the complex fracture network can be 
seen in Fig. 8. The natural fracture connections to the 
small fracture  are important to analyze the pressure 
behavior using EDFM.  
 
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Fig. 8. Closer look of the complex fracture network . 
A reservoir model is thus created to represent a DFIT test 
with complex natural fractures . The pressure response 
from the generated  small  fracture  is simulated using 
computer modeling group (CMG) reservoir simulator. 
The new workflow was able to estimate the  pressure 
response for a DFIT test.  
A closer look at the complex fracture network can be seen 
in Fig . 9. The pressure response was initialized in the 
generated  small fracture  and the distribution of the 
pressure  response is seen  throughout the complex nat ural 
fracture network.  
 
 
Fig. 9. Closer look of the complex fracture network . 
The pressure response throughout the 1st, 3rd, and 6th day 
of the new DFIT model can be seen in  Fig 10. (a), (b), and 
(c), respectively. The pressure in the fracture network 
continues to decrease the longer the well is shut -in until 
the reservoir pressure is reached.  
 
 
(a) Pressure distribution after 1 day


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continues to decrease the longer the well is shut -in until 
the reservoir pressure is reached.  
 
 
(a) Pressure distribution after 1 day  
(b) Pressure distribution after 3 days 
 
 
(c) Pressure distribution after 6 days 
Fig. 10. Pressure distribution changes shown from the (a) 1st 
day, (b) 3rd day, and (c) 6th day. 
 
The new DFIT workflow is capability of replicating the 
ACA pressure response using complex natural fractures.  
A visualization of the pressure distribution is captured 
throughout the complex fracture network.  To test the 
impact of changing various fracture  characterization  
parameters, a sensitivity analysis study is presented in the 
next section.  
3. SENSITIVITY ANALY SIS 
Sensitivity analysis was done in this study to test t he 
effects of varying the characterization of complex natural 
fractures  using our new workflow . The model was set up 
using the same generated small fracture for every case. 
The complexity of the smal l fracture depends on the


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using the same generated small fracture for every case. 
The complexity of the smal l fracture depends on the 
connected natural fracture which has a great impact on the 
pressure response.  The pressure is observed for after the 
fracture closure point. Therefore, the generated small 
fracture is considered mechanically closed. The following 
parameters were adjusted  in this study: varying the 
density of natural fractures, natural fracture  height, 
natural fracture  half-length, and natural fracture  
conductivity.  Fig 11. (a), (b), and (c) show the DFIT 
model with varying density of natural fracture from 30, 
60, and 90, respectively.  
 
(a) DFIT model with 30 natural fractures  
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(b) DFIT model with 60 natural fractures  
 
(c) DFIT model with 90 natural fractures  
Fig. 11. DFIT model with varying densit ies of natural 
fractures from (a) 30 natural fracture s, (b) 60 natural fractures, 
and (c) 90 natural fractures.  
 
Fig. 12 shows the pressure falloff  response when varying 
the number of natural fractures  using  the new DFIT 
workflow.  
 
 
Fig. 12. Sensitivity analysis on the number of natural 
fractures.  
As the number of natural fractures increase s, the pressure 
falloff  becomes less severe. The phenomenon that is 
happening is due to the number of natural fractures 
connected to the small fracture  becomes greater when 
more natural fractures are added. This would allow for a 
more even distribution of pressure throughout the fracture 
network and therefore a less severe pressure falloff . 
 
Fig. 13 shows the pressure falloff  response  of varying the 
height of the natural fractures  in the new DFIT model.


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Fig. 13 shows the pressure falloff  response  of varying the 
height of the natural fractures  in the new DFIT model.  
  
Fig. 13. Sensitivity analysis on the natural fracture  height.  
There is not a significant difference between the pressure 
falloff  response as you increase the height of the natural 
fractures . 
 
Fig. 14 shows the pressure falloff  response as you 
increase the half -length of the natural fractures .  
 
 
Fig. 14. Sensitivity analysis on the natural fracture  half-length.  
As you increase the half -length of the natural fractures , 
the pressure falloff response  becomes less severe. This 
could be du e to the larger surface area that the natural 
fractures are covering as it gets larger. The natural 
fractures are  creating a larger fracture network as you 
increase the half -length. A larger fracture network proves 
to have a less severe pressure falloff  behavior.  
 
Fig. 15 shows the pressure falloff  response as you


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to have a less severe pressure falloff  behavior.  
 
Fig. 15 shows the pressure falloff  response as you 
increase the conductivity of the natural fractures . 
 
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Fig. 15. Sensitivity analysis on the natural fracture  
conductivity.  
As you increase the conductivity of the natural fractures , 
the pressure falloff response becomes less severe.  
4. SUMMARY AND CONCLUSION  
This paper  implemented a new DFIT workflow with 
complex natural fractures.  Including complex natural 
fractures with a DFIT test enhanc es the understanding of 
the characteristics for unconventional reservoirs. The new 
DFIT workflow allows for characterization of complex 
natural fractures with varying geometry, density, 
aperture, and conductivity.  The impact of varying fracture 
parameters is evident in this study.  The number of natural 
fractures, natural fracture  half-length and natural fracture  
conductivity had an impact on the pressure falloff 
response. The pressure falloff response became less 
severe with the increase in natural fractures, the generated  
small fracture  half-length and the generated  small fracture


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severe with the increase in natural fractures, the generated  
small fracture  half-length and the generated  small fracture  
conductivity. This could be due to the larger surface area 
that the small fracture  is covering. The new DFIT 
workflow was able to estimate the pressure falloff  
behavior during a DFIT test  using the various reservoir 
and natural fracture parameter . The impact of natural 
fractur es on the pressure falloff behavior is evident in this 
study.  
Compared to traditional DFIT analysis, the new DFIT 
workflow was able to implement natural fractures using 
EDFM. The fracture network proved to h ave an impact on 
the pressure falloff  response. Characterization of the 
fracture network was captured and ensured an efficient 
analysis to estimate the reservoir properties. The 
generated fracture during a DFIT test becomes more 
complex when natural fractu res are added to the model. 
The pressure transient behavior can be captured


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complex when natural fractu res are added to the model. 
The pressure transient behavior can be captured 
through out the fracture network. The density of natural 
fractures can be easily added and reduced depending on 
the model demand s. The new DFIT workflow 
demonstrated the ability to handl e complex natural 
fractures while providing a sufficient analysis on the 
reservoi r properties.  DFIT analysis with complex natural fracture geometries will aid in future reservoir evaluation 
and production design.  
5. REFERENCES  
Barree, R.D. 1998. Applications of Pre -Frac Injection/Falloff 
Tests in Fissured Reservoirs - Field Examples. Paper presented 
at the SPE Rocky Mountain Regional/Low -Permeability 
Reservoirs Symposium, Denver, Colorado , USA,  5-8 April 
1998.  
Barree, R.D., Barr ee, V.L., and Craig, D. 2009. Holistic 
Fracture Diagnostics: Consistent Interpretation of Prefrac 
Injection Tests Using Multiple Analysis Methods. SPE 
Production & Operations  24 (03): 396 -406.


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string_value:
Injection Tests Using Multiple Analysis Methods. SPE 
Production & Operations  24 (03): 396 -406.  
McClure, M.W., Blyton, C.A., Jung, H., and Sharma, M.M. 
2014. The Effect of Changing Fracture Compliance on Pressure 
Transient Behavior During Diagnostic Fracture Injection Tests. 
Paper presented at the SPE Annual Technical Conference and 
Exhibition, Amsterdam, The Netherlands, 27 -29 October 2014.   
Moinfar, A., Varav ei, A., Sepehrnoori, K. et al. 2014. 
Development of an Efficient Embedded Discrete Fracture 
Model for 3D Compositional Reservoir Simulation in Fractured 
Reservoirs. SPE Journal  19 (02): 289 -303. 
Nolte, K.G. 1979. Determination of Fracture Parameters from 
Fracturing Pressure Decline. Paper presented at the SPE 
Annual Technical Conference and Exhibition, Las Vegas, 
Nevada,  USA,  23-26 September 1979.  
Nolte, K.G. 1990. Fracturing -Pressure Analysis fo r Nonideal 
Behavior . Journal of Petroleum Technology  43 (02): 210 -218.


key: chroma:document
string_value:
Nolte, K.G. 1990. Fracturing -Pressure Analysis fo r Nonideal 
Behavior . Journal of Petroleum Technology  43 (02): 210 -218. 
Nolte, K.G., Mack, M.G., and Lie, W.L. 1993. A Systematic 
Method for Applying Fracturing Pressure Decline: Part I. Paper 
presented at the Low Permeability Reservoirs Symposium, 
Denver, Colorado , USA, 26-28 April 1993.  
Nolte, K.G., Maniere, J.L., and Owens, K.A. 1997. After -
Closure Analysis of Fracture Calibration Tests. Paper 
presented at the SPE Annual Technical Conference and 
Exhibition, San Antonio, Texas , USA,  5-8 October 1997.  
Nordg ren R .P. 1972. Propagation of a Vertical Hydraulic 
Fracture. Society of Petroleum Engineers Journal 12 (04): 306 -
314. 
Perkins T .K, Kern L .R. 1961. Widths of Hydraulic Fractures.  
Journal of Petroleum Technology 13 (09): 937 -949. 
Soliman M .Y., Craig D .P., Bartko K .M., Rahim Z ., Adams 
D.M. 2005.  Post-Closure Analysis to Determine Formation


key: chroma:document
string_value:
Soliman M .Y., Craig D .P., Bartko K .M., Rahim Z ., Adams 
D.M. 2005.  Post-Closure Analysis to Determine Formation 
Permeability, Reservoir Pressure, Residual Fracture Properties. 
Paper presented at the SPE Middle East Oil and Gas Show and 
Conference, Kingdom of Bahrain, Bahrain, 12 -15 March 2005.  
Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA21/All-ARMA21/ARMA-2021-1387/2479604/arma-2021-1387.pdf/1 by University of Houston user on 30 October 2023


key: chroma:document
string_value:
Wang, H., and Sharma, M.M. 2017. New Variable Compliance 
Method for Estimating In -Situ Stress and Leak -Off from DFIT 
Data. Paper presented at the SPE Annual Technical Conference 
and Exhibition, San Antonio, Texas, USA, 9 -11 October 2017.  
Xu, Y., 2015. Implementation and Application of the 
Embedded Discrete Fracture Model (EDFM) for Reservoir 
Simulation in Fractured Reservoirs. Master Thesis, The 
University of Texas at Austin, Austin, Texas, USA.  
Xu, Y., Cavalcante Filho, J.S., Yu, W., and Sepe hrnoori, K. 
2017a. Discrete -Fracture Modeling of Complex Hydraulic 
Fracture Geometries in Reservoir Simulators. SPE Reservoir 
Evaluation and Engineering  20 (02): 403 -433. 
Xu, Y., Yu, W., and Sepehrnoori, K. 2017b. Modeling Dynamic 
Behaviors of Complex Frac ture in Conventional Reservoir 
Simulators. Paper presented at the SPE/AAPG/SEG 
Unconventional Resources Technology Conference , Austin, 
Texas, USA, 24 -26 July 2017.


key: chroma:document
string_value:
Simulators. Paper presented at the SPE/AAPG/SEG 
Unconventional Resources Technology Conference , Austin, 
Texas, USA, 24 -26 July 2017.  
Yu, W., Xu, Y., Weijermars, R., Wu, K., and Sepehrnnori, K., 
2018. A Numerical Model for Sim ulating Pressure Response of 
Well Interference and Well Performance in Tight Oil 
Reservoirs with Complex -Fracture Geometries Using the Fast 
Embedded -Discrete -Fracture -Model Method . SPE Reservoir 
Evaluation and Engineering  21 (02): 489 -502. Downloaded from http://onepetro.org/ARMAUSRMS/proceedings-pdf/ARMA21/All-ARMA21/ARMA-2021-1387/2479604/arma-2021-1387.pdf/1 by University of Houston user on 30 October 2023


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URTEC-208276-MS
Can ISIP Really Tell Closure Pressure?—Case Study of Consecutive DFITs in
the Eagle Ford
Shintaro Kuroda , Shunichi Watanabe, and Kenji Ueda , INPEX CORPORATION
Copyright 2021, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/AP-URTEC-2021-208276
This paper was prepared for presentation at the SPE/AAPG/SEG Asia Pacific Unconventional Resources Technology Conference to be held virtually on 16–18
November, 2021.
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


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risk. The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper without the written
consent of URTeC is prohibited.
Abstract
The objective of this paper is to investigate how to acquire fracture closure pressure data accurately and cost-
effectively in shale development activities. If the injection volume is small during a hydraulic fracturing
job, it is a common practice to consider the ISIP (Instantaneous Shut-In Pressure) as a proxy of fracture
closure pressure, which generally requires a long falloff period to evaluate. However, ISIP should consist
of variable parameters such as the original closure pressure, net pressure, stress shadow effect, and mid-
field fracture complexity.
In this paper, we introduce the consecutive DFITs (Diagnostic Fracture Injection Test) approach. Closure
pressure is evaluated by falloff pressure analysis after a micro fracturing injection operation, and pore


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pressure is evaluated by falloff pressure analysis after a micro fracturing injection operation, and pore
pressure could also be evaluated if the falloff period is long enough. This micro fracturing operation is
generally called DFIT. In order to evaluate how the ISIP, closure pressure, and pore pressure change from
stage to stage, we performed DFITs consecutively at the sequential hydraulic fracturing stages in a horizontal
well drilled in the Eagle Ford shale.
The consecutive DFITs revealed that the ISIP gradually increased up to certain level from fracturing stage
to stage as expected. However, the observed closure pressure was almost constant in the sequential stages,
which was against our expectations. In addition, the evaluated pore pressure was also almost constant.
Initially we expected that closure pressure would increase because of the uplift due to the stress shadow
effect. Since the consecutive DFITs showed the same closure pressure in each stage, we concluded that stress


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effect. Since the consecutive DFITs showed the same closure pressure in each stage, we concluded that stress
uplift could disappear before the fracture closure in next stage or that the stress shadow had little impact on
the closure pressure and the pore pressure in next stage under the current fracture design. On the other hand,
the ISIP could be affected by the stress shadow in the short term or by the mid-field fracture complexity
becoming higher than the previous stage. The correlation between the ISIP and the closure pressure was
established with these consecutive DFITs results. Although the gap between the ISIP and closure pressure
varies from stage to stage, it was confirmed that the correlation, with some uncertainties, could be used to
estimate the closure pressure within an acceptable range.
This paper presents the Eagle Ford case study, which confirmed how accurately ISIP can determine


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This paper presents the Eagle Ford case study, which confirmed how accurately ISIP can determine
closure pressure considering multiple factors. There are hydraulic fracturing operations in huge number of
horizontal wells in the shale development. Therefore, the correlation built by consecutive DFITs is usefulDownloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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2 URTEC-208276-MS
because that correlation can provide operators with the confidence to optimize the completion design based
on the ISIP which can be obtained at a low cost.
Introduction
Many hydraulic fracturing stages are routinely performed in shale development activities, but it is rare to
spend additional time and money for data acquisition. ISIP (Instantaneous Shut-In Pressure) is an important
parameter by which operators can obtain subsurface information during the hydraulic fracturing job without
extra effort. This ISIP equals the pressure in the fracture just after pump shut-in, and after friction forces in
the wellbore, perforations, and near-wellbore region dissipate. Although many operators often use the ISIP
at the wellhead rather than at the bottom hole for its ease, we use ISIP at bottom hole in this paper, calculating
its value from the ISIP measured by the wellsite supervisor at wellhead pressure and the fluid density.


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its value from the ISIP measured by the wellsite supervisor at wellhead pressure and the fluid density.
If the injection volume is small during the hydraulic fracturing job, it is common practice to consider
ISIP as a proxy of fracture closure pressure, which generally requires a long falloff period to evaluate. Craig
(2005)  showed the injection volume ranged from less than 200 to greater than 10,000 gal, and our case
was 15,000 gal considering the multiple perforation clusters. Smaller injection volume can create smaller
fracture volume, which means lower net pressure. If the net pressure is so low as to be negligible, the
obtained ISIP can be close to the fracture closure pressure. However, Bazan and Meyer (2015)  showed
that there are other factors to consider, including mid-field fracture complexity, back stress, also called
stress shadow effect, as well as the net pressure between the ISIP and the closure pressure. Considering


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stress shadow effect, as well as the net pressure between the ISIP and the closure pressure. Considering
the existence of several parameters between the ISIP and the closure pressure, the objective of this paper
is to investigate how to acquire fracture closure pressure data accurately and cost-effectively in shale
development activities.
The study field in this paper is the Eagle Ford shale play located in South Texas, in the United States as
shown in Fig. 1 . The Eagle Ford shale is the second most productive oil play in the United States as of 2020
and it is a Late Cretaceous package of organic-rich marl, limestone, and mudstone overlain by the Austin
chalk and bounded below by the Buda limestone ( Engle et al. 2020 ).
Figure 1—Location of the project.
Methods
A Diagnostic Fracture Injection Test (DFIT) is a small pump-in treatment performed to help design the
follow-up hydraulic fracturing treatment of wells so as to characterize the subject reservoir ( Barree et al.


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follow-up hydraulic fracturing treatment of wells so as to characterize the subject reservoir ( Barree et al.
2015 ). It is a micro fracturing injection test for data acquisition, and it is also called a mini frac, fractureDownloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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URTEC-208276-MS 3
calibration test, or fracture injection and falloff test. Through the DFIT operation and analysis, we expect to
get several parameters such as the ISIP, the fracture closure pressure, the net pressure, the fluid efficiency, the
reservoir pore pressure, and the permeability, depending on the pressure behavior. The DFIT analysis period
can be divided into two portions: before closure and after closure. The closure pressure is evaluated by a
falloff pressure analysis in the period before closure. Barree and Mukherjee (1996)  described several types
of normal leakoff phenomena including pressure dependent leakoff, tip extension after shut-in, variable
fracture compliance, height recession or transverse storage. Liu and Economides (2015) considered variable
compliance and many other abnormal leakoff behaviors, and McClure et al. (2014 , 2016 ) introduced the
fracture compliance method. In this paper, we did not apply the fracture compliance method but applied the


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fracture compliance method. In this paper, we did not apply the fracture compliance method but applied the
conventional tangent line method in a G-function plot for the simplified analysis workflow. Soliman et al.
(2005)  have shown that after-closure analysis can provide reservoir pore pressure and permeability if the
flow regime reaches pseudo linear flow or pseudo radial flow. A flow identification plot is used to identify
these flow regimes after closure, then a linear flow time function or a radial flow time function are used to
evaluate the reservoir pore pressure or permeability.
A DFIT is generally performed in the toe stage of horizontal wells before starting the main fracturing
treatment and to perform DFIT in the middle stages is not common for shale development because it requires
a certain shut-in period leading to non-productive time during the completion operation. However, there are


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a certain shut-in period leading to non-productive time during the completion operation. However, there are
still DFIT challenges in the toe stage. In the author’s past DFIT practice, using a toe-opened sleeve after
the toe preparation job in a toe stage has not been used because any potential near wellbore damage by
the wellbore clean-up job may make it difficult to analyze data.. Therefore, a new, fresh perforated entry
point is used to enhance data quality. Also, operators don’t know how much these parameters differ from
the middle and heel of the horizontal section, assuming geological and geomechanical heterogeneity in the
lateral. The ISIP obtained in each stage provides useful information to estimate the subsurface stress and
pressure along the lateral sections, other than the toe stage.
There is also the stress shadow effect from the previous fracturing stages. Roussel (2017)  showed ISIP


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There is also the stress shadow effect from the previous fracturing stages. Roussel (2017)  showed ISIP
escalation stage by stage due to the stress shadowing. This stress interference between fracturing stages is
one of the uncertain factors that can affect the fracture propagation. Another consideration is the mid-field
tortuosity. Weijers et al. (2002) states that mid-field tortuosity is recognized by a high apparent ISIP and
rapidly declining pressure during the first few minutes of shut-in. This mid-field tortuosity could be caused
by a pressure choke beyond the near-wellbore region of the fracture (Mayer and Bazan 2011; Bazan and
Meyer 2015 ). Considering these parameters as shown in Fig. 2 , our challenge was how to utilize the ISIP
in order to understand the subsurface stress condition at a low cost.


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in order to understand the subsurface stress condition at a low cost.
Figure 2—Pressure behavior image in falloff after hydraulic fracturing.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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4 URTEC-208276-MS
In this paper, we introduce "the consecutive DFITs" approach. DFITs were performed consecutively at
the selected sequential hydraulic fracturing stages in a horizontal well targeting the productive zone in the
Lower Eagle Ford shale as shown in Fig. 3 . The goal of the consecutive DFITs is to understand the pressure
changes such as the ISIP, the closure pressure, and the pore pressure from stage to stage. Five stages were
carefully selected from the total of 41 stages to avoid the subsurface fault locations identified by seismic
interpretation and a geo-steering evaluation. The tested well was the first development well in the pad.
Therefore, there were uncertainties how the faults would be affected, but no depletion was assumed from
a parent well.
Figure 3—Location of the consecutive DFITs in the horizontal well overlayed on a geo-steering plot.
Before performing these consecutive DFITs, conventional DFITs were performed at the toe section drilled


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Before performing these consecutive DFITs, conventional DFITs were performed at the toe section drilled
in another Eagle Ford area with one-month falloff period. The experience with the one-month falloff DFITs
showed that the created fracture would close within one hour which was much faster than we expected.
Based on the previous experience, we decided on a one-hour falloff for the consecutive DFITs.
In hydraulic fracturing operation workflows in the Eagle Ford development wells, the initial breakdown
injection is routinely performed before the main fracturing treatment. A short period falloff (for example, a
few minutes) after the initial breakdown injection provides the ISIP. For the consecutive DFITs, the falloff
period after the initial breakdown was extended to one hour as shown in Fig. 4 . In addition to the falloff
period extension, we modified some operation procedures such as constant pump rate, hard shut-in, and


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period extension, we modified some operation procedures such as constant pump rate, hard shut-in, and
used the same density fluid in the wellbore for better quality of the closure pressure analysis. One fluid type
in the wellbore can make it easier to calculate the bottomhole pressure from the wellhead pressure.
Figure 4—Falloff period after initial breakdown was extended for DFIT.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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URTEC-208276-MS 5
Results and Discussion
The proposed consecutive DFITs could be performed without any operational issues. The consecutive DFITs
were performed at the five stages from stage 16 to stage 20 in a single-well fracturing operation, not in a
zipper-frac operation. There were three stages where the main fracturing jobs were cancelled because of
abnormally low ISIP caused by the fault zone. As an example of the consecutive DFIT stage results, the
analysis plots in stage 18 are shown in Fig. 5  with the overall treatment, the before-closure analysis with
a G-function plot and a square root time plot, and the after-closure analysis with a flow identification plot.
Fracture closure pressure can be determined in all the five stages successfully in the before-closure analysis
as shown in Fig. 6 . In this paper, we use the pressure gradient calculated from an equation of the pressure


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as shown in Fig. 6 . In this paper, we use the pressure gradient calculated from an equation of the pressure
divided by the true vertical depth for comparison. In addition, reservoir pore pressure can also be evaluated
in four stages based on the pseudo linear flow regime after closure except for stage 16 which is close to a
fault zone. The after-closure analysis in stage 16 showed the pressure derivative increment after a short-time
pseudo linear flow regime in the flow identification plot. The evaluated pore pressure with the short-time
pseudo linear flow regime in stage 16 is higher than in the other stages. It is interpreted as SRV (Stimulated
Reservoir Volume) pressure, meaning temporarily higher pore pressure and higher permeability than the
original at the limited near wellbore area.


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Reservoir Volume) pressure, meaning temporarily higher pore pressure and higher permeability than the
original at the limited near wellbore area.
Figure 5—Treatment plot and G-function plot for one of the consecutive DFIT stages.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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Figure 6—Results of consecutive DFITs. Observed stable closure pressure gradient in five stages.
The observed ISIP gradually increased up to a certain level from fracturing stage to stage as expected.
However, the consecutive DFITs revealed that the observed closure pressure was almost constant in the
sequential stages, which went against our expectations. In addition, the evaluated pore pressure was also
almost constant except for stage 16, which was affected by SRV. Initially we expected that the closure
pressure would increase because of the uplift due to the stress shadow effect as shown in Fig 7 . Since the
consecutive DFITs showed the same closure pressure in each stage, it was concluded that stress uplift could
dissipate before the fracture closure in the next stage or that the stress shadow had little impact on the closure
pressure and the pore pressure in the next stage under the current fracture design. In this field case study, it


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pressure and the pore pressure in the next stage under the current fracture design. In this field case study, it
takes approximately two hours for plug and perforation operation between main fracturing treatments. On
the other hand, the ISIP could be affected by the stress shadow in the short term or by the mid-field fracture
complexity becoming higher than the previous stage. Permeability in the SRV area also can affect the ISIP
because the leakoff volume affects the net pressure.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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URTEC-208276-MS 7
Figure 7—Expected image of the closure pressure before and after consecutive DFIT operations.
The consecutive DFITs showed the variable differences between the ISIP and the evaluated closure
pressure from stage to stage. To establish the correlation between the ISIP and the closure pressure, we
attempted to increase the number of closure pressure data points at stages other than the five consecutive
stages where we conducted DFITs. We did this by using the falloff period from normal operations, which is
shorter than the falloff after the initial breakdown for the consecutive DFIT stages. This attempt succeeded
and gave us eleven additional points though there were five low-reliability stages. The correlation between
the ISIP and the closure pressure was established as shown in Fig. 8 . The correlation shows that uncertainties
of the estimated closure pressure are within +/- 0.07 psi/ft and that coefficient of determination, r2, is 0.77 in


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of the estimated closure pressure are within +/- 0.07 psi/ft and that coefficient of determination, r2, is 0.77 in
this case. The closure pressure is estimated by the correlation as shown in Fig. 9 . Although the gap between
the ISIP and the closure pressure varies from stage to stage, it was confirmed that the correlation, with some
uncertainties, could be used to estimate the closure pressure within an acceptable range.
Figure 8—Correlation between ISIP gradient and closure pressure gradient. In addition to five
consecutive DFIT stages, eleven stages were added. The pre-Frac ISIP was evaluated at the wellsite.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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8 URTEC-208276-MS
Figure 9—Closure pressure profile estimated by ISIP-closure pressure correlation.
There are hydraulic fracturing operations in huge number of horizontal wells in shale development.
Particularly in multi-well pad situations or first areas to develop, cost-effective data acquisition from the
first well is critical to understanding the local geological and geomechanical setting and heterogeneity along
lateral sections. Selection of consecutive DFIT locations needs to be discussed among the members of a
multi-disciplinary team before conducting this operation. The correlation built by consecutive DFITs shown
in this paper provides operators with more insight and confidence to optimize the completion design based
on ISIP which can be obtained at a relatively low cost.
Conclusions
This paper presents the consecutive DFITs approach at the sequential hydraulic fracturing stages in a


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Conclusions
This paper presents the consecutive DFITs approach at the sequential hydraulic fracturing stages in a
horizontal well. These are the findings from consecutive DFIT attempts in the Eagle Ford case study:
1.The proposed consecutive DFITs could be performed without any operational issues. This approach
allows operators to conduct DFIT in stages other than the toe stage and to interpret how closure
pressure and pore pressure look along a lateral section.
2.The evaluated closure pressure was constant in the sequential stages while ISIP gradually increased
up to a certain level, fracturing stage to stage.
3.The evaluated pore pressure was also almost constant in the sequential stages except for one stage
showing higher pressure. This is assumed to be the SRV pressure.
4.The correlation between the ISIP and the closure pressure showed that the closure pressure can be
estimated from the ISIP within an acceptable range although there were some uncertainties.
Acknowledgements


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estimated from the ISIP within an acceptable range although there were some uncertainties.
Acknowledgements
We wish to express our appreciation to INPEX CORPORATION and INPEX Eagle Ford, LLC for
permission to present this paper. We also acknowledge the operation team at INPEX Eagle Ford, LLC for
execution of this operation to acquire the data for this study.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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URTEC-208276-MS 9
SI Metric Conversion Factors
bbl × 1.589 874 E-01 = m3
ft × 3.048 * E-01 = m
lbm × 4.535 9237 * E-01 = kg
lbm/gal × 1.198 264 E+02 = kg/m3
psi × 6.894 757 E+03 = Pa
psi/ft × 2.262 059 E+04 = Pa/m
US gallon × 3.785 412 E-03 = m3
*Conversion factor is exact.
References
Barree, R. D.  and Mukherjee, H.  1996 . Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry.
Paper presented at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 6-9 October
1996. SPE-36424-MS. https://doi.org/10.2118/36424-MS.
Barree, R. D. , Miskimins, J. L. , and Gilbert, J. V. 2015 . Diagnostic Fracture Injection Tests: Common Mistakes, Misfires,
and Misdiagnoses . SPE Prod & Oper 30(02): 84-98. SPE-169539-PA. https://doi.org/10.2118/169539-PA.
Bazan, L. W. and Meyer B. R.  2015 . Fracture Complexity: Analysis Methodology and Signature Pressure Behavior of


key: chroma:document
string_value:
Bazan, L. W. and Meyer B. R.  2015 . Fracture Complexity: Analysis Methodology and Signature Pressure Behavior of
Hydraulic Fracture Propagation from Horizontal Wellbores. Paper presented at the SPE Asia Pacific Unconventional
Resources Conference and Exhibition held in Brisbane, Australia, 9-11 November 2015. SPE-176919-MS. https://
doi.org/10.2118/176919-MS.
Craig, D. P., Eberhard, M. J. , Odegard, C. E.  et al. 2005 . Permeability, Pore Pressure, and Leakoff-Type Distributions in
Rocky Mountain Basins . SPE Prod & Fac 20(01) : 48-59. SPE-75717-PA. https://doi.org/10.2118/75717-PA.
Engle, M. A. , Doolan, C. A. , Pitman, J. A.  et al. 2020 . Origin and Geochemistry of Formation Waters from the Lower
Eagle Ford Group, Gulf Coast Basin, South Central Texas. J Chem Geo  550(2020 ) 119754. https://doi.org/10.1016/
j.chemgeo.2020.119754
Liu, G.  and Ehlig-Economides, C.  2018 . Practical Considerations for Diagnostic Injection Test (DFIT) Analysis. J Pet Sci


key: chroma:document
string_value:
j.chemgeo.2020.119754
Liu, G.  and Ehlig-Economides, C.  2018 . Practical Considerations for Diagnostic Injection Test (DFIT) Analysis. J Pet Sci
and Eng  171(2018 ): 114-136. https://doi.org/10.1016/j.petrol.2018.08.035.
Meyer, B. R. and Bazan, L. W. 2011. A Discrete Fracture Network Model for Hydraulically Induced Fractures - Theory,
Parametric and Case Studies . Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition
held in The Woodlands, Texas, 24-26 January 2011. SPE-140514-MS. https://doi.org/10.2118/140514-MS.
McClure, M.W., Christopher, A.J.B., Jung, H.  et al. 2014 . The Effect of Changing Fracture Compliance on Pressure
Transient Behavior During Diagnostic Fracture Injection Tests. Paper presented at the SPE Annual Technical
Conference and Exhibition held in Amsterdam, The Netherlands, 27-29 October 2014. SPE-170956-MS. https://
doi.org/10.2118/170956-MS.


key: chroma:document
string_value:
Conference and Exhibition held in Amsterdam, The Netherlands, 27-29 October 2014. SPE-170956-MS. https://
doi.org/10.2118/170956-MS.
McClure, M.W., Jung, H. , Cramer, D. et al. 2016 . The Fracture-Compliance Method for Picking Closure Pressure From
Diagnostic Fracture-Injection Tests. SPE J . 21(04): 1321 -1339 . SPE-179725-PA. https://doi.org/10.2118/179725-PA.
Roussel, N. P. 2017 . Analyzing ISIP Stage-by-Stage Escalation to Determine Fracture Height and Horizontal-Stress
Anisotropy . Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The
Woodlands, Texas, USA, 24-26 January 2017. https://doi.org/10.2118/184865-MS.
Soliman, M. Y., Craig, D. , Bartko, K.  et al. 2005 . After-Closure Analysis to Determine Formation Permeability, Reservoir
Pressure, and Residual Fracture Properties . Paper presented at the SPE Middle East Oil and Gas Show and Conference


key: chroma:document
string_value:
Pressure, and Residual Fracture Properties . Paper presented at the SPE Middle East Oil and Gas Show and Conference
held in Bahrain International Centre, Bahrain, 12-15 March 2005. SPE-93419-MS. https://doi.org/10.2118/93419-MS.
Weijers, L., Griffin, L. G., Sugiyama, H.  et al. 2002 . The First Successful Fracture Treatment Campaign Conducted in
Japan: Stimulation Challenges in a Deep, Naturally Fractured Volcanic Rock. Paper presented at the SPE Annual
Technical Conference and Exhibition, San Antonio, Texas, USA, 29 September-2 October 2002. SPE-77678-MS.
https://doi.org/10.2118/77678-MS.Downloaded from http://onepetro.org/URTECAP/proceedings-pdf/21APUR/2-21APUR/D021S008R003/2528605/urtec-208276-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS
Field-Wide Review of Diagnostic Fracture Injection Tests DFIT in Montney
and Duvernay Formations – Part 1: Stress and Pressure Distributions
Behjat Haghshenas , Reservoir Diagnostics Inc. ; Farhad Qanbari, Seven Generations Energy
Copyright 2020, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Canada Unconventional Resources Conference originally scheduled to be held in Calgary, Alberta, Canada, 18 –
19 March 2020. Due to COVID-19 the physical event was postponed until 29 September – 2 October 2020 and was changed to a virtual event. The official proceedings
were published online on 24 September 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
A straightforward test with debatable analysis methods, the diagnostic fracture injection test (DFIT) is
a pressure-transient test extensively used for reservoir and geomechanical characterization of tight/shale
formations. The test provides some key data and information to reservoir and well completion engineers
including instantaneous shut-in pressure (ISIP), pore pressure, closure stress, fluid efficiency, reservoir flow
capacity, and fracture leak-off regime. A comprehensive regional or field-wide study of the DFITs is deemed


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capacity, and fracture leak-off regime. A comprehensive regional or field-wide study of the DFITs is deemed
very useful for operators at any stage of exploration and development.
In this study, DFITs from a group of 174 Montney and Duvernay wells operated by more than 30
producing companies are quality checked and analyzed consistently. The results from DFITs are then
compared against the standard poroelasticity equation.
The data set of the current study covers a wide range of DFIT conditions and reservoir and geomechanical
properties which helps the authors develop reliable correlations for reservoir characterization purposes.
True vertical depth (TVD) of the wells ranges from less than 1000m to more than 4000m leading to a wide
range of pressure and stress conditions. The study also covers all the geographical areas of Montney and
Duvernay. The results ofthe DFITs are used to develop usefulcross-plot betweenpore pressure and closure


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Duvernay. The results ofthe DFITs are used to develop usefulcross-plot betweenpore pressure and closure
pressure.A relationship between closure pressure from compliance method and G-function analysis method
for Montney and Duvernay is also provided. Results of example DFITs from depleted areas were also
provided which gives an idea about the depletion level and the associated well performance degradation.
The current study gives field-wide understanding of the variations and distributions of reservoir and
geomechanical properties in Montney and Duvernay based on DFIT analysis of a sizable population of
wells.
Introduction – Reservoir Initialization and Characterization
Reservoir characterization includes a series of direct and indirect methods that are applied to different
reservoir scales spanning from pore to field. Clarkson et al. (2016) reviewed advances in shale/tight reservoir


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reservoir scales spanning from pore to field. Clarkson et al. (2016) reviewed advances in shale/tight reservoir
characterization at different scales using drill cuttings, cores, well tests, and production data.Pressure
transient analysis (PTA) methods have been historically used as effective tools for characterization of nearDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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2 SPE-199990-MS
wellbore and far-field reservoir and estimation of average reservoir pressure. The methods are used to
interpret well bottom-hole pressure data which is influenced by reservoir properties and limits.
DFIT serves as a PTA tool for unconventional reservoirs which provides estimates of some of the
key reservoir and geomechanical properties of the sampled system as pressure transient during DFIT is
controlled by the hydraulically-induced fractures and native reservoir properties.
Operating companies in unconventional reservoirs usually require an overall understanding of reservoir
conditions and parameters across these giant continuous hydrocarbon systems (in addition to local detailed
studies) using field-wide analysis of reservoir characterization tests such as DFIT. In this study, 134 DFITs
from Montney and 40 DFITs from Duvernay formations are analyzed.The key observations and data trends


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from Montney and 40 DFITs from Duvernay formations are analyzed.The key observations and data trends
are presented withsome examples.The focus of this paper is pressure and stress distribution and leak-off
types in Montney and Duvernay. Permeability estimation from DFIT and fracture treatment analysis during
DFIT will be presented in Part 2 of the paper.
Diagnostic Fracture Injection Test (DFIT)
A DFIT consists of injection of a small volume of liquid or gas at low rate followed by extended shut-in
period when the pressure falloff is recorded ( Craig and Blasingame, 2006). Three key processes occur during
the test including hydraulic fracturing (during injection), early-time fluid leak-off, fracture closure, and late-
time fluid leak-off.DFIT data analysis includes interpretation of the shut-in pressure data usingreservoir
engineering and geomechanicstools.Two parameters for reservoir initialization(pressure and stress) and


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engineering and geomechanicstools.Two parameters for reservoir initialization(pressure and stress) and
two reservoir properties(permeability and leak-off type) are obtained by analyzing the DFIT data ( Fig.
1). Furthermore, treatment pressure during injection period can be used to tune fracture propagation and
tortuosity models.
Figure 1—Parameters and information derived from DFIT analysis.
Like other well test methods, uncertainty sources in DFIT results include measurements, input data (fluid
properties, petrophysical properties, etc.), DFIT analysis models, and interpretations methods.Different
DFIT pre-closure analysis models are available and have been used in literature and industry. G-function
derivative analysis or Holistic method (Nolte, 1979; Barree et al., 2009) and type curves (Craig and
Blasingame, 2005 , 2006 ) have been widelyused to identify fracture closure, estimate closure pressure


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Blasingame, 2005 , 2006 ) have been widelyused to identify fracture closure, estimate closure pressure
(which is considered as an estimate of minimum horizontal stress), and characterize leak-off type. Fracture
compliance method (McClure et al., 2016) has also been used for identification of fracture closure
whichprovides higher closure pressure compared to G-function derivative analysis.The closure pressures
for all of the DFITs of this study are estimated using both theG-function derivative and compliance methods.
Examples of different leak-off types including pressure-dependent leak-off (PDL), normal leak-off, and
storage from Montney formation are provided in Fig. 2  (the red and yellow stars show closure pressures from
G-function derivative analysis and compliance methods, respectively). The common methods for estimation
of permeability and reservoir pressure from DFIT after-closure datainclude Gu et al. (1993), Soliman et al.,


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of permeability and reservoir pressure from DFIT after-closure datainclude Gu et al. (1993), Soliman et al.,
(2005)  Craig and Blasingame (2006) .Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 3
Figure 2—Montney DFIT examples with closure pressures estimated from G-function analysis (red stars) and
compliance method (yellow stars) (a) pressure-dependent leak-off (PDL) (b) normal leak-off and (c) storage.
Montney and Duvernay
Montney and Duvernay are the two key Canadian unconventional plays with significant resource potential
(Fig. 3 ). The black dots and lines on the maps illustrate the location of the current wells which are
mostly on production. Uneven distributions of wells in the playsare mostly due to reservoir development
considerationsand variability ofreservoir properties.
Figure 3—Lithofacies distribution map of Montney formation, on the left side (after Edwards
et al. 1994 ) and Duvernay shale map, on the right side (modified from Switzer et al. 1994).
Reservoir parametersincluding pressure, temperature, stress, porosity, permeability etc. across Montney


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Reservoir parametersincluding pressure, temperature, stress, porosity, permeability etc. across Montney
and Duvernay change geographically and vertically.TVD of the wells drilled in Montney to date range from
800 m to 4000 m ( Fig. 4a ). Unconventional part of Montney is locatedat TVDgreater than 1500 m whereas
the conventional Montney resides at shallower depth. TVD of the wells drilled in Duvernay to date range
from 2000 m to more than 4000 m ( Fig. 4b ).Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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4 SPE-199990-MS
Figure 4—Histogram of TVD for the wells drilled in (a) Montney and (b) Duvernay to date.
Pressure and Stress Variability in Montney and Duvernay
Closure pressure is estimated using the G-function plots (as shown in Fig. 2 ). To estimate reservoir pressure,
the flow regimes areidentified,and then well shut-in pressure is extrapolated using a proper pressure vs.
time plot.Half-slope and zero-slope lines on the log-log diagnostics plots (Fig. 5a and 5b) indicate linear
and radial flow regimes, respectively. All the Montney and Duvernay wells of this study exhibit linear flow.
Radial flow was barely observed for these wells.For consistency, the estimated reservoir pressures from
linear flow are reported. Estimated reservoir pressure from radial flow is preferred if available.The well with
radial flow shown in Fig. 5b  is from Dunvegan formation which has much higher permeability compared


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radial flow shown in Fig. 5b  is from Dunvegan formation which has much higher permeability compared
to Montney and Duvernay. Extrapolation of well shut-in pressures corresponding to linear flow of Fig. 5a
and radial flow of Fig. 5b  are illustrated in Figs. 5c  and 5d.
Figure 5—Flow regime identification and reservoir pressure estimation (a) linear flow (half-slope line) for a Montney well, (b)
linear (half-slope line) and radial flow (zero-slope line) from a Dunvegan well, (c) reservoir pressure estimation corresponding
to the half-slope line in Fig. 5a, and (d) reservoir pressure estimation corresponding to the zero-slope line in Fig. 5b.
Fig. 6  provides the estimates of closure and pore pressure for some of the wells along the blue arrow
shown on the map (TVD increases moving away from the reference point). Similar results are provided


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shown on the map (TVD increases moving away from the reference point). Similar results are provided
for other regions of Montney as shown in Fig. A1 - A3 in Appendix. As shown in Fig. 6 , reservoirDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 5
pressure, closure pressure (minimum horizontal stress) and the corresponding gradients increase with depth.
Furthermore, minimum stress (closure pressure) and reservoir pressure are strongly correlated. This is
explained in more detail in "Equation of Poroelasticity" section.
Figure 6—Distribution of closure and pore pressure along the blue arrow on the
Montney map.Similar results for other regions of Montney are provided in Appendix.
Fig. 7  provides the data for some of the Duvernay wells along the blue arrow shown on the map. Similar
results are provided for another region of Duvernay as shown in Fig. A4  in Appendix.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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6 SPE-199990-MS
Figure 7—Distribution of closure and pore pressure along the blue arrow on the
Duvernay map.Similar results for another region of Duvernay is provided in Appendix.
Leak-off Types in Montney and Duvernay
Fluid leak-off type in DFIT depends of the relative contribution of matrix and natural fractures/fissures in
dissipation of injected fluid and pressure after the pumping period of the DFIT. "Normal leak-off" happens
in the case of a fully contributing matrix system exposed to the hydraulic fracture whereas "pressure-
dependent leak-off (PDL)" occurs in the case of enhanced surface area and permeability in the vicinity of
hydraulic fracture at high injection pressures. "Storage" occurs in cases with partially contributing matrix
and/or storage of excess water in open features with high storage capacity at elevated pressures.
Leak-off type is an important reservoir signature which might impact the efficiency of hydraulic fracture


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Leak-off type is an important reservoir signature which might impact the efficiency of hydraulic fracture
treatment. Leak-off types for the wells of this study (134 Montney wells and 40 Duvernay wells) were
identified using the G-function plot (as shown in Fig. 2 ). The results are summarized in Fig. 8. This graphDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 7
shows that 89% of Montney wells and 52% of Duvernay wells exhibit storage signature. Normal leak-offis
observed in only one Montney well.
Figure 8—Leak-off types in (a) Montney and (b) Duvernay.
Fracture closure time and fluid efficiency distributions in Montney also differ from Duvernay as shown
in Fig 9 . Generally, Montney fractures close faster and therefore fluid efficiency, 100 Gc/(G c+2), is lower
compared to Duvernay. This might be attributed to higher permeability value in Montney.
Figure 9—Distributions of closure parameters in Montney and Duvernay (a) closure time (b) fluid efficiency.
Equation of Poroelasticity
Based on the classic equation of poroelasticity (Terzaghi 1943), the minimum horizontal stress is a function
of pore pressure (p ), vertical and tectonic stresses (σ v and σ t), and rock elastic properties (Poisson's ratio,
v, and Biot's coefficient, α).
(1)


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of pore pressure (p ), vertical and tectonic stresses (σ v and σ t), and rock elastic properties (Poisson's ratio,
v, and Biot's coefficient, α).
(1)
This model is based on some simplifying assumptions and used to explain high-level trends between
minimum horizontal stress and pore pressure and elastic properties on relative basis. Plot of closure pressure
(approximately equal to minimum horizontal stress) from Montney and Duverany DFITs is provided in Fig.
10a. As shown in Fig 10a , (1) there is a reasonably strong correlation between closure and pore pressure
and (2) the poroelasticity plot from both Montney and Duvernay follow the same line. Furthermore, closure
pressure is estimated using Eq. 1 with assumed v = 0.25, bulk density of 2500 kg/m3 and σ t = 0. Fig. 10bDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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shows that the results from Eq. 1 and DFITs are reasonably close. The variability in the results is due to the
variation ofthe reservoir properties across these plays. The results from Eq. 1 can be tuned further by using
measured values of the rock elastic properties.
Figure 10—Poroelasticity in Montney and Duvernay (a) Pore pressure and closure from
Montney and Duvernay DFITs (b) comparison of closure pressure from DFIT against Eq. 1 .
Closure pressures are also estimated using the compliance method. The closure pressure from the
compliance method is usually higher than the G-function analysis method. Fig. 11 provides a cross-plot of
the closure pressure from compliance vs. closure pressure from the G-function analysis for Montney and
Duvernay DFITs of this study. As shown in the plot, the closure pressure from compliance method is on
average 9% greater than the closure pressure from the G-function analysis method.


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average 9% greater than the closure pressure from the G-function analysis method.
Figure 11—Closure pressure from compliance method vs. closure pressure from G-function analysis.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 9
Pressure Depletion
Prediction of infill/child well performance (early- and late-time) is an important task in reservoir
engineering, development, and management of conventional and unconventional systems. Infill/child well
performance primarily depends on reservoir pressure distribution/depletion controlled by production from
the existing/parent wells. Pressure depletion may impact infill/child performance in two ways: fracture
geometry (geomechanics) and material balance (reservoir engineering).
Reservoir simulation can be used to estimate reservoir pressure at the infill locations based on the
reservoir properties and the historical production data from the existing wells. The pressure forecast from
the reservoir model can be compared against direct measurement of reservoir pressure (from DFIT) at the
infill locations. DFITs from different infill/child wells are very useful in constructing a pressure distribution


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infill locations. DFITs from different infill/child wells are very useful in constructing a pressure distribution
line which in turn can be used to analyze performance of infill/child wells or tune the reservoir models.
Four pressure depletion examples diagnosed by DFIT are provided in the following subsections including
three Montney cases and a Duvernay case.
Example 1
A group of vertical wells from a higher-permeability area of Montney (the wells in orange in Fig. 12) were
completed in single hydraulic fracture and put on production mostly in 1996-1997. Pressure buildup test
data from the Vertical Well V1 (shown in Fig. 12 ) gives initial reservoir pressure gradient of ~8.6 kPa/m
and reservoir permeability of ~5 md. The operator completed a few infill multi-fractured horizontal wells
(wells in green color in Fig. 12 ) in 2011 and converted some of the vertical wells into injectors. DFITs


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(wells in green color in Fig. 12 ) in 2011 and converted some of the vertical wells into injectors. DFITs
were run on the horizontal wells prior to completion. Most of the tests were ended before linear/radial flow
is observed. The measured downhole pressure gradient at the end of DFIT from Well H1 and estimated
reservoir pressure from linear flow are 5.4 kPa/m and 5 kPa/m, respectively. That is, reservoir pressure
gradient at the DFIT location is depleted by ~40%. The toe of Well H1 is in a region surrounded by five
vertical wells with total oil production and gas productions of ~330 MSTB and 2.2 Bscf, respectively. This
is a critical piece of information which helps the reservoir development team tune their reservoir models
and improve production forecasts and estimated recoveries.
Figure 12—Depletion Example 1 – horizontal infill wells in high permeability Montney.
Example 2
Eight Montney wells on an infill pad (wells in red in Fig. 13) were completed after four years of production


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Example 2
Eight Montney wells on an infill pad (wells in red in Fig. 13) were completed after four years of production
form the neighbour pads (wells in blue and purple in Fig. 13) in a gas condensate region of Montney. The
wells were completed in three benches (each bench with ~50m thickness as shown in Fig. 13). Based on
DFITs taken from the non-depleted wells in this region, initial reservoir pressure gradient is expected to beDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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10 SPE-199990-MS
12-13 kPa/m. DFITs were also performed on all the infill wells to estimate pressure across the toe of the
wells on the infill pad. The results are provided in Table 1. Well C1 shows the highest depletion as expected
because it is the closest well to the parent well on the the neighbor pad (both horizontally and diagonally)
and the toe of the well is located along the parent well. Well C2 is less depleted than C1 as it is farther from
the parent well and located at a different layer. On the other side of the infill pad, toe of Well C8 is more
depleted than C7 and C6 due to proximity to the parent well on neighbor pad. However, Well C8 is less
depleted than Well C1; one reason is that the toe of C8 is located at the heel of the parent well whereas toe
of C1 is located along the parent well. This observation implies that pressure from DFIT of a child well may
not represent the whole wellbore because the conditions may change along the wellbore due to the relative


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not represent the whole wellbore because the conditions may change along the wellbore due to the relative
position of the well with respect to the parent well.
Figure 13—Depletion Example 2 –an infill pad in Montney.
Table 1—DFIT results for the the wells on infill pad of Fig. 13.
Well C1 C2 C3 C4 C5 C6 C7 C8
True Vertical Depth, TVD (m) 2313 2362 2254 2308 2351 2240 2296 2344
Closure Pressure (MPa) 35.3 41.1 37.3 36.2 40 38 36.2 38
Closure Pressure Gradient (kPa/m) 15.3 17.4 16.5 15.7 17.0 17.0 15.8 16.2
Pressure (MPa) 19.7 26.6 24.7 25.5 27 26.6 26
Pressure Gradient (kPa/m) 8.5 11.3 10.7 10.8 12.1 11.6 11.1
Example 3
Two multi-fractured horizontal wells (Wells H1 and H2 in Fig. 14 ) were completed in cased-hole plug and
perf and put on production in 2009. Both wells were completed on the same bench in Montney. In 2017, Well


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perf and put on production in 2009. Both wells were completed on the same bench in Montney. In 2017, Well
H3 was drilled toeing toward H1 and H2 at different bench which is 100 m deeper than those wells and DFITDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 11
was run shortly after (see well configuration in Fig. 14). DFIT from Wells H1 and H2 give initial reservoir
pressure gradient of ~14 kPa/m whereas DFIT from H3 gives pressure gradient of ~12 kPa/m (i.e. ~2 kPa/
m pressure depletion) at the toe of the well. This provides an insight about how far pressure front can move
vertically which can help with optimizing the development plan regarding the lower target in Montney.
Figure 14—Depletion Example 3 – depletion in a well toeing to existing wells in Montney.
Example 4
A pad including Wells H2-H5 (as shown in Fig. 15 ) were completed after 15 months of production from a
pad including Well H1 ( Fig. 15). Cumulative production from Well H1 at the time of completing Wells H2-
H5 was ~1.0 Bcf. DFITs from Wells H2 and H5 (located at distance of 270 m and 1150 m away from Well
H1) showed that Well H2 was depleted by ~7MPa (~1.7 kPa/m) whereas Well H5 was not depleted.


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H1) showed that Well H2 was depleted by ~7MPa (~1.7 kPa/m) whereas Well H5 was not depleted.
Figure 15—Depletion Example 4 – estimation of pressure distribution
across a new pad completed beside an older pad in Duvernay using DFIT.
Conclusions
A total of 174 DFITs across Montney and Duverany were analyzed in this study. The study gives field-wide
understanding of the variations and distributions of reservoir and geomechanical properties in MontneyDownloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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12 SPE-199990-MS
and Duvernay.Closure pressure and pore pressure from the DFITs show a strong correlation which reads
with standard poroelasticity relationship. The results from DFITs are comparable against the standard
poroelasticity equation. Different DFITs from depleted parts of Montney are also provided which provide
insights regarding the risks associated with depletion in both horizontal and vertical directions.
References
1. Barree, R. D.,  Barree, V . L. and Craig, D., 2009. Holistic fracture diagnostics: consistent
interpretation of prefrac injection tests using multiple analysis methods.  SPE Production &
Operations,  24(03) , pp.396 –406.
2. Clarkson, C. R.,  Haghshenas, B., Ghanizadeh, A., Qanbari, F., Williams-Kovacs, J. D., Riazi,
N., Debuhr, C.  and Deglint, H. J., 2016. Nanopores to megafractures: Current challenges and
methods for shale gas reservoir and hydraulic fracture characterization.  Journal of Natural Gas
Science and Engineering,  31, pp.612–657.


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string_value:
methods for shale gas reservoir and hydraulic fracture characterization.  Journal of Natural Gas
Science and Engineering,  31, pp.612–657.
3. Craig, D. P.  and Blasingame, T. A.,  2005, January. A new refracture-candidate diagnostic test
determines reservoir properties and identifies existing conductive or damaged fractures. In SPE
Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
4. Craig, D. P. and Blasingame, T. A., 2006, January. Application of a new fracture-injection/
falloff model accounting for propagating, dilated, and closing hydraulic fractures.  In SPE Gas
Technology Symposium. Society of Petroleum Engineers.
5. Edwards, D. E.,  Barclay, J. E.,  Gibson, D. W., Kvill, G. E.,  and Halton, E. 1994. Triassic Strata of
the Western Canada Sedimentary Basin; in Geological Atlas of the Western Canada Sedimentary
Basin , G.D. Mossop and I. Shetsen (comp.), Canadian Society of Petroleum Geologists and
Alberta Research Council Terzaghi,


key: chroma:document
string_value:
Basin , G.D. Mossop and I. Shetsen (comp.), Canadian Society of Petroleum Geologists and
Alberta Research Council Terzaghi,
6. Gu, H.,  Elbel, J. L.,  Nolte, K. G., Cheng, A. D. and Abousleiman, Y ., 1993, January. Formation
permeability determination using impulse-fracture injection.  In SPE Production Operations
Symposium. Society of Petroleum Engineers.
7. Nolte, K. G.,  1979, January. Determination of fracture parameters from fracturing pressure
decline.  In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.
8. Soliman, M. Y .,  Craig, D. P.,  Bartko, K. M., Rahim, Z. and Adams, D. M.,  2005, January.
Post-closure analysis to determine formation permeability, reservoir pressure, residual fracture
properties.  In SPE Middle East Oil and Gas Show and Conference. Society of Petroleum
Engineers.


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string_value:
properties.  In SPE Middle East Oil and Gas Show and Conference. Society of Petroleum
Engineers.
9. Terzaghi, K.  1943.  Theoretical Soil Mechanics. John Wiley and Sons.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 13
Appendix
Figure A-1—Distribution of closure and pore pressure along the blue arrow on the Montney map.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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14 SPE-199990-MS
Figure A-2—Distribution of closure and pore pressure along the blue arrow on the Montney map.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-199990-MS 15
Figure A-3—Distribution of closure and pore pressure along the blue arrow on the Montney map.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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Figure A-4—Distribution of closure and pore pressure along the blue arrow on the Duvernay map.Downloaded from http://onepetro.org/SPEURCC/proceedings-pdf/20URCC/3-20URCC/D033S003R005/2367089/spe-199990-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-194348-MS
DFIT Considering Complex Interactions of Hydraulic and Natural Fractures
Amirhossein Kamali and Ahmad Ghassemi, Reservoir Geomechanics and Seismicity Research Group, The
University of Oklahoma
Copyright 2019, 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, 5-7 February
2019.
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
Currently, the closure stress is often predicted using the conventional tangent method (i.e., G-function) or
the variable compliance method. Both methods use several restrictive assumptions such as a single planar
fracture. However, the hydraulic fracture often intersects rock fabric features such as bedding planes and/
or natural fractures causing the pressure transient behavior to become drastically different compared to that
of a single planar hydraulic fracture. Closure of the intersected natural fractures might precede that of the
created HF which impacts the interpretation of the pressure derivate plots and also the closure stress. In this


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created HF which impacts the interpretation of the pressure derivate plots and also the closure stress. In this
paper we present and use an advanced fracture diagnostic model that can help recognize the signatures of
rock fabric features and their impact on estimation of the closure stress. An example field data is used to
illustrate the potential impact on closure stress.
The new DFIT model consists of a fully coupled 3D hydraulic fracture simulator with the ability to
handle the opening, propagation, and closure of natural factures so that the pre- and post-closure stress/
deformation of both the hydraulic and natural fractures can be captured. Fracture propagation, HF-NF
interaction, fracture intersection, and DFIT model are integrated into one simulator to provide a more
realistic view of HF propagation and fracture diagnostics in naturally fractured reservoirs. The current
model is developed without any major assumptions concerning the fluid flow, fracture deformation, and


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model is developed without any major assumptions concerning the fluid flow, fracture deformation, and
propagation path. Rock/fracture deformation is calculated using a boundary element formulation whereas
the transport processes are solved using finite elements method.
Our results indicate that natural fractures affect the pre- and post- shut-in response of the hydraulic
fracture in a number of ways. For example, the fracture propagation path, the pumping pressure profile,
and interfering with the post shut-in pressure response. These factors, indeed, impact the estimation of the
minimum horizontal stress which is a key parameter obtained from DFIT. Moreover, our results show how
the normal stiffness of the fracture surface asperities can impact the minimum stress estimation. Closure
of natural fractures is reflected in the slope of the pressure derivative and G-function plots so that correct
interpretation of these signatures is essential to accurate extraction of the Shmin.


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interpretation of these signatures is essential to accurate extraction of the Shmin.
Closure of natural fractures is often viewed as a pressure depdendent leakoff mechanism that is reflected
on the Gdp/dG curve. The closure behavior of HF-NF sets is, however, not explicitly modeled in the context
of pressure transient analysis. Therefore, it is our objective to study the closure behavior of HF-NF sets usingDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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2 SPE-194348-MS
a 3D coupled simulator. This novel model is applied to actual field data to illustrate the potential impact on
closure stress and to shed light on the subject of fracture diagnostics in naturally fractured reservoirs. Our
results indicate that the closure behavior of hydraulic and natural fractures in a HF-NF set differs from that
of an isolated fracture due to the effect of stress shadowing. Although the system stiffness method results
in distinct signatures on the diagnostic curves, these signatures are not commonly observed in the field
data. The absence of stiffness signatures in the field cases could be interpreted in two ways: 1) the closure
mechanism assumed in the stiffness/compliance method differs from the actual fracture closure mechanism
or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in the system stiffness
after closure.
Introduction


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or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in the system stiffness
after closure.
Introduction
Fracture injection/fall-off tests have been extensively used over the past few decades to obtain fracture
closure pressure and several reservoir properties such as permeability and initial reservoir pressure. The
pioneering work of Nolte (1979)  provided a rigorous means for determining the fracture closure pressure,
leakoff coefficient, and fluid efficiency by introducing the G-function. Nolte (1979) derived the pressure
decline function based on material balance assuming a single planar fracture and constant leakoff from
the fracture surfaces. Following the Nolte's methodology, Castillo (1987) introduced a pressure decline
function where the pressure decline formed a straight line when plotted against the G-function during
the closure. Deviation from the linear portion of the plot was interpreted as the fracture closure. Castillo


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the closure. Deviation from the linear portion of the plot was interpreted as the fracture closure. Castillo
(1987)  also improved the constant leakoff assumption in the Nolte's approach by considering other leakoff
mechanisms such as reservoir dominated and filtrate viscosity dominated leakoff modes and formulated the
required parameters to use in each case. Recognizing that the use of pressure versus G-fucntion could lead
to ambiguous conclusions about the nonlinear leakoff behvaiors, Mukherjee et al. (1991) and Barree and
Mukherjee (1996)  started using the superposition derivative function (i.e., Gdp/dG) along with the pressure
decline plots. Using the combination plots including the P, dP/dG, and GdP/dG plots helps to identify the
cause of the non-linearity in the leakoff behavior. Tip extension, height recession, fissure opening, and
the change of system stiffness can be detected on the Barree and Mukherjee's combination plot. Pivoting


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the change of system stiffness can be detected on the Barree and Mukherjee's combination plot. Pivoting
on the fact that neither one of the assumptions in the leakoff formulation (filter cake dominance and the
square root of time decay) is really true, Mayerhofer and Economides (1997) advocated using the simple
log-log diagnostic plots instead of the widely used G-function analysis. To account for the varying leakoff
rate, Mayerhofer and Economides (1997) used a rate-normalized plot (RNP) and its derivative to detect the
fracture closure and departure from the half-slope line. Craig et al. (2005) conducted a statistical analysis
on the leakoff type and the reservoir permeability of more than 1000 diagnostic fracture injection tests in
the Rocky Mountain Basin, and concluded that the normal leakoff behvaior is very rarely seen. In fact, the
great majority of the tests in their study showed pressure dependent leakoff and other abnormal leakoff


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great majority of the tests in their study showed pressure dependent leakoff and other abnormal leakoff
behaviors which makes the G-function interpretation challenging. As an alternative to the conventional
tangent method, several studies have focused on the use of system stiffness or compliance method ( Barree
and Mukherjee, 1996 ; Raaen et al., 2001; Raaen et al., 2005; McClure et al. 2016) to determine the fracture
closure pressure. Raaen et al., (2001) pointed out that there is a change in the system stiffness upon
closure which is reflected on the pressure and pressure derivative plots. The signature associated with the
change of system stiffness/compliance can therefore help identifying the instance of fracture closure and
the corresponding closure stress. McClure et al., (2016) considered the stiffness change due to the joint
closure as well. On the other hand, the signature of changes caused by the fracture normal stiffness has not


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closure as well. On the other hand, the signature of changes caused by the fracture normal stiffness has not
been widely observed in field data and moreover, the interpretation of stiffness (compliance) changes can
be ambiguous. In particular, HF interaction with natural fractures can result is similar signatures that would
complicate the interpretation.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-194348-MS 3
Traditionally, the impact of natural fractures on the post-shutin pressure decline is implicitly studied
in the context of leakoff behavior. However, the interaction of hydraulic and natural fractures and its
effect on the closure behavior and the pressure decline is not explicitly considered in previous works. In
this work we use a fully 3D hydraulic/natural fracture simulator to investigate the pressure decline in a
system including intersected hydraulic and natural fractures. The mechanical interaction between fractures
is explicitly included in the model to rigorously account for the closure of natural fractures in the diagnostic
fracture injection tests.
Model Development
A fully coupled 3D hydraulic/natural fracture simulator is used in this study to investigate fracture injection
tests and closure stress estimation in the presence of natural fractures. This section describes the constitutive


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tests and closure stress estimation in the presence of natural fractures. This section describes the constitutive
equations that are used to construct this model and the numerical methodology to implement the model.
Constitutive Equations
Hydraulic fracturing is a coupled process that involves rock deformation, fracture propagation, fluid
flow, leakoff, thermal, and poroelastic stress components. Proper constitutive equations are required to
describe and capture this multi-physics problem. Unlike fluid-driven hydraulic fractures, pre-exisitng
natural fractures are closed fractures that carry normal and shear stresses. Therefore, the contact status of
the natural fractures should be carefully addressed.
The solution to the problem of an elastic body deformation must satisfy the governing equations for a
given set of stress/displacement boundary conditions. The formulation of this problem relies on the stress


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given set of stress/displacement boundary conditions. The formulation of this problem relies on the stress
tensor PDE and strain-displacement equations. The solution is completed through a constitutive equation
that relates the stresses to the strains. Using Hooke's law in 3D, this constitutive equation is expressed as
follows ( Love, 2013 ; Timoshenko and Goodier, 1970):
(1)
Where E is the formation's Young's modulus, v is the Poisson's ratio, σij is the stress tensor components, εij
is the strain tensor components, εkk denotes trace of the strain tensor, and δij is the Kronecker delta function.
Another integral part of the hydraulic fracturing is the fluid flow inside the fracture. Assuming small
variations of the fracture width in time and space, the continuity equation can be expressed as:
(2)
Where q is the volumetric flow rate at location s and time t, w is the local fracture aperture, VL is the leakoff


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(2)
Where q is the volumetric flow rate at location s and time t, w is the local fracture aperture, VL is the leakoff
velocity across the fracture surfaces, and Qinj is the pumping rate. The continuity equation can be formulated
in terms of the fluid pressure and the fracture aperture using the Darcy's law ( Witherspoon et al., 1980):
(3)
In which, μ is the viscosity of the fracturing fluid, and ∇P is the pressure gradient along the fracture.
Contact elements are used to represent closed natural fractures. The constitutive equations simply relates
the changes of the normal (shear) stress to that of the normal (shear) displacement discontinuity as shown
below ( Goodman et al., 1968 ):
(4)Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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4 SPE-194348-MS
Where Kn and Ks are the normal and shear stiffness, and Dn and Ds are the normal and shear displacement
discontinutites for each element. The contact status of the elements may change during the simulation in
both the normal and shear mode. Mohr-Coulomb criterion is used to determine the contact status of the
elements in the shear mode (i.e., ′′ stick′′ and ′′ slip′′ ):
(5)
Where c and Ø are the natural fracture's cohesion and friction angle, respectively. More details about the
contact elements and its implementation can be found elsewhere (Kamali and Ghassemi, 2018; Kamali and
Ghassemi, 2017 ; Safari and Ghassemi, 2015; Tao et al., 2011 )
Numerical Methodology
Fully 3D fracture modeling coupled with the fluid flow results in a set of nonlinear partial differential
equations that are often not amenable to analytical treatments. Therefore, numerical modeling is used to
study problems involving complex fracture simulations. Fracture deformations and stresses are solved


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study problems involving complex fracture simulations. Fracture deformations and stresses are solved
using displacement discontinuity (Crouch and Starfield, 1983; Curran and Vandamme, 1989) which is an
indirect boundary element method. Displacement discontuity (DD) is proved to be a powerful tool to model
hydraulic fractures and problems involving contact elements such as natural fracutres, and faults (Asgian,
1988 ; Ghassemi and Tao, 2016; Safari and Ghassemi, 2015 ). Stresses at each point on the fracture is obtained
using the following integral form:
(6)
Where Γ is the displacement discontiuty boundary, 
  is the unit induced stress component ′′ij′′ due to
the instantaneous point source DD component ′′kn′′, and 
  is the in-situ stress component at location
X. Figure 1  shows a discplacement discontinuity elements and is displacement components. Numerical
discretization and implementation is provided in Kumar and Ghassemi (2015).


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discretization and implementation is provided in Kumar and Ghassemi (2015).
Figure 1—Schematic showing a displacement discontinuity element and its displacement componentsDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-194348-MS 5
The fluid flow equations are solved using the finite element method by discretizing the fracture surface
into 4-node quadrilateral elements. A linear variation of the fluid pressure is assumed over the elements.
The details of the finite element discretization is discussed in Kumar and Ghassemi (2016).
Results
The post-shutin pressure transient of HF-NF pairs is analyzed in this section to identify the signatures in the
pressure and pressure derivative plots. A combination of log-log diagnostic plot and G dP/dG plot is used
to pick the closure pressure more confidently. Several analyses are conducted to study the impact of in-situ
stress state, intersection angle, and fracture stiffness on the pressure decline curves and diagnostic plots.
The first example shows a typical HF-NF system with a relatively simple intersection in which the
hydraulic fracture intersects the natural fracture with an intersection angle of 90°. The length of the natural


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hydraulic fracture intersects the natural fracture with an intersection angle of 90°. The length of the natural
fracture is three times larger than that of the hydraulic fracture (see Figure 1  and Table 1).
Table 1—Input parameters (assumed values) used in the base case example.
The post-shuting pressure decline is studied for this example using the G-function and also the log-log
diagnostic plot. Both the hydraulic and natural fractures are pressurized above the maximum horizontal
stress prior to the shutin as shown in Figure 2. Therefore, both fractures are open against the in-situ stresses.
It shoud be noted that the pressure can easily rise above the maximum horizontal stress level and open the
natural fracture given that the stress anistorpy is not high in this example. The pump is then shut in and
the pressure is monitored.
Figure 2—Hydraulic and natural fracture pressure before shutin. The fluid pressure is above


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the pressure is monitored.
Figure 2—Hydraulic and natural fracture pressure before shutin. The fluid pressure is above
the maximum horizontal stress causing both hydraulic and natural fractures to be open.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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6 SPE-194348-MS
The post-shutin pressure is recorded and plotted against the G-function along with the semilog derivative
G dp/dG in Figure 3-a . The G dp/dG plot shows that there are two sudden changes of slope before the hump
corresponding to the change of the system stiffness; the first due to the natural fracture closure and the
second due to hydraulic fracture closure. The first change of slope could also be detected on the pressure
curve at approximately 4300 psi which is regarded as the closure pressure for the natural fracture (marked
by the blue arrow). The second change of the system stiffness occurs when the pressure falls below the
minimum stress and the hydraulic fracture closes (marked by a circle on the G dp/dG and green arrow on
the pressure plot). The closure pressure obtained from the second change of system stiffness is 4000 psi.
The closure pressure is also picked using the conventional tangent method. This method yields a closure


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The closure pressure is also picked using the conventional tangent method. This method yields a closure
pressure of 3950 psi which is a good estimate of the actual input for the minimum stress (i.e., 4000 psi).
Alternatively, the closure pressure is picked from the log-log diagnostic plot in Figure 3-b . The closure
stress obtained from this method (departure from the ½ slope line) is 3950 psi (i.e., Δp = 450 psi) which
is in a good agreement with the tangent method and also the stiffness approach. It is important to note that
although using the stiffness/compliance method provides clear signatures on the G dp/dG plot, one can
misinterpret the fracture closure pressure simply by choosing the first signature which actually corresponds
to the natural fracture closure.
Figure 3—a) Pressure profile and the semilog derivative G dp/
dG for the HF-NF system. b) log-log diagnostic plot for the HF-NF pair.
Angle of Intersection


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dG for the HF-NF system. b) log-log diagnostic plot for the HF-NF pair.
Angle of Intersection
The angle of intersection between the hydraulic and natural fractures affects their mechanical interaction and
therefore impacts the coupled hydro-mechanical response. Moreover, the normal stress acting on the natural
fracture plane varies based on its orientation with respect to in-situ stresses. In this example, the pressure
decline and the semilog G derivative is investigated for different angles of intersections. Considering that
the hydraulic fracture is initiated and extended in the direction of the maximum horizontal stress, the angle
of intersection represents the angle between the natural fracture and the maximum stress. The base case
example is chosen such that the HF and NF are orthogonal meaning that the intersection angle is 90°. The
post shutin pressure decline and G dp/dG plots are shown in Figure 4 for different values of intersection


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post shutin pressure decline and G dp/dG plots are shown in Figure 4 for different values of intersection
angle. It can be observed in this figure that the first signature on the G dp/dG curve has shifted to the right
indicating a larger closure time for the natural fracture and a lower closure pressure. This is, in fact, due to
the lower normal stresses on the natural fracture in the second and third cases. It is also interesting to notice
that the second signature has disappeared in the last case with the lowest intersection angle. It appears that
because of the small difference between the closure pressure of the HF and NF in the third case (4000 andDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-194348-MS 7
4072 psi, respectively) the hydraulic fracture signature is overshadowed by that of the natural fracture or
they are both combined to form a larger signature.
Figure 4—Comparison between the pressure response the the G
dp/dG plots for HF-NF pairs with different angle of intersection.
Fracture stiffness
This example shows the impact of normal fracture stiffness on the post-shutin pressure profile and the
pressure derivative Gdp/dG. Figure 5  compares the pressure profile and its semilog derivate for a HF-NF
set with different stiffness values. The angle of intersection is 90° and the rest of the parameters are similar
to those used in the base case example. It can be seen in this figure that the higher stiffness results in a higher
rate of pressure drop once the natural fracture closes (i.e., p < σ n, NF). Hence, the set with higher stiffness
has a more pronounced stiffness signatures as compared to the softer set. Identifying the stiffness signatures


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has a more pronounced stiffness signatures as compared to the softer set. Identifying the stiffness signatures
could become challenging for softer hydraulic or natural fractures (see the HF signature for the softer case
marked by a circle) which limits the application of the system compliance/stiffness method.
Figure 5—Pressure and derivative comparison for HF-NF sets with different normal stiffness.
Natural fracture sets
The pressure transiet could be different in the presence of multiple natural fractures. This example explores
the characteristics of the pressure decline for a hydraulic fracture intersecting two unparallel natural
fractures. To help envision this problem further, the sequence of fracture closure is shown in Figure 6.
The first plot shows that all fractures are open before shutin. The upper right figure shows that the natural
fracture with 90° intersection angle closes first while the HF and the second NF remain open. This is due to


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fracture with 90° intersection angle closes first while the HF and the second NF remain open. This is due to
the higher in-situ stress on its plane causing it to close earlier as the pressure declines. The second naturalDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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8 SPE-194348-MS
fracture undergoes closure partially on one wing as shown in the lower left figure. This wing which makes a
sharper angle with the HF experiences more induced compression from the HF and therefore closes earlier
than the rest of second NF. Finally, being subject to minimum horizontal stress, the hydraulic fracture is
the last one to close.
Figure 6—Closure sequence for a set of unparallel natural fractures and a hydraulic fracture. (1) all
fractures are open before shutin. (2) the natural fracture which makes a 90° angle with the HF closes first
due to the higher normal stress on its plane. (3) the second NF closes partially on one wing as a result
of higher compression (stress shadow) caused by the HF, and (4) the HF is the last fracture to close.
Figure 7  shows the post-shutin pressure decline and G dp/dG for this example. It can be observed in
this figure that the derivative shows an early jump and change of slope (blue circle and arrow) which is


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this figure that the derivative shows an early jump and change of slope (blue circle and arrow) which is
associated with the change of the system stiffness upon the closure of the first natural fracture. The second
signature (green circle and arrow) shows the partial closure of one wing of the second natural fracture where
higher compression is induced by the HF. The last signature which corresponds to the closure of the HF is
not as pronounced as the previous ones considering that the HF normal stiffness is set to a lower value than
that of the NFs. The tangent method yields a closure pressure of 3900 psi which is 100 psi below its input
value for this example whereas the stiffness approach yields a closure pressure of 4100 psi.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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SPE-194348-MS 9
Figure 7—Pressure and semilog G derivative for the set of unparallel natural fractures.
Field example
A field example is shown in this section to highlight the charactaristics of the pressure decline and the
semilog pressure derivate obtained from a field test. The fracture injection test is conducted in shale by
pumping 22 BBLs of water. The injection test is followed by an extended shutin period. Figure 8-a shows
the pressure profile for this test. Pressure decline and its semilig derivative are plotted against G-time for
this test in Figure 8-b . It can be observed in this figure that the fracture closure process does not show signs
of pressure dependent leakoff (PDL) behavior and the before-hump portion of the Gdp/dG curve follows
a linear trend. Moreover, there is not any noticeable changes of slope or spikes before the hump to signify
changes in the system stiffness. The field data is used to obtain the pressure decline and Gdp/dG using


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changes in the system stiffness. The field data is used to obtain the pressure decline and Gdp/dG using
the compliance/stiffness approach. A relatively low normal stiffness of 0.09 Mpsi/ft is assumed for this
example. It can be seen in Figure 9 that Gdp/dG shows a sudden change of slope even for a soft fracture.
This signature is, however, not observed in the field data. This, in fact, indicates that the fracture closure
mechanism may differ from what is assumed in the system stiffness/compliance method. Alternatively, the
absence of stiffness signatures in the field case shows that the closure of the hydraulic fracture, in this case,
does not contribute to the changes of system stiffness.
Figure 8—(a) Post-shutin pressure decline, and (b) G dp/dG plot for the field example.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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10 SPE-194348-MS
Figure 9—Gdp/dG obtained from the compliance/stiffness method using field data.
Discussion and Conclusions
A fully 3D coupled HF-NF simulator is used in this paper to shed light on the pressure transient of hydraulic
fracture in the presence of natural fractures. Our model is based on a 3D displacement discontinuity method
for the rock/fracture deformation and finite elements method for the fluid flow. Our results indicate that
the pressure profile and the semilog G derivatives differ from that of conventional hydraulic fractures. The
change of slope in the pressure profile as a result of the changes of the system stiffness translates into
distinct signatures on the G-function plot. Having said that, care should be taken when interpreting the
closure pressure as these jumps and changes of slope on the Gdp/dG could cause erronesous interpretations.
As outlined in the simulations, the signature for the natural fracture closure could be wrongly picked as


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As outlined in the simulations, the signature for the natural fracture closure could be wrongly picked as
the closure pressure. Morever, it is often a difficult task to distinguish between actual stiffness signatures
and the noise in the data in field cases. It was shown in the field example that Gdp/dG shows nearly ideal
leakoff behavior and follows a straightline before the hump. The Discrepency between the simulation results
and the actural field example (absence of stiffness signatures in the field case) could be interpreted in two
ways: 1) the closure mechanism assumed in the stiffness/compliance method differs from the actual fracture
closure mechanism or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in
the system stiffness after closure. That said, the stiffness signatures that exist in the diagnostic plots might
be caused by the closure of other features such as intersected natural fracture. Using conventional tangent


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be caused by the closure of other features such as intersected natural fracture. Using conventional tangent
method or log-log diagnostic plots along with the stiffness/compliance method could help identifying the
closure pressure more confidently when it comes to naturally fractured reservoirs.
References
Asgian, M. I. ( 1988 , January 1). A numerical study of fluid flow in a deformable, naturally fractured reservoir: The
influence of pumping rate on reservoir response . American Rock Mechanics Association .
Barree, R. D. , & Mukherjee, H.  (1996 , January 1). Determination of Pressure Dependent Leakoff and Its Effect on Fracture
Geometry . Society of Petroleum Engineers. doi: 10.2118/36424-MS.
Castillo, J. L.  (1987, January 1). Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff.
Society of Petroleum Engineers. doi:10.2118/16417-MS .


key: chroma:document
string_value:
Society of Petroleum Engineers. doi:10.2118/16417-MS .
Craig, D. P., Eberhard, M. J., Odegard, C. E., Ramurthy, M., & Mullen, R. ( 2002 , January 1). Permeability, Pore Pressure,
and Leakoff-Type Distributions in Rocky Mountain Basins. Society of Petroleum Engineers. doi:10.2118/75717-MS.
Crouch, S. L., & Starfield, A. M. ( 1983 ). Boundary element methods in solid mechanics: With applications in rock
mechanics and geological engineering : Winchester, Massachusetts.
Ghassemi, A. , & Tao, Q.  (2016 ). Thermo-poroelastic effects on reservoir seismicity and permeability change.
Geothermics , 63, 210–224.
Goodman, R. E., Taylor, R. L., & Breeke, T. L. ( 1968 ). A model for the mechanics of jointed rocks. ASCE Journal of
Soil Mechanics Found. Div, 94, 637–659.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


key: chroma:document
string_value:
SPE-194348-MS 11
Kamali, A. , & Ghassemi, A.  (2018). Analysis of injection-induced shear slip and fracture propagation in geothermal
reservoir stimulation . Geothermics , 76, 93–105.
Kamali, A. , & Ghassemi, A. ( 2017 , August). Reservoir Stimulation in Naturally Fractured Poroelastic Rocks. In 51st US
Rock Mechanics/Geomechanics Symposium . American Rock Mechanics Association.
Kumar, D. , & Ghassemi, A.  (2015 , November). 3D simulation of multiple fracture propagation from horizontal wells. In
49th US Rock Mechanics/Geomechanics Symposium . American Rock Mechanics Association.
Kumar, D., & Ghassemi, A.  (2016). A three-dimensional analysis of simultaneous and sequential fracturing of horizontal
wells . Journal of Petroleum Science and Engineering, 146, 1006–1025.
Love, A. E. H.  (2013 ). A treatise on the mathematical theory of elasticity . Cambridge university press.


key: chroma:document
string_value:
Love, A. E. H.  (2013 ). A treatise on the mathematical theory of elasticity . Cambridge university press.
Mayerhofer, M. J., & Economides, M. J. ( 1997 , November 1). Fracture-Injection-Test Interpretation: Leakoff Coefficient
vs. Permeability . Society of Petroleum Engineers. doi: 10.2118/28562-PA.
McClure, M. W. , Jung, H., Cramer, D. D. , & Sharma, M. M. (2016, August 1). The Fracture-Compliance Method for
Picking Closure Pressure from Diagnostic Fracture-Injection Tests (see associated supplementary discussion/reply).
Society of Petroleum Engineers. doi: 10.2118/179725-PA.
Mukherjee, H. , Larkin, S., & Kordziel, W.  (1991 , January 1). Extension of Fracture Pressure Decline Curve Analysis to
Fissured Formations . Society of Petroleum Engineers. doi: 10.2118/21872-MS.
Nolte, K. G. ( 1979 , January 1). Determination of Fracture Parameters from Fracturing Pressure Decline. Society of
Petroleum Engineers. doi: 10.2118/8341-MS.


key: chroma:document
string_value:
Petroleum Engineers. doi: 10.2118/8341-MS.
Raaen, A. M. , Horsrud, P. , Kjørholt, H. , & Økland, D.  (2006). Improved routine estimation of the minimum horizontal
stress component from extended leak-off tests. International Journal of Rock Mechanics and Mining Sciences, 43(1),
37–48.
Raaen, A. M. , Skomedal, E. , Kjørholt, H., Markestad, P., & Økland, D. (2001). Stress determination from hydraulic
fracturing tests: the system stiffness approach. International Journal of Rock Mechanics and Mining Sciences, 38(4),
529–541.
Safari, R. , & Ghassemi, A.  (2015 ). 3D thermo-poroelastic analysis of fracture network deformation and induced micro-
seismicity in enhanced geothermal systems . Geothermics, 58, 1–14.
Tao, Q. , Ghassemi, A. , and Ehlig-Economides, C.E.  2011. A fully coupled method to model fracture permeability change
in naturally fractured reservoirs . Int. J. Rock Mech. & Min. Sci., 48( 2), 259–268.


key: chroma:document
string_value:
in naturally fractured reservoirs . Int. J. Rock Mech. & Min. Sci., 48( 2), 259–268.
Timoshenko, S. P. , & Goodier, J. N. Theory of Elasticity, (1970), 433. McGraw-Hill.
Vandamme, L. , & Curran, J. H.  (1989 ). A three-dimensional hydraulic fracturing simulator. International Journal for
Numerical Methods in Engineering , 28(4), 909–927.
Witherspoon, P. A., Wang, J. S., Iwai, K. , & Gale, J. E. ( 1980). Validity of cubic law for fluid flow in a deformable rock
fracture . Water resources research , 16(6), 1016 –1024 .Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/19HFTC/1-19HFTC/D012S001R003/1143681/spe-194348-ms.pdf/1 by University of Houston user on 30 October 2023


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See discussions, st ats, and author pr ofiles f or this public ation at : https://www .researchgate.ne t/public ation/313878526
A New Analysis Technique for Interpreting Injection/Shut-in Tests
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A New Analysis Technique for Interpreting Injection/Shut-in Tests
This paper presents an analysis technique for interpreting fracture treating pressures. The literature contains various models that give rise to analysis 
techniques, all of which rely on material balance. Fundamentally the models are different in their assumption of leak-off phenomenon. There are mainly two schools of thought concerning fluid leak-off. 
The first school of thought considers the fluid leak-off to be a property of the fluid-rock interaction system. It relies on Carter’s equation (Howard 
and Fast 1957, Carter 1957) to describe leak-off and is based on Howard and Fast’s experiments. The disadvantage is its inadequacy to describe the phenomenon if the conditions of Howard and Fast’s experiment are not strictly met during the injection process.
Nordgren (Nordgren 1972), using mass balance, defined the following differential equation for the flow down a fracture:
(1)


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Nordgren (Nordgren 1972), using mass balance, defined the following differential equation for the flow down a fracture:
(1)
It should be noted that the fracture area considered in the above equation is different from the area considered in this paper. The above equation uses 
the fluid loss coefficient defined as: 
(2)
Most of the models existing in the literature rely on the experiments of Howard and Fast (Howard and Fast 1957, Carter 1957), which yield the generally accepted relation: 
(3)
However, the conditions of their experiments may not match the field conditions. As noted by Nordgren (Nordgren 1972) the pressure difference depends on location and time. This was neglected by the original experimental study. The other well-known correction to Equation 3 is the so called 
spurt loss.


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spurt loss.
Based on the above equations, Nolte (K. G. Nolte 1979, K. G. Nolte 1986) presented the well-known G-function method.The second school of thought considers the leak-off as being governed by the flow in porous media. The advantage of this approach is that it describes 
the phenomena adequately. However it is more complicated. Even though the solutions of the linear flow problem are available, the problem becomes complicated once the change in area at each time step is considered.
Mayerhofer,  et al., (1991) and Mayerhofer & Economides (1993) described the leak-off based on the square root of time solution as will be shown later 
in the paper. They considered the pressure drop in the filter cake based on filter cake resistance. They combined the pressure drop due to leak-off and through the filter cake and developed the equation:IntroductionFahd Siddiqui, Mohamed Y . Soliman, Akif Ibragimov, Texas Tech University 
Abstract


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Abstract
The problem of diagnostic fracture injection fall-off tests is considered. A new model is constructed from basic fluid flow and material balance 
equations and making some assumptions about fracture propagation. The resulting equations are solved analytically. 
A thorough analysis methodology has been developed from these solutions to interpret fracture injection pressure tests. Presented method can 
estimate the fracture half-length and height product ( xf.hf) and the closure pressure. The proposed analysis technique is limited to after shut-in and 
before fracture closure period of the test.
The developed model has been validated against two actual field injection data. The datasets serve to augment the demonstration of the application 
steps. Peer Reviewed


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(4)
In the above equation, the fluid leak-off rates depend on the changes in area. Since the equation in its current form is not easy to apply for interpretation, 
Valko and Economides, (1999) offered a graphical form of the Mayerhofer’s method by defining the variables x1,n, x2,n and yn. Since it is not easy to 
establish the leak-off rates ( qloss,j) at each time step, Valko and Economides considered them to be constant and equal to an “apparent” leak-off rate. 
In fact, the authors chose to work with width loss rather than the average apparent leak-off rate. The application procedure still remains complicated, especially as compared to the well-known G-function analysis.
Lamei and Soliman (2014) relied on the linear diffusivity equation to determine leak-off, instead of Carter’s (1957) equation. However, they presented 
a long time solution which does not work for all cases. This fact becomes evident when applying their technique. 
Problem Analysis


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a long time solution which does not work for all cases. This fact becomes evident when applying their technique. 
Problem Analysis 
This study subscribes to the second school of thought and instead of relying on the discrete steps of the Mayerhofer’s method, the whole model is developed from first principles and yields equations that are more continuous (without discrete summation terms). The fluid loss is modeled by the governing partial differential equation (Equation 5 ).
Equation 5  is the well-known partial differential equation used to describe the linear leak-off. This equation governs how the leaking fluid will move 
through the porous media and gives the resulting pressure distribution versus time.
(5)
I
nner Boundary Condition
The inner boundary condition is derived starting from mass balance and accounts for injection followed by shut-in. This model relies on Equation 7


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The inner boundary condition is derived starting from mass balance and accounts for injection followed by shut-in. This model relies on Equation 7 
(K. G. Nolte 1986) to describe the width change due to consequent pressure changes. The complete derivation of this equation is given in Appendix 
A. The final form of the fluid loss equation is obtained as follows: 
(6)
W
here U(t - t i) is the unit step-function to account for injection rate and shut-in, at time t i. 
(7)
(8)
E
quation 6 essentially states that the fluid loss (pressure gradient term) is equal to the injection rate (q) less the change in fracture volume (change in 
width due to fracture compliance) at each time, while the fracture area remains constant. Considering the problem accurately from this perspective accounts for the fluid loss based on the physics of fluid flow through porous media. It should be noted that fracture face pressure drop is not considered here and can be introduced as skin factor.


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For verification, two extreme cases were tested. First case is that of no fracture volume change; i.e. all the injected fluid is lost to the formation. In this 
case setting the change in fracture volume to zero (or c
f = 0) results in the conventional boundary condition of constant rate injection followed by 
shut-in (Equation 9 ) This results in the traditional square root of time solution. In the next section, it is showed that the general solution reduces to 
square root of time equation for this case too.
(9)
Th
e second case is that of no leak-off. In this case the diffusivity equation cannot be used since there is no leak-off into the porous media. Hence the 
mobility ( λ) is zero. Based on this, the boundary condition (Equation 6 ) reduces to the following:
(10)
F
rom the definition of width (Equation 7 ), and integrating, the above equation can be written as:
(11)


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Equation 11 is consistent with material balance and shows that the cumulative injected volume (left-hand side) is equal to the created fracture volume 
(right-hand side).
The extreme cases validate the model by obtaining expected results and therefore the problem needs to be solved for the intermediate case.Inner Boundary Condition Assumptions
1.  The fracture area is already in place and injection and shut-in processes tend to cause a change in fracture width only and lead to fluid leak off  
into the formation (Equation 6 ). This assumption limits the applicability to the shut-in period.
2.  After stopping injection (shut-in) the fracture begins to close along the hinge at the tip. This implies a reduction in width (according to fracture
stiffness) while the fracture area remains constant, which is a reasonable assumption.
3.  Since the fracture volume is small and the fluid compressibility is small, their product can be neglected. Hence the fluid storage/compressibility


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effects in the wellbore and the fracture can be neglected.
4. The width is a function of net pressure defined by Equation 7 .
Model Assumptions
Following assumptions were considered for using the linear diffusivity equation and to develop the overall model:
1. Homogeneous and isotropic porous medium.
2. Negligible gravity effects.
3. The fluid is leaking off linearly into the porous media.
4. Isothermal conditions prevail throughout the injection period within the porous medium.
5. Fluid has small, constant compressibility in the porous media.
6. Fracturing fluid has a comparable mobility with the formation fluid.
7. Fracturing fluid behaves like a Newtonian fluid.
8. The fracture has an infinite conductivity, i.e. no pressure drop inside the fracture.
Analytical SolutionThe analytical solution to the problem described by Equations 6 and 5 was obtained using the Laplace transform. Analytical inversion was carried out


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by convolution theorem. Appendix B gives the essential steps required to arrive at the solution in Equations 12 and 13. Equation 13 is the definition 
of the F-function.
(12)
(13)
M
athematical and Physical Inspection
Mathematical inspection of the solution suggests that the expected solution would show a rise in pressure (during injection time) and then begin to decline during the shut-in period. The boundary condition does not effectively model the injection part because it does not account for the propagation of fracture but only the change in width (assumptions 1 and 2). Therefore the injection part of the solution is not useful. However since the fracture area is assumed not to change significantly during the shut in period, the boundary condition effectively models the after shut-in and before closure part. Because of this, the rest of this study will concentrate on this portion and develop an analysis methodology to analyze this part.


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Because setting the fracture stiffness to zero ( c
f = 0) results in a conventional boundary condition of constant rate injection followed by shut-in, setting 
cf = 0 should also reduce the solution presented in Equations 12 and 13 to conventional square root time equation. Careful examination shows that in 
fact that is the case and setting c f = 0 results in Equation 14.
(14)
C
onsequently, this leads to a deeper understanding of the solution in Equations 12 and 13. The first part of the F-function (Equation 13) describes 
the change in pressure due to rate (square root of time solution) and the second part describes the correction to that pressure due to changes in width


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(fracture stiffness). Mathematical inspection of the solution reveals that the solution makes intuitive sense and calculates a pressure response which is coherent with the model description and actual phenomenon. Because we used the partial differential equation for obtaining pressure distribution due to leak-off into the porous media, the model is physically rigorous.


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Solution Validation
The solution was validated by a three prong test.
1. The Laplace space solution was numerically inverted using Stehfest’s algorithm (Stehfest 1970) and found to be matching the analytical solution.
2.  The equation along with its boundary condition was solved numerically using a commercial finite element solver and found to be matching the 
analytical solution.
3. The resulting analysis methodology was applied to real field data and yields reliable results.
Analysis Methodology
A simplified methodology is presented and aided with example data to demonstrate the power and effectiveness of this method. As a first step, the analysis methodology depends on the prior knowledge of fracturing fluid mobility (ratio of permeability to viscosity) and fracture compliance ( c
f). 
Knowing these two parameters, the process described below will aid estimating the fracture half-length times height product (A = 4x fhf). The mobility


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of the fracturing fluid can be estimated by the after closure analysis (Soliman, et al. 2005) if it is not known a priori. 
From the solution in Equations 12 and 13 it may be observed that a plot of (p - pr) vs. F and F.dp/dF vs. F would be a straight line with an intercept of 
zero. Based on this, the methodology can be summarized in the following steps:Step 1 : Convert the time to F-function described by Equation 13
Step 2
:  Plot ( p - p r) vs. F and F.dp/dF vs. F on the same graph paper. It should be noted that F decreases as time increases, and it is suggested to plot F 
in reverse direction.
Step 3 :  B ecause both plots would have the same slope and would be passing through the origin, the straight line can be easily identified. The straight 
line manifests itself when the F.dp /dF vs. F plot superimposes on (p - p r) vs. F. 
Step 4 : Find the slope (m) of the straight line.
Step 5 : Using the slope find the area of the fracture:
(15)


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Step 4 : Find the slope (m) of the straight line.
Step 5 : Using the slope find the area of the fracture:
(15)
Step 6 : Closure pressure can be obtained from the late time deviation of data from the straight line. 
Uncertainty in Analysis
Like all pressure transient analysis problems, the quality of analysis depends on the quality and accuracy of the input parameters: fracture height, Y oung’s modulus, reservoir pressure, and fluid/rock properties. Pressure transient analysis is an inverse problem and therefore there is always a chance of non-unique interpretation, some of which can be mitigated by knowing permeability in advance, thereby diverting the uncertainty towards half-length. The capability of the proposed analysis technique of superimposing the pressure and pressure derivative for obtaining the straight line is a device which mitigates much of the uncertainty associated with finding the correct straight line and hence the fracture half-length.
Application to field data


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Application to field data
The above method was applied to two real field injection shut-in tests dubbed A-1 and A-2.
Example A-1
Figure 1 shows an almost constant rate injection of 20 bpm (0.053 m3/s) for about 22 minutes. Table 1 summarizes the essential input parameters 
needed for analysis.
Figure 1 . Injection pressure and rate data for Example A-1.
The F-function was computed for time larger than shut-in time. The plot of pressure difference ( p - pr) and F.dp/dF was plotted against the F-function 
(Figure 2). The F-function is plotted in reverse direction so that real time is increasing to the right. A straight line was identified based on the conditions that it should pass through the origin and that the pressure difference and pressure derivative will align with each other in that region. Even


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though the pressure derivative is not smooth, it is evident that it begins to oscillate around the pressure difference plot. A least square straight line, fit 
on the pressure difference, through this region, and passing through the origin yields an excellent R2 of 0.999. Qualitatively it can be observed that the 
same line fits through the derivative as well. A G-function plot is also demonstrated in Figure 3.
Figure 2 . F-function plot for A-1.
Analysis RecommendationsThe late deviation from this straight line gives the closure stress. The early deviation is due to the assumption that area is not changing during shut-in, which is being violated initially mainly because of the phenomenon of height recession. This is confirmed by looking at Equation 15. A straight line


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fit through the early time region would yield a gentle slope (larger area). The slope begins to increase (which in turns means a decrease in area) until it becomes constant in the middle time region, after which the fracture closes. Another way of viewing this is by observing that a lower pressure than the straight line in the early time region shows that the pressure is not “sufficient” to keep the area constant, and therefore the area needs to recede to reach equilibrium with the pressure. Once this equilibrium is attained, a straight line is visible in the middle time region. The slope of the line (33 MPa) may now be used to calculate fracture area using Equation 15. Table 2 summarizes the analysis results.
Figure 3 . G-function plot for A-1.Table 1 . Input parameters for Example A-1.
k/μ 2.5E-6 m2/MPa.s 2.5 md.cp-1
cf 1.3E-3 m.MPa-13e-5 ft.psi-1
φ.ct 1.4E-3 MPa-19.5E-6 psi-1
pr 25 MPa 3630 psi
Table 2 . Results of analysis for Example A-1.
Slope  MPa 0 psi
Area 620 m26720 ft2


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φ.ct 1.4E-3 MPa-19.5E-6 psi-1
pr 25 MPa 3630 psi
Table 2 . Results of analysis for Example A-1.
Slope  MPa 0 psi
Area 620 m26720 ft2
xf.hf 155 m21680 ft2
Closure Stress 47 MPa 6815 psi
p-pr=66 F


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The G-function analysis plot confirms these results. The closure stress found from the G-function plot was around 45 MPa (6525 psi) which shows 
close agreement within 5% of this technique.
Example A-2
Figure 4 shows the injection pressure data for A-2. Injection was carried out at almost constant injection rate of 10 bpm (0.0253 m3/s) for about 6 
minutes. Table 1 summarizes the essential input parameters needed for analysis.
The F-function was computed for times larger than shut-in time. Figure 5 shows the F-function plot for A-2. The straight line was identified fairly 
easily from the alignment of the derivative plot with the pressure difference plot. A straight line fit on the pressure difference, through this region, and 
passing through the origin yields an excellent R2 of 0.999. A G-function plot is also demonstrated in Figure 6.
Figure 4 . Injection pressure and rate data for Example A-2.


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Figure 4 . Injection pressure and rate data for Example A-2.
Analysis RecommendationsThe deviations from the straight line are quite different from Example A-1. The authors attribute these deviations to violation of different assumptions. The late deviation from this straight line gives the closure stress. However, in this case, the early deviation is attributed to the phenomenon of after growth. A higher (excess) pressure than the straight line causes the fracture to keep growing after shut in. The growth stops when the pressure dissipation reaches equilibrium with the width reduction and leak-off. This is confirmed with the observations earlier based on Equation 15. The slope


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begins to decrease from the early-time region to the mid-time region. The decrease in slope equates to an increase in area. The increase ceases during the mid-time region, when the slope becomes constant until fracture closure. The slope of the mid-time region was found to be 101 MPa which is used to calculate fracture area using Equation 15. Table 4 summarizes the analysis results.
Figure 5 . F-function plot for A-2.Table 3 . Input parameters for Example A-2.
k/μ 1E- m2/MPa.s 0.1 md.cp-1
cf 1.3E-3 m.MPa-13e-5 ft.psi-1
φ.ct 2.8E-3 MPa-11.9E-5 psi-1
pr 8 MPa 1190 psi


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The G-function plot confirms the early-time deviation, however fracture closure is not unambiguously evident. An approximate value of 85 MPa was 
picked from the plot which matches the F-function analysis result.
Figure 6 . G-function plot for A-2.
Conclusion
The problem of fluid leak-off after shut-in and before closure was solved rigorously based on the linear flow diffusivity equation instead of relying on Carter’s leak-off equation. The resulting solution was used to develop an analysis methodology which gives reliable results for analyzing the before-closure data. This technique yields reliable values for fracture area and closure stress. Application of the technique was demonstrated with two real field data sets.
Nomenclature
A  = F racture Area, m2
Ac  = Cr oss-sectional area of fracture, m2
cf  =  F racture stiffness or the inverse of fracture 
compliance, m.Pa-1
cfluid-loss   = Fl uid loss coefficient, m.s-1/2
cfluid  = Fl uid compressibility, Pa-1


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compliance, m.Pa-1
cfluid-loss   = Fl uid loss coefficient, m.s-1/2
cfluid  = Fl uid compressibility, Pa-1
ct  = T otal compressibility, Pa-1
E'  = P lane strain modulus, Pa [ E'= E/(1-ν2)]
F  = F -Function defined by Equation 13
hf  = F racture height, m
k  = P ermeability, m2 [1 md=9.86923x10-15 m2]
L  = L aplace transform
L-1  = I nverse Laplace transform
ṁ  = M ass flow rate (kg/s)
p  =  M easured pressure at wellbore, Pa  
[1 psi = 6894.76 Pa]
pc  = C losure stress, Pa [1 psi = 6894.76 Pa]
pD  = Dim ensionless pressure
pr  = R eservoir pressure, Pa [1 psi = 6894.76 Pa]
q  = I njection rate, m3/s [1 stb/d = 1.84x10-6]
qloss  = R ate of fluid leak-off, m3/s
R0  = Fi lter-cake resistance, Pa.s/m
RD  = Dim ensionless filter-cake resistancerf  = R adius of fracture, m [Radial Geometry]
t  = T ime, s
tD  = Dim ensionless time
ti  = I njection time, s
tiD  = Dim ensionless injection time
u  = L aplace parameter
U  = U nit step-function
v  = V elocity, m/s


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ti  = I njection time, s
tiD  = Dim ensionless injection time
u  = L aplace parameter
U  = U nit step-function
v  = V elocity, m/s
w  = F racture width, m [1 ft = 0.3048 m]
x  =  Fl uid flow direction orthogonal to fracture area, 
m [1 ft = 0.3048 m]
xD  = Dim ensionless distance
xf  = F racture half-length, m
y  =  Fl uid flow direction along the fracture length,  
m [1 ft = 0.3048 m]
λ  = M obility, m2/Pa.s [ λ = k/μ]
μ  = V iscosity, Pa.s [1 cp = 0.001 Pa.s]
ν  = P oisson’s ratio
ρ  = Fl uid density, kg/m3 [1 lb/ft3 = 16 kg/m3]
τ  = A lternate time, s
τD  = D ummy integration variable
φ  = P orosity
 
 Table 4 . Results of analysis for Example A-2.
Slope  MPa 4500 psi
Area 1 m212 ft2
xf.hf  m25 ft2
Closure Stress 85 MPa 12335 psi


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References
Carter, R. D. 1957. “”Derivation of the General Equation for Estimating the Extent of the Fractured Area” Appendix to: “Optimum Fluid Characteristics  
 f or Fracture Extension” by G. C. Howard and C. R. Fast. ” Mid-Continent District, Division of Production. Tulsa: API-57-261. 261-270.
Howard, G. C., and C. R. Fast. 1957. “Optimum Fluid Characteristics for Fracture Extension. ” Mid-Continent District, Division of Production. Tulsa:  
 AP I-57-261. 261-270.
Lamei, C. H., and M. Y . Soliman. 2014. “New Before Closure Analysis Model for Unconventional Reservoirs. ” SPE/EAGE European Unconventional  
 C onference. Vienna: SPE 167790-MS. doi:http://dx.doi.org/10.2118/167790-MS.
Mayerhofer, M. J., and M. J. Economides. 1993. “Permeability Estimation From Fracture Calibration Treatments. ” SPE Western Regional Meeting.  
 A laska: SPE 20639-MS. doi:10.2118/26039-MS.


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A laska: SPE 20639-MS. doi:10.2118/26039-MS.
Mayerhofer, M. J., M. J. Economides, and K. G. Nolte. 1991. “ An Experimental and Fundamental Interpretation of Fracturing Filtercake Fluid Loss. ”  
 S PE 68th ATCE. Dallas: SPE 22873-MS. doi:http://dx.doi.org/10.2118/22873-MS.
Nolte, K G. 1979. “Determination Of Fracture Parameters From Fracturing Pressure Decline. ” SPE 54th Annual Technical Conference. Las Vegas: SPE  
 8341-MS. do i:http://dx.doi.org/10.2118/8341-MS.
Nolte, K. G. 1986. “ A General Analysis of Fracturing Pressure Decline With Application to Three Models. ” SPE Formation Evaluation (SPE 12941-PA)  
 571-583. do i:http://dx.doi.org/10.2118/12941-PA.
Nordgren, R. P . 1972. “Propagation of a Vertical Hydraulic Fracture. ” SPE 45th Annual Conference. Houston: SPE 3009-PA. doi:http://dx.doi.  
 org/10.2118/3009-PA.
Soliman, M. Y ., D. P . Craig, K. M. Bartko, Z. Rahim, and Z. M. Adams. 2005. “Post-Closure Analysis to Determine Formation Permeability, Reservoir


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Soliman, M. Y ., D. P . Craig, K. M. Bartko, Z. Rahim, and Z. M. Adams. 2005. “Post-Closure Analysis to Determine Formation Permeability, Reservoir  
 P ressure, Residual Fracture Properties. ” SPE Middle East Oil and Gas Show and Conference. Bahrain: SPE 93419-MS. doi:10.2118/93419-MS.
Stehfest, H. 1970. “Numerical Inversion of Laplace Transforms. ” Communication of the ACM 13 47-48. doi:http://dx.doi.org/10.1145/361953.361969.
Valko, P . P ., and M. J. Economides. 1999. “Fluid-leakoff Delineation in High-permeability Fracturing. ” SPE Journal (SPE 56135-PA). doi:http://dx.doi.  
 org/10.2118/56135-PA.
Appendix A: Derivation of Inner Boundary Condition
For x = 0,
  
    
 Recognizing:


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Since fracture volume is small relative to the total injected volume, and compressibility is small, the compressibility term can be neglected.
For the case of shut-in at ti assuming that only width of the fracture is changing due to compliance and area remains constant as the fracture closes 
along the hinge at the tip. By using the step-function U:
 
Appendix B: Solution of Equations 5 and 6
Inner Boundary Condition: 
Initial Condition:  
 
Consider the following dimensionless variables:
Writing the equations in dimensionless variables:
Inner Boundary Condition: 
Initial Condition:  
Outer Boundary Condition:


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Applying Laplace Transform to the inner boundary condition:
Applying Laplace Transform to the partial differential equationSolving the above differential equation and using the initial and outer boundary conditions
  
After substituting from outer boundary condition
Using convolution theorem to invert the above expression
After simplification and removing the step-function:
Carrying out the integrals and simplifying:
Substituting the definitions of dimensionless variables:


