# embeddings_queue

created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5b56-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 2, "chroma:document": "end of pumping and \ud835\udc580 is the original reservoir \npermeability. \ud835\udc43\ud835\udc5c\ud835\udc5f\ud835\udc56\ud835\udc54\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc59  is the pressure where reservoir \npermeability drops to its original value a nd c a free \nparameter controls the evolution of permeability. \ud835\udc58\ud835\udc52 is \nlarger than \ud835\udc580 because the surrounding permeability is \nenhanced by stimulated fracture networks during \npumping. After the pressure drops to or below \ud835\udc43\ud835\udc5c\ud835\udc5f\ud835\udc56\ud835\udc54\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc59 , \nthe stimulated f racture networks close back to the \noriginal in -situ state and the effective permeability \nreturn s to its original value.  Figure.2 demonstrates the \npressure -dependent permeability for different values of c.  \n \nFig. 2 Illustration of pressure -dependent permeab ility with \ndifferent values of c  \n2.4. Pressure Dependent Fracture Compliance  \nFracture closure is a gradual process with increasing \nfracture stiffness (or decreasing fracture compliance) as \nfracture closes from tip to wellbore or closes from higher \nstress region  to lower stress region in layered formations."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5ba6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 2, "chroma:document": "fracture closes from tip to wellbore or closes from higher \nstress region  to lower stress region in layered formations. \nA method t o obtain a pressure -dependent fracture \ncompliance based on fracture geometry, rock properties \nand surface roughness has been well discussed by Wang \nand Sharma (2017a) and Wang et al. (2018). The \ninfluence of surface roughness on fracture compliance is described by a contact law relat ing the  fracture width to \nthe net closure stress for fractured rocks (Willis -Richards \net al. 1996):  \n  \u03c3c=\u03c3ref\n9(w0\nwf\u22121)for  wf\u2264w0     (17) \nwhere wf is the fracture aperture and, w0 is the contact \nwidth, which represents the fracture aperture when the \ncontact normal stress is equal to zero, \u03c3c is the contact \nnormal stress on the fracture, and \u03c3ref is a contact \nreference stress, which denotes the effective normal \nstress at which the aperture is reduced by 90%.  \n3. DFIT IN NATURALLY FR ACTURED \nRESERVOIRS"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5bec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 2, "chroma:document": "reference stress, which denotes the effective normal \nstress at which the aperture is reduced by 90%.  \n3. DFIT IN NATURALLY FR ACTURED \nRESERVOIRS  \nAll reservoirs are fractured to some degree. D epending \non the density  and dimension s of natural fractures and \nthe location where the DFIT is done, the natural \nfractures can impact hydraulic fracture propagation and \nthe adjacent flow capacity. If the reservoir is heavily \nfractured and these natural fra ctures are well -connected, \nas shown in Figure 3, then the formation can be \nconsidered as homogenous within the distance of \ninvestigation and the effective permeability is controlled \nby both fracture and matrix. High -pressure  fluid \ninjection  during the pump ing period enhance s the local \neffective permeability because it widens the natural \nfractures. However, as pressure declines during shut -in, \nthe effective permeability will gradually decline until it \nreaches the original value. The original effective"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5c3c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 2, "chroma:document": "the effective permeability will gradually decline until it \nreaches the original value. The original effective \npermea bility does not necessar ily represent the matrix \npermeability, because the existence of natural fractures \nmay already have enhanced the permeability.  \n \nFig. 3 Heavily fractured reservoir with well -connected natural \nfractures  \n \nIf the reservoir is sparsely or moderately fractured, and \nthe stimulated natural fractures are discrete and not well -\nconnected, then these natural fractures or isolated \nfracture networks will not change the overall flow \ncapacity in the reservoir  (Wang 2017) , but they can \ninteract with  hydraulic fractures, and generate  a complex \nfracture geometry, as shown in Figure  4. Under this \nscenario, the fracture compliance and leak -off surface \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5c82-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "area are impacted by the sequential closure of individual \nfracture segment s or branch es, where the branc hes with \nthe highest normal stress perpendicular to local fracture \norientation will close first, and the fracture segments that \nopen against the minimum principal stress will be the \nlast to close. If  the hydraulic fracture does not initiate \nalong the maxim um principal stress direction because of \nthe local hoop stress around perforations, non -planar \nfracture s can also be formed. In this section, we are \ngoing to investigate the pressure transient behavior \nunder these scenarios and discuss the implications of \nestimating closure stress using  different methods . \n \nFig. 4 Low to Moderate Fractured Reservoir with Discrete \nNatural Fractures  \n3.1. Base Case  \nBefore we embark on investigating the pressure transient \nbehavior with closing  fracture in fractured reservoirs, \nwe\u2019ll first examine pressure decline behavior for a planar"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5cd2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "behavior with closing  fracture in fractured reservoirs, \nwe\u2019ll first examine pressure decline behavior for a planar \nfracture and discuss the causes for the discrepancy for \nestimated closure stress using  established methods. \nTable 1  shows the input parameters for the Base Case \nScenario . \nTable 1. Input parameters for the Base Case scenario  \nFracture type  PKN \nFracture height  12 m  \nFracture half -length  50 m  \nPumping time  5 min  \nISIP 40 MPa  \nMinimum in -situ stress  35 MPa  \nInitial pore pressure  20 MPa  \nYoung's modulus  20 GPa \nTotal compressibility  6.3e -4 MPa-1 \nIn-Situ fluid viscosity  0.3 cP  \nFormation original permeability  0.0005 md \nPoisson's Ratio  0.25  \nInitial porosity  0.03  \nContact width  of asperities  2 mm  \nContact reference stress  of asperities  5 MPa  \n \nWith the known fracture geometry, rock modulus, \nminimum in -situ stress and surface roughness \n(represented by two contact parameters \ud835\udc640 and \ud835\udf0e\ud835\udc5f\ud835\udc52\ud835\udc53),"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5d22-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "With the known fracture geometry, rock modulus, \nminimum in -situ stress and surface roughness \n(represented by two contact parameters \ud835\udc640 and \ud835\udf0e\ud835\udc5f\ud835\udc52\ud835\udc53), \nthe fracture stiffness and volume evolution can be \nuniquely determined at different fluid pressure s (Wang  \nand Sharma 2017a; Wang et al. 2018), the results are shown in Figure 5. As can be seen, when the fluid \npressure inside the fracture is relatively high, the fracture \nvolume declines linearly with pressure under constant \nfracture stiffness (or compliance). However, as the \npressure declines to a certain level the fracture volume \nand pressure depart from a linear relationship, and \nfracture stiffness start s to increase noticeably. In the end, \nwhen the fluid pressure drops to a sufficient low level, \nthe residual  fracture volume (supported by asperities) \nbecomes more or less insensitive to pressure drop with \nextremely high fracture stiffness (low compliance). This \nis because when the pressure inside the fracture is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5d72-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "extremely high fracture stiffness (low compliance). This \nis because when the pressure inside the fracture is \nrelatively high, it is still wide open and its st iffness is a \nconstant . However, as pressure continues to drop, the \nfracture will gradually close from its edges to its center, \nwhich increase s the fracture stiffness gradually.  \n \nFig. 5 Illustration of the fracture stiffness and volume \nevolution from modeling  \nFigure.6 shows  the normalized tiltmeter response (its \nslope is proportional to fracture compliance or the \nreciprocal of fracture stiffness) plotted against wellbore \npressure during the shut -in period of 2B well at three \ndifferent stations from the  GRI/DOE M -site. The \ntiltmeter demonstrates that soon after shut -in, the \nmeasured displacement declines linearly with pressure \n(roughly constant fracture stiffness). After the pressure \ndeclines to a certain level, the measured displacement vs \npressure depa rts from a linear relationship. As pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5db8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "declines to a certain level, the measured displacement vs \npressure depa rts from a linear relationship. As pressure \ncontinues declining, more and more fracture surface area \ncomes into contact with the rough fracture surfaces and \nasperities, and the fracture stiffness increases gradually. \nThis field measurement is consistent wi th the general \ntrend from out modeling results shown in Figure.5. It is \nchallenging to estimate closure stress based on \nmechanical closure from tiltmeter measurement. If we \npick the closure stress using  the \u201ctangent line method\u201d \non tiltmeter measurement (C raig et al. 2017), the closure \nstress is 15 MPa, and if we pick the closure stress using  \nthe \u201ccompliance method\u201d, the closure stress is 21 MPa. \nThere is a 6 MPa discrepancy between these two \nmethods. As discussed by Wang and Sharma (2017b), \nthe \u201ctangent li ne method\u201d only marks the end of fracture \nstorage dominated flow, so it always underestimate s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5e12-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 3, "chroma:document": "the \u201ctangent li ne method\u201d only marks the end of fracture \nstorage dominated flow, so it always underestimate s \nclosure stress while the \u201ccompliance method\u201d can \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5e62-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 4, "chroma:document": "overestimate closure stress,  because it only marks the \nbeginning fracture closure on edges or tips. The \n\u201cvariable  compliance method\u201d proposed by Wang and \nSharma (2017b) provides an alternative way to estimate \nclosure stress that not only accounts for the difference \nbetween two endpoints  (fracture compliance start to \nchange and fracture compliance become small enough to \nbe considered as negligible), but also compensates for \nthe impact of leak -off, which  is reflected on G -function \ntime or the square root of time.  \n \nFig. 6 Tiltmeter measurement from 2B well of GRI/DOE M -\nsite project  \nTo illustrate the benefit  of the \u201cvariable compliance \nmethod\u201d and compare the estimated closure stress from \ndifferent methods, the pressure -dependent fracture \nstiffness from Figure.  5 is used as a boundary condition \nfor Eq.(6) to simulate the pressure decline response, all \nother parameter s are provided in Table 1. Figure.7 shows"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5eb2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 4, "chroma:document": "for Eq.(6) to simulate the pressure decline response, all \nother parameter s are provided in Table 1. Figure.7 shows \nthe pressure decline and its derivatives on the G -function \nand square root of time plots. Compared to the input \nclosure stress of 35 MPa, the estimated closure stress by  \nthe \u201ctangent line method\u201d is 32.2 MPa ( -2.8 MPa error), \nthe estimated closure stress by the \u201ccompliance method\u201d \nis 36.8 MPa (1.8 MPa error), and the estimated closure \nstress by  the \u201cvariable compliance method\u201d is 35.2 MPa \n(0.2 MPa error). It is clear that the closure stress \nestimated by the \u201cvariabl e compliance method\u201d is more \nreliable. Detailed comparisons with different fracture \ngeometry , surface roughness  and reservoir properties \nhave been presented by Wang and Sharma (2017b), and \nhence will not be discussed further.  \nFigure.8 show s the pressure profiles in the formation \naway from the fracture surface at different shut -in times."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5f02-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 4, "chroma:document": "Figure.8 show s the pressure profiles in the formation \naway from the fracture surface at different shut -in times. \nTogether with Fig.6, we can notice that the closure time \nis around 8.85 hr when fluid pressure drops to the close \nstress, and the corresponding distance of i nvestigation is \nless than 7 m at the time of closure. This is very typical \nin low permeability formations.   \nFig. 7 Pressure decline and its derivatives of Base Case \nscenario  \n \nFig. 8 Pressure profile and distance of investigation for Base \nCase Scenario . \nNow the question remains: what unique features will \nemerge from  DFIT data in naturally fractured reservoirs \nand how do we reliably estimate closure stress under \nthese contexts? Are these established methods are \nreliable ways to estimate closure stress?  In  the \nfollowing sections, we\u2019ll examine these cases and \ndiscuss the associated challenges in identify ing closure \nstress in naturally  fractured reservoir."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5f70-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 4, "chroma:document": "discuss the associated challenges in identify ing closure \nstress in naturally  fractured reservoir.  \n3.2. Heavily Fractured Reservoir with Pressure \nDependent Permeability  \nFirst, let\u2019s investigate the case wher e the reservoir is \nheavily fractured and all the stimulated fractures form \nwell-connected networks that alter the effective \npermeability around the hydraulic fracture. The effective \npermeability is highest at the end of pumping and \ngradually declines as pr essure drops and fluid leak-offs \ninto formation . Assumes the effective permeability \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a5fb6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "follows Eq.(12), with c=3 and \ud835\udc43\ud835\udc5c\ud835\udc5f\ud835\udc56\ud835\udc54\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc59  is 4.5 MPa \nbelow the ISIP, all the other input parameters are the \nsame as the base case. Figure.9  shows the pressure \ndecline and its derivatives with different values of \nenhanced effective permeability \ud835\udc58\ud835\udc52 at the end of \npumping. From the results, we can clearly observe that \nthere exists a \u201cbump\u201d on the pressure derivative during \nfracture closure befor e it reaches its final peak. And in \nall cases, the pressure derivatives \u201cbump\u201d end at a \nfracturing pressure that is 4.5 MPa below the ISIP, \nwhich is the exactly value of \ud835\udc43\ud835\udc5c\ud835\udc5f\ud835\udc56\ud835\udc54\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc59 . So the values of \n\ud835\udc43\ud835\udc5c\ud835\udc5f\ud835\udc56\ud835\udc54\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc59  can be readily obtained from f ield DFIT data if \nit exhibits this pressure -dependent permeability \nsignature. We can also observe that the higher the \ud835\udc58\ud835\udc52, the \nlarge the initial slope of pressure derivatives.  \n \n \nFig. 9 Pressure decline and its derivatives with pressure -\ndependent permeab ility \nBecause the effect of pressure -dependent permeability"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6006-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "Fig. 9 Pressure decline and its derivatives with pressure -\ndependent permeab ility \nBecause the effect of pressure -dependent permeability \nmasks the initial phase of fracture closure, so the \nmoment when the fracture stiffness start s to change \ncannot be identified. In such cases , the \u201ccompliance \nmethod\u201d is hard to apply . We can, howev er, modify our \n\u201cvariable compliance method\u201d approach  as follows : first, \nwe identify the dimensionless G -time or the square root \nof time at the end of the first pressure derivative \u201cbump\u201d \n(i.e., end of pressure -dependent permeability) and at the \nintersectio n of pressure derivative and a tangent line \npassing through the origin (i.e., the closure point picked \nby the \u201ctangent line method\u201d). Then average the values \nof these two dimensionless G -time or the square root of \ntime, finally extrapolate back to the pressure curve that"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6056-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "of these two dimensionless G -time or the square root of \ntime, finally extrapolate back to the pressure curve that \ncorresponds to the averaged G -time or the square root of time. Table 2 shows the estimated closures by \u201ctangent \nline method\u201d and \u201cvariable compliance method\u201d. As can \nbe seen, the \u201ctangent line method\u201d consistently \nunderestimates the closure stress. This stems from the \nfact that the \u201ctangent line method\u201d assumes constant \nfracture stiffness and Carter\u2019s leak -off during closure , \nbut these two assumptions are not valid (Wang and \nSharma 2017b). The closure stress estimated by \n\u201cvariable compliance method\u201d gives significantly lower \nerrors and is a more reliable approach to estimate closure \nstress.  \nTable 2. Comparison of estimated closure stress from different \nmethods with pressure -depe ndent permeability  \nScenarios  Tangent Line Method  Variable Compliance Method  \nEstimated  \n \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f   Absolute \nError  Estimated  \n\ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f   Absolute \nError"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a60a6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "Scenarios  Tangent Line Method  Variable Compliance Method  \nEstimated  \n \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f   Absolute \nError  Estimated  \n\ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f   Absolute \nError  \n\ud835\udc58\ud835\udc52=\ud835\udc580 32.2 MPa  -2.8 MPa  35.2 MPa  0.2 MPa  \n\ud835\udc58\ud835\udc52=5\ud835\udc580 32.3 MPa  -2.7 MPa  34.4 MPa  0.4 MPa  \n\ud835\udc58\ud835\udc52=10\ud835\udc580 32.1 MPa  -2.9 MPa  34.5 MPa  0.5 MPa  \n\ud835\udc58\ud835\udc52=20\ud835\udc580 32.2 MPa  -2.8 MPa  34.4 MPa  0.4 MPa  \n \n3.3. Discrete Natural Fractures  \nIn the case of sparsely or moderately fractured reservoirs,  \neven though  the stimulated natural fractures are d iscrete \nand not well -connected, they can interact with \npropagating hydraulic fracture and generate complex \nfracture geometry. To make modeling and analysis \ntrackable, we\u2019ll first investigate a simplified version of \ncomplex fracture geometry that only consist two sets of \nfractures with di fferent orientations, as shown in \nFigure.10, then more general scenarios will be discussed \nat the end. In Figure.10, we can see that the main \nhydraulic fracture (i.e., fracture set 1) is perpendicular to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a60ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "at the end. In Figure.10, we can see that the main \nhydraulic fracture (i.e., fracture set 1) is perpendicular to \nthe minimum principal stress, while the natural frac tures \n(i.e., fracture set 2) are perpendicular to the maximum \nprincipal stress. As pressure declines inside fracture after \nshut-in, the natural fracture that open s against the \nmaximum principal stress will close first, and the \nhydraulic fracture that open s against the minimum \nprincipal stress will be the last to closure. Here, there are \ntwo possible scenarios are likely to happen during this \nsequential closure process: 1) the closed natural fracture \nremain hydraulic connectivity with the main hydraulic \nfracture. 2) the closed natural fracture lost the hydraulic \nconnectivity with the main hydraulic fracture. We\u2019ll \ndiscuss these two scenarios and their implications in \ninterpreting DFIT data separately.  \n3.3.1.  Closed Fracture Remain Hydraulic \nConnectivity"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a613c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 5, "chroma:document": "discuss these two scenarios and their implications in \ninterpreting DFIT data separately.  \n3.3.1.  Closed Fracture Remain Hydraulic \nConnectivity  \nIf the inter section of fractures are well aligned (not \nskewed) and supported by asperities and tortuous walls, \nthen it is likely that the closed natural fractures can \nmaintain  hydraulic connectivity to the open fracture.  \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a618c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 6, "chroma:document": "Fig. 10 Top view  of complex fracture geometry with two sets \nof fracture s. \nIn this case, the sequential closure natural fractures or \nbranches of a complex fracture will not alter the total \nleak-off surface area,  but will change the overall fracture \nstiffness evolution. Ass ume a complex fracture that \nconsists of two sets of fracture, as shown in Figure.10. \nThe total surface areas are \ud835\udc34\ud835\udc531 and  \ud835\udc34\ud835\udc532 for fracture set \n1 and fracture set 2, respectively. The maximum \nprincipal stress is 38 MPa and the minimum principal \nstress is 33 MPa. We further assume that all fracture \ncloses like a PKN fracture. Figure.11 shows the fracture \nstiffness evolution with different surface area ratio. As \ncan be seen, if we only have fracture set 2 (i.e., natural \nfracture), the fracture stiffness w ill increase at 39.5 MPa, \nand if we only have fracture set 1 (i.e., hydraulic \nfracture), the fracture stiffness will increase around 34.5 \nMPa. The overall fracture stiffness evolution is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a61d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 6, "chroma:document": "fracture), the fracture stiffness will increase around 34.5 \nMPa. The overall fracture stiffness evolution is \ncalculated using Eq.(10) with different surface area ratio. \nBecause f or complex fracture geometry, the overall \nfracture stiffness is like a parallel system of capacitors, \nso the changes in fracture stiffness is not directly \nproportional to the surface area ratio, but is mostly \ninfluenced by the fracture set that has the highest ratio of \nsurface area to stiffness.  \n \nFig. 11 Fracture stiffness evolution for a  complex fracture \ngeometry (hydraulic connectivity remains after closure)  \nFigure.12 shows the pressure decline and its derivatives \nof complex fracture geometry when closed  natural \nfractures remain their hydraulic connectivity to the main hydraulic fracture. Because the fracture stiffness \nevolution is smooth and gradual, so the closure of \nnatural fracture is undetectable on G -function or the \nsquare root of time plot. But fro m the pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6222-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 6, "chroma:document": "natural fracture is undetectable on G -function or the \nsquare root of time plot. But fro m the pressure \nderivatives, we can notice that the larger the surface area \nof natural  fracture, the sooner the pressure derivatives \ncurve upward  and the faster the pressure decline during \nclosure . \n \n \nFig. 12 Pressure decline and its derivatives of complex  \nfracture geometry (remain hydraulic connectivity after \nclosure)  \nTable 3 summarizes the estimated closure stress \n(minimum principal stress) by different methods. As \nalways, the \u201ctangent line method\u201d underestimates the \nclosure stress, while \u201ccompliance method\u201d overestimates \nclosure stress. The \u201ccompliance method\u201d gives a much \nlarger error if the surface area of natural fracture is large. \nThis is because \u201ccompliance method\u201d picks the pressure \nwhen natural fracture edges or tips start to closure, \nwhich can  be much higher than the minimum principal \nstress. The \u201cvariable compliance method\u201d yields the \nleast error."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6272-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 6, "chroma:document": "which can  be much higher than the minimum principal \nstress. The \u201cvariable compliance method\u201d yields the \nleast error.  \nTable 3. Comparison of estimated closure stress of complex \nfracture geometry (hydraulic connectivity remains after \nclosure)  \n\ud835\udc68\ud835\udc87\ud835\udfd0\n\ud835\udc68\ud835\udc87\ud835\udfcf Tangent Lin e \nMethod  Compliance \nMethod  Variable Compliance \nMethod  \n\ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \n0.5 31  -2  34.8  1.8  33.4  0.4  \n1 31.1   -1.9  35.4  2.4  33.6  0.6  \n5 31.6   -1.4  37.8  4.8  33.3   0.3  \n10 32  -1  39.2  6.2  33.5   0.5  \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a62b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 7, "chroma:document": "In fact, the information on fracture complexity can\u2019t be \ndetected under such cases, and compared to a single \nhydraulic fracture scenario (i.e., only fracture set 1 on \nFig.10), the impact of natural fractures on overall \nfractures stiffness evolution can be substituted by a \n\u201crougher\u201d fracture walls with larger contact width and \nhigher contact reference stress (Wang and Sharma \n2017b) to obtain earlier and steeper increase in fracture \nstiffness as pressure declines. So based on before -closure \nDFIT data alone, w e may not be able to distinguish the \ncauses  to the increase of fracture stiffness from fracture \ncomplexity or surface roughness or recession in barrier \nlayers. Nevertheless, as discussed by Wang and Sharma \n(2017b), the \u201cvariable compliance method\u201d is insen sitive \nto fracture geometry, surface roughness and reservoir \nproperties, and from the above results, we see that it is \nalso much less sensitive to the existence of natural"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6312-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 7, "chroma:document": "properties, and from the above results, we see that it is \nalso much less sensitive to the existence of natural \nfractures, so the \u201cvariable compliance method\u201d is more \nreliable way of estimate clos ure stress, especially when \nwe are not sure whether the create d fracture geometry is \ncomplex or planar.  \n3.3.2.  Closed Fracture Lost Hydraulic \nConnectivity  \nIf the intersections of fractures are skewed and not well -\naligned (such as T-shaped  fracture), then it is likely that \nthe closed fracture will lose its hydraulic connectivity to \nthe open fracture. In such case, the sequential closure \nnatural fractures or branches of a complex fracture will \nalter both the total leak -off surface area and t he overall \nfracture stiffness evolution. Assume the same complex \nfracture as discussed in the previous section. The \nmaximum principal stress is 37 MPa and the minimum \nprincipal stress is 33 MPa. We further assume the natural"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6362-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 7, "chroma:document": "maximum principal stress is 37 MPa and the minimum \nprincipal stress is 33 MPa. We further assume the natural \nfractures will gradually lose t heir hydraulic connectivity \nto the open hydraulic fracture when fluid pressure drops \naround 37 MPa.  Figure.13 shows the fracture stiffness \nevolution with different surface area ratio when natural \nfractures lose their hydraulic connectivity after closure. \nCompared to Figure.11, we can notice that the overall \nfracture stiffness evolution is not monotonically \nincreasing with declining pressure anymore . The surface \narea ratio will shape the fracture stiffness evolution \nbefore the closure of natural fractures, b ut once the \npressure drops to a certain level and disconnect the \nnatural fractures, the overall fracture stiffness becomes \nthe fracture stiffness of the remaining hydraulic fracture.  \nFigure.14 shows the pressure decline and its derivatives \nof complex fract ure geometry when closed fractures lose"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a63a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 7, "chroma:document": "Figure.14 shows the pressure decline and its derivatives \nof complex fract ure geometry when closed fractures lose \nhydraulic connectivity. It can be clearly observed that \nthere are two peaks on pressure derivatives curve, the \nfirst one is associated with the closure process of natural \nfractures, and the second one is associated w ith the \nclosure process of the hydraulic fracture.  \n  \nFig. 13 Pressure decline and its derivatives of complex \nfracture geometry (lose hydraulic connectivity after closure)  \n \n \nFig. 14 Pressure decline and its derivatives of complex \nfracture geometry (lose hydraulic connectivity after closure)  \nTable 4. Comparison of estimated closure stress of complex \nfracture geometry (lose hydraulic connectivity after closure)  \n\ud835\udc68\ud835\udc87\ud835\udfd0\n\ud835\udc68\ud835\udc87\ud835\udfcf Tangent Line \nMethod  Compliance \nMethod  Variable Compliance \nMethod  \n\ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \n0.5 30.5  -2.5 35.4  2.4 33.4  0.4"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a63f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 7, "chroma:document": "Method  \n\ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \ud835\udf48\ud835\udc89\ud835\udc8e\ud835\udc8a\ud835\udc8f  \n(MPa)  Error \n(MPa)  \n0.5 30.5  -2.5 35.4  2.4 33.4  0.4 \n1 30.6  -2.4 35.5  2.5 33.4  0.4 \n5 30.7  -2.3 35. 2.7 33.6  0.6 \n10 30.9  -2.1 35.8  2.8 33.6  0.6 \n \nIf we only analyzed the portion of data after the first \npeak of pressure derivatives and use it to estimate the \nclosure stress associated with the closure of the \nhydraulic fracture, we can compare the results from \ndifferent methods, as shown in Table 4. Ag ain, we can \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6448-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 8, "chroma:document": "notice that \u201ctangent line method\u201d underestimates closure \nstress while \u201ccompliance method\u201d overestimates closure \nstress. The \u201cvariable compliance method\u201d is more \nreliable and gives the least errors.  \nIn reality, a complex fracture can consist of many \nfracture sets with different orientations and surface area . \nThe approach and analysis presented for our simplified \ncases are still valid for these more general scenarios. \nAssum ing that  a complex fracture has four sets of \nfractures with equal surface area, but open against \ndifferent in -situ stresses (37 MPa, 35 MPa, 33MPa and \n31 MPa, where 31 MPa is the minimum principal stress) \nbecause of their orientations, Figure.15 shows the \nevolutio n of fracture stiffness as a function of fracturing \npressure. As can be seen, if natural fractures gradually \nlose their hydraulic connectivity around the normal \nstress that is perpendicular to that fracture surface, the \noverall fracture stiffness will exhi bit three peaks before"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6498-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 8, "chroma:document": "stress that is perpendicular to that fracture surface, the \noverall fracture stiffness will exhi bit three peaks before \nit finally reflects the fracture stiffness of the last open \nfracture.  \n \nFig. 15 Fracture stiffness evolution of complex fracture \ngeometry with four sets of fracture  \nFigure.16 shows the corresponding pressure decline and \nits derivatives. As expected, four peaks emerge on the \npressure derivatives and if we only analyze the portion \nof data after the third peak to estimate closure stress, the \n\u201ctangent line method\u201d underes timate s the closure stress \nby around 1 MPa. The \u201cvariable compliance method\u201d \ngives a close r value. In general, estimated closure stress \nby the \u201ctangent line method\u201d can be regarded as the \nlower bound of closure stress and the closure stress  \nestimated  by th e \u201ccompliance method\u201d can be viewed as \nthe upper bound of closure stress.  \n4. COMPARISON WITH EXPERIMENT  \nCraig et al. (2017) compared and discussed fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a64de-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 8, "chroma:document": "the upper bound of closure stress.  \n4. COMPARISON WITH EXPERIMENT  \nCraig et al. (2017) compared and discussed fracture \nclosure stress estimated by \u201cCompliance Method\u201d and \n\u201cTangent Line Method\u201d using tiltmeter measurement \nand laboratory experiments.   \n \nFig. 16 Pressure decline and its derivatives of complex \nfracture geometry with four sets of fracture  \nFigure.17 shows the G -function plots using data \nextracted from laboratory experiments from their study. \nAs expected  the pressure decline is affected by tip \nextension and fluid transient behavior along the fracture \nsoon after shut -in, so a brief pressure derivative spike \noften immediately follows shut -in. In many cases, this \npressure derivative spike may mask the \u201copen fract ure \nperiod \u201d (with constant stiffness) and make it difficult to \nlocate the moment when the fracture stiffness starts to \nincrease. If the closure time is not long enough, this \nearly time abnormal pressure (large pressure drop during"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6556-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 8, "chroma:document": "increase. If the closure time is not long enough, this \nearly time abnormal pressure (large pressure drop during \na short time interval) c an\u2019t be distingu ished from the \nsignature of pressure -dependent permeability, which is \nnormally the case in laboratory experiments where the \nfracture closes in less than 1 minute. In the soft rock case \nof Figure.17, the imposed closure stress is 7 MPa, but \nthe closure stress estimated by the \u201cTangent Line \nMethod\u201d is only 3 MPa, which is significantly lower. \nBecause the early -time pressure derivative spike masks a \nlarge portion of before closure data, the \u201ccompliance \nmethod\u201d and \u201cvariable compliance method\u201d a re not \napplicable. In the moderately hard rock case of \nFigure.17, the imposed closure stress is 16 MPa, the \nclosure stress estimated by  \u201cTangent Line Method\u201d is \n14.32 MPa and the closure stress estimated by  \n\u201ccompliance method\u201d is 20.16 MPa. The closure s tress \nestimated by \u201cvariable compliance method\u201d is 17.1 MPa"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a659c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 8, "chroma:document": "\u201ccompliance method\u201d is 20.16 MPa. The closure s tress \nestimated by \u201cvariable compliance method\u201d is 17.1 MPa \nat the averaged G -function time of 1.745. This result is \nconsistent to our simulated synthetic cases presented in \nthis study and previous  study (Wang and Sharma \n2017b) . Laboratory experiments also  show that  the \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a65ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 9, "chroma:document": "\u201cvariable compliance method\u201d gives the least error and \n\u201cTangent Line Method\u201d normally underestimates closure \nstress.  \n \n \nFig. 17 Laboratory fracture closure experiment for soft (upper \nfigure) and moderately hard rock (lower figure) (Craig et  al. \n2017)  \n5. DISCUSSION  \nExamining Eq.(1)~Eq.(9) closely, it is evident that the \npressure decline is governed by a linear Partial \nDifferential Equation (PDE) system in the formation that \nis coupled with an Ordinary Differential Equation \n(ODE) at the fracture surface. The minimum in -situ \nstress is just one of many implicit factors that shape the \nevolution of the fracture pressure  in the boundary ODE. \nThe causes for the error associated with \u201ctangent line \nmethod\u201d stems from the traditional G -function plot \nanalys is, where the assumptions of Carter\u2019s leak -off and \nconstant fracture stiffness during closure (changes \nabruptly to infinite at closure stress) are invalid. The"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a663c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 9, "chroma:document": "constant fracture stiffness during closure (changes \nabruptly to infinite at closure stress) are invalid. The \ncauses for the error associated with \u201c compliance method\u201d is due to the fact that the increase of  fracture \nstiffness can happen even before fracturing pressure \ndrops to minimum in -situ stress.  \nFor a planar fracture geometry, the fracture closes \nprogressively from its edges to the center with a gradual \nincrease in stiffness, if both numerical modeling (as \nshown in Fig. 5) and tiltmeter measurement s (as shown \nin Fig.6) only shows  smooth curves without a clear \nindication of closure  stress, then the pressure decline \nsignature that reflects the combined effects of pressure -\ndependent leak -off and fractures  stiffness evolution is \nnot going to yield additional information on closure \nstress. The \u201cvariable compliance method\u201d, provides an \nalternative way to estimate the minimum in -situ stress. \nBy history matching the DFIT data, using properties of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a668c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 9, "chroma:document": "alternative way to estimate the minimum in -situ stress. \nBy history matching the DFIT data, using properties of \nfracture surfa ce roughness and formation flow capacity, \nthe ranges of un -propped fracture conductivity and \nformation permeability can be obtained for various \nfracture dimension s (Wang and Sharma 2018).  \nIn naturally fractured reservoirs, it is difficult to quantify \nsuch information through a history match. In the case of \npressure -dependent permeability, the pressure response \nis affected by the declining effective permeability and \nthe increase of fracture stiffness. Those two independent \nmechanisms are intertwined and can not be separated \nfrom the before -closure data, especially in the case \nwhere the period of pressure -dependent permeability \nspans a large portion of before -closure data. In other \nwords, the information on the individual evolution of \nfracture stiffness and ef fective permeability is lost and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a66dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 9, "chroma:document": "words, the information on the individual evolution of \nfracture stiffness and ef fective permeability is lost and \ncannot be recovered quantitatively from DFIT data. In \nthe case of complex fracture s, if the closed fracture \nsegments retain their hydraulic connectivity to the main \nhydraulic fracture, we will get a smooth pressure decline \nresponse. In such case s, we do not know what the \ntopology of the complex fracture is and we will not be \nable to constrain the fracture dimension using  a simple \nmaterial balance calculation. Without a good estimation \nof the initial fracture geometry to star t with, a \nmeaningful history match and uncertainty analysis are \nnot possible. If the closed fracture segments lose \nhydraulic connectivity to the main hydraulic fracture, we \nwill observe multiple pressure derivative peaks on G -\nfunction or square  root of tim e plots. In such case s, we \ncan discern, at least, how many sets of fractures (with"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6722-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 9, "chroma:document": "function or square  root of tim e plots. In such case s, we \ncan discern, at least, how many sets of fractures (with \ndifferent orientations) exist. However, we still have no \nknowledge of the fracture t opology, because the \ninformation on the individual fracture surface area and \ntheir stiffn ess are smeared together and can\u2019t be \nseparated. The situation can get more complicated if \nsome of the closed fracture segments retain their \nhydraulic connectivity to the main fracture while other s \ndo not. Nevertheless, our proposed \u201cvariable compliance \nmethod\u201d provides an alternative way to estimate in -situ \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6772-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "stress, which can be more reliable than established \nmethods, even in naturally fractured reservoirs.  \n6. CONCLUSIONS  \nIn this study, we  present a new pressure transient model \nfor DFIT analysis in naturally fractured reservoirs, \nwhich not only preserves the physics of unsteady -state \nreservoir flow behavior, elastic fracture mechanics , \nmaterial balance, varia ble fracture compliance during \nfracture closure,  but also incorporates pressure -\ndependent effective permeability and sequential closure \nof complex fracture branches. Conclusions reached from \nthe analysis presented in this paper include the following:  \n1) Fracture closure stress (i.e., minimum in -situ stress) \ncan\u2019t be pinpointed from DFIT data because of the \nnatur e of progressive fracture closure behav ior. \n2) Heavily fractured reservoirs that exhibit pressure -\ndependent effective permeability can partly mask \nsome information on fracture stiffness (or \ncompl iance) evolution and the associated mechanical"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a67c2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "dependent effective permeability can partly mask \nsome information on fracture stiffness (or \ncompl iance) evolution and the associated mechanical \nclosure process . \n3) In sparsely  or more moderately fractured reservoir s \nwith complex fracture geometry, if the closed fracture \nmaintains  its hydraulic connectivity to the open \nfracture, then fracture complexity cannot be detected \nfrom before -closure data and the pressure decline \nresponse resembles a  fracture with  \u201crougher\u201d fracture \nwalls . However, if the closed fracture lose s its \nhydraulic connectivity to the open fracture, then \nfracture complexity can be detected qualitatively by \nthe existence of multiple peaks on the pressure \nderivative  plot. \n4) The c onventional \u201ctangent line method\u201d consistently \nunderestimates closure stress w hile \u201ccompliance \nmethod\u201d tends to only reflect  the onset of fracture \nclosure . Our proposed \u201cvariable compliance method\u201d \ngives a much more accurate and reliable estimation of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6812-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "closure . Our proposed \u201cvariable compliance method\u201d \ngives a much more accurate and reliable estimation of \nclosure stress in both homogenous and naturally \nfractured reservoirs.  \n \nREFERENCES  \n1. Barree, R.D., Barree, V.L. and Craig, D., 2009. Holistic \nfracture diagnostics: consistent interpretation of prefrac  \ninjection tests using multiple analysis methods.  SPE \nProduction & Operations,  24(03), pp.396 -406. \nhttp://dx.doi.org/ 10.2118/107877 -PA \n2. Craig , D. P., Barree, R. D., Warpinski, N. R., and \nBlasingame, T. A. 2017. Fracture Closure Stress: \nReexamining Field and Laboratory Experiments of \nFracture Closure Using Modern Interpretation \nMethodologies. Paper presented at the SPE Annual \nTechnical Conferenc e and Exhibition, 9 -11 October, \nSan Antonio, Texas, USA.  https://doi.org/10.2118/187038 -MS \n3. Fu, Y., Dehghanpour, H., Ezulike, D. O., and Jones, R. \nS. 2017. Estimating Effective Fracture Pore Volume \nFrom Flowback Data and Evaluating Its Relationship to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6862-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "S. 2017. Estimating Effective Fracture Pore Volume \nFrom Flowback Data and Evaluating Its Relationship to \nDesign Parameters of Multistage -Fracture Completion. \nSPE Production & Operations, Vol  (32)04:423 -439.  \nhttps://doi.org/10.2118/175892 -PA \n4. Loughry, D., Epps, D. and Forrest, J., 2015. Using Pad \nISIP, DFIT, and ES P Data to Generate a Pore Pressure \nModel for the Midland Basin. Paper presented at the \nUnconventional Resources Technology Conference, \nSan Antonio, Texas, USA, 20 -22 July. \nhttps://doi.org/10.15530/URTEC -2015 -2162973  \n5. McClure, M.W., Jung, H., Cramer, D.D. an d Sharma, \nM.M., 2016. The Fracture Compliance Method for \nPicking Closure Pressure from Diagnostic Fracture -\nInjection Tests.  SPE Journal 21(04):1321 -1339. \nhttp://dx.doi.org/10.2118/179725 -PA \n6. Mirani, A., Ma rongiu -Porcu, M., Wang, H., Philippe, \nE. Production -Pressure -Drawdown Management for \nFractured Horizontal Wells in Shale -Gas Formations."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a68a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "E. Production -Pressure -Drawdown Management for \nFractured Horizontal Wells in Shale -Gas Formations. \n2017. SPE Reservoir Evaluation & Engineering \n(Preprint ). http://dx.doi.org/10.2118/181365 -PA \n7. Nolte, K. G. 1979. Determi nation of Fracture \nParameters from Fracturing Pressure Decline.  Paper \n8341 presented at the SPE Annual Technical \nConference and Exhibition, Las Vegas, Nevada, 23 -26 \nSeptember. http://dx.doi.org/10.2118/8341 -MS \n8. Nolte, K. G. 1986. A General Analysis of Fract uring \nPressure Decline with Application to Three Models. \nSPE Formation Evaluation. Vol (1) 06:571 -583. \nhttp://dx.doi.org/10.2118/12941 -PA \n9. Potocki , D. J. 2012. Understanding Induced Fracture \nComplexity in Different Geological Settings Using \nDFIT Net Fracture Pressure. Paper SPE 162814 \npresented at the SPE Canadian Unconventional \nResources Conference, Calgary, Alberta, Canada, 30 \nOctober -1 November.  \nhttp://dx.doi.org/10.2118/162814 -MS"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a68f8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "Resources Conference, Calgary, Alberta, Canada, 30 \nOctober -1 November.  \nhttp://dx.doi.org/10.2118/162814 -MS \n10. Ramurthy , M., Barree, R.D., Kundert, D.P., Petre, J.E. \nand Mullen, M.J., 2011. Surface -area vs. conductivity -\ntype fracture treatments in shale reservoirs.  SPE \nProduction & Operations,  26(04), pp.357 -367. \nhttps://doi.org/10.2118/140169 -PA \n11. Wang, H and Sharma, M.M. 2017a. A Non -Local \nModel for Fracture Closure on Rough Fracture Faces \nand Asperities. Journal of Petroleum Science and \nEngineering, Vol  (154):425 -437. http://dx.doi.org/ \n10.1016/j.petrol.2017.04.024  \n12. Wang, H and Sharma, M.M. 2017b. New Variable \nCompliance Method for Estimating Closure Stress and \nFracture Compliance from DFIT data. Paper SPE \n187348 presented at the SPE Annual Technical \nConference and Exhi bition held in San Antonio, TX, \nUSA, 09 \u2013 11 October. http://dx.doi.org/10.2118/"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6948-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 10, "chroma:document": "187348 presented at the SPE Annual Technical \nConference and Exhi bition held in San Antonio, TX, \nUSA, 09 \u2013 11 October. http://dx.doi.org/10.2118/ \n187348 -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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a698e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 11, "chroma:document": "13. Wang, H. 2015. Numerical Modeling of Non -Planar \nHydraulic Fracture Propagation in Brittle and Ductile \nRocks using XFEM with Cohesive Zone Method. \nJournal of Petroleum Science and Engineering , Vol \n(135):127-140. \nhttp://dx.doi.org/10.1016/j.petrol.2015.08.010  \n14. Wang, H. 2016. Numerical Investigation of Fracture \nSpacing and Sequencing Effects on Multiple Hydraulic \nFracture Interference and Coalescence in Brittle an d \nDuctile Reservoir Rocks. Engineering Fracture \nMechanics, Vol (157): 107 -124.  \nhttp://dx.doi.org/10.1016/j.engfracmech.2016.02.025  \n15. Wang, H. 2017. What Factors Control Shale Gas \nProduction and Production Decline Trend in Fractured \nSystems: A Comprehensive Analysis and Investigation. \nSPE Journal, Vol 22(02): 562 -581.  \nhttp://dx.doi.org/10.2118/179967 -PA \n16. Wang, H. and Sharma, M.M. 2018. Estimating Un -\npropped Fracture Conductivity and Fracture \nCompliance from Diagnostic Fracture Injection Tests. \nSPE Journal (Pr eprint)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a69de-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 11, "chroma:document": "propped Fracture Conductivity and Fracture \nCompliance from Diagnostic Fracture Injection Tests. \nSPE Journal (Pr eprint).  \nhttp://dx.doi.org/10.2118/189844 -PA  \n17. Wang, H., Marongiu -Porcu, M., and Economides, M. J. \n2016. Poroelastic and Poroplastic Modeling of \nHydraulic Fracturing in Brittle and Ductile Formations, \nJournal of SPE Production & Operations , 31(01): 47 \u2013\n59. http://dx.doi.org/10.2118/168600 -PA \n18. Wang, H. , Yi ,S., and Sharma, M.M.  2018. A \nComputationally Efficient Approach to Modeling \nContact Problems  and   Fracture  Closure  Using  \nSuperposition  Method.  Theoretical and  Applied  \nFracture Mechanics, Vol(93): 27 6-287. \nhttps://doi.org/10.1016/j.tafmec.2017.09.009  \n19. Willis -Richards, J., K. Watanabe, H. Takahashi. 1996. \nProgress toward a stochastic rock mechanics model of \nengineered geothermal systems. Journal of Geophysical \nResearch 101 (B8): 17481 -17496 . \nhttp://dx.doi.org/10.1029/96JB00882."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6a2e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2018-225.pdf", "page": 11, "chroma:document": "Research 101 (B8): 17481 -17496 . \nhttp://dx.doi.org/10.1029/96JB00882.  \n \n \n \n \n \n \n \n \n \n \n \n \n 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6a7e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "1. INTRODUCTION  \nDiagnostic fracture injection tests (DFIT), also referred to \nas a minifrac  test, have been a standard stimulation \ntechnique in unconventional reservoirs to determine the \nreservoir characteristics. DFIT analysis can estimate key \nreservoir parameters such as reservoir permeability and \ninitial reservoir pressure to aid in future frac ture designs. \nA typical DFIT test consists of pumping small amounts of \nfluid, usually water, down the wellbore to initiate the \nstimulation test in the reservoir. Enough water is pumped \ndown hole to initiate a small fracture to breakdown the \nformation. The fracture  will continue to propagate until \npumping is completed and the well is shut in. Once shut -\nin occurs, the pressure falloff  response is recorded over a \nlong period of time which can be from a few days to \nweeks. An analysis on the pressure data recorded is do ne \nto estimate several reservoir characteristics.  \nThe pressure response from a DFIT analysis can be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6ac4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "to estimate several reservoir characteristics.  \nThe pressure response from a DFIT analysis can be \nseparated into two parts: before -closure analysis (BCA) \nand after -closure analysis (ACA). The BCA region of a DFIT test is considered the period when water is injected \ninto the wellbore to create a small fracture  until the \ncreated fracture is mechanically closed. Key parameters \nthat can be determined from BCA are fracture closure \npressure, instantaneous shut -in pressure (ISP), closure \ngradient, net fracture p ressure, fluid efficiency and leak -\noff coefficient. The ACA region of the DFIT test is the \ntime after the fracture is closed to the end of the shut -in \nperiod.  Fig. 1 shows a typical pressure response during a \nDFIT test.  \nKey parameters that can be determined from ACA are \nflow regime, permeability, and transmissibility. Several \nnumerical and analytical models are available to analyze \nthe pressure response recorded during BCA and ACA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6b3c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "numerical and analytical models are available to analyze \nthe pressure response recorded during BCA and ACA.  \nTraditional DFIT before closure  analysi s does not \nconsider natural fractures. The Perkins -Kern -Nordgren \n(PKN) fracture geometry model created by Perkins and \nKern and later improved by Nordgren ( Nordgren , 1972; \nNolte , 1979; Perkins and Kern , 1961 ) derived several key \nparameters: fluid loss coeff icient, fluid efficiency,             \nARMA 21\u20131387                                                                 \n \nNew Diagnostic Fracture Injection Test Model with  \nComplex Natural Fractures using Embedded Discrete Fracture Model  \n \nBruno , Jonathan and Sun, He \nThe University of Texas at Austin, Austin, TX, USA  \nYu, Wei  \nSim Tech LLC, Houston, Texas, USA  \nSepehrnoori, Kamy  \nThe University of Texas at Austin, Austin, TX, USA  \n \nCopyright 20 21 ARMA, American Rock Mechanics Association"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6b8c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "Sepehrnoori, Kamy  \nThe University of Texas at Austin, Austin, TX, USA  \n \nCopyright 20 21 ARMA, American Rock Mechanics Association  \nThis paper was prepared for presentation at the 55th US Rock Mechanics/Geomechanics Symposium held in Houston, Texas, USA, 20-23 June  \n2021. This paper was selected for presentation at the symposium by an ARMA Tech nical Program Committee based on a technical and critical \nreview of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any pos ition of ARMA, its \nofficers, or m embers. Electronic reproduction, distrib ution, or storage of any part of this paper for commercial purposes without the written consent \nof 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 \nabstract must contain conspicuous acknowledgement of where and by whom the paper was presented."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6bd2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.   \n \n \n ABSTRACT:  Application of diagnostic fracture injection tests (DFIT) are used in unconventional reservoirs to determine rese rvoir \ncharacteristics for future fracture design and production. The presence of natural fractures can heavily influence the pre - and post -\nshut-in pressure data obtained from DFIT. Traditional DFIT models do not capture the complexity of hydraulic and natu ral fracture \nnetworks into an integrated workflow. This work uses an embedded discrete fracture model (EDFM) to add natural fracture \ncomplexity into a new DFIT model in conjunction with any reservoir simulator to simulate the pressure response. Incorporati ng \nfracture modeling tools will enhance the existing reservoir model by creating a more accurate representation of an unconventi onal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6c22-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "fracture modeling tools will enhance the existing reservoir model by creating a more accurate representation of an unconventi onal \nreservoir for future development strategies. EDFM can easily incorporate complex fractures and accurately be embedded in st ructed \nmatrix block. Pressure data from the DFIT analysis can be separated into two parts: before -closure analysis (BCA) and after -closure \nanalysis (ACA). Past models have analyzed BCA and ACA independently, which can lead to misinterpretation. The new DFI T model \ncombines the BCA and ACA while including complex natural fractures into a single workflow. Data from the Lower Eagle Ford \nFormation was used to validate the model by accurately matching the same field data with the new workflow. The workflow consi sts \nof identifying random natural factures connected to the generated small fracture  to observe the true pressure response during DFIT."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6c72-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 0, "chroma:document": "of identifying random natural factures connected to the generated small fracture  to observe the true pressure response during DFIT. \nThe workflow in this study can be applied to any DFIT data. Understanding the impact complex natural fractures have on pr essure \nresponse through an integrated DFIT model with EDFM is important to determine reservoir characteristic and geomechanics for \nfuture fracture designs.  \n \n \n  \n \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6cc2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 1, "chroma:document": "fracture closure pressure, fracture length, and fracture \nwidth. Nolte, in his G -function model, was able to easily \ndistinguish the closure pressure using a plot of a derived \nG-function and pressure.  Nolte\u2019s derivation did not \nconsider the complexity of natural fractures. His work \nonly considered a simple planar fracture  with no natural \nfractures. The effects of natural fractures cannot be \ncharacterized or evaluated.  \n \nFig. 1. Typical DFIT test pressure response diagram  (Wang \nand Sharma, 2017) . \nTraditional DFIT A fter closure analysis also does not \nconsider natural fractures. Soliman ( Soliman et al. , 2005 ) \nhas worked on the pressure fall off analysis to estimate \nthe formation permeability and pressure. From the \npressure r esponse, each flow regime can be identified. \nFormation permeability can be estimated based on the \ntransient pressure behavior.  ACA analysis fails to \nconsider the fracture complexity."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6d44-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 1, "chroma:document": "Formation permeability can be estimated based on the \ntransient pressure behavior.  ACA analysis fails to \nconsider the fracture complexity.  \nIn this work, n atural fractures can heavily influence the \nbefore closure  and after closure pressure response during \na DFIT test. Traditional BCA and ACA DFIT models do \nnot capture the complexity of the natural fracture network \nconnected to a small fracture . The pressure transient \nbehavior will be influenced by the geometry and density \nof the natural fractures. Implementing natural fractures \nwould give a more accurate representation of \nunconventional reservoirs. The pressure data during a \nDFIT test can be co herently interpreted using a single \nworkflow.  This work will show the new workflow \nconsidering complex natural fractures coherently with a \ncase study. The objective of this work is to understand and \nimplement a new DFIT workflow with natural fractures. \nThis work is important to understand the impact of natural"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6dbc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 1, "chroma:document": "implement a new DFIT workflow with natural fractures. \nThis work is important to understand the impact of natural \nfracturs on reservoir pressure and permeability.  \n2. THEORY AND MODEL DEVELOPMENT  \nSeveral analytical models have been developed by Nolte \nthat are available for DFIT analysis (Nolte , 1979, 1990; Nolte et al., 1993; Nolte et al. , 1997). Nolte pioneered the \nG-function technique for BCA and ACA analysis based \noff the Carter leak -off model (Nolte , 1979).  In 2014, \nMcClure developed a fracture -compliance method for \nestimating the closure pressure for DFIT test a ssuming a \nvariable fracture compliance (McClure et al. , 2014). The \nG-function derivative plot was analyzed with a changing \nfracture compliance during closure (McClure et al. , \n2014). The variable compliance method was created by \nWang et al. (2017) where the  fracture closure point is \ndetermined to be average of the fracture closure points \npicked using the fracture -compliance method and tangent"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6e34-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 1, "chroma:document": "determined to be average of the fracture closure points \npicked using the fracture -compliance method and tangent \nline method. The tangent line method is considered the \nupper bound while the fracture -compliance method is \nconsidered  the lower bound for the fracture closure point.  \nIn this study, the G -function technique was used  to \ndetermine the closure point . \nThe application of G -function technique across multiple \nleak-off factors validated Nolte\u2019s model. The original G -\nfunction mode l from Nolte is based on the following \nassumptions:  \n(i) constant fracture compliance  \n(ii) constant fracture height  \n(iii) constant closure pressure  \n(iv) constant fracture surface after shut -in \n(v) leak-off coefficient independent of pressure \nchange  \n(vi) material balance between leak -off fluid volume \nand fracture volume  \nThe analytical solution for Nolte\u2019s G -function time is the \nfollowing:  \n \n\ud835\udc54(\u2206\ud835\udc61\ud835\udc37)=\n{(1+\u2206\ud835\udc61\ud835\udc37)sin\u22121(1+\u2206\ud835\udc61\ud835\udc37)\u22121\n2+\u2206\ud835\udc61\ud835\udc371\n2    \ud835\udefc=1\n2\n4\n3((1+\u2206\ud835\udc61\ud835\udc37)3\n2\u2212\u2206\ud835\udc61\ud835\udc373"}


created_at: 2023-11-16 17:06:54
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id: 6b8a6eac-84a2-11ee-9ca1-0242ac1c000c
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metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 1, "chroma:document": "The analytical solution for Nolte\u2019s G -function time is the \nfollowing:  \n \n\ud835\udc54(\u2206\ud835\udc61\ud835\udc37)=\n{(1+\u2206\ud835\udc61\ud835\udc37)sin\u22121(1+\u2206\ud835\udc61\ud835\udc37)\u22121\n2+\u2206\ud835\udc61\ud835\udc371\n2    \ud835\udefc=1\n2\n4\n3((1+\u2206\ud835\udc61\ud835\udc37)3\n2\u2212\u2206\ud835\udc61\ud835\udc373\n2)                             \ud835\udefc=1          (1) \n\ud835\udc3a(\u2206\ud835\udc61\ud835\udc37)=4\n\ud835\udf0b[\ud835\udc54(\u2206\ud835\udc61\ud835\udc37)\u2212\ud835\udc540]   (2) \n\ud835\udc540=\ud835\udc54(\u2206\ud835\udc61\ud835\udc37=0)    (3) \n\u2206\ud835\udc61\ud835\udc37=\ud835\udc61\u2212\ud835\udc61\ud835\udc5d\n\ud835\udc61\ud835\udc5d    (4) \n \n \nwhere t is the shut -in time and t p is the total pump time. A \n\u03b1 value of 1/2 refers to a formation with low fluid leak -\noff. A \u03b1 value of 1 refers to a formation with high fluid \nleak-off. The G -function time solution starts at the shut -\nin or when the instantaneous shut -in pressure (ISIP) is \nzero. From Nolte\u2019s G -function time model, Barree used a \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6f06-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 2, "chroma:document": "diagnostic approach to identify the fracture closure \npressure (Barree , 1998; Barree et al. , 2009). The \ncomposite derivative of G -function, G *dp/dG, is used to \nshow where the pressure change occurs. A s traight line \ncan be drawn from the origin from the plot of G *dp/dG \nagainst G -function time. The deviation point from the \nG*dp/dG curve from the straight line is used as the \nfracture closure point. The closure point was estimated to \nbe 25.30 G -function time . Fig. 2 shows the of G *dp/dG \nagainst G -function time.  \n \n \nFig. 2. Closure point selection using G*dp/dG versus G time . \nThe closure point is important to estimate the closure \nstress of the formation from the DFIT data. Using Nolte\u2019s \nG-function time model, the closure pressure is estimated \nto be 7100 psi. Fig . 3 shows the corresponding pressure \nprofile using Nolte\u2019s analytic al solution for G -function \ntime.  \n \n \nFig. 3. Closure pressure corresponding to the previously \nestablished closure point."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6f4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 2, "chroma:document": "time.  \n \n \nFig. 3. Closure pressure corresponding to the previously \nestablished closure point.  \nOnce the fracture closure point is found, the simulation \nmodel can be developed. Fig . 4 shows the steps of the new \nDFIT workflow used in this case study.  \n  \nFig. 4. New DFIT workflow . \nThe new workflow consists of starting with a single \nfracture to represent the small fracture  created  in a DFIT \ntest. With our new DFIT model fracture height , half -\nlength, conductivity  and closure pressure can be \nmanipulated to satisfy your model setup. The new DFIT \nworkflow allows the user more flexibility when setting up \na DFIT model which previous workflows do not allow \nfor. The base case model in thi s paper was set up using \nthe following parameters in Table 1.  \n \nTable 1. Base case parameters for DFIT reservoir model  \nBase Case  \nGenerated  Fracture  Height (ft)  50 \nGenerated  Fracture  Half-length (ft)  200 \nGenerated  Fracture  Conductivity (mD -ft) 10"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6fa6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 2, "chroma:document": "Base Case  \nGenerated  Fracture  Height (ft)  50 \nGenerated  Fracture  Half-length (ft)  200 \nGenerated  Fracture  Conductivity (mD -ft) 10 \nNumber of Natural Fractures  60 \nNatural Fracture Height (ft)  30-50 \nNatural Fracture Half -length (ft)  30-70 \nNatural Fracture Conductivity (mD -ft) 2.4-5.6 \nMatrix Permeability (mD)  0.001  \n \nAn embedded discrete fracture model (EDFM) is used to \nimplement a small fracture  in the reservoir model .  ED FM \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a6fec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 3, "chroma:document": "can represent fractures with a grid outside normal models \nand uses special connections to model fluid and pressure \ntransport.  This method is easy  and efficient to model any \ncomplex fracture geometries using structured gridding \n(Moinfar et al. , 2014; Xu , 2015; Xu et al. , 2017a, 2017b). \nThe complex fractures are discretized into fracture \nsegments based on the interaction between the fracture \ngeometry  and the structured matrix grid boundary. The \nfluid flow between the matrix and fractures can be \nsimulated using a commercial reservoir simulator such as \nCMG by using non -neighboring connections (NNCs) ( Yu \net al, 2018).  Fig. 5 shows a visualization of the EDFM \nmethodology.  \n \n \nFig. 5. Explanation of EDFM method with commercial \nreservoir simulato rs to handle 3D complex fractures (Xu et al., \n2017a)  \nThere are four types of NNCs: fluid flow between matrix \nand fractures, between fracture segments within a single \nfracture, between intersecting fracture segments within"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a703c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 3, "chroma:document": "and fractures, between fracture segments within a single \nfracture, between intersecting fracture segments within \ndifferent fractures, and between fractures and wellbores. \nMore information on the EDFM methodology is available \nin the work by Xu et al. (2017a, 12017b).  This paper \nintroduces the use of EDFM  to implement random  natural \nfractures  into a DFIT model . The model flexibility is \ndemonstrated by characterizing d ifferent complex natural \nfracture cas es.  \nValidation of the DFIT model is shown through a DFIT \ncase study.  The pressure transient behavior is captured \nthroughout the fracture network. The new DFIT model \ncan predict the pressure decline response. Evaluation of \nthe natural fractures and a gener ated small fracture  is done to show the effects of changing characterization with \nvarying geometry, density, half-length , and conductivity. \nThe new DFIT model can increase and decrease the \ndensity of natural fractures with ease."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a708c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 3, "chroma:document": "The new DFIT model can increase and decrease the \ndensity of natural fractures with ease.   \nOnce a small fracture  is generated, random natural \nfractures are implemented into the model using EDGS. \nEDGS allows you to generate random natural fractures \nwith various geometries and density. Fig . 6 shows the \ngenerated  small fracture  along with the random natural \nfractures.  \n \n \nFig. 6. Generated base case for the new DFIT workflow with \ncomplex natural fractures.  \nThe pressure response is initialized in the generated a \nsmall fracture  using a natural fracture connectivity code. \nThe connectivity code can identify the natural fractures \nthat are connected to the generated small fracture . Fig. 7 \nshows the DFIT model  after running the connectivity \ncode. The areas in red are the natural frac tures that have \nbeen identified that are not connected to the generated  \nsmall fracture . \n \n \nFig. 7. Connectivity code evaluation of natural fractures not"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a70dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 3, "chroma:document": "been identified that are not connected to the generated  \nsmall fracture . \n \n \nFig. 7. Connectivity code evaluation of natural fractures not \nconnected to the  generated  small fracture . \nA closer look at the complex fracture network can be \nseen in Fig. 8. The natural fracture connections to the \nsmall fracture  are important to analyze the pressure \nbehavior using EDFM.  \n \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7122-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 4, "chroma:document": "Fig. 8. Closer look of the complex fracture network . \nA reservoir model is thus created to represent a DFIT test \nwith complex natural fractures . The pressure response \nfrom the generated  small  fracture  is simulated using \ncomputer modeling group (CMG) reservoir simulator. \nThe new workflow was able to estimate the  pressure \nresponse for a DFIT test.  \nA closer look at the complex fracture network can be seen \nin Fig . 9. The pressure response was initialized in the \ngenerated  small fracture  and the distribution of the \npressure  response is seen  throughout the complex nat ural \nfracture network.  \n \n \nFig. 9. Closer look of the complex fracture network . \nThe pressure response throughout the 1st, 3rd, and 6th day \nof the new DFIT model can be seen in  Fig 10. (a), (b), and \n(c), respectively. The pressure in the fracture network \ncontinues to decrease the longer the well is shut -in until \nthe reservoir pressure is reached.  \n \n \n(a) Pressure distribution after 1 day"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7172-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 4, "chroma:document": "continues to decrease the longer the well is shut -in until \nthe reservoir pressure is reached.  \n \n \n(a) Pressure distribution after 1 day  \n(b) Pressure distribution after 3 days \n \n \n(c) Pressure distribution after 6 days \nFig. 10. Pressure distribution changes shown from the (a) 1st \nday, (b) 3rd day, and (c) 6th day. \n \nThe new DFIT workflow is capability of replicating the \nACA pressure response using complex natural fractures.  \nA visualization of the pressure distribution is captured \nthroughout the complex fracture network.  To test the \nimpact of changing various fracture  characterization  \nparameters, a sensitivity analysis study is presented in the \nnext section.  \n3. SENSITIVITY ANALY SIS \nSensitivity analysis was done in this study to test t he \neffects of varying the characterization of complex natural \nfractures  using our new workflow . The model was set up \nusing the same generated small fracture for every case. \nThe complexity of the smal l fracture depends on the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a71ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 4, "chroma:document": "using the same generated small fracture for every case. \nThe complexity of the smal l fracture depends on the \nconnected natural fracture which has a great impact on the \npressure response.  The pressure is observed for after the \nfracture closure point. Therefore, the generated small \nfracture is considered mechanically closed. The following \nparameters were adjusted  in this study: varying the \ndensity of natural fractures, natural fracture  height, \nnatural fracture  half-length, and natural fracture  \nconductivity.  Fig 11. (a), (b), and (c) show the DFIT \nmodel with varying density of natural fracture from 30, \n60, and 90, respectively.  \n \n(a) DFIT model with 30 natural fractures  \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a723a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 5, "chroma:document": "(b) DFIT model with 60 natural fractures  \n \n(c) DFIT model with 90 natural fractures  \nFig. 11. DFIT model with varying densit ies of natural \nfractures from (a) 30 natural fracture s, (b) 60 natural fractures, \nand (c) 90 natural fractures.  \n \nFig. 12 shows the pressure falloff  response when varying \nthe number of natural fractures  using  the new DFIT \nworkflow.  \n \n \nFig. 12. Sensitivity analysis on the number of natural \nfractures.  \nAs the number of natural fractures increase s, the pressure \nfalloff  becomes less severe. The phenomenon that is \nhappening is due to the number of natural fractures \nconnected to the small fracture  becomes greater when \nmore natural fractures are added. This would allow for a \nmore even distribution of pressure throughout the fracture \nnetwork and therefore a less severe pressure falloff . \n \nFig. 13 shows the pressure falloff  response  of varying the \nheight of the natural fractures  in the new DFIT model."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7280-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 5, "chroma:document": "Fig. 13 shows the pressure falloff  response  of varying the \nheight of the natural fractures  in the new DFIT model.  \n  \nFig. 13. Sensitivity analysis on the natural fracture  height.  \nThere is not a significant difference between the pressure \nfalloff  response as you increase the height of the natural \nfractures . \n \nFig. 14 shows the pressure falloff  response as you \nincrease the half -length of the natural fractures .  \n \n \nFig. 14. Sensitivity analysis on the natural fracture  half-length.  \nAs you increase the half -length of the natural fractures , \nthe pressure falloff response  becomes less severe. This \ncould be du e to the larger surface area that the natural \nfractures are covering as it gets larger. The natural \nfractures are  creating a larger fracture network as you \nincrease the half -length. A larger fracture network proves \nto have a less severe pressure falloff  behavior.  \n \nFig. 15 shows the pressure falloff  response as you"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a72da-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 5, "chroma:document": "to have a less severe pressure falloff  behavior.  \n \nFig. 15 shows the pressure falloff  response as you \nincrease the conductivity of the natural fractures . \n \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a732a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "Fig. 15. Sensitivity analysis on the natural fracture  \nconductivity.  \nAs you increase the conductivity of the natural fractures , \nthe pressure falloff response becomes less severe.  \n4. SUMMARY AND CONCLUSION  \nThis paper  implemented a new DFIT workflow with \ncomplex natural fractures.  Including complex natural \nfractures with a DFIT test enhanc es the understanding of \nthe characteristics for unconventional reservoirs. The new \nDFIT workflow allows for characterization of complex \nnatural fractures with varying geometry, density, \naperture, and conductivity.  The impact of varying fracture \nparameters is evident in this study.  The number of natural \nfractures, natural fracture  half-length and natural fracture  \nconductivity had an impact on the pressure falloff \nresponse. The pressure falloff response became less \nsevere with the increase in natural fractures, the generated  \nsmall fracture  half-length and the generated  small fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a737a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "severe with the increase in natural fractures, the generated  \nsmall fracture  half-length and the generated  small fracture  \nconductivity. This could be due to the larger surface area \nthat the small fracture  is covering. The new DFIT \nworkflow was able to estimate the pressure falloff  \nbehavior during a DFIT test  using the various reservoir \nand natural fracture parameter . The impact of natural \nfractur es on the pressure falloff behavior is evident in this \nstudy.  \nCompared to traditional DFIT analysis, the new DFIT \nworkflow was able to implement natural fractures using \nEDFM. The fracture network proved to h ave an impact on \nthe pressure falloff  response. Characterization of the \nfracture network was captured and ensured an efficient \nanalysis to estimate the reservoir properties. The \ngenerated fracture during a DFIT test becomes more \ncomplex when natural fractu res are added to the model. \nThe pressure transient behavior can be captured"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a73ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "complex when natural fractu res are added to the model. \nThe pressure transient behavior can be captured \nthrough out the fracture network. The density of natural \nfractures can be easily added and reduced depending on \nthe model demand s. The new DFIT workflow \ndemonstrated the ability to handl e complex natural \nfractures while providing a sufficient analysis on the \nreservoi r properties.  DFIT analysis with complex natural fracture geometries will aid in future reservoir evaluation \nand production design.  \n5. REFERENCES  \nBarree, R.D. 1998. Applications of Pre -Frac Injection/Falloff \nTests in Fissured Reservoirs - Field Examples. Paper presented \nat the SPE Rocky Mountain Regional/Low -Permeability \nReservoirs Symposium, Denver, Colorado , USA,  5-8 April \n1998.  \nBarree, R.D., Barr ee, V.L., and Craig, D. 2009. Holistic \nFracture Diagnostics: Consistent Interpretation of Prefrac \nInjection Tests Using Multiple Analysis Methods. SPE \nProduction & Operations  24 (03): 396 -406."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7410-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "Injection Tests Using Multiple Analysis Methods. SPE \nProduction & Operations  24 (03): 396 -406.  \nMcClure, M.W., Blyton, C.A., Jung, H., and Sharma, M.M. \n2014. The Effect of Changing Fracture Compliance on Pressure \nTransient Behavior During Diagnostic Fracture Injection Tests. \nPaper presented at the SPE Annual Technical Conference and \nExhibition, Amsterdam, The Netherlands, 27 -29 October 2014.   \nMoinfar, A., Varav ei, A., Sepehrnoori, K. et al. 2014. \nDevelopment of an Efficient Embedded Discrete Fracture \nModel for 3D Compositional Reservoir Simulation in Fractured \nReservoirs. SPE Journal  19 (02): 289 -303. \nNolte, K.G. 1979. Determination of Fracture Parameters from \nFracturing Pressure Decline. Paper presented at the SPE \nAnnual Technical Conference and Exhibition, Las Vegas, \nNevada,  USA,  23-26 September 1979.  \nNolte, K.G. 1990. Fracturing -Pressure Analysis fo r Nonideal \nBehavior . Journal of Petroleum Technology  43 (02): 210 -218."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7460-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "Nolte, K.G. 1990. Fracturing -Pressure Analysis fo r Nonideal \nBehavior . Journal of Petroleum Technology  43 (02): 210 -218. \nNolte, K.G., Mack, M.G., and Lie, W.L. 1993. A Systematic \nMethod for Applying Fracturing Pressure Decline: Part I. Paper \npresented at the Low Permeability Reservoirs Symposium, \nDenver, Colorado , USA, 26-28 April 1993.  \nNolte, K.G., Maniere, J.L., and Owens, K.A. 1997. After -\nClosure Analysis of Fracture Calibration Tests. Paper \npresented at the SPE Annual Technical Conference and \nExhibition, San Antonio, Texas , USA,  5-8 October 1997.  \nNordg ren R .P. 1972. Propagation of a Vertical Hydraulic \nFracture. Society of Petroleum Engineers Journal 12 (04): 306 -\n314. \nPerkins T .K, Kern L .R. 1961. Widths of Hydraulic Fractures.  \nJournal of Petroleum Technology 13 (09): 937 -949. \nSoliman M .Y., Craig D .P., Bartko K .M., Rahim Z ., Adams \nD.M. 2005.  Post-Closure Analysis to Determine Formation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a74b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 6, "chroma:document": "Soliman M .Y., Craig D .P., Bartko K .M., Rahim Z ., Adams \nD.M. 2005.  Post-Closure Analysis to Determine Formation \nPermeability, Reservoir Pressure, Residual Fracture Properties. \nPaper presented at the SPE Middle East Oil and Gas Show and \nConference, Kingdom of Bahrain, Bahrain, 12 -15 March 2005.  \nDownloaded 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"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 7, "chroma:document": "Wang, H., and Sharma, M.M. 2017. New Variable Compliance \nMethod for Estimating In -Situ Stress and Leak -Off from DFIT \nData. Paper presented at the SPE Annual Technical Conference \nand Exhibition, San Antonio, Texas, USA, 9 -11 October 2017.  \nXu, Y., 2015. Implementation and Application of the \nEmbedded Discrete Fracture Model (EDFM) for Reservoir \nSimulation in Fractured Reservoirs. Master Thesis, The \nUniversity of Texas at Austin, Austin, Texas, USA.  \nXu, Y., Cavalcante Filho, J.S., Yu, W., and Sepe hrnoori, K. \n2017a. Discrete -Fracture Modeling of Complex Hydraulic \nFracture Geometries in Reservoir Simulators. SPE Reservoir \nEvaluation and Engineering  20 (02): 403 -433. \nXu, Y., Yu, W., and Sepehrnoori, K. 2017b. Modeling Dynamic \nBehaviors of Complex Frac ture in Conventional Reservoir \nSimulators. Paper presented at the SPE/AAPG/SEG \nUnconventional Resources Technology Conference , Austin, \nTexas, USA, 24 -26 July 2017."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7546-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/arma-2021-1387.pdf", "page": 7, "chroma:document": "Simulators. Paper presented at the SPE/AAPG/SEG \nUnconventional Resources Technology Conference , Austin, \nTexas, USA, 24 -26 July 2017.  \nYu, W., Xu, Y., Weijermars, R., Wu, K., and Sepehrnnori, K., \n2018. A Numerical Model for Sim ulating Pressure Response of \nWell Interference and Well Performance in Tight Oil \nReservoirs with Complex -Fracture Geometries Using the Fast \nEmbedded -Discrete -Fracture -Model Method . SPE Reservoir \nEvaluation 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7596-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 0, "chroma:document": "URTEC-208276-MS\nCan ISIP Really Tell Closure Pressure?\u2014Case Study of Consecutive DFITs in\nthe Eagle Ford\nShintaro Kuroda , Shunichi Watanabe, and Kenji Ueda , INPEX CORPORATION\nCopyright 2021, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/AP-URTEC-2021-208276\nThis paper was prepared for presentation at the SPE/AAPG/SEG Asia Pacific Unconventional Resources Technology Conference to be held virtually on 16\u201318\nNovember, 2021.\nThe URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents\nof 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\nresponsibility 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7640-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 0, "chroma:document": "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\nconsent of URTeC is prohibited.\nAbstract\nThe objective of this paper is to investigate how to acquire fracture closure pressure data accurately and cost-\neffectively in shale development activities. If the injection volume is small during a hydraulic fracturing\njob, it is a common practice to consider the ISIP (Instantaneous Shut-In Pressure) as a proxy of fracture\nclosure pressure, which generally requires a long falloff period to evaluate. However, ISIP should consist\nof variable parameters such as the original closure pressure, net pressure, stress shadow effect, and mid-\nfield fracture complexity.\nIn this paper, we introduce the consecutive DFITs (Diagnostic Fracture Injection Test) approach. Closure\npressure is evaluated by falloff pressure analysis after a micro fracturing injection operation, and pore"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a76cc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 0, "chroma:document": "pressure is evaluated by falloff pressure analysis after a micro fracturing injection operation, and pore\npressure could also be evaluated if the falloff period is long enough. This micro fracturing operation is\ngenerally called DFIT. In order to evaluate how the ISIP, closure pressure, and pore pressure change from\nstage to stage, we performed DFITs consecutively at the sequential hydraulic fracturing stages in a horizontal\nwell drilled in the Eagle Ford shale.\nThe consecutive DFITs revealed that the ISIP gradually increased up to certain level from fracturing stage\nto stage as expected. However, the observed closure pressure was almost constant in the sequential stages,\nwhich was against our expectations. In addition, the evaluated pore pressure was also almost constant.\nInitially we expected that closure pressure would increase because of the uplift due to the stress shadow\neffect. Since the consecutive DFITs showed the same closure pressure in each stage, we concluded that stress"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7758-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 0, "chroma:document": "effect. Since the consecutive DFITs showed the same closure pressure in each stage, we concluded that stress\nuplift could disappear before the fracture closure in next stage or that the stress shadow had little impact on\nthe closure pressure and the pore pressure in next stage under the current fracture design. On the other hand,\nthe ISIP could be affected by the stress shadow in the short term or by the mid-field fracture complexity\nbecoming higher than the previous stage. The correlation between the ISIP and the closure pressure was\nestablished with these consecutive DFITs results. Although the gap between the ISIP and closure pressure\nvaries from stage to stage, it was confirmed that the correlation, with some uncertainties, could be used to\nestimate the closure pressure within an acceptable range.\nThis paper presents the Eagle Ford case study, which confirmed how accurately ISIP can determine"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a77b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 0, "chroma:document": "This paper presents the Eagle Ford case study, which confirmed how accurately ISIP can determine\nclosure pressure considering multiple factors. There are hydraulic fracturing operations in huge number of\nhorizontal 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a77f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 1, "chroma:document": "2 URTEC-208276-MS\nbecause that correlation can provide operators with the confidence to optimize the completion design based\non the ISIP which can be obtained at a low cost.\nIntroduction\nMany hydraulic fracturing stages are routinely performed in shale development activities, but it is rare to\nspend additional time and money for data acquisition. ISIP (Instantaneous Shut-In Pressure) is an important\nparameter by which operators can obtain subsurface information during the hydraulic fracturing job without\nextra effort. This ISIP equals the pressure in the fracture just after pump shut-in, and after friction forces in\nthe wellbore, perforations, and near-wellbore region dissipate. Although many operators often use the ISIP\nat the wellhead rather than at the bottom hole for its ease, we use ISIP at bottom hole in this paper, calculating\nits value from the ISIP measured by the wellsite supervisor at wellhead pressure and the fluid density."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7848-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 1, "chroma:document": "its value from the ISIP measured by the wellsite supervisor at wellhead pressure and the fluid density.\nIf the injection volume is small during the hydraulic fracturing job, it is common practice to consider\nISIP as a proxy of fracture closure pressure, which generally requires a long falloff period to evaluate. Craig\n(2005)  showed the injection volume ranged from less than 200 to greater than 10,000 gal, and our case\nwas 15,000 gal considering the multiple perforation clusters. Smaller injection volume can create smaller\nfracture volume, which means lower net pressure. If the net pressure is so low as to be negligible, the\nobtained ISIP can be close to the fracture closure pressure. However, Bazan and Meyer (2015)  showed\nthat there are other factors to consider, including mid-field fracture complexity, back stress, also called\nstress shadow effect, as well as the net pressure between the ISIP and the closure pressure. Considering"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a78ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 1, "chroma:document": "stress shadow effect, as well as the net pressure between the ISIP and the closure pressure. Considering\nthe existence of several parameters between the ISIP and the closure pressure, the objective of this paper\nis to investigate how to acquire fracture closure pressure data accurately and cost-effectively in shale\ndevelopment activities.\nThe study field in this paper is the Eagle Ford shale play located in South Texas, in the United States as\nshown in Fig. 1 . The Eagle Ford shale is the second most productive oil play in the United States as of 2020\nand it is a Late Cretaceous package of organic-rich marl, limestone, and mudstone overlain by the Austin\nchalk and bounded below by the Buda limestone ( Engle et al. 2020 ).\nFigure 1\u2014Location of the project.\nMethods\nA Diagnostic Fracture Injection Test (DFIT) is a small pump-in treatment performed to help design the\nfollow-up hydraulic fracturing treatment of wells so as to characterize the subject reservoir ( Barree et al."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a791a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 1, "chroma:document": "follow-up hydraulic fracturing treatment of wells so as to characterize the subject reservoir ( Barree et al.\n2015 ). 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7960-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 2, "chroma:document": "URTEC-208276-MS 3\ncalibration test, or fracture injection and falloff test. Through the DFIT operation and analysis, we expect to\nget several parameters such as the ISIP, the fracture closure pressure, the net pressure, the fluid efficiency, the\nreservoir pore pressure, and the permeability, depending on the pressure behavior. The DFIT analysis period\ncan be divided into two portions: before closure and after closure. The closure pressure is evaluated by a\nfalloff pressure analysis in the period before closure. Barree and Mukherjee (1996)  described several types\nof normal leakoff phenomena including pressure dependent leakoff, tip extension after shut-in, variable\nfracture compliance, height recession or transverse storage. Liu and Economides (2015) considered variable\ncompliance and many other abnormal leakoff behaviors, and McClure et al. (2014 , 2016 ) introduced the\nfracture compliance method. In this paper, we did not apply the fracture compliance method but applied the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a79b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 2, "chroma:document": "fracture compliance method. In this paper, we did not apply the fracture compliance method but applied the\nconventional tangent line method in a G-function plot for the simplified analysis workflow. Soliman et al.\n(2005)  have shown that after-closure analysis can provide reservoir pore pressure and permeability if the\nflow regime reaches pseudo linear flow or pseudo radial flow. A flow identification plot is used to identify\nthese flow regimes after closure, then a linear flow time function or a radial flow time function are used to\nevaluate the reservoir pore pressure or permeability.\nA DFIT is generally performed in the toe stage of horizontal wells before starting the main fracturing\ntreatment and to perform DFIT in the middle stages is not common for shale development because it requires\na certain shut-in period leading to non-productive time during the completion operation. However, there are"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7a00-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 2, "chroma:document": "a certain shut-in period leading to non-productive time during the completion operation. However, there are\nstill DFIT challenges in the toe stage. In the author\u2019s past DFIT practice, using a toe-opened sleeve after\nthe toe preparation job in a toe stage has not been used because any potential near wellbore damage by\nthe wellbore clean-up job may make it difficult to analyze data.. Therefore, a new, fresh perforated entry\npoint is used to enhance data quality. Also, operators don\u2019t know how much these parameters differ from\nthe middle and heel of the horizontal section, assuming geological and geomechanical heterogeneity in the\nlateral. The ISIP obtained in each stage provides useful information to estimate the subsurface stress and\npressure along the lateral sections, other than the toe stage.\nThere is also the stress shadow effect from the previous fracturing stages. Roussel (2017)  showed ISIP"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7a46-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 2, "chroma:document": "There is also the stress shadow effect from the previous fracturing stages. Roussel (2017)  showed ISIP\nescalation stage by stage due to the stress shadowing. This stress interference between fracturing stages is\none of the uncertain factors that can affect the fracture propagation. Another consideration is the mid-field\ntortuosity. Weijers et al. (2002) states that mid-field tortuosity is recognized by a high apparent ISIP and\nrapidly declining pressure during the first few minutes of shut-in. This mid-field tortuosity could be caused\nby a pressure choke beyond the near-wellbore region of the fracture (Mayer and Bazan 2011; Bazan and\nMeyer 2015 ). Considering these parameters as shown in Fig. 2 , our challenge was how to utilize the ISIP\nin order to understand the subsurface stress condition at a low cost."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7a96-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 2, "chroma:document": "in order to understand the subsurface stress condition at a low cost.\nFigure 2\u2014Pressure 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7ae6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 3, "chroma:document": "4 URTEC-208276-MS\nIn this paper, we introduce \"the consecutive DFITs\" approach. DFITs were performed consecutively at\nthe selected sequential hydraulic fracturing stages in a horizontal well targeting the productive zone in the\nLower Eagle Ford shale as shown in Fig. 3 . The goal of the consecutive DFITs is to understand the pressure\nchanges such as the ISIP, the closure pressure, and the pore pressure from stage to stage. Five stages were\ncarefully selected from the total of 41 stages to avoid the subsurface fault locations identified by seismic\ninterpretation and a geo-steering evaluation. The tested well was the first development well in the pad.\nTherefore, there were uncertainties how the faults would be affected, but no depletion was assumed from\na parent well.\nFigure 3\u2014Location of the consecutive DFITs in the horizontal well overlayed on a geo-steering plot.\nBefore performing these consecutive DFITs, conventional DFITs were performed at the toe section drilled"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7b36-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 3, "chroma:document": "Before performing these consecutive DFITs, conventional DFITs were performed at the toe section drilled\nin another Eagle Ford area with one-month falloff period. The experience with the one-month falloff DFITs\nshowed that the created fracture would close within one hour which was much faster than we expected.\nBased on the previous experience, we decided on a one-hour falloff for the consecutive DFITs.\nIn hydraulic fracturing operation workflows in the Eagle Ford development wells, the initial breakdown\ninjection is routinely performed before the main fracturing treatment. A short period falloff (for example, a\nfew minutes) after the initial breakdown injection provides the ISIP. For the consecutive DFITs, the falloff\nperiod after the initial breakdown was extended to one hour as shown in Fig. 4 . In addition to the falloff\nperiod extension, we modified some operation procedures such as constant pump rate, hard shut-in, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7b7c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 3, "chroma:document": "period extension, we modified some operation procedures such as constant pump rate, hard shut-in, and\nused the same density fluid in the wellbore for better quality of the closure pressure analysis. One fluid type\nin the wellbore can make it easier to calculate the bottomhole pressure from the wellhead pressure.\nFigure 4\u2014Falloff 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7bcc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 4, "chroma:document": "URTEC-208276-MS 5\nResults and Discussion\nThe proposed consecutive DFITs could be performed without any operational issues. The consecutive DFITs\nwere performed at the five stages from stage 16 to stage 20 in a single-well fracturing operation, not in a\nzipper-frac operation. There were three stages where the main fracturing jobs were cancelled because of\nabnormally low ISIP caused by the fault zone. As an example of the consecutive DFIT stage results, the\nanalysis plots in stage 18 are shown in Fig. 5  with the overall treatment, the before-closure analysis with\na G-function plot and a square root time plot, and the after-closure analysis with a flow identification plot.\nFracture closure pressure can be determined in all the five stages successfully in the before-closure analysis\nas shown in Fig. 6 . In this paper, we use the pressure gradient calculated from an equation of the pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7c12-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 4, "chroma:document": "as shown in Fig. 6 . In this paper, we use the pressure gradient calculated from an equation of the pressure\ndivided by the true vertical depth for comparison. In addition, reservoir pore pressure can also be evaluated\nin four stages based on the pseudo linear flow regime after closure except for stage 16 which is close to a\nfault zone. The after-closure analysis in stage 16 showed the pressure derivative increment after a short-time\npseudo linear flow regime in the flow identification plot. The evaluated pore pressure with the short-time\npseudo linear flow regime in stage 16 is higher than in the other stages. It is interpreted as SRV (Stimulated\nReservoir Volume) pressure, meaning temporarily higher pore pressure and higher permeability than the\noriginal at the limited near wellbore area."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7c62-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 4, "chroma:document": "Reservoir Volume) pressure, meaning temporarily higher pore pressure and higher permeability than the\noriginal at the limited near wellbore area.\nFigure 5\u2014Treatment 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7cb2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 5, "chroma:document": "6 URTEC-208276-MS\nFigure 6\u2014Results of consecutive DFITs. Observed stable closure pressure gradient in five stages.\nThe observed ISIP gradually increased up to a certain level from fracturing stage to stage as expected.\nHowever, the consecutive DFITs revealed that the observed closure pressure was almost constant in the\nsequential stages, which went against our expectations. In addition, the evaluated pore pressure was also\nalmost constant except for stage 16, which was affected by SRV. Initially we expected that the closure\npressure would increase because of the uplift due to the stress shadow effect as shown in Fig 7 . Since the\nconsecutive DFITs showed the same closure pressure in each stage, it was concluded that stress uplift could\ndissipate before the fracture closure in the next stage or that the stress shadow had little impact on the closure\npressure and the pore pressure in the next stage under the current fracture design. In this field case study, it"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7cf8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 5, "chroma:document": "pressure and the pore pressure in the next stage under the current fracture design. In this field case study, it\ntakes approximately two hours for plug and perforation operation between main fracturing treatments. On\nthe other hand, the ISIP could be affected by the stress shadow in the short term or by the mid-field fracture\ncomplexity becoming higher than the previous stage. Permeability in the SRV area also can affect the ISIP\nbecause 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7d48-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 6, "chroma:document": "URTEC-208276-MS 7\nFigure 7\u2014Expected image of the closure pressure before and after consecutive DFIT operations.\nThe consecutive DFITs showed the variable differences between the ISIP and the evaluated closure\npressure from stage to stage. To establish the correlation between the ISIP and the closure pressure, we\nattempted to increase the number of closure pressure data points at stages other than the five consecutive\nstages where we conducted DFITs. We did this by using the falloff period from normal operations, which is\nshorter than the falloff after the initial breakdown for the consecutive DFIT stages. This attempt succeeded\nand gave us eleven additional points though there were five low-reliability stages. The correlation between\nthe ISIP and the closure pressure was established as shown in Fig. 8 . The correlation shows that uncertainties\nof the estimated closure pressure are within +/- 0.07 psi/ft and that coefficient of determination, r2, is 0.77 in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 6, "chroma:document": "of the estimated closure pressure are within +/- 0.07 psi/ft and that coefficient of determination, r2, is 0.77 in\nthis case. The closure pressure is estimated by the correlation as shown in Fig. 9 . Although the gap between\nthe ISIP and the closure pressure varies from stage to stage, it was confirmed that the correlation, with some\nuncertainties, could be used to estimate the closure pressure within an acceptable range.\nFigure 8\u2014Correlation between ISIP gradient and closure pressure gradient. In addition to five\nconsecutive 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 7, "chroma:document": "8 URTEC-208276-MS\nFigure 9\u2014Closure pressure profile estimated by ISIP-closure pressure correlation.\nThere are hydraulic fracturing operations in huge number of horizontal wells in shale development.\nParticularly in multi-well pad situations or first areas to develop, cost-effective data acquisition from the\nfirst well is critical to understanding the local geological and geomechanical setting and heterogeneity along\nlateral sections. Selection of consecutive DFIT locations needs to be discussed among the members of a\nmulti-disciplinary team before conducting this operation. The correlation built by consecutive DFITs shown\nin this paper provides operators with more insight and confidence to optimize the completion design based\non ISIP which can be obtained at a relatively low cost.\nConclusions\nThis paper presents the consecutive DFITs approach at the sequential hydraulic fracturing stages in a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7e6a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 7, "chroma:document": "Conclusions\nThis paper presents the consecutive DFITs approach at the sequential hydraulic fracturing stages in a\nhorizontal well. These are the findings from consecutive DFIT attempts in the Eagle Ford case study:\n1.The proposed consecutive DFITs could be performed without any operational issues. This approach\nallows operators to conduct DFIT in stages other than the toe stage and to interpret how closure\npressure and pore pressure look along a lateral section.\n2.The evaluated closure pressure was constant in the sequential stages while ISIP gradually increased\nup to a certain level, fracturing stage to stage.\n3.The evaluated pore pressure was also almost constant in the sequential stages except for one stage\nshowing higher pressure. This is assumed to be the SRV pressure.\n4.The correlation between the ISIP and the closure pressure showed that the closure pressure can be\nestimated from the ISIP within an acceptable range although there were some uncertainties.\nAcknowledgements"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 7, "chroma:document": "estimated from the ISIP within an acceptable range although there were some uncertainties.\nAcknowledgements\nWe wish to express our appreciation to INPEX CORPORATION and INPEX Eagle Ford, LLC for\npermission to present this paper. We also acknowledge the operation team at INPEX Eagle Ford, LLC for\nexecution 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7f32-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 8, "chroma:document": "URTEC-208276-MS 9\nSI Metric Conversion Factors\nbbl \u00d7 1.589 874 E-01 = m3\nft \u00d7 3.048 * E-01 = m\nlbm \u00d7 4.535 9237 * E-01 = kg\nlbm/gal \u00d7 1.198 264 E+02 = kg/m3\npsi \u00d7 6.894 757 E+03 = Pa\npsi/ft \u00d7 2.262 059 E+04 = Pa/m\nUS gallon \u00d7 3.785 412 E-03 = m3\n*Conversion factor is exact.\nReferences\nBarree, R. D.  and Mukherjee, H.  1996 . Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry.\nPaper presented at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 6-9 October\n1996. SPE-36424-MS. https://doi.org/10.2118/36424-MS.\nBarree, R. D. , Miskimins, J. L. , and Gilbert, J. V. 2015 . Diagnostic Fracture Injection Tests: Common Mistakes, Misfires,\nand Misdiagnoses . SPE Prod & Oper 30(02): 84-98. SPE-169539-PA. https://doi.org/10.2118/169539-PA.\nBazan, L. W. and Meyer B. R.  2015 . Fracture Complexity: Analysis Methodology and Signature Pressure Behavior of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7f78-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 8, "chroma:document": "Bazan, L. W. and Meyer B. R.  2015 . Fracture Complexity: Analysis Methodology and Signature Pressure Behavior of\nHydraulic Fracture Propagation from Horizontal Wellbores. Paper presented at the SPE Asia Pacific Unconventional\nResources Conference and Exhibition held in Brisbane, Australia, 9-11 November 2015. SPE-176919-MS. https://\ndoi.org/10.2118/176919-MS.\nCraig, D. P., Eberhard, M. J. , Odegard, C. E.  et al. 2005 . Permeability, Pore Pressure, and Leakoff-Type Distributions in\nRocky Mountain Basins . SPE Prod & Fac 20(01) : 48-59. SPE-75717-PA. https://doi.org/10.2118/75717-PA.\nEngle, M. A. , Doolan, C. A. , Pitman, J. A.  et al. 2020 . Origin and Geochemistry of Formation Waters from the Lower\nEagle Ford Group, Gulf Coast Basin, South Central Texas. J Chem Geo  550(2020 ) 119754. https://doi.org/10.1016/\nj.chemgeo.2020.119754\nLiu, G.  and Ehlig-Economides, C.  2018 . Practical Considerations for Diagnostic Injection Test (DFIT) Analysis. J Pet Sci"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a7fc8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 8, "chroma:document": "j.chemgeo.2020.119754\nLiu, G.  and Ehlig-Economides, C.  2018 . Practical Considerations for Diagnostic Injection Test (DFIT) Analysis. J Pet Sci\nand Eng  171(2018 ): 114-136. https://doi.org/10.1016/j.petrol.2018.08.035.\nMeyer, B. R. and Bazan, L. W. 2011. A Discrete Fracture Network Model for Hydraulically Induced Fractures - Theory,\nParametric and Case Studies . Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition\nheld in The Woodlands, Texas, 24-26 January 2011. SPE-140514-MS. https://doi.org/10.2118/140514-MS.\nMcClure, M.W., Christopher, A.J.B., Jung, H.  et al. 2014 . The Effect of Changing Fracture Compliance on Pressure\nTransient Behavior During Diagnostic Fracture Injection Tests. Paper presented at the SPE Annual Technical\nConference and Exhibition held in Amsterdam, The Netherlands, 27-29 October 2014. SPE-170956-MS. https://\ndoi.org/10.2118/170956-MS."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a800e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 8, "chroma:document": "Conference and Exhibition held in Amsterdam, The Netherlands, 27-29 October 2014. SPE-170956-MS. https://\ndoi.org/10.2118/170956-MS.\nMcClure, M.W., Jung, H. , Cramer, D. et al. 2016 . The Fracture-Compliance Method for Picking Closure Pressure From\nDiagnostic Fracture-Injection Tests. SPE J . 21(04): 1321 -1339 . SPE-179725-PA. https://doi.org/10.2118/179725-PA.\nRoussel, N. P. 2017 . Analyzing ISIP Stage-by-Stage Escalation to Determine Fracture Height and Horizontal-Stress\nAnisotropy . Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The\nWoodlands, Texas, USA, 24-26 January 2017. https://doi.org/10.2118/184865-MS.\nSoliman, M. Y., Craig, D. , Bartko, K.  et al. 2005 . After-Closure Analysis to Determine Formation Permeability, Reservoir\nPressure, and Residual Fracture Properties . Paper presented at the SPE Middle East Oil and Gas Show and Conference"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a805e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-208276-ms.pdf", "page": 8, "chroma:document": "Pressure, and Residual Fracture Properties . Paper presented at the SPE Middle East Oil and Gas Show and Conference\nheld in Bahrain International Centre, Bahrain, 12-15 March 2005. SPE-93419-MS. https://doi.org/10.2118/93419-MS.\nWeijers, L., Griffin, L. G., Sugiyama, H.  et al. 2002 . The First Successful Fracture Treatment Campaign Conducted in\nJapan: Stimulation Challenges in a Deep, Naturally Fractured Volcanic Rock. Paper presented at the SPE Annual\nTechnical Conference and Exhibition, San Antonio, Texas, USA, 29 September-2 October 2002. SPE-77678-MS.\nhttps://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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 0, "chroma:document": "SPE-199990-MS\nField-Wide Review of Diagnostic Fracture Injection Tests DFIT in Montney\nand Duvernay Formations \u2013 Part 1: Stress and Pressure Distributions\nBehjat Haghshenas , Reservoir Diagnostics Inc. ; Farhad Qanbari, Seven Generations Energy\nCopyright 2020, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Canada Unconventional Resources Conference originally scheduled to be held in Calgary, Alberta, Canada, 18 \u2013\n19 March 2020. Due to COVID-19 the physical event was postponed until 29 September \u2013 2 October 2020 and was changed to a virtual event. The official proceedings\nwere published online on 24 September 2020.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a80f4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 0, "chroma:document": "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\nconsent 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\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nA straightforward test with debatable analysis methods, the diagnostic fracture injection test (DFIT) is\na pressure-transient test extensively used for reservoir and geomechanical characterization of tight/shale\nformations. The test provides some key data and information to reservoir and well completion engineers\nincluding instantaneous shut-in pressure (ISIP), pore pressure, closure stress, fluid efficiency, reservoir flow\ncapacity, and fracture leak-off regime. A comprehensive regional or field-wide study of the DFITs is deemed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8144-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 0, "chroma:document": "capacity, and fracture leak-off regime. A comprehensive regional or field-wide study of the DFITs is deemed\nvery useful for operators at any stage of exploration and development.\nIn this study, DFITs from a group of 174 Montney and Duvernay wells operated by more than 30\nproducing companies are quality checked and analyzed consistently. The results from DFITs are then\ncompared against the standard poroelasticity equation.\nThe data set of the current study covers a wide range of DFIT conditions and reservoir and geomechanical\nproperties which helps the authors develop reliable correlations for reservoir characterization purposes.\nTrue vertical depth (TVD) of the wells ranges from less than 1000m to more than 4000m leading to a wide\nrange of pressure and stress conditions. The study also covers all the geographical areas of Montney and\nDuvernay. The results ofthe DFITs are used to develop usefulcross-plot betweenpore pressure and closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a818a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 0, "chroma:document": "Duvernay. The results ofthe DFITs are used to develop usefulcross-plot betweenpore pressure and closure\npressure.A relationship between closure pressure from compliance method and G-function analysis method\nfor Montney and Duvernay is also provided. Results of example DFITs from depleted areas were also\nprovided which gives an idea about the depletion level and the associated well performance degradation.\nThe current study gives field-wide understanding of the variations and distributions of reservoir and\ngeomechanical properties in Montney and Duvernay based on DFIT analysis of a sizable population of\nwells.\nIntroduction \u2013 Reservoir Initialization and Characterization\nReservoir characterization includes a series of direct and indirect methods that are applied to different\nreservoir scales spanning from pore to field. Clarkson et al. (2016) reviewed advances in shale/tight reservoir"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 0, "chroma:document": "reservoir scales spanning from pore to field. Clarkson et al. (2016) reviewed advances in shale/tight reservoir\ncharacterization at different scales using drill cuttings, cores, well tests, and production data.Pressure\ntransient 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a822a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 1, "chroma:document": "2 SPE-199990-MS\nwellbore and far-field reservoir and estimation of average reservoir pressure. The methods are used to\ninterpret well bottom-hole pressure data which is influenced by reservoir properties and limits.\nDFIT serves as a PTA tool for unconventional reservoirs which provides estimates of some of the\nkey reservoir and geomechanical properties of the sampled system as pressure transient during DFIT is\ncontrolled by the hydraulically-induced fractures and native reservoir properties.\nOperating companies in unconventional reservoirs usually require an overall understanding of reservoir\nconditions and parameters across these giant continuous hydrocarbon systems (in addition to local detailed\nstudies) using field-wide analysis of reservoir characterization tests such as DFIT. In this study, 134 DFITs\nfrom Montney and 40 DFITs from Duvernay formations are analyzed.The key observations and data trends"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8270-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 1, "chroma:document": "from Montney and 40 DFITs from Duvernay formations are analyzed.The key observations and data trends\nare presented withsome examples.The focus of this paper is pressure and stress distribution and leak-off\ntypes in Montney and Duvernay. Permeability estimation from DFIT and fracture treatment analysis during\nDFIT will be presented in Part 2 of the paper.\nDiagnostic Fracture Injection Test (DFIT)\nA DFIT consists of injection of a small volume of liquid or gas at low rate followed by extended shut-in\nperiod when the pressure falloff is recorded ( Craig and Blasingame, 2006). Three key processes occur during\nthe test including hydraulic fracturing (during injection), early-time fluid leak-off, fracture closure, and late-\ntime fluid leak-off.DFIT data analysis includes interpretation of the shut-in pressure data usingreservoir\nengineering and geomechanicstools.Two parameters for reservoir initialization(pressure and stress) and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a82ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 1, "chroma:document": "engineering and geomechanicstools.Two parameters for reservoir initialization(pressure and stress) and\ntwo reservoir properties(permeability and leak-off type) are obtained by analyzing the DFIT data ( Fig.\n1). Furthermore, treatment pressure during injection period can be used to tune fracture propagation and\ntortuosity models.\nFigure 1\u2014Parameters and information derived from DFIT analysis.\nLike other well test methods, uncertainty sources in DFIT results include measurements, input data (fluid\nproperties, petrophysical properties, etc.), DFIT analysis models, and interpretations methods.Different\nDFIT pre-closure analysis models are available and have been used in literature and industry. G-function\nderivative analysis or Holistic method (Nolte, 1979; Barree et al., 2009) and type curves (Craig and\nBlasingame, 2005 , 2006 ) have been widelyused to identify fracture closure, estimate closure pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a831a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 1, "chroma:document": "Blasingame, 2005 , 2006 ) have been widelyused to identify fracture closure, estimate closure pressure\n(which is considered as an estimate of minimum horizontal stress), and characterize leak-off type. Fracture\ncompliance method (McClure et al., 2016) has also been used for identification of fracture closure\nwhichprovides higher closure pressure compared to G-function derivative analysis.The closure pressures\nfor all of the DFITs of this study are estimated using both theG-function derivative and compliance methods.\nExamples of different leak-off types including pressure-dependent leak-off (PDL), normal leak-off, and\nstorage from Montney formation are provided in Fig. 2  (the red and yellow stars show closure pressures from\nG-function derivative analysis and compliance methods, respectively). The common methods for estimation\nof permeability and reservoir pressure from DFIT after-closure datainclude Gu et al. (1993), Soliman et al.,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8360-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 1, "chroma:document": "of permeability and reservoir pressure from DFIT after-closure datainclude Gu et al. (1993), Soliman et al.,\n(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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a83b0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 2, "chroma:document": "SPE-199990-MS 3\nFigure 2\u2014Montney DFIT examples with closure pressures estimated from G-function analysis (red stars) and\ncompliance method (yellow stars) (a) pressure-dependent leak-off (PDL) (b) normal leak-off and (c) storage.\nMontney and Duvernay\nMontney and Duvernay are the two key Canadian unconventional plays with significant resource potential\n(Fig. 3 ). The black dots and lines on the maps illustrate the location of the current wells which are\nmostly on production. Uneven distributions of wells in the playsare mostly due to reservoir development\nconsiderationsand variability ofreservoir properties.\nFigure 3\u2014Lithofacies distribution map of Montney formation, on the left side (after Edwards\net al. 1994 ) and Duvernay shale map, on the right side (modified from Switzer et al. 1994).\nReservoir parametersincluding pressure, temperature, stress, porosity, permeability etc. across Montney"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a83f6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 2, "chroma:document": "Reservoir parametersincluding pressure, temperature, stress, porosity, permeability etc. across Montney\nand Duvernay change geographically and vertically.TVD of the wells drilled in Montney to date range from\n800 m to 4000 m ( Fig. 4a ). Unconventional part of Montney is locatedat TVDgreater than 1500 m whereas\nthe conventional Montney resides at shallower depth. TVD of the wells drilled in Duvernay to date range\nfrom 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8446-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 3, "chroma:document": "4 SPE-199990-MS\nFigure 4\u2014Histogram of TVD for the wells drilled in (a) Montney and (b) Duvernay to date.\nPressure and Stress Variability in Montney and Duvernay\nClosure pressure is estimated using the G-function plots (as shown in Fig. 2 ). To estimate reservoir pressure,\nthe flow regimes areidentified,and then well shut-in pressure is extrapolated using a proper pressure vs.\ntime plot.Half-slope and zero-slope lines on the log-log diagnostics plots (Fig. 5a and 5b) indicate linear\nand radial flow regimes, respectively. All the Montney and Duvernay wells of this study exhibit linear flow.\nRadial flow was barely observed for these wells.For consistency, the estimated reservoir pressures from\nlinear flow are reported. Estimated reservoir pressure from radial flow is preferred if available.The well with\nradial flow shown in Fig. 5b  is from Dunvegan formation which has much higher permeability compared"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 3, "chroma:document": "radial flow shown in Fig. 5b  is from Dunvegan formation which has much higher permeability compared\nto Montney and Duvernay. Extrapolation of well shut-in pressures corresponding to linear flow of Fig. 5a\nand radial flow of Fig. 5b  are illustrated in Figs. 5c  and 5d.\nFigure 5\u2014Flow regime identification and reservoir pressure estimation (a) linear flow (half-slope line) for a Montney well, (b)\nlinear (half-slope line) and radial flow (zero-slope line) from a Dunvegan well, (c) reservoir pressure estimation corresponding\nto the half-slope line in Fig. 5a, and (d) reservoir pressure estimation corresponding to the zero-slope line in Fig. 5b.\nFig. 6  provides the estimates of closure and pore pressure for some of the wells along the blue arrow\nshown on the map (TVD increases moving away from the reference point). Similar results are provided"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 3, "chroma:document": "shown on the map (TVD increases moving away from the reference point). Similar results are provided\nfor 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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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 4, "chroma:document": "SPE-199990-MS 5\npressure, closure pressure (minimum horizontal stress) and the corresponding gradients increase with depth.\nFurthermore, minimum stress (closure pressure) and reservoir pressure are strongly correlated. This is\nexplained in more detail in \"Equation of Poroelasticity\" section.\nFigure 6\u2014Distribution of closure and pore pressure along the blue arrow on the\nMontney map.Similar results for other regions of Montney are provided in Appendix.\nFig. 7  provides the data for some of the Duvernay wells along the blue arrow shown on the map. Similar\nresults 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a85a4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 5, "chroma:document": "6 SPE-199990-MS\nFigure 7\u2014Distribution of closure and pore pressure along the blue arrow on the\nDuvernay map.Similar results for another region of Duvernay is provided in Appendix.\nLeak-off Types in Montney and Duvernay\nFluid leak-off type in DFIT depends of the relative contribution of matrix and natural fractures/fissures in\ndissipation of injected fluid and pressure after the pumping period of the DFIT. \"Normal leak-off\" happens\nin the case of a fully contributing matrix system exposed to the hydraulic fracture whereas \"pressure-\ndependent leak-off (PDL)\" occurs in the case of enhanced surface area and permeability in the vicinity of\nhydraulic fracture at high injection pressures. \"Storage\" occurs in cases with partially contributing matrix\nand/or storage of excess water in open features with high storage capacity at elevated pressures.\nLeak-off type is an important reservoir signature which might impact the efficiency of hydraulic fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a85ea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 5, "chroma:document": "Leak-off type is an important reservoir signature which might impact the efficiency of hydraulic fracture\ntreatment. Leak-off types for the wells of this study (134 Montney wells and 40 Duvernay wells) were\nidentified 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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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 6, "chroma:document": "SPE-199990-MS 7\nshows that 89% of Montney wells and 52% of Duvernay wells exhibit storage signature. Normal leak-offis\nobserved in only one Montney well.\nFigure 8\u2014Leak-off types in (a) Montney and (b) Duvernay.\nFracture closure time and fluid efficiency distributions in Montney also differ from Duvernay as shown\nin Fig 9 . Generally, Montney fractures close faster and therefore fluid efficiency, 100 Gc/(G c+2), is lower\ncompared to Duvernay. This might be attributed to higher permeability value in Montney.\nFigure 9\u2014Distributions of closure parameters in Montney and Duvernay (a) closure time (b) fluid efficiency.\nEquation of Poroelasticity\nBased on the classic equation of poroelasticity (Terzaghi 1943), the minimum horizontal stress is a function\nof pore pressure (p ), vertical and tectonic stresses (\u03c3 v and \u03c3 t), and rock elastic properties (Poisson's ratio,\nv, and Biot's coefficient, \u03b1).\n(1)"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a868a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 6, "chroma:document": "of pore pressure (p ), vertical and tectonic stresses (\u03c3 v and \u03c3 t), and rock elastic properties (Poisson's ratio,\nv, and Biot's coefficient, \u03b1).\n(1)\nThis model is based on some simplifying assumptions and used to explain high-level trends between\nminimum horizontal stress and pore pressure and elastic properties on relative basis. Plot of closure pressure\n(approximately equal to minimum horizontal stress) from Montney and Duverany DFITs is provided in Fig.\n10a. As shown in Fig 10a , (1) there is a reasonably strong correlation between closure and pore pressure\nand (2) the poroelasticity plot from both Montney and Duvernay follow the same line. Furthermore, closure\npressure is estimated using Eq. 1 with assumed v = 0.25, bulk density of 2500 kg/m3 and \u03c3 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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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a86d0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 7, "chroma:document": "8 SPE-199990-MS\nshows that the results from Eq. 1 and DFITs are reasonably close. The variability in the results is due to the\nvariation ofthe reservoir properties across these plays. The results from Eq. 1 can be tuned further by using\nmeasured values of the rock elastic properties.\nFigure 10\u2014Poroelasticity in Montney and Duvernay (a) Pore pressure and closure from\nMontney and Duvernay DFITs (b) comparison of closure pressure from DFIT against Eq. 1 .\nClosure pressures are also estimated using the compliance method. The closure pressure from the\ncompliance method is usually higher than the G-function analysis method. Fig. 11 provides a cross-plot of\nthe closure pressure from compliance vs. closure pressure from the G-function analysis for Montney and\nDuvernay DFITs of this study. As shown in the plot, the closure pressure from compliance method is on\naverage 9% greater than the closure pressure from the G-function analysis method."}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8720-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 7, "chroma:document": "average 9% greater than the closure pressure from the G-function analysis method.\nFigure 11\u2014Closure 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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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8770-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 8, "chroma:document": "SPE-199990-MS 9\nPressure Depletion\nPrediction of infill/child well performance (early- and late-time) is an important task in reservoir\nengineering, development, and management of conventional and unconventional systems. Infill/child well\nperformance primarily depends on reservoir pressure distribution/depletion controlled by production from\nthe existing/parent wells. Pressure depletion may impact infill/child performance in two ways: fracture\ngeometry (geomechanics) and material balance (reservoir engineering).\nReservoir simulation can be used to estimate reservoir pressure at the infill locations based on the\nreservoir properties and the historical production data from the existing wells. The pressure forecast from\nthe reservoir model can be compared against direct measurement of reservoir pressure (from DFIT) at the\ninfill locations. DFITs from different infill/child wells are very useful in constructing a pressure distribution"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a87c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 8, "chroma:document": "infill locations. DFITs from different infill/child wells are very useful in constructing a pressure distribution\nline which in turn can be used to analyze performance of infill/child wells or tune the reservoir models.\nFour pressure depletion examples diagnosed by DFIT are provided in the following subsections including\nthree Montney cases and a Duvernay case.\nExample 1\nA group of vertical wells from a higher-permeability area of Montney (the wells in orange in Fig. 12) were\ncompleted in single hydraulic fracture and put on production mostly in 1996-1997. Pressure buildup test\ndata from the Vertical Well V1 (shown in Fig. 12 ) gives initial reservoir pressure gradient of ~8.6 kPa/m\nand reservoir permeability of ~5 md. The operator completed a few infill multi-fractured horizontal wells\n(wells in green color in Fig. 12 ) in 2011 and converted some of the vertical wells into injectors. DFITs"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8810-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 8, "chroma:document": "(wells in green color in Fig. 12 ) in 2011 and converted some of the vertical wells into injectors. DFITs\nwere run on the horizontal wells prior to completion. Most of the tests were ended before linear/radial flow\nis observed. The measured downhole pressure gradient at the end of DFIT from Well H1 and estimated\nreservoir pressure from linear flow are 5.4 kPa/m and 5 kPa/m, respectively. That is, reservoir pressure\ngradient at the DFIT location is depleted by ~40%. The toe of Well H1 is in a region surrounded by five\nvertical wells with total oil production and gas productions of ~330 MSTB and 2.2 Bscf, respectively. This\nis a critical piece of information which helps the reservoir development team tune their reservoir models\nand improve production forecasts and estimated recoveries.\nFigure 12\u2014Depletion Example 1 \u2013 horizontal infill wells in high permeability Montney.\nExample 2\nEight Montney wells on an infill pad (wells in red in Fig. 13) were completed after four years of production"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8856-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 8, "chroma:document": "Example 2\nEight Montney wells on an infill pad (wells in red in Fig. 13) were completed after four years of production\nform the neighbour pads (wells in blue and purple in Fig. 13) in a gas condensate region of Montney. The\nwells were completed in three benches (each bench with ~50m thickness as shown in Fig. 13). Based on\nDFITs 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a88a6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 9, "chroma:document": "10 SPE-199990-MS\n12-13 kPa/m. DFITs were also performed on all the infill wells to estimate pressure across the toe of the\nwells on the infill pad. The results are provided in Table 1. Well C1 shows the highest depletion as expected\nbecause it is the closest well to the parent well on the the neighbor pad (both horizontally and diagonally)\nand the toe of the well is located along the parent well. Well C2 is less depleted than C1 as it is farther from\nthe parent well and located at a different layer. On the other side of the infill pad, toe of Well C8 is more\ndepleted than C7 and C6 due to proximity to the parent well on neighbor pad. However, Well C8 is less\ndepleted than Well C1; one reason is that the toe of C8 is located at the heel of the parent well whereas toe\nof C1 is located along the parent well. This observation implies that pressure from DFIT of a child well may\nnot represent the whole wellbore because the conditions may change along the wellbore due to the relative"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a88ec-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 9, "chroma:document": "not represent the whole wellbore because the conditions may change along the wellbore due to the relative\nposition of the well with respect to the parent well.\nFigure 13\u2014Depletion Example 2 \u2013an infill pad in Montney.\nTable 1\u2014DFIT results for the the wells on infill pad of Fig. 13.\nWell C1 C2 C3 C4 C5 C6 C7 C8\nTrue Vertical Depth, TVD (m) 2313 2362 2254 2308 2351 2240 2296 2344\nClosure Pressure (MPa) 35.3 41.1 37.3 36.2 40 38 36.2 38\nClosure Pressure Gradient (kPa/m) 15.3 17.4 16.5 15.7 17.0 17.0 15.8 16.2\nPressure (MPa) 19.7 26.6 24.7 25.5 27 26.6 26\nPressure Gradient (kPa/m) 8.5 11.3 10.7 10.8 12.1 11.6 11.1\nExample 3\nTwo multi-fractured horizontal wells (Wells H1 and H2 in Fig. 14 ) were completed in cased-hole plug and\nperf and put on production in 2009. Both wells were completed on the same bench in Montney. In 2017, Well"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8946-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 9, "chroma:document": "perf and put on production in 2009. Both wells were completed on the same bench in Montney. In 2017, Well\nH3 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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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a898c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 10, "chroma:document": "SPE-199990-MS 11\nwas run shortly after (see well configuration in Fig. 14). DFIT from Wells H1 and H2 give initial reservoir\npressure gradient of ~14 kPa/m whereas DFIT from H3 gives pressure gradient of ~12 kPa/m (i.e. ~2 kPa/\nm pressure depletion) at the toe of the well. This provides an insight about how far pressure front can move\nvertically which can help with optimizing the development plan regarding the lower target in Montney.\nFigure 14\u2014Depletion Example 3 \u2013 depletion in a well toeing to existing wells in Montney.\nExample 4\nA pad including Wells H2-H5 (as shown in Fig. 15 ) were completed after 15 months of production from a\npad including Well H1 ( Fig. 15). Cumulative production from Well H1 at the time of completing Wells H2-\nH5 was ~1.0 Bcf. DFITs from Wells H2 and H5 (located at distance of 270 m and 1150 m away from Well\nH1) showed that Well H2 was depleted by ~7MPa (~1.7 kPa/m) whereas Well H5 was not depleted."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a89dc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 10, "chroma:document": "H1) showed that Well H2 was depleted by ~7MPa (~1.7 kPa/m) whereas Well H5 was not depleted.\nFigure 15\u2014Depletion Example 4 \u2013 estimation of pressure distribution\nacross a new pad completed beside an older pad in Duvernay using DFIT.\nConclusions\nA total of 174 DFITs across Montney and Duverany were analyzed in this study. The study gives field-wide\nunderstanding 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8a2c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 11, "chroma:document": "12 SPE-199990-MS\nand Duvernay.Closure pressure and pore pressure from the DFITs show a strong correlation which reads\nwith standard poroelasticity relationship. The results from DFITs are comparable against the standard\nporoelasticity equation. Different DFITs from depleted parts of Montney are also provided which provide\ninsights regarding the risks associated with depletion in both horizontal and vertical directions.\nReferences\n1. Barree, R. D.,  Barree, V . L. and Craig, D., 2009. Holistic fracture diagnostics: consistent\ninterpretation of prefrac injection tests using multiple analysis methods.  SPE Production &\nOperations,  24(03) , pp.396 \u2013406.\n2. Clarkson, C. R.,  Haghshenas, B., Ghanizadeh, A., Qanbari, F., Williams-Kovacs, J. D., Riazi,\nN., Debuhr, C.  and Deglint, H. J., 2016. Nanopores to megafractures: Current challenges and\nmethods for shale gas reservoir and hydraulic fracture characterization.  Journal of Natural Gas\nScience and Engineering,  31, pp.612\u2013657."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8aa4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 11, "chroma:document": "methods for shale gas reservoir and hydraulic fracture characterization.  Journal of Natural Gas\nScience and Engineering,  31, pp.612\u2013657.\n3. Craig, D. P.  and Blasingame, T. A.,  2005, January. A new refracture-candidate diagnostic test\ndetermines reservoir properties and identifies existing conductive or damaged fractures. In SPE\nAnnual Technical Conference and Exhibition. Society of Petroleum Engineers.\n4. Craig, D. P. and Blasingame, T. A., 2006, January. Application of a new fracture-injection/\nfalloff model accounting for propagating, dilated, and closing hydraulic fractures.  In SPE Gas\nTechnology Symposium. Society of Petroleum Engineers.\n5. Edwards, D. E.,  Barclay, J. E.,  Gibson, D. W., Kvill, G. E.,  and Halton, E. 1994. Triassic Strata of\nthe Western Canada Sedimentary Basin; in Geological Atlas of the Western Canada Sedimentary\nBasin , G.D. Mossop and I. Shetsen (comp.), Canadian Society of Petroleum Geologists and\nAlberta Research Council Terzaghi,"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8aea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 11, "chroma:document": "Basin , G.D. Mossop and I. Shetsen (comp.), Canadian Society of Petroleum Geologists and\nAlberta Research Council Terzaghi,\n6. Gu, H.,  Elbel, J. L.,  Nolte, K. G., Cheng, A. D. and Abousleiman, Y ., 1993, January. Formation\npermeability determination using impulse-fracture injection.  In SPE Production Operations\nSymposium. Society of Petroleum Engineers.\n7. Nolte, K. G.,  1979, January. Determination of fracture parameters from fracturing pressure\ndecline.  In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.\n8. Soliman, M. Y .,  Craig, D. P.,  Bartko, K. M., Rahim, Z. and Adams, D. M.,  2005, January.\nPost-closure analysis to determine formation permeability, reservoir pressure, residual fracture\nproperties.  In SPE Middle East Oil and Gas Show and Conference. Society of Petroleum\nEngineers."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8b3a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 11, "chroma:document": "properties.  In SPE Middle East Oil and Gas Show and Conference. Society of Petroleum\nEngineers.\n9. 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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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 12, "chroma:document": "SPE-199990-MS 13\nAppendix\nFigure A-1\u2014Distribution 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"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 13, "chroma:document": "14 SPE-199990-MS\nFigure A-2\u2014Distribution 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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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 14, "chroma:document": "SPE-199990-MS 15\nFigure A-3\u2014Distribution 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"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199990-ms.pdf", "page": 15, "chroma:document": "16 SPE-199990-MS\nFigure A-4\u2014Distribution 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 0, "chroma:document": "SPE-194348-MS\nDFIT Considering Complex Interactions of Hydraulic and Natural Fractures\nAmirhossein Kamali and Ahmad Ghassemi, Reservoir Geomechanics and Seismicity Research Group, The\nUniversity of Oklahoma\nCopyright 2019, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The Woodlands, Texas, USA, 5-7 February\n2019.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof 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\nany 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8d06-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 0, "chroma:document": "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\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nCurrently, the closure stress is often predicted using the conventional tangent method (i.e., G-function) or\nthe variable compliance method. Both methods use several restrictive assumptions such as a single planar\nfracture. However, the hydraulic fracture often intersects rock fabric features such as bedding planes and/\nor natural fractures causing the pressure transient behavior to become drastically different compared to that\nof a single planar hydraulic fracture. Closure of the intersected natural fractures might precede that of the\ncreated HF which impacts the interpretation of the pressure derivate plots and also the closure stress. In this"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8d56-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 0, "chroma:document": "created HF which impacts the interpretation of the pressure derivate plots and also the closure stress. In this\npaper we present and use an advanced fracture diagnostic model that can help recognize the signatures of\nrock fabric features and their impact on estimation of the closure stress. An example field data is used to\nillustrate the potential impact on closure stress.\nThe new DFIT model consists of a fully coupled 3D hydraulic fracture simulator with the ability to\nhandle the opening, propagation, and closure of natural factures so that the pre- and post-closure stress/\ndeformation of both the hydraulic and natural fractures can be captured. Fracture propagation, HF-NF\ninteraction, fracture intersection, and DFIT model are integrated into one simulator to provide a more\nrealistic view of HF propagation and fracture diagnostics in naturally fractured reservoirs. The current\nmodel is developed without any major assumptions concerning the fluid flow, fracture deformation, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8da6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 0, "chroma:document": "model is developed without any major assumptions concerning the fluid flow, fracture deformation, and\npropagation path. Rock/fracture deformation is calculated using a boundary element formulation whereas\nthe transport processes are solved using finite elements method.\nOur results indicate that natural fractures affect the pre- and post- shut-in response of the hydraulic\nfracture in a number of ways. For example, the fracture propagation path, the pumping pressure profile,\nand interfering with the post shut-in pressure response. These factors, indeed, impact the estimation of the\nminimum horizontal stress which is a key parameter obtained from DFIT. Moreover, our results show how\nthe normal stiffness of the fracture surface asperities can impact the minimum stress estimation. Closure\nof natural fractures is reflected in the slope of the pressure derivative and G-function plots so that correct\ninterpretation of these signatures is essential to accurate extraction of the Shmin."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8dec-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 0, "chroma:document": "interpretation of these signatures is essential to accurate extraction of the Shmin.\nClosure of natural fractures is often viewed as a pressure depdendent leakoff mechanism that is reflected\non the Gdp/dG curve. The closure behavior of HF-NF sets is, however, not explicitly modeled in the context\nof 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8e3c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "2 SPE-194348-MS\na 3D coupled simulator. This novel model is applied to actual field data to illustrate the potential impact on\nclosure stress and to shed light on the subject of fracture diagnostics in naturally fractured reservoirs. Our\nresults indicate that the closure behavior of hydraulic and natural fractures in a HF-NF set differs from that\nof an isolated fracture due to the effect of stress shadowing. Although the system stiffness method results\nin distinct signatures on the diagnostic curves, these signatures are not commonly observed in the field\ndata. The absence of stiffness signatures in the field cases could be interpreted in two ways: 1) the closure\nmechanism assumed in the stiffness/compliance method differs from the actual fracture closure mechanism\nor 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in the system stiffness\nafter closure.\nIntroduction"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8e82-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in the system stiffness\nafter closure.\nIntroduction\nFracture injection/fall-off tests have been extensively used over the past few decades to obtain fracture\nclosure pressure and several reservoir properties such as permeability and initial reservoir pressure. The\npioneering work of Nolte (1979)  provided a rigorous means for determining the fracture closure pressure,\nleakoff coefficient, and fluid efficiency by introducing the G-function. Nolte (1979) derived the pressure\ndecline function based on material balance assuming a single planar fracture and constant leakoff from\nthe fracture surfaces. Following the Nolte's methodology, Castillo (1987) introduced a pressure decline\nfunction where the pressure decline formed a straight line when plotted against the G-function during\nthe closure. Deviation from the linear portion of the plot was interpreted as the fracture closure. Castillo"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8ed2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "the closure. Deviation from the linear portion of the plot was interpreted as the fracture closure. Castillo\n(1987)  also improved the constant leakoff assumption in the Nolte's approach by considering other leakoff\nmechanisms such as reservoir dominated and filtrate viscosity dominated leakoff modes and formulated the\nrequired parameters to use in each case. Recognizing that the use of pressure versus G-fucntion could lead\nto ambiguous conclusions about the nonlinear leakoff behvaiors, Mukherjee et al. (1991) and Barree and\nMukherjee (1996)  started using the superposition derivative function (i.e., Gdp/dG) along with the pressure\ndecline plots. Using the combination plots including the P, dP/dG, and GdP/dG plots helps to identify the\ncause of the non-linearity in the leakoff behavior. Tip extension, height recession, fissure opening, and\nthe change of system stiffness can be detected on the Barree and Mukherjee's combination plot. Pivoting"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8f22-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "the change of system stiffness can be detected on the Barree and Mukherjee's combination plot. Pivoting\non the fact that neither one of the assumptions in the leakoff formulation (filter cake dominance and the\nsquare root of time decay) is really true, Mayerhofer and Economides (1997) advocated using the simple\nlog-log diagnostic plots instead of the widely used G-function analysis. To account for the varying leakoff\nrate, Mayerhofer and Economides (1997) used a rate-normalized plot (RNP) and its derivative to detect the\nfracture closure and departure from the half-slope line. Craig et al. (2005) conducted a statistical analysis\non the leakoff type and the reservoir permeability of more than 1000 diagnostic fracture injection tests in\nthe Rocky Mountain Basin, and concluded that the normal leakoff behvaior is very rarely seen. In fact, the\ngreat majority of the tests in their study showed pressure dependent leakoff and other abnormal leakoff"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8f68-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "great majority of the tests in their study showed pressure dependent leakoff and other abnormal leakoff\nbehaviors which makes the G-function interpretation challenging. As an alternative to the conventional\ntangent method, several studies have focused on the use of system stiffness or compliance method ( Barree\nand Mukherjee, 1996 ; Raaen et al., 2001; Raaen et al., 2005; McClure et al. 2016) to determine the fracture\nclosure pressure. Raaen et al., (2001) pointed out that there is a change in the system stiffness upon\nclosure which is reflected on the pressure and pressure derivative plots. The signature associated with the\nchange of system stiffness/compliance can therefore help identifying the instance of fracture closure and\nthe corresponding closure stress. McClure et al., (2016) considered the stiffness change due to the joint\nclosure as well. On the other hand, the signature of changes caused by the fracture normal stiffness has not"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8fb8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 1, "chroma:document": "closure as well. On the other hand, the signature of changes caused by the fracture normal stiffness has not\nbeen widely observed in field data and moreover, the interpretation of stiffness (compliance) changes can\nbe ambiguous. In particular, HF interaction with natural fractures can result is similar signatures that would\ncomplicate 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a8ffe-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 2, "chroma:document": "SPE-194348-MS 3\nTraditionally, the impact of natural fractures on the post-shutin pressure decline is implicitly studied\nin the context of leakoff behavior. However, the interaction of hydraulic and natural fractures and its\neffect on the closure behavior and the pressure decline is not explicitly considered in previous works. In\nthis work we use a fully 3D hydraulic/natural fracture simulator to investigate the pressure decline in a\nsystem including intersected hydraulic and natural fractures. The mechanical interaction between fractures\nis explicitly included in the model to rigorously account for the closure of natural fractures in the diagnostic\nfracture injection tests.\nModel Development\nA fully coupled 3D hydraulic/natural fracture simulator is used in this study to investigate fracture injection\ntests and closure stress estimation in the presence of natural fractures. This section describes the constitutive"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9076-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 2, "chroma:document": "tests and closure stress estimation in the presence of natural fractures. This section describes the constitutive\nequations that are used to construct this model and the numerical methodology to implement the model.\nConstitutive Equations\nHydraulic fracturing is a coupled process that involves rock deformation, fracture propagation, fluid\nflow, leakoff, thermal, and poroelastic stress components. Proper constitutive equations are required to\ndescribe and capture this multi-physics problem. Unlike fluid-driven hydraulic fractures, pre-exisitng\nnatural fractures are closed fractures that carry normal and shear stresses. Therefore, the contact status of\nthe natural fractures should be carefully addressed.\nThe solution to the problem of an elastic body deformation must satisfy the governing equations for a\ngiven set of stress/displacement boundary conditions. The formulation of this problem relies on the stress"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a90d0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 2, "chroma:document": "given set of stress/displacement boundary conditions. The formulation of this problem relies on the stress\ntensor PDE and strain-displacement equations. The solution is completed through a constitutive equation\nthat relates the stresses to the strains. Using Hooke's law in 3D, this constitutive equation is expressed as\nfollows ( Love, 2013 ; Timoshenko and Goodier, 1970):\n(1)\nWhere E is the formation's Young's modulus, v is the Poisson's ratio, \u03c3ij is the stress tensor components, \u03b5ij\nis the strain tensor components, \u03b5kk denotes trace of the strain tensor, and \u03b4ij is the Kronecker delta function.\nAnother integral part of the hydraulic fracturing is the fluid flow inside the fracture. Assuming small\nvariations of the fracture width in time and space, the continuity equation can be expressed as:\n(2)\nWhere q is the volumetric flow rate at location s and time t, w is the local fracture aperture, VL is the leakoff"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9120-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 2, "chroma:document": "(2)\nWhere q is the volumetric flow rate at location s and time t, w is the local fracture aperture, VL is the leakoff\nvelocity across the fracture surfaces, and Qinj is the pumping rate. The continuity equation can be formulated\nin terms of the fluid pressure and the fracture aperture using the Darcy's law ( Witherspoon et al., 1980):\n(3)\nIn which, \u03bc is the viscosity of the fracturing fluid, and \u2207P is the pressure gradient along the fracture.\nContact elements are used to represent closed natural fractures. The constitutive equations simply relates\nthe changes of the normal (shear) stress to that of the normal (shear) displacement discontinuity as shown\nbelow ( Goodman et al., 1968 ):\n(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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9170-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 3, "chroma:document": "4 SPE-194348-MS\nWhere Kn and Ks are the normal and shear stiffness, and Dn and Ds are the normal and shear displacement\ndiscontinutites for each element. The contact status of the elements may change during the simulation in\nboth the normal and shear mode. Mohr-Coulomb criterion is used to determine the contact status of the\nelements in the shear mode (i.e., \u2032\u2032 stick\u2032\u2032 and \u2032\u2032 slip\u2032\u2032 ):\n(5)\nWhere c and \u00d8 are the natural fracture's cohesion and friction angle, respectively. More details about the\ncontact elements and its implementation can be found elsewhere (Kamali and Ghassemi, 2018; Kamali and\nGhassemi, 2017 ; Safari and Ghassemi, 2015; Tao et al., 2011 )\nNumerical Methodology\nFully 3D fracture modeling coupled with the fluid flow results in a set of nonlinear partial differential\nequations that are often not amenable to analytical treatments. Therefore, numerical modeling is used to\nstudy problems involving complex fracture simulations. Fracture deformations and stresses are solved"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a91c0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 3, "chroma:document": "study problems involving complex fracture simulations. Fracture deformations and stresses are solved\nusing displacement discontinuity (Crouch and Starfield, 1983; Curran and Vandamme, 1989) which is an\nindirect boundary element method. Displacement discontuity (DD) is proved to be a powerful tool to model\nhydraulic fractures and problems involving contact elements such as natural fracutres, and faults (Asgian,\n1988 ; Ghassemi and Tao, 2016; Safari and Ghassemi, 2015 ). Stresses at each point on the fracture is obtained\nusing the following integral form:\n(6)\nWhere \u0393 is the displacement discontiuty boundary, \n  is the unit induced stress component \u2032\u2032ij\u2032\u2032 due to\nthe instantaneous point source DD component \u2032\u2032kn\u2032\u2032, and \n  is the in-situ stress component at location\nX. Figure 1  shows a discplacement discontinuity elements and is displacement components. Numerical\ndiscretization and implementation is provided in Kumar and Ghassemi (2015)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 3, "chroma:document": "discretization and implementation is provided in Kumar and Ghassemi (2015).\nFigure 1\u2014Schematic 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9256-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 4, "chroma:document": "SPE-194348-MS 5\nThe fluid flow equations are solved using the finite element method by discretizing the fracture surface\ninto 4-node quadrilateral elements. A linear variation of the fluid pressure is assumed over the elements.\nThe details of the finite element discretization is discussed in Kumar and Ghassemi (2016).\nResults\nThe post-shutin pressure transient of HF-NF pairs is analyzed in this section to identify the signatures in the\npressure and pressure derivative plots. A combination of log-log diagnostic plot and G dP/dG plot is used\nto pick the closure pressure more confidently. Several analyses are conducted to study the impact of in-situ\nstress state, intersection angle, and fracture stiffness on the pressure decline curves and diagnostic plots.\nThe first example shows a typical HF-NF system with a relatively simple intersection in which the\nhydraulic fracture intersects the natural fracture with an intersection angle of 90\u00b0. The length of the natural"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a92a6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 4, "chroma:document": "hydraulic fracture intersects the natural fracture with an intersection angle of 90\u00b0. The length of the natural\nfracture is three times larger than that of the hydraulic fracture (see Figure 1  and Table 1).\nTable 1\u2014Input parameters (assumed values) used in the base case example.\nThe post-shuting pressure decline is studied for this example using the G-function and also the log-log\ndiagnostic plot. Both the hydraulic and natural fractures are pressurized above the maximum horizontal\nstress prior to the shutin as shown in Figure 2. Therefore, both fractures are open against the in-situ stresses.\nIt shoud be noted that the pressure can easily rise above the maximum horizontal stress level and open the\nnatural fracture given that the stress anistorpy is not high in this example. The pump is then shut in and\nthe pressure is monitored.\nFigure 2\u2014Hydraulic and natural fracture pressure before shutin. The fluid pressure is above"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a92ec-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 4, "chroma:document": "the pressure is monitored.\nFigure 2\u2014Hydraulic and natural fracture pressure before shutin. The fluid pressure is above\nthe 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a933c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 5, "chroma:document": "6 SPE-194348-MS\nThe post-shutin pressure is recorded and plotted against the G-function along with the semilog derivative\nG dp/dG in Figure 3-a . The G dp/dG plot shows that there are two sudden changes of slope before the hump\ncorresponding to the change of the system stiffness; the first due to the natural fracture closure and the\nsecond due to hydraulic fracture closure. The first change of slope could also be detected on the pressure\ncurve at approximately 4300 psi which is regarded as the closure pressure for the natural fracture (marked\nby the blue arrow). The second change of the system stiffness occurs when the pressure falls below the\nminimum stress and the hydraulic fracture closes (marked by a circle on the G dp/dG and green arrow on\nthe pressure plot). The closure pressure obtained from the second change of system stiffness is 4000 psi.\nThe closure pressure is also picked using the conventional tangent method. This method yields a closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a938c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 5, "chroma:document": "The closure pressure is also picked using the conventional tangent method. This method yields a closure\npressure of 3950 psi which is a good estimate of the actual input for the minimum stress (i.e., 4000 psi).\nAlternatively, the closure pressure is picked from the log-log diagnostic plot in Figure 3-b . The closure\nstress obtained from this method (departure from the \u00bd slope line) is 3950 psi (i.e., \u0394p = 450 psi) which\nis in a good agreement with the tangent method and also the stiffness approach. It is important to note that\nalthough using the stiffness/compliance method provides clear signatures on the G dp/dG plot, one can\nmisinterpret the fracture closure pressure simply by choosing the first signature which actually corresponds\nto the natural fracture closure.\nFigure 3\u2014a) Pressure profile and the semilog derivative G dp/\ndG for the HF-NF system. b) log-log diagnostic plot for the HF-NF pair.\nAngle of Intersection"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 5, "chroma:document": "dG for the HF-NF system. b) log-log diagnostic plot for the HF-NF pair.\nAngle of Intersection\nThe angle of intersection between the hydraulic and natural fractures affects their mechanical interaction and\ntherefore impacts the coupled hydro-mechanical response. Moreover, the normal stress acting on the natural\nfracture plane varies based on its orientation with respect to in-situ stresses. In this example, the pressure\ndecline and the semilog G derivative is investigated for different angles of intersections. Considering that\nthe hydraulic fracture is initiated and extended in the direction of the maximum horizontal stress, the angle\nof intersection represents the angle between the natural fracture and the maximum stress. The base case\nexample is chosen such that the HF and NF are orthogonal meaning that the intersection angle is 90\u00b0. The\npost shutin pressure decline and G dp/dG plots are shown in Figure 4 for different values of intersection"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9422-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 5, "chroma:document": "post shutin pressure decline and G dp/dG plots are shown in Figure 4 for different values of intersection\nangle. It can be observed in this figure that the first signature on the G dp/dG curve has shifted to the right\nindicating a larger closure time for the natural fracture and a lower closure pressure. This is, in fact, due to\nthe lower normal stresses on the natural fracture in the second and third cases. It is also interesting to notice\nthat the second signature has disappeared in the last case with the lowest intersection angle. It appears that\nbecause 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9468-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 6, "chroma:document": "SPE-194348-MS 7\n4072 psi, respectively) the hydraulic fracture signature is overshadowed by that of the natural fracture or\nthey are both combined to form a larger signature.\nFigure 4\u2014Comparison between the pressure response the the G\ndp/dG plots for HF-NF pairs with different angle of intersection.\nFracture stiffness\nThis example shows the impact of normal fracture stiffness on the post-shutin pressure profile and the\npressure derivative Gdp/dG. Figure 5  compares the pressure profile and its semilog derivate for a HF-NF\nset with different stiffness values. The angle of intersection is 90\u00b0 and the rest of the parameters are similar\nto those used in the base case example. It can be seen in this figure that the higher stiffness results in a higher\nrate of pressure drop once the natural fracture closes (i.e., p < \u03c3 n, NF). Hence, the set with higher stiffness\nhas a more pronounced stiffness signatures as compared to the softer set. Identifying the stiffness signatures"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a94b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 6, "chroma:document": "has a more pronounced stiffness signatures as compared to the softer set. Identifying the stiffness signatures\ncould become challenging for softer hydraulic or natural fractures (see the HF signature for the softer case\nmarked by a circle) which limits the application of the system compliance/stiffness method.\nFigure 5\u2014Pressure and derivative comparison for HF-NF sets with different normal stiffness.\nNatural fracture sets\nThe pressure transiet could be different in the presence of multiple natural fractures. This example explores\nthe characteristics of the pressure decline for a hydraulic fracture intersecting two unparallel natural\nfractures. To help envision this problem further, the sequence of fracture closure is shown in Figure 6.\nThe first plot shows that all fractures are open before shutin. The upper right figure shows that the natural\nfracture with 90\u00b0 intersection angle closes first while the HF and the second NF remain open. This is due to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9508-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 6, "chroma:document": "fracture with 90\u00b0 intersection angle closes first while the HF and the second NF remain open. This is due to\nthe 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a954e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 7, "chroma:document": "8 SPE-194348-MS\nfracture undergoes closure partially on one wing as shown in the lower left figure. This wing which makes a\nsharper angle with the HF experiences more induced compression from the HF and therefore closes earlier\nthan the rest of second NF. Finally, being subject to minimum horizontal stress, the hydraulic fracture is\nthe last one to close.\nFigure 6\u2014Closure sequence for a set of unparallel natural fractures and a hydraulic fracture. (1) all\nfractures are open before shutin. (2) the natural fracture which makes a 90\u00b0 angle with the HF closes first\ndue to the higher normal stress on its plane. (3) the second NF closes partially on one wing as a result\nof higher compression (stress shadow) caused by the HF, and (4) the HF is the last fracture to close.\nFigure 7  shows the post-shutin pressure decline and G dp/dG for this example. It can be observed in\nthis figure that the derivative shows an early jump and change of slope (blue circle and arrow) which is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a959e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 7, "chroma:document": "this figure that the derivative shows an early jump and change of slope (blue circle and arrow) which is\nassociated with the change of the system stiffness upon the closure of the first natural fracture. The second\nsignature (green circle and arrow) shows the partial closure of one wing of the second natural fracture where\nhigher compression is induced by the HF. The last signature which corresponds to the closure of the HF is\nnot as pronounced as the previous ones considering that the HF normal stiffness is set to a lower value than\nthat of the NFs. The tangent method yields a closure pressure of 3900 psi which is 100 psi below its input\nvalue 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a95e4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 8, "chroma:document": "SPE-194348-MS 9\nFigure 7\u2014Pressure and semilog G derivative for the set of unparallel natural fractures.\nField example\nA field example is shown in this section to highlight the charactaristics of the pressure decline and the\nsemilog pressure derivate obtained from a field test. The fracture injection test is conducted in shale by\npumping 22 BBLs of water. The injection test is followed by an extended shutin period. Figure 8-a shows\nthe pressure profile for this test. Pressure decline and its semilig derivative are plotted against G-time for\nthis test in Figure 8-b . It can be observed in this figure that the fracture closure process does not show signs\nof pressure dependent leakoff (PDL) behavior and the before-hump portion of the Gdp/dG curve follows\na linear trend. Moreover, there is not any noticeable changes of slope or spikes before the hump to signify\nchanges in the system stiffness. The field data is used to obtain the pressure decline and Gdp/dG using"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a965c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 8, "chroma:document": "changes in the system stiffness. The field data is used to obtain the pressure decline and Gdp/dG using\nthe compliance/stiffness approach. A relatively low normal stiffness of 0.09 Mpsi/ft is assumed for this\nexample. It can be seen in Figure 9 that Gdp/dG shows a sudden change of slope even for a soft fracture.\nThis signature is, however, not observed in the field data. This, in fact, indicates that the fracture closure\nmechanism may differ from what is assumed in the system stiffness/compliance method. Alternatively, the\nabsence of stiffness signatures in the field case shows that the closure of the hydraulic fracture, in this case,\ndoes not contribute to the changes of system stiffness.\nFigure 8\u2014(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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a96ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 9, "chroma:document": "10 SPE-194348-MS\nFigure 9\u2014Gdp/dG obtained from the compliance/stiffness method using field data.\nDiscussion and Conclusions\nA fully 3D coupled HF-NF simulator is used in this paper to shed light on the pressure transient of hydraulic\nfracture in the presence of natural fractures. Our model is based on a 3D displacement discontinuity method\nfor the rock/fracture deformation and finite elements method for the fluid flow. Our results indicate that\nthe pressure profile and the semilog G derivatives differ from that of conventional hydraulic fractures. The\nchange of slope in the pressure profile as a result of the changes of the system stiffness translates into\ndistinct signatures on the G-function plot. Having said that, care should be taken when interpreting the\nclosure pressure as these jumps and changes of slope on the Gdp/dG could cause erronesous interpretations.\nAs outlined in the simulations, the signature for the natural fracture closure could be wrongly picked as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a96fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 9, "chroma:document": "As outlined in the simulations, the signature for the natural fracture closure could be wrongly picked as\nthe closure pressure. Morever, it is often a difficult task to distinguish between actual stiffness signatures\nand the noise in the data in field cases. It was shown in the field example that Gdp/dG shows nearly ideal\nleakoff behavior and follows a straightline before the hump. The Discrepency between the simulation results\nand the actural field example (absence of stiffness signatures in the field case) could be interpreted in two\nways: 1) the closure mechanism assumed in the stiffness/compliance method differs from the actual fracture\nclosure mechanism or 2) the stiffness of the hydraulic fracture is too low to cause any significant changes in\nthe system stiffness after closure. That said, the stiffness signatures that exist in the diagnostic plots might\nbe caused by the closure of other features such as intersected natural fracture. Using conventional tangent"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9742-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 9, "chroma:document": "be caused by the closure of other features such as intersected natural fracture. Using conventional tangent\nmethod or log-log diagnostic plots along with the stiffness/compliance method could help identifying the\nclosure pressure more confidently when it comes to naturally fractured reservoirs.\nReferences\nAsgian, M. I. ( 1988 , January 1). A numerical study of fluid flow in a deformable, naturally fractured reservoir: The\ninfluence of pumping rate on reservoir response . American Rock Mechanics Association .\nBarree, R. D. , & Mukherjee, H.  (1996 , January 1). Determination of Pressure Dependent Leakoff and Its Effect on Fracture\nGeometry . Society of Petroleum Engineers. doi: 10.2118/36424-MS.\nCastillo, J. L.  (1987, January 1). Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff.\nSociety of Petroleum Engineers. doi:10.2118/16417-MS ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9792-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 9, "chroma:document": "Society of Petroleum Engineers. doi:10.2118/16417-MS .\nCraig, D. P., Eberhard, M. J., Odegard, C. E., Ramurthy, M., & Mullen, R. ( 2002 , January 1). Permeability, Pore Pressure,\nand Leakoff-Type Distributions in Rocky Mountain Basins. Society of Petroleum Engineers. doi:10.2118/75717-MS.\nCrouch, S. L., & Starfield, A. M. ( 1983 ). Boundary element methods in solid mechanics: With applications in rock\nmechanics and geological engineering : Winchester, Massachusetts.\nGhassemi, A. , & Tao, Q.  (2016 ). Thermo-poroelastic effects on reservoir seismicity and permeability change.\nGeothermics , 63, 210\u2013224.\nGoodman, R. E., Taylor, R. L., & Breeke, T. L. ( 1968 ). A model for the mechanics of jointed rocks. ASCE Journal of\nSoil Mechanics Found. Div, 94, 637\u2013659.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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a97e2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 10, "chroma:document": "SPE-194348-MS 11\nKamali, A. , & Ghassemi, A.  (2018). Analysis of injection-induced shear slip and fracture propagation in geothermal\nreservoir stimulation . Geothermics , 76, 93\u2013105.\nKamali, A. , & Ghassemi, A. ( 2017 , August). Reservoir Stimulation in Naturally Fractured Poroelastic Rocks. In 51st US\nRock Mechanics/Geomechanics Symposium . American Rock Mechanics Association.\nKumar, D. , & Ghassemi, A.  (2015 , November). 3D simulation of multiple fracture propagation from horizontal wells. In\n49th US Rock Mechanics/Geomechanics Symposium . American Rock Mechanics Association.\nKumar, D., & Ghassemi, A.  (2016). A three-dimensional analysis of simultaneous and sequential fracturing of horizontal\nwells . Journal of Petroleum Science and Engineering, 146, 1006\u20131025.\nLove, A. E. H.  (2013 ). A treatise on the mathematical theory of elasticity . Cambridge university press."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9828-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 10, "chroma:document": "Love, A. E. H.  (2013 ). A treatise on the mathematical theory of elasticity . Cambridge university press.\nMayerhofer, M. J., & Economides, M. J. ( 1997 , November 1). Fracture-Injection-Test Interpretation: Leakoff Coefficient\nvs. Permeability . Society of Petroleum Engineers. doi: 10.2118/28562-PA.\nMcClure, M. W. , Jung, H., Cramer, D. D. , & Sharma, M. M. (2016, August 1). The Fracture-Compliance Method for\nPicking Closure Pressure from Diagnostic Fracture-Injection Tests (see associated supplementary discussion/reply).\nSociety of Petroleum Engineers. doi: 10.2118/179725-PA.\nMukherjee, H. , Larkin, S., & Kordziel, W.  (1991 , January 1). Extension of Fracture Pressure Decline Curve Analysis to\nFissured Formations . Society of Petroleum Engineers. doi: 10.2118/21872-MS.\nNolte, K. G. ( 1979 , January 1). Determination of Fracture Parameters from Fracturing Pressure Decline. Society of\nPetroleum Engineers. doi: 10.2118/8341-MS."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9878-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 10, "chroma:document": "Petroleum Engineers. doi: 10.2118/8341-MS.\nRaaen, A. M. , Horsrud, P. , Kj\u00f8rholt, H. , & \u00d8kland, D.  (2006). Improved routine estimation of the minimum horizontal\nstress component from extended leak-off tests. International Journal of Rock Mechanics and Mining Sciences, 43(1),\n37\u201348.\nRaaen, A. M. , Skomedal, E. , Kj\u00f8rholt, H., Markestad, P., & \u00d8kland, D. (2001). Stress determination from hydraulic\nfracturing tests: the system stiffness approach. International Journal of Rock Mechanics and Mining Sciences, 38(4),\n529\u2013541.\nSafari, R. , & Ghassemi, A.  (2015 ). 3D thermo-poroelastic analysis of fracture network deformation and induced micro-\nseismicity in enhanced geothermal systems . Geothermics, 58, 1\u201314.\nTao, Q. , Ghassemi, A. , and Ehlig-Economides, C.E.  2011. A fully coupled method to model fracture permeability change\nin naturally fractured reservoirs . Int. J. Rock Mech. & Min. Sci., 48( 2), 259\u2013268."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a98be-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-194348-ms.pdf", "page": 10, "chroma:document": "in naturally fractured reservoirs . Int. J. Rock Mech. & Min. Sci., 48( 2), 259\u2013268.\nTimoshenko, S. P. , & Goodier, J. N. Theory of Elasticity, (1970), 433. McGraw-Hill.\nVandamme, L. , & Curran, J. H.  (1989 ). A three-dimensional hydraulic fracturing simulator. International Journal for\nNumerical Methods in Engineering , 28(4), 909\u2013927.\nWitherspoon, P. A., Wang, J. S., Iwai, K. , & Gale, J. E. ( 1980). Validity of cubic law for fluid flow in a deformable rock\nfracture . Water resources research , 16(6), 1016 \u20131024 .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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a990e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 0, "chroma:document": "See discussions, st ats, and author pr ofiles f or this public ation at : https://www .researchgate.ne t/public ation/313878526\nA New Analysis Technique for Interpreting Injection/Shut-in Tests\nArticle  \u00b7 Mar ch 2016\nCITATIONS\n5READS\n273\n3 author s:\nFahd Siddiqui\nIllumina\n27 PUBLICA TIONS \u00a0\u00a0\u00a0205 CITATIONS \u00a0\u00a0\u00a0\nSEE PROFILE\nMohamed Y Soliman\nUniv ersity of Houst on\n395 PUBLICA TIONS \u00a0\u00a0\u00a03,669  CITATIONS \u00a0\u00a0\u00a0\nSEE PROFILE\nAkif Ibr agimo v\nTexas T ech Univ ersity\n172 PUBLICA TIONS \u00a0\u00a0\u00a0966 CITATIONS \u00a0\u00a0\u00a0\nSEE PROFILE\nAll c ontent f ollo wing this p age was uplo aded b y Fahd Siddiqui  on 21 April 2017.\nThe user has r equest ed enhanc ement of the do wnlo aded file."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a995e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 1, "chroma:document": "A New Analysis Technique for Interpreting Injection/Shut-in Tests\nThis paper presents an analysis technique for interpreting fracture treating pressures. The literature contains various models that give rise to analysis \ntechniques, 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. \nThe first school of thought considers the fluid leak-off to be a property of the fluid-rock interaction system. It relies on Carter\u2019s equation (Howard \nand Fast 1957, Carter 1957) to describe leak-off and is based on Howard and Fast\u2019s experiments. The disadvantage is its inadequacy to describe the phenomenon if the conditions of Howard and Fast\u2019s experiment are not strictly met during the injection process.\nNordgren (Nordgren 1972), using mass balance, defined the following differential equation for the flow down a fracture:\n(1)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a99a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 1, "chroma:document": "Nordgren (Nordgren 1972), using mass balance, defined the following differential equation for the flow down a fracture:\n(1)\nIt 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 \nthe fluid loss coefficient defined as: \n(2)\nMost 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: \n(3)\nHowever, 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 \nspurt loss."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a99f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 1, "chroma:document": "spurt loss.\nBased 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 \nthe 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.\nMayerhofer,  et al., (1991) and Mayerhofer & Economides (1993) described the leak-off based on the square root of time solution as will be shown later \nin 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 \nAbstract"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9a44-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 1, "chroma:document": "Abstract\nThe problem of diagnostic fracture injection fall-off tests is considered. A new model is constructed from basic fluid flow and material balance \nequations and making some assumptions about fracture propagation. The resulting equations are solved analytically. \nA thorough analysis methodology has been developed from these solutions to interpret fracture injection pressure tests. Presented method can \nestimate the fracture half-length and height product ( xf.hf) and the closure pressure. The proposed analysis technique is limited to after shut-in and \nbefore fracture closure period of the test.\nThe developed model has been validated against two actual field injection data. The datasets serve to augment the demonstration of the application \nsteps. Peer Reviewed"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9a8a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 2, "chroma:document": "(4)\nIn 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, \nValko and Economides, (1999) offered a graphical form of the Mayerhofer\u2019s method by defining the variables x1,n, x2,n and yn. Since it is not easy to \nestablish the leak-off rates ( qloss,j) at each time step, Valko and Economides considered them to be constant and equal to an \u201capparent\u201d leak-off rate. \nIn 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.\nLamei and Soliman (2014) relied on the linear diffusivity equation to determine leak-off, instead of Carter\u2019s (1957) equation. However, they presented \na long time solution which does not work for all cases. This fact becomes evident when applying their technique. \nProblem Analysis"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9ada-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 2, "chroma:document": "a long time solution which does not work for all cases. This fact becomes evident when applying their technique. \nProblem Analysis \nThis study subscribes to the second school of thought and instead of relying on the discrete steps of the Mayerhofer\u2019s 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 ).\nEquation 5  is the well-known partial differential equation used to describe the linear leak-off. This equation governs how the leaking fluid will move \nthrough the porous media and gives the resulting pressure distribution versus time.\n(5)\nI\nnner Boundary Condition\nThe inner boundary condition is derived starting from mass balance and accounts for injection followed by shut-in. This model relies on Equation 7"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9b2a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 2, "chroma:document": "The inner boundary condition is derived starting from mass balance and accounts for injection followed by shut-in. This model relies on Equation 7 \n(K. G. Nolte 1986) to describe the width change due to consequent pressure changes. The complete derivation of this equation is given in Appendix \nA. The final form of the fluid loss equation is obtained as follows: \n(6)\nW\nhere U(t - t i) is the unit step-function to account for injection rate and shut-in, at time t i. \n(7)\n(8)\nE\nquation 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 \nwidth 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."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9b7a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 2, "chroma:document": "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 \ncase setting the change in fracture volume to zero (or c\nf = 0) results in the conventional boundary condition of constant rate injection followed by \nshut-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 \nsquare root of time equation for this case too.\n(9)\nTh\ne 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 \nmobility ( \u03bb) is zero. Based on this, the boundary condition (Equation 6 ) reduces to the following:\n(10)\nF\nrom the definition of width (Equation 7 ), and integrating, the above equation can be written as:\n(11)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9bca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 3, "chroma:document": "Equation 11 is consistent with material balance and shows that the cumulative injected volume (left-hand side) is equal to the created fracture volume \n(right-hand side).\nThe 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\n1.  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  \ninto the formation (Equation 6 ). This assumption limits the applicability to the shut-in period.\n2.  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\nstiffness) while the fracture area remains constant, which is a reasonable assumption.\n3.  Since the fracture volume is small and the fluid compressibility is small, their product can be neglected. Hence the fluid storage/compressibility"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9c38-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 3, "chroma:document": "effects in the wellbore and the fracture can be neglected.\n4. The width is a function of net pressure defined by Equation 7 .\nModel Assumptions\nFollowing assumptions were considered for using the linear diffusivity equation and to develop the overall model:\n1. Homogeneous and isotropic porous medium.\n2. Negligible gravity effects.\n3. The fluid is leaking off linearly into the porous media.\n4. Isothermal conditions prevail throughout the injection period within the porous medium.\n5. Fluid has small, constant compressibility in the porous media.\n6. Fracturing fluid has a comparable mobility with the formation fluid.\n7. Fracturing fluid behaves like a Newtonian fluid.\n8. The fracture has an infinite conductivity, i.e. no pressure drop inside the fracture.\nAnalytical SolutionThe analytical solution to the problem described by Equations 6 and 5 was obtained using the Laplace transform. Analytical inversion was carried out"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9c88-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 3, "chroma:document": "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 \nof the F-function.\n(12)\n(13)\nM\nathematical and Physical Inspection\nMathematical 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."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8a9cce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 3, "chroma:document": "Because setting the fracture stiffness to zero ( c\nf = 0) results in a conventional boundary condition of constant rate injection followed by shut-in, setting \ncf = 0 should also reduce the solution presented in Equations 12 and 13 to conventional square root time equation. Careful examination shows that in \nfact that is the case and setting c f = 0 results in Equation 14.\n(14)\nC\nonsequently, this leads to a deeper understanding of the solution in Equations 12 and 13. The first part of the F-function (Equation 13) describes \nthe 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa03e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 3, "chroma:document": "(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."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa0fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 4, "chroma:document": "Solution Validation\nThe solution was validated by a three prong test.\n1. The Laplace space solution was numerically inverted using Stehfest\u2019s algorithm (Stehfest 1970) and found to be matching the analytical solution.\n2.  The equation along with its boundary condition was solved numerically using a commercial finite element solver and found to be matching the \nanalytical solution.\n3. The resulting analysis methodology was applied to real field data and yields reliable results.\nAnalysis Methodology\nA 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\nf). \nKnowing these two parameters, the process described below will aid estimating the fracture half-length times height product (A = 4x fhf). The mobility"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa17e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 4, "chroma:document": "of the fracturing fluid can be estimated by the after closure analysis (Soliman, et al. 2005) if it is not known a priori. \nFrom 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 \nzero. Based on this, the methodology can be summarized in the following steps:Step 1 : Convert the time to F-function described by Equation 13\nStep 2\n:  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 \nin reverse direction.\nStep 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 \nline manifests itself when the F.dp /dF vs. F plot superimposes on (p - p r) vs. F. \nStep 4 : Find the slope (m) of the straight line.\nStep 5 : Using the slope find the area of the fracture:\n(15)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa200-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 4, "chroma:document": "Step 4 : Find the slope (m) of the straight line.\nStep 5 : Using the slope find the area of the fracture:\n(15)\nStep 6 : Closure pressure can be obtained from the late time deviation of data from the straight line. \nUncertainty in Analysis\nLike all pressure transient analysis problems, the quality of analysis depends on the quality and accuracy of the input parameters: fracture height, Y oung\u2019s 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.\nApplication to field data"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa282-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 4, "chroma:document": "Application to field data\nThe above method was applied to two real field injection shut-in tests dubbed A-1 and A-2.\nExample A-1\nFigure 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 \nneeded for analysis.\nFigure 1 . Injection pressure and rate data for Example A-1.\nThe 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 \n(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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa304-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 5, "chroma:document": "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 \non 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 \nsame line fits through the derivative as well. A G-function plot is also demonstrated in Figure 3.\nFigure 2 . F-function plot for A-1.\nAnalysis 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa386-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 5, "chroma:document": "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 \u201csufficient\u201d 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.\nFigure 3 . G-function plot for A-1.Table 1 . Input parameters for Example A-1.\nk/\u03bc 2.5E-6 m2/MPa.s 2.5 md.cp-1\ncf 1.3E-3 m.MPa-13e-5 ft.psi-1\n\u03c6.ct 1.4E-3 MPa-19.5E-6 psi-1\npr 25 MPa 3630 psi\nTable 2 . Results of analysis for Example A-1.\nSlope \u0017\u0017 MPa \u001a\u0016\u00170 psi\nArea 620 m26720 ft2"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa408-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 5, "chroma:document": "\u03c6.ct 1.4E-3 MPa-19.5E-6 psi-1\npr 25 MPa 3630 psi\nTable 2 . Results of analysis for Example A-1.\nSlope \u0017\u0017 MPa \u001a\u0016\u00170 psi\nArea 620 m26720 ft2\nxf.hf 155 m21680 ft2\nClosure Stress 47 MPa 6815 psi\np-pr=66 F"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa48a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 6, "chroma:document": "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 \nclose agreement within 5% of this technique.\nExample A-2\nFigure 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 \nminutes. Table 1 summarizes the essential input parameters needed for analysis.\nThe 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 \neasily from the alignment of the derivative plot with the pressure difference plot. A straight line fit on the pressure difference, through this region, and \npassing through the origin yields an excellent R2 of 0.999. A G-function plot is also demonstrated in Figure 6.\nFigure 4 . Injection pressure and rate data for Example A-2."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa50c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 6, "chroma:document": "Figure 4 . Injection pressure and rate data for Example A-2.\nAnalysis 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"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa58e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 6, "chroma:document": "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.\nFigure 5 . F-function plot for A-2.Table 3 . Input parameters for Example A-2.\nk/\u03bc 1E-\u0019 m2/MPa.s 0.\u00111 md.cp-1\ncf 1.3E-3 m.MPa-13e-5 ft.psi-1\n\u03c6.ct 2.8E-3 MPa-11.9E-5 psi-1\npr 8\u0011\u000f\u0017 MPa 11\u001790 psi"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa610-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 7, "chroma:document": "The G-function plot confirms the early-time deviation, however fracture closure is not unambiguously evident. An approximate value of 85 MPa was \npicked from the plot which matches the F-function analysis result.\nFigure 6 . G-function plot for A-2.\nConclusion\nThe 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\u2019s 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.\nNomenclature\nA  = F racture Area, m2\nAc  = Cr oss-sectional area of fracture, m2\ncf  =  F racture stiffness or the inverse of fracture \ncompliance, m.Pa-1\ncfluid-loss   = Fl uid loss coefficient, m.s-1/2\ncfluid  = Fl uid compressibility, Pa-1"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa692-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 7, "chroma:document": "compliance, m.Pa-1\ncfluid-loss   = Fl uid loss coefficient, m.s-1/2\ncfluid  = Fl uid compressibility, Pa-1\nct  = T otal compressibility, Pa-1\nE'  = P lane strain modulus, Pa [ E'= E/(1-\u03bd2)]\nF  = F -Function defined by Equation 13\nhf  = F racture height, m\nk  = P ermeability, m2 [1 md=9.86923x10-15 m2]\nL  = L aplace transform\nL-1  = I nverse Laplace transform\n\u1e41  = M ass flow rate (kg/s)\np  =  M easured pressure at wellbore, Pa  \n[1 psi = 6894.76 Pa]\npc  = C losure stress, Pa [1 psi = 6894.76 Pa]\npD  = Dim ensionless pressure\npr  = R eservoir pressure, Pa [1 psi = 6894.76 Pa]\nq  = I njection rate, m3/s [1 stb/d = 1.84x10-6]\nqloss  = R ate of fluid leak-off, m3/s\nR0  = Fi lter-cake resistance, Pa.s/m\nRD  = Dim ensionless filter-cake resistancerf  = R adius of fracture, m [Radial Geometry]\nt  = T ime, s\ntD  = Dim ensionless time\nti  = I njection time, s\ntiD  = Dim ensionless injection time\nu  = L aplace parameter\nU  = U nit step-function\nv  = V elocity, m/s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa70a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 7, "chroma:document": "ti  = I njection time, s\ntiD  = Dim ensionless injection time\nu  = L aplace parameter\nU  = U nit step-function\nv  = V elocity, m/s\nw  = F racture width, m [1 ft = 0.3048 m]\nx  =  Fl uid flow direction orthogonal to fracture area, \nm [1 ft = 0.3048 m]\nxD  = Dim ensionless distance\nxf  = F racture half-length, m\ny  =  Fl uid flow direction along the fracture length,  \nm [1 ft = 0.3048 m]\n\u03bb  = M obility, m2/Pa.s [ \u03bb = k/\u03bc]\n\u03bc  = V iscosity, Pa.s [1 cp = 0.001 Pa.s]\n\u03bd  = P oisson\u2019s ratio\n\u03c1  = Fl uid density, kg/m3 [1 lb/ft3 = 16 kg/m3]\n\u03c4  = A lternate time, s\n\u03c4D  = D ummy integration variable\n\u03c6  = P orosity\n \n Table 4 . Results of analysis for Example A-2.\nSlope \u0014\u0012\u0017 MPa 45\u001900 psi\nArea 1\u001a\u0017\u0016 m2\u001312\u0011\u0011 ft2\nxf.hf \u0015\u001a\u0011 m25\u0013\u001a\u0011 ft2\nClosure Stress 85 MPa 12335 psi"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8aa78c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 8, "chroma:document": "References\nCarter, R. D. 1957. \u201c\u201dDerivation of the General Equation for Estimating the Extent of the Fractured Area\u201d Appendix to: \u201cOptimum Fluid Characteristics  \n f or Fracture Extension\u201d by G. C. Howard and C. R. Fast. \u201d Mid-Continent District, Division of Production. Tulsa: API-57-261. 261-270.\nHoward, G. C., and C. R. Fast. 1957. \u201cOptimum Fluid Characteristics for Fracture Extension. \u201d Mid-Continent District, Division of Production. Tulsa:  \n AP I-57-261. 261-270.\nLamei, C. H., and M. Y . Soliman. 2014. \u201cNew Before Closure Analysis Model for Unconventional Reservoirs. \u201d SPE/EAGE European Unconventional  \n C onference. Vienna: SPE 167790-MS. doi:http://dx.doi.org/10.2118/167790-MS.\nMayerhofer, M. J., and M. J. Economides. 1993. \u201cPermeability Estimation From Fracture Calibration Treatments. \u201d SPE Western Regional Meeting.  \n A laska: SPE 20639-MS. doi:10.2118/26039-MS."}


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id: 6b8aa804-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 8, "chroma:document": "A laska: SPE 20639-MS. doi:10.2118/26039-MS.\nMayerhofer, M. J., M. J. Economides, and K. G. Nolte. 1991. \u201c An Experimental and Fundamental Interpretation of Fracturing Filtercake Fluid Loss. \u201d  \n S PE 68th ATCE. Dallas: SPE 22873-MS. doi:http://dx.doi.org/10.2118/22873-MS.\nNolte, K G. 1979. \u201cDetermination Of Fracture Parameters From Fracturing Pressure Decline. \u201d SPE 54th Annual Technical Conference. Las Vegas: SPE  \n 8341-MS. do i:http://dx.doi.org/10.2118/8341-MS.\nNolte, K. G. 1986. \u201c A General Analysis of Fracturing Pressure Decline With Application to Three Models. \u201d SPE Formation Evaluation (SPE 12941-PA)  \n 571-583. do i:http://dx.doi.org/10.2118/12941-PA.\nNordgren, R. P . 1972. \u201cPropagation of a Vertical Hydraulic Fracture. \u201d SPE 45th Annual Conference. Houston: SPE 3009-PA. doi:http://dx.doi.  \n org/10.2118/3009-PA.\nSoliman, M. Y ., D. P . Craig, K. M. Bartko, Z. Rahim, and Z. M. Adams. 2005. \u201cPost-Closure Analysis to Determine Formation Permeability, Reservoir"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 8, "chroma:document": "Soliman, M. Y ., D. P . Craig, K. M. Bartko, Z. Rahim, and Z. M. Adams. 2005. \u201cPost-Closure Analysis to Determine Formation Permeability, Reservoir  \n P ressure, Residual Fracture Properties. \u201d SPE Middle East Oil and Gas Show and Conference. Bahrain: SPE 93419-MS. doi:10.2118/93419-MS.\nStehfest, H. 1970. \u201cNumerical Inversion of Laplace Transforms. \u201d Communication of the ACM 13 47-48. doi:http://dx.doi.org/10.1145/361953.361969.\nValko, P . P ., and M. J. Economides. 1999. \u201cFluid-leakoff Delineation in High-permeability Fracturing. \u201d SPE Journal (SPE 56135-PA). doi:http://dx.doi.  \n org/10.2118/56135-PA.\nAppendix A: Derivation of Inner Boundary Condition\nFor x = 0,\n  \n    \n Recognizing:"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 9, "chroma:document": "Since fracture volume is small relative to the total injected volume, and compressibility is small, the compressibility term can be neglected.\nFor 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 \nalong the hinge at the tip. By using the step-function U:\n \nAppendix B: Solution of Equations 5 and 6\nInner Boundary Condition: \nInitial Condition:  \n \nConsider the following dimensionless variables:\nWriting the equations in dimensionless variables:\nInner Boundary Condition: \nInitial Condition:  \nOuter Boundary Condition:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 10, "chroma:document": "Applying Laplace Transform to the inner boundary condition:\nApplying Laplace Transform to the partial differential equationSolving the above differential equation and using the initial and outer boundary conditions\n  \nAfter substituting from outer boundary condition\nUsing convolution theorem to invert the above expression\nAfter simplification and removing the step-function:\nCarrying out the integrals and simplifying:\nSubstituting the definitions of dimensionless variables:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/Fahd paper.pdf", "page": 11, "chroma:document": "View publication stats"}


