Determination of Fracture Conductivity in Tight Formations with Non-Darcy Flow Behavior

Document Type
Journal Paper
Authors
Feng Zhang (University of Regina) | Daoyong (Tony) Yang (University of Regina)
Document ID
SPE-162548-PA
Source
SPE Journal
Volume
19
Issue
01
Pages
34 - 44
Publication Date
2013
Publisher
Society of Petroleum Engineers
Language
English
DOI
http://dx.doi.org/10.2118/162548-PA
ISSN
1086-055X
Copyright
2013. Society of Petroleum Engineers
Keywords
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Summary

In this paper, a mathematical model has been developed and successfullyapplied to accurately determine the fracture conductivity in tight formationswith non-Darcy flow behavior. A new non-Darcy flow number is first defined toaccount for the effect of characteristic length in a hydraulic fracture. Asemianalytical method is then applied to solve the newly formulatedmathematical model by discretizing the fracture into small segments, assumingthat there exists unsteady flow between the adjacent segments. The newlydeveloped model has been validated by simplifying it to the traditionalForchheimer (i.e., non-Darcy) model and by performing numerical simulation witha reservoir simulator as well. The pressure response and its correspondingderivative type curves have been reproduced to examine non-Darcy flow behaviorunder different fracture conductivities. Both relative minimum permeability andcharacteristic length are found to impose a negative effect on the fractureconductivity. Compared with relative minimum permeability, characteristiclength is a strong function dominating the non-Darcy flow behavior in thefractures. It is obvious that the fracture conductivity can be accuratelydetermined when non-Darcy flow behavior in the fracture network is taken intoaccount.

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References

Al-Otaibi, A.M. and Wu, Y.S. 2011. An Alternative Approach to ModelingNon-Darcy Flow for Pressure Transient Analysis in Porous and FracturedReservoirs. Paper SPE 149123 presented at the SPE/DGS Saudi Arabia SectionTechnical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 15-18 May. http://dx.doi.org/10.2118/149123-MS.

Andrade, J.S. Jr., Almeida, M.P., Medes Filho, J., et al. 1997. Fluid Flowthrough Porous Media: The Role of Stagnant Zones. Phys. Rev.Lett.  79 (20): 3901-3904. http://dx.doi.org/10.1103/PhysRevLett.79.3901.

Barree, R.D. and Conway, M.W. 2004. Beyond Beta Factors: A Complete Modelfor Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media. Paper SPE89325 presented at the SPE Annual Technical Conference and Exhibition,Houston, Texas, 26-29 September. http://dx.doi.org/10.2118/89325-MS.

Cinco-Ley, H. and Samaniego-V., F. 1981. Transient Pressure Analysis forFractured Wells. J. Pet Tech 33 (9): 1749-1766. http://dx.doi.org/10.2118/7490-PA.

Cinco-Ley, H., Samaniego-V., F. and Domínguez A, N. 1978. Transient PressureBehavior for a Well with a Finite-Conductivity Vertical Fracture. SPE J. 18 (4): 253-264. http://dx.doi.org/10.2118/6014-PA.

Geertsma, J. 1974. Estimating the Coefficient of Inertial Resistance inFluid Flow Through Porous Media. SPE J.  14 (5): 445-450. http://dx.doi.org/10.2118/4706-PA.

Gill, J.A., Ozkan, E. and Raghavan, R. 2003. Fractured-Well-Test Design andAnalysis in the Presence of Non-Darcy Flow. SPE Res Eval &Eng  6 (3): 185-196. http://dx.doi.org/10.2118/84846-PA.

Guppy, K.H., Cinco-Ley, H., Ramey, H.J. Jr., et al. 1982a. Non-Darcy Flow inWells with Finite-Conductivity Vertical Fractures. SPE J. 22 (5): 681-698. http://dx.doi.org/10.2118/8281-PA.

Guppy, K.H., Cinco-Ley, H. and Ramey H.J. Jr. 1982b. Pressure BuildupAnalysis of Fractured Wells Producing at High Flow Rates. J. PetTech  34 (11): 2655-2666. http://dx.doi.org/10.2118/10178-PA.

Hill, R.J., Koch, D.L. and Ladd, A.J.C. 2001. Moderate Reynolds Number Flowsin Ordered and Random Arrays of Spheres. J. Fluid Mech. 448: 243-278. http://dx.doi.org/10.1017/S0022112001005936.

Holditch, S.A. and Morse, R.A. 1976. The Effects of Non-Darcy Flow on theBehavior if Hydraulically Fractured Gas Wells. J. Pet Tech 28 (10): 1169-1179. http://dx.doi.org/10.2118/5586-PA.

Lai, B., Miskimins, J.L. and Wu, Y.S. 2012. Non-Darcy Porous Media FlowAccording to the Barree and Conway Model: Laboratory and Numerical ModelingStudies. SPE J.  17 (1): 70-79. http://dx.doi.org/10.2118/122611-PA.

Lee, W.J. and Holditch, S.A. 1982. Application of Pseudotime to Buildup TestAnalysis of Low-permeability Gas Wells with Long-Duration Storage Distortion.J. Pet Tech  34 (12): 2877-2887. http://dx.doi.org/10.2118/9888-PA.

Manrique, M., Muci, V.E. and Gurfinkel, M.E. 2007. EOR Field Experiences inCarbonate Reservoirs in the United States. SPE Res Eval & Eng 10 (6): 667-686. http://dx.doi.org/10.2118/100063-PA.

Manrique, M., Thomas, C., Ravikiran, R., et al. 2010. EOR: Current Statusand Opportunities. Paper SPE 130113 presented at the SPE Improved Oil RecoverySymposium, Tulsa, Oklahoma, 24-28 April. http://dx.doi.org/10.2118/130113-MS.

Martins, J.P., Milton-Tayler, D. and Leung, H.K. 1990. The Effects ofNon-Darcy Flow in Propped Hydraulic Fractures. Paper SPE 20709 presented at theSPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 23-26April. http://dx.doi.org/10.2118/20709-MS.

Miskimins, J.L., Lopez-Hernandez, H.D. and Barree, R.D. 2005. Non-Darcy Flowin Hydraulic Fractures: Does It Really Matter? Paper SPE 96389 presented at theSPE Annual Technical Conference and Exhibition, Dallas, Texas, 9-12 October. http://dx.doi.org/10.2118/96389-MS.

Ozkan, E. and Raghavan, R. 1991. New Solutions for Well-Test-AnalysisProblems: Part 1-Analytical Considerations. SPE Form Eval 6 (3): 359-368. http://dx.doi.org/10.2118/18615-PA.

Settari, A., Stark, A.J. and Jones, J.R. 2000. Analysis of HydraulicFracturing of High Permeability Gas Wells to Reduce Non-Darcy Skin Effects.J. Cdn. Pet. Tech.  39 (5): 56-63. http://dx.doi.org/10.2118/00-05-04.

Smith, M.B., Bale, A., Britt, L.K., et al. 2004. An Investigation ofNon-Darcy Flow Effects on Hydraulic Fractured Oil and Gas Well Performance.Paper SPE 90864 presented at the SPE Annual Technical Conference andExhibition, Houston, Texas, 26-29 September. http://dx.doi.org/10.2118/90864-MS.

Stanley, H.E. and Andrade J.S. Jr. 2001. Physics of the Cigarette Filter:Fluid Flow through Structures with Randomly-Placed Obstacles. Physica A 295 (1-2): 17-30. http://dx.doi.org/10.1016/S0378-4371(01)00140-6.

Stehfest, H. 1970. Algorithm 368: Numerical Inversion of Laplace Transforms[D5]. Commun. ACM  13 (1): 47-49. http://dx.doi.org/10.1145/361953.361969.

Spivey, J.P. 1984. An Investigation of the Use of Pseudotime in TransientTest Analysis of Gas Wells. PhD dissertation, Texas A&M University, CollegeStation, Texas (1984).

Swami, V., Clarkson, C.R. and Settari, A. 2012. Non-Darcy Flow in ShaleNanopores: Do We Have a Final Answer? Paper SPE 162665 presented at the SPECanadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30October-1 November. http://dx.doi.org/10.2118/162665-MS.

Umnuayponwiwat, S., Ozkan, E. and Pearson, C.M. 2000. Effect of Non-DarcyFlow on the Interpretation of Transient Pressure Response of HydraulicallyFractured Wells. Paper SPE 63176 presented at the SPE Annual TechnicalConference and Exhibition, Dallas, Texas, 1-4 October. http://dx.doi.org/10.2118/63176-MS.

Van Kruysdijk, C.P.J.W. 1988. Semianalytical Modeling of Pressure Transientsin Fractured Reservoirs. Paper SPE 18169 presented at the SPE Annual TechnicalConference and Exhibition, Houston, Texas, 2-5 October. http://dx.doi.org/10.2118/18169-MS.

Vincent, M.C., Pearson, C.M. and Kullman, J. 1999. Non-Darcy and MultiphaseFlow in Propped Fractures: Case Studies Illustrate the Dramatic Effect on WellProductivity. Paper SPE 54630 presented at the SPE Western Regional Meeting,Anchorage, Alaska, 26-27 May. http://dx.doi.org/10.2118/54630-MS.

Zeng, F. and Zhao, G. 2010. The Optimal Hydraulic Fracture Geometry UnderNon-Darcy Flow Effects. J. Pet. Sci. Eng.  72 (1-2):143-157. http://dx.doi.org/10.1016/j.petrol.2010.03.012.