Analyzing Production Data From Hydraulically Fractured Wells: The Concept of Induced Permeability Field
- Authors
- Gorgonio Fuentes-Cruz (Texas A&M University) | Eduardo Gildin (Texas A&M University) | Peter P. Valkó (Texas A&M University)
- DOI
- https://doi.org/10.2118/163843-PA
- Document ID
- SPE-163843-PA
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Reservoir Evaluation & Engineering
- Volume
- 17
- Issue
- 02
- Publication Date
- May 2014
- Document Type
- Journal Paper
- Pages
- 220 - 232
- Language
- English
- ISSN
- 1094-6470
- Copyright
- 2014.Society of Petroleum Engineers
- Disciplines
- 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 2 Well Completion, 4.1.2 Separation and Treating, 5.8.2 Shale Gas, 5.1.1 Exploration, Development, Structural Geology
- Keywords
- exponential or linear permeability field, skin factor, maximum and minimum induced permeabilities, hydraulically fractured well, decline curve analysis
- Downloads
- 3 in the last 30 days
- 844 since 2007
- Show more detail
- View rights & permissions
| SPE Member Price: | USD 10.00 |
| SPE Non-Member Price: | USD 30.00 |
Summary
This work introduces a new model for the production-decline analysis (PDA) of hydraulically fractured wells on the basis of the concept of the induced permeability field. We consider the case when the hydraulic-fracturing operation--in addition to establishing the fundamental linear-flow geometry in the drainage volume--alters the ability of the formation to conduct fluids throughout, but with varying degrees depending on the distance from the main fracture plane. We show that, under these circumstances, the reservoir response departs from the uniform-permeability approach significantly. The new model differs from the once promising group of models that are inherently related to power-law-type variation of the permeability-area product and thus are burdened by a mathematical singularity inside the fracture. The analysis of field cases reveals that the induced permeability field can be properly represented by a linear or exponential function characterized by the maximal induced permeability k0 and the threshold permeability k*. Both these permeabilities are induced (superimposed on the formation) by the hydraulic-fracturing treatment; thus, the model can be considered as a simple, but nontrivial, formalization of the intuitive stimulated-reservoir-volume (SRV) concept. It is quite reasonable to assume that the maximum happens at the fracture face and that the minimum happens at the outer boundary of the SRV. The contrast between maximal and minimal permeability, SR-1/4-k0/k*, will be of considerable interest, and thus, we introduce a new term for it: stimulation ratio (SR). Knowledge of these parameters is crucial in evaluating the effectiveness of today’s intensively stimulated well completions, especially multifractured horizontal wells in shale gas. The approach describes, in a straightforward manner, the production performance of such wells exhibiting transient linear flow and late-time boundary-dominated flow affected also by a skin effect (i.e., by an additional pressure drop in the system characterized by linear dependence on production rate). This work provides the induced-permeability-field model within the single-medium concept, and shows that some features widely believed to require a dual-medium (double-porosity) representation are already present. Advantages and drawbacks related to applying the concept in a dual-medium approach will be discussed in an upcoming work. We present the model and its analytical solution in Laplace space. We provide type curves for decline-curve analysis, closed-form approximate solutions in the time domain, field examples, and practical guidelines for the analysis of commonly occurring production characteristics of massively stimulated reservoirs.
| File Size | 1000 KB | Number of Pages | 13 |
References
Al-Hussainy, R., Ramey H.J. Jr., and Crawford, P.B. 1966. The Flow of Real Gases Through Porous Media. J. Pet Tech 18 (5): 624–636. http://dx.doi.org/ 10.2118/1243-A-PA.
Barker, J.A. 1988. A Generalized Radial Flow Model for Hydraulic Tests in Fractured Rock. Water Resources Res. 24 (10): 1796–1804. http://dx.doi.org/10.1029/WR024i010p01796.
Beier, R.A. 1994. Pressure-Transient Model for a Vertically Fractured Well in a Fractal Reservoir. SPE Form Eval 9 (2): 122–128. http://dx.doi.org/10.2118/20582-PA.
Bello, R.O. 2009. Rate Transient Analysis in Shale Gas Reservoirs With Transient Linear Behavior. PhD dissertation, Texas A&M University, College Station, Texas.
Camacho Velazquez, R., Fuentes-Cruz, G., and Vasquez-Cruz, M.A. 2008. Decline-Curve Analysis of Fractured Reservoirs With Fractal Geometry. SPE Res Eval & Eng 11 (3): 606–619. http://dx.doi.org/10.2118/104009-PA.
Chang, J. and Yortsos, Y.C. 1990. Pressure-Transient Analysis of Fractal Reservoirs. SPE Form Eval 5 (1): 31–38. http://dx.doi.org/10.2118/18170-PA.
Cipolla, C.L., Lolon, E., and Mayerhofer, M.J. 2009. Resolving Created, Propped, and Effective Hydraulic-Fracture Length. SPE Prod & Oper 24 (4): 619–628. http://dx.doi.org/10.2118/129618-PA.
Clarkson, C.R. 2012. Modeling 2-Phase Flowback of Multi-Fractured Horizontal Wells Completed in Shale. Paper SPE 162593 presented at the SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30 October–1 November. http://dx.doi.org/10.2118/162593-MS.
Doublet, L.E., Pande, P.K., McCollum, T.J. et al. 1994. Decline Curve Analysis Using Type Curves—Analysis of Oil Well Production Data Using Material Balance Time: Application to Field Cases. Paper SPE 28688 presented at the International Petroleum Conference and Exhibition of Mexico, Veracruz, Mexico, 10–13 October. http://dx.doi.org/10.2118/28688-MS.
El-Banbi, A.H. and Wattenbarger, R.A. 1998. Analysis of Linear Flow in Gas Well Production. Paper SPE 39972 presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15–18 March. http://dx.doi.org/10.2118/39972-MS.
Fetkovich, M.J. 1980. Decline Curve Analysis Using Type Curves. J. Pet Tech 32 (6): 1065–1077. http://dx.doi.org/10.2118/4629-PA.
Fisher, M.K., Wright, C.A., Davidson, B.M. et al. 2002. Integrating Fracture Mapping Technologies to Optimize Stimulations in the Barnett Shale. Paper SPE 77441 presented at the SPE ATCE, San Antonio, Texas, 29 September–2 October. http://dx.doi.org/10.2118/77441-MS.
Fuentes-Cruz G., Camacho-Velázquez R., and Vásquez-Cruz M. 2010. A Unified Approach for Falloff and Buildup Tests Analysis Following a Short Injection/Production Time. Paper SPE 133539 presented at the SPE Western Regional Meeting, Anaheim, California, 27–29 May. http://dx.doi.org/10.2118/133539-MS.
Ge, J. and Ghassemi, A. 2011. Permeability Enhancement in Shale Gas Reservoirs After Stimulation by Hydraulic Fracturing. Paper ARMA 11-514 presented at the 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, California, 26–29 June.
Hagoort, J. 2011. Semisteady-State Productivity of a Well in a Rectangular Reservoir Producing at Constant Rate or Constant Pressure. SPE Res Eval & Eng 14 (6): 677–686. http://dx.doi.org/10.2118/149807-PA.
Helmy, M.W. and Wattenbarger, R.A. 1998. New Shape Factors for Wells Produced at Constant Pressure. Paper SPE 39970 presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, 15–18 March. http://dx.doi.org/10.2118/39970-MS.
Hummel, N. and Shapiro, S.A. 2013. Nonlinear Diffusion-Based Interpretation of Induced Microseismicity: A Barnett Shale Hydraulic Fracturing Case Study. Geophysics 78 (5): B211–B226. http://dx.doi.org/10.1190/geo2012-0242.1.
Marquardt, D. 1963. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. for Industrial and Appl. Math. 11 (2): 431–441. http://dx.doi.org/10.1137/0111030.
Mayerhofer, M.J., Lolon, E., Warpinski, N.R. et al. 2010. What Is Stimulated Reservoir Volume? SPE Prod & Oper 25 (1): 89–98. http://dx.doi.org/10.2118/119890-PA.
Mayerhofer, M.J., Lolon, E., Youngblood, J.E. et al. 2006. Integration of Microseismic Fracture Mapping Results With Numerical Fracture Network Production Modeling in the Barnett Shale. Paper SPE 102103 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. http://dx.doi.org/10.2118/102103-MS.
Nobakht, M. and Clarkson, C.R. 2012. A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition. SPE Res Eval & Eng 15 (3): 370–384. http://dx.doi.org/10.2118/143989-PA.
Palmer, I.D., Moschovidis, Z.A., and Cameron, J.R. 2007. Modeling Shear Failure and Stimulation of the Barnett Shale After Hydraulic Fracturing. Paper SPE 106113 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29–31 January. http://dx.doi.org/10.2118/106113-MS.
Poon, D. 1995. Transient Pressure Analysis of Fractal Reservoirs. Paper SPE-95-34 presented at the 46th Annual Technical Meeting of CIM, Banff, Alberta, Canada, 14–17 May. http://dx.doi.org/10.2118/95-34.
Valkó, P.P. and Abate, J. 2004. Comparison of Sequence Accelerators For the Gaver Method of Numerical Laplace Transform Inversion. Computers & Math. With Applications 48 (3–4): 629–636. http://dx.doi.org/10.1016/j.camwa.2002.10.017.
Van Everdingen, A.F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoir. J. Pet Tech 1 (12): 305–324. http://dx.doi.org/10.2118/949305-G.
Warpinski, N.R., Mayerhofer, M., Agarwal, K. et al. 2013. Hydraulic-Fracture Geomechanics and Microseismic-Source Mechanisms. SPE J. 18 (4): 766–780. http://dx.doi.org/10.2118/158935-PA.
Wattenbarger, R.A., El-Banbi, A.H., Villegas, M.E. et al. 1998. Production Analysis of Linear Flow Into Fractured Tight Gas Wells. Paper SPE 39931 presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, Colorado, 5–8 April. http://dx.doi.org/10.2118/39931-MS.
Wolfram Research, Inc. 2010. Mathematica, Version 8.0, Champaign, Illinois.
