Effect of Stress-Sensitive Fracture Conductivity on Transient Pressure Behavior for a Horizontal Well With Multistage Fractures
- Liwu Jiang (University of Regina) | Tongjing Liu (China University of Petroleum, Beijing) | Daoyong Yang (University of Regina)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2019
- Document Type
- Journal Paper
- 1,342 - 1,363
- 2019.Society of Petroleum Engineers
- tight formation, stress-sensitive fracture conductivity, multistage fractures, slab source function, horizontal well
- 49 in the last 30 days
- 123 since 2007
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In this study, theoretical models have been formulated, validated, and applied to evaluate the transient pressure behavior of a horizontal well with multiple fractures in a tight formation by taking stress-sensitive fracture conductivity into account. On the basis of the superposition principle in the Laplace domain, we propose a coupled matrix/fracture-flow model with consideration of the stress-sensitivity effect in fractures, which strengthens the nonlinearity of the governing equations. More specifically, a new slab-source function in the Laplace domain was developed to describe the transient pressure responses caused by fluid flow from the matrix to the fracture, and a new solution was derived to describe the fluid flow in the fracture under the stress-sensitivity effect. Subsequently, a semianalytical method was applied by discretizing each hydraulic fracture into small segments, and a linearization scheme and an iteration method are adopted to deal with the nonlinear problem in the Laplace domain. Meanwhile, a modified superposition principle was proposed and applied to generate the pressure distributions for buildup tests with consideration of stress-sensitive fracture conductivity. Furthermore, pressure responses and their corresponding derivative type curves were generated to examine the effect of stress-sensitive conductivity. For pressure-drawdown tests, it is found that gradual increases in both pressure drop and pressure derivative occur over time because of the partial closure of the fractures. The stress-sensitivity effect in fractures becomes more evident with a smaller fracture conductivity and a larger fracture-permeability modulus. From the pressure-buildup curves, a one-fourth-slope line characteristic of the bilinear-flow period and constant derivatives of 0.5 representing a pseudoradial-flow regime can be clearly observed. Only fracture conductivity near the wellbore at the shut-in time can be estimated from the buildup pressures obtained in this work, whereas pressure-buildup analysis derived from the traditional superposition principle will result in an erroneous evaluation of the stress-sensitive fracture conductivity. It is also found that the effect of permeability hysteresis in the fractures has a negligible impact on the pressure-buildup responses.
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Abass, H., Sierra, L., and Tahini, A. 2009. Optimizing Proppant Conductivity and Number of Hydraulic Fractures in Tight Gas Sand Wells. Presented at the SPE Saudi Arabia Section Technical Symposium, Al-Khobar, Saudi Arabia, 9–11 May. SPE-126159-MS. https://doi.org/10.2118/126159-MS.
Awoleke, O. O., Zhu, D., and Hill, A. D. 2016. New Propped-Fracture-Conductivity Models for Tight Gas Sands. SPE J. 21 (5): 1508–1517. SPE-179743-PA. https://doi.org/10.2118/179743-PA.
Bennett, C. O., Reynolds, A. C., Raghavan, R. et al. 1986. Performance of Finite-Conductivity, Vertically Fractured Wells in Single-Layer Reservoirs. SPE Form Eval 1 (4): 399–412. SPE-11029-PA. https://doi.org/10.2118/11029-PA.
Berumen, S. and Tiab, D. 1997. Interpretation of Stress Damage on Fracture Conductivity. J Pet Sci Eng 17 (1–2): 71–85. https://doi.org/10.1016/S0920-4105(96)00057-5.
Chen, D., Pan, Z., Ye, Z. et al. 2016. A Unified Permeability and Effective Stress Relationship for Porous and Fractured Reservoir Rocks. J Nat Gas Sci Eng 29 (February): 401–412. https://doi.org/10.1016/j.jngse.2016.01.034.
Chen, D., Ye, Z., Pan., Z. et al. 2017a. A Permeability Model for the Hydraulic Fracture Filled With Proppant Packs Under Combined Effect of Compaction and Embedment. J Pet Sci Eng 149 (20): 428–435. https://doi.org/10.1016/j.petrol.2016.10.045.
Chen, Z., Liao, X., Zhao, X. et al. 2017b. A Comprehensive Productivity Equation for Multiple Fractured Vertical Wells With Non-Linear Effects Under Steady-State Flow. J Pet Sci Eng 149 (20 January): 9–24. https://doi.org/10.1016/j.petrol.2016.09.050.
Chen, H.-T. and Lin, J.-Y. 1991. Application of the Laplace Transform to Nonlinear Transient Problems. Appl Math Model 15 (3): 144–151. https://doi.org/10.1016/0307-904X(91)90023-I.
Chen, H. Y., Poston, S. W., and Raghavan, R. 1991. An Application of the Product Solution Principle for Instantaneous Source and Green’s Functions. SPE Form Eval 6 (2): 161–167. SPE-20801-PA. https://doi.org/10.2118/20801-PA.
Cho, Y., Ozkan, E., and Apaydin, O. G. 2013. Pressure-Dependent Natural-Fracture Permeability in Shale and Its Effect on Shale-Gas Well Production. SPE Res Eval & Eng 16 (2): 216–228. SPE-159801-PA. https://doi.org/10.2118/159801-PA.
Cinco-Ley, H. and Meng, H. Z. 1988. Pressure Transient Analysis of Wells With Finite Conductivity Vertical Fractures in Double Porosity Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 2–5 October. SPE-18172-MS. https://doi.org/10.2118/18172-MS.
Cinco-Ley, H. and Samaniego-V., F. 1981. Transient Pressure Analysis for Fractured Wells. J Pet Technol 33 (9): 1749–1766. SPE-7490-PA. https://doi.org/10.2118/7490-PA.
Cinco-Ley, H., Samaniego-V., F., and Dominguez A., N. 1978. Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture. SPE J. 18 (4): 253–264. SPE-6014-PA. https://doi.org/10.2118/6014-PA.
Clarkson, C. R., Jensen, J. L., and Chipperfield, S. 2012. Unconventional Gas Reservoir Evaluation: What Do We Have to Consider? J Nat Gas Sci Eng 8 (September): 9–33. https://doi.org/10.1016/j.jngse.2012.01.001.
Clarkson, C. R., Qanbari, F., Nobakht, M. et al. 2013. Incorporating Geomechanical and Dynamic Hydraulic-Fracture-Property Changes Into Rate-Transient Analysis: Example From the Haynesville Shale. SPE Res Eval & Eng 16 (3): 303–316. SPE-162526-PA. https://doi.org/10.2118/162526-PA.
Feng, Q., Xia, T., Wang, S. et al. 2017. Pressure Transient Behavior of Horizontal Well With Time-Dependent Fracture Conductivity in Tight Oil Reservoirs. Geofluids 2017: 1–20. https://doi.org/10.1155/2017/5279792.
Guppy, K. H., Cinco-Ley, H., Ramey, H. J. Jr. 1982a. Non-Darcy Flow in Wells With Finite-Conductivity Vertical Fractures. SPE J. 22 (5): 681–698. SPE-8281-PA. https://doi.org/10.2118/8281-PA.
Guppy, K. H., Cinco-Ley, H., and Ramey, H. J. Jr. 1982b. Pressure Buildup Analysis of Fractured Wells Producing at High Flow Rates. J Pet Technol 34 (11): 2655–2666. SPE-10178-PA. https://doi.org/10.2118/10178-PA.
Holditch, S. A. and Morse, R. A. 1976. The Effects of Non-Darcy Flow on the Behavior of Hydraulically Fractured Gas Wells. J Pet Technol 28 (10): 1169–1179. SPE-5586-PA. https://doi.org/10.2118/5586-PA.
Hughes, J. D. 2013. A Reality Check on the Shale Revolution. Nature 494 (7347): 307–308. https://doi.org/10.1038/494307a.
Jiang, L., Liu, T., and Yang, D. 2019. A Semi-Analytical Model for Predicting Transient Pressure Behaviour of a Hydraulically Fractured Horizontal Well in Naturally Fractured Reservoirs With Non-Darcy Flow and Stress-Sensitive Permeability Effects. SPE J. 24 (3): 1322–1341. SPE-194501-PA. https://doi.org/10.2118/194501-PA.
Lee, D. S., Elsworth, D., Yasuhara, H. et al. 2010. Experiment and Modeling to Evaluate the Effects of Proppant-Pack Diagenesis on Fracture Treatments. J Pet Sci Eng 74 (1–2): 67–76. https://doi.org/10.1016/j.petrol.2010.08.007.
Li, K., Gao, Y., Lyu, Y. et al. 2015. New Mathematical Models for Calculating Proppant Embedment and Fracture Conductivity. SPE J. 20 (3): 496–507. SPE-155954-PA. https://doi.org/10.2118/155954-PA.
Luo, W., Liu, P., Tian, Q. et al. 2017. Effects of Discrete Dynamic-Conductivity Fractures on the Transient Pressure of a Vertical Well in a Closed Rectangular Reservoir. Sci Rep 7 (1): 1–12. https://doi.org/10.1038/s41598-017-15785-9.
Luo, W., Tang, C., Feng, Y. et al. 2018. Mechanism of Fluid Flow Along a Dynamic Conductivity Fracture With Pressure-Dependent Permeability Under Constant Wellbore Pressure. J Pet Sci Eng 166 (July): 465–475. https://doi.org/10.1016/j.petrol.2018.03.059.
Manrique, E. J.., Thomas, C. P., Ravikiran, R. et al. 2010. EOR: Current Status and Opportunities. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 24–28 April. SPE-130113-MS. https://doi.org/10.2118/130113-MS.
Mukherjee, H. and Economides, M. J. 1991. A Parametric Comparison of Horizontal and Vertical Well Performance. SPE Form Eval 6 (2): 209–216. SPE-18303-PA. https://doi.org/10.2118/18303-PA.
Ozkan, E. and Raghavan, R. 1991a. New Solutions for Well-Test-Analysis Problems: Part 1—Analytical Considerations. SPE Form Eval 6 (3): 359–368. SPE-18615-PA. https://doi.org/10.2118/18615-PA.
Ozkan, E. and Raghavan, R. 1991b. New Solutions for Well-Test-Analysis Problems: Part 2—Computational Considerations. SPE Form Eval 6 (3): 369–378. SPE-18616-PA. https://doi.org/10.2118/18616-PA.
Pedrosa, O. A. Jr. 1986. Pressure Transient Response in Stress-Sensitive Formations. Presented at the SPE California Regional Meeting, Oakland, California, 2–4 April. SPE-15115-MS. https://doi.org/10.2118/15115-MS.
Raghavan, R., Chen, C.-C., and Agarwal, B. 1997. An Analysis of Horizontal Wells Intercepted by Multiple Fractures. SPE J. 2 (3): 235–245. SPE-27652-PA. https://doi.org/10.2118/27652-PA.
Raghavan, R., Scorer, J., and Miller, F. G. 1972. An Investigation by Numerical Methods of the Effect of Pressure-Dependent Rock and Fluid Properties on Well Flow Tests. SPE J. 12 (3): 267–275. SPE-2617-PA. https://doi.org/10.2118/2617-PA.
Stehfest, H. 1970. Algorithm 368: Numerical Inversion of Laplace Transforms. Commun ACM 13 (1): 47–49. https://doi.org/10.1145/361953.361969.
Tiab, D. 2005. Analysis of Pressure Derivative Data of Hydraulically Fractured Wells by the Tiab’s Direct Synthesis Technique. J Pet Sci Eng 49 (1–2): 1–21. https://doi.org/10.1016/j.petrol.2005.07.001.
van Kruysdijk, C. P. J. W. and Dullaert, G. M. 1989. A Boundary Element Solution of the Transient Pressure Response of Multiple Fractured Horizontal Wells. Proc., ECMOR I–1st European Conference on the Mathematics of Oil Recovery, Cambridge, UK, 25–27 July. https://doi.org/10.3997/2214-4609.201411306.
Vincent, M. C., Pearson, C. M., and Kullman, J. 1999. Non-Darcy and Multiphase Flow in Propped Fractures: Case Studies Illustrate the Dramatic Effect on Well Productivity. Presented at the SPE Western Regional Meeting, Anchorage, 26–27 May. SPE-54630-MS. https://doi.org/10.2118/54630-MS.
Wang, H., Guo, J., and Zhang, L. 2017a. A Semi-Analytical Model for Multilateral Horizontal Wells in Low-Permeability Naturally Fractured Reservoirs. J Pet Sci Eng 149 (20 January): 564–578. https://doi.org/10.1016/j.petrol.2016.11.002.
Wang, J. and Jia, A. 2014. A General Productivity Model for Optimization of Multiple Fractures With Heterogeneous Properties. J Nat Gas Sci Eng 21 (November): 608–624. https://doi.org/10.1016/j.jngse.2014.09.024.
Wang, J., Jia, A., Wei, Y. et al. 2017b. Approximate Semi-Analytical Modeling of Transient Behavior of Horizontal Well Intercepted by Multiple Pressure-Dependent Conductivity Fractures in Pressure-Sensitive Reservoir. J Pet Sci Eng 153 (May): 157–177. https://doi.org/10.1016/j.petrol.2017.03.032.
Weaver, J. D., Rickman, R. D., and Luo, H. 2010. Fracture-Conductivity Loss Caused by Geochemical Interactions Between Man-Made Proppants and Formations. SPE J. 15 (1): 116–124. SPE-118174-PA. https://doi.org/10.2118/118174-PA.
Wen, Q., Zhang, S., Wang, L. et al. 2007. The Effect of Proppant Embedment Upon the Long-Term Conductivity of Fractures. J Pet Sci Eng 55 (3–4): 221–227. https://doi.org/10.1016/j.petrol.2006.08.010.
Yang, D., Zhang, F., Styles, J. A. et al. 2015. Performance Evaluation of a Horizontal Well With Multiple Fractures by Use of a Slab-Source Function. SPE J. 20 (3): 652–662. SPE-173184-PA. https://doi.org/10.2118/173184-PA.
Zhang, F. and Yang, D. 2014a. Determination of Minimum Permeability Plateau and Characteristic Length in Porous Media With Non-Darcy Flow Behaviour. J Pet Sci Eng 119 (July): 8–16. https://doi.org/10.1016/j.petrol.2014.04.018.
Zhang, F. and Yang, D. 2014b. Determination of Fracture Conductivity in Tight Formations With Non-Darcy Flow Behavior. SPE J. 19 (1): 34–44. SPE-162548-PA. https://doi.org/10.2118/162548-PA.
Zhang, F. and Yang, D. 2017. Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation. J. Energy Resour. Technol 140 (3): 032903-1–032903-11. https://doi.org/10.1115/1.4037903.
Zhang, Z., He, S., Liu, G. et al. 2014. Pressure Buildup Behavior of Vertically Fractured Wells With Stress-Sensitive Conductivity. J Pet Sci Eng 122 (October): 48–55. https://doi.org/10.1016/j.petrol.2014.05.006.