A Semianalytical Model for Predicting Transient Pressure Behavior of a Hydraulically Fractured Horizontal Well in a Naturally Fractured Reservoir With Non-Darcy Flow and Stress-Sensitive Permeability Effects
- 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
- 1,322 - 1,341
- 2019.Society of Petroleum Engineers
- naturally fractured reservoirs, multistage hydraulic fractures, stress-sensitivity, Barree-Conway model, horizontal well
- 10 in the last 30 days
- 223 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into mathematical models to take into account the stress-sensitivity effect. In this way, the resulting nonlinearity of the mathematical models is weakened by using Pedrosa’s transform formulation. Then a semianalytical method is applied to solve the coupled nonlinear mathematical models by discretizing each HF into small segments. Furthermore, the pressure response and its corresponding derivative type curve are generated to examine the combined effects of non-Darcy flow and stress sensitivity. In particular, stress sensitivity in HF and natural-fracture (NF) subsystems can be respectively analyzed, while the assumption of an equal stress-sensitivity coefficient in the two subsystems is no longer required. It is found that non-Darcy flow mainly affects the early stage bilinear and linear flow regime, leading to an increase in pressure drop and pressure derivative. The stress-sensitivity effect is found to play a significant role in those flow regimes beyond the compound-linear flow regime. The existence of non-Darcy flow makes the effect of stress sensitivity more remarkable, especially for the low-conductivity cases, while the stress sensitivity in fractures has a negligible influence on the early time period, which is dominated by non-Darcy flow behavior. Other parameters such as storage ratio and crossflow coefficient are also analyzed and discussed. It is found from field applications that the coupled model tends to obtain the most-reasonable matching results, and for that model there is an excellent agreement between the measured and simulated pressure response.
|File Size||2 MB||Number of Pages||20|
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.
Barree, R. D. and Conway, M. W. 2004. Beyond Beta Factors: A Complete Model for Darcy, Forchheimer and Trans-Forchheimer Flow in Porous Media. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September. SPE-89325-MS. https://doi.org/10.2118/89325-MS.
Barree, R. D. and Conway, M. W. 2009. Multiphase Non-Darcy Flow in Proppant Packs. SPE Prod & Oper 24 (2): 257–268. SPE-109561-PA. https://doi.org/10.2118/109561-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.
Bourdet, D., Ayoub, J. A., and Pirard, Y. M. 1989. Use of Pressure Derivative in Well Test Interpretation. SPE Form Eval 4 (2): 293–302. SPE-12777-PA. https://doi.org/10.2118/12777-PA.
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.
Chen, S., Li, H., Zhang, Q. et al. 2008. A New Technique for Production Prediction in Stress-Sensitive Reservoirs. J Can Pet Technol 47 (3): 49–54. PETSOC-08-03-49. https://doi.org/10.2118/08-03-49.
Chen, Z., Liao, X., Zhao, X. et al. 2016a. Development of a Trilinear Flow Model for Carbon Sequestration in Depleted Shale. SPE J. 21 (4): 1386–1399. SPE-176153-PA. https://doi.org/10.2118/176153-PA.
Chen, Z., Liao, X., Zhao, X. et al. 2016b. A Semi-Analytical Mathematical Model for Transient Pressure Behavior of Multiple Fractured Vertical Well in Coal Reservoirs Incorporating With Diffusion, Adsorption and Stress-Sensitivity. J. Nat. Gas Sci. Eng. 29 (February): 570–582. https://doi.org/10.1016/j.jngse.2015.08.043.
Chen, Z., Liao, X., Zhao, X. et al. 2017. A Comprehensive Productivity Equation for Multiple Fractured Vertical Wells With Non-Linear Effects Under Steady-State Flow. J. Pet. Sci. Eng. 149: 9–24. https://doi.org/10.1016/j.petro.2016.09.050.
Cinco-Ley, H. and Meng, H. 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, Texas, 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., Qanbari, F., Nobakht, M. et al. 2013. Incorporating Geomechanical 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.
de Swaan, O. A. 1976. Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing. SPE J. 16 (3): 117–122. SPE-5346-PA. https://doi.org/10.2118/5346-PA.
Diwu, P., Liu, T., You, Z. et al. 2018. Effect of Low Velocity Non-Darcy Flow on Pressure Response in Shale and Tight Oil Reservoirs. Fuel 216: 398–406. https://doi.org/10.1016/j.fuel.2017.11.041.
Forchheimer, P. H. 1901. Wasserbewegung Durch Boden. Zeitz Ver Duetch Ing. 45: 1782–1788.
Gu, D., Ding, D., Gao, Z. et al. 2017. Pressure Transient Analysis of Multiple Fractured Horizontal Wells in Naturally Fractured Unconventional Reservoirs Based on Fractal Theory and Fractional Calculus. Petroleum 3 (3): 326–339. https://doi.org/10.1016/j.petlm.2016.12.005.
Guppy, K. H., Cinco-Ley, H., Ramey Jr., H. J. et al. 1982. 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.
Hassanzadeh, H., Pooladi-Darvish, M., and Atabay, S. 2009. Shape Factor in the Drawdown Solution for Well Testing of Dual-Porosity Systems. Adv. Water Resour. 32 (11): 1652–1663. https://doi.org/10.1016/j.advwatres.2009.08.006.
Hill, R. J., Koch, D. L., and Ladd, A. C. J. 2001. Moderate Reynolds Number Flows in Ordered and Random Arrays of Spheres. J. Fluid Mech. 448: 243–278. https://doi.org/10.1017/s0022112001005936.
Jalali, Y. and Ershaghi, I. 1987. Pressure Transient Analysis of Heterogeneous Naturally Fractured Reservoirs. Paper presented at the SPE California Regional Meeting, Ventura, California, 8–10 April. SPE-16341-MS. https://doi.org/10.2118/16341-MS.
Kazemi, H. 1969. Pressure Transient Analysis of Naturally Fractured Reservoirs With Uniform Fracture Distribution. SPE J. 9 (4): 451–462. SPE-2156-A. https://doi.org/10.2118/2156-A.
Kuchuk, F. and Biryukov, D. 2012. Transient Pressure Test Interpretation From Continuously and Discretely Fractured Reservoirs. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-158096-MS. https://doi.org/10.2118/158096-MS.
Kuchuk, F., Biryukov, D., Fitzpatrick, T. et al. 2015. Pressure Transient Behavior of Horizontal Wells Intersecting Multiple Hydraulic and Natural Fractures in Conventional and Unconventional Unfractured and Naturally Fractured Reservoirs. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 28–30 September. SPE-175037-MS. https://doi.org/10.2118/175037-MS.
Lai, B., Miskimins, J. L., and Wu, Y. 2012. Non-Darcy Porous Media Flow According to the Barree and Conway Model: Laboratory and Numerical Modelling Studies. SPE J. 17 (1): 70–79. SPE-122611-PA. https://doi.org/10.2118/122611-PA.
Li, X., Cao, L., Luo, C. et al. 2017. Characteristics of Transient Production Rate Performance of Horizontal Well in Fractured Tight Gas Reservoirs With Stress-Sensitivity Effect. J. Pet. Sci. Eng. 158: 92–106. https://doi.org/10.1016/j.petrol.2017.08.041.
Liu, M., Xiao, C., Wang, Y. et al. 2015. Sensitivity Analysis of Geometry for Multi-Stage Fractured Horizontal Wells With Consideration of Finite Conductivity Fractures in Shale Gas Reservoirs. J. Nat. Gas Sci. Eng. 22 (January): 182–195. https://doi.org/10.1016/j.jngse.2014.11.027.
Luo, W. and Tang, C. 2015. A Semianalytical Solution of a Vertical Fractured Well With Varying Conductivity Under Non-Darcy-Flow Condition. SPE J. 20 (5): 1028–1040. SPE-178423-PA. https://doi.org/10.2118/178423-PA.
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: 465–475. https://doi.org/10.1016/j.petrol.2018.03.059.
Moradi, M., Shamloo, A., and Dezfuli, A. D. 2017. A Sequential Implicit Discrete Fracture Model for Three-Dimensional Coupled Flow-Geomechanics Problems in Naturally Fractured Porous Media. J. Pet. Sci. Eng. 150: 312–322. https://doi.org/10.1016/j.petrol.2016.12.027.
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. 1986. Pressure Transient Response in Stress-Sensitive Formations. Paper presented at the SPE California Regional Meeting, Oakland, California, 2–4 April. SPE-15115-MS. https://doi.org/10.2118/15115-MS.
Raghavan, R. S., 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.
Ren, Z., Wu, X., Han, G. et al. 2017. Transient Pressure Behavior of Multi-Stage Fractured Horizontal Wells in Stress-Sensitive Tight Oil Reservoirs. J. Pet. Sci. Eng. 157: 1197–1208. https://doi.org/10.1016/j.petrol.2017.07.073.
Stehfest, H. 1970. Algorithm 368: Numerical Inversion of Laplace Transforms. Commun. ACM 13 (1): 47–49. https://doi.org/10.1145/361953.361969.
Thompson, J. M., Nobakht, M., and Anderson, D. M. 2010. Modeling Well Performance Data From Overpressured Shale Gas Reservoirs. Presented at the SPE Canadian Unconventional Resources and International Petroleum Conference, Calgary, Alberta, 19–21 October. SPE-137755-MS. https://doi.org/10.2118/137755-MS.
van Kruysdijk, C. P. J. W. and Dullaert, G. M. 1989. A Boundary Element Solution to the Transient Pressure Response of Multiply Fractured Horizontal Wells. Presented at the ECMOR I-1st European Conference on the Mathematics of Oil Recovery, Cambridge, England, 1 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, Alaska, 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: 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: 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: 157–177. https://doi.org/10.1016/j.petrol.2017.03.032.
Wang, S., Ma, M., Ding, W. et al. 2015. Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability. SPE Res Eval & Eng 18 (4): 523–533. SPE-174299-PA. https://doi.org/10.2118/174299-PA.
Warren, J. E. and Root, P. J. 1963. The Behavior of Naturally Fractured Reservoirs. SPE J. 3 (3): 245–255. SPE-426-PA. https://doi.org/10.2118/426-PA.
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/2118/118174-PA.
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/10.2118/173194-PA.
Yang, D., Zhang, Q., Fan, L. et al. 1999. Inflow Performance of Horizontal Wells in Naturally Fractured Reservoirs. J. Univ. Pet. (Nat. Sci. Ed.) 23 (6): 44–49.
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 (7): 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 Behaviour. 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: 48–55. https://doi.org/10.1016/j.petrol.2014.05.006.