Semianalytical Solution for Modeling the Performance of Complex Multifractured Horizontal Wells in Unconventional Reservoirs
- Etim Hope Idorenyin | Ezeddin Shirif (University of Regina)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- November 2018
- Document Type
- Journal Paper
- 961 - 980
- 2018.Society of Petroleum Engineers
- Flow in porous media, Reservoir simulation, Pressure transient analysis, Rate transient analysis, History matching
- 2 in the last 30 days
- 166 since 2007
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Analytical models have evolved in their capacity to represent the transient response of multifractured horizontal wells producing from unconventional reservoirs. However, as is common with analytical solutions, they are based on simplified reservoir/well geometries and flow-pattern assumptions that inherently restrict their scope of application. Their use for analyzing flow scenarios that transcend their scope is thus prone to errors. This paper documents a semianalytical model that overcomes the aforementioned limitations, and thereby expands analysis to the realm of reservoir/well architectures that are inaccessible to analytical models. Our solution is based on the Laplace-transform boundary-element-method (BEM) implementation of the Green’s function solution of the diffusivity equation. We represent the reservoir as a 2D composite system, with the outer boundaries and the interface between reservoir regions discretized appropriately. With the collocation procedure, the solution is distilled to a system of algebraic equations that is solved for the reservoir’s transient response. The hydraulic fractures need not be regular (equidistant and/or isometric), as is required by most analytical models; instead, they can traverse arbitrary spatial orientations and dimensions with respect to the horizontal well. We demonstrate the application of our solution by modeling multifractured-horizontal-well performance with two verification cases and three synthetic examples. The first example showcases a multifractured horizontal well traversed by identical, evenly spaced, fully penetrating, vertical hydraulic fractures within a stimulated reservoir volume (SRV). The second example models an enhanced-permeability region local to each hydraulic fracture as opposed to a single SRV housing all the fractures. The last example typifies complex fracture geometries, where the fractures have different half-lengths, spacings, and orientations. Besides showing that all the verification and example cases are in excellent agreement with numerical solution, we demonstrate the utility of our solution for modeling variable-rate flow commonly observed in practical field-production scenarios, showing its potential for history matching and forecasting the performance of multifractured horizontal wells.
|File Size||1018 KB||Number of Pages||20|
Abramowitz, M. and Stegun, I. 1965. Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Mineola, New York: Dover Books of Mathematics.
Agarwal, R. G. 1979. “Real Gas Pseudo-Time”—A New Function for Pressure Buildup Analysis of MHF Gas Wells. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23–26 September. SPE-8279-MS. https://doi.org/10.2118/8279-MS.
Al-Hussainy, R., Ramey, H. J., and Crawford, P. B. 1966. The Flow of Real Gases Through PorousMedia. J Pet Technol 18 (5): 624–636. SPE-1243-A-PA. https://doi.org/10.2118/1243-A-PA.
Brown, M. L., Ozkan, E., Raghavan, R. S. et al. 2009. Practical Solutions for Pressure-Transient Responses of Fractured Horizontal Wells in Unconventional Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October. SPE-125043-MS. https://doi.org/10.2118/125043-MS.
Chen, C.-C. 1996. An Approach to Handle Discontinuities by the Stehfest Algorithm. SPE J. 1 (4): 363–368. SPE-28419-PA. https://doi.org/10.2118/28419-PA.
Cinco, L. 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.
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.
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.
Dranchuk, P. M. and Abou-Kassem, H. 1975. Calculation of Z Factors for Natural Gases Using Equations of State. J Can Pet Technol 14 (3): 34–36. PETSOC-75-03-03. https://doi.org/10.2118/75-03-03.
Gringarten, A. C. and Ramey, H. J. 1973. The Use of Source and Green’s Functions in Solving Unsteady-Flow Problems in Reservoirs. SPE J. 13 (5): 285–296. SPE-3818-PA. https://doi.org/10.2118/3818-PA.
Guo, G. and Evans, R. D. 1993. Pressure-Transient Behavior and Inflow Performance of Horizontal Wells Intersecting Discrete Fractures. Presented at the SPE Annual Conference and Exhibition, Houston, 3–6 October. SPE-26446-MS. https://doi.org/10.2118/26446-MS.
Heidari Sureshjani, M. and Clarkson, C. R. 2015. An Analytical Model for Analyzing and Forecasting Production From Multifractured Horizontal Wells With Complex Branched-Fracture Geometry. SPE Res Eval & Eng 18 (3): 356–374. SPE-176025-PA. https://doi.org/10.2118/176025-PA.
Horne, R. N. and Temeng, K. O. 1995. Relative Productivities and Pressure Transient Modeling of Horizontal Wells With Multiple Fractures. Presented at the SPE Middle East Oil Show, Bahrain, 11–14 March. SPE-29891-MS. https://doi.org/10.2118/29891-MS.
Idorenyin, E. H. and Shirif, E. E. 2015. Flow in Linear Composite Reservoirs. SPE Res Eval & Eng 18 (4): 577–589. SPE-178911-PA. https://doi.org/10.2118/178911-PA.
Idorenyin, E. H. and Shirif, E. 2017. Transient Response in Arbitrary-Shaped Composite Reservoirs. SPE Res Eval & Eng 20 (3): 752–764. SE-184387-PA. https://doi.org/10.2118/184387-PA.
Idorenyin, E. H. 2016. Analytical and Semi-Analytical Models for Composite Reservoirs With Complex Well Completions. PhD thesis, University of Regina, Saskatchewan, Canada (April 2016).
KAPPA Engineering. 2013. Ecrin v4.30.01, https://www.kappaeng.com
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.
Kazemi, H., Merrill, L. S., Porterfield, K. L. et al. 1976. Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs. SPE J. 16 (6): 317–326. SPE-5719-PA. https://doi.org/10.2118/5719-PA.
Kikani, J. and Horne, R. N. 1989. Application of Boundary Element Method to Reservoir Engineering Problems. J. Pet. Sci. & Eng. 3 (3): 229–241. https://doi.org/10.1016/0920-4105(89)90020-X.
Kikani, J. and Horne, R. N. 1993. Modeling Pressure-Transient Behavior of Sectionally Homogeneous Reservoirs by the Boundary-Element Method. SPE Form Eval 8 (2): 145–152. SPE-19778-PA. https://doi.org/10.2118/19778-PA.
Larsen, L. and Hegre, T. M. 1994. Pressure Transient Analysis of Multifractured Horizontal Wells. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 25–28 September. SPE-28389-MS. https://doi.org/10.2118/28389-MS.
Lee, A. L., Gonzalez, M. H., and Eakin, B. E. 1966. The Viscosity of Natural Gases. J Pet Technol 18 (8): 997–1000. SPE-1340-PA. https://doi.org/10.2118/1340-PA.
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.
Serra, K., Reynolds, A. C., and Raghavan, R. 1983. New Pressure Transient Analysis Methods for Naturally Fractured Reservoirs. J Pet Technol 35 (12): 2271–2283. SPE-10780-PA. https://doi.org/10.2118/10780-PA.
Stalgorova, E. and Mattar, L. 2012. Analytical Model for History Matching and Forecasting Production in Multifrac Composite Systems. Presented at the SPE Canadian Unconventional Resources Conference, Calgary, 30 October–1 November. SPE-162516-MS. https://doi.org/10.2118/162516-MS.
Stehfest, H. 1970a. Algorithm 368: Numerical Inversion of Laplace Transforms [D5]. Communications of the ACM 13 (1): 47–49. https://doi.org/10.1145/361953.361969.
Stehfest, H. 1970b. Remark on Algorithm 368: Numerical Inversion of Laplace Transforms. Communications of the ACM 13 (10): 624.
Van Everdingen, A. F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoirs. J Pet Technol 1 (12): 305–324. SPE-949305-G. https://doi.org/10.2118/949305-G.
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.