Abstract
Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.
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References
Besson J. Performance of slanted and horizontal wells in an anisotropic medium. Paper SPE 20965 presented at the European Petroleum Conference, 21–24 October 1990, The Hague
Chen G, Tehrani D H and Peden J M. Pressure distribution created by a slanted well with elliptic inner boundary condition. Paper SPE 29121 presented at the SPE Symposium on Reservoir Simulation, 12–15 February 1995, San Antonio
Cinco H. Unsteady-state pressure distributions created by a slanted well or a well with an inclined fracture. Ph.D Dissertation. Stanford University, Stanford, California. 1974
Cinco H, Miller F G and Ramey Jr H J. Unsteady-state pressure distribution created by a directionally drilled well. Journal of Petroleum Technology. 1975a. 27(11): 1392–1400
Cinco H, Ramey Jr H J and Miller F G. Pseudoskin factors for partially penetrating, directionally drilled wells. Paper SPE 5589 presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, 28 September–1 October, 1975b, Dallas
Fair P S. Horizontal well pressure transient analysis for Gulf of Mexico reservoirs (adapting the slant well solution to layered media). SPE 104480, 2008
Harmohan G, Rayed A, Mohammed BI, et al. Pressure transient behavior of horizontal and slant wells intersecting a high permeability layer. Paper SPE 105616 presented at the SPE Middle East Oil and Gas Show and Conference, 11–14 March 2007, Kingdom of Bahrain
Khattab H A, Yeh N S and Agarwd R G. Pressure transient behavior of slanted wells in single and multiple-layered systems. Paper SPE 22730 presented at the SPE Annual Technical Conference and Exhibition, 6–9 October 1991, Dallas
Liao X W. Discussion of a slanted well test model in dual porosity reservoirs with pseudo steady state flow. Petroleum Explorationand Development. 1998. 25(5): 57–61 (in Chinese)
Li W, Lu D T, Wang L, et al. A transient pressure solution for inclined wells with complex boundaries. Well Testing. 2009. 18(6): 1–5 (in Chinese)
Lu P. Horizontal and slanted wells in layered reservoirs with crossflow. MS Thesis. Stanford University, Stanford, California. 1997
Ozkan E and Raghavan R. New solutions for well-test-analysis problems: Part 1—Analytical considerations. SPEFE. 1991a. 6(3): 359–368
Ozkan E and Raghavan R. New solutions for well-test-analysis problems: Part 2—Computational considerations and applications. SPEFE. 1991b. 6(3): 369–378
Ozkan E and Raghavan R. A computationally efficient transient-pressure solution for inclined wells. SPE Reservoir Evaluation & Engineering. 2000. 3(5): 414–425
Stehfest H. Numerical inversion of Laplace transform. Communications of the ACM. 1970. 13(1): 47–49
Van Everdingen A F and Hurst W. The application of the Laplace transformation to flow problems in reservoirs. Transaction of American Institute of Mining, Metallurgical, and Petroleum Engineers(Trans. AIME). 1949. 186: 305–324
Wang D S, Nie L X, Li Z M. Study of the analytic method for the well testing of deflecting wells. Journal of Xi’an Shiyou University (Natural Science Edition). 2006. 21(5): 51–54 (in Chinese)
Wang D S, Nie L X, Li Z M. Well test analysis by using a well drawdown curve in a multiple-deviated well system. Journal of Oil and Gas Technology. 2006. 28(1): 95–97 (in Chinese)
Wang D S, Zhang L, Nie L X, et al. A computationally efficient transient pressure solution for an inclined multiwell system. Journal of Hydrodynamics. 2005. 20(4): 527–530 (in Chinese)
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Wang, H., Zhang, L., Guo, J. et al. An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs. Pet. Sci. 9, 212–222 (2012). https://doi.org/10.1007/s12182-012-0201-1
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DOI: https://doi.org/10.1007/s12182-012-0201-1