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An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs

ISSN号：1671-1815
期刊名称：《科学技术与工程》
时间：0
分类：TP271.2[自动化与计算机技术—控制科学与工程;自动化与计算机技术—检测技术与自动化装置] O242.23[理学—计算数学;理学—数学]
作者机构：[1]State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu,Sichuan 610500, China, [2]Research Institute of Petroleum Exploration ＆ Production, Sinopec Northwest Company, Urumqi, Xinjiang 830011, China
相关基金：financial support from the special fund of China’s central government for the development of local colleges and universities―the project of national first-level discipline in Oil and Gas Engineering, the National Science Fund for Distinguished Young Scholars of China （Grant No. 51125019）;the National Program on Key fundamental Research Project （973 Program, Grant No. 2011CB201005）

作者： Wang Haitao[1], Zhang Liehui[1], Guo Jingjing[1], Liu Qiguo[1], He Xinming[2]

关键词：计算效率, 瞬态压力, 压力响应, 任意倾角, 斜井, 算法, 水库, 数值积分方法, Arbitrary inclination, slanted well, transient pressure behavior, efficient algorithm, variable step-size, piecewise integration

中文摘要：

与垂直、水平的井相比，歪曲的井的短暂压力回答的答案和计算是更复杂的。垂直、水平的井是在特别倾斜的歪曲的井的两个简化盒子，因此为歪曲的井的模型比为垂直、水平的井的另外的模型更一般、更复杂。许多作者在歪曲的井学习了液体的不稳定状态的流动，各种各样的答案被建议了。直到现在，然而，很少出版结果与计算效率相关。是否在时间领域或在 Laplace 领域，复杂功能的集成的计算在获得歪曲的井的压力回答是必要的，当集成的计算复杂、费时间时。为了获得一种完美的类型，弄弯计算时间甚至与高速度的计算机的帮助是不能接受的。这份报纸的目的是介绍一个有效算法计算歪曲的井在水库引起的短暂压力分布。基于严密推导，任何倾斜角度的歪曲的井的短暂压力解决方案被介绍。假定无限传导性的 wellbore，相等压力的点的地点被决定。根据在歪曲的井的一个短暂压力解决方案的被积函数的特征，更重要地，整个不可分的间隔被划分成数字集成被采用的可变替换和可变步尺寸 piecewise 的几小不可分的间隔，然后方法。计算的数量显著地被减少，计算效率极大地被改进。算法在这建议纸彻底地与任何倾斜角度在歪曲的井的短暂压力分发的有效、高速度的计算解决了困难。

英文摘要：

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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