摘要 The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.

Abstract：The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.

基金资助:Project supported by the National Natural Science Foundation of China (Grant No. 51404232), the China Postdoctoral Science Foundation (Grant No. 2014M561074), and the National Science and Technology Major Project, China (Grant No. 2011ZX05038003).

通讯作者:
Yue-Wu Liu
E-mail: liuyuewulxs@126.com

引用本文:

刘文超, 刘曰武, 牛丛丛, 韩国锋, 万义钊. Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient[J]. 中国物理B, 2016, 25(2): 24701-024701.
Wen-Chao Liu, Yue-Wu Liu, Cong-Cong Niu, Guo-Feng Han, Yi-Zhao Wan. Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient. Chin. Phys. B, 2016, 25(2): 24701-024701.