A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis

doi:10.7623/syxb201202011

Editorial office of ACTA PETROLEI SINICA ›› 2012, Vol. 33 ›› Issue (2): 264-268.DOI: 10.7623/syxb201202011

• Petroleum Exploration • Previous Articles Next Articles

A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis

JIANG Ruizhong 1　LI Linkai 2　XU Jianchun 1　YANG Renfeng 3　ZHUANG Yu 1

Received:2011-08-22 Revised:2011-10-29 Online:2012-03-25 Published:2012-05-17

低渗透油藏非线性渗流新模型及试井分析

姜瑞忠 1　李林凯 2　徐建春 1　杨仁锋 3　庄　煜 1

1　中国石油大学石油工程学院　山东青岛　266555；2威德福（中国）能源服务有限公司　天津　300457；3中海油研究总院　北京　100027

通讯作者: 姜瑞忠
作者简介:姜瑞忠，男，1964年4月生，1987年毕业于西南石油学院，现为中国石油大学（华东）教授、博士生导师，主要从事油气田开发方面的教学和科研工作。
基金资助:
国家重大科技专项(2011ZX05051)和国家自然科学基金项目（No.51174223）资助。

Abstract

Abstract:

Based on a capillary model and integrated with the boundary layer theory, we proposed a new mathematical model for seepage in low-permeability reservoirs by introducing two parameters c₁ and c₂that could characterize seepage of low-permeability reservoirs. This model well explained origins of a start-up pressure gradient and nonlinear seepage. According to the new model, a well-testing model considering the influence of moving boundaries was established and solved with the finite difference method, an impact of dimensionless characteristic c_1Dand c_2Dparameters on well-testing curves was investigated as well. The results show that pressure and pressure derivative curves for both the new model and a pseudo pressure gradient model are upward compared with the Darcy model though the upward degree for the new model is gentle. And c_1Dand c_2Dare characteristic parameters that determine the shape of well-testing curves. The upward degree increases with an increase of c_1Dor c_2Dwhen the sum of c_1Dand c_2Dis not a constant, while the upward degree increases with an increase of c_1Dbut a decease of c_2Dwhen the sum of c_1Dand c_2Dis a constant. On well-testing curves, a pressure response to the new model is in agreement with that to the Darcy model both for closed boundaries and for constant pressure boundaries.

Key words: low-permeability reservoir, flow model, nonlinear seepage, well testing, threshold pressure gradient

摘要：

基于毛细管模型，结合边界层理论，通过引入描述低渗透储层渗流的特征参数c₁和 c₂，建立了低渗透油藏渗流新模型，解释了启动压力梯度和非线性渗流产生的根本原因。根据新模型给出了考虑动边界影响的试井模型，并采用数值方法求解，分析了无因次特征参数c_1D和c_2D对试井曲线的影响。结果表明：新模型的压力和压力导数曲线上翘，上翘幅度比拟启动压力梯度模型要小。考虑动边界影响的试井曲线上翘幅度比不考虑时要小。c_1D和 c_2D是决定曲线形态的特征参数。当c_1D与 c_2D之和不为常数时，随着 c_1D或 c_2D增大，上翘幅度增大；当 c_1D与 c_2D之和为常数时，随着 c_1D增大，c_2D减小，上翘幅度增大。对于封闭边界和定压边界在试井曲线上的压力响应，新模型与达西模型一致。

关键词: 低渗透油藏, 渗流模型, 非线性渗流, 试井, 启动压力梯度

JIANG Ruizhong　LI Linkai　XU Jianchun　YANG Renfeng　ZHUANG Yu. A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis[J]. Editorial office of ACTA PETROLEI SINICA, 2012, 33(2): 264-268.

姜瑞忠　李林凯　徐建春　杨仁锋　庄　煜. 低渗透油藏非线性渗流新模型及试井分析[J]. 石油学报, 2012, 33(2): 264-268.

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A nonlinear mathematical model for low-permeability reservoirs and well-testing analysis

低渗透油藏非线性渗流新模型及试井分析

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