变形介质油气藏开采数学模型及其数值解

A mathematical model of reservoir exploitation with deformable medium and its
numerical solution

要子军 邓勇

华北石油工程建设有限公司第三工程处，河北 河间 062450 西南石油大学油气藏地质及开发工程国家重点实验室，四川 成都 610500

在油气藏开采过程中，由于地层压力的不断变化引起地层变形，从而导致地层渗透率及孔隙度随地层压力的变化而变化。在考虑渗透率和孔隙度与地层压力变化关系的基础上，建立了变形介质油气藏开采数学模型，综合采用状态方程隐式处理（IMPES）和Ritchmyer线性化方法，对变形介质油气藏开采渗流问题进行了数值化求解。并假设了某一均质性变形介质油藏，利用该方法对变形介质油藏生产特征进行了计算分析，讨论了由于储层变形引起的渗透率及孔隙度变化对油气藏开发效果的影响。

In the process of oil and gas reservoir exploitation, the formation will be deformed because of the gradual decline of formation
pressure, which can lead to the result as the researvoir permeability and porosity change as the formation pressure changes. Through
considering the above problem, a mathematical model of reservoir exploitation with deformable medium is established in this paper.
On the basis of the model, the methods of IMPES and Richtmyer are used to make numerical solution for the model and some
homogeneous reservoirs with deformable medium are supposed to use the method discussed before to calculate and analyze the
production performance of the homogeneous reservoir. And then the influence of permeability and porosity change caused by
researvoir deformation on the reservoir exploitation is discussed. The result shows that the established mathematical model can
compensate for the shortages of the commercial software.