考虑启动压力梯度的低渗透气藏不稳定渗流模型

An unsteady seepage flow model considering kickoff pressure gradient for low-permeability gas reservoirs

低渗透气藏气体渗流存在启动压力梯度,为准确描述存在启动压力梯度的低渗透气藏的不稳定渗流问题,在前人研究成果的基础上,根据存在启动压力梯度的低速非达西渗流的特点(流体流动边界不断向外扩展),建立了一个考虑启动压力梯度的低渗透气藏非线性渗流数学模型。采用格林函数法与数值逼近法相结合的方式对低渗透气藏的非线性渗流数学模型进行求解,建立了单井控制半径的求解方程,同时制作了计算控制半径的图版,利用该图版可以方便地计算出单井的控制半径。实例计算表明,采用考虑启动压力梯度的不稳定渗流模型能够正确地反映低渗透气藏的渗流机理和开采动态。

Kickoff pressure gradient occurs when gas flows in a low permeability reservoir. In order to describe the unsteady seepage flow in this kind of reservoir, an unsteady state seepage flow mathematical model which takes kickoff pressure gradient into consideration is built up based on predecessors＇ research and the characteristic of start-up pressure gradient existing in low velocity non-Darcy percolation flow （the fluid flow boundary expands outwards constantly）. Combining the Laplace space analytic solution by using Green function method with the numerical approximation, the non-linear mathematical model can be resolved. An equation for calculating single well control radius is established, and a single well control radius chart board is drawn up which can be used to calculate single well control radius. Case study indicates that the unsteady seepage flow model taking kickoff pressure gradient into account can correctly present the percolation mechanism and real production performance of a low-permeabillty gas reservoir.