径向低渗非Darcy渗流动边界半解析模型

A Semi-Analytical Model for Moving Boundary of Radial Non-Darcy Flow in Low Permeability Reservoir

低渗油藏渗流过程中普遍存在启动压力梯度(TPG).考虑低渗渗流特征,建立了平面径向低渗非Darcy渗流动边界数学模型,给出了计算动边界移动速度的公式,通过Laplace变换结合无穷级数方法求得了模型的半解析解,并进行了Stehfest数值反演.详细讨论与分析了动边界问题特性、动边界变化和传播情况,解释了启动压力梯度导致动边界不断向外扩展的现象.计算了启动压力梯度对井底压力、压力导数的影响,并给出不同条件下的地层压力分布曲线和Gringarten-Bourdet图版,同时给出了实例分析.研究发现:低渗渗流模型与常规渗流模型有着显著不同,低渗非Darcy渗流压力降是随时间扩展的,在动边界外的地层压力降为零,压力分布曲线呈现紧支性.针对具有动边界的低渗透问题,需充分考虑启动压力梯度与动边界的影响,该模型为低渗油藏渗流机理和开采动态、解释与数值模拟提供了一定的理论基础.

The threshold pressure gradient（TPG） generally exists in the seepage process of low permeability reservoir. In view of characteristics of low permeability seepage,the mathematical model for the moving boundary of non-Darcy flow was established,and the formula for calculating the moving speed of the boundary was given. The Laplace transform and the infinite series method were used to obtain the model＇s general solution,and the Stehfest numerical inversion was conducted. The characteristics of moving boundary problems,the boundary change and propagation were discussed and explained in detail,and the phenomenon of TPG extending outward was explicated. The TPG effects on the bottom pressure and the pressure derivative were calculated,and the Gringarten-Bourdet charts under different conditions were given. The results show that,the low pressure percolation model is significantly different from the Darcy seepage model. For low permeability cases,the pressure drop expands with time and the pressure distribution curve is of compact support. The study on the low permeability problem with moving boundary,considering the influence of the TPG and the moving boundary,provides a theoretical basis for the seepage mechanism and production performance,interpretation and numerical simulation of low permeability oil reservoirs.