分形油藏低速非达西渗流问题的组合数学模型

将非线性分形几何理论应用于渗流力学,建立分形油藏低速非达西渗流问题的组合模型。该模型由两个同心圆(圆中心为一口定产量的生产井)的分形油藏组成,内域为低速非达西渗流的分形油藏,外域为达西渗流的分形油藏。在内边界定流量和考虑井筒储存、表皮效应影响情况下,建立了分形油藏低速非达西渗流问题的有效井径组合数学模型,应用拉普拉斯变换方法求出了在两区域内压力分布的解析解,应用Stehfest数值反演方法求得井底的无因次压力,并分析了井底压力动态特征和参数影响。

COMBINED MATH MODEL OF LOW NON-DARCY FLOW IN FRACTAL RESERVOIR

The non-linear fractal geometry was applied to fluid flow mechanics, and the combined mathematical model of low non-Darcy flow in fractal reservoir was established. The model consists of two concentric circles of fractal reservoir, in the inner of which the fluid flow is low Darcy flow, while in the outer normal Darcy flow. Based upon fixed inner boundary rate, wellbore storage and skin factor, the combined mathematical model of low non-Darcy flow in fractal reservoir with effective well radius was set up. The analytical solution of pressure distribution in these two parts was presented by using Laplace transform while that of bottom hole dimensionless pressure by Stehfest numerical reversion, according to which we also analyzed bottom hole pressure characterization and related factors.