分形复合油藏非牛顿幂律流体不稳定渗流的数学模型

The Analytical Solutions of Mathematical Model for a Fractal Composite Reservoir with Non

对不稳定渗流的数学模型进行了推导并建立了分形复合油藏不稳定渗流模型.在无限大地层、有界定压、有界封闭三种外边界条件下分别求出了它们在Laplace空间的解析解.对于两区的特殊情况,分析了井底压力动态特征和参数影响,制作了典型曲线.非牛顿幂律流体的幂律指数,分形参数均对典型曲线产生较大的影响,呈现出与牛顿流体和均质油藏明显不同的特征.这对于非均质油藏非牛顿流体的不稳定试井分析和研究非线性渗流特征都是十分重要的.

The Theories and model of well testing analysis for a fractal composite reservoir have been discussed with non-Newtonian power law fluid flow. In order to completely describe the situation of real reservoirs, the fractal composite reservoir is defined as fractal reservoir that consists of many zones with different fluid and different format properties. The initial and three outer boundary conditions such as infinite, finite with constant pressure and closed boundary have been given according to polymer flooding in an oil field. A new effective well radius mathematical model of this fractal composite reservoir is suggested involving the wellborn storage and skin effects. The analytical solutions in Laplace-space for the mathematical model and two special cases of two and three regions are derived by Laplace transformation. The dimensionless wellborn pressure for the modern well test analysis is given by using Stehfest numerical inversion. The well test analysis theories and the pressure behavior of this reservoir are also discussed for the two region model.