基于全隐式有限差分的三元复合驱渗流模型数值计算方法

Numerical Computation Method for Solving Flow Model of ASP Flooding Based on Full Implicit Finite Difference

摘要: 针对三元复合驱缺乏科学的数学模型描述驱油机理，数值求解数值稳定性不高、精度差的问题，本文提出了一种基于全隐式有限差分的数值计算方法。首先综合三元驱替剂(碱、表面活性剂和聚合物)对油、水物理化学特性的影响，以及油水渗流方程和吸附扩散方程，建立了三元复合驱数学模型。然后采用全隐式有限差分法，引入块中心网格系统将数学模型从时间和空间上进行离散，从而将原始的偏微分方程组转化为差分代数方程组。最后，采用Newton-Raphson法进行迭代求解，得到系统的状态和输出。为了验证提出方法的效果，针对四注九采三元复合驱实例，分别采用本文方法和CMG数值模拟软件求解，仿真结果表明，本文提出的方法具有较高的求解精度。

Abstract: For alkali-surfactant-polymer (ASP) flooding, there is lack of scientific mathematical model to describe the flooding mechanism, and the numerical computation has bad numerical stability and low accuracy, this paper presents a new numerical computation method based on full implicit finite difference method. Firstly, a comprehensive ASP flooding model is built with considering the influence on the physicochemical characteristic and seepage equation of oil and water and the adsorption diffusion equation which is caused by the adding of displacing agents. Then the full implicit finite difference method is applied to discretize the mechanism in time and space by block center grid system. Further, the original partial differential equations are transformed into a series of difference differential algebraic equations. At last, the problem is solved iteratively by Newton-Raphson method to get the system state and output. To verify the proposed method, a four-injection-nine-production wells example is introduced which is solved by proposed method and CMG software. Simulation result shows that the proposed method has good accuracy.