各向异性圆形地层渗流的解析解

对各向异性渗透率圆形有界地层向一口中心井的稳定渗流问题进行了研究 ,利用坐标变换将原流动问题转化为各向同性渗透率椭圆形地层向中心椭圆形井筒的流动问题。数值研究发现 ,这个椭圆区域流动问题可以划分为内、外两个区域的流动。内区域流动是两个共轴椭圆间的流动 ,可通过保角变换方法求解 ;外区域流动与两条直线等压边界间的点源流动十分相似 ,可利用相似流动替换方法求解。将内、外两个流动问题的解进行组合得到了原问题的全区域解析解。计算及分析证明 ,该解法的误差非常小。选取典型的油藏参数用解析解法进行了计算 ,结果表明 ,渗透率各向异性和油藏半径对有界油藏产量有明显的影响。

Analytic Solution for Fluid Flow Through a Circular Anisotropic Formation

This paper investigates the problem of the steady flow from a circular anisotropic formation to a central circular wellbore and presents an analytic solution of it. The original problem is transformed to that of the flow from an elliptical isotropic formation to a central elliptical wellbore. The numerical experiments show that the transformed flow can be divided into two flows in inner and outer areas respectively. The inner area is between two confocal elliptical boundaries. The inner flow problem is solved by a conformal transformation. The flow in the outer area is similar to the flow in a point source between two straight line boundaries with a uniform pressure.It is solved by the substitution method with the similar flow. The whole analytic solution of the original problem is obtained by combining the solutions of the inner and outer flow problems. The error of the substitution method is generally negligible. The computed results of the solution with typical parameters of anisotropic reservoirs are compared with that of the isotropic reservoir. The effect of anisotropic permeability on reservoir production is obvious.