Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.     

临界产量Dupuit公式的讨论及一种新的方法

临界产量的确定对底水油藏的高效开发起着重要作用. 然而,临界产量Dupuit 公式反映临界产量随着打开程度的降低而单调增加,存在不合理的地方. 本文与一些学者的研究表明,Dupuit 公式推导过程暗含的“当临界状态时水锥正好处于井底” 的假设不合理,水锥不能稳定在井底位置. 在不作水锥到达井底的假设,假设油井上部为径向流,井底周围为半球形流动的情况下,推导出了一种新的底水临界产量方程. 算例与工程实例表明,该方法比较符合实际,能够求得临界水锥高度和对打开程度进行优化.