使用混合网格计算非达西渗流

Computation of Non-Darcy Flow with Hybrid Grids

针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解.

For low non-Darcy flow in vertically fractured wells, based on the generalized Darcy＇s law, a series of non-Darey flow differential equations and definite conditions of vertical fractured wells are built up. We assume that the stratum and fluid are slightly compressible and the outer edge is circular. Hybrid grids of regular and PEBI grids are used to divide solution domains. Numerical solution of bottomhole pressure is obtained with finite difference method. The bottomhole pressure and its derivative with finite conductivity considering the skin and well-bore storage effects are analysed in detail. The numerical solution doses to the theoretical result.