Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

u–p格式饱和两相介质动力问题的显–隐式交替算法

针对以土骨架位移u和孔隙流体压力p为基本未知量的饱和两相介质动力方程,提出基于中心差分法和精细时程积分法相结合的时域显–隐交替算法,分析饱和两相介质动力反应。该算法对孔压方程非齐次项的计算分别采用Gauss积分,梯形积分和Lagrange二次插值函数近似位移的方法近似模拟;同时提出一种基于精细积分方法的三次样条插值函数法,进而回避了对孔压方程耦合速度项积分时涉及的矩阵求逆运算问题。计算结果与Zienkiewicz显–隐式结果对比,两者结果基本一致,证明了方法的有效性。

应用两步隐式算法求解Navier-Stokes方程

本文提出一种隐式分步算法求解流体的运动方程。研究证明,SIMPLEC算法是这种算法的特例。通过两组层流算例的计算表明,改变加权隐式系数α可以明显加快计算的收敛速度。

考虑启动压力梯度和应力敏感的油-气两相数值试井方法

油-气两相数值试井方法中目前所常用的线性化方法为全隐式方法、半隐式方法和常规的隐压显饱(implicit pressure and explicit saturation, IMPES)方法,其中半隐式和全隐式方法计算精度虽高,但计算量过大,求解困难、速度慢;而常规的IMPES方法虽求解简单、求解速度快,但对时间步长要求过高,稳定性较差。为解决该问题,由物质平衡原理确定地层压力和油相饱和度的关系曲线,再由IMPES方法隐式求解压力,最后由马斯凯特法求解油相饱和度,建立同时考虑启动压力梯度与应力敏感系数的油-气两相数值试井方法,并对影响因素进行敏感性分析。结果表明,考虑启动压力梯度与应力敏感系数时,井底压力导数曲线后期有明显的上翘,既弥补了常规IMPES方法不能采用大步长的缺陷,又保留了与全隐式方法相同的精度和稳定性,并且计算工作量减少了2/3,速度提高了约80%,可广泛用于油-气两相渗流问题的数值试井模型研究。