三维油藏数值模拟的最优变松驰法

Optimal Variable Successive Over Relaxation (OVSOR) Method of Three-Dimensional Reservoir Simulation

本文证明了油藏三维不稳定渗流方程数值解法的最优变松驰定理,提出了最佳变松驰因子的计算公式。最佳变松驰因子随空间点、时间点变化。 使用这个方法,计算机内存小、计算工作量少、计算经费少。三维数值模拟在微机上容易实现。这种方法稳定性好、收敛速度快。对大的时间步长(如一年)、大的空间步长,该法都稳定、收敛,对均质各向同性介质和非均质各向异性介质都同样适用。 在IBM微机上,三维8000个节点,一个时间步长只需2分钟就能达到收敛。 该法完全可以推广到三维热传导方程、三维地下水动力学的数值模拟。对二维问题更显其优越性。

This paper has proved the theorem of Point Optimal Variable Successive Over Relaxation (OVSOR) method of three-dimensional unsteady flow in the reservoir, and put forward the formula of calculating optimal parameters for OVSOR which vary with space points and time points.Using this method, internal memory of computer is the smallest, calculating work is the smallest, and calculating funds are the smallest. It is very easy on microcomputer for three-dimensional reservoir simulation.The method is stability and convergence even if time steps are very big (for example, one year), and so are space steps. It is applicable for homogeneous, isotropic porous medium and heterogeneous, anisotropic porous medium.On IBM microcomputer, 8000 grid points can be calculated for three-dimensional simulation. It only take two minutes to get convergence for one time step.It can be spreaded to three-dimensional heat conduction equation and three-dimensional simulation of ground water flow. It looks much more advantage for two-dimensional simulation.