From such actual conditions as the effects of fluid mechanics in porous media and three- dimensional geology characteristics, the mathematical model and a kind of modified method of second order splitting-up implicit iterative scheme were put forward. For the actual problem of Dongying hollow (single layer) and Huimin hollow (multilayer) of Shengli Petroleum Oil Field, this numerical simulation test and the actual conditions are basically coincident, thus the well-known problem has been solved.

Numerical simulation for evolutionary history of an oil-and gas-bearing basin is to repeat geological and thermodynamic history of basin evolution on a computer and then to quantitate petroleum generation, accumulation and migration. The mathematical model describing geological and thermodynamic history of the basin evolution is characterised by an initial-boundary value problem of a system of nonlinear partial differential equations. In the present paper, a numerical method for three-dimensional problem and the analysis of its stability are established and a numerical result for a practical model is given, which shows that the abnormal pressure and paleo-temperature computed are reasonable and display physical characteristics clearly as well.