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.

Petrodleum origin and accumulation in basin evolution is governed by a system of nonlinear partial differential equations. The mathematical model considered comprises (1) fluid flow (2) heat transport (3) porosity of the media. The pressure, Darcy velocity and temperature are approximated by the finite element method. Optimalorder convergence in L2 and H1 is proved.

Infusing water into oil reservoir by high-pressure pump to squeeze the oil residual out of oil wells is a problem of two-phase immiscible flow displacement. The mathematical model of the problem is the initial bocmdary problem of systems of partial differential eqastions. We set up some computation schemes of the discrete operator method, and study approximation and convergence theory. Computation of the model problem yielded satisfactory results.