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Petroleum science has made remarkable progress in organic geochemistry and in the research into the theories of petroleum origin,its transport and accumulation.In estimating the oil-gas resources of a basin.the knowledge of its evolutionary history and especially the numerical computation of fluid flow and.the history of its changes under heat is vital.The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems.This thesis,from actual conditions such as the effect of fluid compressibility and the characteristic of largescal science-engineering computalion,puts forward a kind of characteristic finite difference alternating-direction scheme.Optimal order estimates in L2 norm are derived for the error in the approximate solutions.