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Computer simulation is widely used by petroleum engineers to understand oil recovery mechanisms and residual oil distribution.We will first briefly review a few mathematical models for petroleum reservoir simulation.Then we focus on a general compositional model and develop a fully-implicit method as well as effective preconditioners for solving the Jacobian systems.We will also discuss efficient parallel implementation of the proposed preconditioners on different platforms.The accuracy,robustness,and parallel scalability of the parallel simulator are then validated using large-scale benchmark problems.