Abstract: Mathematical model with full tensorial permeability and mixed boundaries is presented to simulate single phase flow in heterogeneous reservoirs.A finite element method based on variational principle is proposed to solve the model.Fluid flows in homogeneous and heterogeneous reservoirs are simulated.It demonstrates that the finite element method is reliable and precise in determining flow behavior in heterogeneous reservoirs.It provides an important theoretical basis for detailed reservoir numerical simulation.

Key words: heterogeneity, anisotropy, reservoir, permeability tensor, finite element method, numerical simulation