Finite element methods for geothermal reservoir simulation

Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.