A New Approach to Quasi-Newton Methods With Application to Compositional Modeling

Abstract

ABSTRACT A new approach to quasi-Newton methods for nonlinear equations called quasi-Newton successive substitution (QNSS) is proposed. The use of QNSS does not require the computation nor the inversion of the Jacobian matrix at every iteration. Hence for large sparse systems which arise from the discretization of the reservoir flow equations, substantial savings can be achieved. The new method is applied to the solution of the pressure equation associated with a compositional model. An example shows the drastic improvement in convergence which can be achieved with QNSS compared to a previously published technique. The handling of gas solubility in the water phase using three-phase oil-gas-water flash calculations is also described. The QNSS method is very general and can be applied to any existing simulators.