  In reservoir simulation, solution of the coupled systems of nonlinear
algebraic equations that are associated with fully-implicit (backward Euler)
discretization is challenging. Having a robust and efficient nonlinear solver
is necessary in order for reservoir simulation to serve as the primary tool for
managing the recovery processes of large-scale reservoirs. Here, we develop a
continuation method based on the use of a dissipation operator. We focus on
nonlinear two-phase flow and transport in heterogeneous formations in the
presence of viscous, gravitational, and capillary forces. The homotopy is
constructed by adding numerical dissipation to the coupled discrete
conservation equations. A continuation parameter is introduced to control the
amount of dissipation. Numerical evidence of multi-dimensional models and
detailed analysis of single-cell problems are used to explain how the
dissipation operator improves the nonlinear convergence of the coupled system
of equations. An adaptive strategy to determine the dissipation coefficient is
proposed. The dissipation level is computed locally for each cell interface. We
demonstrate the efficiency of the dissipation-based continuation (DBC)
nonlinear solver using several examples, including 1D scalar transport and 2D
heterogeneous problems with fully-coupled flow and transport. The DBC solver
has better convergence properties compared with the standard damped-Newton
solvers used in reservoir simulation.

Computational Physics