ABSTRACT
In reservoir simulation, the discretization of the fluid flow and energy equations generates systems of nonlinear algebraic equations. These equations are solved using Newton-Raphson iteration. This method works from an approximation, generating a linear sparse system of equations whose solution correct the current approximation. This process is repeated until a satisfactory solution of the nonlinear system is found. In practice, each linear system is solved with an iterative method. The overall efficiency of the simulator depends upon the stopping criteria for the linear (inner-) iteration and the termination rule for the nonlinear (outer-) iteration. In this article, stopping criteria for the inner-iteration in terms of the nonlinear requirements are discussed. The design of an optimal criterion includes knowledge of the approximate location of the regions of linear and quadratic rates of convergence for the nonlinear (outer-) iteration. A comparison of several stopping criteria is given. Their effect on CPU time, number of outer-iterations and time step selection is illustrated. Criteria using relaxed constraints in the linear convergence region are more efficient. The presentation is in the context of block-preconditioned iterative methods for thermal simulation.
