A New Fully Implicit Compositional Simulator

TL;DR: A new fully implicit formulation for compositional simulators improves numerical stability by yielding a more diagonally dominant Jacobian matrix and the number of iterations per time step is almost as low as that required by an IMPES scheme.

Abstract: A new fully implicit formulation for compositional simulators is presented. Rather than solving for pressure, saturations and phase compositions, the new formulation solves for pressure, overall concentrations and K-values. This change of primary unknowns to be solved improves numerical stability by yielding a more diagonally dominant Jacobian. The use of K-values as primary unknowns also allows the composition constraints to be solved separately from the other equations. The solution of the constraint equations is very efficient because they can be reformulated as monotonic functions*. The primary unknowns are further classified into reduced-unknowns and pivotal-unknowns. The latters are eliminated from the mass conservation equations using the fugacity equalities and constraints. The pivotal-unknowns are selected according to the sensitivity of the equations to the unknowns. This selection conforms to the partial pivoting strategy of Gaussian elimination and enhances numerical stability. Finally, a partial solution method is introduced to eliminate unnecessary calculations of those equations which have met the convergence criteria. For a simple system, it is shown that the new formulation results in a more diagonally dominant Jacobian matrix. Numerical experiments involving one dimensional multicontact-miscibile (MCM) and immiscible problems, a two dimensional MCM problem and a three dimensional MCM problem are conductedmore » to illustrate the capability and efficiency of the new formulation. Results indicate that the number of iterations per time step required by the new formulation is only about 40% - 60% of an existing fully implicit scheme. It is almost as low as that required by an IMPES scheme.« less