A New Fully Implicit Compositional Simulator

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 conducted 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.

Numerical modelling of multiphase flow in porous media

“…Among the models based on this approach are those reported by Fussell and Fussell (72), Coats (42), Heinemann (80), and Chien, Lee and Chen (38). This class of formulations treats the discretized flow equations and thermodynamic constraints as a set of simultaneous nonlinear algebraic equations, generally using some Newtonlike iterative scheme to advance between time steps.…”

An implicit numerical model for multicomponent compressible two-phase flow in porous media

“…Later, Chien et al [11] proposed using the equilibrium ratios as a set of unknowns beside the pressure and the overall concentrations rather than saturations and phase compositions.…”

Compositional Space Parameterization: Multicontact Miscible Displacements and Extension to Multiple Phases

“…General-purpose reservoir simulators in wide use employ an EOS or K-value tables to perform the phase equilibrium calculations (Coats 1980;Nghiem et al 1981;Chien et al 1985;Aziz and Wong 1988). In compositional flow simulation, given the temperature, pressure, and overall composition in a gridblock at a particular time, phase behavior computations are used to determine the phase state, and, if two or more phases are present, flash calculations are performed to determine the phase amounts and the component concentrations in each phase.…”