A Mass-Conservative Sequential Implicit Multiscale Method for General Compositional Problems

Abstract

Compositional simulation is necessary for a wide variety of reservoir-simulation applications, and it is especially valuable for accurate modeling of near-miscible gas injection for enhanced oil recovery. Because the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the compositional and saturation gradients. Compositional simulation of highly detailed reservoir models entails the use of small timesteps and large, poorly conditioned linear systems. The high computational cost of solving such systems renders field-scale simulations practically unfeasible. The coupling of the flow and transport to the phase-equilibrium calculations adds to the challenge. This is especially the case for near-miscible gas injection, in which the phase state and the phase compositions are very strong functions of space and time. We present a multiscale solver for compositional displacements with three-phase fluid flow. The thermodynamic phase behavior is described by general nonlinear cubic equations of state (EOS). The fully implicit (FI) natural-variables formulation is used as the basis to derive a sequential implicit (SI) solution strategy, whereby the pressure field is decoupled from the multicomponent transport. The SI scheme is mass conservative without the need to iterate between the pressure and transport equations during the timestep. This conservation property allows the errors caused by fixing the total-velocity field between the pressure- and transport-updating steps to be represented as a volume error. The method computes approximate pressure solutions—within a prescribed residual tolerance—that yield conservative fluxes on the computational grid of interest (fine, coarse, or intermediate). We use basis functions computed using restricted smoothing to allow for generally unstructured grids. The new method is verified against existing research and commercial compositional simulators using a simple conceptual test case and also using more-complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, and pinched-out and eroded cells. The SI method and the implementation described here represent the first demonstrated multiscale method applicable to general compositional problems with complexity relevant for industrial-reservoir simulation.