High-Resolution Methods for Enhanced Oil Recovery Simulation

Enhanced oil recovery processes involve multicomponent, multiphase flow through porous media. Proper numerical modeling and flow prediction are essential for the successful design and evaluation of these processes. Conventional simulation techniques suffer from either excessive artificial diffusion effects or highly spurious oscillations when modeling convection-dominated processes. These artificial effects can lead to a breakdown in the stability of the finite-difference scheme and to inaccurate predictions and erroneous conclusions. In this research we present high-resolution simulation techniques to overcome these problems and to improve the performance of numerical compositional reservoir simulators. We have applied a second-order time-correction method to a explicit scheme with high-order spatial discretization to increase its temporal accuracy and to stabilize the scheme by relaxing the Courant number limits at high cell Peclet numbers. The stability conditions of the Courant number limits as functions of cell Peeler numbers are presented. We use a third-order scheme to approximate the convection term and the Crank-Nicolson scheme to approximate the temporal derivative. The conditions sufficient for a finite-difference scheme to be total variation diminishing (TVD) are derived in a more general form which includes both the implicit and explicit differencing terms. Applying these conditions, we obtain the TVD constraints for both the implicit and explicit flux functions. These constraints form a TVD region which is a function of timestep size. Larger timestep sizes correspond to smaller TVD regions. Under the TVD constraints, the third-order TVD flux limiter is constructed using the third-order flux function to achieve higher accuracy. Accuracy is maintained with nonuniform grids. We have implemented the high-resolution techniques into the IMPES compositional simulators and developed a fully implicit simulator with the high-resolution numerical features. TVD constraints are applied to the species fluxes and the phase fluxes by imposing the TVD third-order limiter functions to the approximations of interface convections and interface relative permeabilities. For the IMPES formulation, the second-order time-correction terms are added to the dispersion coefficients. For the fully implicit formulation, the resulting nonlinear system of residual equations is solved for the primary variables. The flux limiter functions and their derivatives are updated at the end of each iteration. The simulation results show remarkable success in eliminating numerical effects and in resolving shock fronts, even for very highly convection-dominated problems. The high-resolution techniques use several hundred times less computing time to achieve the accuracy obtained using conventional techniques with finer grids. A fully implicit simulator using the high-resolution scheme produces more accurate results than one using conventional techniques and more stable results than the IMPES simulator. The performance of the simulator is greatly improved using suitable timestepping algorithms and efficient solution solvers.