High-resolution monotonic schemes for reservoir fluid flow simulation
Academic Article
Overview
Additional Document Info
View All
Overview
abstract
This paper presents higher-order monotonic schemes for application to reservoir fluid flow problems. For convection-dominated flow, sharp resolution of discontinuities has been achieved by adding a limited antidiffusive flux to an entropy-satisfying first-order scheme. A new flux limiter is introduced that remains third-order accurate in space and time in the smooth regions and results in oscillation-free numerical solutions by imposing the total variation diminishing (TVD) criteria. The third-order scheme proposed here is particularly suitable for reservoir simulators that calculate pressure implicitly and saturation or concentration explicitly. The power of the method lies in its ease of implementation, improved accuracy, and in the fact that additional computational overhead compared to the single-point upstream weighting is negligible. We have applied the flux-limited third-order scheme to the linear convection-diffusion equation at high Peclet numbers and also to the convection of an isolated sine-squared wave. The results exhibit close agreement with analytical solutions and are free of spurious numerical oscillations. Unlike the second-order schemes, no artificial steepening (compression) or clipping of profiles is observed when the third-order limiter is used. For the two-phase Buckley-Leverett problem, use of the flux limiter has resulted in physically meaningful numerical solutions even in the absence of dissipative forces such as capillary pressure. In multidimensional examples, the numerical scheme has been applied to single-phase flow with longitudinal dispersion in a quadrant of a five-spot. Close agreement with the analytical solution has been obtained for the example case studied.
