Simulation of tracer flow through heterogeneous porous media

Improved finite-difference techniques for simulating tracer flows through heterogeneous porous media are developed. These numerical techniques are then used to perform a series of numerical experiments that investigates the combined use of a discrete geologic model and apparent-mixing parameters to represent heterogeneous permeability fields.; Several multidimensional extensions of the one-dimensional, total variation diminishing (TVD), approach to developing flux-limiting functions for high-order finite-difference schemes are investigated. These extensions include using the TVD technique independently in each coordinate direction (TVD), using the TVD technique in successive coordinate sweeps (ADTVD), and using a new class of upstream stable (US) flux-limiting techniques. Additionally, a flux limiter based on a third-order finite-difference scheme is introduced. New algorithms are developed to allow the use of high-throughput (HT) timestepping with flux-limited techniques and to improve the use of HT timestepping for problems with physical dispersion/diffusion. The use of multidimensional TVD extensions combined with HT timestepping give numerical models that are more accurate and more efficient than previous finite-difference models.; Two sets of numerical experiments are performed that investigate the representation of permeability heterogeneities. The first experiment explores the effects of changes in the geologic representation scale (GRS). This experiment shows that reservoir response may continue to change as the GRS is decreased, and indicates that apparent mixing due to sub-GRS heterogeneity must be represented implicitly through apparent-mixing parameters, such as dispersivity. The second numerical study demonstrates a case for which the effects of small and large scale heterogeneities can be represented by a combination of explicit representation through varying gridblock permeabilities and implicit representation through apparent-mixing parameters. Furthermore, the properties of the non-represented permeability field are found to be related to the values of the apparent-mixing parameters. Thus, the non-represented permeability field may be used to determine if apparent-mixing parameters can successfully represent sub-GRS permeability heterogeneity. Finally, it is suggested that the robustness of apparent-mixing parameters can be improved by decoupling the GRS from the scale used to average apparent-mixing parameters.