Numerical simulation of reactive flow and transport through the subsurface

[摘要] Convection-dominated fluid transport problems have long resisted accurate and cost-effective numerical solutions. The near hyperbolic nature of the problem causes spurious oscillations in most numerical schemes or avoiding that, excessive numerical diffusion, both of which can be remedied only at the cost of a large CPU time. The numerical schemes based on characteristic techniques can yield superior solutions for such problems. One such scheme that has been applied to problems in contaminant transport and miscible displacement is the Characteristic-Galerkin method (CGM). Though this method is quite successful, its principal drawbacks are its nonconservative nature, oscillations and the sensitivity to the quadrature rules of integration in the Galerkin part of the procedure. A recently developed ;;Characteristic-Mixed;; method (CMM) replaces the Galerkin part in CGM with a Mixed Finite Element method, to minimize oscillations and help achieve global and local material balance. Finally a ;;Characteristic Conservative;; method (CCM) in three dimensions is described. Here a ;;Volume-Balance;; scheme for velocities is coupled with CMM so that local and global material balance are achieved in practice. Each ;;rectangular grid block;; is treated as a fluid element and its material surface at the previous time level is identified. This is done by following the streamlines originating on the surface of the grid block back in time for the duration of the time-step and then joining the endpoints of these streamlines to obtain the ;;twisted grid block;;. The streamlines are computed from the ;;Volume-Balance;; criterion that the volume of the twisted grid block is equal to the volume of the ;;regular grid block;;; which is a restatement of the incompressibility of the flow. The contribution of the reactions to the change in concentration is found by solving the ordinary differential equations that represent reactions, with the twisted grid block concentration as the initial condition. This method is strictly conservative both locally and globally, in the absence of oscillations. Like CMM, it has no oscillations when a diagonal dispersion tensor is used and shows small overshoot and undershoot for a full dispersion tensor. Simulations show that numerical dispersion with the MMOC (Modified Method of Characteristics) or the Characteristic scheme can be significant in the case of heterogeneous velocity fields. This leads to optimistic estimates for recovery in unstable miscible displacement and for the amount of degradation in in situ bioremediation. A couple of strategies for bioremediation with wells have been studied. When the produced contaminant is reinjected into the injection well, the microbial build up near the injection well causes most of the degradation.

[发布机构] Rice University

[效力级别] Mathematics