COMPARISON OF SOLUTION APPROACHES FOR THE 2-DOMAIN MODEL OF NONEQUILIBRIUM TRANSPORT IN POROUS-MEDIA

The two-domain concept is widely used in modelling transport in hetero geneous porous media and transport of rate-limited sorbing contaminant s. When a first-order kinetic relationship is used to represent the tr ansfer of mass between domains, the model can be expressed as a modifi ed advection-dispersion equation describing general transport coupled to a first-order ordinary differential equation accounting for mass tr ansfer. Different approaches can be used to solve the resulting system , including: simultaneously solving the coupled transport and kinetic equations; discretising and algebraically solving the mass transfer eq uation and substituting it into the transport equation; solving the ma ss transfer equation analytically and substituting the integral soluti on into the transport equation to obtain a single integro-differential equation; and solving the system in Laplace space and back-transformi ng the solution into the time domain. These four approaches - coupled, algebraic substitution, integro-differential, and finite element Lapl ace transform (FELT) - are evaluated on the basis of their general fea tures and on their performance in two test cases. The results indicate that the algebraic substitution approach is robust and, on scalar com puters, very efficient. The FELT approach is easily parallelised and a chieves good speed-up on supercomputers, but the method is restricted to time-invariant velocity and saturation fields, and is only useful f or obtaining the solution at or not too far from the maximum simulatio n time. The integro-differential method is as efficient as but less ro bust than the algebraic substitution approach, requiring a small time step size when the mass transfer coefficient is very large. Finally, t he coupled approach is robust and flexible, but requires the solution of a system of equations twice as large as the other methods. On balan ce, the algebraic substitution and, to a lesser extent, the integro-di fferential methods appear to be the most attractive approaches on scal ar machines while FELT, when applicable, is an appealing alternative f or coarse-grained multiprocessors. Copyright (C) 1996 Elsevier Science Limited