AN APPROACH TO TRANSPORT IN HETEROGENEOUS POROUS-MEDIA USING THE TRUNCATED TEMPORAL MOMENT EQUATIONS - THEORY AND NUMERICAL VALIDATION

In the last decade, the characterization of transport in porous media has benefited largely from numerical advances in applied mathematics a nd from the increasing power of computers. However, the resolution of a transport problem often remains cumbersome, mostly because of the ti me-dependence of the equations and the numerical stability constraints imposed by their discretization. To avoid these difficulties, another approach is proposed based on the calculation of the temporal moments of a curve of concentration versus time. The transformation into the Laplace domain of the transport equations makes it possible to develop partial derivative equations for the calculation of complete moments or truncated moments between two finite times, and for any point of a bounded domain. The temporal moment equations are stationary equations , independent of time, and with weaker constraints on their stability and diffusion errors compared to the classical advection-dispersion eq uation, even with simple discrete numerical schemes. Following the com plete theoretical development of these equations, they are compared fi rstly with analytical solutions for simple cases of transport and seco ndly with a well-performing transport model for advective-dispersive t ransport in a heterogeneous medium with rate-limited mass transfer bet ween the free water and an immobile phase. Temporal moment equations h ave a common parametrization with transport equations in terms of thei r parameters and their spatial distribution on a grid of discretizatio n. Therefore, they can be used to replace the transport equations and thus accelerate the achievement of studies in which a large number of simulations must be carried out, such as the inverse problem condition ed with transport data or for forecasting pollution hazards.