ONE-DIMENSIONAL SOLUTE TRANSPORT MODELING IN AGGREGATED POROUS-MEDIA .1. MODEL DESCRIPTION AND NUMERICAL-SOLUTION

A model for the simulation of solute transport in aggregated porous media is presented. Transport by convection and dispersion in the mobile phase, diffusion of solute inside aggregates of arbitrary shapes and sizes, external mass transfer resistance and linear adsorption are considered. Depth-dependent properties of porous media and size distribution of aggregates are accounted for. The problem of solute diffusion inside arbitrarily shaped aggregates is rigorously and easily treated by application of the Laplace transformation and by introduction of an 'aggregate shape function'. The whole system of equations is solved by: (1) application of the Laplace transformation; (2) introduction of the 'aggregate shape function' to reduce the transport problem to a single ordinary differential equation whatever the geometry of aggregates and the phenomena accounted for (kinetic or instantaneous adsorption, external mass transfer resistance); (3) finite-difference numerical solution of this differential equation; (4) numerical inversion of the solution obtained in the Laplace space. The main advantages of this model are: (1) it incorporates, in a unique frame, the whole variety of models so far proposed for transport modelling in aggregated porous media (zero-, first- and higher order approaches); (2) it simplifies the numerical treatment so that there is no need to make simplifying assumptions about the phenomena; (3) it provides an accurate solution using very little computer time. The model is compared with previous solutions, analytical or numerical, obtained for simple aggregate geometries.