PREDICTING SOLUTE PLUME EVOLUTION IN HETEROGENEOUS POROUS FORMATIONS

Modeling of the time evolution of a solute plume in a heterogeneous po rous formation has often focused on low-order spatial concentration mo ments calculated in comprehensive field experiments in which a plume i s sampled synoptically at successive stages of its postinjection devel opment. Assumptions of a, stochastic nature usually have been invoked to derive equations that predict the time dependence of these spatial moments and permit their interpretation in terms of field concentratio n data. In this paper, expressions for the low-order spatial moments a re derived on the basis of a purely dynamical formulation of plume mot ion in terms of the solution of the autonomous ordinary differential e quation determined by a steady fluid velocity field. The equations der ived stress the importance of spatial interdependence between the (arb itrary) initial state of a solute plume, as defined by its concentrati on field, and the subsequent displacements of moving spatial points de termined by a groundwater velocity field.