General Conservation Equation for Solute Transport in Heterogeneous Porous Media

Abstract

In this study it is shown that in heterogeneous porous media all the ensemble average conservation equations, representing linear reactive and nonreactive transport at a spatial scale one step larger than the Darcy scale, are in the same operator equation form as given by (15) herein for vector cases and by (18) herein for scalar cases to exact second-order closure (they do not need information on third or higher moments or cumulants). This equation acts as a “master key” in that once one determines the particular form of the coefficient operator within a Darcy-scale transport equation, corresponding to a particular linear transport case, one can then write immediately the explicit ensemble average transport equation for this case for the spatial scale that is one-step larger than the Darcy scale. The aforementioned equations are in Eulerian-Lagrangian form since while the spatial coordinate xt is given by time t, the spatial coordinate xt−s is an unknown which is determined by the Lagrangian trajectories...