Stochastic-perturbation analysis of solute transport through porous media with spatially variable retardation factor - Alvarado, Vladimir (Ciencia, 1970)
A closed-form first-order solution to the Laplace transform of the convection-dispersion equation is derived for sorbing or partitioning tracers under conditions of chemical equilibrium. For the given flux boundary condition, the Laplace transform of the transit-time distribution. P(t), is found for retardation factors, R, owing an exponentially decaying covariance function. Moments of P(t), ïƒ¡tnïƒ±, are obtained by taking derivatives of P(S) = L {P(t)}, which means that P(S) is a generator of moments. These moments are emploved to find transport coefficients, in particular the so-called dispersion coefficient, D. The main effect of the variable Ris to enhance the spreading of the sorbing tracer, that increases the value of D. At late times (large distances), the first-order moment is expected to be insensitive to the spatial variation of R. Thus, the mean velocity of a traveling pulse becomes independent of these variations, unless an infinite correlation length is imposed.