STOCHASTIC-PERTURBATION ANALYSIS OF A ONE-DIMENSIONAL DISPERSION-REACTION EQUATION - EFFECTS OF SPATIALLY-VARYING REACTION-RATES

We carry out a stochastic-perturbation analysis of a one-dimensional c onvection-dispersion-reaction equation for reversible first-order reac tions. The Damkohler number, Da, is distributed randomly from a distri bution that has an exponentially decaying correlation function, contro lled by a correlation length, xi. Zeroth- and first-order approximatio ns of the dispersion coefficient, D, are computed from moments of the residence-time distribution obtained by solving a one-dimensional netw ork model, in which each unit of the network represents a Darcy-level transport unit, and the solution of the transfer function in zeroth- a nd first-order approximations of the transport equation. In the zeroth -order approximation, the dispersion coefficient is calculated using t he convection-dispersion-reaction equation with constant parameters, t hat is, perturbation corrections to the local equation are ignored. Th is zeroth-order dispersion coefficient is a linear function of the var iance of the Damkohler number, [(Delta Da)(2)]. A similar result was r eported in a two-dimensional network simulation. The zeroth-order appr oximation does not give accurate predictions of mixing or spreading of a plume when Damkohler numbers, Da much less than 1, and its variance , [(Delta Da)(2)] > 0.25[Da(2)]. On the other hand, the first-order th eory leads to a dispersion coefficient that is independent of the reac tion parameters and to equations that do accurately predict mixing and spreading for Damkohler numbers and variances in the range root[(Delt a Da(2))]/[Da] less than or equal to 0.3.