ISSN:
1573-1634
Keywords:
dispersion
;
reaction
;
perturbation theory
;
stochastic modeling
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Technology
Notes:
Abstract We carry out a stochastic-perturbation analysis of a one-dimensional convection–dispersion-reaction equation for reversible first-order reactions. The Damköhler number, Da, is distributed randomly from a distribution that has an exponentially decaying correlation function, controlled by a correlation length, ξ. Zeroth- and first-order approximations of the dispersion coefficient, D are computed from moments of the residence-time distribution obtained by solving a one-dimensional network model, in which each unit of the network represents a Darcy-level transport unit, and the solution of the transfer function in zeroth- and first-order approximations of the transport equation. In the zeroth-order approximation, the dispersion coefficient is calculated using the convection–dispersion-reaction equation with constant parameters, that is, perturbation corrections to the local equation are ignored. This zeroth-order dispersion coefficient is a linear function of the variance of the Damköhler number, 〈(ΔDa)2〉. A similar result was reported in a two-dimensional network simulation. The zeroth-order approximation does not give accurate predictions of mixing or spreading of a plume when Damköhler numbers, Da ≪ 1 and its variance, 〈(ΔDa)2〉 〉 0.25 〈Da2〉. On the other hand, the first-order theory leads to a dispersion coefficient that is independent of the reaction parameters and to equations that do accurately predict mixing and spreading for Damköhler numbers and variances in the range √〈(ΔDa)2〉/〈Da〉≤0.3
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006575527731
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