Roy Haggerty

Multiple‐Rate Mass Transfer for Modeling Diffusion and Surface Reactions in Media with Pore‐Scale Heterogeneity

Mass transfer between immobile and mobile zones is a consequence of simultaneous processes. We develop a “multirate” model that allows modeling of small-scale variation in rates and types of mass transfer by using a series of first-order equations to represent each of the mass transfer processes. The multirate model is incorporated into the advective-dispersive equation. First, we compare the multirate model to the standard first-order and diffusion models of mass transfer. The spherical, cylindrical, and layered diffusion models are all shown to be specific cases of the multirate model. Mixtures of diffusion from different geometries and first-order rate-limited mass transfer can be combined and represented exactly with the multirate model. Second, we develop solutions to the multirate equations under conditions of no flow, fast flow, and radial flow to a pumping well. Third, using the multirate model, it is possible to accurately predict rates of mass transfer in a bulk sample of the Borden sand containing a mixture of different grain sizes and diffusion rates. Fourth, we investigate the effects on aquifer remediation of having a heterogeneous mixture of types and rates of mass transfer. Under some circumstances, even in a relatively homogeneous aquifer such as at Borden, the mass transfer process is best modeled by a mixture of diffusion rates.

Aquifer remediation: A method for estimating mass transfer rate coefficients and an evaluation of pulsed pumping

When pumping contaminated water from an aquifer, contaminant concentrations often decline rapidly, only to rebound when the pump is shut off. One reason for this behavior is that contaminants in the mobile phase are readily removed, but mass transfer from the immobile to the mobile phase is rate limited. Pulsed pumping, in which the pump is periodically turned off, has been suggested as a means to enhance remediation. We conducted a comprehensive comparison of pulsed pumping and continuous pumping for the case of a Gaussian plume, subject to first- order mass transfer during transport, in an aquifer with no regional gradient and constant mass transfer rate coefficients. We developed a Laplace domain Greens function solution for concentrations during pumping periods and coupled it with an analytic solution for concentrations during resting periods. First, we used this model to provide a simple type curve that can be used to estimate the mobile-immobile phase mass transfer coefficients from field data. Second, the mass and concentration removal histories were determined during pulsed pumping and during continuous pumping. The continuous pumping rate removed the same volume of water over the duration of remediation. We investigated the effects of physical parameters such as the mass transfer rate coefficients, and engineering design parameters such as the length of resting periods. Under the conditions considered, our evaluation shows that (1) for equal volumes of water removed, pulsed pumping does not remove more contaminant mass than pumping continuously at an average rate; (2) if the duration of the resting period is too large, then pulsed pumping removes much less mass than continuous pumping at the average rate, and (3) if the pulsed and continuous pumping rates are the same, pulsed pumping will take longer than continuous pumping to clean up the aquifer, but will require significantly less time during which the pump operates.

Design of multiple contaminant remediation: Sensitivity to rate‐limited mass transfer

Optimal extraction well locations and pumping rates are compared, based on a limited number of deterministic simulations, for multiple contaminant plumes exhibiting rate-limited, or nonequilibrium, mass transfer from a mobile to an immobile phase. This rate-limited mass transfer results in what we define as rate-limited, or nonequilibrium, transport. Two-dimensional, nonequilibrium solute transport simulation and optimization are used to study the simultaneous remediation of carbon tetrachloride, 1,2-dichloroethane and tetrahydrofuran that have been chromatographically separated during transport by groundwater. Minimum total pumping necessary for cleanup is compared for five different well geometries over remediation periods of 3 and 15 years. The sensitivity of these designs to first-order mass transfer rates is examined for equilibrium and for three levels of nonequilibrium transport. The key results of this particular study are that (1) classic contaminant capture at downgradient wells is a poor design for contaminant cleanup; (2) for effective design of multiple plume remediation, the transport characteristics of each contaminant must be considered; (3) if solute transport is limited by mass transfer from an immobile to a mobile phase, there is a minimum remediation time which cannot be reduced by adjustment of pumping rates or changing well locations; (4) the optimal locations and pumping rates of extraction wells are less sensitive to nonequilibrium transport for long-term remediation than for short-term remediation; and (5) competition between pumping wells may significantly affect the feasibility and efficiency of specific multiple-well cleanup designs. In addition, a method and a measurement are presented for evaluating the importance to remediation of rate-limited mass transfer.