A method for estimating distributions of mass transfer rate coefficients with application to purging and batch experiments

Mass transfer between aquifer material and groundwater is often modeled as first-order rate-limited sorption or diffusive exchange between mobile zone s and immobile zones with idealized geometries, Recent improvements in expe rimental techniques and advances in our understanding of pore-scale heterog eneity demonstrate that two (or even a few) rate coefficients are insuffici ent in many cases. Here, we investigate a piece-wise linear model for a con tinuous distribution of rate coefficients, that has several advantages over previously used 'statistical' distribution models (with functional form fr om gamma or lognormal PDF's): (1) distributions of arbitrary, even bimodal, shapes can be represented; (2) linear estimation methods can be applied to determine the distribution from experimental data; (3) the uncertainty in the distribution can be determined for each of its sections; and (4) the re lationship between the time scales of available data and those of estimatab le mass transfer processes can be investigated. A statistical model refinem ent algorithm is presented that reduces the number of parameters (sections of the piece-wise linear model) to the admissible minimum. We show that pur ging experiments allow estimation of a wider zone of the rate distribution than do batch experiments, and hence will provide predictions that are accu rate over a wider range of time scales. Finally, in an application to TCE g as-purging desorption data, the piece-wise linear rate-distribution model h as a higher probability of being adequate than these using a gamma or logno rmal distribution or a single rare coefficient. (C) 1999 Elsevier Science B .V. All rights reserved.