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A METHOD FOR ESTIMATING DISTRIBUTIONS OF MASS TRANSFER RATE COEFFICIENTS WITH APPLICATION TO PURGING AND BATCH EXPERIMENTS. (R825825)
Citation:
Hollenbeck, K., C. Harvey, R. Haggerty, AND C. Werth. A METHOD FOR ESTIMATING DISTRIBUTIONS OF MASS TRANSFER RATE COEFFICIENTS WITH APPLICATION TO PURGING AND BATCH EXPERIMENTS. (R825825). JOURNAL OF CONTAMINANT HYDROLOGY. Elsevier Science Ltd, New York, NY, 37(3-4):367-388, (1999).
Description:
Mass transfer between aquifer material and groundwater is often modeled as first-order rate-limited sorption or diffusive exchange between mobile zones and immobile zones with idealized geometries. Recent improvements in experimental techniques and advances in our understanding of pore-scale heterogeneity demonstrate that two (or even a few) rate coefficients are insufficient in many cases. Here, we investigate a piece-wise linear model for a continuous distribution of rate coefficients, that has several advantages over previously used `statistical' distribution models (with functional form from 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 relationship between the time scales of available data and those of estimatable mass transfer processes can be investigated. A statistical model refinement algorithm is presented that reduces the number of parameters (sections of the piece-wise linear model) to the admissible minimum. We show that purging experiments allow estimation of a wider zone of the rate distribution than do batch experiments, and hence will provide predictions that are accurate over a wider range of time scales. Finally, in an application to TCE gas-purging desorption data, the piece-wise linear rate-distribution model has a higher probability of being adequate than those using a gamma or lognormal distribution or a single rate coefficient.
Author Keywords: Mass transfer; Diffusion; Sorption; Estimation