Bayesian process-identification in bacteria transport in porous media

Abstract

A Bayesian parameter estimation approach is developed for the estimation of joint probability distribution functions for colloid and bacterial fate and transport model parameters describing breakthrough curves (BTCs) obtained through porous media column studies, and is applied to data involving different ionic strength solutions to fit models of differing complexity. Our approach focuses on the simultaneous fitting of a number of BTCs representing different conditions, and it provides a measure of the goodness of model structure, namely Deviance Information Criteria (DIC). Comparison of DIC per model fit enables the evaluation of the significance of various processes through step-wise increases in complexity due to the addition of process model components. We use the method to investigate the transport of both flagellated and non-flagellated strains of Azotobacter vinelandii in a simulated porous media under three ionic strengths. Three different model structures are considered: one without a detachment process and with Langmuirian blocking function, one with detachment, and one with detachment and a second-order blocking function based on random sequential adsorption. First, the model was applied separately to each single BTC. Next, the model was applied comprehensively to the experiments under various ionic strengths, whereas some transport parameters including dispersivity, detachment coefficient, the fraction of cells undergoing irreversible attachment, and the coefficient of the second-order blocking term were assumed to be the same under different ionic strengths. In most cases, including detachment substantially improved the DIC as expected, whereas using the second-order blocking improved DIC for most of the cases when the method was applied to separate BTCs but not when the method was applied collectively to the three BTCs obtained under various ionic strengths. Also, comparing the outcomes of the separate applications of the parameter estimation algorithm versus the collective application indicates that the uncertainty associated with the estimated parameters is substantially smaller when the collective approach is used and also that the estimated parameters are more consistent with the expectations based on the underlying physical processes.