A state-space Bayesian framework for estimating biogeochemical transformations using time-lapse geophysical data

We develop a state-space Bayesian framework to combine time-lapse geophysical data with other types of information for quantitative estimation of biogeochemical parameters during bioremediation. We consider characteristics of end products of biogeochemical transformations as state vectors, which evolve under constraints of local environments through evolution equations, and consider time-lapse geophysical data as available observations, which could be linked to the state vectors through petrophysical models. We estimate the state vectors and their associated unknown parameters over time using Markov chain Monte Carlo sampling methods. To demonstrate the use of the state-space approach, we apply it to complex resistivity data collected during laboratory column biostimulation experiments that were poised to precipitate iron and zinc sulfides during sulfate reduction. We develop a petrophysical model based on sphere-shaped cells to link the sulfide precipitate properties to the time-lapse geophysical attributes and estimate volume fraction of the sulfide precipitates, fraction of the dispersed, sulfide-encrusted cells, mean radius of the aggregated clusters, and permeability over the course of the experiments. Results of the case study suggest that the developed state-space approach permits the use of geophysical data sets for providing quantitative estimates of end-product characteristics and hydrological feedbacks associated with biogeochemical transformations. Although tested here on laboratory column experiment data sets, the developed framework provides the foundation needed for quantitative field-scale estimation of biogeochemical parameters over space and time using direct, but often sparse wellbore data with indirect, but more spatially extensive geophysical data sets.