A Hierarchical Bayesian Model for Estimating Remediation-induced Biogeochemical Transformations Using Spectral Induced Polarization Data: Development and Application to the Contaminated DOE Rifle (CO) Site

Although in-situ bioremediation is often considered as a key approach for subsurface environmental remediation, monitoring induced biogeochemical processes, needed to evaluate the efficacy of the treatments, is challenging over field relevant scales. In this study, we develop a hierarchical Bayesian model that builds on our previous framework for estimating biogeochemical transformations using geochemical and geophysical data obtained from laboratory column experiments. The new Bayesian model treats the induced biogeochemical transformations as both spatial and temporal (rather than just temporal) processes and combines time-lapse borehole ‘point’ geochemical measurements with inverted surface- or crosshole-based spectral induced polarization (SIP) data. This model consists of three levels of statistical sub-models: (1) data model (or likelihood function), which provides links between the biogeochemical end-products and geophysical attributes, (2) process model, which describes the spatial and temporal variability of biogeochemical properties in the disturbed subsurface systems, and (3) parameter model, which describes the prior distributions of various parameters and initial conditions. The joint posterior probability distribution is explored using Markov Chain Monte Carlo sampling methods to obtain the spatial and temporal distribution of the hidden parameters. We apply the developed Bayesian model to the datasets collected from the uranium-contaminated DOE Rifle site for estimating the spatial and temporal distribution of remediation-induced end products. The datasets consist of time-lapse wellbore aqueous geochemical parameters (including Fe(II), sulfate, sulfide, acetate, uranium, chloride, and bromide concentrations) and surface SIP data collected over 13 frequencies (ranging from 0.065Hz to 256Hz). We first perform statistical analysis on the multivariate data to identify possible patterns (or ‘diagnostic signatures’) of bioremediation, and then we invert the time-lapse SIP data for chargeability and time constant using Cole-Cole models. By combining the limited borehole time series data with spatially distributed time-lapse geophysical data, we can obtain the spatial and temporal distribution of the bioremediation end-products (such as volume fraction of FeS and calcite) and their associated uncertainty information. Our study results show how time-lapse SIP datasets, when incorporated into a Bayesian hierarchical model, can be useful for quantifying the spatiotemporal distribution of remediation-induced end-products. The study also documents how the diagnostic geophysical signatures can be useful for identifying when and where critical, remediation-induced system transitions occur, such as those accompanying a rebound in aquifer redox status and the associated impact on immobilized contaminant stability.