A Markov Chain Monte Carlo Inversion Approach for Assessing Reactive Chemistry Along a Flow Path with Application to Subsurface CO2 Injection

A Markov Chain Monte Carlo (MCMC) modeling approach has been developed to identify the distribution of key reactive mineral phases along a flow path between a CO2 injector well and a monitor well at the Weyburn-Midale field in Saskatchewan. The method entailed postulating a spatially-correlated mineral distribution, consisting of calcite, dolomite, anhydrite, and K-feldspar, with specified volume fractions and intrinsic dissolution rates, in contact with an ambient brine composition along a 1-D flow path. Multiple forward reactive transport simulations for the column were run (using PHREEQC for this particular application), with simulated changes in brine chemistry compared with controlled test problem output or real field data. A composite likelihood function was calculated for a set of geochemical parameters consisting of pH and the concentrations of Ca2+, Mg2+, and Si that serves as potential indicators of dissolution reactions along the flow path. New realizations were proposed by replacing a small contiguous section of the column with a new distribution of minerals, but one which was still spatially correlated with the remainder of the column. Proposed realizations were accepted when the ratio of the composite likelihood function value to that of the prior proposal was greater than that of a random number selected from a uniform distribution between 0 and 1 (the well-known Metropolis-Hastings acceptance criteria). If a proposal was accepted, the modified mineral distribution served as the basis for a new distribution, otherwise the modification was rejected as a non-improvement. Application of the inverse modeling approach to a synthetic problem demonstrated nearly complete recovery of a specified initial mineral distribution (i.e., "synthetic truth") along the flow path, provided that parameter data were utilized across the entire column. Partial recovery of the synthetic truth was still achievable as the amount of data available for inversion were reduced to just the column endpoint, mimicking the typical situation in the field. When applied to brine chemistry data from a 1-km x 1-km test area at the Weyburn-Midale reservoir, the inversion approach identified variations in the amounts of dolomite and calcite available for reaction along the flow path, given simplifying assumptions concerning permeability, pressure gradient, mineral specific surface, and the extent of mixing in the formation. These variations are qualitatively consistent with known compositional variability in mineralogy between the CO2 injector and monitoring well locations. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.