Optimizing Sealing of CO2 Leakage Paths with Microbially Induced Calcite Precipitation Under Uncertainty

Abstract

Summary In large-scale CO₂ sequestration, critical pressure build-up can occur due to the high injection rates, which in the worst case can lead to leakage paths for the CO₂ through caprock fractures and/or reactivated faults. A novel leakage mitigation technology is microbially induced calcite precipitation (MICP), where microorganisms are injected to accelerate production of the sealing agent – calcite – from calcium and urea. The MICP technology has been validated on multiple scales, from laboratory to meter-scale experiments. On the field scale, the situation can be challenging since leakage path(s) are possibly tens-of-meter from the injection well, and the subsurface parameters controlling the flow, chemical reactions, and microbial processes can be uncertain. In this work, we consider the optimization problem of maximising sealing of leakage paths in the presence of uncertainty. The control variables can, e.g., be injection rates and periods, or concentration of chemical and biological species, while the uncertain parameters can, e.g., be permeability and porosity. To quantify the effect of parameter uncertainty on control variables, an accelerated Monte Carlo (aMC) method is used, which aims to accelerate the slow convergence of the standard MC method. Even with aMC methods, a significant number of samples of the objective function is needed, that is, multiple runs of the simulator is required. The MICP process at field scale is described by a coupled advection-diffusion-reaction, microbial, and rockaltering equation that is associated with high computational cost to solve. To alleviate the high computational cost, we generate a surrogate (or proxy) model of the original objective function that can be evaluated at negligible cost. The surrogate model is based on the sparse hierarchical multi-linear interpolation (SI) method, where the objective function is approximated to a desired accuracy using significantly fewer function evaluations than traditional interpolation methods. Hence, the computational cost of generating and sampling with the surrogate model is typically lower than the cost of sampling with the original objective function. The novel SI-aMC method is applied to different test cases showing the computational efficiency and accuracy of uncertainty estimates for field-scale MICP optimization problems.