Percolation-theory and fuzzy rule-based probability estimation of fault leakage at geologic carbon sequestration sites

Leakage of CO{sub 2} and displaced brine from geologic carbon sequestration (GCS) sites into potable groundwater or to the near-surface environment is a primary concern for safety and effectiveness of GCS. The focus of this study is on the estimation of the probability of CO{sub 2} leakage along conduits such as faults and fractures. This probability is controlled by (1) the probability that the CO{sub 2} plume encounters a conductive fault that could serve as a conduit for CO{sub 2} to leak through the sealing formation, and (2) the probability that the conductive fault(s) intersected by the CO{sub 2} plume are connected to other conductive faults in such a way that a connected flow path is formed to allow CO{sub 2} to leak to environmental resources that may be impacted by leakage. This work is designed to fit into the certification framework for geological CO{sub 2} storage, which represents vulnerable resources such as potable groundwater, health and safety, and the near-surface environment as discrete 'compartments'. The method we propose for calculating the probability of the network of conduits intersecting the CO{sub 2} plume and one or more compartments includes four steps: (1) assuming that a random network of conduits follows a power-law distribution, a critical conduit density is calculated based on percolation theory; for densities sufficiently smaller than this critical density, the leakage probability is zero; (2) for systems with a conduit density around or above the critical density, we perform a Monte Carlo simulation, generating realizations of conduit networks to determine the leakage probability of the CO{sub 2} plume (P{sub leak}) for different conduit length distributions, densities and CO{sub 2} plume sizes; (3) from the results of Step 2, we construct fuzzy rules to relate P{sub leak} to system characteristics such as system size, CO{sub 2} plume size, and parameters describing conduit length distribution and uncertainty; (4) finally, we determine the CO{sub 2} leakage probability for a given system using fuzzy rules. The method can be extended to apply to brine leakage risk by using the size of the pressure perturbation above some cut-off value as the effective plume size. The proposed method provides a quick way of estimating the probability of CO{sub 2} or brine leaking into a compartment for evaluation of GCS leakage risk. In addition, the proposed method incorporates the uncertainty in the system parameters and provides the uncertainty range of the estimated probability