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

- Author(s): Zhang, Yingqi
- Oldenburg, Curtis M.
- Finsterle, Stefan
- et al.

## Published Web Location

https://doi.org/10.1007/s12665-009-0131-4## Abstract

Leakage of CO2 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 CO2 leakage along conduits such as faults and fractures. This probability is controlled by (1) the probability that the CO2 plume encounters a conductive fault that could serve as a conduit for CO2 to leak through the sealing formation, and (2) the probability that the conductive fault(s) intersected by the CO2 plume are connected to other conductive faults in such a way that a connected flow path is formed to allow CO2 to leak to environmental resources that may be impacted by leakage. This work is designed to fit into the certification framework for geological CO2 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 CO2 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 CO2 plume (P leak) for different conduit length distributions, densities and CO2 plume sizes; (3) from the results of Step 2, we construct fuzzy rules to relate P leak to system characteristics such as system size, CO2 plume size, and parameters describing conduit length distribution and uncertainty; (4) finally, we determine the CO2 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 CO2 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.

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