Bayesian experimental design for CO₂ sequestration with leakage risk assessment

Purpose: The author examine the sequestration of CO₂ in abandoned geological formations where leakages are permitted up to only a certain threshold to meet the international CO₂ emissions standards. Technically, the author address a Bayesian experimental design problem to optimally mitigate uncertainties and to perform risk assessment on a CO₂ sequestration model, where the parameters to be inferred are random subsurface properties while the quantity of interest is desired to be kept within safety margins. Design/methodology/approach: The author start with a probabilistic formulation of learning the leak-age rate, and the author later relax it to a Bayesian experimental design of learning the formations geo-physical properties. The injection rate is the design parameter, and the learned properties are used to estimate the leakage rate by means of a nonlinear operator. The forward model governs a two-phase two-component flow in a porous medium with no solubility of CO₂ in water. The Laplace approximation is combined with Monte Carlo sampling to estimate the expectation of the Kullback–Leibler divergence that stands for the objective function. Findings: Different scenarios, of confining CO₂ while measuring the risk of harmful leakages, are analyzed numerically. The efficiency of the inversion of the CO₂ leakage rate improves with the injection rate as great improvements, in terms of the accuracy of the estimation of the formation properties, are noticed. However, this study shows that those results do not imply in any way that the learned value of the CO₂ leakage should exhibit the same behavior. Also this study enhances the implementation of CO₂ sequestrations by extending the duration given by the reservoir capacity, controlling the injection while the emissions remain in agreement with the international standards. Originality/value: Uncertainty quantification of the reservoir properties is addressed. Nonlinear goal-oriented inverse problem, for the estimation of the leakage rate, is known to be very challenging. This study presents a relaxation of the probabilistic design of learning the leakage rate to the Bayesian experimental design of learning the reservoir geophysical properties.