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Bayesian experimental design for CO2 sequestration with leakage risk assessment

Ben Mansour Dia (College of Petroleum Engineering and Geosciences (CPG), King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia)

Engineering Computations

ISSN: 0264-4401

Article publication date: 4 January 2021

Issue publication date: 15 June 2021




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.


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.


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.


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.



The author would like to thank the two anonymous referees whose suggestions led to paper improvements. He is indebted grateful to Bilal Saad (Baker Hughes, Dhahran Technology Center 4.0) for helpful discussions on the numerical simulation of the forward model and to Mazen Saad (Ecole Centrale de Nantes) for the valuable discussions and comments on the practical aspects of the CO2 sequestration.


Dia, B.M. (2021), "Bayesian experimental design for CO2 sequestration with leakage risk assessment", Engineering Computations, Vol. 38 No. 3, pp. 1385-1401.



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