Uncertainty Quantification of Geologic Energy Storage in Depleted Gas Reservoirs Using Material Balance Equations Embedded in a Hierarchical Errors-in-Variables Model

Abstract The storage potential for gas in geologic settings, such as depleted hydrocarbon reservoirs and solution-mined salt caverns, is becoming salient to future energy infrastructure planning. Technologies such as carbon capture, utilization, and storage, carbon dioxide-enhanced oil recovery, and natural gas and hydrogen storage help meet growing energy demands, reduce carbon emissions to meet climate goals, and provide energy security amid geopolitical uncertainties. Therefore, estimates of underground gas storage capacity could be useful for efficiently navigating the energy transitions. Material balance is a fundamental method in reservoir engineering for estimating original gas in place and potential storage capacity at the scale necessary for national assessments of subsurface pore space resources. However, the deterministic method cannot accommodate multiple data sources or quantify uncertainty in predictions. In this study, a method that embeds material balance equations within a hierarchical errors-in-variables model is proposed which allows the estimation of the distributions of reservoir properties needed for assessments. Uncertainties associated with these reservoir properties have traditionally been expert-elicited, whereas the uncertainty estimates from the proposed models are data-driven. Capacity and uncertainty estimates can be used in a probabilistic resource assessment, supplementing information traditionally used by assessors or even replacing this expert elicitation step when data are unavailable. Various regression models are compared in a case study of the Michigan Basin, a large contributor to the United States’ current natural gas storage capacity. In particular, errors-in-variables models help ameliorate regression dilution and can quantify uncertainty in predictions of pressure in addition to storage capacity. Overfitting is addressed by quantifying generalization error and model averaging in simple and stratified cross-validation against reported working gas capacity, representing the varying quality and quantity of available data. Incorporating a statistical framework into existing numerical methods in reservoir engineering can improve the quality of estimation, and in particular, this method brings rigor to uncertainty quantification as part of a larger effort by the U.S. Geological Survey to assess domestic energy gas storage resources in depleted hydrocarbon reservoirs.