Model selection for CO₂ sequestration using surface deflection and injection data
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In recent years, sequestration of CO₂ in the subsurface has been studied more extensively as an approach to curb carbon emissions into the atmosphere. Monitoring the fate and migration of the CO₂ plume in the aquifer is of utmost interest to regulators and operators. Current monitoring techniques like time-lapse seismic are expensive and have limited applicability. Moreover, these techniques have little predictive value unless embedded within a feedback-style control scheme. Provided that field data such as bottom-hole pressures, well rates, or even surface deformation is available, geologic models for the aquifer can be created and used, as an input to a flow simulator, to predict the migration of CO₂. A history matching approach has been developed, within a model selection framework, to select and refine geologic models within a selected set of models until they represent the spatial heterogeneity of the target aquifer, and produce forecast with relatively small uncertainty. An initial large suite of models can be created based on prior information of the aquifer. Predicting the response from these models however, presents a problem in terms of computational time and expense. A particle-tracking algorithm has been developed to estimate the flow response from geologic models, while significantly reducing computational costs. This algorithm serves as a fast approximation of finite-difference flow simulation models, and is meant to provide a rapid estimation of connectivity of the aquifer models. A finite element method (FEM) solver was also developed to approximate the geomechanical effects in the rock caused by the injection of CO₂. The approach used here utilizes a partial coupling scheme to sequentially solve the flow and geomechanical equilibrium equations. The validity of the proxies is tested on both 2D and 3D field cases, and the solutions are shown to correlate reasonably well with full-physics simulations. We also demonstrate the application of the model selection algorithm to a 3D reservoir with complex topography. The algorithm includes three main steps: (1) predicting the flow and geomechanical response of a large prior ensemble of models using the proxies; (2) grouping models with similar responses into clusters using multidimensional scaling together with a k-means clustering approach; and (3) selecting a model cluster that produces the minimum deviation from the observed field data. The model selection procedure can be repeated using the sub-group of models within a selected cluster in order to further refine the forecasts for future plume migration. This entire iterative model selection scheme is demonstrated using the injection data for the Krechba reservoir in Algeria, which is an active site for CO₂ sequestration.