Data-space approaches for uncertainty quantification of CO2 plume location in geological carbon storage

A data-space inversion (DSI) method is developed and applied to quantify uncertainty in the location of CO2 plumes in the top layer of a storage aquifer. In the DSI procedure, posterior predictions of the CO2 saturation distribution are generated using simulation results for prior geostatistical model realizations along with observed data, which in this case derive from observations at monitoring wells. Posterior (history-matched) geological models are not constructed in the DSI method, so many of the complications that arise in traditional data assimilation methods are avoided. The DSI method treats quantities of interest (QoI), such as the CO2 saturation distribution in the top layer, as random variables. The posterior distribution for these QoI, conditioned to observed data, is formulated in the data space within a Bayesian framework. Samples from this posterior distribution are generated using the randomized maximum likelihood method. We also introduce a procedure to optimize the locations of monitoring wells using only prior-model simulation results. This approach is based on analytical DSI results, and determines monitoring well locations such that the reduction in expected posterior variance of a relevant quantity is maximized. The new DSI procedure is applied to three-dimensional heterogeneous aquifer models involving uncertainties in a wide range of geological parameters, including variogram orientation, porosity and permeability fields, and regional pressure gradient. Multiple monitoring scenarios, involving four to eight monitoring wells, are considered in the evaluation of our data space methodology. Application of DSI with optimal monitoring wells is shown to consistently reduce the posterior variance of average CO2 saturation in the top layer, and to provide detailed saturation fields in reasonable correspondence with the 'true' saturation distribution. Finally, we demonstrate consistent improvement in DSI predictions as data are collected from an increasing number of (optimized) monitoring wells.