A Bayesian framework for the validation of models for subsurface flows: synthetic experiments

We present a new Bayesian framework for the validation of models for subsurface flows. We use a compositional model to simulate CO2 storage in saline aquifers, comparing simulated saturations to observed saturations, together with a Bayesian analysis, to refine the permeability field. At the laboratory scale, we consider a core that is initially fully saturated with brine in a drainage experiment performed at aquifer conditions. Two types of data are incorporated in the framework: the porosity field in the entire core and CO2 saturation values at equally spaced core slices for several values of time. These parameters are directly measured with a computed tomography scanner. We then find permeability fields that (1) are consistent with the measured parameters and, at the same time, (2) allow one to predict future fluid flow. We combine high performance computing, Bayesian inference, and a Markov chain Monte Carlo (McMC) method for characterizing the posterior distribution of the permeability field conditioned on the available dynamic measurements (saturation values at slices). We assess the quality of our characterization procedure by Monte Carlo predictive simulations, using permeability fields sampled from the posterior distribution. In our characterization step, we solve a compositional two-phase flow model for each permeability proposal and compare the solution of the model with the measured data. To establish the feasibility of the proposed framework, we present computational experiments involving a synthetic permeability field known in detail. The experiments show that the framework captures almost all the information about the heterogeneity of the permeability field of the core. We then apply the framework to real cores, using data measured in the laboratory.