Comparison of ensemble filtering algorithms and null-space Monte Carlo for parameter estimation and uncertainty quantification using CO₂ sequestration data

Geological storage of CO₂ requires multiphase flow models coupled with key hydrogeologic features to accurately predict the long-term consequences. The prediction uncertainty during geological CO₂ storage requires a computationally efficient and practically useful framework. This paper presents a comparative study between ensemblebased filtering algorithms (En-As) and calibration-constrained null-space Monte Carlo (NSMC) methods. For the En-As, we use the ensemble Kalman filter (EnKF), ensemble smoother (ES), ES with multiple data assimilation (ES-MDA), and EnKF and ES with the pilot point method. For the NSMC calibrated models with various parameterization, schemes are tested and single and multiple NSMC (M-NSMC) methods are used. A synthetic case with two layers was developed to mimic an actual CO₂ injection pilot test where one injection and two observation wells are located within a short distance. Observed data include bottom hole pressure at injection well and gas saturation (S_g) at two observation wells in the upper layer. Model parameters include horizontal permeability and porosity. Comparison of results shows that both methodologies yield good history match and reasonable prediction results in a computationally efficient way. In particular, the ESMDA and M-NSMC resulted in smaller objective function values and lower prediction uncertainties of Sg profiles compared to other variants tested in this work. The En-As with the pilot point method have higher variability of permeability compared to those without one, but the En-As show smoother permeability fields compared to the NSMC methods. This is because stochastic randomness at a grid scale was included to generate NSMC fields. Both ensemble-based and NSMC algorithms are unable to correct the structural orientation of the prior ensemble members using only the sparse dynamic data from wells, while they obtain reasonable history match, suggesting that structural uncertainty should be incorporated into prior information. Overall, the ES-MDA has an advantage in terms of computational efficiency, but at the expense of additional computation M-NSMC shows applicability for highly nonlinear problems such as multiphase flow problems.