Application of ensemble smoother and multipledata assimilation for estimating relative permeability from coreflood experiments

Relative permeability curves (kr) are flow functions governing multiphase flow in porous media. These functions are an essential component of any large-scale simulator of porous media flow of different phases (oil, water, and gas) with several applications in environmental and petroleum engineering. Unsteady state methods are commonly performed on core samples taken from subsurface reservoirs to obtain the relative permeability curves experimentally. The obtained measurements are then used to calibrate analytical functions (to be embedded in the flow simulator) through automatic history matching. In this study, we evaluate iterative ensemble-based history matching techniques based on the Ensemble-Smoother (ES) formulation. Mainly, the Ensemble Smoother with Multiple-Data Assimilation (ES-MDA) is used for calibrating the parametric relative permeability models using data from unsteady-state core flood experiments. An Ensemble-Smoother updates the model parameters globally by assimilating all the time depended data at once, from the start to the end of the experiment. This is to be contrasted with online updating scheme adopted in Ensemble Kalman Filtering methods. Recently, ES-MDA was developed to improve on ES and to provide reliable uncertainty quantification of the unknown parameters with low computational cost. In the current work, ES-MDA is compared to global optimization methods for calibrating the relative permeability curves. The results of estimating two and three-phase relative permeability curves from three-phase coreflood experiments are presented. The experiments were performed on 65 mD mixed-wet Clashach sandstone core and cumulative productions and pressure drop across the core were measured during the course of experiments. ES-MDA was able to find the global optimum parameters at much faster convergence rates in comparison to genetic algorithm (GA), a widely used global search method. This was evident for the history matching of three-phase unsteady state experiments where optimal solutions were obtained efficiently while preserving uncertainties in the estimated parameters.