A multiobjective Markov chain Monte Carlo approach for history matching and uncertainty quantification

We illustrate the algorithm using a nine-spot waterflood model whereby we use water-cut and bottomhole flowing pressure data to calibrate the permeability field. The permeability field is re-parameterized using a previously proposed Grid Connectivity Transform (GCT) which is a model order reduction technique defined based only on the decomposition of the grid Laplacian. The compression power of GCT allows us to reconstruct the permeability field with few parameters, thus significantly improving the computational efficiency of the McMC approach. Next, we applied the method to the Brugge benchmark case involving 10 water injectors and 20 producers. For both cases, the algorithm provides an ensemble of models all constrained to the history data and defines a probabilistic Pareto front in the objective space. Several experimental runs were conducted to compare the effectiveness of the algorithm with Non-Dominated Sorting Genetic Algorithms (NSGA-II). Higher hypervolume was constantly measured using our algorithm which indicates that more optimal solutions were sampled. Our method provides a novel approach for subsurface model calibration and uncertainty quantification using McMC in which the communication between parallel Markov chains enhances adequate mixing. This significantly improves the convergence without loss in sampling quality.