Heterogeneous reservoir characterization using efficient parameterization through higher order SVD (HOSVD)

Parameter estimation through reduced-order modeling play a pivotal role in designing real-time optimization schemes for the Oil and Gas upstream sector through the closed-loop reservoir management framework. Reservoir models are in general complex, nonlinear, and large-scale, i.e., large number of states and unknown parameters. Consequently, model reduction techniques are of great interest in reducing the computational burden in reservoir modeling and simulation. Furthermore, de-correlating system parameters in all history matching and reservoir characterization problems is an important task due to its effects on reducing ill-posedness of the system. In this paper, we utilize the higher order singular value decomposition (HOSVD) to reparameterize reservoir characteristics, e.g. permeability, and perform several forward reservoir simulations by the resulted reduced order map as an input. To acquire statistical consistency we repeat all experiments for a set of 1000 samples using both HOSVD and Proper orthogonal decomposition (POD). In addition, we provide RMSE analysis for a better understanding in process of comparing HOSVD and POD. Results show that HOSVD provide a better performance in a RMSE point of view.