Computational improvements of instrumented large-scale reservoir simulation are becoming one of the main research topics in the oil industry. In particular, the problem of closed-loop control is capturing a great deal of interest for reliable reservoir management. One of the main difficulties in designing controllers for large-scale reservoir systems has to do with the high dimensional state-space and parameter uncertainties. Hence, lower dimensional models, linear or nonlinear, that approximate the full order system are desirable to either mitigate the cost of large-scale reservoir simulation or design efficient closed-loop control systems. This work aims to compare recent advances in model order reduction techniques applied to reservoir simulation. In general, the problem of reducing the order of a large-scale model is known as approximation of dynamical systems. Several techniques have been developed in the linear dynamical systems framework, namely, the Balanced Truncation, Moment Matching by Krylov techniques, among others and in the nonlinear setting, namely the use of the Proper Orthogonal Decomposition (POD) and its variants. They all share a common approach: they are based on projection techniques. This work provides a comparative analysis of these techniques with particular emphasis on Krylov approaches since they are becoming one of the most active areas of research in large-scale optimal control but yet, they has not been broadly reported within the reservoir community. Preliminary computational experiments reveal that these methods offer promising opportunities to design closed-loop low-order controllers for the management of large-scale smart fields.


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