One of the challenges in reservoir simulation is the study and analysis of large scale models with complex geology and multiphase fluid for considering real life applications. Even with recent increase in the computation power, the fast and reliable simulation of the fine scale models is still resource-intensive and hardly possible. Particularly, in optimization and field planning, it is necessary to simulate the system for varying input parameters. Here, model order reduction (MOR) can be used to significantly accelerate the repeated simulation. Although theory as well as numerical method for linear systems is quite well-established, for nonlinear systems, e.g. reservoir simulation, it is still a challenging problem.

We apply a recently introduced approach for nonlinear model order reduction to reservoir simulation. In order to overcome the issue of nonlinearity, we introduce the bilinear form of the reservoir model. The bilinear approximation is a simple form of the parent system and it is linear in the input and linear in the state but it not linear in both jointly. This technique is independent of input of the systems, and thus is applicable for wide range of input parameters without any training. Also, the formulation allows certain properties of the original models to be preserved in the reduced order models. The basic tools known from tensor theory are applied to allow for a more efficient computation of the reduced-order model as well as the possibility of constructing two-sided projection methods which are theoretically shown to yield more accurate reduced-order models.

Examples are presented to illustrate this recent approach for the case of two phase flow modeling, and comparisons are made with the case of linearized models and the full nonlinear models. We discuss the model reduction techniques to be applied to the two-phase flow system. We conclude the paper with some remarks and point out two ways to generalize the findings of this paper as a future work.


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