Development of a surrogate simulator for two-phase subsurface flow simulation using trajectory piecewise linearization

Abstract

Reduced-order modeling (ROM) is a novel approach in all realms of computational science including reservoir simulation. Among various ROM methods, trajectory piecewise linearization (TPWL) is evolving for reservoir engineering applications. Previous investigations reflect promising future for incorporating TPWL into the next generations of enhanced reservoir simulators. In this work, we employ this method to examine the claimed efficiency, robustness and accuracy of it as a surrogate simulator. The self-construction of the used simulator gives us the opportunity to explore this method and to examine previous assertions on the subject. The efficiency of TPWL is primarily due to direct calculation of new saturation and pressure states using a linearized expansion around previously simulated states instead of traditionally solving the flow equations. For further efficiency and reduction of the required memory, TPWL method needs to accompany a space reducing scheme, through which the captured dynamic of the reservoir is projected into a lower-order space. The projection matrix is conventionally constructed through proper orthogonal decomposition (POD) of converged time stepping solutions known as ‘snapshots’ which are obtained during a serious of preprocessing runs called ‘training’ runs. In this work, we apply TPWL method to a hypothetical three-dimensional heterogeneous reservoir consisting of a compressible rock type. We assume an inverted five-spot production–injection pattern and present the results for a two-phase (oil–water) reservoir model under water flooding scenario, in which the injection well is controlled by injection rate. Achieved results demonstrate that use of TPWL leads to significantly faster simulation compared to high fidelity model. We achieved speedup of a factor of 120 while preserving accuracy and reliability of the results. This study suggests that TPWL methodology will be particularly attractive when many solutions of similar simulation models with different well settings are required for history matching or optimization problems. Future research should focus to assess the applicability of TPWL to conditions with strongly compressible flow or capillary pressure effects.