Title of article :
Enhanced linearized reduced-order models for subsurface flow simulation
Author/Authors :
He، نويسنده , , J. and Sوtrom، نويسنده , , Martin J. and Durlofsky، نويسنده , , L.J.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
Pages :
29
From page :
8313
To page :
8341
Abstract :
Trajectory piecewise linearization (TPWL) represents a promising approach for constructing reduced-order models. Using TPWL, new solutions are represented in terms of expansions around previously simulated (and saved) solutions. High degrees of efficiency are achieved when the representation is projected into a low-dimensional space using a basis constructed by proper orthogonal decomposition of snapshots generated in a training run. In recent work, a TPWL procedure applicable for two-phase subsurface flow problems was presented. The method was shown to perform well for many cases, such as those with no density differences between phases, though accuracy and robustness were found to degrade in other cases. In this work, these limitations are shown to be related to model accuracy at key locations and model stability. Enhancements addressing both of these issues are introduced. A new TPWL procedure, referred to as local resolution TPWL, enables key grid blocks (such as those containing injection or production wells) to be represented at full resolution; i.e., these blocks are not projected into the low-dimensional space. This leads to high accuracy at selected locations, and will be shown to improve the accuracy of important simulation quantities such as injection and production rates. Next, two techniques for enhancing the stability of the TPWL model are presented. The first approach involves a basis optimization procedure in which the number of columns in the basis matrix is determined to minimize the spectral radius of an appropriately defined amplification matrix. The second procedure incorporates a basis matrix constructed using snapshots from a simulation with equal phase densities. Both approaches are compatible with the local resolution procedure. Results for a series of test cases demonstrate the accuracy and stability provided by the new treatments. Finally, the TPWL model is used as a surrogate in a direct search optimization algorithm, and comparison with results using the full-order model demonstrates the efficacy of the enhanced TPWL procedures for this application.
Keywords :
subsurface flow , Two-phase flow , optimization , Model Order Reduction , Reduced-Order Model , Surrogate Model , Trajectory piecewise linearization , TPWL , reservoir simulation , Proper orthogonal decomposition
Journal title :
Journal of Computational Physics
Serial Year :
2011
Journal title :
Journal of Computational Physics
Record number :
1483913
Link To Document :
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