Multigrid Fracture Stimulated Reservoir Volume Mapping Coupled with a Novel Mathematical Optimization Approach to Shale Reservoir Well and Fracture Design

Alzahabi, Ahmed; Berlow, Noah; Soliman, M.Y.; AlQahtani, Ghazi

doi:10.7569/jsee.2016.629521

Cited by 1 publication

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“…In general, there are two kinds of popular acceleration methods for solving the flow equation, one is full-order model, and the other is reduced-order model. The full-order model mainly includes parallel computing (Schrefler et al 1999; Edited by Xiu-Qiu Peng Akhmetzyanov et al 2012;Fung et al 2016;Jambunathan and Levin 2017;Tanaka et al 2018;Ho et al 2019), domain decomposition method (Popov and Power 1999;Stavroulakis and Papadrakakis 2009;Skogestad et al 2013;Birgle et al 2018), multigrid method (Gries et al 2014;Lovett et al 2015;Alzahabi et al 2016;la Cour et al 2016;Wang et al 2017a, b), etc. These methods use CPU/GPU parallel processing, regional partitioning technique and multilevel recursive calculation, respectively, to solve the flow equation efficiently in original full-order space to achieve the acceleration.…”

Section: Introductionmentioning

confidence: 99%

An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

Wang

et al. 2020

Pet. Sci.

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In this paper, an efficient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible flow in porous media. The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of flow equation in original full-order space, and the discrete empirical interpolation method (DEIM) is applied to speed up the solution of Peng–Robinson equation of state in reduced-order subspace. The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reduced-order subspace, which not only preserves good prediction accuracy of full-order model, but also gains dramatic computational acceleration by multigrid and DEIM. Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method. In addition, the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng–Robinson equation of state is demonstrated and carried out in detail. Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors. The general acceleration is up to 50–60 times faster than that of standard semi-implicit method in two-dimensional simulations, but the average relative errors of numerical results between these two methods only have the order of magnitude 10−4–10−6%.

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Section: Introductionmentioning

confidence: 99%

An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

Wang

et al. 2020

Pet. Sci.

View full text Add to dashboard Cite

show abstract

Multigrid Fracture Stimulated Reservoir Volume Mapping Coupled with a Novel Mathematical Optimization Approach to Shale Reservoir Well and Fracture Design

Cited by 1 publication

References 0 publications

An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

An efficient multigrid-DEIM semi-reduced-order model for simulation of single-phase compressible flow in porous media

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