POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

Wang, Yi; Yu, Bo; Sun, Shuyu

doi:10.1515/phys-2016-0061

Cited by 6 publications

(7 citation statements)

References 21 publications

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“…Based on above observations and results analyses, one issue needing to be addressed here is that with the increase of problem complexity, e.g., from one-dimension to multi-dimension, from single-phase to multi-phase, from homogeneity to heterogeneity, etc., to ensure the POD-ROM possesses good reconstruction accuracy, many more POD modes are required in complex problems than that in simple problems. It has been well proved in many previous studies, for instance, Wang et al [33,39] for an incompressible single-phase flow in homogeneous porous medium, and when performing the gas reservoir simulation based on POD-ROM for ideal gases, at least 10 POD modes were needed to ensure good simulation precision; Han et al [40] adopted the POD-ROM to solve steady laminar flows on a simple irregular domain with at least 16 POD modes. Another issue that should be pointed out is that actually there are many factors which may exert impacts on the reconstruction accuracy of POD-ROM, especially the choice of representative snapshots used to construct POD basis functions.…”

Section: (2) Results Discussionmentioning

confidence: 98%

Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media

Tao

Sun

et al. 2019

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Purpose This paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and prediction of two-phase flows in porous media. Design/methodology/approach The key point of the proposed algorithm is to establish an accurate POD reduced-order model (ROM) for two-phase porous flows. To this end, two projection methods including projecting the original governing equations (Method I) and projecting the discrete form of original governing equations (Method II) are respectively applied to construct the POD-ROM, and their distinctions are compared and analyzed in detail. It is found the POD-ROM established by Method I is inapplicable to multiphase porous flows due to its failed introduction of fluid saturation and permeability that locate on the edge of grid cell, which would lead to unphysical results. Findings By using Method II, an efficient IMPES algorithm that can substantially speed up the simulation of two-phase porous flows is developed based on the POD-ROM. The computational efficiency and numerical accuracy of the proposed algorithm are validated through three numerical examples, and simulation results illustrate that the proposed algorithm displays satisfactory computational speed-up (one to two orders of magnitude) without sacrificing numerical accuracy obviously when comparing to the standard IMPES algorithm that without any acceleration technique. In addition, the determination of POD modes number, the relative errors of wetting phase pressure and saturation, and the influence of POD modes number on the overall performances of the proposed algorithm, are investigated. Originality/value 1. Two projection methods are applied to establish the POD-ROM for two-phase porous flows and their distinctions are analyzed. The reason why POD-ROM is difficult to be applied to multiphase porous flows is clarified firstly in this study. 2. A highly efficient IMPES algorithm based on the POD-ROM is proposed to accelerate the simulation of two-phase porous flows. 3. Satisfactory computational speed-up (one to two orders of magnitude) and prediction accuracy of the proposed algorithm are observed under different conditions.

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Section: (2) Results Discussionmentioning

confidence: 98%

Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media

Tao

Sun

et al. 2019

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“…It has been applied in many fields, such as turbulence flow, heat conduction and convective heat transfer, two‐phase flow, and gas flow . Recently, the POD method has been extended to simulate flow in porous media . Some representative research is reviewed here.…”

Section: Introductionmentioning

confidence: 99%

“…Some representative research is reviewed here. Wang et al applied the POD‐Galerkin modeling method to incompressible single‐phase flow in porous media. Their conclusions showed that the acceleration effect is obvious with very high precision.…”

Section: Introductionmentioning

confidence: 99%

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

Han

Tang

et al. 2020

Energy Science & Engineering

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Using traditional high‐fidelity numerical simulation to simulate fluid flow in fractured porous media in a real field remains challenging. It involves a large number of degrees of freedom when matrix and fracture equations are solved. To address this challenge, we propose a Galerkin‐free framework to construct a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD). Compared with the typical POD‐based modeling process commonly used in previous studies, the POD‐ROM can be built without performing the Galerkin projection of flow equations onto the low‐dimensional space spanned by the POD basis functions. The numerical integration method was incorporated to obtain the POD time coefficients based on the flow equations solved by the conventional finite volume method. Two complex fracture cases reflecting high‐contrast porous media in a two‐dimensional domain were designed to verify the accuracy and efficiency of the established Galerkin‐free POD‐ROM. Sensitivity analysis of parameters was conducted to examine the adaptability of the ROM. The results illustrate that, compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions.

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“…It has been widely utilized for many non-porous-medium flow problems [13][14][15] and also proved to be efficient for some liquid flow cases in single-continuum porous media [16,17]. In reference [16], Ghommem et al discussed a high-precision mode decomposition method for a time-dependent incompressible single-phase flow, but did not describe the acceleration performance of the method.…”

Section: Introductionmentioning

confidence: 99%

“…In reference [16], Ghommem et al discussed a high-precision mode decomposition method for a time-dependent incompressible single-phase flow, but did not describe the acceleration performance of the method. In reference [17], a POD Galerkin model is proposed for an incompressible single-phase flow. Only four samples and two modes used in the model can predict hundreds of cases with high-precision and fast-computation.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of Gas Flow Simulations in Dual-Continuum Porous Media Based on the Mass-Conservation POD Method

Wang

Sun

2017

Energies

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Reduced-order modeling approaches for gas flow in dual-porosity dual-permeability porous media are studied based on the proper orthogonal decomposition (POD) method combined with Galerkin projection. The typical modeling approach for non-porous-medium liquid flow problems is not appropriate for this compressible gas flow in a dual-continuum porous media. The reason is that non-zero mass transfer for the dual-continuum system can be generated artificially via the typical POD projection, violating the mass-conservation nature and causing the failure of the POD modeling. A new POD modeling approach is proposed considering the mass conservation of the whole matrix fracture system. Computation can be accelerated as much as 720 times with high precision (reconstruction errors as slow as 7.69 × 10 −4 %~3.87% for the matrix and 8.27 × 10 −4 %~2.84% for the fracture).

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POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

Cited by 6 publications

References 21 publications

Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media

Numerical investigation of the POD reduced-order model for fast predictions of two-phase flows in porous media

A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

Acceleration of Gas Flow Simulations in Dual-Continuum Porous Media Based on the Mass-Conservation POD Method

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