Efficient analytical upscaling method for elliptic equations in three-dimensional heterogeneous anisotropic media

Liao，Qinzhuo1; Lei，Gang1; Wei，Zhijie2; Zhang，Dongxiao3; Patil，Shirish1

2020-04-01

10.1016/j.jhydrol.2020.124560

JOURNAL OF HYDROLOGY   影响因子和分区

0022-1694

1879-2707

We propose an efficient analytical upscaling method to compute the equivalent conductivity tensor for elliptic equations in three-dimensional space. Our approach uses perturbation expansion and Fourier analysis, and considers heterogeneity, anisotropy and geometry of coarse gridblocks. Through low-order approximation, the derived analytical solution accurately approximates the central-difference numerical solution with periodic boundary conditions. Numerical tests are performed to demonstrate the capability and efficiency of this analytical approach in upscaling fluid flow in heterogeneous formations. We test the method in synthetic examples and benchmark cases with both Gaussian random fields and channelized non-Gaussian fields. In addition, we examine the impact of each parameter on the upscaled conductivity, and investigate the sensitivity of the variance and correlation lengths to the coefficients. We also indicate how to extend this approach to multiphase flow problems.

Anisotropy Conductivity tensor Equivalent conductivity Heterogeneity Upscaling

EI ; SCI

英语

通讯

[2016ZX05025-003-007] ; King Fahd University of Petroleum and Minerals[] ; National Natural Science Foundation of China[51604013]

Engineering ; Geology ; Water Resources

Engineering, Civil ; Geosciences, Multidisciplinary ; Water Resources

WOS:000527388300025

Elsevier B.V.

20200708155753

Anisotropy ; Flow of fluids ; Fourier analysis ; Gaussian distribution ; Tensors

Fluid Flow, General:631.1 ; Mathematics:921 ; Algebra:921.1 ; Probability Theory:922.1 ; Physical Properties of Gases, Liquids and Solids:931.2 ; Materials Science:951

ENGINEERING

2-s2.0-85079099803

Scopus

1.CPG,King Fahd University of Petroleum and Minerals,Dhahran,Saudi Arabia
2.CNOOC Research Institute CO.,Ltd.,Beijing,China
3.School of Environmental Science and Engineering,Southern University of Science and Technology,Shenzhen,China

Liao，Qinzhuo,Lei，Gang,Wei，Zhijie,et al. Efficient analytical upscaling method for elliptic equations in three-dimensional heterogeneous anisotropic media[J]. JOURNAL OF HYDROLOGY,2020,583.

Liao，Qinzhuo,Lei，Gang,Wei，Zhijie,Zhang，Dongxiao,&Patil，Shirish.(2020).Efficient analytical upscaling method for elliptic equations in three-dimensional heterogeneous anisotropic media.JOURNAL OF HYDROLOGY,583.

Liao，Qinzhuo,et al."Efficient analytical upscaling method for elliptic equations in three-dimensional heterogeneous anisotropic media".JOURNAL OF HYDROLOGY 583(2020).