Multi-scale Asymptotic Analysis of Gas Transport in Shale Matrix

Akkutlu, I. Yücel; Efendiev, Yalchin; Savatorova, Viktoria L.

doi:10.1007/s11242-014-0435-z

Cited by 35 publications

(19 citation statements)

References 21 publications

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“…The choice of the snapshot space depends on the global discretization and the particular application. The appropriate snapshot space (1) yields faster convergence, (2) imposes problem relevant restrictions on the coarse spaces (e.g., divergence free solutions) and (3) reduces the computational cost of building the offline spaces. Each snapshot can be constructed, for example, using random boundary conditions or source terms [9].…”

Section: The Basic Concepts Of Generalized Multiscale Finite Element mentioning

confidence: 99%

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Chung

Efendiev

Hou

2016

Journal of Computational Physics

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214

182

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In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.

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Section: The Basic Concepts Of Generalized Multiscale Finite Element mentioning

confidence: 99%

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Chung

Efendiev

Hou

2016

Journal of Computational Physics

Self Cite

214

182

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“…In the paper by Le et al., the authors used reiterated homogenization procedure to derive the macroscopic behavior of gas flow and transport in multi‐porosity shale gas reservoirs. Building on the work that had been done by Akkutlu and Fathi and Akkutlu et al., Savatorova et al . have developed the model of shale matrix block with dual‐porosity continua associated with organic and inorganic pores.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of gas transport in porous geological media with contrast of properties and irregular distribution of pores

Savatorova

Talonov

2019

Z Angew Math Mech

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In this work, we perform multiscale modeling of gas transport through the geological media having irregular pore structure and contrast of properties on different spatial scales. We assume that the medium consists of inorganic matrix with organic inclusions imbedded into it. There exist a contrast of properties and spatial scales between the matrix and organic inclusions. The pore sizes vary from micro to nanometers, permeability and diffusivity can differ by several orders of magnitude. We consider filtration and molecular diffusion as mechanisms for free gas transport in both inorganic and organic materials, and surface diffusion as the main mechanism for sorbed gas transport through nanoporous organic inclusions. The irregularities of porous structure we characterize by their deviations from the periodic distribution. We implement multiscale homogenization together with an averaging with respect to random deviations of distribution of pores to derive the macroscopic equation for evaluating the free gas amount in-place. It turns out that macroscale parameters characterizing gas transport depend on diffusivity, permeability, and porosity of the components of the system, the amount of inclusions and their spatial distribution. We determine the distribution of gas concentration through the production time and investigate its sensitivity to irregularities of pores distribution. We are also interested in the effect of bottom-hole pressure and study how depletion can be affected by the interchange of gas between kerogen inclusions and inorganic material. K E Y W O R D Sadsorption, diffusion, filtration, gas phase transport, irregular distribution of pores, multi-scale homogenization, organic-rich shales, porous media

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“…have noticed the big differences between kerogen and inorganic matrix in shale and treat them separately [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…They concluded that the permeability of shale is primarily relevant to the relatively large pore and fractures in inorganic matrix, but the molecular behaviors (diffusion transport and nonlinear adsorption) relevant to the pores in kerogen. In 2015, Akkutlu [12] adopted multiscale asymptotic analysis method to solve a one-dimensional dual-porosity continuum model and concluded that both the gas in-place and gas production rate depend on the content of kerogen in shale. Later, Akkutlu [13] employed the generalized multiscale finite element method (GMsFEM) to add the influence of fractures and extended the model to 2D.…”

Section: Introductionmentioning

confidence: 99%

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

Cao

Lin

Jiang

et al. 2017

Fuel

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h i g h l i g h t sA new 3D model coupling organic kerogen and inorganic matrix was developed. The sensitivity analysis on the apparent permeability of shale matrix were operated. Ignoring the contribution of kerogen to the permeability of shale will bring great error in most cases. When the TOC is less than 11% and the pressure is greater than 0.1 Mpa, the effect of kerogen distribution is negligible. a r t i c l e i n f o t r a c tMicrostructure-based quantitative computation of the shale permeability is challenging due to the presence of organic matter with nanoporous features. In this study, a new three-dimensional (3D) coupled model is proposed to investigate the micro-scale permeability of organic-rich-shale matrix. The coupled model consists of two subdomains, organic matter and inorganic matrix. They are described by the pore network model (PNM) and continuum model to capture the non-Darcy and Darcy flow, respectively, and the gas flow in the two subdomains are coupled by finite element mortars (Mortar). The convergence error, grid discretization and parallel scheme are also investigated to get the optimal computing parameters for this model. Then, the effects of the total organic content (TOC), kerogen distribution and poresize distribution on the apparent permeability (AP) of shale matrix are studied using the coupled model with computer-generated PNMs. And on the basis of FIB-SEM images, a Longmaxi shale sample from the Sichuan Basin, China is introduced to build a real shale model. Results show that AP is more sensitive to TOC and pore-size distribution than kerogen distribution. Additionally, in order to analyze the necessity of 3D model, a comparison of 3D and two-dimensional (2D) model is made and the error of 2D model is pointed out. The 3D couple model affords a foundation for further upscaling of shale permeability to REV scale and reservoir scale.

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Multi-scale Asymptotic Analysis of Gas Transport in Shale Matrix

Cited by 35 publications

References 21 publications

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods

Mathematical modeling of gas transport in porous geological media with contrast of properties and irregular distribution of pores

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

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