Upscaling of Dual-Porosity Models for Gas Transport in Organic-Rich Shales

Savatorova, Viktoria L.; Talonov, A. V.; Vlasov, A. N.

doi:10.1615/compmechcomputapplintj.v7.i3.40

Cited by 2 publications

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“…have developed the model of shale matrix block with dual‐porosity continua associated with organic and inorganic pores. The present study can be considered as a generalization of the results of Savatorova et al . to the case of irregular distribution of pores within both inorganic and organic materials.…”

Section: Introductionsupporting

confidence: 60%

“…Thus,

Ω = {normalΩ}_{i}^{ε} \cup {normalΩ}_{k}^{ε} \cup \partial {normalΩ}_{k}^{ε}

(see Figure 2a). The physical parameters on the different parts of Ω have to be scaled appropriately to conserve flow: the diffusivity D k (and D s ) have to be scaled by ε 2 in order to maintain a total flow across the union of the interfaces

\partial {normalΩ}_{k}^{ε}

(see Savatorova et al …”

Section: Scaling and Averaging Of The Governing Equationsmentioning

confidence: 99%

“…In Akkutlu et al . and Savatorova et al., the technique of averaging over a periodic cell was applied for single and double porosity models of gas transport in geomaterials with regular periodic structure.…”

Section: Scaling and Averaging Of The Governing Equationsmentioning

confidence: 99%

“…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%

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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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Section: Introductionsupporting

confidence: 60%

“…Thus,

Ω = {normalΩ}_{i}^{ε} \cup {normalΩ}_{k}^{ε} \cup \partial {normalΩ}_{k}^{ε}

\partial {normalΩ}_{k}^{ε}

(see Savatorova et al …”

Section: Scaling and Averaging Of The Governing Equationsmentioning

confidence: 99%

Section: Scaling and Averaging Of The Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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A solute transport in deformable dual-porosity media using mixture-coupling theory

Wang

Tan

et al. 2024

Environmental Geotechnics

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Rock, soil and many porous-like materials are often fractured or structured media, which can exhibit dual-porosity behaviour. Studies on solute transport in deformable dual-porosity media remain challenging due to the multi-physics coupled effects and the complex interaction between fracture (or macropore) and porous matrix. Though several studies exist on constitutive modelling of coupled behaviour in deformable dual-porosity, the previously developed models are not systematic in thermodynamical frameworks. This paper proposes a Mixture Coupling Theory approach based on nonequilibrium thermodynamics to develop the solute transport model with consideration of hydro-mechanical coupling in dual-porosity media (referred to as the ST-HM model). This paper derives the constitutive equations of fully hydro-mechanical coupled behaviour in dual-porosity media and considers the pore and fracture porosity evolution influenced by both hydro and mechanical fields. Therefore, the governing equations of ST-HM are capable of predicting non-reactive solute transport with a fully hydro-mechanical coupled effect in dual-porosity media. Then, the model was verified against existing models and validated by relevant experimental results. Further, a numerical example shows that the presented model significantly improves the accuracy of the prediction of porosity, fluid pressure, and solute concentration compared with previous models, which ignore the fully hydro-mechanical coupled effects on solute transport.

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Upscaling of Dual-Porosity Models for Gas Transport in Organic-Rich Shales

Cited by 2 publications

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

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

A solute transport in deformable dual-porosity media using mixture-coupling theory

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