Using the multiscale homogenization technique for the description of mass transfer in geomaterials having organic nature | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 22 > №3 / 2017 / Pages: 362-377

Using the multiscale homogenization technique for the description of mass transfer in geomaterials having organic nature

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Abstract:

In this study, we perform mathematical modeling of gas transport in geomaterials, consisting of nanoporous organic material, microporous inorganic material, and a system of secondary fractions. We treat the material as a dual porosity system consisting of organic nanoporous and inorganic microporous. Organic material appears as small inclusions scattered in the inorganic matrix. We assume periodic distribution of heterogeneities. The proposed model takes into account processes of molecular diffusion and filtration of free gas through micro pores in inorganic material. It also incorporates desorption of gas from nanoporous organic inclusions. We neglect the permeability of nanoporous organic material, and assume that the primary mechanisms of gas transport in the organic inclusions are molecular diffusion of free gas and surface diffusion of desorbed gas. There exist contrast of spatial scales and physical properties of the matrix and inclusions, and this makes multi-scale consideration to be important for modeling gas storage and transport. We apply multi-scale asymptotic analysis to mass balance equations combined with an equation of state, isotherm of adsorption, and the Darcy-like law of filtration. As a result of homogenization of constitutive equations with appropriate initial and boundary conditions, macroscopic problem of mass transfer in effective medium was derived and solved. The problem contains a source term that represents the flow of desorbed gas from organic inclusions into the inorganic matrix. The characteristics of effective medium were determined from the solution of nonlinear boundary value problem on the periodic cell.

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