scholarly journals A model of solute diffusion in unsaturated double-porosity medium by homogenization

2018 ◽  
Vol 20 (K7) ◽  
pp. 68-75
Author(s):  
Dung Ngoc Tien Tran ◽  
Quang Minh Pham ◽  
Thong Nguyen ◽  
Thanh Pham Phuong Bui ◽  
Tieng Van Tran
Keyword(s):  
Heterogeneous Media ◽  
Diffusion Tensor ◽  
Diffusion Mechanism ◽  
Effective Diffusion ◽  
Double Porosity ◽  
Homogenization Method ◽  
Solute Diffusion ◽  
Macroscopic Model ◽  
Scale Model ◽  
Effective Diffusion Tensor

Solute diffusion is a key process in many fields like for example material science or environmental engineering. Diffusion mechanism in porous media is often described by Fick’s law. However, we could not use this law for nonstandard diffusion behaviors occurring in cases of heterogeneous media. The conception of double-porosity medium can be applied to a class of such media. The double-porosity medium is characterized by two distinct pore sizes: macro-porosity domain and micro-porosity domain, respectively, having the contrasted hydraulic properties. This paper presents the development of a macroscopic model for the solute diffusion in unsaturated double-porosity medium, by using homogenization method. The obtained macroscopic model is a system of two equations coupling on the interface of the macro- and micro-porosity domain for diffusion. This model contains the effective diffusion tensor representing for the entire medium. The developed model is verified by comparing with the reference solution of the fine scale model through a 3D numerical example of hydrogeology problem.

scholarly journals Diffusion Mechanism of Leading Technology in the New Energy Industry Based on the Bass Model

2021 ◽  
Vol 9 ◽  
Author(s):  
Hongying Wang ◽  
Bing Sun
Keyword(s):  
Expected Utility ◽  
Simulation Analysis ◽  
Diffusion Mechanism ◽  
Effective Diffusion ◽  
Energy Industry ◽  
Bass Model ◽  
Property Development ◽  
Industrial Transformation ◽  
New Energy ◽  
The Government

With the increasing difficulties associated with heating, the new energy industry has become the mainstay for property development. The effective diffusion of leading technologies supplies a social edge for enterprise core technologies, and this is also a necessary topic for industrial transformation and optimization. Within the international context of energy conservation and emission reduction, the scientific and in-depth study of the diffusion mechanisms underlying leading technologies in the new energy industry have vital theoretical significance for the promotion of the diffusion of leading technologies. Based on the introduction of the Bass model and one extension model, this paper constructs the diffusion model of the new energy industry’s leading technology and analyzes its diffusion mechanism. The identified mechanism indicates that in the case of imperfect market and policy environments, the diffusion of the leading technology of the new energy industry is mainly influenced by the “expected utility” of innovators and the “actual utility” of imitators. The diffusion of the leading technology in innovator enterprises of the new energy industry is mainly affected by the “expected utility,” while the diffusion in imitator enterprises is affected by the “actual utility.” These influences are verified by simulation analysis. Based on the diffusion mechanism, several suggestions are presented for the promotion of the diffusion mechanism of leading technology, with the aim to provide references for the government, industry associations, and enterprises for relevant decision-making.

Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
I. V. Andrianov ◽  
J. Awrejcewicz ◽  
V. V. Danishevs’kyy ◽  
D. Weichert
Keyword(s):  
Heterogeneous Media ◽  
Asymptotic Series ◽  
Stop Band ◽  
Fourier Method ◽  
Homogenization Method ◽  
Higher Order ◽  
Square Lattice ◽  
Infinite Matrix ◽  
Periodic Composite ◽  
Versus Plane

This work is devoted to a comparison of different methods determining stop-bands in 1D and 2D periodic heterogeneous media. For a 1D case, the well-known dispersion equation is studied via asymptotic approach. In particular, we show how homogenized solutions can be obtained by elementary series used up to any higher-order. We illustrate and discuss a possible application of asymptotic series regarding parameters other than wavelength and frequency. In addition, we study antiplane elastic shear waves propagating in the plane through a spatially infinite periodic composite material consisting of an infinite matrix and a square lattice of circular inclusions. In order to solve the problem, a homogenization method matched with asymptotic solution on the cell with inclusion of the large volume fracture is proposed and successfully applied. First and second approximation terms of the averaging method provide the estimation of the first stop-band. For validity and comparison with other approaches, we have also applied the Fourier method. The Fourier method is shown to work well for relatively small inclusions, i.e., when the inclusion-associated parameters and matrices slightly differ from each other. However, for evidently contrasting structures and for large inclusions, a higher-order homogenization method is advantageous. Therefore, a higher-order homogenization method and the Fourier analysis can be treated as mutually complementary.

scholarly journals Macroscopic Model of Two-Phase Compressible Flow in Double Porosity Media

2020 ◽  
Vol 55 (7) ◽  
pp. 936-951
Author(s):  
M. B. Panfilov ◽  
Zh. D. Baishemirov ◽  
A. S. Berdyshev
Keyword(s):  
Compressible Flow ◽  
Double Porosity ◽  
Macroscopic Model ◽  
Two Phase

scholarly journals Anisotropic Solute Diffusion Tensor in Porcine TMJ Discs Measured by FRAP with Spatial Fourier Analysis

2010 ◽  
Vol 38 (11) ◽  
pp. 3398-3408 ◽  
Author(s):  
Changcheng Shi ◽  
Jonathan Kuo ◽  
P. Darwin Bell ◽  
Hai Yao
Keyword(s):  
Fourier Analysis ◽  
Diffusion Tensor ◽  
Solute Diffusion

Effective Diffusion Coefficient

2018 ◽  
Vol 384 ◽  
pp. 130-135
Author(s):  
Jorge A. Gordillo
Keyword(s):  
Interdiffusion Coefficient ◽  
Nanocrystalline Materials ◽  
Effective Diffusion ◽  
Average Frequency ◽  
Solute Diffusion ◽  
Segregation Coefficient ◽  
Two Phase ◽  
Random Walk Theory ◽  
And Diffusion ◽  
Impurities And Diffusion

The diffusion of a B element into an A matrix was studied by the random walk theory. Considering that concentration of B element in the A matrix is very low, the jumps of diffusing atoms are independent of each other. The A matrix is a two-region material with different properties, such as a two-phase material, a single crystal with dislocations, or regions influenced by other solute and a polycrystalline material.It is assumed that material B has a penetration that allows it to cross each region of material A several times. This implies that jumps across the surface between those regions have an average frequency and, as a consequence, there is an interdiffusion coefficient between them. The interdiffusion coefficient between those regions is different than the coefficient of the diffusion in each region.Expressions were obtained that allow to delimit the ranges of validation with greater precision than the corrected Hart-Mortlock equation for solute diffusion. In addition, an original relationship was obtained between the segregation coefficient and parameters specific to the diffusion. New powerful tools were also found that can help to understand diffusion in nanocrystalline materials, diffusion in metals influenced by impurities and diffusion produced by different mechanisms.

Strong solvability up to clogging of an effective diffusion–precipitation model in an evolving porous medium

2016 ◽  
Vol 28 (2) ◽  
pp. 179-207 ◽  
Author(s):  
R. SCHULZ ◽  
N. RAY ◽  
F. FRANK ◽  
H. S. MAHATO ◽  
P. KNABNER
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Level Set ◽  
Diffusion Tensor ◽  
Effective Diffusion ◽  
Partial Differential ◽  
Linear Diffusion ◽  
Precipitation Model ◽  
Effective Coefficients ◽  
Diffusion Precipitation

In the first part of this article, we extend the formal upscaling of a diffusion–precipitation model through a two-scale asymptotic expansion in a level set framework to three dimensions. We obtain upscaled partial differential equations, more precisely, a non-linear diffusion equation with effective coefficients coupled to a level set equation. As a first step, we consider a parametrization of the underlying pore geometry by a single parameter, e.g. by a generalized “radius” or the porosity. Then, the level set equation transforms to an ordinary differential equation for the parameter. For such an idealized setting, the degeneration of the diffusion tensor with respect to porosity is illustrated with numerical simulations. The second part and main objective of this article is the analytical investigation of the resulting coupled partial differential equation–ordinary differential equation model. In the case of non-degenerating coefficients, local-in-time existence of at least one strong solution is shown by applying Schauder's fixed point theorem. Additionally, non-negativity, uniqueness, and global existence or existence up to possible closure of some pores, i.e. up to the limit of degenerating coefficients, is guaranteed.

Two-Dimensional Pore Pressure Distribution Model to Evaluate Effects of Shale Semipermeable Membrane Characteristics

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jia Wei ◽  
Yuanfang Cheng ◽  
Chuanliang Yan
Keyword(s):  
Diffusion Coefficient ◽  
Pressure Distribution ◽  
Pore Pressure ◽  
Effective Diffusion Coefficient ◽  
Early Stage ◽  
Drilling Fluid ◽  
Effective Diffusion ◽  
Solute Diffusion ◽  
Sensitivity Analyses ◽  
Distribution Model

During the drilling of shale formations, drilling fluids can intrude into the wellbore, raise the pore pressure, and lead to wellbore instability. Based on the thermodynamic theory, a new model was established to calculate pore pressure. The model considers the effects of solute diffusion and solution convection and conducts sensitivity analyses. The results show that the drilling fluid activity significantly affects the pore pressure distribution. The pore pressure under high drilling fluid activity will increase rapidly in the early stage. Low drilling fluid activity can effectively suppress the growth of pore pressure. And a low effective diffusion coefficient of solute and a high membrane efficiency also help to reduce pore pressure. Therefore, reducing drilling fluid activity should be conducted in priority in drilling fluid design. Lowering its solute effective diffusion coefficient and increasing its viscosity can also be considered as auxiliary methods.

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