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Pre-Darcy flow is widely found in many naturally porous media, such as low-permeability clay. Nonflowing liquid boundary layers strongly influence fluid flow in low-permeability porous media. There is evidence in the literature that the porosity and permeability of low-permeability porous media change with variations in the effective stress, which is called stress sensitivity. In this paper, a new mathematical model for pre-Darcy flow in low-permeability porous media is developed and validated with experimental data from the literature. The nonflowing boundary layer thickness can be obtained from the proposed model instead of the empirical equation. First, an equation for calculating the pore radius with stress sensitivity is derived. Two parameters ε p and ε r are defined to calculate the nonflowing boundary layer thickness. Second, based on the capillary bundle model, the apparent flow velocity and apparent liquid permeability of the porous media are determined. Finally, the stress sensitivity and boundary-layer effects on the apparent flow velocity and apparent liquid permeability are analyzed. The research results show that the effect of stress sensitivity on apparent flow velocity increases with increasing pore compressibility. When the pore compressibility C p >0 MPa−1, the apparent liquid permeability increases continuously with increasing pressure gradient. When the pore compressibility C p =0 MPa−1, the apparent liquid permeability continues to increase with increasing pressure gradient. The apparent liquid permeability eventually tends to a constant value. The apparent flow velocity decreases with ε p , and ε r decreases at a given pressure gradient. The larger ε p and ε r are, the faster the rate of increase in the apparent liquid permeability with increasing pressure gradient. The proposed model can estimate the apparent flow velocity at different pressure gradients with a high accuracy. This work is important for understanding flow phenomena in low permeability porous media, such as landslides caused by seepage of water in clay. • A low-velocity pre-Darcy flow model in low permeability porous media is developed. • The nonflowing boundary layer thickness was obtained from a new model. • The relationship between the boundary layer and the pressure gradient is established. • The effect of stress sensitivity on velocity and permeability is analyzed. • The effect of nonflowing boundary layer on velocity and permeability is analyzed. [ABSTRACT FROM AUTHOR]

Loosening local equilibrium assumptions in two-phase flow in porous media gives rise to new, unknown variables. More specifically, when loosening the local thermal equilibrium assumption, one has to describe the heat transfer between multiple phases, present at the same mathematical point. In this paper, we calibrate a macro-scale mathematical model which is free of local equilibrium assumptions to experimental observations. We emphasize the correct determination and upscaling of necessary input parameters from the experimental data achieved by image analysis. By choosing an appropriate scaling parameter, we are able to reproduce experimental measurements satisfactorily. This is a first step towards quantifying heat transfer in two-phase flow in porous media. Ultimately, our aim is to find the limits of the applicability of local equilibrium assumptions in two-phase flow in porous media. [ABSTRACT FROM AUTHOR]

In this paper, we consider the mixed Stokes–Darcy problem which describes a fluid flow coupled with a porous media. We present a modified two-grid method for decoupling this mixed model. Stability is proved and optimal error estimates are derived. The numerical results show that the modified two-grid method is effective and has the same accuracy as the coupling scheme when we choose h = H 2 . [ABSTRACT FROM AUTHOR]

Abstract: Analogizing with Rocha et al.’s [L.A.O. Rocha, S. Lorente, A. Bejan, Int. J. Heat Mass Transfer 45 (8) (2002) 1643–1652] heat conduction model of a disc-shaped body, a “disc-point” mass transfer model with porous media is investigated by using Constructal theory. The heat flow with Fourier law is considered in Rocha et al.’s heat conduction model, while the mass flow with both Darcy law and Hagen–Poiseuille law are considered in the mass transfer model, respectively. The optimal constructs of radial- and branched-pattern discs are obtained by taking maximum pressure drop minimization as optimization objective. The results show that there exist optimal aspect ratios which lead to the minimization of maximum pressure drop of the radial-pattern disc with Darcy flow and Hagen–Poiseuille flow in the channels, respectively. For the first order branched-pattern disc, different definitions of the first order channel fraction lead to different optimization results. When the first order open space fraction is defined as the ratio of the total open space surface area of the whole disc to the whole disc area, there exists an optimal elemental open space fraction which leads to the minimum dimensionless maximum pressure drop of the first order branched-pattern disc. When the product of the cubic of first order open space fraction and the reciprocal of the dimensionless permeability of low permeability porous media is 1000, the critical dimensionless radius, which determines whether the radial- or branched-pattern design is adopted, is 1.78. That is, when the radius of the branched-pattern disc is higher than the critical radius, branched-pattern design should be adopted, otherwise the radial-pattern design should be adopted. The comparison between the optimal constructs of the mass transfer model in this paper and Rocha et al.’s heat conduction model are carried out. [Copyright &y& Elsevier]

Abstract: Numerical simulations are essential to the understanding of the long-term geological storage of CO2. Physical modelling of geological storage of CO2 has been based on Darcy’s law, together with the equations of conservation of mass and energy. Modelling and simulations can be used to predict where CO2 is likely to flow, to interpret the volume and spatial distribution of CO2 under storage conditions, and to optimise injection operations. The state of the art of physical modelling and numerical simulation of CO2 dispersion is briefly reviewed in this paper, which calls for more accurate and more efficient modelling approaches. A systematic evaluation of the numerical methods used and a comparison between the streamline based methods and the grid based methods would be valuable. Multi-scale modelling may prove to be of great value in predicting the long-term geological storage of CO2, while highly accurate numerical methods such as high-order schemes may be employed in numerical simulations of CO2 dispersion for local transport calculations. [Copyright &y& Elsevier]

Abstract: This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces and analyzes two mathematical models for coupling the incompressible Navier–Stokes equations with the porous media flow equations. A numerical method that uses continuous finite elements in the incompressible flow region and discontinuous finite elements in the porous medium, is proposed. Existence and uniqueness results under small data condition of the numerical solution are proved. Optimal a priori error estimates are derived. Numerical examples comparing the two models under varying physical parameters are provided. [Copyright &y& Elsevier]