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A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster $D_{\mathrm{\text{cT}}\sigma }$ become bigger with an increase of stress. However, the pore fractal dimension of solid cluster $D_{\mathrm{\text{cf}}\sigma }$ and capillary bundle $D_{\mathrm{\text{pf}}\sigma }$ remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

This paper explores the interaction of different flow paths in a porous medium by observing the effect of having more than one drain in a simple model domain with a single source. The work is based on three-dimensional numerical simulations of the flow of injected water in a sandbox domain with porous volume completely filled by water and oil. The calculation uses the OpenFOAM library to solve Darcy’s equations for the dynamics of a two-phase flow: water as the wetting, oil as the nonwetting fluid. We observe the interactions of flows in different paths under changes of number of drains and their relative positions.

We develop our existing two-dimensional lattice-gas model to simulate the flow of single phase, binary immiscible and ternary amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of "no-slip" boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.

We consider a class of processes in which the flow of an incompressible fluid through a porous matrix is accompanied by a mass exchange between the constituents. This paper is in two parts. In the first part we use an upscaling procedure to derive a macroscopic law for the flow, starting from the analysis of the phenomena at the pore scale. To this end we utilize a simplified geometry of the solid matrix. The resulting governing equation is of Darcy type, as expected, but, owing to mass exchange, it contains a complicated nonlocal dependence on the hydraulic conductivity. In the second part we look directly for the formulation of a macroscopic model in the framework of mixture theory. We emphasize the basic role of energy dissipation: the two methods lead to the same conclusions, provided that the same dissipation rates are postulated.

Fluid flow is essential for the transport of metabolites to, from and within the intervertebral disc (IVD). By applying quadriphasic mixture theory experimentally, this study relates fluid flow within the bovine nucleus pulposus (NP) to the applied fluid pressure gradients and fixed charge and mobile ion concentration gradients. 24 plugs of NP tissue (diameter 10 mm, height 1020 ± 122 μm (mean ± SD)), orientated in the axial direction, were harvested from bovine tail discs. The plugs were permeated with either; 0 M NaCl, 0.15 M NaCl or 3 M NaCl solutions by subjecting them to 30, 45 and 60 kPa fluid pressure gradients applied in a random sequence. The hypertonic solution was assumed to render all non-fluid pressure gradients negligible, whilst the hypotonic solution was assumed to render the mobile ion concentration gradient negligible. The effects of these gradients on fluid flow were expressed as a percentage of the applied fluid pressure. Fluid velocity was significantly increased through the tissue in the isotonic case compared to the hypertonic case by up to 55% of the applied fluid pressure. The fixed charges accounted for between 26% and 43% and the mobile ion gradient responsible for 12–26% of this increased fluid flow. These results highlight the importance of using a constitutive equation for permeability that includes mobile ions and fixed charges as separate phases when modeling cartilaginous tissue in order to better describe fluid flow, and thus convective transfer of metabolites, within the tissue.

We consider classical solutions to the initial boundary value problem for the non-isentropic compressible Euler equations with damping in several space dimensions. We establish a global existence theory for classical solutions to this system when the initial data are sufficiently small. We prove that the pressure and the velocity converge exponentially toward some constants, while the entropy and the density in general do not approach constants. Finally, we prove that, as the time goes to infinity, the pressure and the velocity components of the non-isentropic Euler equations with damping converge exponentially toward those of an associated nonlinear diffusion system, and the global existence of classical solutions to these nonlinear diffusion equations is also established.

In order to research the seepage phenomena of one kind of granite materials, investigations on the seepage characteristics on the granite materials by experiments, numerical simulation and theoretical analysis had been carried out. A surrounding rock with an internal cavity, which would be filled with the TNT explosive charge and exploded, was taken as the research object. Firstly, a two dimensional cylindrical symmetrical mathematical model of dual porosity and dual permeability was built by taking into account of gas permeation in porous media, gas diffusion and heat conduction between gas and surrounding rock. And some related experiments of gas seepage in granite were carried out too, in which, the TNT explosive charge was exploded in the center cavity of the granite. Taking the detonation product CO as the trace gas, the amount of gas permeability and the arrival time of the gas seepage were obtained. Comparison with experimental results shows that the numerical simulation results are accurate and reliable. Then, based on the Darcy’s law, considering the influence of some major factors, like the rock fracture, the porosity and the permeability of the granite materials, analytical formulas of some important parameters of the research object, which mainly include the amount of gas permeability and the arrival time of the gas seepage, were derived. Meanwhile, the formulas were used to calculate the results in one of the experiments introduced before. The important parameters in seepage phenomena, such as the arrival time and the total volume of the seepage gas, calculated by these formulas compared very well with the corresponding experiment.