Transport in Porous Media

Based on Fick’s law in matrix and Darcy flow in cleats and hydraulic fractures, a new semi-analytical model considering the effects of boundary conditions was presented to investigate pressure transient behavior for asymmetrically fractured wells in coal reservoirs. The new model is more accurate than previous model proposed by Anbarci and Ertekin, SPE annual technical conference and exhibition, New Orleans, 27–30 Sept 1998 because new model is expressed in the form of integral expressions and is validated well through numerical simulation. (1) In this paper, the effects of parameters including fracture conductivity, coal reservoir porosity and permeability, fracture asymmetry factor, sorption time constant, fracture half-length, and coalbed methane (CBM) viscosity on bottomhole pressure behavior were discussed in detail. (2) Type curves were established to analyze both transient pressure behavior and flow characteristics in CBM reservoir. According to the characteristics of dimensionless pseudo pressure derivative curves, the process of the flow for fractured CBM wells was divided into six sub-stages. (3) This paper showed the comparison of transient steady state and pseudo steady state models. (4) The effects of parameters including transfer coefficient, wellbore storage coefficient, storage coefficient of cleat, fracture conductivity, fracture asymmetry factor, and rate coefficient on the shape of type curves were also discussed in detail, indicating that it is necessary to keep a bigger fracture conductivity and fracture symmetry for enhancing well production and reducing pressure depletion during the hydraulic fracturing design.

Flow in a porous medium with a random hydraulic conductivity tensor K(x) is analyzed when the mean conductivity tensor $$\overline K$$ (x) is a non-constant function of position x. The results are a non-local expression for the mean flux vector $$\overline q$$ (x) in terms of the gradient of the mean hydraulic head $$\overline \varphi$$ (x), an integrodifferential equation for $$\overline \varphi$$ (x), and expressions for the two point covariance functions of q(x) and ϕ(x). When K(x) is a Gaussian random function, the joint probability distribution of the functions q(x) and ϕ(x) is determined.

Pore structures have a major impact on the transport and electrical properties of electrochemical devices, such as batteries and electric double-layer capacitors (EDLCs). In this work we are concerned with the prediction of the electrical conductivity, ion diffusivity and volumetric capacitance of EDLC electrodes, manufactured from hierarchically porous carbons. To investigate the dependence of the effective properties on the pore structures, we use a structurally resolved parametric model of a random medium. Our approach starts from 3D FIB-SEM imaging, combined with automatic segmentation. Then, a random set model is fitted to the segmented structures and the effective transport properties are predicted using full field simulations by iterations of FFT on 3D pore space images and calculations based on the geometric properties of the structure model. A parameter study of the model is used to investigate the sensitivity of the effective conductivity and diffusivity to changes in the model parameters. Finally, we investigate the volumetric capacitance of the EDLC electrodes with a geometric model, make a comparison with experimental measurements and do a parameter study to suggest improved microstructures.

We study the evolution of the water–oil front for two-phase, immiscible flow in heterogeneous porous media. Our analysis takes into account the viscous coupling between the pressure field and the saturation map. Although most of previously published stochastic homogenization approaches for upscaling two-phase flow in heterogeneous porous media neglect this viscous coupling, we show that it plays a crucial role on the dynamics of the front. In particular, when the mobility ratio is favorable, the viscous coupling induces a transverse flux that stabilizes the water–oil front, which follows a stationary behavior, at least in a statistical sense. Calculations are based on a double perturbation expansion of equations at first order: the local velocity fluctuation is defined as the sum of a viscous term related to perturbations of the saturation map, on one hand, plus the perturbation induced by the heterogeneity of the permeability field with a base-state saturation map, on the other hand. In this first paper, we focus on flows in stratified reservoirs, with stratification parallel to the mean flow. Our results allow to predict the evolution of large Fourier mode of the front, and the emergence of a stationary front, for favorable mobility ratios. Numerical experiments confirm our predictions. Our approach is applied to downscaling. Extension of our theory to isotropic media is presented in the companion paper.

In this work we develop the volume averaged form of the frequency-dependent governing equations for electrohydrodynamics in a saturated porous medium. The concept of local electrical equilibrium is identified, and when this condition is valid we obtain a one-equation model describing the coupled transport of momentum and electric charge. When local electrical equilibrium is not valid, separate forms of Maxwell's equations must be developed for both the fluid and solid phases.

The present work concerns the effect of hematocrit-dependent viscosity on pulsatile flow of blood through narrow tube with porous walls. Two-fluid model of blood is assumed to be consisting of a core region (Casson fluid) and a plasma region (Newtonian fluid). No slip condition is assumed on wall and pressure gradient has been considered as periodic function of time. The wall of the blood vessel composed of a thin porous (Brinkman) layer. The stress jump condition has been employed at the fluid–porous interface in the plasma region. Up to first order, approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in resistance offered against the flow between our model and previously studied single and two-fluid models without porous walls has also been done. Mathematical expressions for velocity, rate of flow and resistance offered against the flow have been obtained analytically for different regions and influence of plasma layer thickness, varying viscosity, stress jump parameter, permeability and viscosity ratio parameter on above quantities are pictorially discussed. It is perceived that the values of flow rate for two-fluid model with porous region near walls are higher in comparison with two-fluid model without porous region near walls. Dependency of hematocrit (Ht) on the porosity parameters is graphically discussed. The study reveals a significant impact of various parameters on hematocrit (Ht). A novel observation is that a slight increase in pressure wave amplitude leads to significant fluctuation in hematocrit (Ht) which also indicates how systole and diastole (which controls the pressure gradient amplitudes) leads to changes on blood hematocrit (Ht).

A screen composed of in-plane thin strips is embedded in a porous medium. The screen is either normal or parallel to the applied pressure gradient which forces a flow through the anisotropic porous medium. The principal axes of anisotropy are assumed to be aligned with that of the screen. The governing equation is fourth order and cannot be factored as in the isotropic case. The solutions are found by eigenfunction superposition (with complex eigenvalues) and point match. Anisotropy has first-order effects on the flow and the drag on the screen. Extrapolation yields fundamental results for the drag of a single slat in an anisotropic porous medium.

This paper exemplifies discrete analogs obtained by transformation of the continuum equations governing porous media flow to a system of algebraic equations. To give insight in the underlying physics, the numerical examples are worked out algebraically. The volume-centered approximation turns out to be a reasonable simplification of the algebraically exact face-centered method.

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.