Permeability Of Porous Matrix Research Articles

Onset of solutal convection in layered sorbing porous media with clogging

The effect of pore clogging on the onset of solute-driven convection in a layered sorbing porous medium consisting of two sublayers with distinct permeabilities is investigated. Solute transport in the medium is described by the nonlinear MIM model involving the Langmuir equation. The solute is divided into two phases. The first one is a mobile phase that drifts with flow and the second one is an immobile phase captured by porous matrix and reducing the total pore space. The model takes into account the saturation concentration, which is a maximal possible amount of solute adsorbed by a unit volume of porous medium. The degree of pore clogging is determined through a clogging coefficient proportional to the saturation concentration. Another coefficient is a sorption parameter including the ratio of adsorption and desorption rates. By varying these coefficients, we obtain the threshold solutal Rayleigh–Darcy number for the onset of convection in the following three types of layered sorbing systems: (1) system with the upper thin highly permeable sublayer, (2) system with the lower thin highly permeable sublayer, and (3) system with equal thick sublayers. The results show that convection onset delays due to the enhancement of clogging effect in all of the three systems. It is more difficult to induce convection here because the pore plugging together with an increase in adsorption rate as compared to desorption rate reduces the mean porosity and permeability of porous matrix. Forward and reverse transitions between the critical convective rolls with different wavelengths are found to occur in the systems 1 and 2 containing the upper or lower thin highly permeable sublayers as the sorption parameter increases. A sequence of “local convection – large-scale convection – local convection” transitions is observed in system 1. There is an opposite sequence of “large-scale convection – local convection – large-scale convection” transitions in system 2. The preferred convective roll width at the onset of convection changes by almost fifth times at the described forward and reverse transitions. It roughly corresponds to the ratio of the total thickness of porous system to that of the thin highly permeable sublayer where local convection generates.

Settling of weighting agents in non-Newtonian fluids to off-shore drilling wells: Modeling, parameter estimation and analysis of constitutive equations

High-density solids such as barite and hematite are generally added to drilling fluids to increase their density, allowing the control of subsurface pressures. However, a variety of problems in drilling wells has been related to the gravitational settling of particulate materials. In this work, the dynamic behavior of barite settling in a synthetic paraffin-based drilling fluid was evaluated experimentally by monitoring the solid concentration as a function of time and height. The tests were conducted in a gravitational settling bench-scale rig using a gamma-ray attenuation technique. Following the standard approach of continuum mechanics, a mathematical model was developed to yield a single set of partial differential equations capable of describing all settling zones inherent in a batch sedimentation process. Further, by means of the predicted solid concentration profiles, it was possible to obtain the height of bottom piled up solids. The mathematical model takes particles compressibility under their own weight and permeability of the sediment into consideration. The parameters of the proposed constitutive equations for the effective pressure on solids and porous matrix permeability were estimated and statistically analyzed from the experimental profiles of solid concentration. In particular, the results obtained in this work indicated a good agreement between the model predictions and the experimental data.

PERMEABILITY OF MICROCRACKED POROUS SOLIDS THROUGH A MICROMECHANICAL MODEL

This paper investigates the permeability of solids containing a crack network with finite connectivity through micromechanical method. The main factors of permeability include crack density, connectivity, crack opening and permeability of porous matrix. Firstly, for solids with unconnected cracks, the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability considering crack density $\rho $ and crack opening $b$. Then, for networks containing randomly oriented cracks with intersection, the amplification of permeability by crack connectivity is quantified for local crack clusters. This amplification effect is modeled by arranging parallel cracks on transport direction. By introducing the definition of hypothetically parallel crack density $\rho^{\rm h}$, the hypothetically parallel cracks are embedded in a host matrix whose permeability are those of the effective medium. In this way the IDD model is extended to evaluate the permeability of part-connected networks before total percolation occurs, considering the permeability of porous matrix $K_{\rm m}$, crack density $\rho $, opening aperture $b$ and parallel crack density $\rho^{\rm h}$. Finally, the representative volume element is built for cracked solids with cracks having random spatial locations and the permeability is solved by finite element method. Through this numerical tool, the validity and accuracy of IDD solutions for non-connected and part-connected crack networks are confirmed by several case analysis. The results show that: (1) For non-connected networks, crack opening is found to have little impact on the effective permeability due to the continuous matrix and its low permeability; (2) For part-connected networks, when crack density $\rho <1.1$ (uncorrelated networks, the fractal dimension is 2.0), 1.2 (correlated networks, the fractal dimension is 1.75), the IDD extended model show a good agreement with numerical results and loses its accuracy due to the clustering effect at more higher $\rho $ level.

Permeability of Microcracked Solids with Random Crack Networks: Role of Connectivity and Opening Aperture

This paper investigates the permeability of microcracked porous solids containing 2D random crack networks. The past works on permeability of crack networks are firstly reviewed. The geometry analysis is performed on numerical samples of crack networks with different crack length distributions, crack densities, domain size ratios and clustering degrees. The parameters from continuum percolation theory are used to characterize the geometry of random networks including the percolation threshold, the scaling exponents for percolation probability and correlation length of crack clusters, and the fractal dimension of spanning clusters. The crack density is used as the basic percolation variable, and a new connectivity factor is proposed for the cluster spanning in finite domain. Then the effective permeability of porous matrix containing 2D random crack networks is analyzed on numerical samples via finite element method. A scaling law for effective permeability is established near the percolation threshold taking into account the matrix permeability, crack opening aperture, crack connectivity and tortuosity. The results from geometry analysis and permeability analysis show that: (1) The new connectivity factor is proved pertinent to network percolation, related to both crack density and crack clustering degree; (2) the percolation parameters of uncorrelated crack networks are rather near to the universal values from the continuum percolation theory, but their values change with the clustering degree of crack networks; (3) the numerical results confirm the scaling law proposed for effective permeability, and the permeability is found to scale with the crack opening through a power law.

Permeability of cracked porous solids through percolation approach

This paper investigates the permeability of microcracked porous solids incorporating random crack networks in terms of continuum percolation theory. Main factors of permeability include the geometry of crack networks, permeability of porous matrix, and crack opening. For the two-dimensional random crack networks, a new connectivity factor is defined to take into consideration the spanning cluster of cracks, fractal dimension of networks, and the size of a finite domain. For an infinite domain, the connectivity factor around a percolation threshold observes the scaling law, so this definition of connectivity is proved to be consistent with the percolation concepts. Geometric analysis reveals that the local clustering will not necessarily contribute to the global connectivity of networks. It is also found that too strong a local clustering of cracks will decrease the probability of the global percolation, and this adverse aspect of the local clustering effect has never been reported in the literature. The percolation threshold changes with the crack pattern of networks and the scaling exponents of percolation are not constant but depend on the fractal dimension of the crack networks. On the basis of connectivity and tortuosity of crack networks, the scaling law for permeability is established, K=K0(Km,b)(-c), taking into consideration the geometris characteristics through (-c), the permeability of porous matrix Km, and the crack opening aperture b. Then the permeability of a solid incorporating random crack networks is solved by finite element methods: all the cracks are idealized as 2-node elements and the matrix is divided into 6-node triangle elements. The fluid is assumed to be incompressible and Newtonian. With these assumptions the effective permeability of numerical samples is evaluated through Darcy's law. The scaling exponents of the permeability obtained numerically are very near to the theoretical values, and the impact of crack opening is less important as the crack density is far below the percolation threshold and the effect of crack opening becomes significant only as the crack density approaches the percolation threshold. Influence of crack opening on the permeability is strongly dependent on the opening aperture of the cracks. Finite element simulation results show that K0 depends on b through a power law near the percolation threshold and this dependence disappears as the ratio between the local permeability of crack and the matrix permeability exceeds 106.

An equivalent medium model for wave simulation in fractured porous rocks

ABSTRACTSeismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid.The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.

Non-isothermal Permeability Impairment by Fines Migration and Deposition in Porous Media including Dispersive Transport

Particle migration and deposition, and resulting permeability impairment occurring in porous media are described by a practical phenomenological model considering temperature variation and particle transport by advection and dispersion. Variation of the filter coefficient and permeability of porous matrix by temperature and particle deposition, and other essential factors are considered by means of the special correlations of the relevant variables and dimensionless numbers. Comparison of the numerical results, obtained using a finite-difference numerical scheme with and without considering the dispersion mechanism and temperature variation, reveals the significance of such effects on fines migration and deposition, and consequent permeability impairment in porous media. Improved model presented in this article can be instrumental for scientifically guided experimentation, analysis, and optimal design of processes involving in transport of colloidal and fine particles through geological subsurface formations.

Lateral freezing of an anisotropic porous medium saturated with an aqueous salt solution

Lateral freezing of a porous medium saturated with an aqueous salt solution was investigated experimentally and theoretically to obtain the improved understanding of the solute redistribution during solid/liquid phase change. The emphasis was on the interaction between hydrodynamics and transport of energy and species in the solidifying and unsolidified regions and on the effect of the flow characteristics possessed by the porous matrix and dendrite arrays. Freezing experiments were performed in a square cross-section enclosure chilled and heated from the side by imposing uniform but different temperatures, and filled with the artificial porous structure. The latticed structure of the porous matrix phase and the shadowgraph enabled the flow visualization and the observation of the solidus and liquidus positions. Simultaneous measurements of local temperature and liquid composition at selected locations were also made. An analytical model based on heat and species conservation and relations from the phase diagram is suggested, and the predictions are compared with experimental data. The effect of porous matrix permeability was examined over a wide range of parameters by performing numerical experiments. The porous matrix phase affected the freezing of an aqueous salt solution by offering an additional resistance to the motion of the fluid and migration of separated crystals. The amount of macrosegregation was found to be mainly controlled by the porous matrix permeability in the direction of gravity. Macrosegregation was decreased when the permeabilities of the porous matrix phase and/or dendrite arrays were decreased.

A Study on Squeeze Films between Porous Rubber Surface and Rigid Surface. 2nd Report. Effects of Permeability of Porous Matrix and Fluid Inertia Force in Squeeze Film.

A theoretical study is carried out to investigate the squeeze film phenomena between a cylindrical porous rubber block and a rigid plate. The porous rubber block is stationary, while the rigid plate is oscillated sinusoidally in the direction perpendicular to its surface or dropped on the porous rubber surface, subjected to its own weight and the squeeze film force. The deformation of the porous rubber block is evaluated with an axisymmetric continuum model based on a three element visco elastic model. The approximate solutions for the film pressure including the fluid inertia effect are obtained using the perturbation method. for each type of rigid plate motion, the numerical results show various effects of the permeability of porous rubber block and the fluid inertia force on squeeze film characteristics such as the film pressure, force, thickness and the leakage flow from the squeeze film.