Dimensionless Permeability Research Articles

Theoretical investigation of electroviscous flows in hydrophilic slit nanopores: Effects of ion concentration and pore size

Nanopores with various shapes are well developed in unconventional reservoirs, and the transport phenomena of solutions in these reservoir rocks are ubiquitous but have not yet been fully understood. This article investigates the flow characteristics of solutions in hydrophilic slit nanopores through the combination of a modified Poisson–Boltzmann (MPB) model and the modified Navier–Stokes (NS) equation. To account for the nanoconfinement effects on ion concentration and fluid viscosity, an electrochemical potential term is used in the MPB model and a varying viscosity model (VVM) is introduced in the NS equation. The model rationality is first confirmed, and then the influences of ion concentration and pore size on the transport capacities of solutions in nanopores are illuminated. In addition, the hydrodynamic features of liquids in nanopores and the limitations of this coupled model are discussed as well. The results show that the dimensionless apparent permeability of the slit increases with an increase in ion concentration and pore size. The relative contributions of the electroviscous effect (EVE) and VVM to the total flow resistance reveal different varying trends as ion concentration or pore size increases, which is greatly related to the surface charge density and the sign of the charged wall. Additionally, although the effects of EVE and VVM resulting from the nanoconfinement are considered, average velocities of fluids in nanopores exhibit a linear correlation with the pressure gradient, which cannot be used to explain the nonlinear flow mechanism occurring in tight reservoirs. Furthermore, we also compare the velocity difference between the classical PB and MPB models. We hope that the findings in this work can help improve our understanding of the characteristics of liquid flow in tight reservoirs and provide vital practical implications for diverse engineering applications.

INFLUENCE OF MAGNETIC FIELD ON THE STOKES FLOW THROUGH POROUS SPHEROID: HYDRODYNAMIC PERMEABILITY OF A MEMBRANE USING CELL MODEL TECHNIQUE

The present work concerns an analysis of the creeping flow of steady, axisymmetric Stokes flow of an electrically conducting, viscous, incompressible fluid through a swarm of porous spheroidal particles in the presence of a uniform magnetic field. Cell model technique has been used to model the problem. Four known boundary conditions, Happel's, Kuwabara's, Kvashnin's, and Cunningham's (Mehta-Morse's), are used to find the hydrodynamic permeability of the membrane built up by porous spheroidal particles by using the perturbation method. The stress jump boundary condition for tangential stresses, along with the continuity of normal stress and velocity components, is used at the fluid-porous interface. The variation of the dimensionless hydrodynamic permeability of the membrane with the stress jump coefficient, the Hartmann number, and the dimensionless permeability of the porous region and particle volume fraction are discussed. The presented model can be used for the evaluation of changing hydrodynamic permeability of a membrane under the influence of a uniform magnetic field in pressure-driven processes (nano-, reverse osmosis, and microfiltration).

Effect of first order chemical reactions on the dispersion coefficient associated with laminar flow through fibrosis affected lung

In this paper, we worked on the effective area average concentration and dispersion coefficient associated with the unsteady flow, to understand the dispersion in the fibrosis-affected lung. We assumed that the tube wall (i.e. alveolar or pulmonary capillary wall) is thicker than its normal size due to fibrosis and chemical species may go through linear first-order kinetic reactions, one is reversible phase exchange with the wall material and other is irreversible absorption into the tube wall. By considering diffusivity as a function of thickness, the dispersion can be calculated by the distribution of concentration of gas along a tube. Mathematical modeling is done by using diffusion equation; and effects of various dimensionless parameters e.g., the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ), thickness and permeability of wall are observed. Numerical simulation shows that the diffusion rate through the respiratory wall is decreased significantly as the thickness of wall increases, while it increased with the increment in the porosity of wall, the concentration of species increased when the tube wall thickness increases; which cause reduction in the spread of the species; additionally, the dispersion coefficient achieves the steady-state values in a very short time when 0 < DA ⩽1 and absorption rate < 1, while for 1 < DA ⩽20 and absorption rate = 1 long time dispersion is achieved.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

Transport through random bimodal and multimodal fiber structures

Random walk simulation results are reported for the transport and structural properties of random bimodal fibrous media for a range of values of the porosity, relative fiber size, and relative fiber density. Analytical expressions are derived for the mean intercept length of random bimodal and multimodal fiber structures, and are validated through simulations. A fiber dispersity factor emerges from the derivations, accounting for the deviation of the mean intercept length of such structures from that of unimodal fiber beds of the same porosity. Tortuosity factors in all diffusion regimes for in-plane and transverse flow through bimodal fibrous media of moderate or high porosity are practically independent of the relative fiber size and density and equal to those reported earlier for beds of unimodal fibers. The same holds for the formation factor of such structures, accounting for the dimensionless effective bulk diffusivity, thermal and electrical conductivity, magnetic permeability, dielectric constant and refractive index. The dimensionless viscous permeability of bimodal and multimodal fiber structures of moderate or high porosity may be obtained from that of unimodal fiber structures through simple multiplication by the square of the dispersity factor. This result is in line with a multitude of experimental data of the literature.

A FRACTAL PERMEABILITY MODEL FOR POROUS–FRACTURE MEDIA WITH THE TRANSFER OF FLUIDS FROM POROUS MATRIX TO FRACTURE

The transfer of fluids from porous matrix to fracture is a key issue to accurately predict the fluid flow behavior in porous–fracture media. In this work, to take into account the transfer of fluids, the analytical model of dimensionless permeability is proposed based on the fractal geometry theory for porous media. The proposed model is expressed as a function of microstructural parameters of the porous matrix and fracture, such as the pore area fractal dimension [Formula: see text], fractal dimension [Formula: see text] for tortuosity of tortuous capillaries, the ratio [Formula: see text] of the maximum pore size in porous matrix to fracture aperture, as well as the ratio [Formula: see text] of the pressure difference along the fracture to that along the porous matrix layers. The model reveals that the ratios [Formula: see text] and [Formula: see text] have significant influences on the permeability contribution from the porous matrix to the seepage behavior of the fracture. While the contribution of porosity of leak-wall porous surface of the fracture to the permeability is less than 10%. The present results may provide an important theoretical foundation for exploration of petroleum, gas and geothermal energy extraction systems.

Filtration Permeability of Dendritic Structure in Condition of Diffusion-Capillary Coalescence of Secondary Side Branches

The problem state of computer analysis of shrinkage defects in castings is analysed based on a review of theoretical and experimental studies the filtration permeability of solidifying alloys. It is shown that the use of the dimensionless permeability coefficient and its modification by introducing various corrections to the Karman-Kozeni equation, obtained for the stationary morphology of non-intersecting filtration channels, is inapplicable for the conditions of continuous change of their geometry during formation of dendrite structure. A computer model of the permeability for the mesoscale ensemble of secondary dendritic branches under the conditions of their diffusion-capillary coalescence is developed. Based on the thermodynamic apparatus and solidification modeling the influence of composition of Al-Cu-Mg alloys and heat removal velocity on the permeability coefficient under the evolution of the dendritic structure is analysed.

Study on Flow and Heat Transfer Characteristics of Porous Media in Engine Particulate Filters Based on Lattice Boltzmann Method

To investigate the laminar flow characteristics of porous media in the inner core of engine particulate filters, a two-dimensional lattice Boltzmann–Cellular Automata (LB–CA) probabilistic model is used to simulate the flow characteristics of porous media. The variation of dimensionless permeability of various numerical structures on pore scale with Reynolds number is analyzed, and the heat transfer as well as particle filtration are considered. The results show that the flow law of different structures obeys Darcy law under the condition of low Reynolds number (Re &lt; 1). The dimensionless permeability coefficient of the ordered structure is significantly higher than that of the disordered structure; however. the filtration efficiency of the ordered structure decreases. With the increase of Reynolds number, the heat transfer increases. Furthermore, it is found that the particle size has a great influence on the filtration efficiency.

Fine/ultrafine particle air filtration and aerosol loading of hollow-fiber membranes: A comparison of mathematical models for the most penetrating particle size and dimensionless permeability with experimental data

Hollow-fiber membranes (HFMs) have widely been applied to many liquid treatment applications such as wastewater treatment, membrane distillation and membrane contactor/bioreactor applications. However, they have rarely been used for aerosol filtration thus far. In this work, we tested air filtration performance of air filter modules composed of polypropylene HFMs. The experimental results of most penetrating particle size (MPPS) and permeability were then compared with theoretically predicted values. Filtration efficiency and MPPS were measured using a monodisperse (20, 35, 50, 70, 100, 140, 280 and 400 nm) and a polydisperse aerosol (15–594 nm). Dimensionless permeability was predicted using models assuming isotropic 3D pore structure and compared with permeability measured using capillary flow porometry. Finally, an experiment to observe pressure drop with long-term particle loading was carried out. In the experiments with the monodisperse aerosol, no penetration was observed regardless of particle size. Therefore, face velocity was increased and high concentrations of the polydisperse aerosol were used to increase the penetration. The MPPS was then found to be 333 and 250 nm at a flowrate of 10 and 40 L/min, respectively. The MPPS model for diffusion and interception dominant regime proposed by Lee and Liu (1986) was closest to these results. Dimensionless permeability varied depending on the conditions for which the individual models were derived. For example, the RUC (representative unit cell) model underestimates the results while the results predicted using the empirical formula of Davies (1953) differ significantly from the measured values. The loading experiments have shown significantly prolonged fouling by high concentrations of submicron particles compared to conventional fibrous filters.

Hydrodynamic self-lubricating journal bearings analysis using Rabinowitsch fluid lubricant

Abstract In this study, the effects of non-Newtonian pseudo-plastic lubricants behavior, using Rabinowitsch fluid model, on static characteristics of circular self-lubricating porous journal bearings of finite length with sealed ends are highlighted. The nonlinear Reynolds equation based on the Rabinowitsch fluid model has been developed specifically for porous journal bearing cases by considering the fluid flow in the porous matrix described by Darcy's law. The Governing equations are discretized using a centered finite difference scheme and solved numerically using an iterative method. Following to the absence of the porous matrix or the non-Newtonian fluid behavior, the obtained results showed a good agreement with those of the literature review. The static characteristics of hydrodynamic lubrication are calculated numerically for various parameters such as bearing dimensions; the porous bush permeability and the lubricant pseudo-plastic coefficient. It is shown that the dimensionless permeability has significant effects on the static characteristics of the bearings. The pseudo-plastic lubricant coefficient decreases the bearing characteristics (load capacity, pressure) compared to Newtonian lubricant cases. The use of the pseudo-plastic fluids reduces the performance of the bearings and this reduction grows with the porous bearing properties.

Absolute Permeability Calculation by Direct Numerical Simulation in Porous Media

Simulating fluid flow at micro level is an ongoing problem. Simplified macroscopic flow models like Darcy’s law is unable to estimate fluid dynamic properties of porous media. The digital sample reconstruction by high resolution X-ray computed tomography scanning and fluid-dynamics simulation, together with the increasing power of super-computers, allow to carry out pore-scale simulations through digitally-reconstructed porous samples. The pore-scale flows which derived from computational fluid dynamic are then evaluated using the finite volume method implemented in the open-source platform OpenFOAM®. In this work to verify the solver in porous media we simulated fluid flow around sphere in body-centered cubic (bcc) lattice and calculated the dimensionless permeability for a wide range of radius and porosity; the results are comparable with those obtained by using carman-kozeny equation. Then this solver is performed on realistic sample to investigate the effect of sample size on calculated permeability and tortuosity and the mesh refinement levels for a fixed image resolution.

Hybrid‐permeability model evaluation through concepts of tortuosity and resistance rate: Properties of manufactured hybrid laminate

The mechanical properties of composite structures depend on the preform impregnation and a successful impregnation can be achieved using the permeability relation in the case of an infusion process. The objective of this study is to develop an analytical model to predict the permeability K of carbon and glass fabrics through hybrid laminate using different stacking sequence, applying an average‐permeability model. Preforms permeabilities were evaluated through tortuosity and void‐volume fraction. The model allows the analysis of different stacking sequence combinations (interleaved and in block), measuring the contribution of each material type. As a result, hybrid average‐permeability model was validated through experimental permeability tests, dimensionless permeability, and tortuosity results, besides enabling predictions of the flow front behavior with &lt;10% of deviation. Carbon fiber preforms exhibited higher flow resistance, which is explained via tortuosity concept. A combination of carbon/glass preforms presented an increased permeability, which means a synergy that provides higher value of K. In addition, the use of hybrid preforms, especially Hybrid 2 stacking sequence, reduce the injection time and void formation, ensuring composite impregnation quality. POLYM. ENG. SCI., 59:1215–1222 2019. © 2019 Society of Plastics Engineers

Transient-Flow Modeling of Vertical Fractured Wells with Multiple Hydraulic Fractures in Stress-Sensitive Gas Reservoirs

Massive hydraulic fracturing of vertical wells has been extensively employed in the development of low-permeability gas reservoirs. The existence of multiple hydraulic fractures along a vertical well makes the pressure profile around the vertical well complex. This paper studies the pressure dependence of permeability to develop a seepage model of vertical fractured wells with multiple hydraulic fractures. Both transformed pseudo-pressure and perturbation techniques have been employed to linearize the proposed model. The superposition principle and a hybrid analytical-numerical method were used to obtain the bottom-hole pseudo-pressure solution. Type curves for pseudo-pressure are presented and identified. The effects of the relevant parameters (such as dimensionless permeability modulus, fracture conductivity coefficient, hydraulic-fracture length, angle between the two adjacent hydraulic fractures, the difference of the hydraulic-fracture lengths, and hydraulic-fracture number) on the type curve and the error caused by neglecting the stress sensitivity are discussed in detail. The proposed work can enrich the understanding of the influence of the stress sensitivity on the performance of a vertical fractured well with multiple hydraulic fractures and can be used to more accurately interpret and forecast the transient pressure.

A novel fractal solution for permeability and Kozeny-Carman constant of fibrous porous media made up of solid particles and porous fibers

This paper presents a novel fractal solution to investigate the permeability and the Kozeny-Carman (KC) constant of fibrous porous media made up of solid particles and porous fibers. The proposed model has been verified with satisfying agreements of the permeability and KC constant of fibrous porous media obtained by our model and those obtained by experimental data, analytical solution, and numerical simulation reported in literature. The results demonstrate that 1) an increase in particle diameter leads to an increase in the absolute permeability; 2) an increase in the tortuosity fractal dimension leads to an increase in the KC constant and decreases in the dimensionless permeability and absolute permeability; 3) an increase in the porosity results in increases in the dimensionless permeability and absolute permeability of the fibrous porous media; 4) increases in the fiber diameter yields an increase in the absolute permeability of fibrous porous media. The proposed fractal model explicitly relates the KC constant and the permeability to the microstructural parameters of the fibrous porous media, and consequently facilitating the understanding of the detailed physical mechanisms for fluids transport through fibrous porous media.

Investigation of drag properties for flow through and around square arrays of cylinders at low Reynolds numbers

The drag properties of flow through and around square arrays of 10 × 10 evenly spaced circular cylinders with a wide range of solid fraction ϕ from 9.69×10-11 to 0.785 and Reynold number of the array Re from 1 to 50 are investigated numerically. The purpose of the present study is to better understand the phenomena of flow through and around permeable bodies that appear in bioreactors and fluid–solid reactors, for example. Instead of using the semi-empirical porous medium model, the direct numerical simulation is employed in order to investigate the flow mechanism from a microscopic point of view. A peak in drag coefficient is observed for the range of ϕ investigated, which appears at a smaller ϕ as Re increases. Three flow regimes are identified based on the shape effects quantified via the averaged velocity within the array, and the drag property in each regime is analyzed. A novel drag formula is also found by investigating the dependence of drag on ϕ and R (Reynolds number based on the mean velocity within the array). Finally, the dimensionless macroscopic permeability Da is estimated via the Darcy’s law. The drag ratio computed is in a good agreement with the previous results from porous media models.

Simulation of a fluid flow and investigation of a permeability-porosity relationship in porous media with random circular obstacles using the curved boundary lattice Boltzmann method

In this paper, the fluid flow between two parallel flat plates filled with porous media was investigated numerically using the Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM). The obstacles representing porous media were considered as random, circular, rigid and granular ones with uniform diameters and without overlap. The fluid was supposed to be a single-phase viscous Newtonian fluid and the flow to be incompressible, steady and laminar. The uniform velocity profile was considered at the entrance of the canal and the no-slip condition was imposed at solid walls. For applying curved boundary conditions, the linear interpolation method ( $ \Delta$ fraction) was used in this work. The effect of varying the Reynolds number on the pressure gradient and the Darcy drag was studied. The porous medium was supposed to be isotropic and having scalar permeability. The dimensionless permeability was calculated as a function of the Knudsen number. Also, the dimensionless permeability versus porosity was investigated and the results were compared with the Clague equation for different materials. Because of rather low precision of the Clague equation at high porosities, an extension to the Clague equation was presented. The permeability-porosity relationship was surveyed and the corresponding curve was plotted in the LBM scale. It was seen from numerical results that the enhancement of the Knudsen number increases the dimensionless permeability. The change of streamlines tortuosity in terms of porosity was explored and the results were compared with the revised Bruggeman equation. The obtained results demonstrate that the Lattice Boltzmann Method is very useful in the challenging problems of fluid dynamics such as fluid flow simulation through porous media.

Permeability prediction for flow normal to columnar solidification structures by large–scale simulations of phase–field and lattice Boltzmann methods

Computer simulation is the most promising approach for the systematical permeability prediction of liquid flow in the mushy zone for various solidification conditions. In this study, we propose a permeability prediction method by using large–scale simulation of phase–field and lattice Boltzmann methods. Using the proposed method, permeability predictions are performed for the flow normal to the columnar solidification structures with multiple dendrites/cells. In addition, the prediction is also performed for columnar solidification structures with periodically arranged dendrites/cells to evaluate the permeability in the full range of solidification fraction and investigate the effect of primary arm array on the permeability. As a result, it is concluded that the dimensionless permeability using a specific interface area of columnar solidification structures can be well approximated by that of a regular hexagonal array of cylinders. Moreover, it is confirmed that the columnar dendrite/cell structure with a periodic regular hexagonal array provides realistic permeability predictions for columnar solidification structures.

Experimental study on water sensitivity and salt sensitivity of lignite reservoir under different pH

The water sensitivity and salt sensitivity of lignite reservoirs are important factors affecting the productivity of the coalbed methane (CBM) well. This paper took the lignite of Erlian Basin as the research object. The content and occurrence of mineral was analyzed by LTA + XRD combined with scanning electron microscopy (SEM), and distribution of each functional group of lignite was analyzed by infra-red spectrum. Based on the above analysis, standard salt water with different pH and salinity was used as the experimental injection fluid, and water sensitivity (salt sensitivity) experiments were performed under the condition of constant effective stress. The experimental results show that the sample contains a large number of water-sensitive minerals (kaolinite and illite/smectite mixed layer mineral), and the ratio of carbonyl, hydroxybenzene and carboxyl groups is 10:7:1. Hydrogen bonds are mainly OH⋯N hydrogen bonds. The lignite reservoirs with different pH have different degrees of water-sensitive damage, and the damage rates from high to low are partial alkalinity conditions (54.18%), partial acidity conditions (42.6%), and strong alkalinity conditions (23.67%). The dimensionless permeability changes with the decrease of salinity, which can be divided into three stages (no water sensitivity stage, particle migration water sensitivity stage, particle expansion water sensitivity stage) with 1250 mg/L and 10000 mg/L as the boundary. The displacement pressure and pH are the main controlling factors at different stages, and pH controls the wettability of pulverized coal and the hydration expansibility of clay minerals. The dimensionless permeability of lignite reservoir increases with the increase of salinity under the acidic condition. Under alkaline conditions, it is characterized by no-weak salt sensitivity. The greater the alkalinity, the stronger the salt sensitivity, which is mainly controlled by the change of the thickness of the water film under the influence of pH.

Changes in the anisotropic permeability of low-rank coal under varying effective stress in Fukang mining area, China

Fractures are coalbed methane (CBM) migration pathways and key factors in determining coal reservoir permeability. During the depletion of CBM wells, the increase of effective stress with water pumping and gas desorption will affect gas production by changing reservoir permeability. However, the current understanding of the impacts of fracturing in different directions on CBM recovery is inadequate. In this work, we collected 4 types of cubic coal samples (samples cut parallel to face and butt cleats and perpendicular to the bedding plane) from the Fukang mining area in China to investigate the anisotropic characteristics of P-wave velocity, fractures and permeability under varying effective stresses from 3.5 to 8.5 MPa in the laboratory. The results indicate that the permeability exponentially decreased with increasing P-wave velocity. The acoustic wave velocities significantly decreased from direction perpendicular to the bedding plane to the butt cleat direction to the face cleat direction. However, the fracture aperture exhibited the opposite trend. The maximum acoustic wave velocities ratios of the perpendicular bedding plane direction to the parallel bedding plane direction are 1.12, 1.23, 1.05 and 1.15 for sample LY, DH, XG and QM, respectively. However, the ratios of butt cleat direction to face cleat direction are 1.23, 1.21, 1.01 and 1.07. A good coupling effect was detected between the aperture, porosity, connectivity, and permeability. The permeability decreased exponentially as the effective stress increased in the selected coal samples. Under the 3.5–6.5 MPa effective stress conditions, the permeability decreased rapidly, and from 6.5 to 8.5 MPa, the permeability decreased more slowly. Contrary to the permeability loss rate (PLR), the stress sensitivity coefficient and dimensionless permeability parallel to the bedding plane were greater than perpendicular to the bedding plane. The effective stress returned from 8.5 MPa to 3.5 MPa, and the permeability rebounded but did not fully recover. The irreversible permeability loss rate (IPLR) showed that the permeability was restored the least in the direction perpendicular to the bedding plane. The maximum IPLR ratios of the perpendicular to the bedding plane direction to the parallel bedding plane direction are 3.39, 5.34, 1.86 and 23.00 in sample LY, DH, XG and QM, respectively. According to the study of anisotropic fractures and permeability, multi-lateral well is recommended as the appropriate well type to obtain the optimal CBM recovery effect.

A discrete-fracture-network fault model revealing permeability and aperture evolutions of a fault after earthquakes

The present study aims to illustrate the evolutions of fault aperture during earthquake-induced fault deformation and the following fault healing process. We consider the coupled shear-flow properties of fault, and establish a DFN-fault model that contains a discrete fracture network (DFN) embedded with a deformable fault. The calculated equivalent permeability with varying shear displacement of the fault is compared with that of in-situ measurements in the Wenchuan earthquake fault zone. Based on the best-fitted shear displacement, the closure of fault aperture over time in the post-earthquake stage is calculated and presented. We define a dimensionless permeability and a dimensionless aperture that is the ratio of permeability/aperture at a certain shear displacement and a certain depth to their original values recorded after an initial earthquake. Our analysis suggests that the dimensionless permeability decreases over time following linear functions, while the dimensionless aperture decreases following quadratic functions in the post-earthquake stage. The ranges of dimensionless permeability increment during an earthquake and reduction afterward are approximately twice of those of dimensionless aperture increment and reduction, respectively. The results revealed an increasing manner of closure rates of the fault in each post-earthquake stage, which cannot be effectively accommodated by previous experimental observations and theoretical/numerical models that generally obtain decreasing closure rates over time. The unusually high hydraulic diffusivity measured in the fault zone implies strong water circulation that could result in rapid transport of mass/minerals of props, which added by precipitation on throat flow paths in the damage zone may be partially responsible to this difference.