Inside Porous Media Research Articles

Modelling fluid flow in karst reservoirs using Darcy Model with estimated permeability distribution

The existence of free-flow regions (fractures, vugs and caves) inside porous media at multiple-scales affects the flow paths in aquifers and underground reservoirs. To simulate advection-dominant phenomena with a reasonable level of accuracy, the Stokes-Brinkman and the Darcy-Stokes models have been separately proposed to model the simultaneous flow of fluids in the free-flow regions and the porous regions of karst reservoirs. However, the computational cost associated with the use of Stokes-Brinkman is much higher when compared with the use of the Darcy's model while Darcy-Stokes requires the implementation of the interface conditions.This paper introduces an approximation technique that assigns different permeability values to the grids in the free-flow region. The technique provides a way for computing apparent permeability values for different grid locations in the free-flow regions. This method makes it possible for the Darcy's model to closely approximate the Stokes-Brinkman's model. This proposed approach makes it possible to replace the Stokes-Brinkman model with the Darcy's model without significant loss of accuracy in modelling flood fronts. The values of the apparent permeabilities of the grids inside the free-flow region and the surrounding porous media are calculated from the analytical solution of Stokes-Brinkman's equation. Four examples are presented to illustrate the effectiveness of this technique. In the first three examples, the principal axes of the cave (free-flow region) are aligned with those of the porous media. The fourth example consists of a more complex scenario in which the principal axes of the cave are not in alignment with those of the porous media.

Experimental analysis of the flow near the boundary of random porous media

The aim of this work is to experimentally examine flow over and near random porous media. Different porous materials were chosen to achieve porosity ranging from 0.95 to 0.99. In this study, we report the detailed velocity measurements of the flow over and near random porous material inside a rectangular duct using a planar particle image velocimetry (PIV) technique. By controlling the flow rate, two different Reynolds numbers were achieved. We determined the slip velocity at the interface between the porous media and free flow. Values of the slip velocity normalized either by the maximum flow velocity or by the shear rate at the interface and the screening distance K1/2 were found to depend on porosity. It was also shown that the depth of penetration inside the porous material was larger than the screening length using Brinkman’s prediction. Moreover, we examined a model for the laminar coupled flow over and inside porous media and analyzed the permeability of a random porous medium. This study provided detailed analysis of flow over and at the interface of various specific random porous media using the PIV technique. This analysis has the potential to serve as a first step toward using random porous media as a new passive technique to control the flow over smooth surfaces.

吸水性ポリマーを用いた多孔体ダクト乱流の多孔体界面および内部流動のＰＩＶ計測

吸水性ポリマーを用いた多孔体ダクト乱流の多孔体界面および内部流動のＰＩＶ計測

Direct numerical method for studying heat transfer behaviors in an enclosure with dispersed thermal conductive particles

Numerical simulations in a two-dimensional (2-D) thermal energy storage (TES) unit were carried out to investigate the thermal behaviors of phase change materials (PCMs) - sodium nitrate (NaNO3) inside porous media. The porous media are composed of randomly distributed particles with high thermal conductivity. The effects of heat conduction through particles, natural convection of liquid PCM, and the geometric parameters such as porosity and particle shape were numerically examined. The results show that for the TES dispersed with square particles, the heat transfer coefficient of the system can be increased up to 27–310% for the porosity ranging from 60% to 90%; while for the particles of expanded graphite (EG)-like structure, the heat transfer coefficient of the TES at 60% porosity can be raised as much as 93.3 times. The high weight fraction of particles in the TES could depress the happening of natural convection, especially for EG-like particles. The Rayleigh number considering the permeability of material (RaK) was proposed to evaluate the roles of heat conduction and natural convection. When RaK is lower than 20.6, the heat conduction starts to dominate the heat transfer inside the composite that leads to the total heat performance of the composite with square particles is lower than that of the system with pure liquid PCM.

Absorption of picoliter droplets by thin porous substrates

Absorption of picoliter (pL) droplets into porous substrates is studied experimentally and numerically. In the case of pL droplets, major phenomena involved in the interaction between droplet and porous media develop at different time scales: spreading and wetting at microseconds, absorption and wicking at milliseconds, and evaporation at seconds. Therefore, one can decouple these processes to minimize the complexity of the study. A high‐speed imaging system capable of 1 million frames per second is used to visualize individual droplets impacting, spreading, and imbibing on substrates. To simulate droplet dynamics, the governing equations for flow outside and inside porous media are proposed and solved using an in‐house developed computational fluid dynamics solver. The simulation results are in good agreement with the experimental data. The effect of drop impact velocity and fluid properties on final dot shape in the porous substrates is investigated through a series of parametric numerical studies. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1690–1703, 2017

Particle-induced viscous fingering

The Saffman–Taylor fingering instability arises when a less viscous fluid displaces a more viscous one inside porous media, which has been extensively studied for decades. Conversely, the invasion of a more viscous fluid into a less viscous fluid is inherently stable to interfacial instabilities. However, Tang et al. [1] first observed that the addition of particles to a viscous invading fluid can destabilize the fluid-fluid interface, even in the absence of the unstable viscosity ratio. Building on the previous observations, we experimentally characterize the particle-induced fingering patterns in a radial source flow for varying particle volume fractions and gap sizes. The onset of fingering is observed to be highly dependent on the particle volume fraction and also, to a lesser extent, on the channel gap thickness. The key physical mechanism behind this instability is the particle accumulation on the interface that stems from the shear-induced migration of particles far upstream of the interface. We model the particle-laden flow as a continuum in the quasi-steady region away from the interface, based on the suspension balance approach, and successfully validate the effects of shear-induced migration on the particle accumulation and subsequent fingering.

Modeling free-surface flow in porous media with modified incompressible SPH

This paper presents a modified incompressible smoothed particle hydrodynamics (MISPH) method for fluid-porous media interaction problems. Navier–Stokes and Brinkman Equations are considered for modeling the fluid flow outside and inside porous media. The MISPH method utilizes a truly incompressible divergence free velocity formulation. The equations are solved by using a robust two-step semi-implicit exact projection method. Turbulence stresses are evaluated by using an semi-analytical Smagorinsky model. The representative volume of the particles changes with the porosity. Interface conditions are imposed implicitly by using Darcy velocity and modified Pressure Poisson Equation (PPE) with porosity in the source/sink term. Impermeable boundary conditions are simulated with fixed ghost particles. The model is validated by using existing experimental results of dambreak flow through a homogeneous porous block in a wet bed. Simulation results show good agreement with experimental data. An application to heterogeneous porous media demonstrates the applicability and adaptability of the proposed framework. The numerical model is capable of efficiently capturing the interaction of fluid in porous and nonporous media.

Understanding and Modelling Turbulence Over and Inside Porous Media

To understand turbulence over porous media, a series of PIV measurements were carried out in porous-walled channel flows. The porous walls were made of three types of foamed ceramics which had the same porosity but different permeability. For turbulence inside porous media, LES studies of fully developed flows in three different model porous media were performed. Referring to these databases, a multi-scale k − e four equation eddy viscosity model for turbulence around and/or inside porous media was developed. Through the comparison to the experimental results, the proposed model was validated with satisfactory accuracy.

Pore-scale simulation of fluid flow passing over a porously covered square cylinder located at the middle of a channel, using a hybrid MRT-LBM–FVM approach

A comprehensive study was performed to analyze the unsteady laminar flow characteristics around a porously covered, a fully porous, and a solid squared section cylinder located in the middle of a plane channel. In order to simulate fluid flow inside porous media and porous–fluid interface accurately (minimizing modeling error), the porous region was analyzed in pore scale, using LBM. Additionally, to minimize the LBM-related compressibility error through the porous region, a multi-block multiple relaxation time lattice Boltzmann method (MRT-LBM) was used. Also, to decrease CPU time, a Navier–Stokes flow solver, based on finite volume method and SIMPLE algorithm, was coupled with MRT-LBM to simulate flow around the porous obstacle. It should be noted that the flow inside the porous layer is in continuum regime, and hence, the no-slip boundary condition was used to treat the solid walls inside the porous media. In our simulations, we considered variations of porosity and Reynolds number ranging from 0.75 to 0.94 and from 60 to 240, respectively. The effects of porosity and Reynolds number on vortex pattern, mean drag coefficient, amplitude of lift coefficient, and Strouhal number were investigated. Comparison of our results with the ones obtained using Open FOAM, as well as published by others, shows the suitable accuracy of our computations. It is seen that at low Reynolds numbers or at low porosities, where the mean flow does not have large enough momentum to penetrate porous media, the resulting flow field and aerodynamic coefficients are relatively close for three different configurations used. However, as the flow Reynolds number or permeability increases, the mean flow penetrates easier into the porous media and thus provides different shedding characteristics and aerodynamic coefficients for different obstacle shapes.

On the Characterization of Lifting Forces During the Rapid Compaction of Deformable Porous Media

Abstract In a recent paper, Wu et al. (2005, “Dynamic Compression of Highly Compressible Porous Media With Application to Snow Compaction,” J. Fluid Mech., 542, pp. 281–304) developed a novel experimental and theoretical approach to investigate the dynamic lift forces generated in the rapid compression of highly compressible porous media, (e.g., snow layer), where a porous cylinder-piston apparatus was used to measure the pore air pressure generation and a consolidation theory was developed to capture the pore-pressure relaxation process. In the current study, we extend the approach of Wu et al. to various porous materials such as synthetic fibers. The previous experimental setup was completely redesigned, where an accelerometer and a displacement sensor were employed to capture the motion of the piston. The pore-pressure relaxation during the rapid compaction of the porous material was measured. The consolidation theory developed by Wu et al. was modified by introducing the damping effect from the solid phase of the porous materials. One uses Carman–Kozeny's relationship to describe the change in the permeability as a function of compression. By comparing the theoretical results with the experimental data, we evaluated the damping effect of the soft fibers, as well as that of the pore air pressure for two different porous materials, A and B. The experimental and theoretical approach presented herein has provided an important methodology in quantifying the contributions of different forces in the lift generation inside porous media and is an extension of the previous studies done by Wu et al.

On the Theory of Sound Transfer in Rigid-Frame Porous Materials

The modeling of the macroscopic propagation of sound inside porous media is usually based on first order acoustical quantities. Single or multiple layers are treated as an equivalent impedance network which can be also solved with a transfer matrix formulation. In this work the one dimensional, time averaged, macroscopic sound transfer process in rigid-frame porous media is reinterpreted with the concepts developed in the field of sound intensity. An algebraic derivation shows that the active intensity is proportional to the spatial gradient of the sound energy density, so that the two quantities obey a diffusion equation. The name sound conductivity is suggested for the related coefficient, and the expressions of the sinks of sound energy and of the sources of reactivity in the material are formalized. Moreover a differential formulation for the energy densities inside the material is developed and solved analytically.

Factors Affecting Well Productivity - I. Drilling Fluid Filtration

Published in Petroleum Transactions, AIME, Volume 210, 1957, pages 126–131. Abstract This paper is concerned with:an analysis and interpretation of the filtration characteristics of drilling muds on filter paper, andan interpretation of early stage "filtration" on consolidated synthetic porous media, herein referred to as the "surge loss" period. It is shown that water-loss data can be plotted so as to disclose the existence of a surge period, a non-uniform cake thickness period, and a constant pressure filtration period. The same periods occur during exposure of consolidated porous media to muds. The data on consolidated porous media indicate that:mud particles bridge pores inside porous media during the surge period, and"filter cake" build-up inside porous media occurs during subsequent filtration. The data also show that the surge loss increases with sample permeability and with pressure differential. Introduction The phenomenon of mud filtrate invasion into porous sands of a drilling well has been recognized for many years. Part of API Code 29 is concerned with the filtration testing of a drilling mud to yield data on this subject. In a number of investigations "plastering properties" of muds were studied, "plastering" apparently meaning cake forming properties. In such studies the characteristics (thickness, permeability, and toughness) of the cake and the rate at which the liquid phase of the mud was separated from the solids (filtration rate through the cake, commonly referred to as water loss) were measured or at least considered. From the standpoint of its effect on well productivity, filtrate invasion into "clean" water-wet pay sands (i.e., those containing no clay minerals) may not necessarily be a serious problem. An increase in water saturation in the zone immediately around the wellbore would cause loss of oil permeability. However, in such a system, much of this water may be removed by oil production. If filtration occurs into "dirty" sands (i.e., those containing appreciable clay minerals), clay swelling or other mechanisms may cause losses in oil permeability which cannot be overcome by oil production.