scholarly journals A generalised model for electro-osmotic flow in porous media

2019 ◽  
Vol 29 (12) ◽  
pp. 4895-4924
Author(s):  
Simona Di Fraia ◽  
P. Nithiarasu

Purpose This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential. Design/methodology/approach The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF. Findings The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces. Originality/value To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

Author(s):  
Simona Di Fraia ◽  
Nicola Massarotti ◽  
P. Nithiarasu

Purpose This paper aims to provide a comprehensive literature review on modelling electro-osmotic flow in porous media. Design/methodology/approach Modelling electro-osmosis in fluid systems without solid particles has been first introduced. Then, after a brief description of the existing approaches for porous media modelling, electro-osmotic flow in porous media has been considered by analysing the main contributions to the development of this topic. Findings The analysis of literature has highlighted the absence of a universal model to analyse electro-osmosis in porous media, whereas many different methods and assumptions are used. Originality/value For the first time, the existing approaches for modelling electro-osmotic flow in porous have been collected and analysed to provide detailed indications for future works concerning this topic.


Author(s):  
Mehdi Jamei ◽  
H Ghafouri

Purpose – The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection. Design/methodology/approach – The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations. Findings – The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements. Research limitations/implications – The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible. Practical implications – The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media. Originality/value – The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.


Langmuir ◽  
2001 ◽  
Vol 17 (22) ◽  
pp. 6771-6781 ◽  
Author(s):  
Bruce R. Locke ◽  
Michael Acton ◽  
Stephen J. Gibbs

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
C. Ahamed Saleel ◽  
Saad Ayed Alshahrani ◽  
Asif Afzal ◽  
Maughal Ahmed Ali Baig ◽  
Sarfaraz Kamangar ◽  
...  

PurposeJoule heating effect is a pervasive phenomenon in electro-osmotic flow because of the applied electric field and fluid electrical resistivity across the microchannels. Its effect in electro-osmotic flow field is an important mechanism to control the flow inside the microchannels and it includes numerous applications.Design/methodology/approachThis research article details the numerical investigation on alterations in the profile of stream wise velocity of simple Couette-electroosmotic flow and pressure driven electro-osmotic Couette flow by the dynamic viscosity variations happened due to the Joule heating effect throughout the dielectric fluid usually observed in various microfluidic devices.FindingsThe advantages of the Joule heating effect are not only to control the velocity in microchannels but also to act as an active method to enhance the mixing efficiency. The results of numerical investigations reveal that the thermal field due to Joule heating effect causes considerable variation of dynamic viscosity across the microchannel to initiate a shear flow when EDL (Electrical Double Layer) thickness is increased and is being varied across the channel.Originality/valueThis research work suggest how joule heating can be used as en effective mechanism for flow control in microfluidic devices.


Author(s):  
David Jon Furbish

The concept of conservation of mass holds a fundamental role in most problems in fluid physics. For a given problem this concept is cast in the form of an equation of continuity. Such an equation describes a condition—conservation of mass—that must be satisfied in any formal analysis of a problem. Thus an equation of continuity often is one of several complementary equations that are solved simultaneously to arrive at a solution to a flow problem, for example, the flow velocity as a function of coordinate position in a flow field. (Typically these complementary equations, as we will see in later chapters, involve conservation of momentum or energy, or both.) Although we did not explicitly use this idea in analyzing the one-dimensional flow problems at the end of Chapter 3, it turns out that continuity was implicitly satisfied in setting up each problem. We will return to these problems to illustrate this point. We will develop equations of continuity for three general cases: purely fluid flow, saturated single-phase flow in porous media, and unsaturated flow in porous media. The most general of the three equations is that for unsaturated flow, where pores are partially filled with the fluid phase of interest, such that the degree of saturation with respect to that phase is less than one. We will then show that this equation reduces, in the special case in which the degree of saturation equals one, to a simpler form appropriate for saturated single-phase flow. Then, this equation for saturated flow could be reduced further, in the special case in which the porosity equals one, to a form appropriate for purely fluid flow. For pedagogical reasons, however, we shall reverse this order and consider purely fluid flow first. In addition we will consider conservation of a solid or gas dissolved in a liquid, and take this opportunity to introduce Fick’s law for molecular diffusion. For simplicity we will consider only species that do not react chemically with the liquid, nor with the solid phases of a porous medium. Most of the derivations below are based on the idea of a small control volume of specified dimensions embedded within a fluid or porous medium.


2019 ◽  
Vol 30 (8) ◽  
pp. 4083-4101 ◽  
Author(s):  
Aneela Bibi ◽  
Hang Xu ◽  
Qiang Sun ◽  
Ioan Pop ◽  
Qingkai Zhao

Purpose This study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended. Design/methodology/approach The generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0. Findings Results show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy. Originality/value Free convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.


1970 ◽  
Vol 10 (01) ◽  
pp. 51-55 ◽  
Author(s):  
Robert A. Albrecht ◽  
Sullivan S. Marsden

Abstract Although foam usually will flow in porous media, under certain controllable conditions it can also be used to block the flow of gas, both in unconsolidated sand packs and in sandstones. After steady gas or foam flow has been established at a certain injection pressure pi, the pressure is decreased until flow pressure pi, the pressure is decreased until flow ceases at a certain blocking pressure pb. When flow is then reestablished at a second, higher pi, blocking can again occur at another pb that will usually be greater than the first pi. The relationship between pi and Pb depends on the type of porous medium and the foamer solution saturation in the porous medium. A process is suggested whereby porous medium. A process is suggested whereby this phenomenon might be used to impede or block leakage in natural gas storage projects. Introduction The practice of storing natural gas in underground porous rocks has developed rapidly, and it now is porous rocks has developed rapidly, and it now is the major way of meeting peak demands in urban areas of the U. S. Many of these storage projects have been plagued with gas leakage problems that have, in some cases, presented safety hazards and resulted in sizeable economic losses. Usually these leaks are due to such natural factors as faults and fractures, or to such engineering factors as poor cement jobs and wells that were improperly abandoned. For the latter, various remedies such as spot cementing have been tried but not always with great success. In recent years several research groups have been studying the flow properties of aqueous foams and their application to various petroleum engineering problems. Most of this work has been done under problems. Most of this work has been done under experimental conditions such that the foam would flow in either tubes or porous media. However, under some extreme or unusual experimental conditions, flow in porous media becomes very difficult or even impossible. This factor also has suggested m us as well as to others that foam can be used as a gas flow impeder or as a sealant for leaks in gas storage reservoirs. In such a process, the natural ability of porous media to process, the natural ability of porous media to generate foam would be utilized by injecting a slug of foamer solution and following this with gas to form the foam in situ. This paper presents preliminary results of a sandy on the blockage of gas flow by foam in porous media. It also describes how this approach might be applied to a field process for sealing leaks in natural gas storage reservoirs. Throughout this report, we use the term "foam" to describe any dispersed gas-liquid system in which the liquid is the continuous phase, and the gas is the discontinuous phase. APPARATUS AND PROCEDURE A schematic drawing of the apparatus is shown in Fig. 1. At least 50 PV of filtered, deaerated foamer solution were forced through the porous medium to achieve liquid saturation greater than 80 percent. Afterwards air at controlled pressures was passed into the porous medium in order to generate foam in situ. Table 1 shows the properties and dimensions of the several porous media that were used. The beach sands were washed, graded and packed into a vibrating lucite tube containing a constant liquid level to avoid Stoke's law segregation over most of the porous medium. JPT P. 51


Author(s):  
Mehdi Jamei ◽  
H Ghafouri

Purpose – The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme. Design/methodology/approach – The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings – Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media. Research limitations/implications – The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible. Practical implications – The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers. Originality/value – The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.


Author(s):  
A. V. Kuznetsov ◽  
A. A. Avramenko

In this paper, a model of bioconvection in a suspension of gyrotactic motile microorganisms in a fluid saturated porous medium is suggested. The microorganisms considered in this paper are heavier than water and gyrotactic behavior results in their swimming towards the regions of most rapid downflow. Because of that, the regions of downflow become denser than the regions of upflow. Buoyancy increases the upward velocity in the regions of upflow and downward velocity in the regions of downflow, thus enhancing the velocity fluctuations. The experiments performed by Kessler (1986) and the numerical results of Kuznetsov and Jiang (2001) indicate that if the permeability of porous medium is sufficiently small it will prevent the development of convection instability. However, for practical purposes, in order to maximize the flux of the cells in the upward direction it is desirable to have the permeability of the porous medium as high as possible. The aim of this paper is to investigate the value of critical permeability. If permeability is smaller than this critical value bioconvection does not occur and microorganisms simply swim in the upward direction.


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