Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 60

Search results for: darcy forcheimer

60 Thermal Analysis for Darcy Forchheimer Effect with Hybrid Ferro Fluid Flow

Authors: Behzad Ali Khan, M. Zubair Akbar Qureshi


The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.

Keywords: darcy forcheimer, hybrid ferro fluid, porous medium, porous channel

Procedia PDF Downloads 53
59 Entropy Production in Mixed Convection in a Horizontal Porous Channel Using Darcy-Brinkman Formulation

Authors: Amel Tayari, Atef Eljerry, Mourad Magherbi


The paper reports a numerical investigation of the entropy generation analysis due to mixed convection in laminar flow through a channel filled with porous media. The second law of thermodynamics is applied to investigate the entropy generation rate. The Darcy-Brinkman Model is employed. The entropy generation due to heat transfer and friction dissipations has been determined in mixed convection by solving numerically the continuity, momentum and energy equations, using a control volume finite element method. The effects of Darcy number, modified Brinkman number and the Rayleigh number on averaged entropy generation and averaged Nusselt number are investigated. The Rayleigh number varied between 103 ≤ Ra ≤ 105 and the modified Brinkman number ranges between 10-5 ≤ Br≤ 10-1 with fixed values of porosity and Reynolds number at 0.5 and 10 respectively. The Darcy number varied between 10-6 ≤ Da ≤10.

Keywords: entropy generation, porous media, heat transfer, mixed convection, numerical methods, darcy, brinkman

Procedia PDF Downloads 313
58 On the Well-Posedness of Darcy–Forchheimer Power Model Equation

Authors: Johnson Audu, Faisal Fairag


In a bounded subset of R^d, d=2 or 3, we consider the Darcy-Forchheimer power model with the exponent 1 < m ≤ 2 for a single-phase strong-inertia fluid flow in a porous medium. Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence and uniqueness of solution (u, p) in L^(m+1 ) (Ω)^d X (W^(1,(m+1)/m) (Ω)^d ⋂L_0^2 (Ω)^d) and its stability.

Keywords: porous media, power law, strong inertia, nonlinear, monotone type

Procedia PDF Downloads 231
57 A Fractional Derivative Model to Quantify Non-Darcy Flow in Porous and Fractured Media

Authors: Golden J. Zhang, Dongbao Zhou


Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments.

Keywords: fractional derivative, darcy’s law, non-darcian flow, fluid dynamics

Procedia PDF Downloads 5
56 Soret and Dufour Effect on Variable Viscosity and Thermal Conductivity of an Inclined Magnetic Field with Dissipation in Non-Darcy Porous Medium

Authors: Rasaq A. Kareem, Sulyman O. Salawu


The study of Soret and Dufour effect on variable viscosity and thermal conductivity of an inclined magnetic field with dissipation in non-Darcy porous medium over a continuously stretching sheet for power-law variation in the sheet temperature and concentration are investigated. The viscosity of the fluid flow and thermal conductivity are considered to vary as a function of temperature. The local similarity solutions for different values of the physical parameters are presented for velocity, temperature and concentration. The result shows that variational increase in the values of Soret and Dufour parameters increase the temperature and concentration distribution. Finally, the effects of skin friction, Nusselt and Sherwood numbers which are of physical and engineering interest are considered and discussed.

Keywords: Dufour, non-Darcy Flow, Soret, thermal conductivity, variable viscosity

Procedia PDF Downloads 253
55 Effect of Different Porous Media Models on Drug Delivery to Solid Tumors: Mathematical Approach

Authors: Mostafa Sefidgar, Sohrab Zendehboudi, Hossein Bazmara, Madjid Soltani


Based on findings from clinical applications, most drug treatments fail to eliminate malignant tumors completely even though drug delivery through systemic administration may inhibit their growth. Therefore, better understanding of tumor formation is crucial in developing more effective therapeutics. For this purpose, nowadays, solid tumor modeling and simulation results are used to predict how therapeutic drugs are transported to tumor cells by blood flow through capillaries and tissues. A solid tumor is investigated as a porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multi scale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. In this work, the mathematical model in our previous studies is developed by considering two model of momentum equation for porous media: Darcy and Brinkman. The mathematical method involves processes such as fluid flow through solid tumor as porous media, extravasation of blood flow from vessels, blood flow through vessels and solute diffusion, convective transport in extracellular matrix. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model does.

Keywords: solid tumor, porous media, Darcy model, Brinkman model, drug delivery

Procedia PDF Downloads 235
54 Effect of Viscous Dissipation and Axial Conduction in Thermally Developing Region of the Channel Partially Filled with a Porous Material Subjected to Constant Wall Heat Flux

Authors: D Bhargavi, J. Sharath Kumar Reddy


The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γp on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: porous material, channel partially filled with a porous material, axial conduction, viscous dissipation

Procedia PDF Downloads 66
53 Asymptotic Analysis of the Viscous Flow through a Pipe and the Derivation of the Darcy-Weisbach Law

Authors: Eduard Marusic-Paloka


The Darcy-Weisbach formula is used to compute the pressure drop of the fluid in the pipe, due to the friction against the wall. Because of its simplicity, the Darcy-Weisbach formula became widely accepted by engineers and is used for laminar as well as the turbulent flows through pipes, once the method to compute the mysterious friction coefficient was derived. Particularly in the second half of the 20th century. Formula is empiric, and our goal is to derive it from the basic conservation law, via rigorous asymptotic analysis. We consider the case of the laminar flow but with significant Reynolds number. In case of the perfectly smooth pipe, the situation is trivial, as the Navier-Stokes system can be solved explicitly via the Poiseuille formula leading to the friction coefficient in the form 64/Re. For the rough pipe, the situation is more complicated and some effects of the roughness appear in the friction coefficient. We start from the Navier-Stokes system in the pipe with periodically corrugated wall and derive an asymptotic expansion for the pressure and for the velocity. We use the homogenization techniques and the boundary layer analysis. The approximation derived by formal analysis is then justified by rigorous error estimate in the norm of the appropriate Sobolev space, using the energy formulation and classical a priori estimates for the Navier-Stokes system. Our method leads to the formula for the friction coefficient. The formula involves resolution of the appropriate boundary layer problems, namely the boundary value problems for the Stokes system in an infinite band, that needs to be done numerically. However, theoretical analysis characterising their nature can be done without solving them.

Keywords: Darcy-Weisbach law, pipe flow, rough boundary, Navier law

Procedia PDF Downloads 255
52 MHD Mixed Convection in a Vertical Porous Channel

Authors: Brahim Fersadou, Henda Kahalerras


This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers respectively, as well as the Joule heating represented by Eckert number on the velocity and temperature fields, are examined. The main results show an augmentation of heat transfer rate with the decrease of Darcy number and the increase of Ri and Ha when Joule heating is neglected.

Keywords: heat sources, magnetic field, mixed convection, porous channel

Procedia PDF Downloads 295
51 Quadratic Convective Flow of a Micropolar Fluid in a Non-Darcy Porous Medium with Convective Boundary Condition

Authors: Ch. Ramreddy, P. Naveen, D. Srinivasacharya


The objective of the present study is to investigate the effect of nonlinear temperature and concentration on the mixed convective flow of micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of convective boundary condition. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by spectral method. By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the coupling number and inclination of angle tend to decrease the skin friction, mass transfer rate and the reverse change is there in wall couple stress and heat transfer rate. The nominal effect on the wall couple stress and skin friction is encountered whereas the significant effect on the local heat and mass transfer rates are found for high enough values of Biot number.

Keywords: convective boundary condition, micropolar fluid, non-darcy porous medium, non-linear convection, spectral method

Procedia PDF Downloads 175
50 Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration

Authors: Maria Neagu


This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parameters. These results are verified using the finite differences method applied to the conservation equations.

Keywords: finite difference method, natural convection, porous medium, scale analysis, thermal stratification

Procedia PDF Downloads 258
49 Temperature Fields in a Channel Partially-Filled by Porous Material with Internal Heat Generations: On Exact Solution

Authors: Yasser Mahmoudi, Nader Karimi


The present work examines analytically the effect internal heat generation on temperature fields in a channel partially-filled with a porous under local thermal non-equilibrium condition. The Darcy-Brinkman model is used to represent the fluid transport through the porous material. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions for the solid and fluid temperature fields are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio Darcy number, as the non-dimensional energy terms in fluid and solid as parameters. Results show that considering any of the two models and under zero or negative heat generation (heat sink) and for any Darcy number, an increase in the porous thickness increases the amount of heat flux transferred to the porous region. The obtained results are applicable to the analysis of complex porous media incorporating internal heat generation, such as heat transfer enhancement (THE), tumor ablation in biological tissues and porous radiant burners (PRBs).

Keywords: porous media, local thermal non-equilibrium, forced convection, heat transfer, exact solution, internal heat generation

Procedia PDF Downloads 382
48 Performances Analysis of the Pressure and Production of an Oil Zone by Simulation of the Flow of a Fluid through the Porous Media

Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled


This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

Procedia PDF Downloads 80
47 Prediction of Permeability of Frozen Unsaturated Soil Using Van Genuchten Model and Fredlund-Xing Model in Soil Vision

Authors: Bhavita S. Dave, Jaimin Vaidya, Chandresh H. Solanki, Atul K.


To measure the permeability of a soil specimen, one of the basic assumptions of Darcy's law is that the soil sample should be saturated. Unlike saturated soils, the permeability of unsaturated soils cannot be found using conventional methods as it does not follow Darcy's law. Many empirical models, such as the Van Genuchten Model and Fredlund-Xing Model were suggested to predict permeability value for unsaturated soil. Such models use data from the soil-freezing characteristic curve to find fitting parameters for frozen unsaturated soils. In this study, soil specimens were subjected to 0, 1, 3, and 5 freezing-thawing (F-T) cycles for different degrees of saturation to have a wide range of suction, and its soil freezing characteristic curves were formulated for all F-T cycles. Changes in fitting parameters and relative permeability with subsequent F-T cycles are presented in this paper for both models.

Keywords: frozen unsaturated soil, Fredlund Xing model, soil-freezing characteristic curve, Van Genuchten model

Procedia PDF Downloads 55
46 Thermal Instability in Rivlin-Ericksen Elastico-Viscous Nanofluid with Connective Boundary Condition: Effect of Vertical Throughflow

Authors: Shivani Saini


The effect of vertical throughflow on the onset of convection in Rivlin-Ericksen Elastico-Viscous nanofluid with convective boundary condition is investigated. The flow is stimulated with modified Darcy model under the assumption that the nanoparticle volume fraction is not actively managed on the boundaries. The heat conservation equation is formulated by introducing the convective term of nanoparticle flux. A linear stability analysis based upon normal mode is performed, and an approximate solution of eigenvalue problems is obtained using the Galerkin weighted residual method. Investigation of the dependence of the Rayleigh number on various viscous and nanofluid parameter is performed. It is found that through flow and nanofluid parameters hasten the convection while capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern the stationary convection. Using the convective component of nanoparticle flux, critical wave number is the function of nanofluid parameters as well as the throughflow parameter. The obtained solution provides important physical insight into the behavior of this model.

Keywords: Darcy model, nanofluid, porous layer, throughflow

Procedia PDF Downloads 60
45 Sand Production Modelled with Darcy Fluid Flow Using Discrete Element Method

Authors: M. N. Nwodo, Y. P. Cheng, N. H. Minh


In the process of recovering oil in weak sandstone formations, the strength of sandstones around the wellbore is weakened due to the increase of effective stress/load from the completion activities around the cavity. The weakened and de-bonded sandstone may be eroded away by the produced fluid, which is termed sand production. It is one of the major trending subjects in the petroleum industry because of its significant negative impacts, as well as some observed positive impacts. For efficient sand management therefore, there has been need for a reliable study tool to understand the mechanism of sanding. One method of studying sand production is the use of the widely recognized Discrete Element Method (DEM), Particle Flow Code (PFC3D) which represents sands as granular individual elements bonded together at contact points. However, there is limited knowledge of the particle-scale behavior of the weak sandstone, and the parameters that affect sanding. This paper aims to investigate the reliability of using PFC3D and a simple Darcy flow in understanding the sand production behavior of a weak sandstone. An isotropic tri-axial test on a weak oil sandstone sample was first simulated at a confining stress of 1MPa to calibrate and validate the parallel bond models of PFC3D using a 10m height and 10m diameter solid cylindrical model. The effect of the confining stress on the number of bonds failure was studied using this cylindrical model. With the calibrated data and sample material properties obtained from the tri-axial test, simulations without and with fluid flow were carried out to check on the effect of Darcy flow on bonds failure using the same model geometry. The fluid flow network comprised of every four particles connected with tetrahedral flow pipes with a central pore or flow domain. Parametric studies included the effects of confining stress, and fluid pressure; as well as validating flow rate – permeability relationship to verify Darcy’s fluid flow law. The effect of model size scaling on sanding was also investigated using 4m height, 2m diameter model. The parallel bond model successfully calibrated the sample’s strength of 4.4MPa, showing a sharp peak strength before strain-softening, similar to the behavior of real cemented sandstones. There seems to be an exponential increasing relationship for the bigger model, but a curvilinear shape for the smaller model. The presence of the Darcy flow induced tensile forces and increased the number of broken bonds. For the parametric studies, flow rate has a linear relationship with permeability at constant pressure head. The higher the fluid flow pressure, the higher the number of broken bonds/sanding. The DEM PFC3D is a promising tool to studying the micromechanical behavior of cemented sandstones.

Keywords: discrete element method, fluid flow, parametric study, sand production/bonds failure

Procedia PDF Downloads 244
44 Unsteady Natural Convection in a Square Cavity Partially Filled with Porous Media Using a Thermal Non-Equilibrium Model

Authors: Ammar Alsabery, Habibis Saleh, Norazam Arbin, Ishak Hashim


Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal non-equilibrium model is studied in this paper. The left vertical wall is maintained at a constant hot temperature and the right vertical wall is maintained at a constant cold temperature, while the horizontal walls are adiabatic. The governing equations are obtained by applying the Darcy model and Boussinesq approximation. COMSOL's finite element method is used to solve the non-dimensional governing equations together with specified boundary conditions. The governing parameters of this study are the Rayleigh number, the modified thermal conductivity ratio, the inter-phase heat transfer coefficien and the time independent. The results presented for values of the governing parameters in terms of streamlines in both fluid/porous layer, isotherms of fluid and solid porous layer, isotherms of fluid layer, and average Nusselt number.

Keywords: unsteady natural convection, thermal non-equilibrium model, Darcy model

Procedia PDF Downloads 309
43 Thermal Performance of Fully Immersed Naturally Cooled Server

Authors: Yaser Al-Anii, Abdulmajeed Almaneea, Jonathan L. Summers, Harvey M. Thompson, Nikil Kapur


The natural convection cooling system of a fully immersed server in a dielectric liquid is studied numerically. In the present case study, the dielectric liquid represents working fluid and it is in contact with server inside capsule. The capsule includes electronic component and fluid which can be modeled as saturated porous media. This medium follow Darcy flow regime and assumed to be in balance between its components. The study focus is on role of spatial parameters on thermal behavior of convective heat transfer. Based on server known unit, which is 1U, two parameters Ly and S are changed to test their effect. Meanwhile, wide-range of modified Rayleigh number, which is 0.5 to 300, are covered to better understand thermal performance. Navier-Stokes equations are used to model physical domain. Furthermore, successive over-relaxation and time marching techniques are used to solve momentum and energy equation. From obtained correlation, the in-between distance S is more effective on Nusselt number than distance to edge Ly by approximately 14%. In addition, as S increases, the average Nusselt number of the upper unit increases sharply, whereas the lower one keeps on the same level.

Keywords: convective cooling of server, Darcy flow, liquid-immersed server, porous media

Procedia PDF Downloads 326
42 Effects of Variable Properties and Double Dispersion on Magnetohydrodynamic (MHD) Mixed Convection in a Power-Law Fluid Saturated Non-Darcy Porous Medium

Authors: Pranitha Janapatla, Venkata Suman Gontla


The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

Procedia PDF Downloads 163
41 Thermal Performance of Fully Immersed Server into Saturated Fluid Porous Medium

Authors: Yaser Al-Anii, Abdulmajeed Almaneea, Jonathan L. Summers, Harvey M. Thompson, Nikil Kapur


The natural convection cooling system of a fully immersed server in dielectric liquid is studied numerically. In present case study, the dielectric liquid represents working fluid and it is in contact with server inside capsule. The capsule includes electronic component and fluid, which can be modelled as saturated porous media. This medium follow Darcy flow regime and assumed to be in balance between its components. The study focus is on role of spatial parameters on thermal behavior of convective heat transfer. Based on server known unit, which is 1U, two parameters Ly and S are changed to test their effect. Meanwhile, wide range of modified Rayleigh number, which is 0.5 to 300, are covered to better understand thermal performance. Navier-Stokes equations are used to model physical domain. Furthermore, successive over relaxation and time marching techniques are used to solve momentum and energy equation. From obtained correlation, the in-between distance S is more effective on Nusselt number than distance to edge Ly by approximately 14%. In addition, as S increase, the average Nusselt number of the upper unit is increased sharply, whereas the lower one keeps on same level.

Keywords: convective cooling of server, darcy flow, liquid-immersed server, porous media

Procedia PDF Downloads 330
40 Estimation of Relative Permeabilities and Capillary Pressures in Shale Using Simulation Method

Authors: F. C. Amadi, G. C. Enyi, G. Nasr


Relative permeabilities are practical factors that are used to correct the single phase Darcy’s law for application to multiphase flow. For effective characterisation of large-scale multiphase flow in hydrocarbon recovery, relative permeability and capillary pressures are used. These parameters are acquired via special core flooding experiments. Special core analysis (SCAL) module of reservoir simulation is applied by engineers for the evaluation of these parameters. But, core flooding experiments in shale core sample are expensive and time consuming before various flow assumptions are achieved for instance Darcy’s law. This makes it imperative for the application of coreflooding simulations in which various analysis of relative permeabilities and capillary pressures of multiphase flow can be carried out efficiently and effectively at a relative pace. This paper presents a Sendra software simulation of core flooding to achieve to relative permeabilities and capillary pressures using different correlations. The approach used in this study was three steps. The first step, the basic petrophysical parameters of Marcellus shale sample such as porosity was determined using laboratory techniques. Secondly, core flooding was simulated for particular scenario of injection using different correlations. And thirdly the best fit correlations for the estimation of relative permeability and capillary pressure was obtained. This research approach saves cost and time and very reliable in the computation of relative permeability and capillary pressures at steady or unsteady state, drainage or imbibition processes in oil and gas industry when compared to other methods.

Keywords: relative permeabilty, porosity, 1-D black oil simulator, capillary pressures

Procedia PDF Downloads 362
39 Heat and Mass Transfer of an Oscillating Flow in a Porous Channel with Chemical Reaction

Authors: Zahra Neffah, Henda Kahalerras


A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.

Keywords: chemical reaction, heat and mass transfer, oscillating flow, porous channel

Procedia PDF Downloads 338
38 Convective Brinkman-Forchiemer Extended Flow through Channel Filled with Porous Material: An Approximate Analytical Approach

Authors: Basant K. Jha, M. L. Kaurangini


An approximate analytical solution is presented for convective flow in a horizontal channel filled with porous material. The Brinkman-Forchheimer extension of Darcy equation is utilized to model the fluid flow while the energy equation is utilized to model temperature distribution in the channel. The solutions were obtained utilizing the newly suggested technique and compared with those obtained from an implicit finite-difference solution.

Keywords: approximate analytical, convective flow, porous material, Brinkman-Forchiemer

Procedia PDF Downloads 262
37 Dynamic Characterization of Shallow Aquifer Groundwater: A Lab-Scale Approach

Authors: Anthony Credoz, Nathalie Nief, Remy Hedacq, Salvador Jordana, Laurent Cazes


Groundwater monitoring is classically performed in a network of piezometers in industrial sites. Groundwater flow parameters, such as direction, sense and velocity, are deduced from indirect measurements between two or more piezometers. Groundwater sampling is generally done on the whole column of water inside each borehole to provide concentration values for each piezometer location. These flow and concentration values give a global ‘static’ image of potential plume of contaminants evolution in the shallow aquifer with huge uncertainties in time and space scales and mass discharge dynamic. TOTAL R&D Subsurface Environmental team is challenging this classical approach with an innovative dynamic way of characterization of shallow aquifer groundwater. The current study aims at optimizing the tools and methodologies for (i) a direct and multilevel measurement of groundwater velocities in each piezometer and, (ii) a calculation of potential flux of dissolved contaminant in the shallow aquifer. Lab-scale experiments have been designed to test commercial and R&D tools in a controlled sandbox. Multiphysics modeling were performed and took into account Darcy equation in porous media and Navier-Stockes equation in the borehole. The first step of the current study focused on groundwater flow at porous media/piezometer interface. Huge uncertainties from direct flow rate measurements in the borehole versus Darcy flow rate in the porous media were characterized during experiments and modeling. The structure and location of the tools in the borehole also impacted the results and uncertainties of velocity measurement. In parallel, direct-push tool was tested and presented more accurate results. The second step of the study focused on mass flux of dissolved contaminant in groundwater. Several active and passive commercial and R&D tools have been tested in sandbox and reactive transport modeling has been performed to validate the experiments at the lab-scale. Some tools will be selected and deployed in field assays to better assess the mass discharge of dissolved contaminants in an industrial site. The long-term subsurface environmental strategy is targeting an in-situ, real-time, remote and cost-effective monitoring of groundwater.

Keywords: dynamic characterization, groundwater flow, lab-scale, mass flux

Procedia PDF Downloads 98
36 Analysis of a Double Pipe Heat Exchanger Performance by Use of Porous Baffles and Nanofluids

Authors: N. Targui, H. Kahalerras


The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy-Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: double pipe heat exchanger, nanofluids, nanoparticles, porous baffles

Procedia PDF Downloads 168
35 Forced Heat Transfer Convection in a Porous Channel with an Oriented Confined Jet

Authors: Azzedine Abdedou, Khedidja Bouhadef


The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: forced convection, porous media, oriented confined jet, fluid mechanics

Procedia PDF Downloads 304
34 Effect of Coriolis Force on Magnetoconvection in an Anisotropic Porous Medium

Authors: N. F. M. Mokhtar, N. Z. A. Hamid


This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

Procedia PDF Downloads 136
33 Investigation of the Cooling and Uniformity Effectiveness in a Sinter Packed Bed

Authors: Uzu-Kuei Hsu, Chang-Hsien Tai, Kai-Wun Jin


When sinters are filled into the cooler from the sintering machine, and the non-uniform distribution of the sinters leads to uneven cooling. This causes the temperature difference of the sinters leaving the cooler to be so large that it results in the conveyors being deformed by the heat. The present work applies CFD method to investigate the thermo flowfield phenomena in a sinter cooler by the Porous Media Model. Using the obtained experimental data to simulate porosity (Ε), permeability (κ), inertial coefficient (F), specific heat (Cp) and effective thermal conductivity (keff) of the sinter packed beds. The physical model is a similar geometry whose Darcy numbers (Da) are similar to the sinter cooler. Using the Cooling Index (CI) and Uniformity Index (UI) to analyze the thermo flowfield in the sinter packed bed obtains the cooling performance of the sinter cooler.

Keywords: porous media, sinter, cooling index (CI), uniformity index (UI), CFD

Procedia PDF Downloads 328
32 Double Diffusive Natural Convection in Horizontal Elliptical Annulus Containing a Fluid-Saturated Porous Medium: Effects of Lewis Number

Authors: Hichem Boulechfar, Mahfoud Djezzar


Two-dimensional double diffusive natural convection in an annular elliptical space filled with fluid-saturated porous medium, is analyzed by solving numerically the mass balance, momentum, energy and concentration equations, using Darcy's law and Boussinesq approximation. Both walls delimiting the annular space are maintained at two uniform different temperatures and concentrations. The external parameter considered is the Lewis number. For the present work, the heat and mass transfer for natural convection is studied for the case of aiding buoyancies, where the flow is generated in a cooperative mode by both temperature and solutal gradients. The local Nusselt and Sherwood numbers are presented in term of the external parameter.

Keywords: double diffusive, natural convection, porous media, elliptical annulus

Procedia PDF Downloads 136
31 Effects of G-jitter Combined with Heat and Mass Transfer by Mixed Convection MHD Flow of Maxwell Fluid in a Porous Space

Authors: Faisal Salah, Z. A. Aziz, K. K. Viswanathan


In this article, the effects of g-jitter induced and combined with heat and mass transfer by mixed convection of MHD Maxwell fluid in microgravity situation is investigated for a simple system. This system consists of two heated vertical parallel infinite flat plates held at constant but different temperatures and concentrations. By using modified Darcy’s law, the equations governing the flow are modelled. These equations are solved analytically for the induced velocity, temperature and concentration distributions. Many interesting available results in the relevant literature (i.e. Newtonian fluid) is obtained as the special case of the present general analysis. Finally, the graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for different values of the material constants.

Keywords: g-jitter, heat and mass transfer, mixed convection, Maxwell fluid, porous medium

Procedia PDF Downloads 398