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The problem of hydrodynamic dispersion in non-Darcy free convection heat and mass transfer from vertical surface embedded in a porous medium has been presented. The Forchheimer extension is considered in the flow equations. The flow, temperature and concentration fields in Darcy and non-Darcy porous media are observed to be governed by complex interactions among the diffusion rate Le, buoyancy ratio N, and the parameters @c, @z, F"0, Ra"d. Numerical results for the details of the velocity, temperature and concentration profiles which are shown on graphs have been presented. The combined effect of thermal dispersion and solutal diffusivity, for the two cases Darcy and non-Darcy porous medium, on the heat transfer rate which are entered in tables is discussed.

This paper studied the problem of free convection with mass transfer flow for a micropolar fluid bounded by a vertical infinite surface with an exponentially decaying heat generation, under the action of a transverse magnetic field. Numerical calculations are carried out for the various parameters entering into the problem. The numerical values of the skin friction, the wall couple stress, the rate of heat transfer, the concentration gradient at the wall and the boundary layer thickness are shown graphically as functions of the magnetic field parameter.

//; thi.K article, the linearized theory is used to study the effect of small amplitude time-dependent sutface temperature oscillations on free convection to a vertical plate embedded in a mm-Darcy porous medium. Forchheimer extension is considered in the flow equations. The time-dependent perturbations are used to transform the i^ovemin^ equations to nvo groups — similar ami nonsimilar. respectively. For the nonsimilar equations, the second-level local nonsimikirity method is used to convert It to a ,vc? of ordinary differential equations. The numerical .solutions are obtained in the comple.x domaiit for a rani-e of the non-Darcy parameter D and the frequency variable t,.

The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent λ as well as Eckert number.

The effects of both first- and second-order resistance, due to the solid matrix of non-Darcy porous medium, Joule heating and viscous dissipation on forced convection flow from a horizontal circular cylinder under the action of a transverse magnetic field, has been studied. The case of variable wall temperature conditions is considered. The second-level local non-similarity method is used to convert the non-similar equations into a system of ordinary differential equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.

An analysis is presented to investigate the influences of viscous dissipation on buoyancy-induced flow over (a horizontal or a vertical flat plate) embedded in a non-Newtonian fluid saturated porous medium under the action of a transverse magnetic field. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface heat flux, for each position of the plate. Numerical results for the details of the velocity and temperature profiles are shown on graphs, for the two cases horizontal and vertical plate, for different values of the magnetic field parameter, power-law index n and the exponent λ as well as the Eckert number. Values of the excess surface temperature which are entered in tables or plotted in figures have been presented for different values of the different parameters, for the two cases, horizontal and vertical plate.

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid bounded by a vertical infinite surface under the action of a transverse magnetic field. Approximate solutions of the coupled nonlinear governing equations are obtained for different values of the microrotation- and the magnetic-parameters. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, angular velocity, temperature and concentration profiles are shown graphically. The numerical values of the skin friction, the wall couple stress, the rate of heat transfer and the concentration gradient at the wall are entered in tables.

A boundary layer analysis has been presented to study the influence of thermal radiation and lateral mass flux on non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained and the combined effect of thermal radiation and fluid suction/injection on the heat transfer rate is discussed. Numerical results for the details of the velocity and temperature profiles as well as Nusselt number have been presented.

The present study is devoted to investigate the influences of thermal radiation on buoyancy induced flow over horizontal flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained with prescribed variable surface temperature. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions which are entered in tables have been presented for different values of the power-law index n and the exponent λ as well as radiation parameter and the temperature difference.

The effects of thermal dispersion and thermal radiation on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium are studied. Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained. Numerical results for the details of the velocity and temperature profiles which are shown on graphs have been presented. The combined effect of thermal dispersion and thermal radiation, for the two cases Darcy and non-Darcy porous medium, on the heat transfer rate which are entered in tables is discussed.

In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi–Douglas–Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described.

In the present paper, a mathematical model and numerical simulation to describe the nanoparticles-water suspension imbibes into a water-oil two-phase flow in a porous medium is introduced. We extend the model to include the negative capillary pressure and mixed relative permeabilities correlations to fit with the mixed-wet system. Also, buoyancy and capillary forces as well as Brownian diffusion are considered. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles and check for possible enhancement of the oil recovery process using numerical experiments.

Geological storage of anthropogenic CO2 emissions in deep saline aquifers has recently received tremendous attention in the scientific literature. Injected CO2 plume buoyantly accumulates at the top part of the deep aquifer under a sealing cap rock, and some concern that the high-pressure CO2 could breach the seal rock. However, CO2 will diffuse into the brine underneath and generate a slightly denser fluid that may induce instability and convective mixing. Onset times of instability and convective mixing performance depend on the physical properties of the rock and fluids, such as permeability and density contrast. The novel idea is to adding nanoparticles to the injected CO2 to increase density contrast between the CO2-rich brine and the underlying resident brine and, consequently, decrease onset time of instability and increase convective mixing. As far as it goes, only few works address the issues related to mathematical and numerical modeling aspects of the nanoparticles transport phenomena in CO2 storages. In the current work, we will present mathematical models to describe the nanoparticles transport carried by injected CO2 in porous media. Buoyancy and capillary forces as well as Brownian diffusion are important to be considered in the model. IMplicit Pressure Explicit Saturation-Concentration (IMPESC) scheme is used and a numerical simulator is developed to simulate the nanoparticles transport in CO2 storages.

In this work, the problem of flow and heat transfer of nanofluids in spirally fluted tubes is investigated numerically using the CFD code Fluent. The tube investigated in this work is characterized by the existence of helical ridging which is usually obtained by embossing a smooth tube. A tube of diameter of 15 mm, 1.5 mm groove depth and a single helix with pitch of 64 mm is chosen for simulation. This geometry has been chosen for simulation because it has been investigated experimentally for pure fluids and would, therefore, provide a verification framework with our CFD model. The result of our CFD investigation compares very well with the experimental work conducted on this tube geometry. Interesting patterns are highlighted and investigated including the existence of flow swirl as a result of the existence of the spirally enhanced ridges. This swirl flow enhances heat transfer characteristics of this system as reported in the literatures. This study also shows that further enhancement is achieved if small amount of nanoparticles are introduced to the fluid. These nanoparticles (metallic-based nanoparticles) when introduced to the fluid enhances its heat transfer characteristics.

In this work, the problem of structural deformation with two-phase flow of carbon sequestration is presented. A model to simulate miscible CO2 injection with structural deformation in the aqueous phase is established. In the first part of this paper, we developed analytical solution for the problem under consideration with certain types of boundary conditions, namely, Dirichlet and Neumann boundary conditions. The second part concerns to numerical simulation using IMPDES scheme. A simulator based on cell-centered finite difference method is used to solve this equations system. Distributions of CO2 saturation, and horizontal and vertical displacements have been introduced.

The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cell- centered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.

1 Computational Transport Phenomena Laboratory (CTPL), Division of Physical Sciences and Engineering (PSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia 2 Mathematics Department, Faculty of Science, Aswan University, Aswan 81528, Egypt 3 Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4 4 Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

The low-density gas jet injected into a high-density ambient has particular interest in several industrial applications such as fuel leaks, engine exhaust, diffusion flames, materials processing, as well as natural phenomena such fires and volcanic eruptions. The most interesting application of this problem nowaday is the hydrogen leaks in air; since when it mixes with air, fire or explosion can result. The expected extensive usage of hydrogen increases the probability of its accidental release from hydrogen vessel infrastructure. Hydrogen energy has much promise as a new clean energy and is expected to replace fossil fuels; however, hydrogen leakage is considered to be an important safety issue and is a serious problem that hydrogen researchers must address. Hydrogen leaks may occur from loose fittings, o-ring seals, pinholes, or vents on hydrogen-containing vehicles, buildings, storage facilities, or other hydrogen-based systems. Hydrogen leakage may be divided into two classes, the first is a rapid leak causing combustion, while the other is an unignited slow-leak. However, hydrogen is ignited in air by some source of ignition such as static electricity (autoignition) or any external source. Classic turbulent jet flame models can be used to model the first class of hydrogen leakage; cf. (Schefer et al., 2006; Houf & Schefer, 2007; Swain et al., 2007; Takeno et al., 2007). This work is focused on the second class of unignited slow-leaks. Previous work introduced a boundary layer theory approach to model the concentration layer adjacent to a ceiling wall at the impinging and far regions in both planar and axisymmetric cases for small-scale hydrogen leakage El-Amin et al. (2008); El-Amin & Kanayama (2009a; 2008). This kind of buoyant jets ’plume’ is classed as non-Boussinesq; since the initial fractional density difference is high, which is defined as, Δρ0 = (ρ∞ − ρ0) , where ρ0 is the initial centerline density (density at the source) and ρ∞ is the ambient density. Generally, for binary selected low-densities gases at temperature 15◦C, the initial fractional density differences are 0.93 for H2 − Air, 0.86 for He− Air, 0.43 for CH4 − Air and 0.06 for C2H2 − N2. (Crapper & Baines, 1977) suggested that the upper bound of applicability of the Boussinesq approximation is that the initial fractional density difference Δρ0/ρ∞ is 0.05. In general, one can say that the Boussinesq approximation is valid for small initial fractional density difference, Δρ0/ρ∞ << 1. However, in these cases of invalid Boussinesq approximation a density equation must be used. Moreover, a discussion of this classification is given by (Spiegel & Veronis, 1960); and M.F. El-Amin and Shuyu Sun King Abdullah University of Science and Technology (KAUST), Thuwal Kingdom of Saudi Arabia 2

Transport phenomena in porous media describe the motion of fluids in media of porous structure which may be accompanied by heat/mass transfer and/or chemical reactions. While transport phenomena in fluid continua have been, to a large extent, very much comprehended, the subject matters in porous media are still under careful investigation and extensive research. Several reasons may be invoked to explain the difficulties associated with the study of transport phenomena in porous media. Probably the most obvious one is the fact that fluids move in porous media in complex, tortuous, and random passages that are even unknown a priori. Consequently, the governing laws may not be solved in any sense for the apparent difficulties in defining flow boundaries. Further complexities may be added should there exists heat transfer mechanisms associated with the flow and the interactions of heat transfer between themoving fluid and the solidmatrix. Moreover, chemical reactions describe essential feature of transport in porousmedia. It is hardly to find transport processes in porous media without chemical reaction of some sort or another. Chemical reactions in porous media can occur naturally as a result of the interactions between the moving fluid and the surface of the solid matrix. These kinds of chemical reactions, which are usually slow, are pertinent to groundwater geochemistry, or it can be made to occur by utilizing the porous media surfaces to catalyze chemical reactions between reacting fluids. The study of these complex processes in porous media necessitate complete information about the internal structure of the porous media, which is far beyond the reach of our nowadays capacities. A fundamental question, thus, arises, in what framework do we need to cast the study of transport in porous media? In other words, do we really need to get such complete, comprehensive information about a given porous medium in order to gain useful information that could help us in our engineering applications? Do we really need to know the field variables distribution at each single point in the porous medium in order to be able to predict the evolution of this system with time, for example? Is it possible to make precise measurements within the porous media for field variables? And, even if we might be able to gain such detailed information, are we going to use them in their primitive forms for further analysis and development? The answer to these kind of questionsmay be that, for the sake of engineering applications, we do not need such a complete, comprehensive details, neither will we be able to obtain them nor will they 2

We introduce 2D numerical investigations of the problem of gravity and inlet/outlet location effects of water-oil two-phase cocurrent imbibition in a porous medium. Three different cases of side-, top-, and bottom-inlet location are considered. Two-dimensional computations are carried out using the finite element method. Intensive comparisons are done between considering and neglecting gravity effect on water saturation, pressures of water and oil as well as water velocity. Results are introduced either in curves or as 2D visualization graphs. The results indicate that the buoyancy effects due to gravity force take place depending on inlet location. So, the buoyancy force in the momentum equations of the co-current imbibition model cannot be neglected as done by several previous studies. Also, we note that the 2D zero gravity model has a uniform flow and may be represented as 1D flow unlike the 2D nonzero gravity model showing a nonuniform flow.

The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter $\chi$ , the cone angle parameter $m$ , the radiation-conduction parameter ${R}_{d}$ , and the surface temperature parameter $H$ .

Scaling laws of laboratory imbibition experiments are very important to be used to predict oil recovery from matrix blocks. The importance of this concept being the oil recovery from reservoir matrix blocks in the field can be predicted experimentally from tests on small samples in laboratory. Laboratory results of oil recovery are commonly represented as a function of dimensionless time which in turn is a universal parameter including several physical parameters of fluids and rocks. It is considered as a good scaling group if the measured oil recovery is represented in a single universal curve with sharing less primary physical parameters. In the present work, we introduce a new dimensionless time formula in terms of characteristic velocity (e.g. injection velocity) which in turn is very important of some enhanced oil recovery (EOR) mechanisms such as water injection stage. We derive a power-law formula for dimensionless time that reduces the number of complexities in characterizing two-phase imbibition through a porous medium. The theory and characteristic velocity function is tested against some oil recovery experimental data for oil-water system from the literature. Through a comprehensive evaluation of available time scaling formulas, a simplified tool is provided for characterizing two-phase flow, through the use of a reference capillary number. In this context, we introduce a theoretical analysis and numerical computations of the counter-current imbibition. The one-dimensional macroscopic governing equation is transformed into a non-dimensional form which includes the dimensionless physical parameters (capillary number Ca and Darcy number Da). Additionally, numerical experiments are performed for wide ranges of values of capillary and Darcy numbers to illustrate their influences on water saturation as well as relative water/oil permeabilities. In the second part of this talk we introduce numerical and theoretical investigations of the problem of gravity and the inlet/outlet location effects of a two-phase countercurrent and cocurrent imbibition in a porous medium. We consider 2D computations of the problem with considering different locations of the open-boundary. The results indicate that gravity has a significant effect depending on open-boundary location. Then 1D computation for dimensional and non-dimensional cases and a theoretical analysis of the problem under consideration are carried out. A time-scale based on characteristic velocity is used to transform the macroscopic governing equations into a non-dimensional form. The resulting dimensionless governing equations involved some important dimensionless physical parameters such as Bond number Bo, capillary number Ca and Darcy number Da. Numerical experiment on Bond number effect is performed for two cases, gravity opposing and assisting. The theoretical analysis illustrates that common formulations of the time-scale enforce the coefficient Da1/2/Ca to be equal to one, while, formulation of dimensionless time based on a characteristic velocity allows to the capillary and Darcy numbers to appear in the dimensionless governing equation which leads to a wide range of scales and physical properties of fluids and rocks. The results indicate that the buoyancy effects due to gravity force take place depending on the location of the open-boundary.

In most of real-world applications, such as the case of heat stores, inlet is not kept at a constant temperature but it may vary with time during charging process. In this paper, a vertical water jet injected into a rectangular storage tank is measured experimentally and simulated numerically. Two cases of study are considered; one is a hot water jet with uniform inlet temperature (UIT) injected into a cold water tank, and the other is a cold water jet with non-uniform inlet temperature (NUIT) injected into a hot water tank. Three different temperature differences and three different flow rates are studied for the hot water jet with UIT which is injected into a cold water tank. Also, three different initial temperatures with constant flow rate as well as three different flow rates with constant initial temperature are considered for the cold jet with NUIT which is injected into a hot water tank. Turbulence intensity at the inlet as well as Reynolds number for the NUIT cases are therefore functions of inlet temperature and time. Both experimental measurements and numerical calculations are carried out for the same measured flow and thermal conditions. The realizable k-e model is used for modeling the turbulent flow. Numerical solutions are obtained for unsteady flow while pressure, velocity, temperature and turbulence distributions inside the water tank are analyzed. The simulated results are compared to the measured results, and they show a good agreement at low temperatures.

Through this paper, analyses of components of the unheated/heated turbulent confined jet are introduced and some models to describe them are developed. Turbulence realizable k–ɛ model is used to model the turbulence of this problem. Numerical simulations of 2D axisymmetric vertical hot water confined jet into a cylindrical tank have been done. Solutions are obtained for unsteady flow while velocity, pressure, temperature and turbulence distributions inside the water tank are analyzed. For seeking verification, an experiment was conducted for measuring of the temperature of the same system, and comparison between the measured and simulated temperature shows a good agreement. Using the simulated results, some models are developed to describe axial velocity, centerline velocity, radial velocity, dynamic pressure, mass flux, momentum flux and buoyancy flux for both unheated (non-buoyant) and heated (buoyant) jet. Finally, the dynamics of the heated jet in terms of the plume function which is a universal quantity and the source parameter are studied and therefore the maximum velocity can be predicted theoretically.

SUMMARY Hot water heat stores (HWHS) are generally used to overcome the diurnal or seasonal mismatch in the availability and demand of thermal energy. To enhance the system efficiency, good thermal stratification of the HWHS is required. In order to simulate different flow processes in stratified HWHS the effects of stratification on the turbulence are to be considered. Benchmark experiments have been conducted on turbulent flows into a continuously stratified HWHS. Based on these benchmark experiments, different two-equation turbulence transport models namely the RNG (ReNormalizable Group) and the realizable k–e turbulence models have been calibrated. The major improvement is provided to the e-equation by introducing the effects of the buoyancy field on the turbulence dissipation rate. It is achieved by calibrating the coefficient of the dissipation term (Ce2 in the RNG and C2 in the realizable k–e model) based on the benchmark experiments. A re-definition of the turbulent Prandtl number (Prt) incorporating the effects of stratification on turbulent thermal diffusivity improved the calibration further. The calibrated computational fluid dynamic models are found to predict the charging, discharging and storing processes of typical HWHS with good accuracy. Copyright r 2008 John Wiley & Sons, Ltd.

In this special issue, a number of papers have been accepted for publication. The special issue concerns with theoretical investigation and mathematical analysis that are very important for all scientific, engineering, and environmental applications. Frommathematical modeling to computational analysis and all the way to developing analytical and numerical solutions, studying solutions properties, and so forth, the theoretical, mathematical, and computational analyses are indispensable bases. Rapid progress has been seen in the analysis of flow and transport phenomena especially in the recent years because of the significance of flow and transport to science and engineering.

In this paper, a finite difference scheme is developed to solve the unsteady problem of combined heat and mass transfer from an isothermal curved surface to a porous medium saturated by a non-Newtonian fluid. The curved surface is kept at constant temperature and the power-law model is used to model the non-Newtonian fluid. The explicit finite difference method is used to solve simultaneously the equations of momentum, energy and concentration. The consistency of the explicit scheme is examined and the stability conditions are determined for each equation. Boundary layer and Boussinesq approximations have been incorporated. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles are shown graphically. It is found that as time approaches infinity, the values of wall shear, heat transfer coefficient and concentration gradient at the wall, which are entered in tables, approach the steady state values.

In this work, we present a numerical treatment for the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which can reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes. Selected simulation results such as pc–Sw–awn surface, capillary pressure, saturation and specific interfacial area with various values of model parameters have been introduced. The simulation results show a good agreement with those in the literature using either pore network modeling or Darcy scale modeling.

Nanoparticles are particles that are between 1 and 100 nanometers in size. They present possible dangers to the environment due to the high surface to volume ratio, which can make the particles very reactive or catalytic. Furthermore, rapid increase in the implementation of nanotechnologies has released large amount of the nanowaste into the environment. In the last two decades, transport of nanoparticles in the subsurface and the potential hazard they impose to the environment have attracted the attention of researchers. In this work, we use numerical simulation to investigate the problem regarding the transport phenomena of nanoparticles in anisotropic porous media. We consider the case in which the permeability in the principal direction components will vary with respect to time. The interesting thing in this case is the fact that the anisotropy could disappear with time. We investigate the effect of the degenerating anisotropy on various fields such as pressure, porosity, concentration and velocities.

In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is solved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Numerical example for regular heterogenous permeability is considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graphically.

The problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.

This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.

In the current paper, a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium is presented. Both capillary forces as well as Brownian diffusion are considered in the model. A numerical example of countercurrent water-oil imbibition is considered. We monitor the changing of the fluid and solid properties due to the addition of the nanoparticles using numerical experiments. Variation of water saturation, nanoparticles concentration and porosity ratio are investigated. Introduction In the recent years, the applications of nanometer particles (nanoparticles) have been reported in many disciplines. These nanoparticles can modify the rheology, mobility, wettability, and other properties of the fluids and therefore need comprehensive investigations. Using the nanoparticles in oil and gas exploration and production is also a promising field of research. For example, certain types of nanoparticles can be used as tracers for oil and gas exploration. These nanoparticles are designed such that they do not stick to the rock surface or hydrocarbon phases and move faster than the traditional chemical tracers. Moreover, nanoparticles can be used in the oilfields to enhance water injection by virtue of changing the wettability of reservoir rock through their adsorption on porous walls. The nanometer unit and nanoparticles are often associated with the field of nanotechnology. The nanometer (nm) unit is equal to one billionth of a meter (nm=10

Injection of CO2 in hydrocarbon reservoir has double benefit. On the one hand, it is a profitable method due to issues related to global warming, and on the other hand it is an effective mechanism to enhance hydrocarbon recovery. Such injection associates complex processes involving, e.g., solute transport of dissolved materials, in addition to local changes in density of the phases. Also, increasing carbon dioxide injection may cause a structural deformation of the medium, so it is important to include such effect into the model. The structural deformation modelling in carbon sequestration is important to evaluate the medium stability to avoid CO2 leakage to the atmosphere. On the other hand, geologic formation of the medium is usually heterogeneous and consists of several layers of different permeability. In this work we conduct numerical simulation of two-phase flow in a heterogeneous porous medium domain with dissolved solute transport as well as structural deformation effects. The solute transport of the dissolved component is described by concentration equation. The structural deformation for geomechanics is derived from a general local differential balance equation with neglecting the local mass balance of solid phase and the inertial force term. The flux continuity condition is used at interfaces between different permeability layers of the heterogeneous medium. We analyze the vertical migration of a CO2 plume injected into a 2D layered reservoir. Analysis of distribution of flow field components such as saturation, pressures, velocities, and CO2 concentration are presented.