Mohamed F. El-Amin

Modeling and Simulation of Nanoparticle Transport in a Two-Phase Flow in Porous Media

Abstract 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

Numerical and dimensional investigation of two-phase countercurrent imbibition in porous media

In this paper, we introduce a numerical solution of the problem of two-phase immiscible flow in porous media. In the first part of this work, we present the general conservation laws for multiphase flows in porous media as outlined in the literature for the sake of completion where we emphasize the difficulties associated with these equations in their primitive form and the fact that they are, generally, unclosed. The second part concerns the 1D computation for dimensional and non-dimensional cases and a theoretical analysis of the problem under consideration. A time-scale based on the 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 experiments on the Bond number effect is performed for two cases, gravity opposing and assisting. The theoretical analysis illustrates that common formulations of the time-scale forces the coefficient Da^1^/^2/Ca to be equal to one, while formulation of dimensionless time based on a characteristic velocity allows 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.

Modeling and Simulation of Nanoparticle Transport in Multiphase Flows in Porous Media: CO2 Sequestration

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.

An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

Non-Boussinesq turbulent buoyant jet of a low-density gas leaks into high-density ambient

Abstract In this article, we study the problem of low-density gas jet injected into high-density ambient numerically which is important in applications such as fuel injection and leaks. It is assumed that the local rate of entrainment is consisted of two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. The integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some similarity transformations. The resulting system is solved to determine the centerline quantities which are used to get the mean axial velocity, mean concentration and mean density of the jet. Therefore, the centerline and mean quantities are used together with the governing equation to determine some important turbulent quantities such as, cross-stream velocity, Reynolds stress, velocity–concentration correlation, turbulent eddy viscosity and turbulent eddy diffusivity. Throughout this paper the developed model is verified by comparing the present results with experimental results and jet/plume theory from the literature.

Numerical Aspects Related to the Dynamic Update of Anisotropic Permeability Field During the Transport of Nanoparticles in the Subsurface

Abstract 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.

Three-Dimensional, Numerical Investigation of Flow and Heat Transfer in Rectangular Channels Subject to Partial Blockage

Numerical simulation of flow and heat transfer in two adjacent channels is conducted with one of the channels partially blocked. This system simulates typical channels of a material testing reactor. The blockage is assumed due to the buckling of one of the channel plates inward along its width. The blockage ratio considered in this work is defined as the ratio between the cross-sectional area of the blocked and the unblocked channel. In this work, we consider a blockage ratio of approximately 40%. However, the blockage is different along the width of the channel, ranging from 0% at the end of the channel to 90% in the middle. The channel walls are sandwiching volumetric heat sources that vary spatially as chopped cosine functions. Interesting patterns are highlighted and investigated. The reduction in the flow area of one channel results in the flow redistributing among the two channels according to the changes in their hydraulic conductivities. The results of the numerical simulations show that the maximum wall temperature in the blocked channel is well below the boiling temperature at the operating pressure.

On the stability of the finite difference based lattice Boltzmann method

Abstract 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.

A Conditionally Stable Scheme for a Transient Flow of a Non- Newtonian Fluid Saturating a Porous Medium

Abstract 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.

An Iterative Implicit Scheme for Nanoparticles Transport with Two-Phase Flow in Porous Media

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.