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This book presents a collection of contributions from experts working on flow and transport in porous media around the globe. The book includes chapters authored by engineers, scientists, and mathematicians on single and multiphase flow and transport in homogeneous as well as heterogeneous porous media. Addressing various experimental, analytical, and modeling aspects of transport in sub-surface domains, the book offers a valuable resource for graduate students, researchers, and professionals alike.

### Fines Migration in Aquifers and Oilfields: Laboratory and Mathematical Modelling

Migration of natural reservoir fines is one of the main causes of formation damage in oil and gas fields. Yet, fines migration can be employed for enhancing reservoir sweep and water production control. Permeability decline due to fine particles’ detachment from reservoir rocks, mobilisation, migration and straining has been widely reported in the petroleum industry since the 1960s and is being researched worldwide. The topic of colloidal-suspension flows with particle detachment is also of wide interest in environmental, chemical and civil engineering. The current work begins with a detailed introduction on laboratory and mathematical modelling of fines migration, along with new mathematical models and experimental results. Each of the next three sections explores a particular cause of fines mobilisation, migration and straining. Section 2 covers high flow velocity that causes particle detachment accompanied by consequent permeability decline. Section 3 covers low-salinity water injection, where the decreased electrostatic attraction leads to particle mobilisation. Section 4 covers the effect of high temperature on production rate and low-salinity water injection in geothermal reservoirs. We attribute the long permeability stabilisation period during coreflooding with fines migration, to slow fines rolling and sliding and to diffusive delay in particle mobilisation. We derive the analytical models for both phenomena. Laboratory fines-migration coreflood tests are carried out, with the measurement of breakthrough fines concentration and pressure drop across the whole core and the core’s section. Treatment of the experimental data and analysis of the tuned coefficients show that the slow-particle model contains fewer coefficients and exhibits more typical strained concentration dependencies of the tuned parameters than does the delay-release model.

Y. Yang, F. D. Siqueira, A. Vaz, A. Badalyan, Z. You, A. Zeinijahromi, T. Carageorgos, P. Bedrikovetsky

### Migration and Capillary Entrapment of Mercury in Porous Media

Accidental spills or industrial disposals of elemental mercury (Hg0) result in contamination of subsurface soil and groundwater. Hg0 is a highly dense non-aqueous fluid whose physico-chemical properties govern its fate and transport in the subsurface. Owing to its liquid state and high density, it percolates down the subsurface by gravity forces and tends to pool when it reaches any impervious barrier. On the other hand, its low solubility and high interfacial tension tend to counteract its downward gravity movement and favour entrapment of a small volume of Hg0 in the pore spaces of the subsurface. The trace fraction of entrapped Hg0 termed as residual Hg0 may bring about severe groundwater contamination due to its chemical and biological transformations to more mobile and more toxic inorganic and organic mercury compounds. It is hypothesized that Hg0 behaves as a typical dense non-aqueous liquid and migrates under the influence of capillary, gravity and viscous forces, and eventually gets entrapped in void spaces of the subsurface. The entrapment process and residual Hg0 quantification can be described by two-phase capillary pressure water saturation (Pc–Sw) experiments and pore-scale micromodel experiments.

M. Devasena, Indumathi M. Nambi

### New Insight into Immiscible Foam for Enhancing Oil Recovery

Gas flooding is a widely applied enhanced oil recovery method. But, the full potential of this method is not realized in the reservoir conditions due to poor vertical and areal sweep efficiency of the injected gas. Foaming of the injected gas can potentially improve gas flooding performance by reducing the mobility of gas phase and thereby increasing volumetric sweep efficiency during gas flooding into oil reservoirs. In this study, the behavior of immiscible form generated by nitrogen and C14-16 alpha olefin sulfonate in natural sandstone porous media was investigated. Effect of surfactant concentration on the foam strength and foam propagation was examined. X-ray CT scans were obtained to visualize the foam displacement process and to determine fluid saturations at different times. The results revealed that stable foam could be obtained in the presence of water-flood residual oil. CT scan images, fluid saturation, and mobility reduction factor profiles demonstrated that foam exhibited a good mobility control in the presence of water-flood residual oil. The results also proved that immiscible foam displaced additional oil from water-flooded sandstone cores, supporting the idea that foam is potentially an effective EOR method.

Mohammad Simjoo, Pacelli L. J. Zitha

### Numerical Simulation of Flows in a Channel with Impermeable and Permeable Walls Using Finite Volume Methods

Laminar flows in a channel with permeable and impermeable walls are simulated using finite volume computational fluid dynamics (CFD). The CFD-simulated velocity profiles in the channel are compared with analytical solutions in the literature for impermeable walls (no-slip boundary condition) and with the authors’ analytical model for permeable walls (with slip boundary condition). The CFD results show very good agreement with the analytical solutions. A series of parametric studies show that when the slip coefficient α decreases from 4.0 to 0.1, the slip velocity at the channel-porous medium interface increases, but the velocity at the channel centre decreases, leading to a ‘flatter’ velocity profile, approaching that of a plug flow. This suggests a lower shear stress at the interface and a lower skin friction for a smaller slip coefficient. The lower skin friction leads to lower pressure drop per unit length along the channel. It is also found that when the wall permeability decreases, the slip velocity at the channel-porous medium interface decreases, leading to an increase in shear stress and skin friction, hence the increase in pressure drop per unit length along the channel. When the permeability k is less than a certain threshold, the slip velocity at the interface becomes very small and therefore, the shear stress and pressure drop values approach those of the no-slip boundary cases. The effect of the Reynolds number on the velocity profiles is insignificant for the range of values (0.5–7) studied in the chapter, but it has a much more pronounced effect on the pressure drops along the channel.

Z. F. Tian, C. Xu, P. A. Dowd

### A Comparative Analysis of Mixed Finite Element and Conventional Finite Element Methods for One-Dimensional Steady Heterogeneous Darcy Flow

Accurate simulation of Darcy flux is essential to simulate contaminant transport in groundwater accurately. The mixed finite element method has been used to obtain highly accurate flux distribution in groundwater flow applications. However, the method has not been widely adopted because of the lack of understanding of its merits, lack of comparison of its solution to those obtained from conventional schemes, and the usually mathematically rigorous presentation of the theory behind the method, which is not easily comprehensible. Hence, the objective of this paper is to present a simplified conceptual description of the mixed finite element method, to compare the solutions obtained from the method to those of the conventional finite element methods and to analyze any special properties of the solutions obtained from the mixed finite element methods. It has been shown in this paper that the solutions obtained from the mixed finite element method are highly accurate in rapidly changing flux distributions and heterogeneous flow distributions even when coarse grids are used to obtain the solution.

Debasmita Misra, John L. Nieber

### Subsurface Acid Sulphate Pollution and Salinity Intrusion in Coastal Groundwater Environments

Water is vital for humans and this paper explores subsurface water or groundwater––a natural storage of water that may replace the large expensive dams that cost a lot and can fail. The pollution of groundwater is a major area of research and various studies have examined subsurface environments—nature of pollution and possible remediation of the coastal groundwaters. This paper reviews work done by the author and colleagues on acidity, salinity and flow using partial differential and time-series methods, but the models themselves are not the focus. A brief review of the nature of groundwater modelling is presented first with the focus on Acid Sulphate Soils (ASS) and salinity pollution. Models used to investigate groundwater acidity, salinity and flow in coastal areas and some methods that deal with pollution are then examined. This is followed by an examination of difficulties with the modelling packages that were used. A possible alternative of desalination is then presented for potable water but it has its own problems. A summary and conclusion then concludes the paper on subsurface pollution.

Gurudeo Anand Tularam, Rajibur Reza

### Fully Developed Magnetoconvective Heat Transfer in Vertical Double-Passage Porous Annuli

This study examines the combined analytical and numerical investigations of fully developed mixed convective flow in vertical double-passage porous annuli formed by three vertical concentric cylinders. Also, the effects of viscous dissipation and magnetic field are considered. The governing fully developed equations are analytically solved in the absence of viscous dissipation, while an implicit finite difference technique has been applied to solve the governing equations when the viscous dissipation effects are taken into consideration. Detailed and systematic numerical simulations are carried out to explore the effects of porosity, magnetic field, viscous dissipation, modified Grashof number, baffle position and radius ratio on the flow pattern, temperature distribution and heat transfer rate and are discussed through the graphs. The numerical results reveal that the presence of viscous dissipation has profound influence of thermal distribution, whereas the velocity profiles are significantly altered by the Darcy and Hartmann numbers.

M. Sankar, N. Girish, Z. Siri

### Effect of Nonuniform Heating on Natural Convection in a Vertical Porous Annulus

This study reports numerical investigation of natural convection in a vertical annular cavity filled with fluid-saturated porous media. The inner and outer walls are subjected to two spatially varying sinusoidal temperature distributions with different amplitudes and phase deviations, while the top and bottom walls are thermally insulated. The governing nonlinear, coupled partial differential equations have been solved using a stable, implicit finite difference method. Numerical results are presented for wide range of Rayleigh number, Darcy number, amplitude ratio, phase deviation, and aspect ratio for a fixed Prandtl number of Pr = 0.7. The computational results are presented in the form of streamlines, isotherm contours, local and the average Nusselt numbers as a function of nondimensional parameters of the problem. Through detailed numerical simulations, the influence of nonuniform heating on the flow and thermal fields, and heat transfer characteristics are successfully captured in the porous annulus.

M. Sankar, S. Kiran, Younghae Do

### Natural Convection in an Inclined Parallelogrammic Porous Enclosure

This paper reports the numerical investigation of natural convection in an inclined parallelogrammic porous enclosure. The vertical sloping sidewalls of the enclosure are maintained at different, uniform temperatures, while the top and the bottom walls are kept at adiabatic. Using Darcy’s law, the governing equations are modeled and are solved using an implicit finite difference method. Detailed numerical computations are performed for wide range of Rayleigh numbers, aspect ratio of the cavity, tilt angle of the parallelogrammic enclosure, and tilt angle of the sloping sidewalls. The main objective of this analysis is to explore the effect of two tilt angles combined with other two parameters on the flow pattern, thermal fields, and heat transfer rates. Through comprehensive and systematic numerical simulations, the effects of all parameters are successfully captured in our study. We found that the streamlines, isotherms, and average Nusselt numbers are significantly altered by the tilt angle of the enclosure compared to non-inclined parallelogrammic enclosure. Further, the tilt angle of enclosure is dominant in modifying the flow pattern and heat transfer performance in the enclosure compared to the tilt angle of the sloping walls.

Bongsoo Jang, R. D. Jagadeesha, B. M. R. Prasanna, M. Sankar

### Natural Convection of Cold Water Near Its Density Maximum in a Porous Wavy Cavity

The aim of the present numerical study is to investigate the buoyant convective flow and heat transfer of cold water near its density maximum in a wavy porous square cavity. The vertical left wall of the cavity is heated, while the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adapted for fluid flow through the porous medium inside the cavity. The governing equations are solved numerically using the finite volume method over a range of wavy wall’s amplitude and a number of undulation, density inversion parameter, and Darcy–Rayleigh numbers. The waviness of the cavity enhances the heat transfer. The density maximum leaves a strong effect on fluid flow and temperature distribution inside the cavity.

S. Sivasankaran

### Convective Mass and Heat Transfer of a Chemically Reacting Fluid in a Porous Medium with Cross Diffusion Effects and Convective Boundary

An examination is offered to analyse the cross diffusion and convective boundary condition effects on unsteady free convective flow, mass and heat transfers subject to heat generation/absorption, chemical reaction and suction/injection effects. The similarity transformation is used to convert the modelled PDEs into ODEs, which are solved numerically. The skin friction, mass and heat transfers rates as well as the effects of several parameters on temperature, concentration and velocity are examined. The chemical reaction effect is important in concentration field compared to temperature and velocity.

M. Bhuvaneswari, S. Sivasankaran

### Local Non-similar Solution of Induced Magnetic Boundary Layer Flow with Radiative Heat Flux

This study is concerned with the motion of the steady 2-D boundary layer viscous and heat transfer flow past a stretching surface under the influence of aligned magnetic field with thermal radiation. The stretching plate is maintained at prescribed surface heat flux and moving in its own plate with a power law velocity. The effect of an induced magnetic field is taken into account. The non-similar governing equations of mass, momentum, induction, and energy are obtained using a suitable transformation. The transformed boundary layer governing equations are solved numerically using Local Non-Similar method (LNS). We then employ the numerical results to bring out the effects of velocity exponent parameter(p), the wall heat flux exponent parameter (m), radiation parameter (N), magnetic force parameter $$( \beta )$$ and reciprocal of the magnetic Prandtl number $$\left( \lambda \right)$$ on velocity profile (f′), induced magnetic field function (g), induced magnetic field gradient (g′), and temperature profile ($$\theta$$). The skin frictions coefficient and the local Nusselt number are presented for the various parameters. The result shows that the observed parameters have significanct influence on the flow, heat, and mass transfer. The study has applications in electromagnetic nanomaterials’ processing.

M. Ferdows, Sakawat Hossain