Mass Transfer in Multiphase Systems and its Applications Part 1 pot

El-Amin, Amgad Salama and Shuyu Sun Multiphase Modelling of Thermomechanical Behaviour of Early-Age Silicate Composites 49 Anna Kiełbus-Rąpała and Joanna Karcz Gas-Liquid Mass Transfer i

MASS TRANSFER IN MULTIPHASE SYSTEMS AND ITS APPLICATIONS

Edited by Mohamed El-Amin

Mass Transfer in Multiphase Systems and its Applications

Edited by Mohamed El-Amin

Published by InTech

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in Porous Media - Theory and Modeling 1

Jennifer Niessner and S Majid Hassanizadeh

Solute Transport With Chemical Reaction

in Singleand Multi-Phase Flow in Porous Media 23

M.F El-Amin, Amgad Salama and Shuyu Sun

Multiphase Modelling of Thermomechanical Behaviour of Early-Age Silicate Composites 49

Anna Kiełbus-Rąpała and Joanna Karcz

Gas-Liquid Mass Transfer in an Unbaffled Vessel Agitated by Unsteadily Forward-Reverse Rotating Multiple Impellers 117

Masanori Yoshida, Kazuaki Yamagiwa, Akira Ohkawa and Shuichi Tezura

Toward a Multiphase Local Approach in the Modeling of Flotation and Mass Transfer

in Gas-Liquid Contacting Systems 137

Jamel Chahed and Kamel M’Rabet

Mass Transfer in Two-Phase Gas-Liquid Flow

in a Tube and in Channels of Complex Configuration 155

Nikolay Pecherkin and Vladimir Chekhovich

Contents

Laminar Mixed Convection Heat and Mass Transfer with Phase Change and Flow Reversal in Channels 179

Brahim Benhamou, Othmane Oulaid, Mohamed Aboudou Kassim and Nicolas Galanis

Liquid-Liquid Extraction With and Without a Chemical Reaction 207

Claudia Irina Koncsag and Alina Barbulescu

Modeling Enhanced Diffusion Mass Transfer in Metals during Mechanical Alloying 233

Boris B Khina and Grigoriy F Lovshenko

Mass Transfer in Steelmaking Operations 255

Roberto Parreiras Tavares

Effects of Surface Tension on Mass Transfer Devices 273

Honda (Hung-Ta) Wu and Tsair-Wang Chung

Overall Mass-Transfer Coefficient for Wood Drying Curves Predictions 301

Rubén A Ananias, Laurent Chrusciel,André Zoulalian, Carlos Salinas-Lira and Eric Mougel

Transport Phenomena in Paper and Wood-based Panels Production 313

Helena Aguilar Ribeiro, Luisa Carvalho,Jorge Martins and Carlos Costa

Control of Polymorphism and Mass-transfer

in Al 2 O 3 Scale Formed by Oxidation

of Alumina-Forming Alloys 343

Satoshi Kitaoka, Tsuneaki Matsudaira and Masashi Wada

Mass Transfer Investigation

of Organic Acid Extraction with Trioctylamine and Aliquat 336 Dissolved in Various Solvents 367

Monwar Hossain

New Approaches for Theoretical Estimation

of Mass Transfer Parameters

in Both Gas-Liquid and Slurry Bubble Columns 389

Stoyan Nedeltchev and Adrian Schumpe

Influence of Mass Transfer and Kinetics

on Biodiesel Production Process 433

Ida Poljanšek and Blaž Likozar

Condensation Capture of Fine Dust in Jet Scrubbers 459

M.I Shilyaev and E.M Khromova

Mass Transfer in Filtration Combustion Processes 483

David Lempert, Sergei Glazov and Georgy Manelis

Mass Transfer in Hollow Fiber Supported Liquid Membrane for As and Hg Removal from Produced Water in Upstream Petroleum Operation in the Gulf of Thailand 499

U Pancharoen, A.W Lothongkum and S Chaturabul

Mass Transfer in Fluidized

Bed Drying of Moist Particulate 525

Yassir T Makkawi and Raffaella Ocone

Simulation Studies on the Coupling Process

of Heat/Mass Transfer in a Metal Hydride Reactor 549

Fusheng Yang and Zaoxiao Zhang

Mass Transfer around Active Particles in Fluidized Beds 571

Fabrizio Scala

Mass Transfer Phenomena and Biological Membranes 593

Parvin Zakeri-Milani and Hadi Valizadeh

Heat and Mass Transfer

in Packed Bed Drying of Shrinking Particles 621

Manoel Marcelo do Prado and Dermeval José Mazzini Sartori

Impact of Mass Transfer on Modelling

and Simulation of Reactive Distillation Columns 649

Zuzana Švandová, Jozef Markoš and Ľudovít Jelemenský

Mass Transfer through Catalytic Membrane Layer 677

Nagy Endre

Mass Transfer in Bioreactors 717

Ma del Carmen Chávez, Linda V González,

Mayra Ruiz, Ma de la Luz X Negrete,

Oscar Martín Hernández and Eleazar M Escamilla

Analytical Solutions of Mass Transfer around a Prolate

or an Oblate Spheroid Immersed in a Packed Bed 765

J.M.P.Q Delgado and M Vázquez da Silva

This book covers a number of developing topics in mass transfer processes in phase systems for a variety of applications The book eff ectively blends theoretical, numerical, modeling, and experimental aspects of mass transfer in multiphase sys-tems that are usually encountered in many research areas such as chemical, reactor, environmental and petroleum engineering From biological and chemical reactors to paper and wood industry and all the way to thin fi lm, the 31 chapters of this book serve as an important reference for any researcher or engineer working in the fi eld of mass transfer and related topics

multi-The fi rst chapter focuses on the description and modeling of mass transfer processes occurring between two fl uid phases in a porous medium, while the second chapter is concerned with the basic principles underlying transport phenomena and chemical reaction in single- and multi-phase systems in porous media Chapter 3 introduces the multiphase modeling of thermomechanical behavior of early-age silicate composites The surfactant transfer in multiphase liquid systems under conditions of weak gravita-tional convection is presented in Chapter 4

In the fi ft h chapter the volumetric mass transfer coeffi cient for multiphase cally agitated gas–liquid and gas–solid–liquid systems is obtained experimentally Further, gas-liquid mass transfer analysis in an unbaffl ed vessel agitated by unsteadily forward-reverse rotating multiple impellers is provided in Chapter 6 Chapter 7 dis-cuses the kinetic model of fl otation based on the theory of mass transfer in gas-liquid bubbly fl ows The eighth chapter deals with experimental investigation of mass trans-fer and wall shear stress, and their interaction at the concurrent gas-liquid fl ow in a vertical tube, in a channel with fl ow turn, and in a channel with abrupt expansion The laminar mixed convection with mass transfer and phase change of fl ow reversal in channels is studied in the ninth chapter, and the tenth chapter exemplifi es the theoreti-cal aspects of the liquid-liquid extraction with and without a chemical reaction and the dimensioning of the extractors with original experimental work and interpretations.The eleventh chapter introduces analysis of the existing theories and concepts of solid-state diff usion mass transfer in metals during mechanical alloying In Chapter 12 the mass transfer coeffi cient is given for diff erent situations (liquid-liquid, liquid-gas and liquid-solid) of two-phase mass transfer of steelmaking processes Chapter 13 discuss-

mechani-es the eff ect of Marangoni Instability on thin liquid fi lm, thinker liquid layer and mass transfer devices

Chapter 14 provides a review of model permitt ing the determination of wood drying rate represented by an overall mass transfer coeffi cient and a driving force Moreoever, transport phenomena in paper and wood-based panels’ production are discussed in Chapter 15.

In the sixteenth chapter the eff ect of lutetium doping on oxygen permeability in crystalline alumina wafers exposed to steep oxygen potential gradients was evaluated

poly-at high temperpoly-atures to investigpoly-ate the mass-transfer phenomena Mass transfer vestigation of organic acid extraction with trioctylamine and aliquat336 dissolved in various solvents is introduced in Chapter 17

in-Chapter 18 is focused on the development of semi-theoretical methods for calculation

of gas holdup, interfacial area and liquid-phase mass transfer coeffi cients in gas-liquid and slurry bubble column reactors Chapter 19 investigates the infl uence of mass trans-fer and kinetics on biodiesel (fatt y acid alkyl) production process

The physical-mathematical model of heat and mass transfer and condensation capture

of fi ne dust on fl uid droplets dispersed in jet scrubbers is suggested and analyzed in Chapter 20, while Chapter 21 is devoted to investigate mass transfer in fi ltration com-bustion processes

The twenty-second chapter describes the merits of using hollow fi ber supported liquid membranes (HFSLM), one of liquid membranes in supported (not clear) structures, and how mass transfer involves step-by-step in removing arsenic (As) and mercury (Hg) The twenty-third chapter presents an overview of the various mechanisms contribut-ing to particulate drying in a bubbling fl uidized bed and the mass transfer coeffi cient corresponding to each mechanism A mathematical model and numerical simulation for hydriding/dehydriding process in a tubular type MH reactor packed with LaNi5 were provided in the twenty-fourth chapter Chapter 25 is dedicated to the mass trans-fer coeffi cient around freely moving active particles in the dense phase of a fl uidized bed Chapter 26 is aimed at reviewing transport across biological membranes, with

an emphasis on intestinal absorption, its model analysis and permeability prediction The objective of the twenty-seventh chapter is to provide comprehensive information

on theoretical-experimental analysis of coupled heat and mass transfer in packed bed drying of shrinking particles The twenty-eighth chapter focuses on vapour-liquid mass transfer infl uence on the prediction of RD column behaviour neglecting the liq-uid-solid and intraparticle mass transfer Mass transfer through catalytic membrane layer is studied in Chapter 29 In chapter 30 three types of bioreactors and stirred tank applied to biological systems are introduced and a mathematical model is developed Finally in Chapter 31 analytical solutions of mass transfer around a prolate or an oblate spheroid immersed in a packed bed are obtained

Mohamed Fathy El-Amin

Physical Sciences and Engineering DivisionKing Abdullah University of Science and Technology (KAUST)

Mass and Heat Transfer During Two-Phase Flow in

Porous Media - Theory and Modeling

or condensation, for example

Such mass transfer processes are crucial in many applications involving flow and transport inporous media Major examples are found in soil science (where the evaporation from soils is

of interest), soil and groundwater remediation (like thermally-enhanced soil vapor extractionwhere dissolution, evaporation, and condensation play a role), storage of carbon dioxide inthe subsurface (where the dissolution of carbon dioxide in the surrounding groundwater is acrucial storage mechanism), CO2-enhanced oil recovery (where after primary and secondaryrecovery, carbon dioxide is injected into the reservoir in order to mobilize an additional 8-20per cent of oil), and various industrial porous systems (such as certain types of fuel cells).Let us have a closer look at a few of these applications and identify where interphase masstransfer is relevant Four specific examples are shown in Fig 2 and briefly described

solid phase

fluid

Fig 1 Mass transfer processes (evaporation, dissolution, condensation) imply a transfer ofparticles across fluid–fluid interfaces

1

2 Mass Transfer

(a) Carbon dioxide storage in the subsurface

(figure from IPCC (2005))

(b) Soil contamination and remediation

(c) Enhanced oil recovery (figure from

www.oxy.com)

groundwater

precipitation radiation

evaporation infiltration

(d) Evaporation from soil

Fig 2 Four applications of flow and transport in porous media where interphase masstransfer is important

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling 3

(a) Carbon capture and storage (Fig 2 (a)) is a recent strategy to mitigate the greenhouse

effect by capturing the greenhouse gas carbon dioxide that is emitted e.g by coal powerplants and inject it directly into the subsurface below an impermeable caprock Here, threedifferent storage mechanisms are relevant on different time scales: 1) The capillary barriermechanism of the caprock This geologic layer is meant to keep the carbon dioxide in thestorage reservoir as a separate phase 2) Dissolution of the carbon dioxide in the surroundingbrine (salty groundwater) This is a longterm storage mechanism and involves a masstransfer process as carbon dioxide molecules are “transferred” from the gaseous phase tothe brine phase 3) Geochemical reactions which immobilize the carbon dioxide throughincorporation into the rock matrix

(b) Shown in Fig 2 (b) is a cartoon of a light non-aqueous phase liquid (LNAPL)

soil contamination and its clean up by injection of steam at wells located around the

contaminated soil The idea behind this strategy is to mobilize the initially immobile(residual) LNAPL by evaporation of LNAPL component at large rates into the gaseousphase The soil gas is then extracted by a centrally located extraction well It means that theremediation mechanism relies on the evaporation of LNAPL component which represents amass transfer from the liquid LNAPL phase into the gaseous phase

(c) In order to produce an additional 8-20% of oil after primary and secondary recovery,carbon dioxide may be injected into an oil reservoir, e.g alternatingly with water, see

Fig 2 (c) This is called enhanced oil recovery The advantage of injecting carbon dioxide lies

in the fact that it dissolves in the oil which in turn reduces the oil viscosity, and thus, increasesits mobility The improved mobility of the oil allows for an extraction of the otherwisetrapped oil Here, an interphase mass transfer process (dissolution) is responsible for animproved recovery

(d) The last example (Fig 2 (d)) shows the upper part of the soil The water balance of this part

of the subsurface is extremely important for agriculture or plant growth in general Plants

do not grow well under too wet or too dry conditions One of the very important factors

influencing this water balance (besides surface runoff and infiltration) is the evaporation of

water from the soil, which is again an interphase mass transfer process.

1.2 Purpose of this work

Mass transfer processes are essential in a large variety of applications—the presentedexamples only show a small selection of systems A common feature of all these applications isthe fact that the relevant processes occur in relatively large domains such that it is not possible

to resolve the pore structure and the fluid distribution in detail (left hand side of Fig 3).Instead, a macro-scale approach is needed where properties and processes are averaged over

a so-called representative elementary volume (right hand side of Fig 3) This means that thecommon challenge in all of the above-mentioned applications is how to describe mass transferprocesses on a macro scale This transition from the pore scale to the macro scale is illustrated

in Fig 3 where on the left side, the pore-scale situation is shown (which is impossible to beresolved in detail) while on the right hand side, the macro-scale situation is shown

2 Overview of classical mass transfer descriptions

4 Mass Transfer

s

solid phase

w

wetting fluid phase

n

non−wetting fluid phase

Fig 3 Pore-scale versus macro-scale description of flow and transport in a porous medium.scale From there, we try to get a better understanding of the macro-scale physics of masstransfer, which is our scale of interest

In Fig 1 we have seen that interphase mass transfer is inherently a pore-scale process asit—naturally—takes place across fluid–fluid interfaces Let us imagine a situation where twofluid phases, a wetting phase and a non-wetting phase, are brought in contact as shown in

Fig 4 Commonly, when the two phases are brought in contact (time t=t0), equilibrium isquickly established directly at the interface With respect to mass transfer, this means thatthe concentration of non-wetting phase particles in the wetting phase at the interface as well

as the concentration of wetting-phase particles in the non-wettting phase at the interface are

both at their equilibrium values, C 1,eq2 and C 2,eq1 At t=t0, away from the interface, there

is still no presence ofα-phase particles in the β-phase At a later time t=t1, concentrationprofiles develop within the phases However, within the bulk phases, the concentrations arestill different from the respective equilibrium concentration at the interface Considering a

still later point of time, t=t2, the equilibrium concentration is finally reached everywhere inthe bulk phases

These considerations show that mass transfer on the pore scale is inherently a kinetic processthat is very much related to phase-interfaces But how is this process represented on the macroscale, i.e on a volume-averaged scale? This is what we will focus on in the next section

C 1 2,eq

C 2 1,eq

x

t = t 0

solid phase

fluid phase 1 fluid phase 2

C

x

t = t 2

C21,eq

Fig 4 Pore-scale picture of interphase mass transfer

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling 5

2.2 Current macro-scale descriptions

In Fig 3, we illustrated the fact that when going from the pore scale to the macro scale,information about phase-interfaces is lost The only information present on the macro scale isrelated to volume ratios, such as porosity and fluid saturations But, as mentioned earlier,mass transfer is strongly linked to the presence of interfaces and interfacial areas and allthe information about phase-interfaces disappears on the macro scale This means that thedescription of mass transfer on the macro scale is not straight forward Classical approachesfor describing mass transfer generally rely on one of the following two principles:

1 assumption of local chemical equilibrium within an averaging volume or

2 kinetic description based on a fitted (linear) relationship

These two classical approaches will be discussed in more detail in the following Analternative approach which accounts for the phase-interfacial area will be presented later inSec 3

2.2.1 Local equilibrium assumption

The assumption of local chemical equilibrium within an averaging volume means that theequilibrium concentrations are reached instantaneously everywhere within an averagingvolume (in both phases) That means it is assumed that everywhere within the averaging

volume, the situation at t=t2in Fig 4 is reached from the beginning (t=t0) Thus, at eachpoint in the wetting phase and at each point in the non-wetting phase within the averagingvolume, the equilibrium concentration of the components of the other phase is reached.This is an assumption which may be good in case of fast mass transfer, but bad in case ofslow mass transfer processes To be more precise, the assumption that the composition of

a phase is at or close to equilibrium may be good if the characteristic time of mass transfer

is small compared to that of flow However, if large flow velocities occur as e.g during airsparging, the local equilibrium assumption gives completely wrong results, see Falta (2000;2003) and van Antwerp et al (2008) We will investigate and quantify this issue later in Sec 3.3

Local equilibrium models for multi-phase systems have been introduced and developede.g by Miller et al (1990); Powers et al (1992; 1994); Imhoff et al (1994); Zhang & Schwartz(2000) and have been used and advanced ever since Let us consider a system with a liquid

phase (denoted by subscript l) and a gaseous phase (denoted by subscript g) composed of

air and water components Then, Henry’s Law is employed to determine the mole fraction

of air in the liquid phase, while the mole fraction of water in the gas phase is determined byassuming that the vapor pressure in the gas phase is equal to the saturation vapor pressure

Denoting the water component by superscript w and the air component by superscript a, this

l [−] is the mole fraction of air in the liquid phase, x w

g [−]is the mole fraction of water

in the gaseous phase, H a

2.2.2 Classical kinetic approach

Kinetic mass transfer approaches are traditionally applied to the dissolution of contaminants

in the subsurface which form a separate phase from water, the so-called non-aqueous phaseliquids (NAPLs) If such a non-aqueous phase liquid is heavier than water, it is called

“dense non-aqueous phase liquid” or DNAPL When an immobile lense of DNAPL is present

at residual saturation (i.e at a saturation which is so low that the phase is immobile) anddissolves into the surrounding groundwater, the kinetics of this mass transfer process usuallyplays an important role: the dissolution of DNAPL is a rate-limited process This is alsothe case when a pool of DNAPL is formed on an impermeable layer In these relativelysimple cases, only the mass transfer of a DNAPL component from the DNAPL phase intothe water phase has to be considered For these cases, classical models acknowledge thefact that the rate of mass transfer is highly dependent (proportional to) interfacial area andassume a first-order rate of kinetic mass transfer between fluid phases in a porous medium

on a macroscopic (i.e volume-averaged) scale which can be expressed as (see e.g Mayer &Hassanizadeh (2005)):

to the local equilibrium case

In the absence of a physically-based estimate of interfacial area in classical kinetic models, the

mass transfer coefficient k κ α→β and the specific interfacial area a αβare often lumped into onesingle parameter (Miller et al (1990); Powers et al (1992; 1994); Imhoff et al (1994); Zhang &Schwartz (2000)) This yields, in a simplified notation,

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling 7

where D m

m2

s



is the aqueous phase molecular diffusion coefficient, and d50[m]is the mean

size of the grains The Sherwood number is then related to Reynold’s number Re and DNAPL saturation S n [−]by

where p, q, and r are dimensionless fitting parameters This is a purely empirical relationship.

Although interphase mass transfer is proportional to specific interfacial area in the original

Eq (5), this dependence cannot explicitly be accounted for as the magnitude of specificinterfacial area is not known

An alternative classical approach for DNAPL pool dissolution has been proposed by Falta(2003) who modeled the dissolution of DNAPL component by a dual domain approachfor a case with simple geometry For this purpose, they divided the contaminated porousmedium into two parts: one that contains DNAPL pools and one without DNAPL Fortheir simple case, the dual domain approach combined with an analytical solution forsteady-state advection and dispersion provided a means for modeling rate-limited interphasemass transfer While this approach provided good results for the case of simplified geometry,

it might be oversimplified for the modeling of realistic situations

3 Interfacial-area-based approach for mass transfer description

3.1 Theoretical background

Due to a number of deficiencies of the classical model for two-phase flow in porous media(one of which is the problem in describing kinetic interphase mass transfer on the macroscale), several approaches have been developed to describe two-phase flow in an alternativeand thermodynamically-based way Among these are a rational thermodynamics approach

by Hassanizadeh & Gray (1980; 1990; 1993b;a), a thermodynamically constrained averagingtheory approach by Gray and Miller (e.g Gray & Miller (2005); Jackson et al (2009)),mixture theory (Bowen (1982)) and an approach based on averaging and non-equilibriumthermodynamics by Marle (1981) and Kalaydjian (1987) While Marle (1981) and Kalaydjian(1987) developed their set of constitutive relationships phenomenologically, Hassanizadeh &Gray (1990; 1993b); Jackson et al (2009), and Bowen (1982) exploited the entropy inequality

to obtain constitutive relationships To the best of our knowledge, the two-phase flow models

of Marle (1981); Kalaydjian (1987); Hassanizadeh & Gray (1990; 1993b); Jackson et al (2009)are the only ones to include interfaces explicitly in their formulation allowing to describehysteresis as well as kinetic interphase mass and energy transfer in a physically-based way Inthe following, we follow the approach of Hassanizadeh & Gray (1990; 1993b) as it includesthe spatial and temporal evolution of phase-interfacial areas as parameters which allows

us to model kinetic interphase mass transfer in a much more physically-based way than isclassically done

It has been conjectured by Hassanizadeh & Gray (1990; 1993b) that problems of the classicaltwo-phase flow model, like the hysteretic behavior of the constitutive relationship betweencapillary pressure and saturation, are due to the absence of interfacial areas in the theory.Hassanizadeh and Gray showed (Hassanizadeh & Gray (1990; 1993b)) that by formulatingthe conservation equations not only for the bulk phases, but additionally for interfaces,and by exploiting the residual entropy inequality, a relationship between capillary pressure,saturation, and specific interfacial areas (interfacial area per volume of REV) can be derived.This relationship has been determined in various experimental works (Brusseau et al (1997);Chen & Kibbey (2006); Culligan et al (2004); Schaefer et al (2000); Wildenschild et al (2002);

7

Mass and Heat Transfer During Two-Phase Flow in Porous Media - Theory and Modeling

8 Mass Transfer

Chen et al (2007)) and computational studies (pore-network models and CFD simulations

on the pore scale, see Reeves & Celia (1996); Held & Celia (2001); Joekar-Niasar et al (2008;2009); Porter et al (2009)) The numerical work of Porter et al (2009) using Lattice Boltzmansimulations in a glass bead porous medium and experiments of Chen et al (2007) showthat the relationship between capillary pressure, the specific fluid-fluid interfacial area, andsaturation is the same for drainage and imbibition to within the measurement error Thisallows for the conclusion that the inclusion of fluid–fluid interfacial area into the capillarypressure–saturation relationship makes hysteresis disappear or, at least, reduces it down

to a very small value Niessner & Hassanizadeh (2008; 2009a;b) have modeled two-phaseflow—using the thermodynamically-based set of equations developed by Hassanizadeh &Gray (1990)—and showed that this interfacial-area-based model is indeed able to modelhysteresis as well as kinetic interphase mass and also energy transfer in a physically-basedway

3.2 Simplified model

After having presented the general background of our interfacial-area-based model, we willnow proceed by discussing the mathematical model The complete set of balance equationsbased on the approach of Hassanizadeh & Gray (1990) is too large to be handled numerically

In order to do numerical modeling, simplifying assumptions need to be made In thefollowing, we present such a simplified equation system as was derived in Niessner &Hassanizadeh (2009a)

This set of balance equations can be described by six mass and three momentum balanceequations These numbers result from the fact that mass balances for each component of eachphase and the fluid–fluid interface (that is 2×3) while momentum balances are given for thebulk phases and the interface Governing equations were derived by Hassanizadeh & Gray(1979) and Gray & Hassanizadeh (1989; 1998) for the case of flow of two pure fluid phaseswith no mass transfer Extending these equations to the case of two fluid phases, each made

of two components, we obtain the following equations

mass balance for phase components (κ=w, a):