21

CHAPTER 2

THEORETICAL BACKGROUND

2.1. General ideas about adsorption

2.1.1. Introduction

Adsorption, a surface phenomenon, is one of the most important industrial practices

of today’s world for the purpose of separation and purification of a mixture of

components. Adsorption is defined as a process in which atoms or molecules or ions

from gas and liquid phase accumulate over the surface of a solid (or liquid), which

arises due to interactions between the individual atoms, ions or molecules of an

adsorbate and those present in the adsorbent surface. Molecules or ions that have been

adsorbed onto solid surfaces are referred to as adsorbate and the surface where

adsorption occurs is called the adsorbent. The process of adsorption arises due to the

presence of unbalanced or residual forces at the surface of liquid or solid phase and

these residual forces attract and retain the atomic, ionic or molecular species on the

surface. The forces responsible for these interactions have their origin in

electromagnetic interactions (Weber and van Vliet, 1980).

The adhesion or cohesion type of attraction forces can arrange the molecules into

layers or films on the surface. Depending on the nature of the interactions, adsorption

can be classified into following four types (Weber, 1985):

(i) Exchange adsorption: This involves electrostatic attachment of ionic species to

surface sites of an adsorbent bearing opposite charges with subsequent

displacement of these species by other ionic adsorbates of greater electrostatic

affinity.

(ii) Physical adsorption or Physisorption: This type of adsorption results from the

action of van der Waals forces between the adsorbate and adsorbent molecules,

which are comprised of both London type dispersion forces and classical

electrostatic forces. For physisorption, the interaction forces are less than 40

kJ/mol, generally related to van der Waals type of weak forces.

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(iii) Chemical adsorption or Chemisorption: This type of adsorption involves a

strong adsorbate-adsorbent interactions (more than 40 kJ/mol), which results in

formation of stronger bonds (equivalent to either ionic or covalent bonds) between

the adsorbate and adsorbent. In physisorption, the adsorbed molecules remains

intact and can be desorbed in the same form, while in chemisorption, the adsorbed

molecules might have been broken into fragments on the surface, leading to what

is known as dissociative chemisorption.

(iv) Specific adsorption: It involves the attachment of adsorbate molecules at

functional groups present on the adsorbent surface through specific interactions,

which do not result in adsorbate transformation. These interactions exhibit a range

of binding energies from values associated with physical adsorption to the higher

energies involved in chemisorption.

Adsorption is distinguished from absorption which is mainly related to the

movement of atoms or molecules into the bulk of a porous adsorbent material. Both

adsorption and absorption could be generalized by the common term “Sorption”. The

extent of adsorption depends on physical parameters such as temperature, pressure and

concentration in the bulk phase and the surface area of the adsorbent as well as on

chemical parameters such as the elemental nature of the adsorbate and the adsorbent.

Low temperatures, high pressures, high surface areas and highly reactive adsorbates or

adsorbents generally favor adsorption.

The adsorbents are used usually in the form of spherical pellets, rods, moldings, etc.

They must have high abrasion resistance, high thermal stability and small micropore

diameter, which result in higher exposed surface area and hence high capacity for

adsorption. The adsorbents must also have a distinct macro pore structure which enables

fast transport of the gaseous molecules. The ability of an adsorbent to separate molecule

A from molecule B is known as its selectivity. The selectivity is given by the separation

factor (αα), which is defined as (Thomas and Crittenden, 1998),

αα = (Xi /Yi) / (Xj /Yj) (2.1)

23

where, Xi and Yi are the equilibrium mole fractions of component i and Xj and Yj are

the equilibrium mole fractions of component j, in the adsorbed and fluid phases

respectively. Selectivity arises in a separation process due to one or more of the

followings:

(i) Differences may exist in the thermodynamic equilibria for each adsorbate-

adsorbent interaction (the equilibrium effect).

(ii) Differences may exist in the rates at which different adsorbates move into the

internal structure of the adsorbent (kinetic effect).

(iii) Pore openings may be too small to allow penetration by one or more of the

adsorbates (molecular sieving effect, an extreme case of the kinetic effect).

(iv) Differences may exist in the rate at which different adsorbates can be

desorbed from the adsorbent (desorption effect).

The equilibrium separation factor depends on the followings:

Ø The nature of the adsorbent interactions, i.e., whether the surface is polar,

non polar, hydrophilic, hydrophobic, etc., and

Ø The conditions under which the process is carried out, i.e., temperature,

pressure and concentration.

Kinetic separation is possible only with molecular sieve adsorbents such as zeolites

and carbon sieves and it is largely determined by the ratio of micropore diffusivities of

the components being separated. For a useful separation to be based on kinetics, the size

of the adsorbent micro pores must be comparable with the dimensions of the diffusing

adsorbate molecules.

2.1.2. Adsorption Technology

The ability of some solids to remove colour from solutions containing dyes has been

known for over a century. Similarly, air contaminated with unpleasant odors could be

rendered odorless by passage the air through a vessel containing charcoal. Although

such phenomena were not well understood prior to the early twentieth century, they

24

represent the dawn of adsorption technology, which has survived as a means of

purifying and separating both gases and liquids to the present day. In the last few years,

the adsorption science and technology has expanded tremendously and has become an

increasingly important tool for separation and purification purpose as like other well-

established process technologies. This has stimulated research into adsorbate-adsorbent

interactions. Thomas and Crittenden (1998) have given an overview of the history and

development of the adsorption technology, particularly with respect to how theory is put

into commercial practice. The classical experiments of several scientists including

Brunauer, Emmet and Teller, McBain and Bakr, Langmuir and later by Barrer, all in the

early part of the twentieth century, have resulted in the emergence of quantitative

theories to explain the mechanism of the adsorption processes (Thomas and Crittenden,

1998). As a result of these studies, quantitative theories emerged, which have withstood

the test of time. It has been found that the best results are achieved with porous solids

and that adsorption occurs due to interactions between the surface atoms of the solids

and the molecules being removed from the bulk phase.

Adsorption process has wide applications in many natural physical, biological and

chemical systems. In biological systems, adsorption of atoms and molecules onto the

surface of a cell membrane is the first step in molecular recognition. Industrial

applications of adsorbents became common practice following the widespread use of

charcoal for decolorizing liquids and, in particular, its use in gas masks during the 1914-

18 World War for the protection of military personnel from poisonous gases.

Some finely divided solids have great adsorptive properties. Finely divided particles

of platinum or nickel, for example, can hold hydrogen molecules on their surfaces and

therefore it has wide application in various industrially important processes like alkene

hydrogenation, in the production of sulfuric acid by the contact process and in the

preparation of ammonia. Another example is the use of bone charcoal in industry to

remove colours from solutions. Colouring of cloth by different dyes also follows the

theory of adsorption.

Adsorption is employed in the hydrogenation of oils, in gas analysis and in

chromatography. Other examples include the segregation of surfactant molecules to the

surface of a liquid, the bonding of reactant molecules to the solid surface of a

25

heterogeneous catalyst, adhesion, lubrication and migration of ions to the surface of a

charged electrode.

Early commercial application of adsorption included use of naturally occurring clays

to refine oils and fats (Mantell, 1951). Fuller’s earth was used for removing grease from

woolen materials for a very long time. It is also used for removing contaminants of

petroleum fractions and oil, fats and waxes. Other naturally occurring clays like

kaolinite and bentonite were used for bleaching oils and petroleum spirits. Bauxite

consisting of hydrated aluminium oxide was in use for decolourizing residual oil stocks

and also for drying of gases and vapors.

Some types of carbon were in common use for decolorizing and removing odors

from wide variety of materials. The decolourization of liquids, including the refining of

sugar melts, was accomplished by mixing the carbon adsorbent with the liquid to be

bleached followed by filtration. Activated carbons were in general use during the first

three decades of the twentieth century for the purification of air and for recovering

solvents from vapour streams. Some activated carbons also have medical applications to

eliminate bacteria and other toxins, etc.

Dehumidification of moisture-laden air and dehydration of gases were, and still are,

done by adsorption using silica gel as an adsorbent. Naturally occurring and synthesized

silica-alumina minerals due to the micro porosity in their unique crystalline structures

have wide applications as excellent separating agents. Barrer (1978) extensively

researched and reviewed the adsorptive properties of these materials, referred to as

zeolites. Walker et al. (1966a, 1966b) thoroughly investigated the adsorptive properties

of microporous carbons and laid the foundation for the development of molecular sieve

carbons, which are less hydrophilic than zeolites and can therefore separate wet gaseous

streams effectively.

Adsorption is carried out by both batch and continuous flow equipments, the

important consideration for the design of which has been to ensure adequate contact

between the adsorbent and the fluid containing the component to be removed. To be

technically effective in a commercial separation process, an adsorbent material must

have high internal volume, accessible to the components being removed from the fluid

phase. The internal surface areas of adsorbents should be within the range of 100 m2/g

to over 3000 m2/g. The adsorbent must also have good mechanical properties such as

26

strength and resistance to attrition and it must have good kinetic properties, making it

capable of transferring, adsorbing molecules rapidly to the adsorption sites. In most

applications, the adsorbent must be regenerated after use and therefore it is desirable

that regeneration can be carried out efficiently and without damage to mechanical and

adsorptive properties.

2.1.3. The Adsorption Process

The accumulation of a substance over a solid surface is essentially due to the

attraction of adsorbate molecules to the adsorbent surface and this interaction between

adsorbate and adsorbent ultimately lead to a thermodynamic equilibrium between the

adsorbate and the adsorbent. At equilibrium conditions, the rates of adsorption and

desorption are equal and the net loading on the solid cannot increase further. The

adsorption system is devised in a way to ensure maximum contact between the

adsorbate and the solid adsorbent. The adsorption processes are carried out in any of the

following three ways:

a) Batch process,

b) Fixed bed process, or

c) Moving bed process.

(a) Batch process

In a batch process (Thomas and Crittenden, 1998), the adsorbent is allowed to move

and it moves relative to the walls of the containment vessel. This process involves the

mixing of a batch of adsorbent with a batch of liquid, most commonly a solution of the

adsorbate. The mixture is agitated for a predetermined time interval and the adsorbent is

separated from the liquid by sedimentation, filtration, etc., either for disposal or for

reuse. When sufficient time is allowed for equilibrium to be reached, the loading of the

adsorbate on the adsorbent surface will be related to the final concentration of the

adsorbate in the solution through an isotherm equation. Powdered or granular

adsorbents are usually added to the adsorption reactor in slurry form in a way to allow

adequate dispersion and mixing. The adsorbent can be removed as a settled sludge. In

case of large quantities of adsorbent, a multiple batch or cross-flow system may be

27

designed. After separation of the fluid from the adsorbent, the fluid is contacted with

another fresh batch of adsorbent. Each subsequent batch of adsorbent removes less and

less impurity as the concentration of the impurity in the fluid decreases.

(b) Fixed and moving bed processes

A fixed bed process represents a cyclic batch system in which the adsorbent bed is

saturated and regenerated in a periodic manner. Separations in fixed bed process are

conventionally carried out with the liquid moving through a stationary bed of adsorbent

particles. An alternative is the moving bed process in which both the liquid and the

adsorbent move in a counter current process. In moving bed mode, the liquid can be

recycled.

Vessels and columns, which hold the adsorbent in a fixed position, appear initially

to provide distinct advantages over their counterparts in which the adsorbent is allowed

to move. First, such equipment is simple and relatively inexpensive to fabricate.

Secondly, minimal attrition of adsorbent occurs when it remains fixed in position.

However, despite their simplicity, the fixed bed processes have the following

disadvantages (Thomas and Crittenden, 1998):

(i) In a fixed bed process, as the fluid is passed through the fixed adsorbent bed, the

transfer of adsorbate molecules from the feed fluid to the solid initially occurs at

the bed entrance. Once the adsorbent in this region becomes saturated with the

adsorbate molecules, the zone in which the active adsorption occurs, called the

mass transfer zone (MTZ), moves progressively through the bed towards the exit.

During the process, the adsorbent particles upstream to the MTZ, will be in

equilibrium with the adsorbate molecules and therefore cannot adsorb further

adsorbate molecules. On the other hand the adsorbent particles downstream to the

MTZ, will not have been in contact with any adsorbate molecules and therefore,

will also be unable to adsorb adsorbate molecules. Thus at any instant in time, the

adsorbent particles upstream or downstream to the MTZ do not participate in the

mass transfer processes.

(ii) When breakthrough of the adsorbate begins to occur, it is necessary to take the bed

off-line so that the adsorbate can be regenerated. Therefore, in order to have a

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continuous stream of product, it is necessary to have more than one bed of

adsorbent in the overall process. The regeneration time for the second bed must

not be longer than the time to reach breakthrough of the adsorbate during

adsorption in the first bed.

(iii) The main advantages of fixed bed systems are the simplicity of equipment needed

and they are relatively inexpensive to fabricate. Despite the apparent simplicity of

fixed beds, they are difficult to design accurately because the progress of the MTZ

introduces time into the design equations which brings complications in the

design. Although several short-cut design techniques exist, they can vary

considerably in their accuracy.

(iv) Adsorption is an exothermic process and therefore, desorption can be influenced

by raising the temperature of the system. In thermal regeneration processes, it is

difficult to heat and cool large beds of highly porous adsorbent materials quickly

because the heat transfer processes are not good due to poor heat transfer

characteristics of porous materials. Poor heat transfer usually leads to long heating

and cooling times, which thereby creates the need for large beds. Poor heat

transfer also results in a rise in the temperature of the bed in or near to the MTZ

due to the exothermic nature of the adsorption process.

Moving bed processes are much more efficient than fixed bed processes and the

main advantage associated with the moving bed processes is that the adsorbent can be

regenerated as soon as its role in the adsorption process is completed. Besides, heat

transfer in moving bed process is better than in fixed bed process.

However, the equipment required for a moving bed process is more complex and

hence it is more expensive than fixed bed process. In addition, the equipment will need

to be provided to cope with attrition of the adsorbent which will inevitably occur in

moving bed process. To gain the best advantages of both fixed bed and moving bed

processes, a single fixed bed could be operated in such a way that a continuous steady

state process can be simulated to overcome the technical challenges of designing

adsorbents.

A fixed bed adsorber usually consists of vertical, cylindrical vessels. While

horizontal vessels are occasionally used, vertical orientation is preferred to avoid the

29

creation of flow misdistribution when settling of a bed or movement of particles within

it occurs.

2.2. Basic theories of adsorption equilibrium

In adsorption, it is important to know (i) how the process has occurred, (ii) how

effective is the adsorbent for a particular adsorbate, (iii) whether the process is

thermodynamically favorable or not, (iv) how the rates are controlled (kinetics), etc.

Answers to these questions are provided by thermodynamics of the processes and the

adsorption isotherms. For this purpose, various computation models are applied to

obtain the values of various parameters which can be compared with the experimentally

determined values. If the two sets tally with each other, the theory developed can be

accepted as valid. A few of these studies are discussed below:

2.2.1. Adsorption kinetics and mechanisms

Kinetic study on sorption process is significant as it provides valuable information

about the reaction pathways and the mechanism of sorption interactions. Besides, it

describes the solute uptake rate which controls the residence time of sorbate at the

solid–solution interface. Therefore, it is important to predict the rate at which a pollutant

is removed from aqueous solutions for designing appropriate water treatment processes.

Any adsorption process can be divided into following three diffusion steps (Moreno-

Piraján et al., 2006):

Ø Transport of the solute from bulk solution to the exterior surface of the

liquid film surrounding the adsorbent particles.

Ø Diffusion of the solute across the film to the surface of the adsorbent

particles, and

Ø Diffusion from the surface of the solid particles into the pores where the

solute molecules/ions/atoms are adsorbed at the active sites.

The overall rate of the adsorption process is determined from the slowest of these

three steps. Step (ii) leads to surface adsorption and step (iii) leads to intra-particle

adsorption or pore adsorption. It is generally accepted that the actual rate-controlling

30

step is not the physical attachment of adsorbate to adsorbent surface but rather intra-

particle transport of the solute within the porous structure of the adsorbent to the

available surface. Many factors govern the rate of adsorption such as the initial

adsorbate concentration, adsorbent dose and turbulence state of the solution and under

some circumstances, inter particle transport from bulk solution to the external surface of

adsorbent may also have some effects on the overall rate of adsorption.

The important characteristics of the adsorbent that determine equilibrium capacity

(qe) and rate are

i) The surface area,

ii) The physico-chemical nature of the surface,

iii) The availability of that surface to adsorbate molecules or ions,

iv) The physical size and form of the adsorbent particles.

System parameters such as temperature and pH can also markedly influence adsorption

as they affect one or more of the above parameters.

Many attempts have been made to formulate a general expression describing the

kinetics of sorption on solid surfaces. This has led to the existence of a series of kinetic

equations that are used to model adsorbate transport onto adsorbent surfaces

(Auguastine et al., 2007). The rate law describing a sorption system should address the

requirements of the knowledge of all the molecular details of the interactions including

the energetics and the stereochemistry, inter atomic distances and angles throughout the

course of the reaction, and the individual molecular steps involved in the mechanism.

Several kinetic models are in use to explain the mechanism of the adsorption

processes. A few of these are discussed below:

(a) First order kinetics

Several kinetic models may be used to explain the mechanism of the adsorption

processes and amongst them the Lagergren model is the most useful and widely

accepted (Lagergren, 1898; Ho, 2003; Wan Nagah et al., 2004; Bhattacharyya and Sen

Gupta, 2006) to understand the mechanism of solute-sorbent interactions. When

adsorption preceded by diffusion through a boundary, the kinetics in most cases follows

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the pseudo first order rate equation of Lagergren (Annadurai et al., 2002; Ozacar and

Sengil, 2002). The Lagergren equation is given by,

dqt / dt = k1 (qe - qt) (2.2)

where qt and qe are the amount adsorbed at time t and at equilibrium, k1 (L/min) is the

rate constant of the pseudo first order adsorption process. The integrated rate law, after

applying the boundary conditions of qt = 0 at t = 0, is

log (qe - qt) = log qe – (k1 /2.303).t (2.3)

Plot of log (qe - qt) vs. t gives a straight line for first order kinetics, which allows

computation of the adsorption rate constant, k1.

The first order kinetics is considered to be valid when the values of qe obtained from

the intercept of the Lagergren plots and those from experiments are comparable.

However, the Lagergren plots, even being linear, do not necessarily assure a first order

mechanism (Ho and McKay, 1999a). This may be mainly due to the inherent

disadvantage of correctly estimating the values of qe. In most cases in the literature, the

pseudo-first order equation of Lagergren does not fit well for the whole range of contact

time and is generally applicable over the initial 20 to 30 minutes of the sorption process.

(b) Second order kinetics

If the qe values obtained from the intercept of the Lagergren plots show large

deviation from the experimental values of qe, it is necessary to test the kinetics

according to pseudo second order kinetics (Ho and McKay, 1999b). A second order rate

law expression demonstrates how the rate depends on the sorption capacity but not the

concentration of the sorbate (Ho and McKay, 1999b, 2000). The linear form of second

order kinetic equation is given by (Ho and McKay, 1999b)

t/qt = 1/h + (1/qe).t (2.4)

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where h = k2qe2 can be regarded as the initial adsorption rate as t → 0. The plot of t/qt

vs. t gives a linear relationship allowing computation of qe, k2 and h without having to

know any other parameter. The test of validity can again be administered by comparing

the experimental ‘qe’ value with that obtained from the second order plots.

The second-order rate expression was used to describe chemisorption involving

valence forces through the sharing or exchange of electrons between the adsorbent and

adsorbate as covalent forces, and ion exchange. In recent years, the second-order rate

expression has been widely applied to the adsorption of pollutants from aqueous

solutions. The advantage of using this model is that there is no need to know the

equilibrium capacity from the experiments, as it can be calculated from the model. In

addition, the initial adsorption rate can also be obtained from the model.

(c) Intra-particle diffusion model

Adsorption is a multi-step process which involves the transport of the solute

molecules from the aqueous phase to the surface of the adsorbent particles and then,

diffusion of the solute molecules into the interior of the pores – which is likely to be a

slow process and is therefore considered as rate determining step. Diffusion results from

a concentration gradient either in the fluid phase or on the solid phase (Satapathy and

Natarajan, 2006). When the intra-particle diffusion process controls the rate of

adsorption or when adsorption takes place inside the pores by a diffusion mechanism,

the intra particle diffusion model is applied and the intra-particle diffusion rate constant

(ki) is given by the equation (Weber and Morris, 1963):

qt = ki t 0.5

(2.5)

where, ki is the intra-particle diffusion rate coefficient. When this relation is valid, ki

values under different conditions are calculated from the slopes of the straight line

portion of the plot. One significant feature of the plot is that it has zero intercept.

2.2.2. Adsorption isotherm study

The accumulation of adsorbate molecules over the surface of a solid adsorbent is

mainly due to the attraction of adsorbate molecules to the adsorbent surface and the

33

adsorbate molecules form attachments with the adsorbent surface through physical or

chemical bonds. Physisorption of a gas or vapour which involves weak van der Waals

forces of interactions between adsorbate and adsorbent is normally accompanied by

decrease in enthalpy of 10 to 40 kJ mol-1

, but the adsorption enthalpy of a solute from a

liquid onto a solid surface is strongly dependent on the nature of the solid adsorbent.

In order to find out the applicability of newer adsorbents, it is essential to establish

the most appropriate adsorption equilibrium correlation (Srivastava et al., 2006) that

allows a reliable prediction of adsorption parameters and quantitative comparison of

adsorbent behavior for different adsorbent systems (or for varied experimental

conditions) (Ho et al., 2002; Gimbert et al., 2008). In this context, study of adsorption

isotherm is very fundamental and useful in describing the interactive behavior between

solute and adsorbent (Ofomaja et al., 2005; Ho, 2006). The isotherm is a mathematical

relationship between the amount adsorbed on the adsorbent surface and the pressure (in

case of gaseous adsorbate) or the concentration (in case of liquid) of the adsorbate in

equilibrium at a constant temperature. The study of adsorption isotherm generally yields

values for certain coefficients that quantitatively describe the adsorbate-adsorbent

interactions along with information about the adsorbent surface (Ofomaja et al., 2005)

and it provides the general idea about the effectiveness of the absorbent for a particular

adsorbate. A variety of isotherm equations have been in use, some of which have a

theoretical foundation and some being of mere empirical in nature. Many of these

equations are valid over small relative pressures or concentration changes but do not fit

experimental data when tested over the full range of relative pressures or

concentrations. In the present work, the following three commonly used isotherms have

been tested.

(i) Langmuir isotherm: In 1916, Irving Langmuir proposed an empirical isotherm for

gases adsorbed on solids, which is based on four hypotheses:

Ø The surface of the adsorbent is uniform, that is, all the adsorption sites have

equal energy and affinity for taking up adsorbate molecules.

Ø Adsorbed molecules do not interact with each other.

Ø The same mechanism applies to all adsorption interactions.

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Ø At the maximum adsorption, only a monolayer is formed, i.e. adsorbate

molecules do not accumulate on already adsorbed molecules, they adsorb

only on the free surface of the adsorbent.

However, all the four points are seldom true because there are always imperfections

on the surface, adsorbed molecules are not necessarily inert, the mechanism of

adsorption is clearly not the same from the very first molecule to the last and the

adsorbate molecules often deposit on other already adsorbed molecules to form

multilayer over the surface.

Langmuir isotherm has traditionally been used to quantify and contrast the

performance of different sorbents (Langmuir, 1916). The Langmuir isotherm assumes a

dynamic equilibrium between the adsorbate and the adsorbent. Since chemical bond

formation (ionic or covalent) between the surface of the adsorbent and the adsorbate

molecules or ions cannot be expected to go beyond a monolayer, Langmuir isotherm

was originally devised to describe chemisorption processes only.

The mathematical expression of Langmuir isotherm model is,

1/qe = (1/a) + (1/abCe) (2.6)

where Ce is the concentration of the adsorbate in liquid phase in equilibrium, ‘a’ is the

number of moles of solute adsorbed per unit weight of adsorbent in forming a

monolayer on the surface, commonly known as the Langmuir monolayer coverage, b is

a constant related to the equilibrium constant of adsorbate-adsorbent equilibrium. Plots

of 1/qe against 1/Ce yield the Langmuir isotherm and the slope and the intercept of the

plots could be utilized to find both ‘a’ and ‘b’.

In order to predict whether the adsorption process is favorable or unfavorable for the

Langmuir type of adsorption, Weber and Chakravorti (Weber and Chakravorti, 1974)

defined a dimensionless equilibrium coefficient, known as the separation factor (RL)

represented as;

RL = 1/ (1 + b.Co) (2.7)

35

where b (L/mg) refers to the Langmuir coefficient and C0 is the adsorbate initial

concentration (mg/L). For an adsorption system under study, the values of RL between 0

and 1 indicates favorable adsorption, while RL > 1 represents unfavorable adsorption,

RL = 1 linear adsorption and RL = 0 irreversible adsorption (Hall et al., 1966,

Karthikeyan et al., 2005).

(ii) Freundlich isotherm: Freundlich isotherm is one of the first empirical isotherms

suggested by Freundlich and Küster in 1894. Freundlich isotherm (Freundlich, 1906)

describes the non-ideal and reversible adsorption and is not restricted to the formation

of a monolayer. Freundlich isotherm is generally applicable to physico-chemical

adsorption on heterogeneous surfaces. The empirical equation given by Freundlich is:

qe = Kf . (Ce) 1/n

(2.8)

where qe is the amount adsorbed per unit mass in equilibrium, Ce is the concentration of

the adsorbate in equilibrium in the liquid phase and Kf and 1/n are Freundlich

coefficients. The linear form of the equation is given by:

log qe = (1/n) log Ce + log Kf (2.9)

A plot of log qe vs. log Ce gives a straight line, the slope gives the value of 1/n and the

intercept gives the value of Kf.

Kf is a parameter related to temperature and 1/n is a characteristic constant for the

adsorption system under study. The constants, Kf and 1/n, represent the adsorption

capacity and intensity of adsorption respectively. The numerical value of 1/n < 1

indicates favourable adsorption process and formation of relatively stronger bond

between adsorbate and adsorbent under study (Mehrotra et al., 1999). The numerical

value of 1/n varies between 0 and 1, and is a measure of adsorption intensity or surface

heterogeneity. When the value of 1/n gets closer to zero, then the surface becomes more

heterogeneous. A value of 1/n < 1 implies a chemisorption process whereas 1/n > 1 is

indicative of cooperative adsorption (Haghseresht and Lu, 1998). Since this isotherm

does not predict any saturation of the adsorbent by the adsorbate molecules, therefore a

36

infinite surface coverage is predicted mathematically which indicates multilayer

adsorption on the surface (Hasany et al., 2002).

(iii) Temkin isotherm: Temkin isotherm is one of the early isotherm models, which

was proposed to describe the adsorption of hydrogen onto platinum electrodes in acidic

solutions. The derivation of the Temkin isotherm is based on the assumption that the

heat of adsorption decreases linearly with coverage unlike a logarithmic decrease as in

case of Freundlich isotherm (Aharoni and Ungarish, 1977). The isotherm (Tempkin and

Pyzhev, 1940) contains a factor that explicitly takes into account the adsorbent-

adsorbate interactions. The expression for Temkin model is:

qe = (RT/bT) ln (AT Ce) (2.10)

The linearised form of this equation is:

qe = B lnAT + B lnCe (2.11)

where, B = RT/bT and is related to sorption enthalpy and AT is the Temkin coefficient

(mg/L). From the slope and intercept of the plot of qe vs. ln Ce, B and AT can be

calculated. As implied in the equation, its derivation is characterized by a uniform

distribution of binding energies.

2.2.3. Thermodynamics of adsorption

Adsorption is a surface phenomenon in which adsorbate molecules get attracted

towards the adsorbent surface and these interactions consist of molecular forces

embracing permanent dipole, induced dipole and quadrupole electrostatic effects,

otherwise known as van der Waals forces. Adsorption is essentially an exothermic

process and the heat evolved during adsorption of a solute from a liquid onto a solid

surface is strongly dependent on the source and the solid adsorbent. It is important to

estimate the strength of binding of a species to a solid surface. During adsorption, when

an isolated species approaches the surface of a solid, several interactions come into

37

play, each of which contributes to the heat or energy of physical adsorption (Thomas

and Thomas, 1997). In general, the interaction potential may be written as

U = Ud + Ur + Up + Ufd + Ufq + Usp (2.12)

where, Ud is the attractive (dispersion) potential, Ur the close-range repulsion term, Up

the polarization energy, Ufd the field-dipole interaction, Ufq the field-gradient–

quadrupole interaction, and Usp a self-potential, which takes into account adsorbate-

adsorbent interactions. The first three terms on the right hand side of the above equation

are always present, irrespective of the nature of the adsorbate and adsorbent. The next

two, Ufd and Ufq, depend upon the presence or absence of permanent dipoles or

quadrupoles respectively in the adsorbate; and Usp vanishes for small uptakes.

The important thermodynamic parameters viz. entropy (S), enthalpy (H) and Gibbs

energy (G) for the adsorption process can be obtained from the following two

fundamental relationships:

ΔG0 = ΔH

0 – TΔS

0 (2.13)

ΔG0 = – 2.303 RT log K (2.14)

where, ΔG0, ΔH

0 and

ΔS

0 represent standard Gibbs energy change, standard enthalpy

change and standard entropy change for the adsorption process respectively, and K is

the equilibrium constant for the adsorbate-adsorbent equilibrium. The classic van’t Hoff

equation is given by,

log (qe/Ce) = ΔS/ (2.303R) – ΔH/ (2.303 RT) (2.15)

where, the ratio qe/Ce is called the adsorption affinity. A plot of log (qe/Ce) vs. 1/T gives

straight lines and from the plots, Gibbs energy, enthalpy and entropy changes (ΔG, ΔH,

ΔS) for the adsorption process can be obtained using equations (2.14) and (2.15).

2.3. Column studies

The dynamic column adsorption method allows the solute solution to flow

continuously through a fixed bed packed with the adsorbent. The bed height, the rate of

38

flow and the concentration of the solute could be varied and column adsorption is

monitored by continuously measuring the concentration of the solute in the eluent with

time or volume flowing out of the column. The experiment normally aims at

determination of the breakthrough point at which the concentration of the solute in the

eluent becomes equal to the initial concentration and the adsorbent bed becomes

saturated with the solute.

At first, the adsorbent in the column is fresh with all its adsorption sites. As time

passes, some of the adsorption sites are used up and concentration in the effluent rises

with time. The efficiency of the column can be explained by means of the breakthrough

curves. A breakthrough curve is obtained by plotting column effluent concentration

versus volume treated or time of treatment (Moreno-Piraján et al., 2006). The shape of

the graph may vary considerably for different situations. However, in general an S-

shaped breakthrough curve is obtained. Breakthrough is deemed to have occurred at

some time tb, break point time, when the concentration of the adsorbate leaving the bed

increases to an arbitrarily defined value, Ce, break point concentration, which is often

the minimum detectable or maximum allowable concentration of the component to be

removed. In other words, the breakthrough point can be defined as the point at which

the effluent concentration increases rapidly (Nidheesh et al., 2012).

Breakthrough capacity, exhaustion capacity, degree of column utilization and mass

transfer zone (MTZ) are the important features of the breakthrough curves. The

breakthrough capacity is defined as the mass of sorbate removed by the sorbent bed at

break point concentration or break point time. The exhaustion capacity is defined as the

mass of the sorbate removed by unit weight of the sorbent at saturation point and the

degree of column utilization is defined as the mass sorbed at breakthrough point divided

by the mass sorbed at complete saturation. The mass transfer zone (MTZ) in a packed

bed system is defined as the zone of the packed column where the active adsorption

happens.

In packed-bed column, since the feed solution is introduced through the inlet of the

column, the solute is sorbed most rapidly and effectively by the upper few layers of the

fresh sorbent during the initial stages of the operations. The mass transfer zone,

represented by δ, is concentrated near the top or influent end of the column. As the

polluted feed water continues to flow into the column, the top layers of the sorbent

39

become practically saturated or in other words becomes exhausted with the incoming

solute and then the mass transfer zone starts moving downward to a region of fresher

sorbent in the column. When the MTZ moves across the adsorbent bed, it leaves behind

a section of adsorbent bed, which is completely exhausted, and in front of MTZ, there

exists only fresh adsorbent. The MTZ will continue to move through the packed bed

until it hits its breakthrough point, when a preset concentration of the adsorbate in the

effluent is reached. When breakthrough occurs the adsorbent will need to be replaced to

keep excessive concentrations of impurities out of the effluent.

Typical breakthrough curves are shown in Fig. 2.1 (Tchobanoglous et al., 2003,

Ahamad and Jawed, 2011) and Fig. 2.2 (Moreno-Piraján et al., 2006).

Fig. 2.1. Typical breakthrough curve for column study.

40

Fixed bed adsorption process has been found to be very useful and active with

existence of a large number of models. These models can be complex, requiring

extensive computation and needing thorough verification. For this purpose, the essential

requirements are (a) accurate and available fundamental data and (b) the number and

importance of the assumptions and approximations that have been made to arrive at the

data. For the simplest case, in which many simplified assumptions and approximations

are made, the solution may be analytical. The events occurring in the MTZ during

adsorption are,

Ø Transfer of adsorbate molecules from the bulk fluid to the solid surface

by convection or diffusion across the fluid film which is external to the

solid surface.

Ø The adsorbate penetrates the fluid film through surface diffusion

mechanisms, and adsorb onto the internal surface with release of the heat

of adsorption.

An additional complexity during sorption is that the flow through a packed bed may

not be uniform across its entire cross-sectional area. This may be due to channeling of

the fluid at the wall or because of temperature gradients created when the heat of

adsorption is released.

Fig. 2.2. The breakthrough curve and its characteristic parameters

41

Empirical or short-cut methods are used extensively for designing of fixed bed

columns. This is not only due to their simplicity and reliability but also because of the

formidable nature of the more rigorous alternatives. The various types of short-cut

methods available for designing fixed bed column are as follows (Thomas and Thomas,

1997),

(i) The length or weight of unused bed (LUB or WUB)

(ii) The mass transfer zone length (MTZL)

(iii) The empty bed contact time (EBCT)

(iv) The transfer unit approach (NTU and HTU)

(v) The bed depth service time (BDST)

(vi) The capacity at breakpoint

A few descriptive ideas about these short-cut methods are given below:

(i) Length of unused bed (LUB): Length of unused Bed (LUB) method was the first

short-cut method to design or scale-up of a fixed bed process. The concept of LUB,

which represents the distance that is not saturated at the breakthrough time (Moreno-

Piraján, et al., 2006), is used to design and scale-up of small-scale laboratory

experiments particularly for dilute single-component systems in which there is a

favorable isotherm.

In a fixed bed adsorption process, one side of the concentration front in the

adsorbent bed moves faster than the other side, causing a widening of the front. The

LUB method is based on the insertion of a hypothetical ideal stoichiometric front across

the actual mass transfer front so that areas A and B (as shown in Fig. 2.2) are

equivalent. The length of the bed behind the stoichiometric time point (t*) is called the

length equilibrium section (LES), which is the required length of the bed if the system is

ideal. The other section, called as the LUB, is an additional section of the bed that is

required to account for the spreading of the concentration front. The LUB depends only

on the adsorbate-adsorbent combination, the temperature and the fluid velocity. But

under constant pattern behaviour, it is independent of column length (Moreno-Piraján,

et al., 2006). The foundation of the scale-up process based on the fact that the LUB does

not vary with the overall length of the bed, since the slope of the curve does not vary.

42

Therefore, the LUB can be measured at the design velocity in small-scale laboratory

column packed with the selected adsorbent. The total length of the scaled-up adsorbent

bed required for a real system can be obtained by adding the LUB to LES i.e. the length

of bed needed to achieve the required stoichiometric capacity. The LUB method should

not be used for adsorbate-adsorbent system where isotherm is unfavorable and special

consideration should be taken if the isotherm is linear.

(ii) The mass transfer zone length (MTZL): The mass transfer zone (MTZ) method

using the linear driving force approximation is the most common and frequently used

technique for designing columns and the analysis of sorption kinetics from a fixed-bed

breakthrough curve. However, the sorption kinetics obtained from MTZ method

includes approximations and estimation of errors (Kawakita et al., 2013). In packed-

bed system due to the continuous sorption, the flow of contaminated fluid creates a

wave front as it flows through the packed sorbent bed. This wave front is known as the

mass transfer zone (MTZ) and within the MTZ of a packed bed, active adsorption

happens (Chiang and Hwang, 1989). The length of the MTZ is a function of the influent

flow rate and the rate of sorption. This means that any parameter that changes the rate of

adsorption will also change the length of the MTZ to some extent. The movement of the

MTZ through a packed bed can be graphically represented in what is called a

breakthrough curve. It is far preferable to obtain the MTZL from small-scale laboratory

experiments on the adsorbate-adsorbent system under consideration and with

temperatures and velocities. The main disadvantage of the MTZL method is that if a bed

length is obtained by adding together the equilibrium zone length and the MTZ length,

then more adsorbent will be installed than necessary because some adsorption actually

occurs in the mass transfer zone. A convenient equation to calculate the length of the

MTZ is,

Length of the MTZ = L (ts - tb)/ ts (2.16)

where, L is the length of the entire packed bed, tb and ts are the time required to reach

breakthrough point and complete exhaustion respectively.

43

(iii) The empty bed contact time (EBCT): EBCT method is generally used by the

water industry for designing large-scale columns. In this method, numbers of pilot scale

columns in series are used to obtain breakthrough curves with desired flow rates. Three

or more columns are usually used to represent different bed depths and different contact

times. The empty bed contact time (EBCT) is defined as,

EBCT = bed volume / flow rate.

(iv) Transfer unit approach (NTU and HTU): The method of transfer units is a newer

concept in the analysis of packed column and the results of this analysis are normally

expressed in transfer units. The transfer unit approach is more appropriate because the

changes in compositions of the liquid and vapour phases occur differentially in a packed

column rather than in stepwise fashion as in trayed column. In this method, required

packing height (z) or the length of the MTZ can be determined either based on the gas-

phase or the liquid-phase using the following equation;

z = N x H (2.17)

where, N is the number of transfer units (NTU) and H is the height of transfer units

(HTU), having dimension of length and is a measure of the separation effectiveness of

the particular packing for a particular separation process (Foust et al., 1980). NTU, the

number of transfer units is a measure of the difficulty of the separation. A transfer unit

usually gives the change of composition of one of the phases equal to the average

driving force producing the change (Foust et al., 1980).

(v) The bed depth service time (BDST): The BDST model is a simple model for

predicting the relationship between bed depth and service time in terms of concentration

(Han et al., 2009, Nidheesh et al., 2012). The BDST method, also known as the Bohart-

Adams model is based on the surface reaction theory (Goel et al., 2005; Nidheesh et al.,

2012) and it assumes that the adsorption rate is proportional to both the residual

adsorbent capacity (No) and the remaining adsorbent concentration (Muraleedharan et

al., 1994; Lehman et al., 2001). For predicting the performance of a column for

44

continuous adsorption, the Bohart–Adams model uses the following equation (Ghorai

and Pant, 2004):

tb = (No/Coʋ)[ D – (ʋ / kNo) ln (Co/Cb – 1)] (2.18)

where tb is the breakpoint time (min); Co the influent/inlet concentration (mg/L); Cb the

concentration at breakthrough (mg/L); No the initial adsorptive capacity of the adsorbent

(mg/g); D the bed depth of column (cm); ʋ the linear flow rate (cm/min); k the rate

coefficient (L/g/h). The critical bed depth of the column is the theoretical depth of

adsorbent that is just sufficient to prevent the effluent concentration from exceeding Cb

at zero time and is equal to the mass transfer zone length (MTZL). The critical bed

depth may be calculated by substituting tb = 0 into equation (2.18).

Dtheory or MTZL = (ʋ / kNo) ln (Co/Cb – 1) (2.19)

A simplified form of the Bohart–Adams Model is,

tb = aD + b (2.20)

where ‘a’ and ‘b’ are given by

a = No / (Coʋ) and b = - 1/(Cok) ln (Co/Cb – 1)

The two coefficients a and b for the BDST model are slope and intercept which can

be obtained from the plots of time against bed length (iso-removal lines) respectively.

The BDST equation describes how the mass transfer zone progresses through a single

fixed bed of adsorbent. For getting accurate results the required condition is that the

MTZ should move through the column at a constant rate and so a constant pattern of

MTZ, a constant feed concentration and a constant feed flow rate are required.

(vi) The capacity at breakpoint: The capacity at breakpoint can be defined as the mass

percent or fraction of adsorbate retained by an initially adsorbate-free bed up to the

breakpoint. This parameter does not vary appreciably with operating conditions other

than temperature and therefore it can be used for designing column study. As the

45

adsorbate solution passes through the column, the adsorption zone or MTZ starts

moving out of the column and the effluent concentration start rising with time. The time

taken for the effluent concentration to reach a specific breakthrough concentration of

interest is called the break though time. The breakthrough time (tb) for each of the

columns operation was defined as the time when the effluent concentration (Ce) reached

50% of the feed concentration (C0).

The approach of Treybal (1980) has been adopted for calculating the column

capacity for the removal of an adsorbate. Breakthrough capacity (at 50 % or Ce/C0 =

0.5) expressed in mg of the adsorbate adsorbed per gram of adsorbent is calculated

using the following relation:

Breakthrough capacity (at 50%) = [adsorbate adsorbed on adsorbent bed (mg)]

/ [mass of adsorbent in bed (g)]

= [breakthrough time (at 50 %) (h) x flow

rate (L/h) x feed concentration (mg/L)] /

[mass of adsorbent in bed (g)]

2.4. Desorption and regeneration of the adsorbent

Desorption is a process opposite to the state of sorption equilibrium between the

bulk phase (fluid phase) and the adsorbing solid surface. Desorption and regeneration

study in adsorption process is very important, because the success of an economical

adsorption system usually depends on the regenerability of the adsorbent. But exception

is found for those systems in where, there are very long adsorption or loading cycles due

to very low concentration of solute in the inlet feed; this type of system usually uses the

adsorbent only once on a “throw-away” basis and safe disposal is a key problem

(Sarma, 2004). In some applications it may be more economical to discard the adsorbent

after use. Disposal would be favoured when the adsorbent is of very low cost, and is

very difficult to regenerate due to strong chemical forces between adsorbent and

adsorbate, and the non-adsorbed component is the desired product of very high value. In

most of the adsorption systems, the disposal of adsorbents as waste is not an economic

46

option and therefore in such systems, regeneration of the adsorbent is carried out to an

extent, so that it can be reused.

Practical methods for desorption and regeneration includes one, or more, usually a

combination, of the followings:

Ø Increase in temperature,

Ø Reduction in partial pressure,

Ø Purging with an inert fluid,

Ø Reduction in concentration,

Ø Displacement with a more strongly adsorbing species,

Ø Change of chemical condition such as pH.

The most common methods for this purpose are changes in temperature (thermal

swing adsorption) and changes in pressure (pressure swing adsorption). From

thermodynamic point of view, a change in temperature is much more effective for

desorption and regeneration than a change in pressure. As the temperature increases,

desorption occurs, because the increase in temperature provides energy to break the

bonds between adsorbent and adsorbate.

Temperature, pH and solvent also play important role on desorption of the adsorbate

from the adsorbent and its regeneration. For example, Chern and Wu (2001) had

demonstrated the effects of temperature, pH and alcohol on desorption of dyes from

activated carbon beds. However, the final choice of desorption and regeneration

methods depends upon technical and economic considerations.