1 Mass Transfer

8/16/2019 1 Mass Transfer

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dvanced Mass Transfer

1-Fundamentals

Saeed GUL, Dr.Techn, M.Sc. Engg.

Associate Professor and Chairman

Department of Chemical Engineering,

University of Engineering & Technology Peshawar, PAKISTAN


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Introduction on of Mass Transfer

28 November 2015 Dr. Saeed GUL, Department of Chemical Engineering, UET Peshawar, Pakistan2

• The term mass transfer is used to denote the transference of acomponent in a mixture from a region where its concentration

is high to a region where the concentration is lower.

• Mass transfer process can take place in a gas or vapour or in a

liquid, and it can result from the random velocities of themolecules (molecular diffusion) or from the circulating or eddy

currents present in a turbulent fluid (eddy diffusion).

• Fractional distillation depends on differences in volatility, gas

absorption on differences in solubility of the gases in aselective absorbent and, similarly, liquid- liquid extraction is

based on the selectivity of an immiscible liquid solvent for one

of the constituents.


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Cont….


• The mass transfer rate dependent on both the driving force(concentration difference) and the mass transfer resistance.

Example:

• A simple example of a mass transfer process is that occurring in

a box consisting of two compartments, each containing adifferent gas, initially separated by an impermeable partition.

When the partition is removed the gases start to mix and the

mixing process continues at a constantly decreasing rate until

eventually (theoretically after the elapse of an infinite time) thewhole system acquires a uniform composition. The process is

one of molecular diffusion in which the mixing is attributable

solely to the random motion of the molecules.


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Mass Transfer in a Single Phase (Binary Diffusion)


• The rate of diffusion is governed by Fick's Law, first proposed by

Fick in 1855 which expresses the mass transfer rate as a linear

function of the molar concentration gradient.

• In a mixture of two gases A and B, assumed ideal, Fick's Law for

steady state diffusion may be written as:

• Where N A is the molar flux of A (moles per unit area per unit

time)• C A is the concentration of A (moles of A per unit volume),

• D AB is known as the diffusivity or diffusion coefficient for A in B,

and y is distance in the direction of transfer.


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The negative sign indicates that J is positive when movement is down

the gradient, i.e., the negative sign cancels the negative gradient

along the direction of positive flux.

Diffusion occurs in response to a

concentration gradient expressed as the

change in concentration due to a change in

position, . The local rule for movement or

flux J is given by Fick's law of diffusion:

in which the flux NA [cm-2

s-1

] is proportional to the diffusivity [cm2

/s]and the negative gradient of concentration, [cm-3 cm-1] or [cm-4].

Fick's law of diffusion



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• An equation of exactly the same form may be written for B:

• where DBA is the diffusivity of B in A.

• As for an ideal gas mixture, at constant pressure (C A + CB) = constant

so

• The condition for the pressure or molar concentration to

remain constant in such a system is that there should be no net

transference of molecules. The process is then referred to as

one of equimolecular counter diffusion



7/9728 November 2015 Dr. Saeed GUL, Department of Chemical Engineering, UET Peshawar, Pakistan7

• This relation is satisfied only if DBA = D AB

•

If circulating currents or eddies are present, then the molecularmechanism will be reinforced and the total mass transfer rate

may be written as:

• Whereas D is a physical property of the system and a function

only of its composition, pressure and temperature, ED, which is

known as the eddy diffusivity, is dependent on the flow pattern

and varies with position.




• As the pressure P increases, the molecules become closer

together and the mean free path is shorter and consequentlythe diffusivity is reduced, with D for a gas becoming

approximately inversely proportional to the pressure.

• When diffusion is occurring in the small pores of a catalyst

particle the effects of collision with the walls of the pores may

be important even at moderate pressures.

• Where the main resistance to diffusion arises from collisions ofmolecules with the walls, the process is referred to Knudsen

diffusion , with a Knudsen diffusivity DKn which is proportional

to the product uml, where l is a linear dimension of the

containing vessel.




• Each resistance to mass transfer is proportional to the

reciprocal of the appropriate diffusivity and thus, when both

molecular and Knudsen diffusion must be considered together,the effective diffusivity De is obtained by summing the

resistances as:

• In liquids, the effective mean path of the molecules is so smallthat the effects of Knudsen type diffusion need not be

considered.



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If A and B are ideal gases in a mixture, the ideal gas law is given by

• where n A and nB are the number of moles of A and B and n is

the total number of moles in a volume V, and P A , PB and P arethe respective partial pressures and the total pressure.

Mass Transfer in a Single Phase(Binary Diffusion in Gas Mixtures)

Properties of binary mixtures


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where C A and C B are mass concentrations and M A and MB molecular weights, and C A, C B , C T are, the molar concentrations of

A and B respectively, and the total molar concentration of the

mixture.

From Dalton's Law of partial pressures:




• where X A and X B are the mole fractions of A and B. Thus for asystem at constant pressure P and constant molar

concentration CT.

• The mass transfer rates N A and NB can be expressed in terms of

partial pressure gradients rather than concentration gradients.

Furthermore, NA and NB can be expressed in terms of gradients

of mole fraction.




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Equimolecular Counter Diffusion


When the mass transfer rates of the two components are equal

and opposite, the process is said to be one of equimolecular

counter diffusion.

In binary distillation applications in which the molar heats of

vaporization for species A and B are approximately equal, bothspecies are diffusing, but at equal rates in opposite directions.

Another example, consider diffusion that occurs in a tube

connecting two tanks containing a binary gas mixture of species

A and B. If both tanks as well as the connecting tube are at a

uniform pressure and temperature, the total molar

concentration would be uniform throughout the tanks and the

connecting tube.



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In the case of Equimolecular counter diffusion, the differentialforms of equation for N A may be simply integrated, for

constant temperature and pressure, to give respectively

Differential form Integrated form


Similar equations apply to NB which is equal to -NA, and suffixes

1 and 2 represent the values of quantities at positions y 1 and y 2

respectively.



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may be written as:

where hD = D/(y 2 — y 1 ) is a mass transfer coefficient with the

driving force expressed as a difference in molar concentration;its dimensions are those of velocity (LT -1 ).

may be written as:

Similarly:

where k'G = D/[RT(y 2 — y 1 ] is a mass transfer coefficient with the

driving force expressed as a difference in partial pressure. It

should be noted that its dimensions here, NM-1L-1T, are different

from those of hD



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may be written as:

where kx = DCT/(y

1 — y

2) is a mass transfer coefficient with the

driving force in the form of a difference in mole fraction. The

dimensions here are NL-2T-1

It is always important to use the form of mass transfer coefficient

corresponding to the appropriate driving force.

The mass transfer coefficient is a diffusion rate constant that

relates the mass transfer rate, and concentration gradient as

driving force



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Mass Transfer in a Single Phase

(Binary Diffusion in Gas Mixtures)

Mass transfer through a stationary second component

(Stefan’s diffusion)

In several important processes, one component in a gaseous

mixture will be transported relative to a fixed plane, such as a

liquid interface, and the other will undergo no net movement.

In gas absorption a soluble gas A is transferred to the liquid

surface where it dissolves, whereas the insoluble gas B

undergoes no net movement with respect to the interface.

In evaporation from a free surface, the vapour moves away

from the surface but the air has no net movement.

The mass transfer process therefore differs from equimolecular

counter diffusion and called Stefan’s diffusion



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Mass transfer through a

stationary gas B

For the absorption of a soluble gasA from a mixture with an insoluble

gas B, the respective diffusion rates

are given by:

Since the total mass transfer rate of B is zero, there must be a"bulk flow" of the system towards the liquid surface exactly to

counterbalance the diffusional flux away from the surface, as

shown in Figure where:


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(Stefan’s diffusion) The corresponding bulk flow of A must be CA/CB times that of B,

since bulk flow implies that the gas moves en masse.

Thus:

Therefore the total flux of A, N' A , is given by:

The above equation is known as Stefan's Law.

Thus the bulk flow enhances the mass transfer rate by a factor

CT/CB, known as the drift factor

f l h


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Fluxes of components of a gas mixture

f l h


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As:

On integration:

By definition, C Bm , the logarithmic mean of C B1 and C B2 is given by:

Thus, substituting for In (CB2/CB1) :


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In terms of partial pressures:

Similarly, in terms of mole fractions:

This can be simplified when the concentration

of the diffusing component A is small.

Under these conditions C A is small compared with C T , and the

equation becomes:

M T f i Si l Ph


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For small values of C A , C T — C Ai Ξ C T and only the first term in the

series is significant

The above equation is identical to equation for equimolecular

counterdiffusion, Thus, the effects of bulk flow can be

neglected at low concentrations

M T f i Si l Ph


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The above equation can be written in terms of a mass transfer

coefficient hD to give:

Where

Similarly, working in terms of partial pressure difference as the

driving force, the equation can be written:

Where

M T f i Si l Ph


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Using mole fractions as the driving force, the equation becomes:


It may be noted that all the transfer coefficients here are greater

than those for equimolecular counter diffusion by the factor

(CT/CBm)(= P/PBm ), which is an integrated form of the drift factor.

When the concentration C A of the gas being transferred is low,

C T /C Bm then approaches unity and the two sets of coefficients

become identical.

Where

M T f i Si l Ph


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Ammonia gas is diffusing at a constant rate through a layer of

stagnant air 1 mm thick. Conditions are such that the gas

contains 50 per cent by volume ammonia at one boundary ofthe stagnant layer. The ammonia diffusing to the other

boundary is quickly absorbed and the concentration is negligible

at that plane. The temperature is 295 K and the pressure

atmospheric, and under these conditions the diffusivity ofammonia in air is 1.8 x 10-5 m2/s. Estimate the rate of diffusion

of ammonia through the layer.


Example 10.1

M T f i Si l Ph


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If the subscripts 1 and 2 refer to the two sides of the stagnant

layer and the subscripts A and B refer to ammonia and air

respectively, then the rate of diffusion through a stagnant layer is

given by:

Solution:

In this case, x = 0.001 m, D = 1.8 x 10-5 m2 /s, R = 8314 J/kmol K,

T = 295 K and P = 101.3 kN/m2 and hence:



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Thus, substituting in equation




gives:



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Mass transfer velocities



It is convenient to express mass transfer rates in terms ofvelocities for the species under consideration where:

which, in the S.I system, has the units

(kmol/m2s)/(kmol/m3) = m/s.

For diffusion according to Fick's Law:

Since NB = -NA, then:

and

As a result of the diffusional process, there is no net overall

molecular flux arising from diffusion in a binary mixture, the two

components being transferred at equal and opposite rates.



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If the physical constraints placed upon the system result in a bulk

flow, the velocities of the molecular species relative to one

another remain the same, but in order to obtain the velocity

relative to a fixed point in the equipment, it is necessary to add

the bulk flow velocity.

The flux of A has been given as Stefan's Law



Mass transfer velocities



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Whatever the physical constraints placed on the system, thediffusional process causes the two components to be

transferred at equal and opposite rates and the values of the

diffusional velocities UDA and UDB are always applicable.

It is the bulk flow velocity uF which changes with imposed

conditions and which gives rise to differences in overall mass

transfer rates.

In equimolecular counterdiffusipn, uF is zero,

In the absorption of a soluble gas A from a mixture the bulk

velocity must be equal and opposite to the diffusional velocity

of B as this latter component undergoes no net transfer.

General case for gas-phase mass transfer in a binary mixture





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28 November 2015 Dr. Saeed GUL, Department of Chemical Engineering, UET Peshawar, Pakistan 33



In genera], for any component:Total transfer = Transfer by diffusion + Transfer by bulk flow


For component A:

Total transfer (moles/area time) = N'A

Diffusional transfer according to Fick's Law

Transfer by bulk flow

Thus for A:

and for B:



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28 November 2015Dr. Saeed GUL, Department of Chemical Engineering, UET Peshawar, Pakistan

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Substituting:

Similarly for B:

For equimolecular counterdiffusion N’A = N’B and equation 3

above reduces to Fick's Law. For a system in which B undergoes

no net transfer, N’ B = 0 and equation 3 is identical to Stefan's

Law



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For the general case: fN' A = -N' B

If in a distillation column, for example the molar latent heat of

A is f times that of B, the condensation of 1 mole of A (taken

as the less volatile component) will result in the vaporization

of f moles of B and the mass transfer rate of B will be f timesthat of A in the opposite direction

Substituting into equation ( )

becomes:

Thus:



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If x A changes from x Al to X A2 as y goes from y 1 to y 2

then:

Thus:

Or:






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Diffusion as a mass flux

Fick's Law of diffusion is normally expressed in molar units or:

where X A is the mole fraction of component A.

The corresponding equation for component B indicates that

there is an equal and opposite molar flux of that component. If

each side of equation is multiplied by the molecular weight of A,

M A , then:

where J A is a flux in mass per unit area and unit time (kg/m2 s in

S.I units), and C A is a concentration in mass terms, (kg/m3 )





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Similarly, for component B:

Although the sum of the molar concentrations is constant in an

ideal gas at constant pressure, the sum of the mass concentrations

is not constant, and dc A /dy and dcB /dy are not equal and

opposite,

Thus, the diffusional process does not give rise to equal and

opposite mass fluxes.

Or:

and:

Thus:

Diffusion as a mass flux



Q i # 1


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Quiz # 1


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Ammonia is absorbed in water from a mixture with air

using a column operating at 1 bar and 295 K. Theresistance to transfer may be regarded as lying entirely

within the gas phase. At a point in the column, the partial

pressure of the ammonia is 7.0 kN/m2. The back pressure

at the water interface is negligible and the resistance totransfer may be regarded as lying in a stationary gas film

1 mm thick. If the diffusivity of ammonia in air is 236 x

10-5 m2/s, what is the transfer rate per unit area at that

point in the column? How would the rate of transfer be

affected if the ammonia air mixture were compressed to

double the pressure?



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(Diffusion in Liquids)

The diffusion of solution in a liquid is governed by the sameequations as for the gas phase.

The diffusion coefficient D is about two orders of magnitude

smaller for a liquid than for a gas.

The diffusion coefficient is a much more complex function of

the molecular properties.

For an ideal gas, the total molar concentration C T is constant

at a given total pressure P and temperature T.

This approximation holds quite well for real gases and

vapors, except at high pressures.



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For a mixture of ethanol and water for example, the massdensity will range from about 790 to 1000 kg/m3 whereas the

molar density will range from about 17 to 56 kmol/m3.

For this reason the diffusion equations are frequently written

in the form of a mass flux J A (mass/area x time) and theconcentration gradients in terms of mass concentrations, such

as c A .

Thus, for component A, the mass flux is given by:


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where ρ is mass density (now taken as constant), and ω A is the

mass fraction of A in the liquid.





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For component B:

Thus, the diffusional process in a liquid gives rise to a situation

where the components are being transferred at approximately

equal and opposite mass (rather than molar) rates.

Liquid phase diffusivities are strongly dependent on theconcentration of the diffusing component which is in strong

contrast to gas phase diffusivities which are substantially

independent of concentration.





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Values of liquid phase diffusivities which are normally quoted

apply to very dilute concentrations of the diffusingcomponent, the only condition under which analytical

solutions can be produced for the diffusion equations.

For this reason, only dilute solutions are considered here, and

in these circumstances no serious error is involved in usingFick's law expressed in molar units.

The molar flux is given by:

where D is now the liquid phase diffusivity and C A is the molarconcentration in the liquid phase.

D/(y 2— y 1 ) is the liquid phase mass transfer coefficient.



On integration:

M T f Ph B d


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Mass Transfer across a Phase Boundary

In many important applications of mass transfer, material is

transferred across a phase boundary

In distillation a vapor and liquid are brought into contact inthe fractionating column

In gas absorption, the soluble gas diffuses to the surface,

dissolves in the liquid, and then passes into the bulk of theliquid

In liquid -liquid extraction however, a solute is transferredfrom one liquid solvent to another across a phase boundary

These processes is characterized by a transference of materialacross an interface.

• Because no material accumulates there, the rate of transferon each side of the interface must be the same


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M T f Ph B d


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• The mass transfer rate between two fluid phases depend on

the physical properties of the two phases, the concentrationdifference, the interfacial area, and the degree of turbulence.

• Mass transfer equipment is therefore designed to give a large

area of contact between the phases and to promote

turbulence in each of the fluids.

• In most industrial equipment, the flow pattern is so complex

that it is not capable of expression in mathematical terms, and

the interfacial area is not known precisely• A number of mechanisms (models) have been suggested to

represent conditions in the region of the phase boundary


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M T f Ph B d


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Theoretical models have been developed to describe mass

transfer between a fluid and an interface

The two-film theory

The Penetration Theory

Surface Renewal Theory


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Models for Mass Transfer at a Fluid-fluid Interface




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Mass Transfer across a Phase BoundaryModels for Mass Transfer at a Fluid-fluid Interface

The two-film theory

The two-film theory of WHITMAN was the first serious attemptto represent conditions occurring when material is transferred

from one fluid stream to another

Although it does not closely reproduce the conditions in most

practical equipment, the theory gives expressions which can beapplied to the experimental data which are generally available,

and for that reason it is still extensively used.

In this approach, it is assumed that turbulence dies out at the

interface and that a laminar layer exists in each of the two fluids.Outside the laminar layer, turbulent eddies supplement the

action caused by the random movement of the molecules, and

the resistance to transfer becomes progressively smaller.



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The two-film theory


For equimolecular counterdiffusion the concentration gradient istherefore linear close to the interface, and gradually becomes

less at greater distances as shown in Figure by the full lines ABC

and DEF

AGC and DHFindicate the

hypothetical

concentration

distributions

L1 and L2:

thicknesses of

the two films



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The two-film theory

Integrated form of Fick’s law

Can be written in terms of

two film theory

Because material does not accumulate at

the interface, the two rates of transfer

must be the same and:

Equilibrium is assumed to exist at the interface and therefore therelative positions of the points C and D are determined by the

equilibrium relation between the phases.



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The penetration theory was propounded in 1935 by HlGBlE He was investigating whether or not a resistance to transfer

existed at the interface when a pure gas was absorbed in aliquid.

In his experiments, a slug-like bubble of carbon dioxide wasallowed rise through a vertical column of water in a 3 mmdiameter glass tube.

As the bubble rose, the displaced liquid ran back as a thin filmbetween the bubble and the tube,

Higbie assumed that each element of surface in this liquid wasexposed to the gas for the time taken for the gas bubble topass it; that is for the time given by the quotient of the bubblelength and its velocity.


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It was further supposed

that during this short

period, which varied

between 0.01 and 0.1 s

in the experiments,

absorption took place as

the result of unsteady

state molecular diffusion

into the liquid, and, for Penetration of solute into a solventthe purposes of calculation, the liquid was regarded as infinite

in depth because the time of exposure was so short.



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• Dankwerts surface renewal theory (1951), represents an

extansion to penetration theory.

• Higbie always presupposed that the contact time between the

phases was the same at all positions in the apparatus.

• Dankwerts went on to suggest that fluid elements which

come into contact with each other, have different residence

times which can be described by a residence time spectrum.

• One has to imagine that mass exchange between two

different materials in the fluid phase takes place in individual

fluid cells.


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Regular Surface Renewal Theory



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• After a certain amount of time an element can be dislodged

from the contact area and be replaced by another one.

• It has been successfully applied in the absorption of gases

from agitated liquids.

• However the fraction of time for surface renewal is equally as

unknown as the contact time in penetration theory, so both

theories are useful for the understanding of mass transfer

processes, often neither is applicable for the calculation of thequantities involved in mass transfer


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yModels for Mass Transfer at a Fluid-fluid Interface

Regular Surface Renewal Theory

Phase Equilibria


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A limit to mass transfer is reached if the two phases come to

equilibrium and the net transfer of material ceases.

For a practical process, which must have a reasonable

production rate, equilibrium must be avoided, as the rate of

mass transfer at any point is proportional to the driving force,

which is the departure from equilibrium at that point.

To evaluate driving forces, a knowledge of equilibria between

phases is therefore of basic importance.

Several kinds of equilibria are important in mass transfer.

In nearly all situations two phases are involved, and all

combinations are found except two solid phases.


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Phase Equilibria

Phase Equilibria


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Phase Equilibria


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More specifically, there are three important criteria for differentphases to be in equilibrium with each other:

The temperature of the two phases is the same at

equilibrium.

The partial pressure of every component in the two phases isthe same at equilibrium.

The Gibbs free energy' of every component in the two phases

is the same at equilibrium.

Single Component Phase Equilibrium


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Single-Component Phase Equilibrium

If there is only a single component in a mixture, there is only asingle possible temperature (at a given pressure) for which phaseequilibrium is possible.

For example, water at standard pressure (1 atm) can only remain inequilibrium at 100°C.

Below this temperature, all of the water condenses, and above it,all of the water vaporizes into steam.

At a given temperature, the unique atmospheric pressure at which apure liquid boils is called its vapor pressure.

If the atmospheric pressure is higher than the vapor pressure, theliquid will not boil.

Vapor pressure is strongly temperature-dependent. Water at 100°C

has a vapor pressure of 1 atmosphere, which explains why water onEarth (which has an atmosphere of about 1 atm) boils at 100°C.Water at a temperature of 20°C(a typical room temperature) willonly boil at pressures under 0.023 atm, which is its vapor pressureat that temperature.


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Multiple-Component Phase Equilibrium:


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p p qPhase Diagrams

In general, chemical engineers are not dealing with single

components; instead they deal with equilibrium of mixtures. When a mixture begins to boil, the vapor does not, in general,

have the same composition as the liquid. Instead, the substance

with the lower boiling temperature (or higher vapor pressure)

will have a vapor concentration higher than that with the higherboiling temperature, though both will be present in the vapor.

A similar argument applies when a vapor mixture condenses.

The concentrations of the vapor and liquid when the overall

concentration and one of the temperature or pressure are fixed

can easily be read off of a phase diagram.

In order to read and understand a phase diagram, it is necessary

to understand the concepts of bubble point and dew point for a

mixture.


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Bubble Point and Dew Point


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Bubble Point and Dew Point


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To predict the phase behavior of a mixture, the limits of phase

changes should be examine, and then utilize the laws ofthermodynamics to determine what happens in between those

limits. The limits in the case of gas-liquid phase changes are called

the bubble point and the dew point.

The bubble point is the point at which the first drop of a liquidmixture begins to vaporize.

The dew point is the point at which the first drop of a gaseous

mixture begins to condense.

If you are able to plot both the bubble and the dew points on the

same graph, you come up with what is called a Pxy or a Txy

diagram, depending on whether it is graphed at constant

temperature or constant pressure.

Pxy Diagram


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Pxy Diagram


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what causes a liquidto vaporize?

Increasing the temperature

Decreasing the pressure

the two lines intersect at two

ends These intersections are

the pure-component vapor

pressures

Pxy Diagram

http://upload.wikimedia.org/wikibooks/en/3/3f/Benztol_pxy_diagram.PNGhttp://upload.wikimedia.org/wikibooks/en/3/3f/Benztol_pxy_diagram.PNGhttp://upload.wikimedia.org/wikibooks/en/3/3f/Benztol_pxy_diagram.PNGhttp://upload.wikimedia.org/wikibooks/en/3/3f/Benztol_pxy_diagram.PNG


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Composition of each component in a 2-phase mixture,


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overall composition and the

vapor pressure.

start on the x-axis at the

overall composition

go up to the pressure

Then from this point, go

left until you reach the

bubble-point

go to the right until reach

the dew-point curve to find

the vapor composition

Txy Diagram

http://en.wikibooks.org/wiki/File:Benztol_phase_calc_example.PNGhttp://en.wikibooks.org/wiki/File:Benztol_phase_calc_example.PNG


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Txy Diagram


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Txy Diagram


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Txy Diagram


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VLE phase diagram summary


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VLE phase diagram summary

You can use it to tell you what phase(s) you are in at a given

composition, temperature, and/or pressure.

You can use it to tell you what the composition of each phase

will be, if you're in a multiphase region.

You can use it to tell you how much of the original solution is

in each phase, if you're in a multiphase region.

You can use it to gather some properties of the pure materials

from the endpoints (though these are usually the best-known

of all the mixture properties).


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To summarize, here's the information you can directly garner

from a phase diagram. Many of these can be used for all types of phase diagrams, not just VLE.


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Qualitative Analysis of Concentration Profiles

d f


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and Mass Transfer



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hypothetical concentration profiles near a gas –liquid interface

Mass transfer can only occur along a negative concentration gradient

Here the concentrations in both

the gas and liquid phase diminish

in the positive direction, causing

solute to transfer from the gas tothe liquid phase.

The fact that the interfacial liquid

mole fraction is higher than the

gas concentration is no

impediment.

It is merely an indication of high

gas solubility, a perfectly normal

and acceptable phenomenon.

Case:-1


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The gas-phase concentration hereincreases in the positive direction

so that no transfer of solute from

gas to liquid can take place.

Neither can there be any transfer in

the opposite sense, because the

liquid concentration rises in the

negative direction.

Such profiles arise only in cases

when solute is generated bychemical reaction at the gas –

liquid interface. The product

solute then diffuses from the

interface into the bulk fluids.

Case:- 2


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This case involves decreasing

concentrations in both phases,

but the decrease is in the

negative direction.

Solute will therefore desorb fromthe liquid into the gas phase.

Gas solubility is low because

the interfacial concentrations

are nearly identical.

Case:- 3


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Case 4:The flat liquid-phaseprofile indicates that the liquid

phase is well

stirred and shows no mass

transfer resistance. Because the

gas phase concentrationdiminishes in the negative

direction, the transfer will be

from

liquid to gas.


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Case 5:What was stated for Case 4

applies here as well, but the transferthis time is from the gas. This follows

from the fact that gas-phase

concentration decreases in the positive

direction.

The question is now asked whether theresults would still be the same if

the gas-phase profiles had in each case

been located above the liquid-phase

counterparts. The answer is yes; transfer

would still take place as indicated

before. The only change would be in the

equilibrium solubility of the gas,

which would now be lower than before.


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Date post:	05-Jul-2018
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