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MASS TRANSFER

ECH 3105Dr. Siti Aslina Hussain

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FUNDAMENTALS OFMASS TRANSFER

Objectives:

1. Able to relate mass transfer with chemicalengineers

2. Able to define mass transfer operations

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DIFFUSION AND MASSTRANSFER

Objectives:

1.To define the mass/molar-averagevelocity, mass flux and diffusion flux

2.To calculate the mass flux

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DIFFUSION1. Diffusion only occurs in mixtures.2. The description of diffusion involves a mathematical model based on

a fundamental hypothesis or law.3. Ficks law of diffusion (fundamental): uses a diffusion coefficient

(D). Allows prediction of concentration as a function of space and

time.4. At which a component is then transferred from one phase to the

other depends upon a so-called mass transfer, or rate, coefficientand upon the degree of departure of the system from equilibrium.The transfer stops when equilibrium is attained.

5. Mass transfer coefficient-based law: involves a mass transfercoefficient (k) as a type of reversible rate constant. It produces

relations developed explicitly in chemical engineering . Allowsprediction of concentration as a function of space only.6. Mass transfer coefficient-based relations are commonly used in

convective mass transfer where the rate k is determined fromempirical correlations.

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MOLECULAR MASS TRANSFER(Molecular Diffusion)

1. Molecular diffusion the movement of individual moleculesthrough a substance by virtue of their thermal energy.

2. Simplified kinetic theory - a molecule is imagined to travel in astraight line at a uniform velocity until it collides with anothermolecule: velocity changes both in magnitude and direction alsotemperature.

3. The molecule thus travels a highly zigzag path, net distance in onedirection which is moves in a given time, the rate of diffusion,

being only small fraction of the length of its actual path - diffusionrate very slow.4. The phenomena of molecular diffusion ultimately leads to a

completely uniform concentration of substance throughout asolution which may initially have been uniform.

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5. The laws of mass transfer show the relation between the flux of thediffusing substance and the concentration gradient responsible forthis mass transfer.

6. It is often desired to know the diffusion rate of a specific componentmay possess a different mobility, the mixture velocity must beevaluated by averaging the velocities of all components present.

Concentration (case 1 & case 2) Velocities and Fluxes (case 3) Maxwell-Stefan Relations Ficks First Law Binary Mixture

7. Rates known as molar flux or mol/(area)(time)8. 2 fluxes to describe the motion of one constitute : the flux relative to

a fixed location in space (N) and the flux of a constituent relative tothe average molar velocity of all constituents (J).

*Additional notes: Equations in transparency

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CASE 1 :

A gas containing 88% (by volume) CH4, 4%C2H2,5% n-C3H8 and 3% n-C4H10 at 300K and 500kPa

will be scrubbed by contact with a nonvolatile oil

in a gas absorber. The objective of thehydrocarbons in the feed (see Figure) Calculate:

a) A total molar concentration in the gas feed;

b) Density of the gas;

c) Composition of the gas feed, expressed in termsof mass transfer.

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CASE 2 :In the manufacture of potassium nitrate,potassium chloride reacts with a hot aqueoussolution of sodium nitrate according to:

KCI+NaNO3 KNO3+NaClThe reaction mixture is cooled down to 293K andpure KNO3 crystals and an aqueous solution of

both KNO3 and NaCl (see Figure). The equilibriumsolubility of KNO3 in water at 293K is 24% (by

weight), the density of the saturated solution is

1,162kg/m3. Calculate:a) Total molar density of the fresh wash solution;

b) Composition of the fresh wash solution , expressedin terms of molar fractions.

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1. The basic empirical relation to estimate the rate of moleculardiffusion- Ficks First Law: quantifies the diffusion ofcomponent A in an isothermal, isobaric system.

2. Ficks Law- a species can have a velocity relative to the massor molar average velocity known as diffusion velocity only ifgradients in the concentration exist.

3. Multicomponent-normally move at different velocities,requires the averaging of the velocities of each componentpresent.

4. The mass-average velocity is defined in terms of the massdensities.

5. The molar-average velocity is defined in terms of a molarconcentrations of all components.

FLUXES & VELOCITIES

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6. Diffusion rates are most conveniently described in terms offluxes.

7. The mass or molar flux of a component is a vector quantitydenoting the amount of the particular component in eithermass or molar units.

8. Either: mass or molar units that passes per given unit timethrough a unit area normal to the vector.

9. Flux may be defined with reference to coordinates that arefixed in space, coordinates which are moving with the massaverage velocity or coordinates which are moving with the

molar average velocity.

*Additional notes: Equations in transparency

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Diffusion coefficient forbinary ideal gas systems

1. Maxwell Stefans (MS) correlation

2. Ficks correlation

3. Lennard-Joness correlation4. Wilke Lees correlation

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Diffusion coefficient forbinary liquid systems

1. Wilke and Changs correlation

2. Hayduk and Minhass correlation

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Summary: The diffusivity or diffusion coefficient, of aconstituent A in solution in which is a measure of its diffusivemobility, is then defined as the ratio of its flux to itsconcentration gradient which is Ficks Law written for the zdirection.

Negative sign: diffusion occurs in the direction of a drop inconcentration.

Diffusivity is a characteristics of a constituent and its

environment.

z

xcD

z

cDJ

A

AB

A

ABA

x

x!

x

x!

ABD

B

AJ

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If the direction to the right is taken as positive, theflux of relative to the fixed position has beenpositive and the .

Rate out-rate in+ rate of accumulation = rate ofgeneration

*Additional notes: Equations in transparency

AN A

P

NNN BA !

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STEADY STATE MOLECULAR DIFFUSION IN FLUIDS AT REST ANDIN LAMINAR FLOW

1. Molar flux and the equation of continuity2. Steady state molecular diffusion in gases1. Molecular diffusion in gases

1. Steady state diffusion of A through nondiffusing B2. Equimolal counterdiffusion3. Multicomponent mixture

2. Diffusivity of gases

3. Steady state molecular diffusion in liquids1. Molecular diffusion in liquids2. Diffusivity of liquids

*Additional notes: Equations in transparency

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Summary Main Point:1. Mass transfer refers to the movement of a component in a

mixture between regions of different composition. The maingoal of separations is to drive the process of mass transfers tocreate sharp concentration gradients.

2. The mechanisms for mass transfer include: moleculardiffusion, eddy diffusion and bulk flow.

3. Molecular diffusion occurs because of several driving forces,including; concentration gradients, pressure, temperatureand external fields.

4. Concentration gradients are the most important cause of

molecular diffusion. This mechanism is described by FicksFirst law: . This states that the flux of species due to moleculardiffusion is proportional to the negative of the concentrationsgradient, with a proportionality constant of the diffusivity ofthe species.