CE20095 - Mass Transfer Models Flashcards
How is convective diffusion found?
Na = -DdCa/dz + vCa
Where v = (Na + Nb) / Ctot
Convective diffusion considers bulk movement of particles (via convection) as well as random diffusivity motion
What occurs in equimolar counter diffusion?
N a = - N b
What is diffusion and convection?
Diffusion – mass transfer of individual molecules by random molecular motion and associated with a driving force such as a concentration gradient.
Example: dissolving sugar in water
Convection – is the collective motion of particles in a fluid
Example: Flow of fluid in a pipe
- Convection also includes diffusion and that is why we use the term convective diffusion
How is convective mass transport calculated?
N = v*C
Mass flux of comp. A = fluid velocity * conc A
What occurs in diffusion in stagnant components?
N.B = 0
How can the equation for convective diffusion be simplified when considering equimolar diffusion?
N.A = D/RT * ((PA1 - PA2)/ z2 - z1))
! Derive
How is the equation for stagnant diffusion simplified for stagnant diffusion?
N.A = D/RT * PT/(z2-z1) * ln ((PT - PA2 / PT - PA1 ))
! Derive
What are the three main mass transfer models, used to represent conditions near a boundary?
Two film theory
Penetration theory (Higbie)
Surface renewal theory (Higbie-Danckwerts)
What’s the (Two-) film theory?
A model to represent conditions near the boundary.
Basic concept – the resistance to diffusion can be considered equivalent to that in hypothetical film of a certain thickness.
It postulates that near the interface there exists a laminar film . This laminar film is hypothetical since we really don’t know the details of the velocity profile near the interface.
How does film theory take place?
Basic concept – the resistance to diffusion can be considered equivalent to that in hypothetical film of a certain thickness.
Mass transfer occurs by molecular diffusion through a fluid layer at phase boundary
- The theory assumes that for equimolar counter diffusion (EMCD) there is no turbulence at the interface, and a laminar layer exists in two films.
- In reality, the concentration gradient is linear close to the interface, and becomes less as one moves away from it.
It assumes that the resistance to mass transfer lies in 2 layers (one either side of the interface).
Inside these layers, the model assumes that the concentration gradient is linear; the thickness of the films are shown by Zg and ZL.
- It is assumed that equilibrium exists at the interface and therefore the relative position of points are determined by the equilibrium between the two phases (hence the ‘jump’ from point a to b).
How is the rate of mass transfer per unit area in terms of the two-film theory for EMCD given?
From liquid film:
N(A.l) = (D.l/z.l)*(C.Ai - C.A)
= k.l * (C.Ai - C.A)
Where k.l is liquid film mass transfer coefficient
From gas film:
N(A.g) = (D.g/Z.g*RT) * (P.A - P.Ai)
= k.g(P.A - P.Ai)
Where k.g is gas film mass transfer coefficient
k.l/k.g = (P.A - P.Ai) / (C.Ai - CA)
It’s assumed there is no accumulation.
What’s Henry’s law?
P.A = H * C.A
Where H is Henry’s constant
What does the penetration theory suggest?
It’s a model to represent conditions near the boundary.
It assumes that eddies bring an element of the fluid (e.g. liquid) to the interface, the fluid is exposed to the second phase (e.g. gas) for a set time interval; after this time interval the surface element (liq) is remixed with the bulk.
What are basic assumptions of the penetration theory?
1) Unsteady state mass transfer (by diffusion) occurs to a liquid element as long as it is in contact with the bubbles or other phase
2) Equilibrium exists at the gas-liquid interface
3) Each if the liquid elements stays in contact with the gas for a fixed period of time
What is Fick’s 2nd law?
Law for unsteady state concentration gradient:
dC.A/dt = DA.B * d2C.A/dy2
It is true for equimolar counter diffusion.
It is only true for absorption when concentrations of the diffusing material are low.
From this, surface flux and average flux can be found.
Fick’s first law considers changes in concentration with distance WHEREAS Fick’s second law considers this with time.
What is surface flux?
The mass transfer rate per unit area of surface
What is the mass transfer coefficient in penetration theory?
k = (D.AB / pi*t )^0.5
Average k = double the above
What are the drawbacks of penetration theory?
It assumes the same contact time for all liquid elements (however different sized particles would have different contact times)
Some elements may be quickly swept away by the eddies or some element may stay at the gas liquid interface for longer time. (age distribution)
It assumes constant time period
What are the assumptions of the surface renewal theory?
Liquid elements at the gas liquid interface are being randomly replaced by fresh liquid (random distribution of ages)
Unsteady state mass transfer occurs at the gas liquid interface
It takes place over a time distribution (whereas penetration occurs over a fixed period of time)
What is S in the surface renewal theory equations?
Danckwerts parameter
S is an age distribution parameter (independent of the age of the element) or fractional rate of surface renewal. (S ≈ 1/tm) ; mean residence time (tm).
What does the size of the k value for mass transfer coefficients suggest?
Larger k means more effective mass transfer.
As k increases, film resistance decreases (film theory).
What are the boundary conditions for penetration theory?
At t=0, for all values of y, Ca = Ca0 (bulk value)
At t>0, if y=0, Ca = Cai (interface value)
if y = infinity, Ca = Ca0
Ca0 constant as it’s so far from the interface
What’s the inverse of mass transfer coefficient equal to?
Resistance (1 / K)
Overall resistance is equal to the sum of individual resistances
The term (gas film control) refers to the resistance lie in the gas film.
The term (liquid film control) refers to the resistance lie in the liquid film.
What problems does the use of an overall mass transfer coefficient solve?
Problem 1 is the difference of concentration at different heights in the column
Problem 2 is that the interfacial area is unknown.
Incorporate the area into the M.T.C. and calculate K multiplied by a (a is the interfacial area).
What’s scrubbing?
Absorption
Gas absorption: It is a mass transfer operation in which one or more gas solutes is removed by dissolution in a liquid.
Absorption operation is of two types; physical and chemical
What’s stripping?
Desorption.
It’s the reverse of absorption
How do packed columns and plate systems differ?
In the continuous-contact process
– Packed column: Equilibrium is not attained, and rate
effects are controlling. (Absorption often)
– Plate systems, Equilibrium conditions principally determine the separation performance. (Distillation)
The height of the packed column must be calculated by considering the rate of mass transfer.
How do x-y graphs differ for distillation and absorption?
For distillation, the equilibrium curve is above the operating line.
For absorption, the curve is below the operating line.
It is thermodynamically favourable for the component to go from liquid to vapour.
How is the height of a packed tower found?
Z = HOG * NOG
Where
H.OG is the height of one transfer unit (HTU) based on gas phase and is a function of flow rate and Ka
N.OG is the number of transfer units (NTU) based on the gas phase and calculated from equilibrium data
How is the height of a tray tower formed?
Z = H*N
Where:
H is the distance between two trays
N is the number of trays, based on equilibrium data
What are the 3 steps involved in designing an absorption column?
(i) Overall mole balances, (Fixing G and L to specify how large a process is needed also gives you the operating line)
(ii) Cross-sectional area, Good liquid/gas contacting only occurs in a narrow range of flows. This determines the tower diameter
(iii) Tower height, even if the flows are good. The solute must have enough time to diffuse from the gas to the liquid, this time depends upon the height of the tower.
What’s the purpose of packing in absorption columns?
The purpose of the packing is to provide a large contact area between gas and liquid.
Packing should also be cheap, light, inert, and offer minimal flow resistance.
What are the 3 main problems to do with flow through packing (in absorption columns)?
Channelling
Loading
Flooding
What are problems with fluid channeling?
The gas or liquid flow is much greater at some points than at others, leads to poor mass transfer.
What are problems with fluid loading?
The liquid flow is reduced due to the increased gas flow; liquid is held in the void space between packing.
What are the problems with fluid flooding?
The liquid stops flowing altogether and collects in the top of the column due to very high gas flow
Flooding dramatically reduces mass transfer. The flux can be reduced at design stage by increasing the tower C.S.A. This area can usually be found by the use of an empirical correlation.
What’s H.OG?
The height of one transfer unit (HTU) based on gas phase and is a function of (flowrate (G, L) and K.a)
What’s N.OG?
The number of transfer unit (NTU) based on gas phase, and it can be calculated based on equilibrium data.
What are H and N in tray tower height calculations?
H : is the distance between two trays, and it is given (0.3 - 0.7 m).
N : is the number of trays, and it can be calculated based on equilibrium data.
How is the minimum liquid (solvent) flow rate found/calculated?
It’s calculated when the exit solvent concentration from the absorber (xb) is in equilibrium with the entering gas concentration to the absorber (yb).
Exit solvent concentration is calculated, xb = yb / m
What 2 factors affect (absorption) column cross-sectional areas?
Type of packing
Nature of fluid flow
