Introduction to mass transfer principles and applications by Upv/ehu

Mass Transfer Introduction

Topic 1: INTRODUCTION
Mass Transfer
Gorka Elordi
Department of Chemical Engineering - UPV/EHU
TENCEPHOTOLIBRA
cc
BY NO SAIMPORTANCE OF THE MASS TRANSFER

• Most separation processes are based on mass transfer (distillation,
  absorption, extraction, leaching, adsorption, crystallization,
  separation by membranes, etc.)
• Vapour pressure, solubility, or differences in diffusivity are used in
  these processes in order to separate the components from the
  mixture.
• Velocity and temperature gradient are the driving forces of
  momentum and heat transfer, respectively. In mass transfer, the
  driving force is the concentration gradient or the activity gradient.
• Analysing the laws that describe the mass transfer and the
  equipment used for it is a key factor in the preparation of
  Biotechnology students and Chemical Engineering students.

Basics of Mass Transfer

BASICS OF THE MASS TRANSFER
•
Proof:
SCIENCEPHOTOLIBRA
•
Base: the movement of electrons, atoms, ions, and molecules
•
State: gas, liquid, and solid
•
Useful parameters: length, area, temperature, concentration
http://youtu.be/H7QsDs8ZRMIBASICS OF MASS TRANSFER

• The movement of electrons only depends on T. Besides, molecules or
  atoms are always moving in fluids. Thus, the movement of particles is
  always taking place.
• In any case, when the concentration or activity gradient disappears, the net
  mass flow approaches 0.
• This mechanism of mass transfer is called: Ordinary diffusion, concentration
  diffusion, mass diffusion, or molecular transport of mass.
• Other types of diffusion: thermal diffusion (stainless steel), pressure
  diffusion (reverse osmosis), etc.
• Apart from the transport based on the movement of the molecule, mass is
  moved due to the movement applied to a fluid (convective transport).

Forefathers of Diffusion

FOREFATHERS OF DIFFUSION
"Diffusion. Mass Transfer in Fluid Systems". E. L. Cussler. Cambridge Univ. Press, 3rd Ed.

• Thomas Graham (1805 - 1869). Chemist. Research based on a diffusion tube.
  H
  Air
  2
  Stucco plug
  V
  Glass tube
  Diffusing gas
  H2 (diffusion gas) exits, air enters.
  H2 diffuses faster, then, water level .
  For P=const. Tube descends
  Water
  "The diffusion (or spontaneous intermixture of two gases in contact) is effected by an inter-
  change of position of infinitely minute volumes, being, in the case of each gas, inversely
  proportional to the square root of the density of the gas."
  Rate
  =
  1
  M.
  M
  2
  Rate2
  1
  Rate_ diffusion index of gas 1 (mol /time)
  Rate2 diffusion index of gas 2
  M1 molecular weight of gas 1
  M2 molecular weight of gas 2

Thomas Graham's Diffusion Research

FOREFATHERS OF DIFFUSION

• Thomas Graham (1805 - 1869). Research based on a diffusion tube.
  Glass
  plate
  (a)
  (b)
  (a) Different concentrations
  (b) Concentrate solution in a pure liquid
  He used to measure concentrations after several
  days.
  His conclusions:
  "Diffusion in liquids is at least several thousand times slower than in gases."
  "Diffusion must necessarily follow a diminishing progression."
  "The quantities diffused appear to be closely in proportion to the quantity of salt in the
  diffusion solution."
  In other words, the flow due to diffusion is proportional to the difference in salt concentration.

Adolf Fick's Contributions to Diffusion

FOREFATHERS OF DIFFUSION

• Adolf Fick (1829 - 1901). Medical doctor and physician.
  "The diffusion of the dissolved material [ ... ] is left completely to the
  influence of the molecular forces basic to the same law [ ... ] for the
  spreading of warmth in a conductor and which has already been
  applied with such great success to the spreading of electricity."
  Fick suggested using the same mathematical base to describe diffusion
  as the law that Fourier proposed to describe heat transfer.
• Fick's contribution:
  - He said that diffusion is a dynamic molecular process.
  - He understood the difference between the real equilibrium and steady
  state.

Fick's Laws of Diffusion

FOREFATHERS OF DIFFUSION

• Adolf Fick (1829 - 1901). 1D for steady flow (Fick's 1 st law):
  JE-D
  dc1
  dz
  1
  "J1 is the flux per unit area across which diffusion occurs,
  C1 is concentration, z is distance and D the constant
  depending on the nature of the substances (diffusion
  coefficient)."
• Following Fourier's approach, he suggested a conservation equation (Fick's
  2nd law):
  dc1
  ∂
  2
  c1
  =D
  ôt
  2
  +
  A ôz ôz
  1 0 A 0c1
  > A= const >
  OC1=D
  02
  2º C1
  2
  1D unsteady-state diffusion
  ôt
  . In order to demonstrate the similarities between the heat and mass
  transport (to see how well the equations fit):
  1) Analytical integration of the former equation (numerical effort),
  2) Measurement of d2c1/dz2 (experimental difficulties)
  3) NaCl diffusion in water

Confirmation of Fick's Hypothesis

FOREFATHERS OF DIFFUSION

• Adolf Fick (1829 - 1901). Confirmation of the hypothesis
  1.10
  Funnel
  Specific gravity
  Z
  MA
  1.05
  Tube
  V
  Z
  O
  0
  2
  4
  6
  Distance z
  OC1
  =D
  ∂
  +
  1 0 A 0 c1
  A dz ôz
  > A=const,
  dc1
  ôt
  1=0>0=D
  2
  O"C1
  2
  ôt
  @ c1
  22 C1
  1 0 A 0 c1
  at
  02
  0 z
  +
  2
  A dz ôz
  >A=f(z),
  2
  ∂
  1 0 A OC1
  +
  2
  OC1=0-
  ôt
  =0>
  0= D
  A dz ôz
  )
  2
  =DFOREFATHERS OF DIFFUSION
• Adolf Fick (1829 - 1901). Confirmation of the hypothesis
  1.2
  cil
  con
  1.0
  2 C1
  1 0 A 0c1
  0= D
  +
  2
  A dz ô z
  0.8-
  T
  V 0.6
  T
  0.4 -
  ∂
  0= D
  ,2
  0.2
  0.0-
  0
  1
  2
  4
  5
  6
  .
  .
  .
  .
  ..

Molecular Transport Phenomena

MOLECULAR TRANSPORT
"Transport Phenomena". R.B. Bird, W.E. Stewart, E.N. Lightfoot, John Wiley & Sons, 2nd Ed.

• At t=0 pure He is fed at the lower face of a silica slab of surface A and thickness Y.
  However, at the upper face, there is a flow of air (completely insoluble in silica) .
  @A=0
  Thickness of
  slab of fused silica = Y
  (substance B)
  t<0
  t=0
  WA= WAO
  WA (y, t)
  Small t
  1
  WA (y)
  y
  Large t
  x
  WA=0
  WA = WAO
  · Helium (A) gets into the silica (B) and
  rises up towards the upper face.
  · Concentration is given in mass fraction
  (W and WB). Thus, at each microscopic
  volume element:
  WAS
  PA
  PA+PB
  Fig. 17.1-1. Build-up to the
  steady-state concentration pro-
  file for the diffusion of helium
  (substance A) through fused sil-
  XA=
  CA
  CA+CB
  ica (substance B). The symbol @) A
  stands for the mass fraction of
  helium, and wA0 is the solubility
  of helium in fused silica, ex-
  pressed as the mass fraction. See
  Figs. 1.1-1 and 9.1-1 for the anal-
  ogous momentum and heat
  transport situations.

Molar Flow and Fick's Law in 3D

MOLECULAR TRANSPORT

• At steady state (t>>>>>0), the molar flow of the component A in the direction y is
  proportional to the surface unit with the difference of molar fraction and the division of
  the thickness of the plate.
  NAy = CD
  A
  m Ay
  AB
  XAO-0
  Y
  JA =- CDAB
  dx A =- DAB
  dy
  dc
  A
  dy
  A
  =OD
  AB
  WAO
  Y
  JAY =- PD
  AB
  dw A
  dy
  =- D
  AB
  deA
  dy
• c is the molar density of the system silica-helium (mol L-3), p density (M L-3), D
  diffusivity of helium in silica (L2 t-1), J
  Ay
  the diffusional molar flux of A in direction y (mol
  L-2 t-1), and jay mass flux (M L-2 t-1).
  AB
  For 3D diffusion, a vectorial expression of Fick's law is used:
  A-CD
  JA =- PD
  AB
  AB
  VX-D
  A
  CA
  AB
  V WA =- DABPWAMOLAR AND MASS CONCENTRATIONS
  "Transport Phenomena". R.B. Bird, W.E. Stewart, E.N. Lightfoot, John Wiley & Sons, 2nd Ed.
• Either mass or mol quantities can be used to express concentration.
  Table 17.7-1 Notation for Concentrations
  Basic definitions:
  Pa
  = mass concentration of species «
  (A)
  p = > pa = mass density of solution
  a=1
  Wa = Pa/p = mass fraction of species «
  (C)
  Ca
  = molar concentration of species «
  N
  (E)
  (D)
  c = > ca = molar density of solution
  a=1
  Xa = Ca/c = mole fraction of species a
  (F)
  M = p/c = molar mean molecular weight of solution
  (G)
  Algebraic relations:
  Ca = Pa/ Ma
  (H)
  Pa = caMa
  (I)
  N
  Exa = 1
  6
  a=1
  N
  ΣxΜα=Μ
  (L)
  α/Ma=1/Μ
  (M)
  a=1
  X Ma
  Wa =
  (O)
  X =
  N
  Σ (ωβ/Μβ)
  B=
  N
  Σ (ΧβMg)
  B=1
  (K)
  a=1
  N
  a=1
  @g/Ma
  (N)
  N
  (B)

Diffusivity and Non-Dimensional Numbers

MOLECULAR TRANSPORT

• For mass diffusivity (DAB), thermal diffusivity (x=k/pC ) and momentun diffusivity
  (kinematic viscosity, v= p/p) dimensions are L't-1, and the relationships among
  them are well-known. The following non-dimensional numbers are widely
  used :
  Prandt = Pr=
  Pr= = CPM
  k
  Schmidt = Sc =
  ν
  D
  =
  μ
  AB
  PD
  AB
  k
  Lewis=Le=
  α
  =
  D
  AB
  PCPDA
  AB
• D of gases at low densities, is not a function of w, increases with T and
  decreases with P.
• D of liquids and solids is a function of concentration and it generally
  increases with T.

Experimental Diffusivities in Gases

MOLECULAR TRANSPORT
Table 17.1-1 Experimental Diffusivitiesª and Limiting Schmidt
Numbers of Gas Pairs at 1 Atmosphere Pressure

Experimental Diffusivities in Liquids

Table 17.1-2 Experimental Diffusivities in the Liquid Statea,b

" The data for the first two pairs are taken from a review article by P. A. Johnson and A. L. Babb, Chem.
Revs., 56, 387-453 (1956). Other summaries of experimental results may be found in: P. W. M. Rutten,
Diffusion in Liquids, Delft University Press, Delft, The Netherlands (1992); L. J. Gosting, Adv. in Protein
Chem., Vol. XI, Academic Press, New York (1956); A. Vignes, I. E. C. Fundamentals, 5, 189-199 (1966).
The ethanol-water data were taken from M. T. Tyn and W. F. Calus, J. Chem. Eng. Data, 20, 310-316
(1975).
Sc

Experimental Diffusivities in Solids and Polymers

MOLECULAR TRANSPORT
Table 17.1-3 Experimental Diffusivities in the Solid Stateª

ª It is presumed that in each of the above pairs, component A is present
only in very small amounts. The data are taken from R. M. Barrer, Diffusion
in and through Solids, Macmillan, New York (1941), pp. 141, 222, and 275.
Table 17.1-4 Experimental Diffusivities of Gases in Polymers.ª
Diffusivities, 9 AB, are given in units of 10-6 (cm2/s). The values
for N2 and O2 are for 298K, and those for CO2 and H2 are for
198K.

" Excerpted from D. W. van Krevelen, Properties of Polymers, 3rd edition,
Elsevier, Amsterdam (1990), pp. 544-545. Another relevant reference is
S. Pauly, in Polymer Handbook, 4th edition (J. Brandrup and E. H.
Immergut, eds.), Wiley-Interscience, New York (1999), Chapter VI.