同济化工原理课件第八章吸收2

Transfer of solute in absorption: (1) from gas phase to the interface, driven by pA pAi ;
pA
gas
pAi
liquid
cAi cA
mass solvation mass transfer transfer interface
8.3.2 Diffusivity
usually determined experimentally, or estimated from semi-empirical formula.
The order of magnitude of D: Gases 105 m2/s Liquid 109 m2/s
Dependence of D upon T and p: Gases:
T D D0 T 0
1.81
p0 p
(8-24)
Liquids:
T D D0 T 0 0
(8-26)
8.3.3 Mass transfer by convection Laminar flow:
diffusion diffusion + convection
g l
Turbulence: Eddy diffusion is in all directions, and the molecular diffusion is important in the boundary layer only.
2. Diffusion of component A through a stagnant fluid (general cases)
The diffusion induced convection may be significant.
NA JA (NA NB ) cA cM
(8-16)
cBm
cA1 cA 2
In dilute solutions, cA is small. Expanding cM /cBm in Taylor series as cA 0, and neglecting the infinitesimal in higher order, we have
Relative to the fixed reference, the flux of component A is
NA JA (NA NB ) cA cM
(8-16)
flux relative to the bulk fluid
flux following the bulk fluid or diffusion induced convection
cM total molar concentration of solution
NA JA (NA NB )
cA cM
(8-16)
• In forced convection, the diffusion
induced convection is negligible. • For dilute solutions, the diffusion induced convection << JA. • For equimolecular counter-diffusion, NA + NB = 0
c Bm cB 2 cB1 ln cB 2 cB1
(8-21)
Comparison:
• For dilute solutions
NA D
• For general cases
NA D cM

( c A1 c A 2 )
(8-17)
how? (8-20)
>1 The diffusion induced convection increases the rate of mass transfer.
• rate of mass transfer
NA D

( c A1 c A 2 )
(8-17)
Compare to the expression mass transfer driving rate of mass = coefficient force transfer the mass transfer coefficient k = D/, and the resistance to mass transfer is /D.
Component B is insoluble, so that NB = 0
cA N A 1 cM dcA D dz
cA N A 1 cM
dcA D dz
B. C.: at z = 0, cA = cA1; at z = , cA = cA2 . The integration leads to
(2) solvation at the interface;
(3) from the interface to the liquid, by cAi cA.
8.3 Molecular Diffusion and Mass Transfer in a Bulk Phase Mechanism of mass transfer in a bulk phase:
For an one dimensional diffusion, the rate of diffusion is given by Fick’s law:
J A DAB dcA dz
(8-9)
A B
JA mass flux, DAB diffusion coefficient, m2/s The direction of diffusion is opposite to that of concentration gradient. kmol/m2s
A1
N A J A DAB
dcA dz
= const.

cA2 z
B. C.: at z = 0, cA = cA1 ; at z = , cA = cA2 .
The integration leads to • the concentration distribution
c A1 c A c A1 c A 2 z
Newton’s law of mass transfer: The rate of mass transfer in gas phase is NA = kG(p pi) (8-28) p
It can be proven that in a binary system, DAB = DBA = D (8-12) JA = JB (8-13) It is an equimolecular counter-diffusion process. A B
gas
liquid
In an absorption process, the mass transfer relative to a fixed reference consists of two parts: • molecular diffusion • diffusion induced convection
NA D c M cA 2 c M c A1

c M ln
It may be written asБайду номын сангаас
NA D cM
cBm
cA1 cA 2
(8-20)
where cM = cA + cB , and cBm is the logarithmic mean concentration of component B
pA
gas
pAi
liquid
cAi cA
mass solvation mass transfer transfer interface
• molecular diffusion • convection
We will consider the cases at steady state.
8.3.1 Diffusion in a two-component system
A
2
x
2

A
2
y
2

A
2
z
2
0
A1 A2
x
i.e.,
d A
2
dx
2
0
d A
2
B. C.： at x = 0, A = A1; at x = , A = A2 .
Integration twice gives the concentration distribution of component A,
cM c Bm 1
Eq. (8-20) reduces to Eq. (8-17). Above results are applicable to gas and liquid phases (c = p/RT).
To solve the diffusion in dilute solutions by applying the differential equation of mass transfer: For constant DAB and , the equation is
With the diffusion induced convection,
NA JA (NA NB ) cA cM
(8-16)
Without or with negligible diffusion induced convection,
N A J A DAB dcA dz