Page 248 - Chiral Separation Techniques

226 9 Modeling and Simulation in SMB for Chiral Purification

Initial conditions:
t = 0: c = q = 0 (19)
ij ij
Boundary conditions for section j:
D dc ij
z = 0 : c − L j = c (20)
ij ν ij 0,
j dz
where c is the inlet concentration of species i in section j.
ij,0
z = L :
j
For the eluent node ν I
c = c (21a)
iIV ν iI,0
IV
For the extract node c = c (21b)
iI iII,0
For the feed node ν ν
c = III c − F c F (21c)
iII ν iIII,0 ν i
II II
For the raffinate node c = c (21d)
iIII iIV,0
And q = q , q = q ,q = q ,q = q (22)
iIV iI,0 iI iII,0 iII iIII,0 iIII iIV,0
Global balances:
Eluent node ν = ν + ν (23a)
I IV E
Extract node ν = ν – ν (23b)
II I X
Feed node ν = ν + ν (23c)
III II F
Raffinate node ν = ν – ν (23d)
IV III R
Multicomponent adsorption equilibrium isotherm:
*
q * = f (c , c ) and q = f (c , c ) (24)
Aj A Aj Bj Bj B Aj Bj
*
Introducing the dimensionless variables x = z/L and θ = t/τ , with τ = L /u = N t ,
j s s j s s
where τ is the solid space time in a section of a TMB unit, L is the length of a TMB
s j
section, and N is the number of columns per section in a SMB unit, the model equa-
s
tions become:

2
∂c ij = γ  ∂ c ij − ∂c  1 − ε) * (25)
ij  (
 1
 −
∂θ j  Pe j ∂x 2 ∂x  ε α q −( ij q )
ij
j


∂q ij = ∂q ij + * (26)
∂θ ∂x α q −( ij q )
ij
j