Unformatted text preview: c
Therefore, the Langmuir isotherm becomes:
q* = q* = 0.738
6.94 × 106 c
, where q* is in g/cm3 of particles and c is
1 + 98,700(194.4)c 1 + 19.19 × 10 c The initial conditions for adsorption step of the first cycle are: c = 0 for t = 0 and q = 0 at t = 0
The boundary condition for all adsorption steps is:
cF = yFPM/RT = (0.000236)(3.06)(124.08)/[(82.06)(294)] = 3.72 x 10-6 g/cm3 at z = 0.
The cycle calculations are conveniently carried out by a modification of the FORTRAN program
in Table 15.9, based on using the method of lines to obtain a set of ODEs, similar to the
equations for TSA, with a stiff integrator, such as LSODES. The program in Table 15.9, which
is for TSA, consists of:
Main program to:
Set initial parameters.
Perform cycles for:
Write cycle results
Subroutine FEX to:
Compute derivatives of the set of ODEs
For VSA, the program must add:
Repressurization step Exercise 15.32
Subject: Model equations for the separation of air by PSA
Given: Feed of air to be separated into oxygen-rich and nitrogen-rich products in fixed
isothermal, adiabatic beds, with mass-transfer resistances and extended Langmuir isotherms.
Assumptions: Constant fluid velocity and negligible axial dispersion.
Find: Model equations for the two main steps and a numerical procedure for solving the
Analysis: Let subscripts X = oxygen and N = nitrogen.
Species Mass Balances:
From a modification of Eq. (15-102),
u ∂c X ∂c X
1 − ε b ∂q X
∂t u ∂cN ∂c N
1 − ε b ∂q N
∂t Total Mass Balance: ∂ct
1 − εb
εb ∂q X ∂q N
∂t Component Mass-Transfer Rates:
From Eq. (105) for the LDF model, ∂q X
= k X q* − q X
= k N q* − qN
Extended Langmuir Isotherms: q* =
N qm X K X c X
1 + K X c X + K N cN qm N K N c N
1 + K X c X + K N cN where, ct = cX + cN Exercise 15.32 (continued)
Boundary conditions for starting adsorption with a clean bed: q X z ,0 = c X z ,0 = 0
q N z ,0 = c N z ,0 = 0
c X 0, t = cFX
cN 0, t = cFN
Boundary conditions for desorption are the conditions in the bed at the end of adsorption and a
feed containing purge gas.
The equations can be solved by the Method of Lines in a manner similar to that described on for
TSA, letting: φ i = ci / cFi
ψ i = qi / q Fi Exercise 15.33
Subject: Descriptions and possible uses of cycling operations of (1) parametric pumping and
(2) cycling zone adsorption.
Given: Reference to an article by Sweed, based on inventions by Wilhelm and by Pigford and
Find: Detailed descriptions of (1) parametric pumping and (2) cycling zone adsorption. Can
either or both be used for gas-phase and liquid-phase adsorption?
The separation of binary liquid or gas mixtures by parametric pumping was first proposed,
analyzed, and substantiated by experiments in articles by R. H. Wilhelm, A. W. Rice, and A. R.
Bendelius, I&EC Fundamentals, 5, 141-144 (196...
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