Page 218 - Pressure Swing Adsorption

194 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 195

is assumed that there 1s no nuxmg in the midsectmns of the coiumns. The Table 5.6. Equations for PSA Simulation Using Pore Diffusion Model
feed and the product ends-of the high-pressure column are connected to
the oroduct and feed ends. respectively, of the low-pressure column. The Except for the followmg changes all other equations m Table 5.2 a_pplv. The subscnp! i has the
gas from the corresponding haivcs 1s assumed to be uniformly mixed, with same meaning as rn Tahle 5.2.
Mass transfer rale across the extern11l Jilm:
due allowance for the difference in initial pressures and therefore m the
number of moles of gas miHally present m each half-column. The resulting iJci,- 3
T, = 71k1( C, -d-R,) (I)
gas mixtures are then uniformly distributed through the relevant halves of '
the two columns. Velocuv boundarv condition tor pressunzat1on:
3. Jn the particle mass balance it is assumed that the ~dsorbent consists of vlz~L = 0 (2)
uniform microporous spheres; any macropore diffusional resistance 1s
Equation 2, which replaces Eq. IOa 1n Table 5.2, as a more appropriate ve1oc1tv boundary
negiected. This is a good approximation, since, m a kinetically selective
condition for the pressunzat1on step. Moreover. with this boundarv condition 1t 1s no longer
adsorbent such as carbon molecular sieve, the diffusional resistance of the necessary IO specify pressurization gas quantuy as an mpui.
microoores is much iarger than that of the macrooores. (The relevant Particle balance:
particle radius m the time constant 1s that of the microparticles.) aq, =""-[r .!1.(o' a,,,)]
4. The gradient of chemical potentiai is taken as the ctnvmg force for iJt r2 Jr ' Br (3)
rn1cropore diffusion with a constant intrinsic mobility. This leads to a
Boundarv conditions:
Fickian diffusion eauat1on 1n which the diffusivity is a function only of the
adsorbed-phase concentrations. Ideal Fickian diffusion with constant dif- - -o
""'I r-o - ( 4)
iJr
fusivity is also investigated for comparison. aq, I
5. The fluid ·and the solid phases are linked through an external film D;a, r'""Rp =k1(c;-C;lr-Rp) (5)
resistance, even though a large value 1s usually assigned to the external
film mass transfer coefficient to approximate equilibnum at the particle c,-1,~np m Ea. 5 is related to q 1l,-n~ through the equilibnum isotherm:
surface. In conjunction with the collocat1on method this proves s1moler q,I;~•, = 0, = b,c,1,-•/( I+ I;h,,,1,-•,,)
than the alternative approach involvmg the direct application of the (6)
eouilibnum boundary condition at the particle surface.
Equation 6, written for the two components and I hen solved s1mulfaneously, v1elds
The model equations subject to these assumottons are summanzed m c,1,-R, = 'o:•/( I -~•1) (7)
Table 5.6. Equations that are similar to those m Table 5.2 are not repeated in
Table 5.6. Equations 1) 2a, 3, and 7-11 in Table 5.2 together with Eqs. 1, 2, 7 Constanr Diffus1vity. If the m1cropore diffusivity (D;) is mdependem of concc:ntraoon, Eq. J
anct the approoriate set of diffus10n equations (Eus. 4, 5, and 8 for the becomes:
constant-diffusivity case, and Eos. 11-14 and 4 for the concentration-depen-
dent diffus1v1ty case) in Table 5.6 are rearranged and written m dimensionless (8)
form. The dimensionless equal!ons may then be solved by the method of
The associated boundarv conditions, Eos. 4 and 5, remam the same.
orthogonal collocation to obtain the gas-phase composition as a function of
Concentration-dependent dijfusidtY, The expressions tor the diffusivities m a binarv Langmuir
dimensmniess bed length (zjL), and the solid-phase composition as a system with consiant mmns1c mobilities (DAO• D 80 ) have been given by Habgood 54 and Round
functton of both the dimensionless bed length and the dimensionless particle et al.55a.
radius (r/Rp) for various values of time. Details of the collocation form are
given In Appendix B. Starting from a given initial condition the computations (9)
are continued as usual until cyclic steady state is reached.
The air separation data for nitrogen production on a carbon molecular (10)
18
sieve reported by Hassan et al. are chosen to illustrate the importance of
the concentration deoendence of the micropore diffusivity on the perfor- (Conwwed)
mance of the kinetically controlled PSA separation. The experiments, carried
out m a two-bed PSA unit using the modified cycle with pressure eaualiza-
tion and no purge, were conducted over a wide range of high operating