Page 228 - Pressure Swing Adsorption

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204 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 205

'
Table 5.9. Continuous Countercurrent Flow Model Equations for ;, Table 5.9. (Contmued)
a Bulk PSA Separation Process"
' From Eqs. 4 and 8 we get:
Assumptmns I-7 discussed in connection with the LDF model apply.
_ akmq 1 j. 1 +(1-a)k;1.qti
C'ompo£lent mass balance: q;= ak +(1-a)k;1. . ('I)
d(vic 1 J 1- 8 dii;j 111
m -----az + -e- -di= 0 (1) I Substituting Eo. 9 into 4 and rearranging yields:
dQ,'f
m
Commuuy condition: ' -= (n-l+ma) e, iH- q*) (10)
k -(q*
'
dt
d.
I where n. = 1 for high-pressure flow and 2 for purge flow; and
Lc 1 =C; (constant) (2)
Overall mass balance: (11)
l/ak11- 1 + 1/(1- a)k,1.
. d,•, I-£" dQ;j
mC 1 7z +-e- L, dt ... 0 (3) Combinmg Eqs. i, 3, and J() gives:
deli 1-e I
Mass transfer rates: V1dz+ e (n-I~ma)(ke;(qfH-q;*L)
dif;; _ * _
dl-k;iCq,.i-q;) (4)
- X;1 ~kei(qfH - qf'd) = 0 ( 12)
Adsorption equilibrium:
/13)
(5)
Equation 12 for i = A and Eq. 13 are simultaneously m!egrated for high- and low-pressure flow
In lhese equa11ons, = A for component A and 8 for component 8, J =Hor L, and m =+I or usmg the fourth-order Runge-Kutta method to obtatn cA; and tr; at differem axial Jocanons m
- L The vaiues _, = H fl,lld m = + I represent high-pressure flow, J = L and m = - l represent the bed. The boundary conditions for high-pressure flow are knoWn at z = 0 and those for purge
purge flow. are given at z = L; therefore, the soiuhon procedure requires 1terahon. Values of the dependent
BoundatY conditions: high-pressure flow variables for purge flow are guessed at z = 0. The integration 1s then performed from z = 0 to
L, which 1s repeated until known boundarv conditions for purge !flow at z = L are satisfied.
(6)
Jacobian analysis 1s performed to update the trial vaiues, which accelerates the speed of
purge fl.ow convergence. Values of c i a1 different locations are obtamed bv difference from total concen•
8
tration. Steady-state adsorbed-phase concentrat1ons are then calculated from Eq. 9.
(7)
" The material balance Eqs. J and 3 should acmallv be wrmen m terms of equivalent velocities in
The concentration boundary condition for purge flow represents the fact that part of the order to ensure that the total volume of feed and purge used in actual operalion are the same m the
high-pressure product is expanded to low pressure and used for purge. v 0 1. and v 0 H are relatecl steady-stare represent-allon. However, such a restriction on the mass balance leads lo an equivalent
hy the purge to feed veioc1ty ratio, G. purge to reed velocity ratm given by G[(l-a)/a). For a=0.5 G[(l,a)/orl=G, but when a--1,
The assumption of zero net accumulation in the solid phase leads to: G .... 0, and when o -,. O, G .... w, and therefore the CCF model fails for Cycles in which the adsorption
and desorption steps are unequal (i.e., a ,,..0.5). The present form of material baiancc equations,
although iess accurate from the paint of mass balance between the act1,1al operation and steadv-st!lle
Ct dii;!! + (1- •)· dq._ IL= 0 (8)
dt dl approx1mat10n (except when a= 0.5), extends the usefulness of the CCF model to the cvcles m which
a 'F 0.5.
ln this equation a - i . j(t + 11,). The factors a and (1- a) with the solid phase accumulat1on
11 11
terms for the high- and low-pressure steps. respectively, have been mtroduced to mamtam
consistency m mass transfer raies between the CCF apprmumat1on and the transient simulation.
(Contmued)