Page 198 - Pressure Swing Adsorption

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174 PRESSURE SWING ADSORPTION DYNAMIC MODELING OF A PSA SYSTEM 175

Variable Column Pressure Table 5.2. Model Equations for PSA Simulation Usmg LPF Approximation"
When the column pressure changes with the time, the overall material The equations are written m general terms for component j ( ~ A for component A and ... 8
balance equat10n 1s: for component B) in bed j ( = I for betl I and = 2 for bed 2). /\:!though the subscript ; should
.av ac 1 - e .; azy, ideally appear with all the dependeni variables, rt ts not shown h~re tor s1mp!icitv.
C az + at + -.- L, at = 0 (5.9) Fluid-phase mass balance:
,.,,] D iflc, ac. i!v ac, I - ,.. rJ?f
+
- L ~ l' 7iz + C; az + Ti + -,- ""J"t = 0 (I)
which when substituted mto Ea. 5.1 yields:
azy,
{
ck, ac, ~ _ .;:., azy, ) Continuity condition:
az + at + e I:C,-c*f<zl
+ 1)- \ ot Y; L, a, (5.W)
. , ... 1
ac
-y,at = 0 - f(1), pressurization and b!owdown (2a)
* f(i), high~pressure adsorpnon nnd purge (2b)
Appiymg the 1ctea1 gas law, the component anct overall material balance
Overall mass balance; high-pressure adsorpuon :inti purge {Qr a constanc pressure step tn
equations, under variable column oressure, assume the following form: general)
(3)
pressunzat1on and blowdown (or a variable pressure step m genera])
(5.11)
av ac 1 - e " aq;
c az + 7it + ~--~ L, ii( "" 0 ( 4)
,
(5.12) Mass transfer rates:
iJii; * -
At this oomt 1t 1s· -important to recall that the elementary steos that ar=k;(q, ~q;) (5)
constitute· a PSA Skarstrom cycle are oressunzation, purified product re-
Adsorption equilibnum:
moval durmg the high-pressure feed step, and countercurrent blowdown to
'the iow pressure followed by the low-pressure ourge step. Modified versions (6)
of this cycle include vanous combinations of the following steps: pressure
equalization or cocurrent depressunzation (before the countercurrent blow-
Boundary conditions for fluid flow: pressurization, high-pressure adsorption, and purge
down step), vacuum desorption or low-pressure desorotion without a purge
stream, and Partial- pressurization with product stream before pressunzat1on D ,,, I I I ) ,,, I
Lifz1z-0=-1:lz=o(C;_.-o--c1z--n ;az z-L=.O (7)
with feed (see Chapter 3). The form of the fluid flow model appropriate for
each of the elementary steps will be determined by the nature of the
( c1iz -o- )purge= ;;; ( c,J,. ~ t.)ausorpcmn (8)
seoarat'ion (ollrification or bulk separation) and the pressure history of the
column over a complete cycle. The standard (Danckwerts) inlet and exit blowdown
a,.,
boundary conditions for a dispersed plug flow system 29 apply for the comoo- ~.:11
nent matenai balance m all the elementary steos. The velocity boundary a:z•O=O; llz , _ i. - -0 (9)
conditions follow from the ph)isical conditions controlling the cycle operation. EQuation 7, which defines the standard (Danckwerts) inlet and exit boundarv conditions for a
Details of the flow boundary conditions are given in Table 5.2. dispersed olug flow system, reduces to Eq. 9 when the 10let velocnv ts set 10 zero. Similar
In an actual -ooerat1on the- column pressure changes continuously, and a boundarv conditions applv for desorption without ex1ernal purge. EquatJOn {8) defines miet gas
rnodei ·including the vanable pressure condition should more closely repre- (Conrmw:d)
sent the real s1tt1ation. An mteresting observation is that Eas. 5.7 and 5.11,
which are the component balance equations for constant and variable column
pressure conditions, rest>ect1vety, are of similar form. The rumor difference
anses from the fact that some of the coefficients in Eq. 5.11 are functions of
time, but that ctoes not mtroctuce any additional complexity m the numencal