Page 347 - Pressure Swing Adsorption

324 PRESSURE SWING ADSORPTION APPENDIX B 325

The collocatmn forms of the equilibnum isotherms are: Table B.2. Summarv of the Changes to Eqs. 8.33 - B.43 and Eqs. B. 13- 8.15
j Necessary for Describing the Individual Steps of a Modified Skarstrom
, ·)- I XcA(;,N+ I}
I l Cvcle with Pressure Equalization and No PUrge
YAr•~lli -7.,-I - (.N 1) ( N+l)' (B.41}
+
fJA -xcA J, -xcn l, I
I \leloc1ty profile
I Xc (i,N+ I) Operauon f(JI along the column
8
/3AYE 1 - XcAiJ, N + I) - Xc 8 (1, N + 1) · 1· Pressunzat1on ofbc<.i 2 Given by Eq. B.J7
;
l
1 = 2, ... , M + I 2 (square wave From Eq. 8.3➔
xc)J. N + I) and Xc (J,N + I) are obtamed from Eas. B.42 and B.43. change rn
8
pressure)
The boundary conditions at the particle surface (Eas. B.30 and B.3 I) Blowndown of bed (I From Eqs. 8.38 and
written m the collocatton form and then combined With Ea. B.41 lead to a set 1 (square wave B.15
of coupled nonlinear aigebra1c equations: change in
pressure)
N High-pressure flow
L A(N + I, i)xcA(j,i) +A(N + 1, N + l)xcAU, N + 1) (B.42) i in bed 2 (constam 2 From Eqs. B.JR and
1=1 I pressure) B.15
! "Self-purging" of (I From Eqs. B.JS anti
bed 1
B.15
:J
I "The subscnpt j ( = I for heJ I and 2 for bed 2), which should propC:rlv appear with all the dependent
v,1riables and the parameters ,J,, {3_. 1 • r. and I". ts om1t1ed from the: equations for s1mplicitv. Durrng
l pressunzauon and high-pressure ;idsorp11on m hcd 2, }'Ai: ~o 1s the mmc frac11on of compcmenc A in
I the Iced gas. For hlowdown and self-purging steps m bed L Y...iL:-0 = .\'Ai(]). ib./3,.1-L und f"' have
difforen1 values for low- and high-pressure steps.
Eoualtons B.33-B.43 are the collocat10n forms of the (vanable-diffus1v1ty)
N oore diffusion model equations describing a constant-oressure step with flow
I;A(N+ 1,i)xc (;,i) +A(N+ l,N+ l}xc (J,N+ I) (B.43} at the column inlet. The approonate changes to these general equations
8
8
1=! necessary for describing the individual steos m a tWo-bed process operated
r· on a modified Skarstrom cycie with pressure equalization and no purge are
---[1-xc (J,N+ l)j
8
-YKYS summarized m Table B.2. In a modified Skarsttom cycle with oressure
equalization and no purge (see Figure 3.16) steps 3 and 6 are the oressure
I XcnU, N + I}
X \ I - yA(j) equalization steps. The pressure equalization step 1s difficult to handle m a
f3AYE I - XcAU, N + 1) - XcnU, N + rigorous manner. The approximate representation of this step 1s discussed in
+f'xc (1,N+ 1} Sect10n 5.2. Steps l and 2 differ from steps 4 and 5 only m the direction of
8
fluid flow. Followmg the same procedure discussed here, a similar set of
x(y j - 1 XcA(;,N + I) ·i=O, collocation eauatlons was derived for steps 4 and 5. A set of coupled
_A() (3A l-xc,CJ,N+l)-xcn(1,N+l) alg~bra1c (linear and nonlinear) and ordinary differential equations describes
the operations m steps 1, 2, 4, and 5 in the two beds. The nonlinear algebraic
i J = 2, ... , M + I
eauations were solved by the IMSL routme NEQNF (Ref. 50 m Chaoter 5).
The solution of this set of coupled nonlinear algebraic eauations gives The linear algebraic eauations were solved by Gaussian elimmatJon. The
I XciJ,N + I) and Xc.(J, N + I). ordinary differential equations were integrated in· the time ctomam using
In these equations M 1s the number of internal collocation oomts along
Gear's stiff (variable-step) integration algorithm as Provided in the FORSIM
I the coiumn axis (j refers to axial location). (Note: J used in these eauations is package (Ref. 49 in Chapter 5).
different from the subscnpt J used in Table B.2.) N is the number of internal
collocation points along the radius of the adsorbent particle (k refers to
I,
' location inside a microparticlc).
t
I