Page 341 - Pressure Swing Adsorption

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318 PRESSURE SWING ADSORPTION APPENDIX B 319

subscript J mentioned m Table B.1. In the preceding eauat1ons: M 1s the Boundary conditions for fluid flow:
number of internal collocat1on oomts. In Ea. B.10: Pm = 1/Pe. In Eas. B.10, acA I .
B.13, and B.14: DL -az = -vl,.o(cAl,-o·- cAIPo);
z=O
(8.19)
A, = 1/(Ax( I, M + 2) - [ A, Ax( M + 2, M + 2)]}
A, = Ax( M + 2, M + 2)/{Ax( I, M + 2) - [A, Ax( M + 2, M + 2)])
The velocity boundary conditions for the steps other than oressunzat1on:
A,= [Ax(l, I) - Pe ii(l)j/ Ax( M + 2, I) For vl,. 0 see Eqs. !Ob-ct m Table 5.2;
A 4 = 1/Ax(M + 2, !) (ou/oz)l,-1. = O (8.20)
In the dimensmnless form Ea. I m Table 5.6 becomes:
A = A A
5 2 4
ayA [
Eauatrons B.10-B.15 are the collocat1on forms of the LDF model equa- a-r = r YA - YAPl11=d;
tions describing a variable pressure step with flow at the column mlet. The r (8.21)
aY 8
appropriate changes to these general eouations necessary for describing the a:,= Ys[! -YA -Yspl,.ij
individual steps in a two-bed process operated on a Skarstrom cycle are
summarized in Table B.1. In a Skarstrom cycle (see Figure 3.4) steps 1 and 2 Subst1tutmg Ea. B.21 m the dimens10nJess form of Ea. B.18, we obtam:
differ from steps 3 and 4 only m the direction of flow. Followmg the same au ,J,r
procedure discussed here, a similar set of collocation equations was denved az = ---w[(YA -YArl,.,) + (1-yA -y•Pln-1)] (B.22)
for steps 3 and 4. The set of coupled algebraic and ordinary differential
equations thus obtained describing steps 1-4 m the two beds was solved by Equation B.16 wnttcn m dimensionless form and combined with Eq. B.22
Gaussian elimmation and numerical integration, resoectively. For numerical yields:
integrat10n the Adam·s variable-step integration algorithm as provided in the
ayA I a'yA _ ayA [ ,
FORSIM package (Ref. 49 m Chapter 5) was used. Tr= Pe Waz' -vW az + ,J,f (l -yA)(YA -yAPln-il (B.23)
+yA(1 - YA -Ysrlr1)J
B.3 Dimensionless Form of the Pore Diffusion The fluid flow boundary conditions (Eq. 8.19) assume the following dimen-
Model Equations (Table 5.6) sionless form:

The discussion here 1s also restricted to a two~comoonent system, but the
eauations are developed m general terms for a constant-pressure step with (B.24)
flow at the column mlet. Tbe variable diffus1v1ty case 1s considered. The ayA I -o
followmg equat10ns are taken from Table 5.2, Fluid Phase mass balance: az z-1 -
The velocity boundary conditions given by Ea. B.20 take the followmg
I (B.16) dirnensioniess fonn:
av I - o
Continuity condition: az z=1 - (B.25)
I cA + Cn = C (constant) (B.17) The dimensionless form of the velocity boundary conditions for pressunza-

t1on (given by Eq. 2 m Table 5.6) 1s:
I Overall mass balance: ( B.26)
au ] - e ( oijA aqB) _ O
C -+-- -+- - (B.18) The following dimensionless equations are obtained from the oarticle bal-
Dz e a, at
ance equations (Eqs. JI and 12 in Table 5.6) and the related boundary