Page 344 - Pressure Swing Adsorption

ii I
320
PRESSURE SWING ADSORPTION
APPENDIX B
321
conditions (Eqs. 4, 13, and 14):
obtamect:
dXcA 1 [ (a'xcA 2 axCA \ d M+I
'1
""7f:r ~ 1-xcA -xca (! -xca) ~ a:;, J (B.27) J; (j) ~ I: (QmBx(J,i) - Wi'(j)Ax(j,i)]yA(i) (8.33)
+
,=2
-A,[Qm Bx(J, 1) - W1°(i)Ax( , I)]
1
M+ J
X I; I A, Ax( M + 2, i) - Ax( I, i)] y A(i)

+A 1[QmBx(J,M + 2) - Wii(j)Ax(J,M + 2)]
M+I
(B.28)
X L [A,Ax(M+ 2,i) - Ax(l,i)]yA(i)
,j •=2 M+>

-A,[QmBx(1, I) - Wf(j)Ax(J, I)] I: Ax(M + 2,i)yA(i)
i
! +A,[Qm Bx(j, 1) - W1•(i)Ax(1, !)]Pe r(l)yAlz-n·
' -A 1[Qm Bx(J, M + 2) - Wf(i)Ax(J, M+ 2)]Pe f(!)y)z.n-
i
OXco I ~ 0 j
aTJ 'I) =o (B.29) l + ,t,f{[yA(j) - ll[yA(j) -yAPl,-1U)J
i +yA(j}[I - YA(j) - Yoel,.,(j)]},
(B.30)
j 1~2, ... , M + l
I"' YA,-1,.,(j)and Y,wl,.,U)areot,tained from Ea. B.41. y,,(l)and yA(M+ 2)
- 'YKYs XcA(l - YA - Ya,1,-i)
are given by Eas. B.13 and 8.14, respectively.
OXca I f'
y
~1) ~ -y (1 - Xc8 )(1 - YA - YaPl,-1) (B.31) B.4.1 Pressurization
11=1 K S
'
-f'xca\YA -yA,l,-1) The following set of linear algebraic eauat1ons is obtained when the dimen-
· 1 SJOnless overall material. balance eauat,ons (Ea. B.22) and the velocity bound-
The eauilibnum isotherms (Ea. 7 in Table 5.6) assume the followmg dimen- ' ary condition (Ea. B.26) are combined and wntten m the collocat1on form:
sionless form:
M+I
L AH(J,i)ii(i) ~ - ";{ ([Y,1U) -yA,,/,.,U)I (8.34)
!=2
(B.32)
} XCB + 11 - YAU) - Ynrl,-1U)]),
Yori,-,~ /3 ·y 1 -x -x
A E CA CB 1~2, ... , M + i
The tnal functmn chosen to satisfy the zero exist velocity boundary condition
is:
B.4 Collocation Form of the Dimensionless Pore Diffusion
M M+l
Model Equations v = (1 - z) I; a,P,_i(z) ~ I; t,z'·' ( 8.35)
I= I
When Ea. B.23 with the boundary conditions given by Ea. B.24 1s written in Vl,-o ~ v(l) ~ §, (B.36)
the collocat1on form, the followmg set of ordinary differential equations 1s
Solution of Eo. B.34 gives velocities along the column at the internal