Page 339 - Pressure Swing Adsorption

PRESSURE SWING ADSORPTION APPENDIX B 317
316

Eouatlon B.4 now becomes:
(B.l I)

clx 8 . [ /3n[l - YA(i)] • ]
dT (J) = aB I+ f3AyA(j) + !3.[, - yA(i)] - Xe(/) '

1 = 2, ... ,M + 1 1:;, ~1~·
The following set of linear algebraic equations is obtained when the dimen-
sionless overall material balance eauatlon (Ea. B.7) and the velocity bound-
~
0
ary conditions (Eq. B.8) are combined and wntten m collocatmn form: .Q 0
" •
0 "' .5
M~• (A (. ") _ Ax(M + 2,i)Ax(J,M+ 2))-(") (B.12) ,. " "'
;_, XJ,l Ax(M+2M 2\ VI ' 0 • '5
•=2 - ' • + ; :;:
j3AyA(i) · )
(
= -,fr [ aA 1 + j3AyA(i) + J3.[1 - YA(i)] - xA(i) "- .
%!~
I "I ';, 0 0
13,.[1 - y,,(i)] ( )] -l<c "- C 0.
+ Ys<r 11 -,---'--=~-'-''"[r'-''---~-)~] - x n j)
(
+ /JAy,,(j) + /311 ] - y,,(j
·- N N
-[Ax(_ ) _ Ax(J, M + 2)Ax(M -r 2, 1) )-< ) _ l_ ap
I
J,l Ax(M+ 2,M+ 2) v Par·
~ t'
J = 2, ... , M + 1 '5 -. ;;
0 0 - O 0 0 .
The followmg ·eauat10ns, which are denved from the boundary conditions, .5 .Q _g.::: Q
~
~
N
give the values at J = l and M + 2: ~ ·c N .s ~ •
n
E
0 ~ 1!' E ·o
M+I ~ Js .a e .5
YA(!)= -A, L [A,Ax(M + 2,i) -Ax(l,i)]YA(i) (B.13) ~ 0 -
M+I
-A L Ax(M+2,i)yA(i) +A,Peii(l)YAlz-o- " e
4 ~
!-2
M+i
YA(M+2) =A, L (A,Ax(M+2,i)-Ax(l,i)]yA(i) (B.14)
-A, Pe v(l)YAlz-o-
v(M + 2) = Ax(M + 2, 1) (1) (B.15)
Ax( M + 2, M + 2) v
\ I
M+ I
- ~ Ax(M+2,i)v(i))/Ax(M+2,M+2)
(
1 2
Note: Here J refers to the axiai locatton m the bed and is different from tile