Membrane Separations Technology: Single-Stage, Multistage, and Differential Permeation

Appendix 5: Differential Permeation with Point Permeate Withdrawal

The objective is to determine the membrane area required for up to 100% transfer of the feedstream F =L 1, starting at its bubble point, where V =V 1 =0.

Table A5.1: Excel Spreadsheet Designators and Formulas for Differential Permeation with Point Permeate Withdrawal Calculations

Column

Equation or Designator

Spreadsheet Formula

A

(x F) i

(given)

B

(x F) j

(given)

C

P i

(given)

D

P j

(given)

E

P L

(fixed)

F

P V

(fixed)

G

V/F (signifies bubble-point condition for L1 = F)

(fixed at zero)

H

L/F= 1-V/F

(will be unity)

I

Skip

J

V or V ? (for bubble-point calc)

(trial and error)

K

K i = P i PL/(V+ P i PV)

C7*E7/(J7+C7*F7)

L

K j = P jP L/(V+ P jP V)

D7*E7(J7+D7*F7)

M

x i = (x F) i/[(V/F)K i + L/F]

A7/(G7*K7+H7)

N

x j = (x F) j /[(V/F)K j + L/F]

B7/(G7*L7+H7)

O

y i = K i x i

K7*M7

P

y i = K j x j

L7*N7

Q

?x i = 1

SUM(O8: P8)

R

1/(x i y i)

1/(M7-O7)

S

[1/(x i y i)] av ?x i

((R7+R8)/2)*(M8-M7)

T

Partial Sum of S

T7+S8

U

L/L 1 = 1/exp(Partial Sum)

1/EXP(T8)

V

P L x i

E7*M7

W

P

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