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

Appendix 3: Single-Stage Membrane Separations

Overview

Numbers are used to designate a particular component in column A, and the number 7 may range on up through, say, 16 or however many different components there are to be; that is, i varies from i = 7 through i = 16, or the number of components involved, as per column A. For a binary mixture, for convenience, i ranges only from i = 7 through i = 8; that is, i = 7 and j = 8. Furthermore, the calculation is to be trial-and-error in the variable V such that ?x i, = 1 (and ? i = 1).

The relationships in Table A3.1 apply, as per the accompanying tabulation and spreadsheet calculations, where the asterisk symbol (*) stands for multiplication and the slash symbol (/) for division.

Table A3.1: Excel Spreadsheet Designators and Formulas for Single-Stage Membrane Separation Calculations

Column

Equation or Designator

Spreadsheet Formula

A

Component

B

(x F) i

(given)

C

P i

(given)

D

P L

(fixed)

E

P V

(fixed)

F

V/F

(specified)

G

L/F = 1 ? V/F

G7 = 1 ? F7

H (skip column)

I

V ?

(trial and error)

J

K i = P iP L/(V+ P i P V)

J7 = C7*D7/(J7+C7*E7)

K

x i = (x F) i /(V/Fk i + L/F)

K7 = B7/(F7*J7+G7)

Sum = 1

?

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