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

Appendix 2: Membrane Permeation Relationships

The units of permeability may appear in several forms, as spelled out in Chapters 1 and 2, albeit the same symbol P i is used for each set of units. For convenience, the transformation or conversion between the several forms are furnished in spreadsheet notation as follows, with corresponding spreadsheet examples appended for each calculation.

Table A2.1: Excel Spreadsheet Designators and Formulas for Membrane Permeation Relationship Calculations for Example 2.1

Column

Equation or Designator

Spreadsheet Formula

A

Basic P i (units of 10 ?9 cm 3 per cm 2-sec-cm Hg/cm)

(given)

B

Basic P i* (10 ?3)(76), 10 ?6 cm 3 per cm 2-atm/cm or 10 ?6 cm 2 per sec-atm

A10*POWER(10, 3)*76

C

Thickness = ? m (microns or 10 ?4 cm)

(fixed)

D

Overall P i = Basic P i* (10 ?9)* (76/22,414)* [1/ ? m(10 ?4)]*10 1 (units of g-moles per cm 2-sec-atm

A10*POWER(10, ?9)*(76/22,414)*(1/C10*POWER(10, 4))*10

E

Overall P i = D*(30.48) 2* (3600/453.9)*(1/14.696), lb-moles per ft 2-hr-psi

D10*POWER(30.48,2)*(3600)/453.9*14.696

F

Area, cm 2

(set at 1000 cm 2)

G

P L P V

(set at 1 atm)

H

Permeation Flux (g-moles/1000 cm 2-sec-1 atm difference, where 929 cm 2 = 1 ft 2)

D10*F10*G10

I

Permeation Flux (lb-moles/ft 2-hr-atm difference)

H10*3600/453.6*(929/1000)

J

Diffusivity, cm 2/sec at 1 atm

B10*G10

Table A2.2: Membrane Permeation...

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