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

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.
| 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 |