A feed to a column has the composition given in the table below, and is at a pressure of 14 bar and a temperature of 60^{\circ} C. Calculate the flow and composition of the liquid and vapour phases. Take the equilibrium data from the Depriester charts given in Chapter 8.
| kmol/h | Z_{i} | ||
| Feed | \text { ethane }\left( C _{2}\right) | 20 | 0.25 |
| \text { propane }\left(C_{3}\right) | 20 | 0.25 | |
| \text { isobutane }\left( iC _{4}\right) | 20 | 0.25 | |
| \text { n-pentane }\left( nC _{5}\right) | 20 | 0.25 | |
For two phases to exist the flash temperature must lie between the bubble point and dew point of the mixture.
From equations 11.5a and 11.5b:
\text { bubble point: } \sum y_{i}=\sum K_{i} x_{i}=1.0 (11.5a)
\text { and dew point: } \sum x_{i}=\sum \frac{y_{i}}{K_{i}}=1.0 (11.5b)
\sum K_{i} z_{i}>1.0
\sum \frac{z_{i}}{K_{i}}>1.0
Check feed condition
| K_{i} | K_{i} z_{i} | z_{i} / K_{i} | |
| C _{2} | 3.8 | 0.95 | 0.07 |
| C _{3} | 1.3 | 0.33 | 0.19 |
| iC _{4} | 0.43 | 0.11 | 0.58 |
| nC _{5} | 0.16 | 0.04 | 1.56 |
therefore the feed is a two phase mixture.
Flash calculation
| K_{i} | \text { Try } L / V=1.5 | Try L/V = 3.0 | |||
| A_{i}=L / V K_{i} | V_{i}=F z_{i} /\left(1+A_{i}\right) | A_{i} | V_{i} | ||
| C _{2} | 3.8 | 0.395 | 14.34 | 0.789 | 11.17 |
| C _{3} | 1.3 | 1.154 | 9.29 | 2.308 | 6.04 |
| iC _{4} | 0.43 | 3.488 | 4.46 | 6.977 | 2.51 |
| nC _{5} | 0.16 | 9.375 | 1.93 | 18.75 | 1.01 |
| V_{ calc }=30.02 | V_{\text {calc }}=20.73 | ||||
| L / V=\frac{80-30.02}{30.02}=1.67 | L / V=2.80 | ||||
Hengstebeck’s method is used to find the third trial value for L/V. The calculated values are plotted against the assumed values and the intercept with a line at 45^{\circ} (calculated = assumed) gives the new trial value, 2.4.
| Try L/V = 2.4 | y_{i}=V_{i} / V | x_{i}=\left(F z_{i}-V_{i}\right) / L | ||
| A_{i} | V_{i} | |||
| C _{2} | 0.632 | 12.26 | 0.52 | 0.14 |
| C _{3} | 1.846 | 7.03 | 0.30 | 0.23 |
| iC _{4} | 5.581 | 3.04 | 0.13 | 0.30 |
| nC _{5} | 15.00 | 1.25 | 0.05 | 0.33 |
| V_{ cal }=23.58 | 1.00 | 1.00 | ||
| L=80-23.58=56.42 kmol / h | ||||
| L / V \text { calculated }=56.42 / 23.58=2.39\text{ closeenoughto the assumed value of } 2.4. | ||||
Adiabatic flash
In many flash processes the feed stream is at a higher pressure than the flash pressure and the heat for vaporisation is provided by the enthalpy of the feed. In this situation the flash temperature will not be known and must be found by trial and error. A temperature must be found at which both the material and energy balances are satisfied.