# Distillation of a Complex Mixture. Part II: Performance Analysis of a Distillation Column Using Exergy

^{*}

## Abstract

**:**

**17**, is presented graphically to evaluate the cumulative irreversibilities from the overhead to the bottom. This presentation is equivalent to the Grassmann diagram.

## 1. Introduction

- Heat transfer due to a finite temperature difference δT
- Mass transfer due to the mixing liquid and vapour streams
- Heat losses through the column wall.

## 2. Theoretical Considerations

_{0}, P

_{0}), its expression is written:

_{min}is the exergy of the same stream when it is in equilibrium with the ambient conditions (T

_{0}, P

_{0}) defined as being the dead state. By definition, the exergy function has as an expression:

_{ref}, P

_{ref}).. As the mathematical expression allowing the calculation of the enthalpy was presented in part I, the expression of the entropy is presented in appendix ADI. In addition, for a real system, site of an irreversible transformation, effective work (useful) is lower than that calculated for a reversible process. Thus, the variation of available work for a system working in steady state is a measurement of the net degradation of exergy irreversibility which accompanies the real transformation. Technical thermodynamics shows that mechanical work is a very noble form of energy and of higher quality compared to heat. The conversion factor connecting them is the factor of Carnot [22]:

_{Qj}being the thermal exergy exchanged with the tray J, given by following equation:

## 3. Simulation of the Column

- Negligible pressure losses.
- Adiabatic column except at the ends.
- The tray obeys the model of continuously stirred reactor.

- The compositions, the temperatures and the stream flow rates at each tray are determined by the iterative methods of nonlinear algebraic Thomas equations. In order to initialize calculations, it is supposed that the temperature profile is linear along the column with the temperatures at the ends (condenser and reboiler) determined by the method of bubble.
- The balance calculation is completed when convergence criteria are met.
- At this step, the program will calculate the exergy of the various streams after having considered the ambient conditions as the dead state whose temperature is T0 = 298.15 K.
- The last step of the execution consists in calculating the exergetic efficiency by using Equation (15).

**Figure 3.**Flow chart of simulation and exergetic calculationsfor the distillation column of complex mixtures.

## 4. Results and Discussion

_{.}

Component | C_{1} | C_{2} | C_{3} | Iso-C_{4} | n-C_{4} | Iso-C_{5} | n-C_{5} | C_{6}^{+} |

Composition (% mol. ). | 1.00 | 3.00 | 55.00 | 10.50 | 25.00 | 5.00 | 0.50 | Traces |

#### 4.1. Profile of key component composition versus tray position

_{trays}) presented in Figure 4 are not derivable and that for component C3, the trays higher than 24 are almost inactive. Such a result is confirmed by the local exergetic analysis. However, due to the complexity of the interactions in the mixture to be distilled, the profile of component C4 composition continues its progression according to a profile identical to that of the temperature up to the reboiler where the temperature is equal to that of bubble point of the residue. Indeed, this complexity in the distillation of the mixtures requires systematic methods for column sequence determinations. The problem would more become complicated for highly non ideal systems or with chemical reaction (reactive distillation) where the resolution of the equations of the model leads to multiple solutions. In such cases, the geometrical methods are particularly effective in the localization of the solutions

**Figure 4.**Key components composition profiles in the column. Feed tray = 14. Saturated liquid flow rate = 100 kmol/hr.

#### 4.2. Influence of the feed rate on the exergetic efficiency.

#### 4.3. Distribution of the exergy losses in the column

**Figure 6.**Exergy losses distribution in the rectifying section (condenser and feed tray not included).

**Figure 7.**Distribution of exergy losses in the stripping section (reboiler and feed tray not included).

#### 4.4. Profile of the variation of the irreversibilities with tray position

Section | Operating parameters Exchanged heat and exergy | F=100 kmol/hr D= 0.72 m. | F=150 kmol/hr D=0.87 m. | F=200 kmol/hr D=1.05 m. |
---|---|---|---|---|

Rectifying section | Q_{c} (kcal/hr) exchanged heat at the condenser | 6.846 10^{5} | 1.0264 10^{6} | 1.4820 10^{6} |

IQc (kcal/hr): exergy exchanged at the condenser | 1.850 10^{4} | 2.7730 10^{4} | 4.1100 10^{4} | |

Itot (kcal/hr): Irreversibilities consumed at the section | 3.848 10^{4} | 5.7650 10^{4} | 8.7430 10^{4} | |

Stripping section | Qr (kcal/hr): exchanged heat at the reboiler | 7.123 10^{5} | 1.0680 10^{6} | 1.5298 10^{6} |

IQr (kcal/hr): exergy exchanged at the reboiler | 4.456 10^{3} | 6.8160 10^{3} | 9.8040 10^{4} | |

Itot (kcal/hr): Irreversibilities consumed at the section | 3.485 10^{4} | 5.2280 10^{4} | 7.1530 10^{4} | |

Total exergy loss (kcal/hr) | 8.3288 10^{4} | 1.24811 10^{5} | 1.8790 10^{5} | |

Minimum separation work (kcal/hr) | 4.2069 10^{4} | 6.3163 10^{4} | 7.2796 10^{4} | |

Exergy consumed (kcal/hr) | 1.2536 10^{5} | 1.8790 10^{5} | 2,.070 10^{5} |

## 5. Conclusions

- Temperature pinch δT (= (TN - T1)).
- Thermal power exchanged at the condenser (Qc) and the reboiler (Qr).

## Nomenclature

COP | Coefficient of performance | |

D | Distillate flow rate | (kmol/hr) |

Ex | Stream exergy | (kcal/kmol) |

F | Feed rate | (kmol/hr) |

H | Stream enthalpy | (kcal/kmol) |

I | Irreversibilities flux | (kcal/hr) |

L | Liquid stream flow rate | (kmol/hr) |

M | Liquid side stream | (kmol/hr) |

m | Stream molar flow rate | (kmol/hr) |

P_{o} | Ambient medium pressure | (1 atm.) |

Q_{c} | Heat rate exchanged at the condenser | (kcal/hr) |

Q_{r} | Heat rate exchanged at the reboiler | (kcal/hr) |

S | Stream entropy | (kcal/kmol) |

T_{ref} | Reference temperature | (K) |

T_{o} | Ambient medium temperature | (273.15 K) |

U | Vapor side stream | (298.15K) |

V | Stream flow rate | (kmol/hr) |

W | Applied mechanical work | (kcal/kmol) |

Subscripts | ||

i | Component i in the mixture | |

j | Tray number | |

Greek Symbols | ||

Φ | Carnot’s coefficient | |

η_{ex} | Exergetic efficiency |

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**MDPI and ACS Style**

Mustapha, D.; Sabria, T.; Fatima, O.
Distillation of a Complex Mixture. Part II: Performance Analysis of a Distillation Column Using Exergy. *Entropy* **2007**, *9*, 137-151.
https://doi.org/10.3390/e9030137

**AMA Style**

Mustapha D, Sabria T, Fatima O.
Distillation of a Complex Mixture. Part II: Performance Analysis of a Distillation Column Using Exergy. *Entropy*. 2007; 9(3):137-151.
https://doi.org/10.3390/e9030137

**Chicago/Turabian Style**

Mustapha, Douani, Terkhi Sabria, and Ouadjenia Fatima.
2007. "Distillation of a Complex Mixture. Part II: Performance Analysis of a Distillation Column Using Exergy" *Entropy* 9, no. 3: 137-151.
https://doi.org/10.3390/e9030137