# Selection of Optimum Separation Sequence for Multicomponent Distillation

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## Abstract

**:**

## 1. Introduction

## 2. Limiting Capabilities of a Multicomponent Fractional Distillation Columns

- Mass transfer on a plate or in a packing section is equimolar and the fluid stream changes abruptly at the feed point.
- At every plate or packing section the pressure and the temperature of the fluid and the vapor streams are equal (they differ from one plate to another).
- Diffusion effects between consequent plate are negligible.
- The enthalpy of outgoing streams is being transferred to the incoming ones and the irreversibility of this process is negligible.
- The stream of the mixture being separated comes to the column at the plate where the temperature of the liquid stream is equal to the one of the feed and the entropy generation due to the mixing of streams with different compositions is negligible (It is not quite clear whether this last assumption is always acceptable. This question is the subject of the current research).

- Molar fractions of components in the feed stream ${x}_{Fi}$, boiling points ${T}_{i}^{0}$ and molar latent heats of vaporization ${r}_{i}$, $i=1,\dots ,n$ (at standard conditions). It is assumed the from $i<j$ follows that ${T}_{i}^{0}<{T}_{j}^{0}$.
- The composition of products: the distillate ${x}_{Di}$ and the bottom product ${x}_{Bi}$.
- Parameters of a column: pressure $\overline{P}$, temperature in reboiler ${T}_{B}$, temperature in condenser ${T}_{D}$ (Figure 1). These values depend on a chosen separation order.

#### Thermodynamic Balance Equations for Binary Distillation and Relationship Between Energy Consumption and Capacity of Column

## 3. Optimal Separation Sequence for Multicomponent Fractional Distillation

#### Cascade of Two Binary Distillation Columns

**Rule**is true: If the first column of the cascade has the highest capacity, the separation sequence must be chosen in the way in which the efficiency of one stage is greater than the one of next stages.

#### Cascade of Three Binary Distillation Columns

## 4. Parametrization of the Column Capacity as the Function of the Energy Consumption

#### Complete Separation

## 5. Computation of the Thermal Efficiency

- The temperature in the condenser ${T}_{D}$, compositions of the feed and product streams ${x}_{F}$, ${x}_{D}$, ${x}_{B}$ and Antoine equation coefficients ${A}_{i}$, ${B}_{i}$, ${C}_{i}$ are given for every component.
- The VLE equation for the reboiler (35) is solved numerically to find ${T}_{B}$.

#### Example 1. Two-Component Mixture

#### Example 2. Multi-Component Mixture

## 6. Results

## Author Contributions

## Funding

## Conflicts of Interest

## Notation

x — molar fraction of component in the liquid phase; |

y — molar fraction of component in the vapor phase; |

T — temperature, K; |

g — material stream, mole/s; |

$\epsilon $ — fraction of the upper product; |

r — molar latent heat of vaporization, J/mole; |

h — molar enthalpy, J/mole; |

s — molar entropy, J/(mole·K); |

q — heat stream, W; |

$\sigma $ — entropy generation, W/K; |

$\mu $ — chemical potential, J/mole; |

R — gas constant, 8.31 J/(mole·K); |

W — work of a reversible separation, J/mole; |

p — power, W; |

$\eta $ — efficiency; |

$\gamma $ — fraction of the total power; |

C — thermodynamic difficulty of a separation; |

$\beta $ — heat transfer coefficient, W/K; |

k — mass transfer coefficient, mole${}^{2}$·K/(J·s); |

a — irreversibility coefficient, mole·s/J${}^{2}$; |

b — reversible efficiency, mole/J; |

K — VLE equilibrium ratio; |

P — pressure; |

$A,\phantom{\rule{0.222222em}{0ex}}B,\phantom{\rule{0.222222em}{0ex}}C$ — Antoine equation coefficients. |

## Indices

$i,\phantom{\rule{0.222222em}{0ex}}j$ — corresponding to the i-th or j-th component; |

F — corresponding to the feed stream; |

B — corresponding to the reboiler; |

D — corresponding to the condenser; |

+ — corresponding to the heating fluid; |

− — corresponding to the cooling fluid; |

0 — corresponding to some standard or ideal condition; |

$min$ — minimum value; |

c — Carnot (for ex. Carnot efficiency); |

G — corresponding to streams of matter (for ex. work of separation); |

$rev$ — reversible; |

* — optimum or bounding value; |

m — molar (when there is ambiguity); |

overline — total (for ex. pressure); |

## References

- Green, D.W.; Southard, M.Z. (Eds.) Approximate Multicomponent Distillation Methods. In Perry’s Chemical Engineers’ Handbook; McGraw-Hill Education: New York, NY, USA, 2019. [Google Scholar]
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**2017**, 42, 359–369. [Google Scholar] [CrossRef] - Poling, B.E.; Prausnitz, J.M.; O’Connell, J.P. Properties of Gases and Liquids; McGraw-Hill: New York, NY, USA, 2004. [Google Scholar]
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Component | ${\mathit{x}}_{\mathit{F}}$ | ${\mathit{x}}_{\mathit{D}}$ | ${\mathit{x}}_{\mathit{B}}$ | A | B | C | r, kJ/mole |
---|---|---|---|---|---|---|---|

Benzene | 0.4 | 0.95 | 0.1 | 4.01814 | 1203.835 | −53.226 | 33.9 |

Toluene | 0.6 | 0.05 | 0.9 | 4.07827 | 1343.943 | −53.773 | 37 |

Component | ${\mathit{x}}_{\mathit{F}}$ | ${\mathit{x}}_{\mathit{D}}$ | ${\mathit{x}}_{\mathit{B}}$ | A | B | C | r | ${\mathit{T}}_{0}$, K |
---|---|---|---|---|---|---|---|---|

Methane | 0.26 | 0.435 | 0 | 3.9895 | 443.028 | −0.49 | 8.5 | 111.65 |

Ethane | 0.09 | 0.15 | 0 | 4.50706 | 791.3 | −6.422 | 9.76 | 184 |

Propane | 0.25 | 0.41 | 0.01 | 4.53678 | 1149.36 | 24.906 | 16.25 | 231 |

n-Butane | 0.17 | 0.005 | 0.417 | 4.35576 | 1175.581 | −2.071 | 22.4 | 272 |

n-Pentane | 0.11 | 0 | 0.274 | 3.9892 | 1070.617 | −40.454 | 26.5 | 309 |

n-Hexane | 0.12 | 0 | 0.299 | 3.45604 | 1044.038 | −53.893 | 31 | 341 |

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**MDPI and ACS Style**

Tsirlin, A.; Sukin, I.; Balunov, A.
Selection of Optimum Separation Sequence for Multicomponent Distillation. *ChemEngineering* **2019**, *3*, 69.
https://doi.org/10.3390/chemengineering3030069

**AMA Style**

Tsirlin A, Sukin I, Balunov A.
Selection of Optimum Separation Sequence for Multicomponent Distillation. *ChemEngineering*. 2019; 3(3):69.
https://doi.org/10.3390/chemengineering3030069

**Chicago/Turabian Style**

Tsirlin, Anatoly, Ivan Sukin, and Alexander Balunov.
2019. "Selection of Optimum Separation Sequence for Multicomponent Distillation" *ChemEngineering* 3, no. 3: 69.
https://doi.org/10.3390/chemengineering3030069