# Dividing-Wall Column Design: Analysis of Methodologies Tailored to Process Simulators

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## Abstract

**:**

## 1. Introduction

## 2. Design Methodologies for DWCs

^{®}. For the analysis of internal flows, the method of minimum vapor diagram (Vmin) is examined. Finally, the design methodology by Sotudeh & Shahraki (S&S), which provides feasible internal flows, followed by the column topology, is also investigated.

#### 2.1. Triantafyllou & Smith (T&S) Methodology

#### 2.2. Vmin Diagram Method

#### 2.3. Sotudeh & Shahraki (S&S) Method

#### 2.4. A Modified S&S Method (MS&S)

#### 2.5. Optimal Design of DWCs

^{®}, coupled with the Aspen Plus process simulator. The optimization problem consists of a constrained, mixed-integer optimization model, and the model is given by Equations (13)–(19).

## 3. Case Studies and Simulation Parameters

## 4. Results and Discussion

#### 4.1. Results for Mixtures with ESI Close to 1

#### 4.1.1. Case Study Involving Benzene, Toluene, and o-Xylene (BTX)

#### 4.1.2. Case Study Involving n-Pentane, n-Hexane, and n-Heptane (PHH)

#### 4.2. Results for the Case Study with ESI > 1.5

#### Case Study Involving n-Butane, i-Pentane, and n-Pentane (BPP)

#### 4.3. Results for Mixtures with ESI < 0.5

#### 4.3.1. Case Study Involving i-Butane, n-Butane, and n-Hexane (BBH)

#### 4.3.2. Case Study Involving i-Pentane, n-Pentane, and n-Hexane (PPH)

#### 4.4. Comparison of the Design Methodologies

#### 4.5. Selection of the Liquid Split in the S&S Methodology

#### 4.6. Perspectives and Future Directions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DWCs | Dividing-wall columns |

Vmin | Minimum vapor |

T&S | Triantafyllou and Smith |

S&S | Sotudeh and Shahraki |

DWC | Dividing-wall column |

FUGK | Fenske-Underwood-Gilliland-Kirkbride |

ESI | Ease of separation index |

L/D | Reflux ratio |

V/B | Boilup ratio |

MS&S | Modified S&S Method |

GA | Genetic Algorithm |

TAC | Total annual cost |

BTX | Benzene, Toluene, and o-Xylene mixture |

PHH | n-Pentane, n-Hexane, and n-Heptane mixture |

BPP | n-Butane, i-Pentane, and n-Pentane mixture |

BHH | i-Butane, n-Butane, and n-Hexane mixture |

PPH | i-Pentane, n-Pentane, and n-Hexane mixture |

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**Figure 8.**Sensitivity analysis for the DWC design obtained with the Vmin method for the BBH mixture.

Case 1. BTX |

Benzene (A), Toluene (B), Xilene (C) |

$F=1kmol\u2215s$,$T=358K$ |

Feed Composition $\left({Z}_{A},{Z}_{B},{Z}_{C}\right)=\left(0.3,0.3,0.4\right)$ |

Relative volatility $\left({\alpha}_{A},{\alpha}_{B},{\alpha}_{C}\right)=\left(7.49,2.92,1\right)$ |

Thermodynamic model: Chao-Seader |

$ESI=0.83$ |

Case 2. PHH |

n-Pentane (A), n-Hexane (B), n-Heptane (C) |

$F=45.4kmol\u2215h$,${P}_{Feed}=2.04atm$ |

Feed Composition $\left({Z}_{A},{Z}_{B},{Z}_{C}\right)=\left(0.33,0.33,0.34\right)$ |

Relative volatility $\left({\alpha}_{A},{\alpha}_{B},{\alpha}_{C}\right)=\left(6.02,2.92,1\right)$ |

Thermodynamic model: RK-Soave |

$ESI=1.04$ |

Case 3. BPP |

n-Butane (A), i-Pentane (B), n-Pentane (C) |

$F=45.4kmol\u2215h$,${P}_{Feed}=6.17atm$ |

Feed Composition $\left({Z}_{A},{Z}_{B},{Z}_{C}\right)=\left(0.33,0.33,0.34\right)$ |

Relative volatility $\left({\alpha}_{A},{\alpha}_{B},{\alpha}_{C}\right)=\left(2.05,1.21,1\right)$ |

Thermodynamic model: RK-Soave |

$ESI=1.86$ |

Case 4. BBH |

i-Butane (A), n-Butane (B), n-Hexane (C) |

$F=45.4kmol\u2215h$,${P}_{Feed}=7.7atm$ |

Feed Composition $\left({Z}_{A},{Z}_{B},{Z}_{C}\right)=\left(0.33,0.33,0.34\right)$ |

Relative volatility $\left({\alpha}_{A},{\alpha}_{B},{\alpha}_{C}\right)=\left(7.47,5.66,1\right)$ |

Thermodynamic model: RK-Soave |

$ESI=0.18$ |

Case 5. PPH |

i-Pentane (A), n-Pentane (B), n-Hexane (C) |

$F=45.4kmol\u2215h$,${P}_{Feed}=2.55atm$ |

Feed Composition $\left({Z}_{A},{Z}_{B},{Z}_{C}\right)=\left(0.33,0.33,0.34\right)$ |

Relative volatility $\left({\alpha}_{A},{\alpha}_{B},{\alpha}_{C}\right)=\left(3.45,2.69,1\right)$ |

Thermodynamic model: RK-Soave |

$ESI=0.47$ |

Case 1 BTX | Vmin | T&S | S&S | MS&S | OPT | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 24 | 48 | 20 | 44 | 17 | 35 | 22 | 42 | 22 | 43 |

Feed stage | 15 | 15, 39 | 12 | 14, 34 | 9 | 10, 27 | 11 | 9, 31 | 12 | 9, 31 |

Side stage | 24 | 20 | 19 | 17 | 17 | |||||

Reflux ratio | 2.94 | 2.98 | 3.76 | 2.95 | 2.75 | |||||

L-p (kmol/h) | 817 | 901 | 1013 | 857 | 846 | |||||

V-p (kmol/h) | 2297 | 2321 | 2648 | 2205 | 2342 | |||||

Diameter (m) | 9.74 | 9.86 | 10.78 | 9.76 | 9.69 | |||||

QC (kW) | 38,353 | 39,025 | 46,456 | 38412 | 36,577 | |||||

QR (kW) | 41,215 | 41,661 | 48,740 | 40904 | 39,103 | |||||

TAC ($/year) | 12,390,000 | 12,433,000 | 14,177,296 | 12,178,000 | 11,717,000 | |||||

Difference (%) | 5.7 | 6.1 | 21.0 | 3.9 | 0 |

Case 1 PHH | Vmin | T&S | S&S | MS&S | OPT | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 26 | 52 | 22 | 46 | 19 | 38 | 24 | 45 | 22 | 43 |

Feed stage | 16 | 15, 41 | 14 | 13, 35 | 10 | 9, 29 | 12 | 9, 33 | 14 | 9, 31 |

Side stage | 24 | 18 | 18 | 17 | 20 | |||||

Reflux ratio | 3.36 | 3.95 | 9.78 | 3.27 | 3.30 | |||||

L-p (kmol/h) | 11.9 | 12.4 | 15.0 | 14.3 | 15.9 | |||||

V-p (kmol/h) | 27.3 | 28.9 | 37.0 | 32.2 | 34.2 | |||||

Diameter (m) | 0.79 | 0.83 | 1.15 | 0.80 | 0.80 | |||||

QC (kW) | 467 | 530 | 1161 | 459 | 461 | |||||

QR (kW) | 469 | 531 | 1163 | 461 | 463 | |||||

TAC ($/year) | 255,630 | 272,240 | 485,648 | 245,570 | 243,050 | |||||

Difference (%) | 5.7 | 6.1 | 21.0 | 3.9 | 0 |

CASE BPP | Vmin | T&S | S&S | MS&S | OPT | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 61 | 123 | 69 | 124 | 64 | 119 | 69 | 124 | 67 | 123 |

Feed stage | 35 | 15, 76 | 38 | 12, 81 | 32 | 10, 74 | 32 | 7, 76 | 36 | 6, 73 |

Side stage | 26 | 18 | 24 | 18 | 21 | |||||

Reflux ratio | 14.20 | 13.49 | 43.41 | 12.83 | 12.65 | |||||

L-p (kmol/h) | 36.5 | 32.8 | 53.2 | 43.6 | 36.0 | |||||

V-p (kmol/h) | 46.7 | 44.3 | 72.1 | 55.4 | 47.0 | |||||

Diameter (m) | 1.00 | 0.98 | 1.71 | 0.98 | 0.96 | |||||

QC (kW) | 1282 | 1219 | 3761 | 1169 | 1156 | |||||

QR (kW) | 1268 | 1206 | 3747 | 1156 | 1143 | |||||

TAC ($/year) | 631,260 | 607,810 | 1,500,009 | 593,970 | 583,800 | |||||

Difference (%) | 8.1 | 4.1 | 156.9 | 1.7 | 0 |

Case BBH | Vmin | T&S | S&S | MS&S | OPT | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 40 | 84 | 34 | 73 | 42 | 79 | 45 | 85 | 43 | 81 |

Feed stage | 20 | 38, 78 | 16 | 36, 70 | 23 | 34, 76 | 12 | 38, 83 | 18 | 36, 79 |

Side stage | 72 | 66 | 71 | 78 | 71 | |||||

Reflux ratio | 43.78 | 14.30 | 13.42 | 10.04 | 8.71 | |||||

L-p(kmol/h) | 11.5 | 10.0 | 10.1 | 14.9 | 13.3 | |||||

V-p(kmol/h) | 30.4 | 28.0 | 37.8 | 37.3 | 30.1 | |||||

Diameter (m) | 1.54 | 0.92 | 0.91 | 0.82 | 0.77 | |||||

QC (kW) | 3359 | 1154 | 1090 | 830 | 728 | |||||

QR (kW) | 3391 | 1185 | 1120 | 861 | 759 | |||||

TAC ($/year) | 1,344,900 | 551,080 | 537,783 | 447,691 | 400,250 | |||||

Difference (%) | 236.0 | 37.7 | 34.4 | 11.9 | 0 |

Case PPH | Vmin | T&S | S&S | MS&S | OPT | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 51 | 115 | 40 | 96 | 48 | 90 | 62 | 120 | 55 | 103 |

Feed stage | 32 | 55, 106 | 24 | 52, 92 | 26 | 37, 85 | 33 | 54, 116 | 13 | 44, 99 |

Side stage | 90 | 83 | 77 | 109 | 89 | |||||

Reflux ratio | 32.32 | 12.54 | 17.89 | 10.58 | 8.07 | |||||

L-p (kmol/h) | 24.3 | 23.9 | 23.6 | 29.9 | 30.9 | |||||

V-p (kmol/h) | 43.9 | 43.5 | 50.4 | 53.1 | 47.1 | |||||

Diameter (m) | 1.77 | 1.17 | 1.37 | 1.13 | 1.01 | |||||

QC (kW) | 3340 | 1360 | 1911 | 1171 | 910 | |||||

QR (kW) | 3331 | 1352 | 1903 | 1162 | 902 | |||||

TAC ($/year) | 1,386,500 | 649,290 | 836,837 | 607,960 | 493,300 | |||||

Difference (%) | 181.1 | 31.6 | 69.6 | 26.3 | 0 |

Case Study | BTX | PHH | BPP | BBH | PPH | |||||
---|---|---|---|---|---|---|---|---|---|---|

PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | PRE | MAIN | |

Stages | 24 | 46 | 27 | 50 | 80 | 146 | 51 | 94 | 58 | 108 |

Feed stage | 12 | 11, 35 | 14 | 10, 37 | 40 | 10, 90 | 28 | 40, 91 | 26 | 45, 103 |

Side stage | 22 | 20 | 23 | 86 | 96 | |||||

Reflux ratio | 3.20 | 3.78 | 14.46 | 14.56 | 13.10 | |||||

L-p (kmol/h) | 1521 | 22 | 85 | 31 | 47 | |||||

V-p (kmol/h) | 3156 | 44 | 104 | 58 | 74 | |||||

Diameter (m) | 10.59 | 0.88 | 1.11 | 0.97 | 1.26 | |||||

QC (kW) | 40,975 | 512 | 1309 | 1168 | 1415 | |||||

QR (kW) | 43,721 | 513 | 1295 | 1199 | 1407 | |||||

TAC ($/year) | 13,110,116 | 278,054 | 700,583 | 595,130 | 705,556 | |||||

Difference (%) | 11.9 | 14.4 | 20.0 | 48.7 | 43.0 |

Methodology | Advantages | Drawbacks |
---|---|---|

Vmin | It is easy to implement as it only uses the Underwood equation, and it is easy to adapt to process simulators. It can provide good designs with near-optimal TACs when ESI is higher than 0.8. | It does not provide information about tray arrangements. When ESI is lower than 0.5, it returns large reflux ratios, which means large TACs. |

T&S | It can provide good designs, independently of the ESI value of the mixture. It is easily tailored to process simulators. | It is more complex than Vmin because T&S applies the FUGK equations, not only the Underwood equations. |

S&S | It provides equations to determine the topological arrangement. | Gaps in the assumptions can influence the economic performance, leading to poor designs. |

MS&S | This methodology helps to reduce the complexity of the S&S method by using process simulators. It allows obtaining improved designs. | It requires several calculations, although all information can be obtained from the process simulator. |

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**MDPI and ACS Style**

Buitimea-Cerón, G.A.; Hahn, J.; Medina-Herrera, N.; Jiménez-Gutiérrez, A.; Loredo-Medrano, J.A.; Tututi-Avila, S.
Dividing-Wall Column Design: Analysis of Methodologies Tailored to Process Simulators. *Processes* **2021**, *9*, 1189.
https://doi.org/10.3390/pr9071189

**AMA Style**

Buitimea-Cerón GA, Hahn J, Medina-Herrera N, Jiménez-Gutiérrez A, Loredo-Medrano JA, Tututi-Avila S.
Dividing-Wall Column Design: Analysis of Methodologies Tailored to Process Simulators. *Processes*. 2021; 9(7):1189.
https://doi.org/10.3390/pr9071189

**Chicago/Turabian Style**

Buitimea-Cerón, Gloria A., Juergen Hahn, Nancy Medina-Herrera, Arturo Jiménez-Gutiérrez, José A. Loredo-Medrano, and Salvador Tututi-Avila.
2021. "Dividing-Wall Column Design: Analysis of Methodologies Tailored to Process Simulators" *Processes* 9, no. 7: 1189.
https://doi.org/10.3390/pr9071189