# Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental and Process Modeling

#### 2.1. Materials

#### 2.2. Methods

#### 2.3. Simulation

#### 2.4. Optimization

_{C1}, N

_{C2}) and the feed stage locations of C1 and C2 (NF

_{C1}, NF

_{C2}). The continuous design variables include the distillation flow rates of C1 and C2 (DF

_{C1}, DF

_{C2}) and the reflux ratios of C1 and C2 (RR

_{C1}, RR

_{C2}). The sequence iterative optimization procedure of DCDS can be manipulated as follows:

- (1)
- Specify the initial operation parameters and use Design specifications and vary modules in simulation to maintain target purity. Herein, target purity is achieved by manipulating DF
_{C1}, DF_{C2}, RR_{C1}, and RR_{C2}using these two modules. - (2)
- Adjust NF
_{C1}and NF_{C2}to minimize the total heat duty (Q_{reb1}+ Q_{reb2}). - (3)
- If the TAC is minimized with N
_{C1}, obtain the optimum N_{C1}; if not, adjust N_{C1}and go back to step 2. - (4)
- If the TAC is minimized with N
_{C2}, obtain the optimum N_{C2}; if not, adjust N_{C2}and go back to step 2. - (5)
- Obtain the optimum parameters of DCDS.

_{CL}, N

_{CR}), the feed stages location of CL and CR (NF

_{LDWC}, N

_{AB_IN}, N

_{BC_IN}), and the side-draw stages location of CL and CR (N

_{AB_OUT}, N

_{BC_OUT}, N

_{B}). The seven continuous variables are the distillation flow rates and reflux ratios of CL and CR section (DF

_{CL}, DF

_{CR}, RR

_{CL}, RR

_{CR}), the flow rates of liquid-only transfer streams AB and BC(F

_{AB}, F

_{BC}), and the side-draw stage flow rate (F

_{B}). In the sequence iterative optimization procedure of LDWC, the optimum parameters can be obtained as follows:

- (1)
- Specify the initial operation parameters and use design specifications in Aspen Plus to maintain target purity. Herein, target purity is obtained by manipulating DF
_{CL}, DF_{CR}, RR_{CL}, RR_{CR}, and F_{B}using these two modules. - (2)
- Adjust NF
_{LDWC}, N_{AB_OUT}, N_{BC_OUT}, N_{AB_IN}, N_{BC_IN}, and N_{B}to minimize the total heat duty (QR_{L}+ QR_{R}). - (3)
- If the TAC is minimized with N
_{L}, get the optimum N_{L}; if not, adjust N_{L}and go back to step 2. - (4)
- If the TAC is minimized with N
_{R}, get the optimum N_{R}; if not, adjust N_{R}and go back to step 2. - (5)
- Get the optimum parameters of DCDS.

## 3. Results and Discussion

#### 3.1. Phase Equilibrium Data

_{i}and y

_{i}are mole fractions of component i in the liquid and vapor phases, respectively; γ

_{i}is the activity coefficient of component i in the liquid phase; R is the gas constant; and V

_{i}

^{L}is the liquid mole volume of pure component i.

_{i}

^{v}and φ

_{i}

^{s}represent the fugacity coefficient of component i in the vapor and saturated vapor phases, respectively. The vapor phase can be treated as an ideal gas at 101.3 kPa [32], which means that the last term on the right of Equation (1), φ

_{i}

^{v}

_{,}and φ

_{i}

^{s}can be assumed to be 1. Thus, the VLE relationship can be simplified as Equation (2).

_{i}

^{s}is the saturated vapor pressure of pure component i. It can be calculated by Extended Antoine Equation (3).

_{1i}–C

_{9i}are Extended Antoine Coefficients for component i, which are listed in Table 2.

#### 3.2. Thermodynamic Consistency Test

_{1}and γ

_{2}is the activity coefficient of component 1 and 2, respectively; x

_{1}is the mole fraction of component 1. When the value of D is no greater than 2 [33], the VLE data can be considered thermodynamically consistency. Meanwhile, the Redlich–Kister plots for two binary systems are illustrated in Figure 7.

^{exp}is the experimental data of y, and y

^{cal}is the calculated value. According to this method, the value of Δy should not be more than 0.01 for thermodynamic consistency [34].

#### 3.3. Data Regression

_{T}, σ

_{P}, σ

_{x}, and σ

_{y}represent the standard deviations of T, p, x, and y, respectively. The nonrandom interaction parameter (α

_{ij}) was set as 0.3 in the NRTL model. Table 4 summarizes all the regressed binary interaction parameters.

_{1}is no more than 0.0018 and 0.0009 for the two binary systems, respectively. RMSD of T is no more than 0.12 and 0.08, while RMSD of y

_{1}is no more than 0.0030 and 0.0012, respectively. Consequently, the VLE data can be effectively correlated using the three models. NRTL is taken for the following study because it presents the least AAD and RMSD for these two binary systems.

#### 3.4. Optimization Results and Comparison

_{C1}and N

_{C2}are 62 and 58, respectively. The optimization process for LDWC is illustrated in Figure 14, which displays the relationship between the stage in the left column CL (N

_{L}) or right column CR (N

_{R}) and TAC. The TAC first rapidly decreases, then slowly increases with the increasing N

_{L}, while it rapidly decreases and then quickly increases with increasing N

_{R}. The minimum TAC of 1,839,766 $/year for LDWC is obtained while the N

_{L}is set as 92 and the N

_{R}is 116.

## 4. Conclusions

_{1}) are no more than 0.10 K and 0.0018, respectively, and RMSD(T) and RMSD(y

_{1}) are no more than 0.12 K and 0.0030, respectively, which indicate that the VLE data can be correlated well with all three models. Based on regression binary interaction parameters, DCDS and LDWC are designed and optimized for separating a ternary mixture including 1,2-ED, 1,3-PD, and 1,4-BD by the NRTL model. As a result, LDWC can reduce TAC by 16.87% and cooling and heating utility consumptions by 28.40% and 19.24%, respectively, compared with DCDS.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. TAC Estimation

Steam Pressure (BarG) | Latent Heat of Vaporization (kJ/kg) | Price ($/GJ) | Temperature (K) |
---|---|---|---|

40 | 1705.71 | 9.18 | 525 |

46 | 1661.15 | 9.42 | 533 |

_{c}denotes the factors, calculated as material factor (F

_{m}) multiplied by pressure factor (F

_{p}); In the case of carbon steel, F

_{m}and F

_{p}have a value of 1; H

_{c}stands for the height of column installation; N

_{actual}is the a of actual trays; the penalty factor θ is set at 1 for DCDS and 1.1 for LDWC [42].

_{c}stands for the related factor of tray, which can be calculated by the sum of material factor (F

_{m}), type factor (F

_{t}), and tray space factor (F

_{s}); F

_{m}= 0, F

_{t}= 0, and F

_{s}= 1 in carbon steel sieve tray column; H

_{t}denotes the column’s stack height, equal to H

_{c}minus 6 m.

_{c}denotes the related factor of the heat exchanger, equal to the product of material factor (F

_{m}) and the sum of type factor (F

_{t}) and pressure factor (F

_{p}); F

_{t}= 1.35, F

_{p}= 0, and F

_{m}= 1 for the shell-tube heat exchanger made of carbon steel in this study; A (m

^{2}) represents the heat exchangers’ area; Q (kW) denotes the heating and cooling heat duty; U (kW/(K·m

^{2})) stands for the coefficient of heat transfer, which is 0.568 in the reboiler and 0.852 in the condenser [43]; ΔT (K) denotes the driving force of temperature [41].

_{R}(GJ/h) and Q

_{C}(GJ/h) represent the heat duty of the reboiler and condenser, respectively; C

_{h}($/GJ) and C

_{c}($/GJ) are the unit cost of heating and cooling utilities, respectively.

## Appendix B. Experimental VLE Data

T/K | x_{1} | y_{1} | γ_{1}^{exp} | γ_{2}^{exp} |
---|---|---|---|---|

470.3 | 1.000 | 1.000 | 0.999 | |

471.2 | 0.951 | 0.978 | 1.000 | 1.202 |

471.7 | 0.923 | 0.966 | 1.003 | 1.162 |

472.6 | 0.874 | 0.944 | 1.008 | 1.133 |

473.3 | 0.841 | 0.931 | 1.012 | 1.079 |

474.9 | 0.767 | 0.895 | 1.018 | 1.060 |

475.9 | 0.718 | 0.869 | 1.026 | 1.055 |

477.0 | 0.663 | 0.838 | 1.038 | 1.051 |

478.6 | 0.595 | 0.796 | 1.049 | 1.042 |

480.0 | 0.542 | 0.759 | 1.055 | 1.038 |

483.3 | 0.434 | 0.668 | 1.057 | 1.035 |

484.7 | 0.387 | 0.624 | 1.065 | 1.033 |

486.3 | 0.341 | 0.575 | 1.066 | 1.030 |

488.2 | 0.286 | 0.514 | 1.078 | 1.022 |

490.9 | 0.219 | 0.424 | 1.080 | 1.014 |

494.7 | 0.132 | 0.285 | 1.089 | 1.003 |

499.1 | 0.039 | 0.096 | 1.107 | 0.998 |

501.1 | 0.000 | 0.000 | 0.997 |

^{a}Standard uncertainties: u(T) = 0.1 K, u(p) = 0.1 kPa, u(x) = 0.005, u(y) = 0.005.

T/K | x_{1} | y_{1} | γ_{1}^{exp} | γ_{2}^{exp} |
---|---|---|---|---|

487.4 | 1.000 | 1.000 | 0.997 | |

487.5 | 0.972 | 0.978 | 1.000 | 1.207 |

488.0 | 0.911 | 0.931 | 1.002 | 1.171 |

488.5 | 0.844 | 0.882 | 1.010 | 1.124 |

489.1 | 0.785 | 0.836 | 1.011 | 1.112 |

489.6 | 0.731 | 0.797 | 1.021 | 1.082 |

491.1 | 0.589 | 0.687 | 1.047 | 1.040 |

491.7 | 0.539 | 0.644 | 1.054 | 1.035 |

492.4 | 0.488 | 0.598 | 1.060 | 1.029 |

493.1 | 0.427 | 0.541 | 1.075 | 1.026 |

494.0 | 0.368 | 0.48 | 1.079 | 1.025 |

494.6 | 0.332 | 0.441 | 1.080 | 1.022 |

495.1 | 0.299 | 0.407 | 1.092 | 1.017 |

497.6 | 0.163 | 0.239 | 1.098 | 1.011 |

498.3 | 0.131 | 0.196 | 1.099 | 1.006 |

499.7 | 0.062 | 0.097 | 1.106 | 1.003 |

500.5 | 0.025 | 0.042 | 1.162 | 0.998 |

501.1 | 0.000 | 0.000 | 0.997 |

^{a}standard uncertainties: u(T) = 0.1 K, u(p) = 0.1 kPa, u(x) = 0.005, u(y) = 0.005.

## Appendix C. Activity Coefficient Models

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**Figure 1.**Diagrammatic schematic of LDWC. Where DF

_{CL}is the distillate flow rate of CL, DF

_{CR}is the distillate flow rate of CR, and F

_{B}is the flow rate of B.

**Figure 2.**Diagrammatic schematic of DCDS. Where DF

_{C1}is the distillate flow rate of C1, DF

_{C2}is the distillate flow rate of C2.

**Figure 3.**Apparatus for the VLE: (1) electric heating rod; (2) a port for liquid-phase sampling; (3) thermometer; (4) condenser tube; (5) U-shaped mercury differential manometer; (6) a port for vapor-phase sampling; (7) nitrogen cylinder; and (8) buffer vessel.

**Figure 7.**Redlich–Kister plots for the binary system of (

**a**) 1,2-ED (1) + 1,4-BD (2), (

**b**) 1,3-PD (1) + 1,4-BD (2).

**Figure 8.**Residual disturbance for the equilibrium temperature (T) with liquid composition (x

_{1}) of (

**a**) 1,2-ED (1) + 1,4-BD (2), (

**b**) 1,3-PD (1) + 1,4-BD (2).

**Figure 9.**Residual disturbance for vapor composition (y

_{1}) with liquid composition (x

_{1}) of (

**a**) 1,2-ED (1) + 1,4-BD (2), (

**b**) 1,3-PD (1) + 1,4-BD (2).

**Figure 10.**T–x–y diagram for (

**a**) 1,2-EG (1) + 1,4-BD (2) and (

**b**) 1,3-PD (1) + 1,4-BD (2) at 101.3 kPa using Wilson, NRTL, and UNIQUAC models.

**Figure 11.**The activity coefficient for experimental and correlated data for 1,2-EG (1) + 1,4-BD (2) using (

**a**) Wilson, (

**b**) NRTL, and (

**c**) UNIQUAC models.

**Figure 12.**The activity coefficient for experimental and correlated data for 1,3-PD (1) + 1,4-BD (2) using (

**a**) Wilson, (

**b**) NRTL, and (

**c**) UNIQUAC models.

Component | CAS | Supplier | Purity (wt %) | Density (g·cm^{−3}) | Boiling Point (K) | Analysis Method | ||
---|---|---|---|---|---|---|---|---|

Exp ^{c} | Lit ^{d} | Exp ^{e} | Lit ^{f} | |||||

1,2-ED | 107-21-1 | Sinopharm, Beijing, China | ≥99.0 | 1112 | 1110 [22] | 470.25 | 470.45 [23] | GC ^{b} |

1,3-PD | 504-63-2 | Accela, Shanghai, China | ≥98.0 | 1053 | 1050 [24] | 487.35 | 487.55 [24] | |

1,4-BD | 110-63-4 | Sinopharm, Beijing, China | ≥99.0 | 1012 | 1016.9 [25] | 501.05 | 501.15 [25] |

^{a}Standard uncertainties of T and p are u(T) = 0.1 K and u(p) = 0.1 kPa, respectively.

^{b}Gas chromatography.

^{d},

^{f}Reported in literature.

^{c}Experiments conducted at 293.75 K.

^{e}Experiments performed at 101.3 kPa.

Component | C_{1i} | C_{2i} | C_{3i} | C_{4i} | C_{5i} | C_{6i} | C_{7i} | C_{8i} | C_{9i} |
---|---|---|---|---|---|---|---|---|---|

1,2-ED ^{b} | 84.09 | 10411 | 0 | 0 | 8.1976 | 1.65 × 10^{−18} | 6 | 260.15 | 720 |

1,3-PD ^{b} | 115.58 | −11732 | 0 | 0 | −13.174 | 6.55 × 10^{−6} | 2 | 246.45 | 724 |

1,4-BD ^{b} | 105.76 | −12811 | 0 | 0 | −11.069 | 9.44 × 10^{−18} | 6 | 293.05 | 667 |

^{a}from Aspen Plus.

^{b}T/K, p/Pa.

System | D | Δy_{1} ^{a} |
---|---|---|

1,2-ED (1)—1,4-BD (2) | 1.77 | 0.0014 |

1,3-PD (1)—1,4-BD (2) | 0.22 | 0.0008 |

^{a}Testified by the NRTL model.

**Table 4.**Correlated parameters of Wilson, NRTL, and UNIQUAC for 1,2-ED (1) + 1,4-BD (2) and 1,3-PD (1) + 1,4-BD (2).

Model | a_{12} | a_{21} | b_{12} | b_{21} | α |
---|---|---|---|---|---|

1,2-ED (1) + 1,4-BD (2) | |||||

Wilson | 1.54 | −5.40 | −479.79 | 2111.72 | - |

NRTL | −19.57 | 12.58 | 9926.34 | 6373.18 | 0.3 |

UNIQUAC | −3.57 | 2.00 | 1497.94 | −823.53 | - |

1,3-PD (1) + 1,4-BD (2) | |||||

Wilson | 4.50 | −8.26 | −2057.22 | 3767.51 | - |

NRTL | −30.09 | 22.47 | 15,144.8 | −11,261.3 | 0.3 |

UNIQUAC | 11.57 | −9.60 | −5820.44 | 4809.73 | - |

1,2-ED (1) + 1,3-PD (2) ^{α} | |||||

Wilson | −141.12 | 91.50 | 0 | 0 | - |

NRTL | −14.78 | 50.33 | 0 | 0 | 0.3 |

UNIQUAC | 116.52 | −154.33 | 0 | 0 | - |

^{α}Binary interaction parameters used in simulation come from our previous work [17].

Model | AAD (T) ^{a} | AAD (y_{1}) ^{a} | RMSD (T) ^{b} | RMSD (y_{1}) ^{b} |
---|---|---|---|---|

1,2-ED (1) + 1,4-BD (2) | ||||

Wilson | 0.10 | 0.0018 | 0.12 | 0.0029 |

NRTL | 0.07 | 0.0014 | 0.08 | 0.0024 |

UNIQUAC | 0.09 | 0.0018 | 0.11 | 0.0030 |

1,3-PD (1) + 1,4-BD (2) | ||||

Wilson | 0.06 | 0.0009 | 0.08 | 0.0012 |

NRTL | 0.05 | 0.0008 | 0.06 | 0.0011 |

UNIQUAC | 0.05 | 0.0008 | 0.06 | 0.0011 |

^{a}AAD = $\frac{\sum _{i=1}^{N}\left|{\theta}_{i,exp}-{\theta}_{i,cal}\right|}{N}$,

^{b}RMSD = ${\left({\sum}_{i=1}^{N}\frac{{({\theta}_{i,exp}-{\theta}_{i,cal})}^{2}}{N}\right)}^{0.5}$. where N is the number of experimental data points, θ is the parameter (T and y in this study).

DCDS | LDWC | |
---|---|---|

Capital cost ($) | 2,028,300 | 2,178,246 |

Shell | 1,196,753 | 1,409,168 |

Tray | 89,091 | 128,568 |

Heat exchanger | 742,456 | 640,510 |

CC Saving (%) | 0 | −7.39 |

Operating cost ($/year) | 2,010,187 | 1,621,942 |

Heating utilities | 1,936,378 | 1,586,162 |

Cooling utilities | 73,809 | 35,779 |

OC Saving (%) | 0 | 19.31 |

TAC * ($/year) | 2,213,017 | 1,839,766 |

TAC Saving (%) | 0 | 16.87 |

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.-Y.; Song, Z.-W.; Rao, J.-B.; Yao, Y.-X.; Wu, B.; Chen, K.; Ji, L.-J.
Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column. *Processes* **2023**, *11*, 3150.
https://doi.org/10.3390/pr11113150

**AMA Style**

Wu Y-Y, Song Z-W, Rao J-B, Yao Y-X, Wu B, Chen K, Ji L-J.
Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column. *Processes*. 2023; 11(11):3150.
https://doi.org/10.3390/pr11113150

**Chicago/Turabian Style**

Wu, Yan-Yang, Zhong-Wen Song, Jia-Bo Rao, Yu-Xian Yao, Bin Wu, Kui Chen, and Li-Jun Ji.
2023. "Separation of Ternary System 1,2-Ethanediol + 1,3-Propanediol + 1,4-Butanediol by Liquid-Only Transfer Dividing Wall Column" *Processes* 11, no. 11: 3150.
https://doi.org/10.3390/pr11113150