Modeling for Simple Batch Distillation of Vanadium OxychlorideTitanium Tetrachloride (VOCl3-TiCl4) Mixture

Modeling for Simple Batch Distillation of Vanadium Oxychloride-Titanium Tetrachloride (VOCl3-TiCl4) Mixture

Tran Duy Hai Tran Anh Khoa* Minh-Vien Le Mai Thanh Phong Phan Dinh Tuan

Ho Chi Minh City University of Natural Resources and Environment, Ho Chi Minh City 700000, Vietnam

Faculty of Chemical Engineering, Ho Chi Minh City University of Technology (HCMUT), Ho Chi Minh City 700000, Vietnam

Vietnam National University Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam

Corresponding Author Email: 
takhoa@hcmunre.edu.vn
Page: 
1805-1811
|
DOI: 
https://doi.org/10.18280/ijht.390614
Received: 
9 November 2021
|
Revised: 
12 December 2021
|
Accepted: 
23 December 2021
|
Available online: 
31 December 2021
| Citation

© 2021 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).

OPEN ACCESS

Abstract: 

VOCl3 and TiCl4 exhibit a similarity of various thermal properties, causing difficulty for these components separation through distillation technique. Dynamic behavior of distillation process of VOCl3-TiCl4 mixture was modeled based on the mass and energy balances, revealing in a model form of the ordinary differential equations. Influences of heating power, airflow, initial concentration, and operating pressure were considered. Simulation results show an ineffective distillation of the mixture under natural pressure. However, the reduction of the operating pressure advanced the pure TiCl4 recovery performance. Compared to experimental data, the relative error of the simulation findings is less than 5%, indicating the potential of the application of the proposed model for describing the distillation of the VOCl3-TiCl4 mixture.

Keywords: 

distillation, modeling, titanium tetrachloride, vanadium oxychloride

1. Introduction

Titanium and its compounds have been widely used in aerospatiale, automotive and biomedical engineering because of specific physicochemical properties such as high mechanical strength, good corrosive resistance, and biocompatibility [1-3]. Natural minerals (ilmenite, rutile, anatase, leucoxene, and brookite) and concentrated sources (titania slag and synthetic rutile) are used as titanium-bearing feedstocks for titanium processing [4, 5]. Until now, metallic titanium and high-grade TiO2 were mainly produced from titanium tetrachloride (TiCl4) – a product of chlorination of titanium sources [6]. However, impurities in raw material, were also chlorinated to the chloride compounds, result in a color change of crude TiCl4 from yellow to dark reddish-brown [7, 8].

Physical, chemical and physo-chemical methods were successfully conducted for purifying TiCl4 with high efficiency [7, 9]. In terms of them, distillation is a powerful technique toward industrial application due to its low cost and controllability [9, 10]. Because of the small difference between the normal boiling point of vanadium oxychloride (VOCl3) (127℃) and the desired TiCl4 product (136.5℃), the removal of VOCl3 through distillation is ineffective [9]. However, the purity of product and the recovery yield of distillation can be controlled and optimized by changing distillation mode and operating conditions [11]. Using modeling and simulation, the instinct properties of many engineering problems under different setup values of variables can be quickly and simply explored [12]. To our best knowledge, the modeling of VOCl3-TiCl4 distillation has not been reported. In this paper, the dynamic behavior of VOCl3-TiCl4 mixture separation in a simple batch distillation column was modeled. The comparison between experimental and simulated results was also presented.

2. The Equations

The scheme of the studied batch distillation system is shown in Figure 1, including a bottom (boiler), a condenser, and a distillation column, which was cooled by outer airflow under forced convection. Assumptions were considered for modeling: (i) negligible temperature change in a cross-section of the distillation column, (ii) equilibrium of heat exchange through the distillation column and heat of condensation of the heavy component (TiCl4), and (iii) small mole fraction of VOCl3 in feedstock.

The heating stage of bottom mixture up to the boiling point of the light component (VOCl3) was ignored. The models were established for the following stage since the temperature at the top of the distillation column has reached the boiling point of VOCl3 until the liquid in the bottom was completely evaporated.

2.1 Modeling for the distillation column

Mathematical models are based on heat and mass balances of a differential volume of the distillation column with a height dz between z and (z+ dz), as shown in Figure 2.

${{m}_{a}}{{c}_{p,a}}d\theta =2\pi hR\left( {{T}_{z}}-\theta  \right)dz$                     (1)

where, ma and cp.a is mass flow (kg.s-1) and constant pressure heat capacity (J.kg-1.K-1) of air, h is convective heat transfer coefficient (W.m-2.K-1), R is the radius of the distillation column (m), Tz is the temperature of the fluid inside the distillation column (℃), $\theta$ and $d \theta$ is temperature and temperature change of air (℃), z is distance from the bottom of distillation column to the differential volume.

Figure 1. Scheme of the batch distillation column

Figure 2. Differential volume of the distillation column

Re-arranging, Eq. (1) can be written as:

${{m}_{a}}{{c}_{p,a}}d\theta =2\pi hR\left( {{T}_{z}}-\theta  \right)dz$        (2)

Integrating (2) from z=0 ($\theta ={{\theta }_{in}}$):

$\int\limits_{{{\theta }_{in}}}^{\theta }{\frac{d\theta }{{{T}_{z}}-\theta }}=\frac{2\pi hR}{{{m}_{a}}{{c}_{p,a}}}\int\limits_{0}^{z}{dz}$             (3)

The temperature of the air as a function of distillation column height was carried out:

$\theta ={{T}_{z}}-\left( {{T}_{z}}-{{\theta }_{in}} \right){{e}^{-\beta z}}$              (4)

where, $\beta =\frac{2\pi hR}{{{m}_{a}}{{c}_{p,a}}}$ (m-1).

At z=H, the outlet temperature of the air, ${{\theta }_{out}}$, is,

${{\theta }_{out}}={{T}_{\text{C}}}-\left( {{T}_{\text{C}}}-{{\theta }_{in}} \right){{e}^{-\beta H}}$       (5)

where, TC is the temperature at the top of the distillation column (℃).

Total exchanged heat Q (W) through the distillation column can be calculated by (6).

$Q={{m}_{a}}{{c}_{p,a}}\left( {{\theta }_{out}}-{{\theta }_{in}} \right)$       (6)

Substituting (5) into (6), the final expression for the total transferred heat was obtained.

$Q={{m}_{a}}{{c}_{p,a}}\left( {{T}_{C}}-{{\theta }_{in}} \right)\left( 1-{{e}^{-\beta H}} \right)$            (7)

It notes that the released heat from the condensation of vapor in the distillation column was assumed to be transferred to outer airflow. Therefore, the total mole of the condensed vapor, $\delta {{V}_{\Sigma }}$, is:

$\delta {{V}_{\Sigma }}=\frac{Q}{\lambda }=\frac{{{m}_{a}}{{c}_{p,a}}}{\lambda }\left( {{T}_{C}}-{{\theta }_{in}} \right)\left( 1-{{e}^{-\beta H}} \right)$         (8)

where, $\lambda$ is the heat of condensation (J.mol-1). Eq. (9) was also obtained.

$\delta {{V}_{\Sigma }}={{L}_{r}}$              (9)

where, Lr is the liquid flow returned from the distillation column to the bottom (mol.s-1).

To separate VOCl3 (light component) from the VOCl3-TiCl4 mixture by distillation technique, the expected temperature at the top of the distillation column was equal to the boiling point of VOCl3. In addition, the mole fraction of VOCl3 in the feedstock was considered in a low range. Therefore, the condensation process, occurred in the distillation column, can be only considered for TiCl4 (the heavy component). It means that the heat of TiCl4 condensation, $\lambda_{2}$, was substituted to the value $\lambda$ in (8).

2.2 Modeling for the boiler

Eq. (10) presents the energy balance for the boiler.

$\frac{d\left( Wh_{W}^{liq} \right)}{dt}={{Q}_{0}}-{{V}_{W}}h_{W}^{vap}+{{L}_{r}}h_{r}^{liq}$            (10)

where, $h_{W}^{liq}$ and $h_{W}^{vap}$ are the enthalpy of the liquid and vapor phase in the bottom (J.mol-1), ${{Q}_{0}}$ is heating power (W), W is the liquid amount in the bottom (moles), Vw is vapor flow moved from the bottom up the distillation column (mol.s-1), $h_{r}^{liq}$ is the enthalpy of the returned liquid flow (J.mol-1).

Because VOCl3 was in a low mole faction, it can apply approximate equation (11).

$h_{W}^{liq}\approx h_{r}^{liq}\approx h_{2}^{liq}$           (11)

where, $h_{2,W}^{liq}$ is the enthalpy of TiCl4 liquid (J.mol-1) at the bottom temperature.

As consequently, Eq. (10) can be written as:

$h_{2,W}^{liq}\frac{dW}{dt}={{Q}_{0}}-{{V}_{W}}h_{W}^{vap}+{{L}_{r}}h_{2,W}^{liq}$             (12)

The mass balance equation for the bottom is represented as (13).

$\frac{dW}{dt}=-{{V}_{W}}+{{L}_{r}}$             (13)

Combining (13) and (12), the boiler dynamic is represented in (14),

$\frac{dW}{dt}=\frac{-{{Q}_{0}}}{h_{W}^{vap}-h_{2,W}^{liq}}+{{L}_{r}}$                (14)

And, Eq. (15) was also carried out.

${{V}_{W}}=\frac{{{Q}_{0}}}{h_{W}^{vap}-h_{2,W}^{liq}}$            (15)

Mass balance for VOCl3 component reveals (16).

$\frac{dW{{x}_{W}}}{dt}=-{{V}_{W}}{{y}_{W}}+{{L}_{r}}{{x}_{r}}$            (16)

where, yW is the mole fraction of VOCl3 vapor in the vapor flow VW (dimensionless), xW and xr is the mole fraction of VOCl3 liquid in the bottom and the returned liquid flow Lr (dimensionless).

Due to the vapor-liquid equilibrium in the bottom, the value of xr can approximate to xW. Then, Eq. (17) was obtained by applying the partial differentiation rule for (16).

${{x}_{W}}\frac{dW}{dt}+W\frac{d{{x}_{W}}}{dt}=-{{V}_{W}}{{y}_{W}}+{{L}_{r}}{{x}_{W}}$                 (17)

Substituting (13) and (15) into (17), the dynamic model of the VOCl3 component can be described by the differential Eq. (18).

$\frac{d{{x}_{W}}}{dt}=\frac{{{Q}_{0}}}{W\left( h_{W}^{vap}-h_{2,W}^{liq} \right)}\left( {{x}_{W}}-{{y}_{W}} \right)$               (18)

2.3 Convective heat transfer coefficient

In term of estimating the heat transfer coefficient of air for particularly forced convection, h, the dimensionless correlation of Nusselt number (Nu), including Reynold number (Re) and Prandtl number (Pr), was considered. For Pr>0.7, the empirical correlation (19), well known as Hilpert correlation [13], has been widely accepted. Definitions of Nu and Re are shown as (20) and (21), respectively.

$\text{Nu}=C{{\operatorname{Re}}^{m}}{{\Pr }^{1/3}}$             (19)

where, C=0.683, m=0.466 for 40<Re<4,000, and C=0.193, m=0.618 for 4,000<Re<40,000 [4].

$\text{Nu}=\frac{h.{{D}_{h}}}{k}$            (20)

$\operatorname{Re}=\frac{u.{{D}_{h}}}{\nu }$         (21)

where, ${{D}_{h}}=2\left( {{R}_{\text{o}}}-R \right)$ is the hydraulic diameter (m), k is the thermal conductivity of the fluid (W.m-1.K-1), u is the flow rate (m.s-1), and v is the kinematic viscosity (m2.s-1).

2.4 Thermodynamic correlations

By regressing database in HSC Chemistry software version 6.0, correlations of the enthalpy of components and temperature were obtained as (22)-(25).

•VOCl3 liquid: $h_{1}^{L}\left( T \right)=h_{1}^{\text{o},L}+150.6T-3,762.9$          (22)

•VOCl3 vapor: $h_{1}^{V}\left( T \right)=h_{1}^{\text{o},V}+94T-2,397.8$              (23)

•TiCl4 liquid:    $h_{2}^{L}\left( T \right)=h_{2}^{\text{o},L}+145.8T-3,651.1$           (24)

•TiCl4 vapor:   $h_{2}^{V}\left( T \right)=h_{2}^{\text{o},V}+98.8T-2,508.3$             (25)

Units: h - J.mol-1, T - ℃.

Enthalpy of an ideal mixture was be calculated from partial molar fractions and enthalpies of pure components as (26) [14]:

$h=\sum{{{f}_{i}}{{h}_{i}}}$             (26)

where, fi is mole fraction (fi =xi for liquid, fi =yi for vapor).

Assuming the VOCl3-TiCl4 characteristic of an ideal mixture, the Raoult’s law was applied for finding the relationship between the vapor mole fraction, yi, and the liquid mole fraction, xi, of component i [15]:

${{y}_{i}}=\frac{p_{i}^{*}}{P}{{x}_{i}}$              (27)

where, i = 1 for VOCl3 and i = 2 for TiCl4, P is the operating pressure in the distillation column (mmHg), $p_{i}^{*}$ is the equilibrium vapor pressure of the pure component i, which depends on temperature as described by the Antoine equation [16]:

$p_{i}^{*}\left( \text{mmHg} \right)={{10}^{A\ -\ \frac{B}{T\ +\ C}}}$             (28)

where, A, B, C are the Antoine coefficients, C in ℃.

The temperature at the top of the distillation column, TC, was considered to be equal to the boiling point of VOCl3, which was decreased by the reduction of the operating pressure according to the Clausius–Clapeyron equation [17]:

${{T}_{\text{C}}}={{\left( \frac{1}{{{T}_{0}}}-\frac{{{R}_{g}}\ln \frac{P}{{{P}_{0}}}}{{{\lambda }_{1}}} \right)}^{-1}}$            (29)

where, T0 is the boiling point of VOCl3 at P0=760 mmHg, Rg=8.314 is the universal gas constant (J.mol-1.K-1), $\lambda_{1}$ is the heat of vaporization of VOCl3 (J.mol-1).

Finally, the sum of the mole fractions of VOCl3 and TiCl4 in the vapor phase is unity:

${{y}_{1}}+{{y}_{2}}=1$            (30)

3. Solution Method

The numerical solution of the ordinary differential Eqns. (14) and (18) for the system was found out by applying Runge-Kutta 4th method, using MATLAB code. Initial conditions (t = 0) are:

$W={{W}_{0}}$            (31)

${{x}_{W}}={{x}_{W}}_{0}$             (32)

Parameters of the simulation were enumerated in Appendix.

As above mentioned, total heat released from condensation in the distillation column was transferred to the outer airflow. It means that the entire space in the column was at a uniform temperature. However, the bottom temperature is approx. 3℃ higher than the top temperature in our experiment result. Therefore, TC+3 was set as the bottom temperature of simulations.

Influences of the heating power, airflow, initial mole fraction of VOCl3, and operating pressure on the dynamic behavior of the distillation process were simulated.

4. Simulation Results

Numerical solutions of the proposed models are presented in Figures 3-6 with 100 moles of the feedstock mixture, revealing the time-dependences of the W and xW. In consideration for all cases, it is observed that the bottom product, W, decreased with time as a linear function, indicating the constant reduction rate of the W in each simulation.

Figure 3 presents the time-dependence of W and xWwith heating power (Q0). The slopes of lines in Figure 3A confirm the faster reduction rate of the W with the increase of the Q0. Figure 3B presents the decrease of the xW with time. For 1.8, 2, and 2.5 kW of the Q0, the xW tended to 2´10-4, 7´10-4, and 3.9´10-3 at 10, 5, and 2.2 hours of distillation time, respectively, when the W is near to zero. This result indicates the heating power cannot improve distillation efficiency of the VOCl3-TiCl4 mixture.

Figure 3. Effects of the heating power on time-dependence of A) W and B) xW. Conditions: P = 760 mmHg, GV = 30 L.s-1, xW = 0.01

Figure 4. Effects of the initial mole fraction of VOCl3 on time-dependence of A) W and B) xW. Conditions: P = 760 mmHg, GV = 30 L.s-1, Q0 = 2 kW

The initial mole fraction of VOCl3, xW0, slightly influenced on the reduction rate of the W, as demonstrated in Figure 4A. This may be due to xW0 in the low range as well as the similar thermal properties of VOCl3 and TiCl4 such as heat of vaporization and boiling point (Appendix). In Figure 4B, the varieties of xW at different xW0 values are in a similar trend. VOCl3 dramatically exists in the bottom product at the end of distillation operation ($W \approx 0$).

Figure 5 shows a strong influence of the airflow, GV, to time-dependence of the W, xW, and air temperature. Increasing the airflow, the convective heat transfer coefficient increase, improving the condensation performance in the distillation column, resulting in the slower reduction rate of the W (Figure 5A). As seen in Figure 5B, the mole fraction of VOCl3 in the bottom product at the end of the distillation process decreased with the increase of airflow. These mole fractions did not tend to zero, indicating that the airflow is not a key parameter for the pure TiCl4 recovery by distillation. However, temperature profiles (Figure 5C) of air along the distillation column significantly changed with the different set airflows. This result may be useful in considerations of mechanical design and/or safe for operators.

Figure 5. Effects of the airflow on time-dependence of A) W and B) xW and C) air temperature. Conditions: P = 760 mmHg, xW0 = 0.005, Q0 = 2 kW

The reduction rate of the W increase with a decrease of the operating pressure, as shown in Figure 6A. This result is attributed to a deviation of the equilibrium state under a change of pressure [18]. At low pressure, the cross association between components in the liquid mixture is reduced, resulting in the significant distinction of equilibrium state for these components [19]. As consequently, the faster reduction of the xW with the lower operating pressure was observed, as shown in Figure 6B. For the operating pressure less than 360 mmHg, the xW reached zero before the liquid in the bottom entirely evaporated. Pure TiCl4 recovery efficiency was calculated to be around 20, 59, 84 % under 360, 160, and 50 mmHg of the operating pressure, respectively. This result indicates that distillation under vacuum conditions is possible to apply for separating the VOCl3-TiCl4 mixture.

Figure 6. Effects of the operating pressure on time-dependence of A) W and B) xW. Conditions: GV = 30 L.s-1xW0 = 0.005, Q0 = 2 kW

5. Comparison of Experimental and Simulated Results

Figure 7. Time-dependence of xW from experiment and simulation

Obtained results from simulation were compared with experimental findings to verify the proposed models. The experiment was performed under conditions: P = 760 mmHg, xW0 = 10-3, Q0 = 2 kW, GV = 20 L.s-1, and W0 = 420 moles. The distillation process occurred under an inert condition. The bottom liquid was sampled at different distillation times (t = 1, 3, 5, 7, and 9 hours) since the top temperature of the distillation column reached 127℃ (t = 0). VOCl3 mole fraction was calculated from vanadium content in the sample, which was determined by the ICP-AES technique. From Figure 7, compatibility between the simulation and the experimental results is observed. As expected, varieties of xW with time from experiment and simulation are in a similar trend. Deviation of the experimental values and the simulation may be due to the instinct non-ideal property of the VOCl3-TiCl4 system. However, the calculated relative error of the simulated results in comparison with the experimental results was less than 5%. This indicates that the proposed models are successfully predicted the dynamic behavior of the distillation of the VOCl3-TiCl4 mixture.

6. Conclusion

In this paper, a simple batch distillation column for the VOCl3-TiCl4 mixture separation was modeled to explore the dynamic behaviors. From simulation results under different conditions, the heating power, the airflow, and the initial mole fraction of VOCl3 almost unaffected to distillation performance. However, operating pressure plays a key parameter. It was found that pure TiCl4 can be recovered by distillation under the operating pressure of less than 360 mmHg, and the TiCl4 recovery efficiency increase as this parameter is decreased. The deviation between the simulation findings and the experimental results was also determined, that revealed a 5% of the maximum relative error. It proved that the obtained models are acceptable for the distillation simulation of the VOCl3-TiCl4 mixture.

Acknowledgment

This work was financially supported by the Vietnam Ministry of Science and Technology through the National Project coded KC.02.02/16-20.

Appendix

Parameters

Symbol

Value

Ref.

Design and operation parameters

Height (m)

H

1.5

 

Inner diameter (m)

R

0.15

 

Outer diameter (m)

R0

0.2

 

Feedstock (mole)

W0

100

 

Temperature of inlet air (°C)

$\theta_{\text {in }}$

35

 

Properties of pure components

VOCl3

Antoine coefficients

A1

7.02483

[20]

B1

1518.94

[20]

C1

239.69

[20]

Standard enthalpy of vapor (J.mol-1)

$h_{1}^{\text{o},V}$

-695.6

[21]

Standard enthalpy of liquid (J.mol-1)

$h_{1}^{\text{o},L}$

-734.7

[21]

Heat of vaporization (J.mol-1)

$\lambda_{1}$

36.78

[21]

Boiling point at 760 mmHg (°C)

T0

127

[22]

TiCl4

Antoine coefficients

A2

7.295

[20]

B2

1668.82

[20]

C2

242.2

[20]

Standard enthalpy of liquid (kJ.mol-1)

$h_{2}^{\text{o},L}$

-804.2

[21]

Heat of vaporization (kJ.mol-1)

$\lambda_{2}$

36.2

[22]

Boiling point at 760 mmHg (°C)

 

136.5

[22]

Properties of air at 40°C, 1 atm

[13]

Thermal conductivity (W.m-1.K-1)

k

26.62×10-3

 

Kinematic viscosity (m2.s-1)

v

1.702×10-5

 

Density (kg.m-3)

$\rho$

1.127

 

Constant pressure heat capacity (J.kg-1.K-1)

cp,a

1007

 

Prandtl number

Pr

0.7255

 

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