7.1 Component material balance

Figure 3 gives flow of vapor and liquid over a plate/tray. As per the reaction of two reactants producing two products, component material balance for various sections of the column can be written as follows:

1. Rectifying and stripping trays

$$\frac{d\left(\mathbf{x}\_{n,j}M\_n\right)}{dt} = L\_{n+1}\mathbf{x}\_{n+1,j} + V\_{n-1}\left.\mathcal{Y}\_{n-1,j} - L\_n\mathbf{x}\_{n,j} - V\_n\left.\mathcal{Y}\_{n,j}\right|\right. \tag{1}$$

Vn <sup>¼</sup> Vn�<sup>1</sup> � <sup>λ</sup>

Ln ¼ Lnþ<sup>1</sup> þ

nipv ¼

loss of species i due to transport, i.e., mass transfer rates. It is given as.

nipl ¼ ð

where Nipl is molar flux of species i at particular point in the two-phase dispersion. Since there is no accumulation at phase interphase, it follows.

The experimental synthesis of methyl acetate esterification was performed in pilot-scale heterogeneous catalytic packed RDC shown in Figure 4. The characteristics of packed RDC are given in Table 2 and temperature data is given in Table 3. From the observations we conclude that the temperature of the reactive zone, from

stage 3 to stage 6, lies between 50 and 70°C, which is an ideal condition for production of methyl acetate catalytic esterification reaction. The temperature of stripping zone lies between 50 and 59°C. Temperature of rectifying section lies

where Nip is molar flux of species i at particular point in the two-phase

ð

where Lpi+<sup>1</sup> is liquid entering the plate p, xpi+<sup>1</sup> is the mole fraction of component i, PLp is liquid added to the column, Lp is the liquid leaving the plate p, and nipl is

dt <sup>¼</sup> Vpi�<sup>1</sup> <sup>∗</sup> ypi�<sup>1</sup>

dmiv

Reactive Distillation: Modeling, Simulation, and Optimization

DOI: http://dx.doi.org/10.5772/intechopen.85433

8. Vapor phase

dispersion.

9. Liquid phase

dmil

dt <sup>¼</sup> Lpiþ<sup>1</sup> <sup>∗</sup> xpiþ<sup>1</sup>

Mt is the accumulation due to mass transfer.

8.1 Pilot-scale experimental results

between 30 and 45°C.

99

8. Case study of methyl acetate synthesis in RDC

ΔHv

λ ΔHv

where Vpi�<sup>1</sup> is vapor entering the plate p, ypi�<sup>1</sup> is the mole fraction of component i, and Pv is vapor added to the column, but these are leaving the column through condenser; therefore negative sign is considered, Vp is the vapor leaving the plate p, and nipv is gain of species i due to transport, i.e., mass transfer rates. It is given as.

Rn,C (7)

Rn,C (8)

Nipv dp (10)

Nipl dp (12)

Mt ¼ nivp � nilp ¼ 0 (13)

� � � Pv � Vp <sup>þ</sup> nipv (9)

� � � PLp � Lp � nipl � ri <sup>∗</sup><sup>V</sup> (11)

2. Reactive trays

$$\frac{d\left(\varkappa\_{n,j}M\_n\right)}{dt} = L\_{n+1}\varkappa\_{n+1,j} + V\_{n-1}\left.\mathcal{y}\_{n-1,j} - L\_n\varkappa\_{n,j} - V\_n\left.\mathcal{y}\_{n,j} + R\_{n,j}\right|\right| \tag{2}$$

3. Feed trays

$$\frac{d\left(\mathbf{x}\_{n,j}M\_n\right)}{dt} = L\_{n+1}\mathbf{x}\_{n+1,j} + V\_{n-1}\mathbf{y}\_{n-1,j} - L\_n\mathbf{x}\_{n,j} - V\_n\ \mathbf{y}\_{n,j} + R\_{n,j} + F\_n\mathbf{z}\_{n,j} \tag{3}$$

4. The net reaction rate for component j on tray n in the reactive zone is given by

$$R\_{n,j} = \upsilon\_j \mathbf{M}\_n (k\_{Fn} \mathbf{x}\_{n,A} \mathbf{x}\_{n,B} - k\_{Bn} \mathbf{x}\_{n,C} \mathbf{x}\_{n,D}) \tag{4}$$

5. Reflux drum

$$\frac{d\left(\mathbf{x}\_{D,j}M\_D\right)}{dt} = V\_{NT}\mathbf{y}\_{NT,j} - D(\mathbf{1} + RR)\mathbf{x}\_{D,j} \tag{5}$$

6. Column base

$$\frac{d\left(\varkappa\_{B,j}M\_B\right)}{dt} = L\_1\varkappa\_{1,j} - B\varkappa\_{B,j} - V\_S\jmath\_{B,j} \tag{6}$$

7. Due to exothermic reaction, the heat of reaction vaporizes some liquid in reactive section. Therefore, the vapor rate increases in the reactive trays, and the liquid rate decreases down through the reactive trays.

Figure 3. Schematic of a tray/plate.

Reactive Distillation: Modeling, Simulation, and Optimization DOI: http://dx.doi.org/10.5772/intechopen.85433

$$V\_n = V\_{n-1} - \frac{\lambda}{\Delta H\_v} R\_{n,C} \tag{7}$$

$$L\_n = L\_{n+1} + \frac{\lambda}{\Delta H\_v} R\_{n,C} \tag{8}$$

8. Vapor phase

7.1 Component material balance

1. Rectifying and stripping trays

d xn,jMn 

2. Reactive trays

3. Feed trays

d xn,jMn 

5. Reflux drum

6. Column base

Figure 3.

98

Schematic of a tray/plate.

d xn,jMn 

sections of the column can be written as follows:

Distillation - Modelling, Simulation and Optimization

d xD,jMD 

> d xB,jMB

liquid rate decreases down through the reactive trays.

Figure 3 gives flow of vapor and liquid over a plate/tray. As per the reaction of two reactants producing two products, component material balance for various

dt <sup>¼</sup> Lnþ<sup>1</sup>xnþ1,j <sup>þ</sup> Vn�<sup>1</sup> yn�1,j � Lnxn,j � Vn yn,j (1)

dt <sup>¼</sup> Lnþ<sup>1</sup>xnþ1,j <sup>þ</sup> Vn�<sup>1</sup> yn�1,j � Lnxn,j � Vn yn,j <sup>þ</sup> Rn,j (2)

Rn,j ¼ vjMnð Þ kFnxn,Axn,B � kBnxn,Cxn,D (4)

dt <sup>¼</sup> VNTyNT,j � <sup>D</sup>ð Þ <sup>1</sup> <sup>þ</sup> RR xD,j (5)

dt <sup>¼</sup> <sup>L</sup>1x1,j � BxB,j � VSyB,j (6)

dt <sup>¼</sup> Lnþ<sup>1</sup>xnþ1,j <sup>þ</sup> Vn�<sup>1</sup> yn�1,j � Lnxn,j � Vn yn,j <sup>þ</sup> Rn,j <sup>þ</sup> Fnzn,j (3)

4. The net reaction rate for component j on tray n in the reactive zone is given by

7. Due to exothermic reaction, the heat of reaction vaporizes some liquid in reactive section. Therefore, the vapor rate increases in the reactive trays, and the

$$\frac{dm\_{iv}}{dt} = \left(V\_{pi-1} \* \mathcal{Y}\_{pi-1}\right) - P\_v - V\_p + n\_{ipv} \tag{9}$$

where Vpi�<sup>1</sup> is vapor entering the plate p, ypi�<sup>1</sup> is the mole fraction of component i, and Pv is vapor added to the column, but these are leaving the column through condenser; therefore negative sign is considered, Vp is the vapor leaving the plate p, and nipv is gain of species i due to transport, i.e., mass transfer rates. It is given as.

$$\mathbf{n}\_{\rm ipv} = \int \mathbf{N}\_{\rm ipv} \, \mathbf{dp} \tag{10}$$

where Nip is molar flux of species i at particular point in the two-phase dispersion.

9. Liquid phase

$$\frac{dm\_{il}}{dt} = \left(L\_{pi+1} \* \varkappa\_{pi+1}\right) - P\_{Lp} - L\_p - n\_{ilp} - r\_i \* V \tag{11}$$

where Lpi+<sup>1</sup> is liquid entering the plate p, xpi+<sup>1</sup> is the mole fraction of component i, PLp is liquid added to the column, Lp is the liquid leaving the plate p, and nipl is loss of species i due to transport, i.e., mass transfer rates. It is given as.

$$\mathbf{n}\_{\rm ipl} = \int \mathbf{N}\_{\rm ipl} \, \mathbf{dp} \tag{12}$$

where Nipl is molar flux of species i at particular point in the two-phase dispersion. Since there is no accumulation at phase interphase, it follows.

$$\mathbf{M}\_{\rm t} = \mathbf{n}\_{\rm inv} - \mathbf{n}\_{\rm ilp} = \mathbf{0} \tag{13}$$

Mt is the accumulation due to mass transfer.
