dHN dt

Component mass balance: dt

Energy balance:

The other equations for the reboiler are same as equations (V.16-V.24) where j is replaced by N.

Cuille and Reklaitis (1986) and Albet et al. (1991) used similar model to simulate batch reactive distillation process. Egly et al. (1979), Reuter et al. (1989), Mujtaba (1989) and Mujtaba and Macchietto (1992, 1997) used a modified version of this model based on constant molar holdup in their studies. Sorensen and Skogestad (1996c), Sorensen et al. (1996b), Balasubramhanya and Doyle III (2000) used simple models for studying control strategies in batch reactive distillation.

Mujtaba and Macchietto (1997) and Greaves (2003) simulated the esterification of ethanol and acetic acid using a Type V-CMH model. The reaction products are ethyl acetate (main product) and water. The reversible reaction scheme together with the boiling point temperatures are shown below:

Acetic Acid + Ethanol <=> Ethyl Acetate + Water (1) (2) (3) (4)

Boiling Points, K 391.1 351.5 350.3 373.2

Ethyl acetate, the main product, has the lowest boiling temperature in the mixture and therefore has the highest volatility. The number of plates (defining the column configuration), feed, feed composition, column holdup, etc. for the problem are given in Table 4.9. Four percent of the total feed charge is considered as the total column holdup in this example. Fifty percent of this holdup is taken as the condenser holdup and the rest is equally divided for the plate holdup. Plate compositions, product accumulator compositions and reflux drum compositions are the differential variables of the model equations. These variables are initialised to the feed compositions at time t = 0 which ensure consistent initialisation of the DAE system used in this work (see Pantelides, 1988 for detail). The vapour liquid equilibrium data and the kinetic data are taken from Simandl and Svrcek (1991) and Bogacki et al. (1989) respectively and are shown in Table 4.10. The vapour and liquid enthalpies are calculated using data from Reid et al. (1977). It is to be emphasised that these data do not account for detailed VLE calculations and for any azeotropic formed. Typical plots of accumulated distillate and reboiler composition profiles with reflux ratio, r = 0.952 are shown in Figures 4.8 and 4.9.

Table 4.9. Input Data for Ethanol Esterification. [Adopted from Mujtaba and Macchietto, 1997]

No. of Ideal Separation Stages

(including a reboiler and a total condenser) = 10

Total Fresh Feed, B0, kmol = 5.0 Feed Composition xB0) molefraction =

<Acetic Acid, Ethanol, Ethyl Acetate, Water> = <0.45, 0.45,0.0,0.1>

Column Holdup, kmol:

Condenser =0.1

Internal Plates = 0.0125

Condenser Vapour Load, kmol/hr = 2.5

Column Pressure, bar =1.013

Table 4.10. VLE and Kinetic Data for Ethanol Esterification [Adopted from Mujtaba and Macchietto, 1997]

Vapour liquid equilibrium:

Acetic Acid + Ethanol <=> Ethyl Acetate + Water (1) (2) (3) (4)

Kinetic Data:

Rate of reaction, gmols/(litre.min); r = kIClC2-k2 C3 C4 where, rate constants are k, = 4.76 x 10"4 and k2 = 1.63 x 10"4 and C, stands for concentration in gmols/litre for the i4 component

----acetic acid ethanol ethyl acetate

4.3. Models for Unconventional Batch Distillation

Referring to Figure 4.10 of a continuous distillation column the model is developed based on the assumptions of constant relative volatility and equimolal overflow and include detailed plate-to-plate calculations. Further assumptions are listed below:

i) |
constant molar holdup for condenser and internal plates. |

ii) |
total condensation without sub-cooling. |

iii) |
negligible vapour holdup. |

iv) |
perfect mixing of liquid and vapour on the plates. |

V) |
negligible heat losses. |

vi) |
theoretical plates |

vii) |
feed mixture at its bubble point. |

First the equations for the condenser will be presented. Then the equations for the accumulator, followed by the equations for the plates in the column and the reboiler are presented. The trays are counted from the top to the bottom.

Bottom

Figure 4.10. Continuous Distillation with Notations

The composition of the distillate and of the liquid reflux is same as that of the vapour going into the condenser. Therefore:

The reflux ratio is defined as:

L = rV (SS.3) The distillate rate to the accumulator or product tank is therefore:

There will be no effect of plate holdup on the steady state mass balance. The component balance on tray j is:

feed plate: ^j-li ~L xji + ^^y'+l,/ ~ >ji)+ FxF = 0

Feed plate total mass balance:

Equilibrium:

aixii

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