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388 Chapter 7

Example 7.2 Sizing a Batch Reactor for Producing Drying Oil _________

This problem is adapted from a problem given by Smith [23]. To illustrate the
method for sizing a batch reactor outlined in Table 7.8, consider the production of
drying oil from acetylated Castor oil. Drying oils are added to paints to aid the
formation of a protective coating when drying. Acetylated Castor oil (AO) de-
composes according to the first order reaction,

(AO) (1) -> CH 3COOH (g) + drying oil (1)

When heating castor oil, drying oil and acetic acid forms. During the reaction the
acid evaporates from the solution. Calculate the reactor volume, the type and area
of the heat exchanger, and the mixer power.

Data
Reaction temperature 300 °C (572 °F)
Acetic acid equivalent in AO 0.156 g of acetic acid/g of AO
Molecular weight of acetic acid 60
Heat capacity of reacting mixture 0.60 Btu/lb-°F (2.5 kJ/kg-K)
Heat of reaction 15,000 cal/gmol (27,000 Btu/lbmol)
Conversion 95%
Average feed rate 10001b/h(453.6kg/h)
3
3
3
AO Density 0.9 g/cm (56.2 lb/ft , 900 kg/m )
Reaction Properties
The reaction is a first order with respect to a pseudo concentration of acetic acid in
acetylated castor oil, i.e., moles of acetic acid per unit volume of castor oil.
r A = k CA r A = moles of acid/unit volume-unit time
Activation energy 44,500 cal/gmol (80,100 Btu/lbmol)
15
Pre-exponential factor 1 .937xl0 min~ '

Follow the calculation procedure given in Table 7.9. First, calculate the reac-
tor volume. Then, calculate the heat-transfer area and the mixer horsepower.
Because the reaction is first order, Equation 7.8.3 becomes TA = k CA. If the
change of volume during the reaction is small, the reaction time, Equation 7.8.4,
for a first order reaction is

15
From Equation 7.8.21, with A = 1.937xl0 mirf ' and E = 80,100 Btu/lbmol,
andat300°C(1032°R),

15
k = 1.937xl0 exp [- 80,100 / 1.987 (1032)] = 0.02102 mirf 1

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