# Process Characteristics

Consider an ideal reactive distillation (Fig. 18.1) with a reversible liquid-phase reaction in the reactive section:

The forward and backward specific rates following the Arrhenius law on tray j are given by kFj = aFe-E"=RTj (18.1)

where aF and aB are the preexponential factors for the forward and backward reactions, respectively; EF and EB are the activation energies; and Tj is the absolute temperature on

Reactive Distillation Design and Control. By William L. Luyben and Cheng-Ching Yu Copyright # 2008 John Wiley & Sons, Inc. Figure 18.1 Reactive distillation with NR rectifying trays, NRX reactive trays, and NS stripping trays with conventional feed arrangement (NF,B = NRX,top and NF,A = NRXjbot).

Figure 18.1 Reactive distillation with NR rectifying trays, NRX reactive trays, and NS stripping trays with conventional feed arrangement (NF,B = NRX,top and NF,A = NRXjbot).

tray j. The reaction rate on tray j can be expressed in terms of mole fractions (xj,) and the liquid holdups (Mj).

where R j,, is the reaction rate of component i on the jth tray (kmol/s), n is the stoichiometric coefficient that takes a negative value for the reactants, and Mj is the molar holdup on tray j (kmol) that is assumed to be constant throughout the simulation. This is typically true for catalyst weight based kinetics.

The assumptions made in this work include the following:

1. Forward reaction rate kF is specified as 0.008/s at 366 K, and backward reaction rate kB is set to 0.004/s at the same temperature. Kinetic and physical property data for the system are given in Table 18.1.1

2. A molar holdup (Mj) of 1000 mol is assumed.1

3. Ideal vapor-liquid equilibrium is assumed, in which constant relative volatilities are used. The tray temperature is computed using the Antoine vapor pressure equation (Table 18.1). Note that as the result of constant relative volatility, the Antoine coefficients (BVP) are the same for all four components.

### 4. Vapor holdup and pressure drop are neglected.

A. Al-Arfaj and W. L. Luyben, Comparison of alternative control structures for an ideal two-product reactive distillation column, Ind. Eng. Chem. Res. 39, 3298-3307 (2000).

 Activation energy (cal/mol) Forward (EF) Backward (EB)