Dynamic Simulation of Semi-Batch Catalytic Distillation Used for Esterfication Reaction

In this paper the detailed mathematical dynamic model of semi-batch reactive distillation is formulated for ethyl acetate synthesis (estrefication reaction). The model is composed of material balance, heat balance, and equilibrium equations. The set of nonlinear ordinary differential equations governing the unsteady state composition profile in a semi-batch reactive distillation column were solved by using fourth order Runge-Kutta integration method with the aid of the powerful MATLAB 6.5 program which used to simulate and optimize the semi-batch reactive distillation column. The simulation provides compositions, temperatures and holdups profiles along the column as a function of time. Also the reactant conversion and ethyl acetate purity in distillate are calculated. Finally, the simulation results are analyzed to find the optimum operating policy of reflux ratio, Ethanol/Acetic acid and catalyst weight.


Introduction
Reactive distillation is an operation in which separation and chemical reaction take place simultaneously within a fractional distillation column.It can be used for a liquid phase reactions systems in three cases: when the reaction needs large excess of one or more reactants, when an equilibrium state can be moved by removal of one or more products as their concentration is increased, or when the product separation is difficult due to azeotrope formation.Reactive distillation offers several important advantages such as reduction in total costs and energy consumption, overcoming of thermodynamic limitations, (e.g.azeotropes) and increased reaction yield and selectivity [1,2].
Generally, the design and control of reactive distillation is more difficult because of the complicated interactions between vapour-liquid equilibrium, reaction kinetics and hydraulics of the column.
Therefore, such interaction processes lead to complicated dynamic behaviour of the system.
Cuille and Reklaitis [3] considered the simulation of reactive batch distillation with reaction occurring on the plates, in the condenser and in the reboiler.The model was posed as a system of differential and algebraic equations (DAEs) and a stiff solution method was employed for integration.Wilson [4]

Mathmatical Model
The mathematical model of any process is a system of equations whose solution gives a specified data representative of the response of the process to a corresponding set of inputs.The simulation operations make it possible to evaluate the influence of the variables on any process theoretically.The simulation is also used to fix the experimental conditions needed for design, optimization and control.
The boiling point range between acetic acid and ethanol is more than (30 o C), therefore using batch reactive distillation is not useful for this type of systems because the concentration of acetic acid will be much lower than ethanol in reacting zone [14,15].For this reason the semi-batch Eng.&Tech.Vol.26,No.7,2008 Dynamic

Model Assumptions
The packed reactive distillation column is vertically divided into a number of segments [16].The condenser and reboiler stages are numbered 1 and N, respectively.The following assumptions were made to simplify the model of semi-batch reactive distillation column [16,17,18]:-1.Neglect of vapor holdup and assume total condensation.
2. Perfect mixing on all stages and in all vessels (condenser and reboiler), and the condenser and the reboiler are treated as equilibrium stages.
3. Ideal vapor phase for all components in mixture.
4. Liquid and vapor phases in thermodynamic phase equilibrium.

Estimation of Model Parameters a. Equilibrium Relations
For non-ideal mixture additional variable γ i appears to represent the degree of deviation from ideality.
Many models were presented to predict the liquid phase activity coefficient (γ i ) such as Wilson, NRTL, UNIFAC and UNIQUAC.Of all of these models the NRTL model was used because this model gives fewer error than other models.Table (2) contains parameters of NRTL model for all components used in this study.

b. Antoine Model
The Antoine equation is used to calculate the vapor pressure of each component where the temperature T is in Kelvin and the pressure in kPa.
Table (3) contains parameters of Antoine equation for all components [19].

c. Bubble Point Calculation
The temperature on each tray was eveluated by trial and error method to calculate the bubble point.The bubble point is calculated by Newton's method, thus according to this method in each trial the improved Eng.&Tech.Vol.26,No.7,2008Dynamic Simulation of Semi-Batch Catalytic Distillation Used for Esterfication Reaction temperature was calculated by applying Newton's formula; where It was found that (0.0001 o C) accuracy could be reached by making five trials.

d. Enthalpy Calculation
The enthalpy of vapor and liquid phases is calculated by using the following equations.
For each component, the vapor or liquid specific heat is related to a temperature by using a polynomial.Table (4) contains a polynomial which can be used to evaluate the vapor and liquid specific heat (C P ) as a function of temperature.

e. Reaction rate
In the present study, the esterification of ethanol (EtOH) and acetic acid (AcOH), to produce ethyl acetate (EtAc) is studied as shown in the following reaction: 10) This reaction is reversible, and the equilibrium composition is a weak function of temperature.The forward reaction rate (ester formation, R 1 ) is a function of EtOH and AcOH concentrations, and the reverse reaction rate (ester hydrolysis, R 2 ) is a function of EtAc and water.The selected catalyst type that used in present model is the ion exchange resin named (Purolite CT179) [14], the kinetic equations are given below: The equilibrium constant K eq is given by the equation: All concentrations are given as mole fractions.Both k 1 and k 2 are functions of temperature, according to the Arrhenius equation: The parameters of Arrhenius equation for the above reaction are shown in Table (5).

Model Equations
Figure ( 1) represents the semibatch packed reactive distillation column.In this column, there is vapor liquid equilibrium in the reboiler and condenser, therefore each of reboiler and condenser can be assumed as a theoretical stage.Each stage is assumed to be in thermodynamic equilibrium in Eng.&Tech.Vol.26,No.7,2008Dynamic Simulation of Semi-Batch Catalytic Distillation Used for Esterfication Reaction which liquid phase is assumed to be a non-ideal solution and vapor phase an ideal gas mixture.The packing section is divided to ten stages, each stage (15 cm) long.
Hence by starting from the upper point of column, the condenser is numbered as stage one and the first section of packing column is numbered stage 2, an so on.The acetic acid was fed at a point above reaction section, while the EtOH was added before starting to the reboiler.
The total material, component and energy balances are made to the various sections of the semibatch ractive distillation column, and by further simplifications of the differential equations lead to the model.

a. Total Material Balance on Condenser
(16) c.Total energy balance: d. Summation:
Expanding the first term of equation ( 20) and arranging gives.
Dividing equation ( 22) by 1 M and rearranging gives, The acetic acid feed stage can be treated in the same way of treating stage n but with adding the other term which is the feed term.
With In all the simulations presented in this section the initial compositions along the column and in the still are equal to 100% ethanol.Different reflux ratio, ethanol to acetic acid and catalys weight was used in column simulations.The above model gives a system of ordinary differential equations (ODE'S) and algebraic equations, the algebraic equation includes physical properties and vapor liquid equilibrium equations, where the differential equations include total material, heat and component balance equations.Numerical methods such as finite differences are used to simplify these equations, but they lead to a large number of ordinary differential equations.
Figure (2) shows the flowchart for the computer simulation for semi-batch reactive distillation.Optimum operating policies reflux ratio, Ethanol/Acetic acid and catalyst weight were estimated by simulating the reactive batch distillation column for different but constant reflux ratios thereby maximizing the production rate of ethyl acetate and ethyl acetate purity.

Model Results
Much more results can be predicted from the dynamic simulation model of semi-batch reactive distillation.The proposed model can be used to determine the following results: • Ethyl acetate purity in the accumulated distillate.
• Amount of distillate.
• Stage by stage composition profile.
• Stage by stage temperature profile.
• Stage by stage flow profile.
• Stage by stage molar holdup.

Results And Discussion
The simulation results are summarized in Table (7), which shows the effect of change in reflux ratio, Ethanol/Acetic acid and catalyst weight, on the accumulated ethyl acetate in distillate, concentration of ethyl acetate in distillate, total batch time.This table shows that the amount of EtAc and EtAc purity obtained in the accumulated distillate increases with increase in reflux ratio but at the expense of higher batch.

Composition and Temperature Profiles
From all 14 simulation runs summarized in Table ( 7), the results of run 3 are selected to be plotted in Figures (3,4,5,6,7,8 and 9). Figures (3,4,5 and 6) represent the model results for Eng.&Tech.Vol.26,No.7,2008Dynamic Simulation of Semi-Batch Catalytic Distillation Used for Esterfication Reaction ethanol, acetic acic, ethyl acetate and water composition profiles in several locations along the column.The distillate composition is illustrated in Figure ( 7).This figure shows that the mole fraction of ethanol in condenser decreases from 1, reaches a steady state value after startup time (0.5 hr after starting) and then gradually falls to zero after 3 hrs.Ethanol mole fraction falls rapidly as it is being consumed by the reaction as well as separated by distillation.The rise in EtAc mole fraction is due to the high rate of reaction initially, however after 2.5 hrs the rate of EtAc production by reaction becomes less than the rate of separation by distillation and therefore there is a fall in the mole fraction of EtAc.Acetic acid concentration gradually increases with time, this behavior is due to acetic acid highest boiling point in the reaction mixture.Acetic acid and ethyl acetate were separated above the acetic acid feed point in the rectification section.Thus, concentrated ethyl acetate and unreacted ethanol will be the first distillation cut and the acetic acid will be the last distillation cut.
The reboiler compositions is plotted in Figure ( 8).This figure shows that the mole fraction of EtAc in reboiler rises from zero, reaches a small value and then after 2.5 hrs falls to zero.The rise in mole fraction is due to the high rate of reaction initially, however after 2.5 hrs the rate of EtAc production by reaction becomes less than the rate of separation by distillation and therefore there is a fall in the mole fraction of EtAc.Acetic acid concentration gradually increases with time, this behavior is due to acetic acid highest boiling point in the reaction mixture also that the acetic acid feed was continuous in first 2 hrs, therefore the acetic acid retains in the lower sections of the column.Ethanol mole fraction falls rapidly as it is being consumed by the reaction as well as separated by distillation.Ethanol is completely consumed in 3 hrs, then the reaction stops and the column behaves like a nonreactive batch distillation column.
Figure ( 9) shows the variation in column temperatures with respect to time.This figure indicates that the reboiler temperature decreases at first and then increases slowly as the reaction proceeds.The initial decrease in temperature is due to more volatile components produced by the reaction, however, as the separation of these components continues, then the reboiler temperature starts increasing.
The model results was compared with the experimental work taken by Ismail et al. [8], and it was found that there is a good agreement in behavior between the mathematical and experimental results.

Used for Esterfication Reaction
In runs 1 to 5 the reflux ratio was varied from 0.5 to 4. The reflux ratio had a very significant effect on the performance of the semi-batch reactive distillation column.The conversion of the reactants and distillate concentration for five different reflux ratios is shown in Figure (10), indicating that the reactant conversion first rises with increasing reflux ratio and then decreases with further increasing of reflux ratio, this behavior is because EtAc concentration depends on both reaction and separation at the same time.On the other hand, the purity of EtAc in distillate increases with increasing the reflux ratio.The optimum reflux ratio at which the production rate is maximum comes out to be 2.The optimum reflux ratio should be carefully selected to give maximum production rate with appropriate purity.
In runs 3, 6, 7, 8, 9 and 10, the effect of the ratio of acetic acid fed in column to the ethanol on reactant conversion and distillate purity is studied.Figure (11) shows that the reactant conversion relatively increases with increasing the ratio of acetic acid fed in column to the ethanol.Also the distillate purity of ethyl acetate increases but rapidly with increasing the ratio of acetic acid feed in column to the ethanol.
In runs 3, 11, 12, 13 and 14, the effect of catalyst weight on reactant conversion and distillate purity is studied.Figure (12) shows that conversion and distillate purity of ethyl acetate increase with rapidly with increasing the catalyst weight used in the column.The increase in the reactant conversion with catalyst loading agrees well with the description of literture [10,14].

Conclusions
This paper outlines detailed mathematical modeling and simulation of reactive semi-batch reactive distillation column for ethyl acetate production.MATLAB 6.5 program is used to perform the dynamic simulation which is then used to derive the optimum operating profiles.
Column behavior was fully investigated and explained in detail by considering the effects of varying reflux ratio, Acetic acid/Ethanol and catalyst weight.
The optimum operating reflux ratio to give maximum ethyl acetate conversion was found to be 2, while ethyl acetate purity increases with increasing the reflux ratio.The reactant conversion and distillate purity increase with increasing the ratio of acetic acid feed to the ethanol.Also the reactant conversion and distillate purity increase linearly to some limit with increasing amount of catalyst used in column.