Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Used for Esterfication Reaction

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

Ziadoon M. Shakor, and Khalid A. Sukkar Received on:28/1/2008 Accepted on:2/4/2008

Abstract In this paper the detailed mathematical dynamic model of semi-batch 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 ratio, Ethanol/Acetic and catalyst weight.

Keywords: Reactive distillation, esterification, semi-batch operation, dynamic simulation.

اﻟﺨــﻼﺻــــــﺔ ﺘﻌﺘﺒﺭ ﻤﻌﺩﺍﺕ ﺍﻟﺘﻘﻁﻴﺭﺫﺍﺕ ﺍﻟﻤﻔﺎﻋل (Reactive Distillation) ﻤﻥ ﺍﻟﻤﻌﺩﺍﺕ ﺍﻟﺤﺩﻴﺜﺔ ﺍﻟﺘﻲ ﺘﺠﻤﻊ ﻋﻤﻠﺘﻲ ﺍﻟﺘﻘﻁﻴﺭ ﻭﺍﻟﺘﻔﺎﻋل ﻓﻲ ﻨﻔـﺱ ﺍﻟﻤﻌﺩﺓ . ﻓﻲ ﻫﺫﺍ ﺍﻟﺒﺤﺙ ﺘﻡ ﺍﻟﺘﻭﺼﻴﻑ ﻭﺍﻟﺘﻤﺜﻴل ﺍﻟﺭﻴﺎﻀﻲ ﻟﻬﺫﺍ ﺍﻟﻨﻭﻉ ﻤﻥ ﺍﻟﻤﻌﺩﺍﺕ ﻓﻲ ﺘﻔﺎﻋل ﺍﻻﺴﺘﺭﺓ ﻻﻨﺘﺎﺝ ﺨﻼﺕ ﺍﻻﺜﻴل . ﺤﻴﺙ ﺘﻤﺕ ﺍﻟﻨﻤﺫﺠﺔ ﺍﻟﺭﻴﺎﻀﻴﺔ ﻋﻠﻰ ﺍﺴﺎﺱ ﻤﻨﻅﻭﻤﺔ ﺭﻴﺎﺩﻴﺔ ﺴﺎﺒﻘﺔ ﻭﺍﻟﺘﻲ ﺘﻌﻤل ﺒﺎﺴـﻠﻭﺏ ﻨﺼـﻑ ﺍﻟﻭﺠﺒﺔ (Semi-batch) ﻭﻜﺎﻥ ﺍﻟﻤﻭﺩﻴل ﺍﻟﺭﻴﺎﻀﻲ ﻤﺒﻨﻴﺎﹰ ﻋﻠﻰ ﺍﺴﺎﺱ ﺍﻋﺘﻤﺎﺩ ﻤﻭﺍﺯﻨﺔ ﺍﻟﻜﺘﻠﺔ ﻭﺍﻟﺤﺭﺍﺭﺓ ﻭﺨﺼﺎﺌﺹ ﺍﻻﺘﺯﺍﻥ ﺒﻴﻥ ﺍﻟﻁﻭﺭﻴﻥ. ﻭﻋﻠﻴﻪ ﻓﺎﻥ ﻤﺠﻤﻭﻋﺔ ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﻔﺎﻀﻠﻴﺔ ﺍﻟﻼﺨﻁﻴﺔ ﺍﻟﺘﻲ ﺘﻭﺼﻑ ﺍﻟﺤﺎﻟﺔ ﻏﻴﺭ ﺍﻟﺴﺘﻘﺭﺓ (Unsteady state) ﺘـﻡ ﺤﻠﻬﺎ ﺒﻁﺭﻴﻘﺔ ﺍﻟﺘﻜﺎﻤــل ﺒﻭﺍﺴﻁﺔ Fourth Order Runge-Kutta ﻭﻤﻥ ﺨﻼل ﺍﺴﺘﺨﺩﺍﻡ ﺒﺭﻨﺎﻤﺞ MATLAB 6.5 ﻟﻠﺤل ﻭﺍﺴﺘﺤﺼﺎل ﺍﻟﻨﺘﺎﺌﺞ ﺍﻟﺨﺎﺼﺔ ﺒﺎﻟﻤﻨﻤﺫ ﺠﺔ ﺍﻟﺭﻴﺎﻀﻴﺔ ﻟﻬﺎ ﺍﻟﻨﻭﻉ ﻤﻥ ﺍﻟﻤﻌﺩﺍﺕ . ﻤﻥ ﺨﻼل ﺍﻟﻤﻭﺩﻴل ﺘﻡ ﺍﺴﺘﺤﺼﺎل ﻨﺘﺎﺌﺞ ﺍﻟﺘﺭﻜﻴﺯ ﻭﺩﺭﺠﺔ ﺍﻟﺤﺭﺍﺭﺓ ﻭﻤﻌﺩﻻﺕ ﺍﻟﺠﺭﻴﺎﻥ ﻟﻜل ﺍﺠﺯﺍﺀ ﺒﺭﺝ ﺍﻟﺘﻘﻁﻴﺭ ﺍﻟﺘﻔﺎﻋﻠﻲ ( Reboiler, Column and condenser) ﻜﺩﺍﻟﺔ ﻟﻠﺯﻤﻥ . ﻜﻤﺎ ﺘﻡ ﺤﺴﺎﺏ ﻨﺴﺒﺔ ﺍﻟﺘﺤﻭل ﻟﻠﻤﻭﺍﺩ ﺍﻟﻤﺘﻔﺎﻋﻠﺔ ﻭﺤﺴﺎﺏ ﻨﻘﺎﻭﺓ ﺍﻟﻤﺎﺩﺓ ﺍﻟﻨﺎﺘﺠﺔ ﻭﺍﻟﺘﻲ ﻫﻲ ﺨﻼﺕ ﺍﻻﺜﻴل (Ethyl Acetate). ﻭﻤﻥ ﺨﻼل ﺍﻟﺘﺤﻠﻴل ﺍﻟﺭﻴﺎﻀﻲ ﺘﻡ ﺍﺴﺘﺤﺼﺎل ﻨــﺘﺎﺌﺞ ﻤﻥ ﺍﻟﻤﻭﺩﻴل ﺘﻤﺜل ﺍﻓﻀــل ﻗﻴﻡ ﻟﻨﺴﺒﺔ ﺍﻟﺭﺍﺠﻊ (Reflux Ratio) (Catalyst Weight) and , (Ethanol/Acetic acid ratio).

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

1. Introduction solution method was employed for Reactive distillation is an integration. Wilson [4] considered operation in which separation and design and operation of batch chemical reaction take place reactive distillation. Mujtaba and simultaneously within a fractional Macchietto [5] proposed distillation column. It can be used polynomial curve fitting for a liquid phase reactions techniques to optimize reactive systems in three cases: when the of ethyl acetate. reaction needs large excess of one In their work they neglected the or more reactants, when an energy balance and changes in equilibrium state can be moved by molar hold-ups. Francis et al. [6] removal of one or more products used reduced model to study the as their concentration is increased, trade off between model accuracy or when the product separation is and computational tractability for difficult due to azeotrope model-based control applied for formation. Reactive distillation batch reactive distillation column offers several important used for esterfication reaction. advantages such as reduction in Then, they used the reduced model total costs and energy in a model predictive control consumption, overcoming of algorithm. thermodynamic limitations, (e.g. azeotropes) and increased reaction Monroy and Alvarez [7] have yield and selectivity [1, 2]. developed a nonlinear PID–type Generally, the design and top product composition controller control of reactive distillation is for ethyl acetate process operated more difficult because of the in batch mode, using reflux ratio as complicated interactions between the manipulated variable. They vapour-liquid equilibrium, reaction showed that their scheme kinetics and hydraulics of the generates the same reflux ratio column. Therefore, such profile as the optimization-based interaction processes lead to approach followed by Mujtaba and complicated dynamic behaviour of Macchietto [5]. Ismail et al. [8] the system. studied experimentally the ethyl Cuille and Reklaitis [3] acetate production in a packed bed considered the simulation of reactive distillation column reactive batch distillation with operated in batch and continuous reaction occurring on the plates, in modes. The effects of the variables the condenser and in the reboiler. such as the reflux ratio, rate The model was posed as a system and feed flow rate on ethyl acetate of differential and algebraic production. They found that, the equations (DAEs) and a stiff packed bed reactive distillation

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction column operated in continuous represent the model are solved mode gave the highest ethyl using fourth order Runge-Kutta acetate composition. Vora and method in MATLAB program to Daoutidis [9] studied the dynamics obtain the detailed column and control of an ethyl acetate dynamics. reactive distillation system and According to previous literature proposed a new feed configuration survey, there are no for the two reactants that allows comprehensive simulations that higher conversion and purity than describe the different process the conventional configuration, interactions that occur in semi- which involves feeding in a single batch reactive distillation. tray. Therefore, the present study aims to formulate a comprehensive On the other hand, Mujtaba et mathematical dynamic model for al. [10] replaced rigorous dynamic semi-batch reactive distillation, model of batch reactive distillation since such model depends on the by a neural network based model analysis of material balance, heat which can predict the column balance, equilibrium, and sum of dynamics very well in few CPU mole fractions equations. seconds. A simple esterification reaction system is used in the 2. Mathmatical Model batch reactive distillation column The mathematical model of any to demonstrate the ideas. Lee et al. process is a system of equations [11] studied a batch reactive whose solution gives a specified distillation with double-feed, they data representative of the response concluded that, this types of of the process to a corresponding columns cannot produce pure ethyl set of inputs. The simulation acetate for the stoichiometric operations make it possible to feeding of acetic acid and ethanol. evaluate the influence of the They state that a higher reflux ratio variables on any process is more harmful to the overall theoretically. The simulation is reaction conversion. Espinosa [12] also used to fix the experimental developed a dynamic conceptual conditions needed for design, model for batch reactive optimization and control. . He assumed a rectifier The range with an infinite number of stages. between acetic acid and ethanol is He concluded that, the operation more than (30 oC), therefore using at constant reflux is very easy to batch reactive distillation is not implement in practice. Patel et al. useful for this type of systems [13] derived a mathematical model because the concentration of acetic and simulation of reactive batch acid will be much lower than distillation column for ethyl ethanol in reacting zone [14, 15]. acetate synthesis. The DAEs which For this reason the semi-batch

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction reactive distillation works by For non-ideal mixture injection of the heavier reacting additional variable γi appears to component above reacting section represent the degree of deviation and the lighter reacting component from ideality. below reacting section. In the γ ⋅ P K = i i . . . (1) present work a new technique is i P used by feeding only the heavier Many models were presented to component above the reaction predict the liquid phase activity section. The semi-batch reactive coefficient (γi) such as Wilson, distillation column is used in this NRTL, UNIFAC and UNIQUAC. search to increase the reactant Of all of these models the NRTL conversion because the batch model was used because this reactive distillation gives lower model gives fewer error than other reactant conversion than semi- models. Table (2) contains batch reactive distillation for the parameters of NRTL model for all several reasons listed above. components used in this study.

2.1 Model Assumptions The packed reactive distillation column is vertically divided into a number of segments [16]. The b. Antoine Model condenser and reboiler stages are The Antoine equation is used to numbered 1 and N, respectively. calculate the vapor pressure of The following assumptions were each component made to simplify the model of C2 C ln( P o ) = C + +C log(T)+C T 5 semi-batch reactive distillation 1 T 3 4 column [16, 17, 18]:- . . . (2) 1. Neglect of vapor holdup and where the temperature T is in assume total condensation. Kelvin and the pressure in kPa. 2. Perfect mixing on all stages Table (3) contains parameters and in all vessels (condenser and of Antoine equation for all reboiler), and the condenser and components [19]. the reboiler are treated as equilibrium stages. 3. Ideal vapor phase for all c. Bubble Point Calculation components in mixture. The temperature on each tray 4. Liquid and vapor phases in was eveluated by trial and error thermodynamic phase equilibrium. method to calculate the bubble point. The bubble point is 2.2 Estimation of Model calculated by Newton’s method, Parameters thus according to this method in a. Equilibrium Relations each trial the improved

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction temperature was calculated by Cation Catalyst applying Newton’s formula; AcOH + EtOH ←⎯→⎯⎯⎯⎯ EtAc + H 2 O f (T ) . . . (10) T = T − . . . (3) n+1 n f ' (T ) This reaction is reversible, and where the equilibrium composition is a c weak function of temperature. The f (T ) = ∑ K i xi − 1 . . . (4) forward reaction rate ( i=1 c dK formation, R1) is a function of f ' (T ) = x i . . . (5) ∑ i dt EtOH and AcOH concentrations, i=1 and the reverse reaction rate (ester It was found that (0.0001 oC) hydrolysis, R ) is a function of accuracy could be reached by 2 EtAc and water. The selected making five trials. catalyst type that used in present

model is the ion exchange resin d. Enthalpy Calculation named (Purolite CT179) [14], the The enthalpy of vapor and kinetic equations are given below: liquid phases is calculated by using R = k x x 1.5 . . . (11) the following equations. 1 1 EtOH AcOH T 2 R2 = k2 xEtHc xH O . . . (12) V 2 H j ,i = Cpi dT . . (6) ∫ The equilibrium constant Keq is T r given by the equation: T2 L h = Cp dT . . . (7) k xEtHc xH O j ,i ∫ i 2 2 K eq = = . . . (13) Tr m k1 xEtOH x AcOH c All concentrations are given as H j = ∑ H j ,i y j ,i . . . (8) i=1 mole fractions. Both k1 and k2 are c functions of temperature, h j = ∑ h j ,i ⋅ x j ,i . . . (9) i=1 according to the Arrhenius For each component, the vapor equation: −E / RT or liquid specific heat is related to A ki = ki,0 e . . . (14) a temperature by using a The parameters of Arrhenius polynomial. Table (4) contains a equation for the above reaction are polynomial which can be used to shown in Table (5). evaluate the vapor and liquid specific heat (CP) as a function of 2.3 Model Equations temperature. Figure (1) represents the semi- batch packed reactive distillation e. Reaction rate column. In this column, there is In the present study, the vapor liquid equilibrium in the esterification of ethanol (EtOH) reboiler and condenser, therefore and acetic acid (AcOH), to each of reboiler and condenser can produce ethyl acetate (EtAc) is be assumed as a theoretical stage. studied as shown in the following Each stage is assumed to be in reaction: thermodynamic equilibrium in

Eng.&Tech.Vol.26,No.7,2008 Dynamic 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 mixture. The packing section is divided to ten Fig.(1) Reactive semi-batch stages, each stage (15 cm) long. distillation column.

Hence by starting from the upper The acetic acid was fed at a point of column, the condenser is point above reaction section, while numbered as stage one and the first the EtOH was added before section of packing column is starting to the reboiler. numbered stage 2, an so on. The The total material, component last stage of the packing column is and energy balances are made to numbered 11, also the reboiler is the various sections of the semi- named stage 12. The model is done batch ractive distillation column, and to simulate a pilot plant semi-batch by further simplifications of the reactive distillation column that differential equations lead to the was constructed in Chemical model. Engineering Department of

University of Technology 2.3.1 Condenser (Baghdad) [15]. The column specification is given in Table (6).

a. Total Material Balance on Condenser dM 1 = V2 − ( L1 + D ) . . . (15) dt b. Component Material Balance d( M x ) 1 i,1 = V y − ( L + D )x . dt 2 2,i 1 i,1 (16) c. Total energy balance:

d( M 1h1 ) = V2 H 2 − ( L1 + D )h1 − Qc dt . . (17) d. Summation: c ∑ x1,i − 1 = 0 . . . (18) i=1

2.3.2 Reboiler

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Section N-2

Section N-1

L N −1

VN

Reboiler M n a. Total MaterialBalance a. Total Material Balance. dM n = L + V − L − V . . . (25) dM dt n−1 n+1 n n N = L − V . . . (19) dt N −1 N b. Component Material Balance

b. Component Material Balance d(Mn xn,i ) = Ln−1xn−1,i +Vn+1 yn+1,i −Ln xn,i d( M N ⋅ x N ,i ) dt = LN −1 x N −1,i − VN y N ,i . dt −Vn yn,i 20) dx (V − L −V ) L n,i = n n−1 n+1 x + n−1 x Expanding the first term of dt M n,i M n−1,i equation (20) and arranging gives. n n V V dx (V − L ) L + n+1 y − n y N ,i = N N −1 ⋅ x + N −1 ⋅ x M n+1,i M n,i dt M N ,i M N −1,i n n N N V − N ⋅ y . . . (27) M N ,i N . . . (21) c. Energy Balance c. Heat Balance d( M n hn ) d( M hN ) = Ln−1 hn−1 +Vn+1 H n+1 − Ln hn N = L h − V H + Q dt dt N −1 N −1 N N R −Vn H n . . . (22) . . . Dividing equation (22) by (28) M1 and rearranging gives, By substitution eqn. (25) in eqn. dhN (VN − LN −1 ) LN −1 (28) then. = hN + hN −1 dt M N M N dhn (Vn − Ln−1 −Vn+1 ) Ln−1 = hn + hn−1 VN Q dt M n M n − H N + M N M N Vn+1 Vn + H n+1 − H n . . . (23) M n M n d. Summation: . . . c (29) ∑ x N ,i − 1 = 0 . . . (24) i=1 d. Summation: c ∑ xn,i − 1 = 0 . . . (30) 2.3.3 General Stage n i=1

Ln-1 Vn

Stage n

Ln Vn+1 Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction 2.3.4 General Reaction stage m c x − 1 = 0 . . . (36) ∑ m,i Lm-1 Vm i=1 The acetic acid feed stage can be treated in the same way of

Stage m treating stage n but with adding the

other term which is the feed term. With the aid of the finite- Lm Vm+1 difference representation, it is useful to evaluate the values of liquid and vapor enthalpy

derivatives dh and dH depending a. Total MaterialBalance dt dt dM m on the values of h and H at = Lm−1 + Vm+1 − Lm − Vm . . . (31) dt previous time steps, by using the b. Component Material Balance following two equations. d( M m xm,i ) dh h( t ) − h( t + ∆t ) = Lm−1 xm−1,i +Vm+1 ym+1,i ≈ . . . (37) dt dt ∆t − Lm xm,i −Vm ym,i +ε iWm Rm,i dH H( t ) − H( t + ∆t ) ≈ . . . (38) . . . dt ∆t (32) These two equations give very

dxm,i (Vm − Lm−1 −Vm+1 ) Lm−1 good results because the = xm,i + xm−1,i dt M m M m contribution to the energy balance V V ε W R from the change in enthalpy with + m+1 y − m y + i m m,i m+1,i m,i time is very small. M m M m M m . . . Also the previous values of (33) molar holdup M could be used to evaluate the value of the total mass dM c. Energy Balance derivative according to the dt d( M m hm ) = Lm−1 hm−1 +Vm+1 H m+1 − Lm hm following equation. dt dM M(t ) − M(t + ∆t ) −Vm H m +Wm Rm,i ∆H R ≈ . . . (39) dt ∆t

. . . (34) 2.4 Dynamic Simulation By substitution eqn. (31) in eqn. This section contains the (34) then. dynamic simulation of the semi- dh (V − L −V ) L m = m m−1 m+1 h + m−1 h batch reactive distillation. An dt M m M m−1 m m MATLAB program was developed V V W R ∆H m+1 m m m,i R to solve the MESH (mass balance, + H m+1 − H m + M m M m M m equilibrium relationships, . . . summation and heat balance) (35) equations using fourth order d. Summation: Runge-Kutta technique. The

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction simulation was carried out by model can be used to determine solving the system of differential the following results: and algebraic equations • Ethyl acetate purity in the simultaneously. In all the accumulated distillate. simulations presented in this • Percent reactant conversion. section the initial compositions • Amount of distillate. along the column and in the • Stage by stage composition are equal to 100% ethanol. profile. Different reflux ratio, ethanol to • Stage by stage temperature acetic acid and catalys weight was profile. used in column simulations. The • Stage by stage flow profile. above model gives a system of • Stage by stage molar ordinary differential equations holdup. (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. 4. Results And Discussion Numerical methods such as finite The simulation results are differences are used to simplify summarized in Table (7), which these equations, but they lead to a shows the effect of change in large number of ordinary reflux ratio, Ethanol/Acetic acid differential equations. and catalyst weight, on the Figure (2) shows the flowchart accumulated ethyl acetate in for the computer simulation for distillate, concentration of ethyl semi-batch reactive distillation. acetate in distillate, total batch Optimum operating policies reflux time. This table shows that the ratio, Ethanol/Acetic acid and amount of EtAc and EtAc purity catalyst weight were estimated by obtained in the accumulated simulating the reactive batch distillate increases with increase in distillation column for different reflux ratio but at the expense of but constant reflux ratios thereby higher batch. maximizing the production rate of ethyl acetate and ethyl acetate 4.1 Composition and purity. Temperature Profiles

From all 14 simulation runs 3. Model Results summarized in Table (7), the Much more results can be results of run 3 are selected to be predicted from the dynamic plotted in Figures (3, 4, 5, 6, 7, 8 simulation model of semi-batch and 9). Figures (3, 4, 5 and 6) reactive distillation. The proposed represent the model results for

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction ethanol, acetic acic, ethyl acetate production by reaction becomes and water composition profiles in less than the rate of separation by several locations along the column. distillation and therefore there is a The distillate composition is fall in the mole fraction of EtAc. illustrated in Figure (7). This Acetic acid concentration figure shows that the mole fraction gradually increases with time, this of ethanol in condenser decreases behavior is due to acetic acid from 1, reaches a steady state highest boiling point in the value after startup time (0.5 hr reaction mixture also that the after starting) and then gradually acetic acid feed was continuous in falls to zero after 3 hrs. Ethanol first 2 hrs, therefore the acetic acid mole fraction falls rapidly as it is retains in the lower sections of the being consumed by the reaction as column. Ethanol mole fraction well as separated by distillation. falls rapidly as it is being The rise in EtAc mole fraction is consumed by the reaction as well due to the high rate of reaction as separated by distillation. initially, however after 2.5 hrs the Ethanol is completely consumed in rate of EtAc production by 3 hrs, then the reaction stops and reaction becomes less than the rate the column behaves like a non- of separation by distillation and reactive batch distillation column. therefore there is a fall in the mole Figure (9) shows the variation fraction of EtAc. Acetic acid in column temperatures with concentration gradually increases respect to time. This figure indicates with time, this behavior is due to that the reboiler temperature acetic acid highest boiling point in decreases at first and then the reaction mixture. Acetic acid increases slowly as the reaction and ethyl acetate were separated proceeds. The initial decrease in above the acetic acid feed point in temperature is due to more volatile the rectification section. Thus, components produced by the concentrated ethyl acetate and reaction, however, as the unreacted ethanol will be the first separation of these components distillation cut and the acetic acid continues, then the reboiler will be the last distillation cut. temperature starts increasing. The model results was The reboiler compositions is compared with the experimental plotted in Figure (8). This figure work taken by Ismail et al. [8], shows that the mole fraction of and it was found that there is a EtAc in reboiler rises from zero, good agreement in behavior reaches a small value and then between the mathematical and after 2.5 hrs falls to zero. The rise experimental results. in mole fraction is due to the high rate of reaction initially, however 4.2 Optimization Results. after 2.5 hrs the rate of EtAc

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction In runs 1 to 5 the reflux ratio (12) shows that conversion and was varied from 0.5 to 4. The distillate purity of ethyl acetate reflux ratio had a very significant increase with rapidly with increasing effect on the performance of the the catalyst weight used in the semi-batch reactive distillation column. The increase in the reactant conversion with catalyst loading column.The conversion of the agrees well with the description of reactants and distillate literture [10, 14]. concentration for five different reflux ratios is shown in Figure (10), indicating that the reactant 5. Conclusions conversion first rises with This paper outlines detailed increasing reflux ratio and then mathematical modeling and decreases with further increasing simulation of reactive semi-batch of reflux ratio, this behavior is reactive distillation column for because EtAc concentration ethyl acetate production. depends on both reaction and MATLAB 6.5 program is used to separation at the same time. On the perform the dynamic simulation other hand, the purity of EtAc in which is then used to derive the distillate increases with increasing optimum operating profiles. the reflux ratio. The optimum Column behavior was fully reflux ratio at which the investigated and explained in production rate is maximum comes detail by considering the effects of out to be 2. The optimum reflux varying reflux ratio, Acetic ratio should be carefully selected acid/Ethanol and catalyst weight. to give maximum production rate The optimum operating reflux with appropriate purity. ratio to give maximum ethyl acetate conversion was found to be In runs 3, 6, 7, 8, 9 and 10, the 2, while ethyl acetate purity effect of the ratio of acetic acid fed increases with increasing the in column to the ethanol on reflux ratio. The reactant reactant conversion and distillate conversion and distillate purity purity is studied. Figure (11) increase with increasing the ratio shows that the reactant conversion of acetic acid feed to the ethanol. relatively increases with increasing Also the reactant conversion and the ratio of acetic acid fed in distillate purity increase linearly to column to the ethanol. Also the some limit with increasing amount distillate purity of ethyl acetate of catalyst used in column. increases but rapidly with The semi-batch reactive increasing the ratio of acetic acid distillation gives reactanat feed in column to the ethanol. conversion and product purity higher than batch reactive In runs 3, 11, 12, 13 and 14, the effect distillation when the difference in of catalyst weight on reactant conversion and distillate purity is studied. Figure

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction boiling points of reactants is higher than 10 oC.

References 1. Katariya, A. M., Moudgalya, K. 5. Mujtaba I. M. and Macchietto M., and Mahajani, S. M., S. “Efficient optimization of Nonlinear dynamic effects in batch distillation withchemical reactive distillation for reaction using polynomial synthesis of TAME. Industrial curve fitting techniques” and Engineering Chemistry Industrial & Engineering Research, 45(12), 4233–4242 Chemistry Research, , 36 (6), (2006). 2287-2295 (1997). 2. Reepmeyer, F., Repke, J., & 6. Francis J. D. and Lalitha S. B Wozny, G.. Time optimal start- “Nonlinear Model-Based up strategies for reactive Control Of A Batch Reactive distillation columns. Chemical Distillation Column” Engineering Science, 59, Department of Chemical 4339–4347 (2004). Engineering University of 3. Cuille P. E. and Reklaitis G. V. Delaware, Newark DE, (1999). “Dynamic simulation of 7. Monroy-Loperena R. and multicomponent batch Alvarez-Ramirez J. “Output- rectification with chemical feedback control of reactive reactions” Computers & batch distillation columns” Chemical Engineering, , 10 (4), Industrial & Engineering 389-398 (1986). Chemistry Research, 39, 378- 4. Wilson, J., I Chem. Eng. Symp. 386 (2000). Ser., 100, p 163 (1987).

8. Ismail S. K. , Baris Z. B. and Dramur U.” Esteriffcation of Acetic Acid with Ethanol Catalysed by an Acidic Ion- Exchange Resin” Turk J Eng.

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction in Environ Sci, 25, 569-577 I.“Reaction Kinetics of the (2001). Esterfication of Ethnol and 9. Vora, N., & Daoutidis, P. Acetic Acid Towards Ethyl “Dynamics and control of an Acetate”Intelligent Column ethyl acetate reactive Internals for Reactive distillation column” Industrial Separations (INTINT), and Engineering Chemistry Deliverable 22, Workpackage Research, , 40, 833–849 6, Technical Report (2001). (2001). 15. Majid S. Radhaa, Khalid A. 10. Mujtaba M. and Greaves M. Sukkar, Jamal M. Ali, A.” Neural Network Based Zaidoon M. Shakoor, and Modeling and Optimization in Niran Manwel Batch Reactive Distillation” "Hydrodynamics, Mass and IChemE (2006 ) Heat Transfer in Reactive 11. Lee, J.W. , Brüggemann S. Distillation", Al-Khwarizmi and Westerberg A.W. Eng. Journal, (Article in Press) “Visualization of the Ethyl (2008). Acetate Reactive Distillation 16. Taylor, R., & Krishna, R. System” Conference (1993). Multicomponent mass transfer. New York: Wiley. 17. Peng, J., Lextrait, S., Edgar, T. F., & Eldridge, R. B. A proceedings (cdrom). Technical comparison of steady-state Report LPT–2001–12.,March equilibrium and rate-based (2001). models for packed reactive 12. Espinosa j.”Assessing the distillation columns. Industrial Performance of Batch Reactive and Engineering Chemistry Distillations through Research, 41, 2735–2744, Conceptual Models” 16th (2002). European Symposium on 18. R. Baur and R. Krishna Computer Aided Process Hardware selection and design Engineering, Published by aspects for reactive distillation Elsevier B.V (2006). columns. A case study on 13. Patel R., Singh K.,Moses V. synthesis of TAME , Chem. and Tade O.” Dynamic Eng. Processing, 41, 445-462, Simulation of Reactive Batch (2002). Distillation Column for Ethyl 19. Coulson, J. M., Richardson, J. Acetate Synthesis” Chemical f.," Chemical Engineering, Product and Process Modeling, Volume Six", 3rd ed., Pergman Vol. 2, Issue 2, Article 5 press company ,(1978). (2007). 20. Gmehling, J., Onken, U. and 14. Hangx G., Kwant G., Maessen Arlt, W. “Vapor-Liquid H., Markusse P., and Urseanu Equilibrium Data Collection”,

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction Vol. I/1-8. DECHEMA 21. Perry, R. H. and Chilton, C. Chemsitry Data Series. W. “Chemical Engineers Frankfurt/Main, Handbook”, Seventh ed., New Germany,(1997). York: McGraw-Hill(1997) (1997

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction NOMENCLATURE Symbol Definition Units Cp : Specific heat J/mol·K D : Distillate molar flowrate mol/hr E : Activation energy kJ/mol h : Enthalpy of a liquid mixture J/mol H : Enthalpy of a vapor mixture J/mol P : Total pressure kPa

Pi : Vapor pressure kPa K : Vapour–liquid equilibrium -

Keq : Reaction equilibrium constant -

K1,K2 : Reaction rate constants mol/(s. gm catalyst) L : Liquid flow rate mol/hr

M : Molar holdup mol n : Number of stages - Q : Reboiler heat duty Watt R : Reflux ratio -

R1,R2 : Forward and reverse reaction rate mol/(s. gm catalyst) T : Temperature K t : Time hr

V : Vapor flow rate mol/hr W : Catalyst weight gm x : Liquid mole fraction - y : Vapor mole fraction - Greek letters ε : Void fraction of the packing - ∆HR : Heat of reaction j/mol

γi : γi liquid phase activity coefficient - Subscripts i : i component index - n : Segment (stage) index - L : Liquid phase - V : Vapour phase - Abbreviation AcOH : Acetic acid - DAE : Differential algebraic equations -

EtAc : Ethyl acetate - EtOH : Ethanol -

H2O : Water - Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Table (1) Physical Properties [19] Molecular Density Boiling Point Latent heat Component weight (kg/m3) (oC) (J/mol) (gm/gmol) Ethanol 789 46.069 78.35 38770 Acetic acid 1094 60.052 117.9 23697 Ethyl acetate 901 88.107 77.1 32238 Water 998 18.016 100 40683

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction Table (2) Constants of NRTL Model for Ethanol(1), Acetic Acid(2), Ethyl Acetate(3),Water (4) mixture [20].

Aij values Bij values

A = A = B = B = - B = - A = 0.0 A =0.0 13 14 B = 0.0 12 13 14 11 12 1.817306 0.806535 11 225.4756 421.289 266.533

A =- B = - B = - B =609.8 A = 0.0 A = 0.0 A = 0.0 24 21 B = 0.0 23 24 21 22 23 1.9763 252.482 22 235.279 886

A =- A =- B =1614. B =515.8 B =1290. 31 A =0.0 A =0.0 34 31 32 B =0.0 34 4.41293 32 33 2.34561 287 212 33 464

A41= A42=3.329 A43=3.853 A =0.0 B41=444.8 B42=- B43=- B =0.0 0.514283 33 826 44 857 723.888 4.42868 44

Table (3) Constants of Antoine Equation for Ethanol-Water-Ethylene Glycol System [19].

C C ln( P o ) = C + 2 + C log(T) + C T 5 1 T 3 4

Component c1 c 2 c 3 c4 c5

Ethanol 73.304 -7122.3 -7.1424 2.8853e-6 2

Acetic acid 53.27 -6304.5 -4.2985 8.8865e-18 6

Ethyl acetate 66.824 -6227.6 -6.41 1.7914e-17 6

Water 73.649 -7258.2 -7.3037 4.1653e-6 2

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Table (4)Vapor and Liquid Enthalpy Calculation [21]. Vapor Specific Heat v 2 3 Cp = C 1 + C 2T + C 3T + C 4T Cpv in J/mol.k T in K c c 4 8 Component 1 2 c 3 × 10 c4 × 10 Ethanol 9.014 0.214 -0.839 0.1373 Acetic acid 4.84 0.2548 -1.753 4.948 Ethyl acetate 7.235 0.4071 -2.091 2.854 Water 32.243 0.001923 0.1055 -0.3596 Liquid Specific Heat L 2 3 4 Cp = C 1 + C 2T + C 3T + C 4T + C 5T Cp L in J/mol.k T in K −2 c 3 5 9 Component c1 × 10 2 c3 × 10 c4 × 10 c5 × 10 Ethanol 1.0264 - - 0.2038 0.0 Acetic acid 1.396 - 0.8985 0.0 0.0 Ethyl acetate 2.2623 - 1.472 0.0 0.0 Water 2.7637 - 8.125 - 9.3701

Table (5) Kinetic parameters for ethyl acetate formation and hydrolysis on Purolite CT179. 6 K1,0 4.24×10 mol/kgcat.s 8 K2,0 4.55×10 mol/kgcat.s EA,1 48.3 kJ/mol EA,2 66. kJ/mol

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction

Table (6) Semi-Batch Reactive Distillation Column Specification. No. of packed column stages 10 Packing height 150 cm Rectifying section 15 cm Reactive section 75 cm, Stripping section 60 cm Column diameter 2.5 cm Condenser holdup 28.3 cm3 Reboiler holdup 2000 cm3 Catalyst location in packing column 15-75 cm Ethyl acetate feed location in packing 75 cm column Acetic acid feed period 2 hr Packing type hollow cylinder glass Packing dimensions L=10 mm , I D=4 mm , OD=5mm Catalyst type Cation, Purolite CT179 Startup period 0.5 hr Ethanol holdup in reboiler initially 17.13 mol Reboiler heat duty 400 Watt Catalyst vaoidage 40 % Backing voidage 60 %

Table (7) Dynamic simulation conditions and resulats.

Acetic Distillate Experime Reflux EtAc/EtO Catalyst Conversio acid concentrat Time (hr) nt No. Ratio H Weight n produced ion 1 0.5 1 100 6.6881 0.2371 0.3905 1.6264 2 1 1 100 9.4357 0.2957 0.5509 2.1819 3 2 1 100 10.9436 0.338 0.639 3.0569 4 3 1 100 10.1917 0.4107 0.5951 3.0944 5 4 1 100 9.7118 0.4743 0.5671 3.1528 6 2 0.6 100 7.6128 0.2726 0.4445 2.7097 7 2 0.8 100 10.5582 0.32 0.6165 3.0986 8 2 1.2 100 10.8336 0.3648 0.6326 2.8514 9 2 1.4 100 10.6142 0.3857 0.6198 2.6861 10 2 1.6 100 10.3202 0.4021 0.6026 2.5472 11 2 1 50 8.8836 0.3007 0.5187 2.8569 12 2 1 150 11.9207 0.3618 0.696 3.0889 13 2 1 200 12.5041 0.3829 0.7301 3.0569 14 2 1 300 13.1796 0.4173 0.7695 2.9597

Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation Used for Esterfication Reaction