Eng.&Tech.Vol.26,No.7,2008 Dynamic Simulation of Semi- Batch Catalytic Distillation 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 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. 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 batch distillation 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, vapor 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. distillations. He assumed a rectifier The boiling point 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].