This document summarizes a study that developed a mathematical model to simulate temperature profiles in a reactive distillation system for the esterification of acetic anhydride and methanol. The model was based on reaction kinetics determined from experimental temperature data. Simulation results showed good agreement with experiments, with deviations less than 4%. An overview of the experimental setup and procedures for thermistor calibration and reactor calibration are also provided.
Experimental and Exergy Analysis of A Double Pipe Heat Exchanger for Parallel...IJERA Editor
This paper presents For Experimental and Exergy Analysis of a Double Pipe Heat Exchanger for Parallel- flow Arrangement. The Double pipe heat exchanger is one of the Different types of heat exchangers. double-pipe exchanger because one fluid flows inside a pipe and the other fluid flows between that pipe and another pipe that surrounds the first.In a parallel flow, both the hot and cold fluids enter the Heatexchanger at same end andmove in same direction. The present work is taken up to carry experimental work and the exergy analysis based on second law analysis of a Double-Pipe Heat Exchanger. In experimental set up hot water and cold water will be used working fluids. The inlet Hot water will be varied from 40 0C and 50 0C and cold water temperature will be varied from between 15 and 20. It has been planned to find effects of the inlet condition of both working fluid flowing through the heat exchanger on the heat transfer characteristics, entropy generation, and Exergy loss. The Mathematical modelling of heat exchanger will based on the conservation equation of mass, energy and based on second law of thermodynamics to find entropy generation and exergy losses.
A study on the edm of al7075+3 wt%sic+3wt% b4c hybrid mmceSAT Journals
Abstract The objective of the project is to investigate the effect of current, pulse on time and pulse off time. For the proposed work Material removal rate (MRR) and Tool wear rate (TWR) were chosen as responses and Current, Pulse on time and pulse off time were chosen as process parameters. Hybrid Aluminium Silicon Carbide (Al 7075 + 3wt. % of SiCp+ 3wt. % of B4C) is used as work material and copper is used as tool material. Design of experiment technique is employed for the experimentation. The mathematical models are prepared by Response Surface Methodology (RSM) technique and Box Behnken Design (BBD) is selected to design the matrix for different combination of process parameters. After completion of the experiments analysis was done using analysis of variance (ANOVA) for 90% confidence level. Keywords: Current, Pulse on time, Pulse off time, Material removal rate (MRR), Tool wear rate (TWR), Design of experiments (DOE), Response surface methodology (RSM), Box-Behken design (BBD), Analysis of variance (ANOVA).
Fatigue Analysis of Acetylene converter reactorIJMER
The structural integrity of mechanical components during several transients should be
assured in the design stage. This requires a fatigue analysis including thermal and structural analysis. As
an example, this study performs a fatigue analysis of the acetylene converter reactor during arbitrary
transients. Using heat transfer coefficients determined based on the operating environments, a transient
thermal analysis is performed and the results are applied to a finite element model along with the
pressure to calculate the stresses. The total stress intensity range and cumulative fatigue usage factor are
investigated to determine the adequacy of the design
Abstract The requirement of energy in any processing industry is not only a need but it is indeed a most wanted utility. In a typical processing or manufacturing industry the most common utility are steam and cooling water. However the cost of these utility are no longer cheap, in fact they are expensive. Therefore saving these utility or minimizing the usage of these utilities is one of the most needed practice in a processing industry. Pinch technology is the most common method, which is aimed at minimizing the requirement of utilities by maximizing the process to process heat transfer. In the present study temperature interval diagram or TID is used to identify the targets for minimum utility requirement and maximum process to process heat transfer in a processing facility. The targets for heat exchanger network are presented and minimization of number of heat exchangers are provided using stream splitting technique. Keywords: Pinch design, stream splitting, HEN synthesis, Utilities, TID
Experimental and Exergy Analysis of A Double Pipe Heat Exchanger for Parallel...IJERA Editor
This paper presents For Experimental and Exergy Analysis of a Double Pipe Heat Exchanger for Parallel- flow Arrangement. The Double pipe heat exchanger is one of the Different types of heat exchangers. double-pipe exchanger because one fluid flows inside a pipe and the other fluid flows between that pipe and another pipe that surrounds the first.In a parallel flow, both the hot and cold fluids enter the Heatexchanger at same end andmove in same direction. The present work is taken up to carry experimental work and the exergy analysis based on second law analysis of a Double-Pipe Heat Exchanger. In experimental set up hot water and cold water will be used working fluids. The inlet Hot water will be varied from 40 0C and 50 0C and cold water temperature will be varied from between 15 and 20. It has been planned to find effects of the inlet condition of both working fluid flowing through the heat exchanger on the heat transfer characteristics, entropy generation, and Exergy loss. The Mathematical modelling of heat exchanger will based on the conservation equation of mass, energy and based on second law of thermodynamics to find entropy generation and exergy losses.
A study on the edm of al7075+3 wt%sic+3wt% b4c hybrid mmceSAT Journals
Abstract The objective of the project is to investigate the effect of current, pulse on time and pulse off time. For the proposed work Material removal rate (MRR) and Tool wear rate (TWR) were chosen as responses and Current, Pulse on time and pulse off time were chosen as process parameters. Hybrid Aluminium Silicon Carbide (Al 7075 + 3wt. % of SiCp+ 3wt. % of B4C) is used as work material and copper is used as tool material. Design of experiment technique is employed for the experimentation. The mathematical models are prepared by Response Surface Methodology (RSM) technique and Box Behnken Design (BBD) is selected to design the matrix for different combination of process parameters. After completion of the experiments analysis was done using analysis of variance (ANOVA) for 90% confidence level. Keywords: Current, Pulse on time, Pulse off time, Material removal rate (MRR), Tool wear rate (TWR), Design of experiments (DOE), Response surface methodology (RSM), Box-Behken design (BBD), Analysis of variance (ANOVA).
Fatigue Analysis of Acetylene converter reactorIJMER
The structural integrity of mechanical components during several transients should be
assured in the design stage. This requires a fatigue analysis including thermal and structural analysis. As
an example, this study performs a fatigue analysis of the acetylene converter reactor during arbitrary
transients. Using heat transfer coefficients determined based on the operating environments, a transient
thermal analysis is performed and the results are applied to a finite element model along with the
pressure to calculate the stresses. The total stress intensity range and cumulative fatigue usage factor are
investigated to determine the adequacy of the design
Abstract The requirement of energy in any processing industry is not only a need but it is indeed a most wanted utility. In a typical processing or manufacturing industry the most common utility are steam and cooling water. However the cost of these utility are no longer cheap, in fact they are expensive. Therefore saving these utility or minimizing the usage of these utilities is one of the most needed practice in a processing industry. Pinch technology is the most common method, which is aimed at minimizing the requirement of utilities by maximizing the process to process heat transfer. In the present study temperature interval diagram or TID is used to identify the targets for minimum utility requirement and maximum process to process heat transfer in a processing facility. The targets for heat exchanger network are presented and minimization of number of heat exchangers are provided using stream splitting technique. Keywords: Pinch design, stream splitting, HEN synthesis, Utilities, TID
Thermal testing, thermo mechanical and dynamic mechanical analysis & chem...Dr.S.Thirumalvalavan
Unit-V: THERMAL TESTING, THERMO-MECHANICAL AND DYNAMIC MECHANICAL ANALYSIS & CHEMICAL TESTING [OTHER TESTING].
Subject Name: OML751 Testing of Materials
Topics: Thermal Testing: Differential scanning calorimetry, Differential thermal analysis. Thermo-mechanical and Dynamic mechanical analysis: Principles, Advantages, Applications. Chemical Testing: X-Ray Fluorescence, Elemental Analysis by Inductively Coupled Plasma-Optical Emission Spectroscopy and Plasma-Mass Spectrometry.
B.E. Mechanical Engineering
Final Year, VII Semester, Open Elective Subject
[As per Anna University R-2017]
In DSC the heat flow is measured and plotted against temperature of furnace or time to get a thermo gram. This is the basis of Differential Scanning Calorimetry (DSC).
The deviation observed above the base (zero) line is called exothermic transition and below is called endothermic transition.
The Addition of Aluminum Nanoparticles to Polypropylene Increases Its Thermal...IJERA Editor
This work reports the thermal degradation kinetics of isotactic polypropylene (iPP) and iPP with incorporated Al nanoparticles. The Friedman, Flynn-Wall–Ozawa (FWO), ASTM E698 and Coats-Redfern methods were used to calculate the activation energy of the samples from thermogravimetric data. The thermal stability of the iPP was improved by the introduction of the nanoparticles: the maximum decomposition temperature of the nanocomposite increased from 453 ºC to 457 ºC and the activation energy from 226 kJ/mol to 244 kJ/mol. The thermal degradation models of iPP can be described by “Contracting Sphere” model, whereas that to nanocomposite by Rn (n= 4.8) model (phase boundary reaction).
Modelling of fouling in heat exchangers using the Artificial Neural Network A...AI Publications
In this paper, modelling by neural networks was used for obtaining a model for the calculation of fouling factors in heat exchangers. The heat exchangers used in this study are a series of four exchangers where a model was obtained for each exchanger after due estimation of its heat load. The basic theme of this paper is the investigation of fouling factors and the determination of relevant indicators followed by combining design and operation factors along with fouling factors in a mathematical model that may be used for the calculation of the fouling factor. The devised model was tested for reliability and its accuracy in predicting new values for the fouling factor was greater than 98% in view of the design of the model Furthermore, the number of elements related to the design and operation was reduced to four developed formulae (developed factors) to which were added later the four factors selected as indicators of the occurrence of fouling. Both were then used as network input, whereas the output was the value of the fouling factor. The importance of this modelling lies in the fact that it enables the operator to continually predict the value of the fouling factor in heat exchangers and it assists him in taking appropriate measures to alleviate fouling effects ensuring thereby continuous operation of the unit and prevention of emergency shut downs.
COMPARATIVE STUDY OF DIFFERENT COMBINED CYCLE POWER PLANT SCHEMESijmech
Combined Cycle Power Plants (CCPPs) are imperative for power generation with the capability for
deciphering power shortage during peak and off peak hours. To perk up the recital of the plant, foremost
locations of exergy losses are to be identified and analyzed. In the present work, exergetic analysis of a
CCPP is carried out using the computer programming tool Engineering Equation Solver (EES). The effects
of overall pressure ratio and turbine inlet temperature on the exergy destruction in the CPR are
investigated. The results obtained are compared with that of simple gas turbine cycle power plant. During
real time operation of CCPP exergy destruction in different components is associated with change in
overall pressure ratio and turbine inlet temperature (TIT). Out of the total exergy destruction in the cycle it
is the combustion chamber (CC) which is responsible for the maximum exergy destruction. Nearly 60% of
the total exergy is destroyed in CC. Results clearly show that with increase in complicacy of the power
plant structure, irreversibility of the processes can be improved.
Introduction to transient Heat conduction, Lamped System Analysis, Approxiamate Analytical and graphical method and Numerical method for one and two dimensional heat conduction by using Explicit and Implicit method
Numerical Study of Entropy Generation in an Irreversible SolarPowered Absorpt...inventionjournals
The ideal three-heat-reservoir (THR) model for absorption refrigeration cycles is extended to include external and internal irreversibilities. Three empirical functions are used to model the internal entropy generation of the cycle. The parameters of these functions are estimated by fitting data obtained by simulation to the predictions of the THR model. The THR model using a linear function or a logarithmic function for the internal entropy generation is able to reproduce performance data for absorption systems with good accuracy
Thermal testing, thermo mechanical and dynamic mechanical analysis & chem...Dr.S.Thirumalvalavan
Unit-V: THERMAL TESTING, THERMO-MECHANICAL AND DYNAMIC MECHANICAL ANALYSIS & CHEMICAL TESTING [OTHER TESTING].
Subject Name: OML751 Testing of Materials
Topics: Thermal Testing: Differential scanning calorimetry, Differential thermal analysis. Thermo-mechanical and Dynamic mechanical analysis: Principles, Advantages, Applications. Chemical Testing: X-Ray Fluorescence, Elemental Analysis by Inductively Coupled Plasma-Optical Emission Spectroscopy and Plasma-Mass Spectrometry.
B.E. Mechanical Engineering
Final Year, VII Semester, Open Elective Subject
[As per Anna University R-2017]
In DSC the heat flow is measured and plotted against temperature of furnace or time to get a thermo gram. This is the basis of Differential Scanning Calorimetry (DSC).
The deviation observed above the base (zero) line is called exothermic transition and below is called endothermic transition.
The Addition of Aluminum Nanoparticles to Polypropylene Increases Its Thermal...IJERA Editor
This work reports the thermal degradation kinetics of isotactic polypropylene (iPP) and iPP with incorporated Al nanoparticles. The Friedman, Flynn-Wall–Ozawa (FWO), ASTM E698 and Coats-Redfern methods were used to calculate the activation energy of the samples from thermogravimetric data. The thermal stability of the iPP was improved by the introduction of the nanoparticles: the maximum decomposition temperature of the nanocomposite increased from 453 ºC to 457 ºC and the activation energy from 226 kJ/mol to 244 kJ/mol. The thermal degradation models of iPP can be described by “Contracting Sphere” model, whereas that to nanocomposite by Rn (n= 4.8) model (phase boundary reaction).
Modelling of fouling in heat exchangers using the Artificial Neural Network A...AI Publications
In this paper, modelling by neural networks was used for obtaining a model for the calculation of fouling factors in heat exchangers. The heat exchangers used in this study are a series of four exchangers where a model was obtained for each exchanger after due estimation of its heat load. The basic theme of this paper is the investigation of fouling factors and the determination of relevant indicators followed by combining design and operation factors along with fouling factors in a mathematical model that may be used for the calculation of the fouling factor. The devised model was tested for reliability and its accuracy in predicting new values for the fouling factor was greater than 98% in view of the design of the model Furthermore, the number of elements related to the design and operation was reduced to four developed formulae (developed factors) to which were added later the four factors selected as indicators of the occurrence of fouling. Both were then used as network input, whereas the output was the value of the fouling factor. The importance of this modelling lies in the fact that it enables the operator to continually predict the value of the fouling factor in heat exchangers and it assists him in taking appropriate measures to alleviate fouling effects ensuring thereby continuous operation of the unit and prevention of emergency shut downs.
COMPARATIVE STUDY OF DIFFERENT COMBINED CYCLE POWER PLANT SCHEMESijmech
Combined Cycle Power Plants (CCPPs) are imperative for power generation with the capability for
deciphering power shortage during peak and off peak hours. To perk up the recital of the plant, foremost
locations of exergy losses are to be identified and analyzed. In the present work, exergetic analysis of a
CCPP is carried out using the computer programming tool Engineering Equation Solver (EES). The effects
of overall pressure ratio and turbine inlet temperature on the exergy destruction in the CPR are
investigated. The results obtained are compared with that of simple gas turbine cycle power plant. During
real time operation of CCPP exergy destruction in different components is associated with change in
overall pressure ratio and turbine inlet temperature (TIT). Out of the total exergy destruction in the cycle it
is the combustion chamber (CC) which is responsible for the maximum exergy destruction. Nearly 60% of
the total exergy is destroyed in CC. Results clearly show that with increase in complicacy of the power
plant structure, irreversibility of the processes can be improved.
Introduction to transient Heat conduction, Lamped System Analysis, Approxiamate Analytical and graphical method and Numerical method for one and two dimensional heat conduction by using Explicit and Implicit method
Numerical Study of Entropy Generation in an Irreversible SolarPowered Absorpt...inventionjournals
The ideal three-heat-reservoir (THR) model for absorption refrigeration cycles is extended to include external and internal irreversibilities. Three empirical functions are used to model the internal entropy generation of the cycle. The parameters of these functions are estimated by fitting data obtained by simulation to the predictions of the THR model. The THR model using a linear function or a logarithmic function for the internal entropy generation is able to reproduce performance data for absorption systems with good accuracy
FUZZY LOGIC Control of CONTINUOUS STIRRED TANK REACTOR ProfDrDuraidAhmed
MATLAB program version 7.6 was used to study dynamic behavior continuous stirred tank reactor and the process control implemented for different control strategies. The results of simulation were compared with experimental data and a good agreement was obtained. However, small differences between the responses were appeared. A comparison has been made between fuzzy logic controller and PID conventional control to test the effectiveness of the behavior of the system. The results showed that, a good improvement was achieved when the fuzzy logic control was used compared to the PID conventional control.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Fuzzy Logic Modeling of Heat Transfer in a double Pipe Heat Exchanger with Wa...ijiert bestjournal
Fuzzy logic is a method which can be used to model the experiments,and it has been introduced for the first time in 1965 by Zadeh . T he present work represents the use of fuzzy logic to model and predict the experimental results of heat transfer in a double Pipe Heat Exchanger with Wavy (Corrugated) Twiste d Tape Inserts . The tape consists of the corrugations and the twisting with various twist ratios (TR=10.7,8.5,7.1) . The length,width and thickness of twisted tape were 1 m,14 mm and 2 mm respectively. The Reynolds number is varied from 5000 to 17 000. T he friction factor is varied from .0384 to .07241 . The Nusselt number is varied from 69.13 to 266.18. Here the results with various twist ratios tapes were compared with results with plain tube. The experimental results showed that the maximum heat tran sfer was obtained with twisted tape with TR � 7.1 . The Nusselt number increased by 172 % and friction factor value increased by 32.11% as compared to the smooth tube values. For Fuzzy Logic system the twist ratio,temperature and Reynolds Numbers were used as input functions and friction factor and Nusselt number were used as output functions. It is found that a fuzzy inference system named Mamdani is a powerful instrument for predicting the experiments due to its low error.
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Photovoltaic (PV) cell from solar energy is one of the most widely adopted renewable energy source and commercially available system that can be used in various applications. More appealing application of PV arrays used in thermoelectric (TE) device was it can convert solar thermal energy from temperature difference into electric energy to act as power generators. In this study, a theoretical model is developed by using conducting steady state energy analysis of a PVT-TE air collector. The matrix inversion method is used to obtain energy balance equation. The effect of various parameters also investigated. The mass flow rate of range 0.01 kg/s to 0.05 kg/s and solar intensity of 400 W/m2, 600 W/m2 and 800 W/m2 was used to obtain outlet temperature, To in the range about 28.9oC to 43.7oC and PV temperature, Tp about 35.3oC to 60oC.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
One-dimensional Lumped-Circuit for Transient Thermal Study of an Induction El...IJECEIAES
Electrical machines lifetime and performances could be improved when along the design process both electromagnetic and thermal behaviors are taken into account. Moreover, real time information about the device thermal state is necessary to an appropriate control with minimized losses. Models based on lumped parameter thermal circuits are: generic, rapid, accurate and qualified as a convenient solution for power systems. The purpose of the present paper is to validate a simulation platform intended for the prediction of the thermal state of an induction motor covering all operation regimes. To do so, in steady state, the proposed model is validated using finite element calculation and experimental records. Then, in an overload situation, obtained temperatures are compared to finite element’s ones. It has been found that, in both regimes, simulation results are with closed proximity to finite element’s ones and experimental records.
Development and theoretical analysis of mathematical expressions for change o...ijsrd.com
This paper introduces a novel technique and algorithm for theoretical study of entropy changes for exothermic reactions by mechanistic modelling and dynamic simulation; considering factors such as kinetics, reaction environment and flow patterns with an ultimate objective of minimization of energy loss and entropy generation in the system. It mainly focuses on exothermic reactors cooled by means of a constant inlet temperature utility fluid which flows along the external surface of the reactor vessel. Using basic concepts of heat and mass balances and definitions in thermodynamics, variation of related system variables with time is modelled and by simulation in MS-Excel, a polynomial fit is generated for sample problems in order to make the illustrations handier. Usages of the developed expressions for energy optimization are also commented upon.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed
EVALUATING MATHEMATICAL HEAT TRANSFER EFFECTIVENESS EQUATIONS USING CFD TECHN...AEIJjournal2
this analysis has shown that although mathematical equations are effective and simple tools in producing results, the results may not reflect the actual physical conditions. The analysis showed that theexhaust gas temperature outlet of a double pipe heat exchanger is actually higher than what were calculated using mathematical equations, and therefore, more heat energy is available for recapturing. k-epsilon RNG turbulence model was found to be the most suitable method in analyzing heat transfer in a finned double pipe heat exchanger.
EVALUATING MATHEMATICAL HEAT TRANSFER EFFECTIVENESS EQUATIONS USING CFD TECHN...AEIJjournal2
Mathematical heat transfer equations for finned double pipe heat exchangers based on experimental work
carried out in the 1970s can be programmed in a spreadsheet for repetitive use. Thus avoiding CFD
analysis which can be time consuming and costly. However, it is important that such mathematical
equations be evaluated for their accuracy. This paper uses CFD methods in evaluating the accuracy of
mathematical equations. Several models were created with varying; geometry, flue gas entry temperature,
and flow rates. The analysis should provide designers and manufacturers a judgment on the expected level
of accuracy when using mathematical modelling methodology. This paper simultaneously identifies best
practices in carrying out such CFD analysis.
Evaluating mathematical heat transfer effectiveness equations using cfd techn...aeijjournal
Mathematical heat transfer equations for finned double pipe heat exchangers based on experimental work carried out in the 1970s can be programmed in a spreadsheet for repetitive use. Thus avoiding CFD analysis which can be time consuming and costly. However, it is important that such mathematical equations be evaluated for their accuracy. This paper uses CFD methods in evaluating the accuracy of mathematical equations. Several models were created with varying; geometry, flue gas entry temperature,
and flow rates. The analysis should provide designers and manufacturers a judgment on the expected level
of accuracy when using mathematical modelling methodology. This paper simultaneously identifies best
practices in carrying out such CFD analysis
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Modeling and simulation of temperature profiles in a reactive
1. Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.10, 2013
51
Modeling and Simulation of Temperature Profiles in a Reactive
Distillation System for Esterification of Acetic Anhydride with
Methanol
N.Asiedu*
, D.Hildebrandt*
, D.Glasser*
Centre of Material and Process Synthesis, School of Chemical and Metallurgical Engineering, University of
Witwatersrand, Private mail Bag X3, Wits 2050, Johannesburg, South Africa.
*Authors to whom correspondence may be addressed:
Emails: nasiedusoe@yahoo.co.uk, Diane.Hildebrandt@wits.ac.za, David.Glasser@wits.ac.za
ABSTRACT
This paper pertains to an experimental and theoretical study of simulation of temperature profiles in a one- stage
adiabatic batch distillation/reactor for the production of methyl acetate and acetic acid from the esterification of
acetic anhydride with methanol. Basically it deals with the development of a mathematical model for
temperature predictions in the reactor. The reaction kinetics of the process was modeled using information
obtained from experimental temperature –time data during the esterification processes. The simulation results
were then compared with the experimental data.
The maximum deviation of the model –predicted temperature form the corresponding experimentally measured
temperature was less than 4% which is quite within the acceptable deviation range of experimental results..
Keywords: Modeling, Simulation, Reactive distillation, Temperature, Esterification, Acetic anhydride,
Methanol
INTRODUCTION
The concept of reactive distillation was introduced in the 1920,s to esterification processes, Key (1932). Reactive
distillation has thus become interesting alternative to conventional processes. Recently this technology has been
recommended for processes of close boiling mixtures for separation. In the last years investigations of kinetics,
thermodynamics for different processes have been made, Bock et al (1997), Teo and Saha (2004), Kenig at al
(2001). Reactive distillation is also applied in process production of fuel ether, Mohl et al (1997). Popken (2001)
studied the synthesis and hydrolysis of methyl acetate using reactive distillation technique using structured
catalytic packing. The synthesis of methyl acetate has been has also been studied by Agreda et al (1990) and
Kerul et al (1998). In this paper, the process considered the reactions of acetic anhydride-methanol for the
production methyl acetate and acetic acid. Most of the works done on the synthesis of synthesis of methyl acetate
through reactive distillation considered acetic acid and methanol reactions. This paper looks at the modeling of
the kinetics of the methanol-acetic anhydride process and develops and simulates a mathematical model for the
temperature-time of the reaction as the process proceed in an adiabatic batch reactor ( one stage batch distillation
process).
THE MATHEMATICAL MODEL OF THE REACTING SYSTEM
Given an adiabatic batch reactor the mathematical model is made up of a set of differential equations resulting
from the mass and energy balances referred only to the reaction mixture because there is no heat transfer.
The stoichiometry of the reaction studied is given below:
(CH3CO)2O + CH3OH → 2CH3COOH + CH3COOCH3
∆H (298K) = -66kJ/mol (1)
For a constant –volume batch reactor one can write:
The energy balance equation can be established as:
Heat generated = Heat absorbed by reactor contents +
Heat transferred through reactor walls (3)
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where (ε) is the extent of reaction, we can rearrange eq(6) to give eq(8) below:
Assume that heat given by stirrer speed (Qstrirrer ) is negligible. Integrating eq(4) gives
The LSH of eq(7) can be used to correct experimental data to adiabatic conditions. It is assumed that the reaction
is independent of temperature, hence correcting the experimental data the adiabatic temperature rise parameter
(∆Tad) can be obtained from the experimental result for the process. This adiabatic temperature rise is equal to
the RHS of eq(9) or we can write;
From eq(9) one can easily show that the energy balance equation of an adiabatic batch reactor reduces to a linear
form given by eq(7) as:
Theoretically the adiabatic temperature rise is by definition obtained when extent of reaction (ε) =1 or
conversion (x) = 1, with respect to the reactant of interest and its value can be computed in advance from the
initial conditions (temperature and heat capacities) of the reacting species. Equation (9) also allows one to find
extent of reaction and or conversion at any instant under adiabatic conditions by using only one measure of
temperature. Then from the initial concentrations of the reactants the concentrations products can be monitored
at any instant in the reactor.
THE EXPERIMENTAL SET-UP
The experimental set- up as shown in figure (6.1) below were used in all the reactions studied. The adiabatic
batch reactor used in the experiments is 18/8 stainless steel thermos-flask of total volume of 500mL equipped
with a removable magnetic stirrer. The flask is provided with a negative temperature coefficient thermistor
connected on-line with a data-logging system. The signal from the sensor (thermistor) is fed to a measuring and a
control unit amplifier and a power interface. The acquisition units are connected to a data processor. A process
control engineering support data management. All physically available analog inputs and outputs as well as
virtual channel are all automatically monitored and the process values are stored. The process values are
transmitted in such a way that the computer screen displays profiles of voltage-time curves. Data acquisition
software was used to convert the compressed data form of the history file on the hard disk into text file format.
The text files are converted to excel spreadsheet and the data are then transported into matlab 2010a for analysis.
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THE THERMISTOR CALIBRATION
This section describes the experimental details concerning the measurements of liquid phase reactions by
temperature-time techniques. Temperature changes are a common feature of almost all chemical reactions and
can be easily measured by a variety of thermometric techniques.
Following the temperature changes is useful especially for fast chemical reactions where the reacting species are
not easily analyzed chemically. This section thus describes the theory and the calibration of the thermistor used
in the experiments described in this paper.
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The Circuit Theory
From Kirchhoff law’s we can write:
Vout – Voltage measured by thermistor during the course of reaction.
VTH – Voltage across resistance (RTH).
From (12) one can write:
From the circuit VTH and Itotal are unknowns. RTH is resistance due to the thermistor, and Itotal is the same through
the circuit and can be determine as :
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Vout is known from experimental voltage –time profile and R (150kΩ) is also known from the circuit. Thus when
Itotal is determined from eq(13), RTH which is the thermistor’s resistance and related to temperature at any time
during the chemical reaction can be determine as:
THE THERMISTOR CALIBRATION
The thermistor used in the experiments was negative temperature coefficient with unknown thermistor constants.
The calibrations involve the determination of the thermistor constants and establish the relationship between the
thermistor’s resistance and temperature.
This was done by fitting both the thermistor and an electronic digital temperature measuring device in a sealed
vessel and the system ws slowly warmed until the voltage reaches it asymptotic state.The thermistor was
connected to a computer with data acquisition software to provide data of voltage –time real-time plot as shown
in figure (3) below. The voltage –time data was used to match the temperature-time data obtained from the
electronic digital temperature device.
Figure(3): The thermistor voltage-time profile
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Figure(4): The thermistor temperature-time profile
RELATIONSHIP BETWEEN THERMISTOR RESISTANCE AND
TEMPERATURE
Thermistor resistance (RTH) and Temperature (T) in Kelvin was modeled using the empirical equation given
developed by Considine (1957)
or
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where the parameters (B) and (C) are the thermistor constants and were obtained from experimental calibration
using warm water. The constants were determined by fitting the “best” least square straight line plot of ln(RTH)
against 1/T, giving the thermistor equation as:
The calibration plot is shown in figure (5) below:
285 290 295 300 305 310
11.8
11.9
12
12.1
12.2
12.3
12.4
12.5
1/T(1/K)
Ln(R)
Thermist Calibration
Ln(R) = -1773.8/T+ 18.178
Figure(5): Regression line of ln(RTH) against 1/T
THE REACTOR (THERMOS-FLASK) CALIBRATION
The reaction vessel used was an ordinary dewer thermos-flask with removable screw cap lid. The flask has a
total volume of 500mL. The calibration involves the determination of the heat transfer coefficient of the flask
and fitting the experimental data to the model described in eq(20) below:
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In this experiment 400.00g of distilled water at 361K (TO) was injected into the reaction vessel and left the
system temperature to fall over a period of time until the temperature-time profile reaches its asymptotic state or
the steady-state temperature (TS). The figure (6) below shows the temperature-time profile of the cooling
process.
0 10 20 30 40 50 60 70 80
290
300
310
320
330
340
350
360
370
Time (hrs)
Temperature(K)
Temperature -time Curve of cooling water in reaction vessel
T = T(s) + [(T(o) -T(s)]exp[-UA/mCp .t]
Fig (6) : Thermos-flask cooling curve at T(0) =361K
From eq(20) the values of To and Ts were obtained from fig(6.6). Rearrangement of eq(18) gives;
Since T and t values are known least square regression analysis was performed and a straight plot of ln(β)
against time is shown in figure (7) below:
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0 500 1000 1500 2000 2500 3000 3500 4000
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Time(s)
Ln(Y)
A Graph of Ln(Y) against Time of Cooling Water
Initial Temperature of water =361K
Ln (Y) = -0.0013.t
Mass of water = 400.0g
Fig (7) :Regression line of heat transfer coefficient of reactor
The slope of the straight line of fig(7) is given by 0.0013s-1
(min-1
) which corresponds to the value of the heat
transfer coefficient of the flask.
EXPERIMENTAL PROCEDURES AND RESULTS
Analytical reagent grade acetic anhydride was used in all the experiments. In all experiments about 1.0 mol of
acetic anhydride was poured into the reaction vessel followed by 3.0mols of the methanol. These volumes were
used so that at least 60% of the length of the sensor (thermistor) would be submerged in the resulting mixture.
Reactants were brought to a steady-state temperature before starting the stirrer. In course of the reaction the
stirrer speed was set 1000/ min and the resulting voltage-time profiles were captured as described above and the
corresponding temperature-time curve was determined using the thermistor equation derive in equation (17)
above. Runs were carried out adiabatically at the following initial temperatures: 290K, 294K and 300K.
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DETERMINATION OF UA/mCp FOR THE REACTION MIXTURE
For a given system (reaction vessel and content) one can write:
In this experiment different amount of water (mw) (200g, 300g and 400g) was injected into the reaction flask at
343.08K, 347.77K and 347.85K and allowed to cool until the temperature reaches a steady-state temperature
(TS). Figures (8a), (9a) and (10a) of the cooling processes are shown below. The cooling process thus follows
equation (18) above. A nonlinear least-square regression analysis was performed on all the three experimental
curves. Using eq(19), the value of UA/mCP for each cooling curve was obtained. Figures (8b),(9b) and (10b)
shows the regression lines.
Fig (8a): Thermos-flask cooling curve at T(0) =343.08K
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Fig (8b): Regression line of heat transfer coefficient of reactor
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Fig (9a): Thermos-flask cooling curve at T(0) =347.77K
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Fig (9b): Regression line of heat transfer coefficient of reactor
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Fig (10a): Thermos-flask cooling curve at T(0) =347.80K
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Fig (10b): Regression line of heat transfer coefficient of reactor
Table (1): Summary of characteristics of figures (6.8)-(6.10)
Mass of water(g) Initial Temperature(K) Final Temperature(K) UA/mCp (min-1
)
200 343.08 292.13 0.00215
300 347.77 293.00 0.00189
400 347.84 293.38 0.00178
From table (1) a plot of mass of water (m) against (mCp/UA) is shown in figure(11) below:
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Fig (11): A plot of mass of water (m) against (mCp/UA)
Table (2) below consist of some of the physical constants of the reacting species which was used in the
determination of the quantity UA/mCP.
Table (2) : Some constants of reacting species
Species Moles Molar mass(g/mol) CP (J/mol.K)
Acetic anhydride 1.0 102.9 189.7
methanol 3.0 32.04 79.5
Equation (21) was used to determine specific heat of the mixture (CP.mix) and the quantity MTCP.mix.
MTCP.mix. was calculated to be 545.19 J/mol. K Since the reaction mixture is not pure water we therefore
determined its equivalent mass of water by dividing 545.19 J/mol. K by the specific heat of water;
From the equation of the line in figure (6.11) the value of the quantity (UA/mCP)mix was determined to be
0.002307/min. This value was plugged in eq(7) above and the corrections of the experimental results to adiabatic
conditions was performed. The figures (12),(13) and (14) below shows the experimental and the corrected
temperature profiles for all the three experiments.
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0 50 100 150 200 250
290
300
310
320
330
340
350
Time(min)
Temperature(K)
Experimental curve
Adiabatic curve
Fig(12): Experimental and Adiabatic curves of experiment-1
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0 20 40 60 80 100 120 140 160 180 200
290
300
310
320
330
340
350
Time(min)
Temperature(K)
Experimental curve
Adiabatic curve
Fig(13): Experimental and Adiabatic curves of experiment-2
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0 50 100 150 200 250 300
290
300
310
320
330
340
350
Time(min)
Temperature(K)
Experimental curve
Adiabatic curve
Fig(14): Experimental and Adiabatic curves of experiment-3
Table (3) : Summary of the characteristics of the above temperature-time plot
Experiment T(0)(K) Tmax(adiabatic)(K) ∆Texp(adiabatic)(K)
1 290.01 345.80 55.69
2 294.00 345.60 51.9
3 299.20 345.30 46.13
From eq(9) the variation of acetic anhydride concentration with temperature/time was deduces as:
The constant (β) in eq(23) was calculated using the initial concentration of the acetic anhydride 4.364 mol/L and
the adiabatic theoretical temperature change (∆T)adiabatic. The figures (15),(16) and (17) show how acetic
anhydride concentration varies with time for the three experiments.
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0 50 100 150 200 250
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
Time(min)
Concentration(mol/L)
Fig (15): Concentration-time plot of acetic anhydride-Exp(1)
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0 20 40 60 80 100 120 140 160 180 200
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
Time (min)
Concentration(mol/L)
Fig (16): Concentration-time plot of acetic anhydride-Exp(2)
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0 50 100 150 200 250
3
3.5
4
4.5
Time (min)
Concentration(mol/L)
Fig (17): Concentration-time plot of acetic anhydride reaction-Exp(3)
VARIATION OF RATE VERSUS CONCENTRATION
Table (4) : Variations of temperature, rate and concentration at T =320K
T=320K
Experiment Concentration Rate Rate constant (k)
1 3.507025023 0.03238313 0.00936158
2 3.620338071 0.033438511 0.00923629
3 3.765872632 0.03500009 0.00929425
Average (k) 0.00936158
Standard deviation (k) 6.27008E-05
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Figure(18): Concentration-rate plot @ T=320K
Table (5) : Variations of temperature, rate and concentration at T =325K
T=325K
Experiment Concentration Rate Rate constant (k)
1 3.363932095 0.025762791 0.007658535
2 3.476755343 0.027443908 0.00789354
3 3.625365284 0.030256856 0.008345878
Average (k) 0.007965984
Standard deviation (k) 0.000349351
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Figure(19): Concentration-rate plot @ 325K
Table (6) : Variations of temperature, rate and concentration at T =335K
T=335K
Experiment Concentration Rate Rate constant (k)
1 3.077605537 0.041685326 0.013544727
2 3.186062023 0.04299617 0.013495082
3 3.339671258 0.045253824 0.013550382
Average (k) 0.013530064
Standard deviation (k) 3.04267E-05
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Figure(20): Concentration-rate plot @ 335K
KINETICS AND THERMODYNAMIC ANALYSIS OF THE
EXPERIMENTS
The rate information obtained from the concentration-time plot enabled one to calculated specific rate constant
k(T) of the processes at any time (t) and temperature (T).
Arrhenius plots was thus generated from which kinetic parameters of the runs was extracted. The figures (21),
(22) and (23) below show the Arrhenius plots for all the three experiments.
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Figure (21): Arrhenius plot of experiment-1
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Figure (22): Arrhenius plot of experiment-2
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Figure (23): Arrhenius plot of experiment-3
The values obtained for the specific rate constants as a function of temperature are given in equations (24),(25)
and (26) below:
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The thermodynamic information extracted from the experiments was the heat of the reaction (∆Hrxn). This was
assumed to be independent of temperature and was determined by using eq(10). Table(7) below shows ∆Hr
values of the various experiments.
Table (7): Thermodynamic information of the experiments
Experiment 1 2 3
∆Hrxn(kJ/mol) 61.59 61.58 61.58
MODELING APPROACH
The experimental work discussed has shown that the reactions between the acetic anhydride and methanol
occurring in adiabatic batch reactor (thermos-flask) exhibit a first order reaction kinetics with respect to the
acetic anhydride. This is discussed in the section 6.8 above. The kinetic parameters of the reactions are discussed
in section 6.9 above. Thus for a first order adiabatic batch process, one can write design equation, rate law
expression and stiochiometry equations describing the process are as follow:
a) Design Equation:
b) Rate law:
c) Stiochiometry:
It assumed that since there is negligible or no change in density during the course of the reaction, the total
volume (V) is considered to be constant. Combining equations (27) –(29), a differential equation describing the
rate of change of conversion (X) with respect to time can be written as:
The kinetic parameters, pre-exponential constant (A) and the activation energy (EA) has been determined
experimentally in all the three reactions as discussed in section 6.9 above. The adiabat of the processes can be
written as:
Differentiating equation (32) with respect to time and plugging in equation (30) gives equation (33):
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For a given process, given To, ∆Ta, A and Ea as initial starting points, simultaneous solution of equations (33)
and (34) with the help of Matlab (R2010a) program was used in the simulations process.
MODEL VALIDATION
The formulated models were validated by direct analysis and comparison of the model –predicted temperature
(T) and the values obtained from experimental measurements for equality. Analysis and the comparison between
the model predicted temperature values and the experimentally measured temperature values show some amount
of deviation of the model-predicted temperature values from the experimentally measured values. The deviation
in model equations results may be due to non-incorporation of some practical conditions in the model equation
and solution strategy. Also assumptions made in the model equation’s development may be responsible in the
deviation of the model results. This can be improved by refining the model equation, and introduction of
correction factor to the bring model- predicted temperature values to those of the experimental values.Percentage
deviation (% Dmodel) of model-predicted temperature from experimentally measured values is given by equation
(35) below:
where the correction factor (β) = -(Dmodel) (36)
and (M)-model-predicted temperature, and (E)-experimentally measured temperature.
The model is also validated by considering the correlation coefficients (R2
) of the model-predicted temperature
and the experimentally measured temperature.
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RESULTS
Figure (24a): Comparison of the model- predicted and experimentally measured temperature for experiment (1)
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Figure (24b): Methya acetate parity plot of experiment (1):
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Figure (24c): Variation of model-predicted temperature with its associated deviation from experimental results-
Experiment (1)
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Figure (24d): Variation of model-predicted temperature with its associated correction factor-Experiment (1)
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Figure (25a): Comparison of the model- predicted and experimentally measured temperature against time for
experiment (2)
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Figure (25b) show the parity plot of model-predicted and experimentally measured temperature of experiment
(2):
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Figure (25c): Variation of model-predicted temperature with its associated deviation from experimental results-
Experiment (2)
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Figure (25d): Variation of model-predicted temperature with its associated correction factor-Experiment (2)
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Figure (26a): Comparison of the model- predicted and experimentally measured temperature against time for
experiment (3)
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Figure (26b) show the parity plot of model-predicted and experimentally measured temperature of experiment
(3)
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Figure (26c): Variation of model-predicted temperature with its associated deviation from experimental results-
Experiment (3)
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Figure (26d): Variation of model-predicted temperature with its associated correction factor-Experiment (3)
DISCUSSIONS
By direct comparison of model-predicted temperature profiles and experimentally measure temperature profiles
it is seen if figures 24a, 25a and 26a the model proposed agree quite well in predicting the experimentally
measure temperatures. The parity plots shown in figures 24b, 25b and 26c are also used as a means of validation
of the proposed model. It is seen from the plots that there is good agreement between model-predicted
temperatures and experimentally measured temperatures. An ideal comparison testing validity of the model is
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achieved by considering the r-squared values (coefficient of determination). Comparing the data from both the
model and the experiment it was noticed that the r-squared values were 0.980,0.991 and 0.994 respectively for
experiments 1, 2 and 3. This suggest proximate agreement between model-predicted temperatures and that of the
experimentally measure temperatures. The maximum percentage deviations of the model-predicted temperatures,
from the corresponding experimental values are 3.18%, 1.83% and 3.86% for experiments 1, 2 and 3. The
deviations are depicted graphically in figures 24c, 25c and 26c. The deviation values are quite within the
acceptable deviation range of experimental results and give an indication of the reliability the usefulness of the
proposed model. The correction factors which were the negative form of the deviations are shown in figures 24d,
25d and 26d. The correction factors take care of the effects of all the issues that were not considered during the
experiments and the assumptions which were not catered for during the model formulation. The model as it
stands can be used to predict liquid- phase temperature of the esterification process of acetic anhydride and
methanol. The predicted temperatures can then be used to predict the liquid phase composition with the help of
equation (9) above during reactive distillation process until the reaction reaches the maximum steady boiling
temperature of 335K. At this near boiling temperature one expects the vapor-phase of the system to consist of
some reactants and products species and by thermodynamic considerations the vapor-phase compositions can be
predicted. This then constitute a step toward the preliminary design of reactive distillation system of the
esterification process of acetic anhydride with methanol.
CONCLUSIONS
The mathematical models developed have shown satisfactory results in simulating the liquid-phase temperatures
of the esterification of acetic anhydride with methanol. The results were found in good agreement with
experimental results. The maximum deviation of the model-predicted temperatures was found to be not more
than 4% in all cases which is quiet within acceptable range of experimental results. Nonetheless, further work
should incorporate more process parameters into the model with the aim of reducing the deviations of the model-
predicted temperature values from those of the experimentally measured observed values. The findings from the
simulation results can be used to develop the technology (reactive distillation) to convert acetic anhydride-
methanol system to methyl acetate and acetic acid.
LIST OF SYMBOLS
∆Hrxn-heat of reaction (KJ/mol)
H-Enthalpy
Ho- Initial Enthalpy
∆T (ad) –adiabatic temperature change (K)
∆ε –extent of reaction
A –preexponential factor
B,C – thermistor constants
CA-concentration of A (mol/L)
CP –specific heat capacity
CP,AA –specific heat capacity of acetic anhydride
CP,m –specific heat capacity of methanol
CP,mix-constant heat capacity of reaction mixture (kJ/mol.K)
CP,W –specific heat capacity of water
Ea – activation energy
Itotal – total current of the circuit
Ko
eqm –Equilibrium constant
m –mass
MAA –Mass of acetic anhydride
Mm –Mass of methanol
Meqv –Equivalent amount of water
MT-mass of reaction mixture(Kg)
NA –mole of A (mol)
Q-heat produced by stirrer
R – molar gas constant
R2 – known resistance in the circuit
-rA –rate of reaction of (A)
RTH – Thermistor resistance
t – time
Tamb –ambient temperature
44. Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.10, 2013
94
Tmax –maximum temperature (K)
To –initial temperature
T-reactor temperature (K)
TS – steady state temperature (K)
U –heat transfer coefficient (J/m2
s.K)
v – total voltage of the circuit
V-Volume of vessel
Vout – voltage measured by thermistor
VTH – voltage across thermistor resistance
X- conversion
β- constant
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