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Modeling of Multiple Reversible Reaction System
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 148 (2016) 970 – 977
4th International Conference on Process Engineering and Advanced Materials
Modeling of Multiple Reversible Reaction System Chiah Yoke Yi, Shuhaimi B Mahadzir* Universiti Teknologi PETRONAS,32610 Seri Iskandar, Perak Darul Ridzuan,Malaysia
Abstract
Growing world population increases food demand. Reaction coupling between ammonia and urea synthesis provides insight in developing fertilizer production plant which is more energy efficient and which in turn enables abundant and cheap food production. The ammonia-urea reaction coupling is still a new field and requires simple and sufficient models to describe the system. Mathematical models derivation, simulation, constants tuning and validations were done using commercial software. Sufficient models were obtained for the future development of reaction coupling conceptual reactor. For urea synthesis reaction, the equilibrium carbon dioxide conversion is close to 80% and the equilibrium urea concentration is around 750mol/m3 at the optimum operating conditions of around 450K and 12MPa. The optimum range of NH3:CO2 feed ratio is 2-3.5. The equilibrium nitrogen conversion of circa 27% and the equilibrium ammonia concentration of 300mol/m3 are obtained for ammonia synthesis at the optimum operating conditions of around 660K and 23MPa. The average percent error for nitrogen equilibrium conversion and ammonia equilibrium molar flow is only 6.154% and 5.932% respectively compared to published data [22]. © by Elsevier Ltd. by ThisElsevier is an open access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPEAM 2016. Peer-review under responsibility of the organizing committee of ICPEAM 2016 Keywords: ammonia; urea; mathematical models; reversible; kinetics; equilibrium;conceptual design.
1. Introduction The growing of global population triggers the rising demand on food. According to the statistics available in Worldometers, the global populations will continue to grow for 0.7 billion people from 7 billion in the year 2011 to 7.7 billion in 2020 [1]. This situation urges for the production of cheaper and abundant food. Many agricultural industries strive for new technology to reduce production cost and achieve mass production. Thus there are many
* Corresponding author. Tel.: +605 - 368 7622 E-mail address: [email protected]
1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPEAM 2016
doi:10.1016/j.proeng.2016.06.482
Chiah Yoke Yi and Shuhaimi B. Mahadzir / Procedia Engineering 148 (2016) 970 – 977
971
research which focus on ammonia and urea production. Ammonia production process consumes huge amount of energy which imposes negative impacts towards the environment, climate and human health [2]. The steam reforming process to produce hydrogen feedstock for the Haber-Bosch ammonia synthesis process consumes more than 1% of the world’s power generation [3]. High energy requirement signifies high fossil fuels consumption and carbon dioxide emission. On the other hand, the challenges in urea production plant include the conversion limit per pass through the reactor, competing side reactions (urea hydrolysis and biuret formation) and the extreme corrosiveness of ammonium carbamate [4]. Thus, a more environmental friendly and energy efficient urea production system is required. Coupling ammonia synthesis with urea synthesis is a potential alternative. Reaction coupling allows cost and energy savings through the consumption of by-products and heat transfer among the coupled reactions. Some examples of reaction coupling includes ethylbenzene dehydrogenation coupled with nitrobenzene hydrogenation, water gas shift and benzene hydrogenation [6, 8, 18]. Ammonia-urea reaction is a new field and a conceptual design of the coupling reactor is required. However, before a conceptual design can be produced, sufficient models for individual ammonia and urea synthesis reaction are required. Kinetic and equilibrium models for individual urea and ammonia synthesis were obtained and simulated using commercial programming software for optimum operating conditions. The simulations verified the models and can be applied in the simulations of the upcoming conceptual design of the coupled reactor. It was hoped that a real integrated-ammonia-urea production system can be realized in the future. The technology of process integration has been introduced since the late 1970s and early of 1980s [15]. Process integration is a technology approach that interconnects the individual steps of a chemical plant. These steps include reaction, separation, heat exchange, pressurization-depressurization and mixing [16]. The aim of process integration is to achieve higher energy and material consumption efficiency, lower environmental emissions, smaller equipment size to save capital cost and inherently safer process. Process integration includes heat integration, power integration, chemical integration and equipment integration [17]. Reaction coupling is a type of process integration where two reaction systems combine into a single system. Mass coupling involves the elimination of by-products from one reaction through the consumption in another reaction. Thermal coupling involves the heat transfer among the coupled reactions. The research gap of reaction coupling includes limitation of performance analysis on wide range of reaction coupling, the complex mathematical models and the lack of conceptual design on coupled reactors. Since 1994, the concept of reaction coupling has been studied for cost and energy savings as well as environmentally friendly process for the of zero by-product generation [18]. Increment of equilibrium conversion of ethylbenzene from around 33% to almost 100% was obtained through the coupling reaction between ethylbenzene dehydrogenation and benzene hydrogenation [18]. Besides, reaction coupling helps to avoid catalyst deactivation through the 1, 4-butanediol dehydrogenation and nitrobenzene hydrogenation coupling [19]. Another study found that ethylbenzene dehydrogenation and catalytic hydrogen combustion found that the reaction coupling contributes to high ethylbenzene conversion of 85% [20]. Ramaswamy and co-workers studied the effect of reaction coupling on reactor conversion and heat transfer. They found that reaction coupling in a co-current reactor better improved the conversion and heat exchange than the counter-current flow reactor [11]. Besides, the recuperative coupled reactor provides operational flexibility compared to the direct coupled reactor whereby the individual stream flow rates can be adjusted independently to achieve the required conversion. The conversion of methane combustion and reforming increases with temperature with the optimum value of 93.6% and 91.7% respectively (at 1088K) when the exothermic methane combustion coupled with the endothermic methane reforming [10]. Next, coupling methanol synthesis with cyclohexane dehydrogenation enhances equilibrium conversion, reduces reactor size and decreases product stream outlet temperature [21]. Later, the coupling reaction between ethylbenzene dehydrogenation and nitrobenzene hydrogenation was optimized using normalized normal constraint (NNC) and normal boundary intersection (NBI) method and there is a trade-off to simultaneously maximize styrene yield and nitrobenzene conversion at 56% and 55% respectively [5]. Apart from that, ethylbenzene dehydrogenation achieved complete conversion even at lower temperature (400oC) after coupled with nitrobenzene hydrogenation reaction [6]. Furthermore, the reaction coupling of ethylbenzene dehydrogenation and reverse water-gas shift reaction was reported with higher styrene yield of 46% and selectivity 98% compared to the styrene yield of 28% and selectivity 96% when reaction coupling is substituted with nitrogen dilution [8]. Modeling of urea synthesis reaction began around 1950s. Singh and Saraf developed suitable pseudo-homogeneous rate expression and effectiveness factor calculation method for ammonia synthesis [22]. Heterogeneous reaction model was used by another group of researchers to simulate and optimize ammonia
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production [23]. At 185oC, highest equilibrium conversion of 84% was obtained at NH 3/CO2 of 5 and H2O/CO2 of 0.12. Besides, the formation of by-products does not affect the equilibrium conversion [24]. The same authors also reported that ratio of H2O/CO2 has direct effect to the equilibrium pressure at temperature above 200 oC [25]. Simulation of liquid phase urea synthesis were done [26, 27] and the result agreed with the result from Inoue and colleagues [24, 25]. The different reactor configurations of two parallel series of CSTR and degrees of concentration back-mixing were compared [27]. Results showed that the carbon dioxide conversion increases with the number of stages of the reactor until a maximum conversion of 67% is achieved at 10 stages with the optimum temperature of 200oC. Later, heterogeneous reaction model which describe the urea synthesis in a series of CSTR was developed [18]. The optimum temperature and number of stages of CSTR is 190oC and 10 stages respectively with carbon dioxide equilibrium conversion of about 64%. Another group of researchers found the optimum temperature and the NH3/CO2 ratio for urea production to be 215oC and 2 respectively [28]. 2. Problem Statements And Objectives Ammonia-urea reaction coupling provides insights for lower cost fertilizer production and it is still a new field which is yet to be explored. Information on ammonia-urea coupling reaction is still lacking. Hence, simple and sufficient models are required to describe the individual ammonia and urea reaction in order to provide information (operating conditions) and simulate the ammonia-urea coupling reactor in the future conceptual design stage. Thus, this research project aims to: x Obtain and verify kinetic and equilibrium models to simulate the temperature and pressure dependence of equilibrium conversion of reactants and the concentration profile of the reactants and products along the reactor for urea synthesis reaction. x Obtain and verify kinetic and equilibrium models to simulate the temperature and pressure dependence of equilibrium conversion of reactants and the concentration profile of the reactants and products along the reactor for ammonia synthesis reaction. 3. Models Development This work provides simple yet sufficient mathematical models for urea and ammonia reaction system for the conceptual design of the coupled ammonia-urea production system. This work will investigate generalized reaction coupling system of reversible multiple reactions. Reversible reactions have equilibrium conversion where the forward reaction rate equals to the backward reaction rate. Consider the reversible reaction as below: Reversible reaction: A+B↔C+D
Fig. 1: Mole species of A in ΔV [13].
Taking A as the basis, based on the law of conservation, the mole balance equation is expressed as follows: (1) General assumptions about the reaction include only axial concentration change is affected by temperature and pressure and the whole reaction is a steady-state vapor reaction. Consequently, along the reactor length, z (m) with constant cross-sectional area, A (m2), (2) FA,Z – FA,Z+∆Z + A.rA∆Z = 0 where rA is the rate of consumption of reactant A which is constant throughout ΔZ, mol/m3.s The flow rate FA can be expressed in terms of concentration CA. Dividing the equation by ΔZ and taking the limit of ∆Z→0, yields
Chiah Yoke Yi and Shuhaimi B. Mahadzir / Procedia Engineering 148 (2016) 970 – 977
where v = volumetric flow rate, m3/s CA= concentration of A, mol/m3 -rA=k1(CACB-CCCD/Keq) (4) with k1=forward reaction rate constant. Equilibrium model is used to determine the behavior of equilibrium conversion of the limiting species at different temperature and pressure. The equilibrium constant at standard condition (298K, 1atm), KPo ln KPo=∆Gfo/RT (5) Equilibrium constant Kp at temperature T: ln KP=ln KPo + ∫(∆HR/RT2) dT (6) (7) ∆HR=∆HRo + ∫∆CP dT with ∆HRo= standard heat of reaction at 298K. The equilibrium constant Keqq in the kinetic model (4) is expressed in term of Kp as shown below. with a,b,c and d are reaction stoichiometric coefficient of A,B, C and D respectively. The temperature profiles can be obtained using the following equation:
The individual reactions together with the overall reaction of urea synthesis are as shown below:
2NH3 + CO2 ↔ NH2CONH2 + H2O (12) The first reaction is very fast and highly exothermic which proceed to almost completion whereas the second reaction is slow and endothermic. The equilibrium constant Kp is expressed as:
Next, consider ammonia synthesis reaction:
The mathematical models were revised until the profiles agree with the published data. Next, the models were tuned in order to minimize the deviation of calculated values from the published data.
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4. Results And Discussion 4.1. Urea Synthesis Reaction Figure 2 below shows the parity plot of equilibrium carbon dioxide and urea concentration. It can be seen that the simulated data are very close to the published data. This means that the mathematical models used are valid at the operating conditions as published data [2].
Fig. 2: Parity plot for equilibrium carbon dioxide conversion and urea concentration.
Figure 3: Conversion profiles of carbon dioxide.
Figure 4: Urea molar flow rate profile.
Figure 3 and 4 show the carbon dioxide conversion and urea molar flow (mol/s) along the reactor length respectively. Since the exact value of rate constants are not available, the values were obtained by solving equation (14) at assumed reactor length of 20m and the respective published equilibrium conversion. Thus, the profiles above show that the carbon dioxide equilibrium conversion and equilibrium urea molar flow achieve at 20m reactor length. Maximum conversion achieved is approximately 79% and maximum urea molar flow is circa 410mol/s. Figure 5 shows that the exothermic urea reaction system temperature increases across the reactor. The temperature increment is larger when the feed water content is smaller. This behavior matches the nature of high heat capacity of water which absorbs large amount of heat before allowing system temperature to increase [29].
Figure 5: Urea synthesis temperature profile.
Figure 6: Equilibrium carbon dioxide conversion at different conditions.
Figure 6 and 7 illustrate the effect of temperature and pressure on equilibrium carbon dioxide conversion and equilibrium urea molar flow respectively. Both of them increase with temperature until an optimum value before undergo downward trend. This trend can be explained by the fact that urea synthesis is an exothermic reversible reaction. Thus, increasing the temperature initially increases molecular collision among the reactants and thus the reactant conversion. However, the negative effect of further temperature increment on the system equilibrium becomes more dominant until the equilibrium CO2 conversion and equilibrium urea molar flow decrease with the rise of temperature.
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Figure 7: Equilibrium urea flow rate at different conditions.
Figure 8: Effect of feed composition on CO2 conversion.
Figure 9: Effect of feed composition on equilibrium urea concentration. Figure 10: Temperature profile of ammonia synthesis reactor.
Figure 8 reveals that equilibrium CO2 conversion increases with higher NH3:CO2 ratio but decreases with higher H2O:CO2 ratio. As water content increases, the system equilibrium shifts backward towards formation of less product since water is one of the product of the urea synthesis. There is an optimum value of NH3:CO2 ratio on equilibrium urea concentration which increases until a maximum value before declining again which ranges from 2 to 3.5. The initial increasing trend is due to the increase of carbon dioxide equilibrium conversion upon high reactant concentration. The possible reason for the decreasing trend is that too high NH 3 concentration dilute the intermediate product concentration and thus less equilibrium urea product. To conclude, the optimum operating temperature and pressure is approximately 449.5K and 11.868MPa respectively with equilibrium carbon dioxide conversion of circa 79% based on the suggested mathematical models in this work. 4.2. Ammonia Synthesis Reaction For the case of ammonia synthesis reaction, the mathematical models were also validated with the literature [22]. In the comparison between the calculated result and the literature data, the average percent error for nitrogen equilibrium conversion and ammonia equilibrium molar flow are 6.154% and 5.932% respectively. Thus, the models are valid at the operating conditions as in the published data [22]. Similar to urea synthesis reactor, the reactor temperature increases until a maximum equilibrium temperature is achieved as shown in Figure 10. Figure 11 and 12 show the nitrogen conversion and ammonia flow rate (mol/s) along the reactor length. The profiles revealed that both of the nitrogen conversion and ammonia molar flow increase until a maximum equilibrium value is achieved. The maximum value for nitrogen conversion and ammonia molar flow are approximately 27.5% and 420mol/s respectively.
Figure 11: Conversion profiles of nitrogen.
Figure 12: Ammonia molar flow profile.
Both of the equilibrium nitrogen conversion and ammonia concentration increase with increasing pressure. From Figure 13 and 14, it can be seen that both of them increase with temperature until a maximum value is achieved and then further increment of temperature will lead to the reduction of both dependent variables. This trend can be explained by the fact that ammonia synthesis is an exothermic reversible reaction. Thus, increases the temperature will initially increase molecular collision among the reactants. However, the negative effect of the further increase in
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temperature on the system equilibrium becomes more apparent until the equilibrium N2 conversion and ammonia concentration decreases with increment of temperature.
Figure 13: Equilibrium nitrogen conversion at different conditions.
Figure 14: Equilibrium ammonia concentration at different conditions.
Figure 15: Effect of catalyst particle size on system pressure drop.
Figure 16: Effect of bed porosity on system pressure drop.
Figure 15 shows that pressure drop across the reactor decreases when the catalyst particle size increases. This can be explained by the fact of easier fluid flow across the bed due to the larger bed void volume when larger catalyst particle is used. Next, Figure 16 shows that the pressure drop increases with decreasing bed porosity. Bed porosity is also known as void fraction, void volume, fractional voidage, voidage or porosity. The increment of pressure drop starts to become more obvious when the bed porosity reduced to around 0.3. The trend correspond to the easier fluid flow across the reactor at larger bed porosity. Bed porosity depends on the particle size, shape [30] and particle arrangement in the packed bed. Optimum bed porosity is required so that the pressure drop is not too low that the reactant conversion is affected and at the same time the pressure drop is not too high that demand high compression energy. The fractional voidage for spherical catalyst with 6.35mm diameter is 0.405 [31]. To conclude, the optimum operating temperature and pressure is 658.15K and 22.899 MPa respectively with the equilibrium nitrogen conversion of circa 27% based on the suggested models. This suggested value was selected based on the validated region in the profiles. 5. Conclusion The mathematical models for urea and ammonia synthesis are derived, simulated and tuned. The models are validate at least at the operating conditions of the published data used for comparison. Based on the suggested mathematical models in this work, the optimum operating temperature and pressure is around 450K and 12MPa with equilibrium carbon dioxide conversion of circa 80% for urea synthesis and 660K and 23MPa with equilibrium nitrogen conversion of circa 27% for ammonia synthesis. This work will be continued with the conceptual design of the coupling reactor. Acknowledgements The patience and support from AP. Dr. Shuhaimi B Mahadzir, Dr. Timothy Ganesan A/L Andrew and Professor Dr. Duvvuri Subarao are gratefully acknowledged for guiding the research progress. References [1] Worldometers-Current World Populations (n.d.) [Online]. Available: http://www.worldometers.info/world-population/
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[2] X. Zhang, S. Zhang, P. Yao and Y. Yuan, Modeling and simulation of high–pressure urea synthesis loop, Computers And Chemical Engineering.. 29 (2005) 983-992. [3] R. Lan, J. T. S. Irvine and S. Tao, Synthesis of ammonia directly from air and water at ambient temperature and pressure, Scientific Reports3, 2013. [4] J J. H. Meesen, ‘’Urea,’’ in Ullmann’s Encyclopedia Of Industrial Chemistry, Weinheim, Germany: Wiley-VCH Verlag GmbH and Co. KGaA, 2012. [5] N. S. Abo-Ghander, F. Logist, J. R. Grace, J. F. M. Van Impe, S. S. E. H. Elnashaie and C. J. Lim, Optimal design of an autothermal membrane reactor coupling the dehydrogenation of ethylbenzene to styrene with the hydrogenation of nitrobenzene to aniline, Chemical Engineering Science.. 65 (2010) 3113-3127. [6] A. Sun, Z. Qin and J. Wang, Reaction coupling of ethylbenzene dehydrogenation with nitrobenzene hydrogenation, Catalysis Letters.. 79 (2001) 33-37. [7] D. Gao, Y. Feng, H. Yin, A. Wang and T. Jiang, Coupling reaction between ethanol dehydrogenation and maleic anhydride hydrogenation catalyzed by Cu/Al2O3, Cu/ZrO2, And Cu/ZnO Catalysts, Chemical Engineering Journal.. 233 (2013) 349-359. [8] A. Sun, Z. Qin and J. Wang, Reaction coupling of ethylbenzene dehydrogenation with water-gas shift, Applied Catalyst A: General.. 234 (2002) 179-189. [9] D. K. Lee, I. H. Baek and W. L. Yoon, A simulation study for the hybrid reaction of methane steam reforming and in situ CO2 removal in a moving bed reactor of a catalyst admixed with a Cao-based CO2 acceptor for H2 production, International Journal of Hydrogen Energy.. 31 (2005) 649-657. [10] F. Yin, S. Ji, H. Mei, Z. Zhou and C. Li, Coupling of highly exothermic and endothermic reactions in a metallic monolith catalyst reactor: a preliminary experimental study, Chemical Engineering Journal.. 155 (2009) 285-291. [11] R. C. Ramaswamy, P. A. Ramachandran and M. P. Dudukovic, Recuperative coupling of exothermic and endothermic reactions, Chemical Engineering Science.. 61 (2005) 459-472. [12] R. C. Ramaswamy, P. A. Ramachandran and M. P. Dudukovic, Coupling exothermic and endothermic reactions in adiabatic reactors, Chemical Engineering Science.. 63 (2007) 1654-1667. [13] H. S. Fogler, Elements Of Chemical Reaction Engineering. Pearson Education, Inc. United States, 2006. [14] Knovel Critical Tables (2nd Edition). Internet: http://app.knovel.com/web/toc.v/cid:kpKCTE000X/viewerType:toc/root_slug:knovel-criticaltables/url_slug:knovel-critical-tables/?, Feb. 1, 2002, [Apr. 7, 2015]. [15] R.H. Perry and D.W. Green, Perry’s Chemical Engineers’ Handbook, 8th ed., McGraw-Hill, New York, 2007. [16] J. A. Dean. Lange’s Handbook of Chemistry, 15th ed., McGraw-Hill, Inc., Knoxville, Tennessee, 1972. [17] M. Hamidipour, N. Mostoufi and R. Sotudeh-Gharebagh, Modeling the synthesis section of an industrial urea plant, Chemical Engineering Journal.. 106 (2004) 249-260. [18] M. E. E. Abashar, Coupling of ethylbenzene dehydrogenation and benzene hydrogenation reactions in fixed bed catalytic reactors, Chemical Engineering And Processing.. 43 (2003) 1195-1202. [19] K. H. P. Reddy, R. Rahul, S. S. V. Reddy, B. D. Raju and K. S. R. Rao, Coupling of 1' 4-butanediol dehydrogenation reaction with the hydrogenation of nitrobenzene over Cu/MgO catalysts, Catalysis Communications.. 10 (2008) 879-883. [20] G. Kolios and G. Eigenberger, Styrene synthesis in a reverse-flow reactor, Chemical Engineering Science.. 54 (1999) 2637-2646. [21] M. H. Khademi, P. Setoodeh, M. R. Rahimpour and A. Jahanmiri, Optimization of methanol synthesis and cyclohexane dehydrogenation in a thermally coupled reactor using differential evolution (DE) method, International Journal Of Hydrogen Energy.. 34 (2009) 6930-6944. [22] C. P. P. Singh and D. N. Saraf, Simulation of ammonia synthesis reactors, Ind. Eng. Chem. Process Des.. 18 (1979) 364-370. [23] S. S. Elnashaie, M. E. Abashar and A. S. Al-Ubaid, simulation and optimization of an industrial ammonia reactor, Ind. Eng. Chem. Res.. 27 (1988) 2015-2022. [24] S. Inoue, K. Kanai and E. Otsuka, Equilibrium of urea synthesis. I, Bulletin Of The Chemical Society Of Japan. 45 (1971) 1339-1345. [25] S. Inoue, K. Kanai and E. Otsuka, Equilibrium of urea synthesis. II, Bulletin Of The Chemical Society Of Japan. 45 (1971) 1617-1619. [26] M. A. Isla and H. A. Irazoqui, Simulation of a urea synthesis reactor. 1. Thermodynamic framework, Ind. Eng. Chem. Res.. 32 (1993) 26622670. [27] M. A. Isla and H. A. Irazoqui, Simulation of a urea synthesis reactor. 2. Reactor model, Ind. Eng. Chem. Res.. 32 (1993) 2671-2680. [28] M. Goharrokhi and M. Otadi, Urea synthesis reactor modeling, in IPCBEE.201186-90. [29] B. Z. Shakhashiri. (2011, Jan.) Chemical of The Week-Water. [Online]. Available: http://scifun.chem.wisc.edu/chemweek/PDF/COWWater-Jan2011.pdf [30] R. Smith, Chemical Process Design And Integration, West Sussex, England: John Wiley and Sons Ltd, 2005. [31] J. F. Richardson and J. H. Harker. Coulson & Richardson’s Chemical Engineering Volume 2: Particle Technology & Separation Processes. India: Elsevier, 2002.
ScienceDirect Procedia Engineering 148 (2016) 970 – 977
4th International Conference on Process Engineering and Advanced Materials
Modeling of Multiple Reversible Reaction System Chiah Yoke Yi, Shuhaimi B Mahadzir* Universiti Teknologi PETRONAS,32610 Seri Iskandar, Perak Darul Ridzuan,Malaysia
Abstract
Growing world population increases food demand. Reaction coupling between ammonia and urea synthesis provides insight in developing fertilizer production plant which is more energy efficient and which in turn enables abundant and cheap food production. The ammonia-urea reaction coupling is still a new field and requires simple and sufficient models to describe the system. Mathematical models derivation, simulation, constants tuning and validations were done using commercial software. Sufficient models were obtained for the future development of reaction coupling conceptual reactor. For urea synthesis reaction, the equilibrium carbon dioxide conversion is close to 80% and the equilibrium urea concentration is around 750mol/m3 at the optimum operating conditions of around 450K and 12MPa. The optimum range of NH3:CO2 feed ratio is 2-3.5. The equilibrium nitrogen conversion of circa 27% and the equilibrium ammonia concentration of 300mol/m3 are obtained for ammonia synthesis at the optimum operating conditions of around 660K and 23MPa. The average percent error for nitrogen equilibrium conversion and ammonia equilibrium molar flow is only 6.154% and 5.932% respectively compared to published data [22]. © by Elsevier Ltd. by ThisElsevier is an open access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPEAM 2016. Peer-review under responsibility of the organizing committee of ICPEAM 2016 Keywords: ammonia; urea; mathematical models; reversible; kinetics; equilibrium;conceptual design.
1. Introduction The growing of global population triggers the rising demand on food. According to the statistics available in Worldometers, the global populations will continue to grow for 0.7 billion people from 7 billion in the year 2011 to 7.7 billion in 2020 [1]. This situation urges for the production of cheaper and abundant food. Many agricultural industries strive for new technology to reduce production cost and achieve mass production. Thus there are many
* Corresponding author. Tel.: +605 - 368 7622 E-mail address: [email protected]
1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICPEAM 2016
doi:10.1016/j.proeng.2016.06.482
Chiah Yoke Yi and Shuhaimi B. Mahadzir / Procedia Engineering 148 (2016) 970 – 977
971
research which focus on ammonia and urea production. Ammonia production process consumes huge amount of energy which imposes negative impacts towards the environment, climate and human health [2]. The steam reforming process to produce hydrogen feedstock for the Haber-Bosch ammonia synthesis process consumes more than 1% of the world’s power generation [3]. High energy requirement signifies high fossil fuels consumption and carbon dioxide emission. On the other hand, the challenges in urea production plant include the conversion limit per pass through the reactor, competing side reactions (urea hydrolysis and biuret formation) and the extreme corrosiveness of ammonium carbamate [4]. Thus, a more environmental friendly and energy efficient urea production system is required. Coupling ammonia synthesis with urea synthesis is a potential alternative. Reaction coupling allows cost and energy savings through the consumption of by-products and heat transfer among the coupled reactions. Some examples of reaction coupling includes ethylbenzene dehydrogenation coupled with nitrobenzene hydrogenation, water gas shift and benzene hydrogenation [6, 8, 18]. Ammonia-urea reaction is a new field and a conceptual design of the coupling reactor is required. However, before a conceptual design can be produced, sufficient models for individual ammonia and urea synthesis reaction are required. Kinetic and equilibrium models for individual urea and ammonia synthesis were obtained and simulated using commercial programming software for optimum operating conditions. The simulations verified the models and can be applied in the simulations of the upcoming conceptual design of the coupled reactor. It was hoped that a real integrated-ammonia-urea production system can be realized in the future. The technology of process integration has been introduced since the late 1970s and early of 1980s [15]. Process integration is a technology approach that interconnects the individual steps of a chemical plant. These steps include reaction, separation, heat exchange, pressurization-depressurization and mixing [16]. The aim of process integration is to achieve higher energy and material consumption efficiency, lower environmental emissions, smaller equipment size to save capital cost and inherently safer process. Process integration includes heat integration, power integration, chemical integration and equipment integration [17]. Reaction coupling is a type of process integration where two reaction systems combine into a single system. Mass coupling involves the elimination of by-products from one reaction through the consumption in another reaction. Thermal coupling involves the heat transfer among the coupled reactions. The research gap of reaction coupling includes limitation of performance analysis on wide range of reaction coupling, the complex mathematical models and the lack of conceptual design on coupled reactors. Since 1994, the concept of reaction coupling has been studied for cost and energy savings as well as environmentally friendly process for the of zero by-product generation [18]. Increment of equilibrium conversion of ethylbenzene from around 33% to almost 100% was obtained through the coupling reaction between ethylbenzene dehydrogenation and benzene hydrogenation [18]. Besides, reaction coupling helps to avoid catalyst deactivation through the 1, 4-butanediol dehydrogenation and nitrobenzene hydrogenation coupling [19]. Another study found that ethylbenzene dehydrogenation and catalytic hydrogen combustion found that the reaction coupling contributes to high ethylbenzene conversion of 85% [20]. Ramaswamy and co-workers studied the effect of reaction coupling on reactor conversion and heat transfer. They found that reaction coupling in a co-current reactor better improved the conversion and heat exchange than the counter-current flow reactor [11]. Besides, the recuperative coupled reactor provides operational flexibility compared to the direct coupled reactor whereby the individual stream flow rates can be adjusted independently to achieve the required conversion. The conversion of methane combustion and reforming increases with temperature with the optimum value of 93.6% and 91.7% respectively (at 1088K) when the exothermic methane combustion coupled with the endothermic methane reforming [10]. Next, coupling methanol synthesis with cyclohexane dehydrogenation enhances equilibrium conversion, reduces reactor size and decreases product stream outlet temperature [21]. Later, the coupling reaction between ethylbenzene dehydrogenation and nitrobenzene hydrogenation was optimized using normalized normal constraint (NNC) and normal boundary intersection (NBI) method and there is a trade-off to simultaneously maximize styrene yield and nitrobenzene conversion at 56% and 55% respectively [5]. Apart from that, ethylbenzene dehydrogenation achieved complete conversion even at lower temperature (400oC) after coupled with nitrobenzene hydrogenation reaction [6]. Furthermore, the reaction coupling of ethylbenzene dehydrogenation and reverse water-gas shift reaction was reported with higher styrene yield of 46% and selectivity 98% compared to the styrene yield of 28% and selectivity 96% when reaction coupling is substituted with nitrogen dilution [8]. Modeling of urea synthesis reaction began around 1950s. Singh and Saraf developed suitable pseudo-homogeneous rate expression and effectiveness factor calculation method for ammonia synthesis [22]. Heterogeneous reaction model was used by another group of researchers to simulate and optimize ammonia
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production [23]. At 185oC, highest equilibrium conversion of 84% was obtained at NH 3/CO2 of 5 and H2O/CO2 of 0.12. Besides, the formation of by-products does not affect the equilibrium conversion [24]. The same authors also reported that ratio of H2O/CO2 has direct effect to the equilibrium pressure at temperature above 200 oC [25]. Simulation of liquid phase urea synthesis were done [26, 27] and the result agreed with the result from Inoue and colleagues [24, 25]. The different reactor configurations of two parallel series of CSTR and degrees of concentration back-mixing were compared [27]. Results showed that the carbon dioxide conversion increases with the number of stages of the reactor until a maximum conversion of 67% is achieved at 10 stages with the optimum temperature of 200oC. Later, heterogeneous reaction model which describe the urea synthesis in a series of CSTR was developed [18]. The optimum temperature and number of stages of CSTR is 190oC and 10 stages respectively with carbon dioxide equilibrium conversion of about 64%. Another group of researchers found the optimum temperature and the NH3/CO2 ratio for urea production to be 215oC and 2 respectively [28]. 2. Problem Statements And Objectives Ammonia-urea reaction coupling provides insights for lower cost fertilizer production and it is still a new field which is yet to be explored. Information on ammonia-urea coupling reaction is still lacking. Hence, simple and sufficient models are required to describe the individual ammonia and urea reaction in order to provide information (operating conditions) and simulate the ammonia-urea coupling reactor in the future conceptual design stage. Thus, this research project aims to: x Obtain and verify kinetic and equilibrium models to simulate the temperature and pressure dependence of equilibrium conversion of reactants and the concentration profile of the reactants and products along the reactor for urea synthesis reaction. x Obtain and verify kinetic and equilibrium models to simulate the temperature and pressure dependence of equilibrium conversion of reactants and the concentration profile of the reactants and products along the reactor for ammonia synthesis reaction. 3. Models Development This work provides simple yet sufficient mathematical models for urea and ammonia reaction system for the conceptual design of the coupled ammonia-urea production system. This work will investigate generalized reaction coupling system of reversible multiple reactions. Reversible reactions have equilibrium conversion where the forward reaction rate equals to the backward reaction rate. Consider the reversible reaction as below: Reversible reaction: A+B↔C+D
Fig. 1: Mole species of A in ΔV [13].
Taking A as the basis, based on the law of conservation, the mole balance equation is expressed as follows: (1) General assumptions about the reaction include only axial concentration change is affected by temperature and pressure and the whole reaction is a steady-state vapor reaction. Consequently, along the reactor length, z (m) with constant cross-sectional area, A (m2), (2) FA,Z – FA,Z+∆Z + A.rA∆Z = 0 where rA is the rate of consumption of reactant A which is constant throughout ΔZ, mol/m3.s The flow rate FA can be expressed in terms of concentration CA. Dividing the equation by ΔZ and taking the limit of ∆Z→0, yields
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where v = volumetric flow rate, m3/s CA= concentration of A, mol/m3 -rA=k1(CACB-CCCD/Keq) (4) with k1=forward reaction rate constant. Equilibrium model is used to determine the behavior of equilibrium conversion of the limiting species at different temperature and pressure. The equilibrium constant at standard condition (298K, 1atm), KPo ln KPo=∆Gfo/RT (5) Equilibrium constant Kp at temperature T: ln KP=ln KPo + ∫(∆HR/RT2) dT (6) (7) ∆HR=∆HRo + ∫∆CP dT with ∆HRo= standard heat of reaction at 298K. The equilibrium constant Keqq in the kinetic model (4) is expressed in term of Kp as shown below. with a,b,c and d are reaction stoichiometric coefficient of A,B, C and D respectively. The temperature profiles can be obtained using the following equation:
The individual reactions together with the overall reaction of urea synthesis are as shown below:
2NH3 + CO2 ↔ NH2CONH2 + H2O (12) The first reaction is very fast and highly exothermic which proceed to almost completion whereas the second reaction is slow and endothermic. The equilibrium constant Kp is expressed as:
Next, consider ammonia synthesis reaction:
The mathematical models were revised until the profiles agree with the published data. Next, the models were tuned in order to minimize the deviation of calculated values from the published data.
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4. Results And Discussion 4.1. Urea Synthesis Reaction Figure 2 below shows the parity plot of equilibrium carbon dioxide and urea concentration. It can be seen that the simulated data are very close to the published data. This means that the mathematical models used are valid at the operating conditions as published data [2].
Fig. 2: Parity plot for equilibrium carbon dioxide conversion and urea concentration.
Figure 3: Conversion profiles of carbon dioxide.
Figure 4: Urea molar flow rate profile.
Figure 3 and 4 show the carbon dioxide conversion and urea molar flow (mol/s) along the reactor length respectively. Since the exact value of rate constants are not available, the values were obtained by solving equation (14) at assumed reactor length of 20m and the respective published equilibrium conversion. Thus, the profiles above show that the carbon dioxide equilibrium conversion and equilibrium urea molar flow achieve at 20m reactor length. Maximum conversion achieved is approximately 79% and maximum urea molar flow is circa 410mol/s. Figure 5 shows that the exothermic urea reaction system temperature increases across the reactor. The temperature increment is larger when the feed water content is smaller. This behavior matches the nature of high heat capacity of water which absorbs large amount of heat before allowing system temperature to increase [29].
Figure 5: Urea synthesis temperature profile.
Figure 6: Equilibrium carbon dioxide conversion at different conditions.
Figure 6 and 7 illustrate the effect of temperature and pressure on equilibrium carbon dioxide conversion and equilibrium urea molar flow respectively. Both of them increase with temperature until an optimum value before undergo downward trend. This trend can be explained by the fact that urea synthesis is an exothermic reversible reaction. Thus, increasing the temperature initially increases molecular collision among the reactants and thus the reactant conversion. However, the negative effect of further temperature increment on the system equilibrium becomes more dominant until the equilibrium CO2 conversion and equilibrium urea molar flow decrease with the rise of temperature.
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Figure 7: Equilibrium urea flow rate at different conditions.
Figure 8: Effect of feed composition on CO2 conversion.
Figure 9: Effect of feed composition on equilibrium urea concentration. Figure 10: Temperature profile of ammonia synthesis reactor.
Figure 8 reveals that equilibrium CO2 conversion increases with higher NH3:CO2 ratio but decreases with higher H2O:CO2 ratio. As water content increases, the system equilibrium shifts backward towards formation of less product since water is one of the product of the urea synthesis. There is an optimum value of NH3:CO2 ratio on equilibrium urea concentration which increases until a maximum value before declining again which ranges from 2 to 3.5. The initial increasing trend is due to the increase of carbon dioxide equilibrium conversion upon high reactant concentration. The possible reason for the decreasing trend is that too high NH 3 concentration dilute the intermediate product concentration and thus less equilibrium urea product. To conclude, the optimum operating temperature and pressure is approximately 449.5K and 11.868MPa respectively with equilibrium carbon dioxide conversion of circa 79% based on the suggested mathematical models in this work. 4.2. Ammonia Synthesis Reaction For the case of ammonia synthesis reaction, the mathematical models were also validated with the literature [22]. In the comparison between the calculated result and the literature data, the average percent error for nitrogen equilibrium conversion and ammonia equilibrium molar flow are 6.154% and 5.932% respectively. Thus, the models are valid at the operating conditions as in the published data [22]. Similar to urea synthesis reactor, the reactor temperature increases until a maximum equilibrium temperature is achieved as shown in Figure 10. Figure 11 and 12 show the nitrogen conversion and ammonia flow rate (mol/s) along the reactor length. The profiles revealed that both of the nitrogen conversion and ammonia molar flow increase until a maximum equilibrium value is achieved. The maximum value for nitrogen conversion and ammonia molar flow are approximately 27.5% and 420mol/s respectively.
Figure 11: Conversion profiles of nitrogen.
Figure 12: Ammonia molar flow profile.
Both of the equilibrium nitrogen conversion and ammonia concentration increase with increasing pressure. From Figure 13 and 14, it can be seen that both of them increase with temperature until a maximum value is achieved and then further increment of temperature will lead to the reduction of both dependent variables. This trend can be explained by the fact that ammonia synthesis is an exothermic reversible reaction. Thus, increases the temperature will initially increase molecular collision among the reactants. However, the negative effect of the further increase in
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temperature on the system equilibrium becomes more apparent until the equilibrium N2 conversion and ammonia concentration decreases with increment of temperature.
Figure 13: Equilibrium nitrogen conversion at different conditions.
Figure 14: Equilibrium ammonia concentration at different conditions.
Figure 15: Effect of catalyst particle size on system pressure drop.
Figure 16: Effect of bed porosity on system pressure drop.
Figure 15 shows that pressure drop across the reactor decreases when the catalyst particle size increases. This can be explained by the fact of easier fluid flow across the bed due to the larger bed void volume when larger catalyst particle is used. Next, Figure 16 shows that the pressure drop increases with decreasing bed porosity. Bed porosity is also known as void fraction, void volume, fractional voidage, voidage or porosity. The increment of pressure drop starts to become more obvious when the bed porosity reduced to around 0.3. The trend correspond to the easier fluid flow across the reactor at larger bed porosity. Bed porosity depends on the particle size, shape [30] and particle arrangement in the packed bed. Optimum bed porosity is required so that the pressure drop is not too low that the reactant conversion is affected and at the same time the pressure drop is not too high that demand high compression energy. The fractional voidage for spherical catalyst with 6.35mm diameter is 0.405 [31]. To conclude, the optimum operating temperature and pressure is 658.15K and 22.899 MPa respectively with the equilibrium nitrogen conversion of circa 27% based on the suggested models. This suggested value was selected based on the validated region in the profiles. 5. Conclusion The mathematical models for urea and ammonia synthesis are derived, simulated and tuned. The models are validate at least at the operating conditions of the published data used for comparison. Based on the suggested mathematical models in this work, the optimum operating temperature and pressure is around 450K and 12MPa with equilibrium carbon dioxide conversion of circa 80% for urea synthesis and 660K and 23MPa with equilibrium nitrogen conversion of circa 27% for ammonia synthesis. This work will be continued with the conceptual design of the coupling reactor. Acknowledgements The patience and support from AP. Dr. Shuhaimi B Mahadzir, Dr. Timothy Ganesan A/L Andrew and Professor Dr. Duvvuri Subarao are gratefully acknowledged for guiding the research progress. References [1] Worldometers-Current World Populations (n.d.) [Online]. Available: http://www.worldometers.info/world-population/
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