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Revista mexicana de ingeniería química

versión impresa ISSN 1665-2738

Rev. Mex. Ing. Quím vol.14 no.3 México sep./dic. 2015

 

Catálisis, cinética y reactores

 

Dynamic stability in an endoreversible chemical reactor

 

Estabilidad dinámica de un reactor químico endoreversible

 

J.C. Chimal-Eguía*

 

* Centro de Investigación en Computación del IPN, Av. Juan de Dios Bátiz s/n esq. Miguel Othón de Mendizabal, col. San Pedro Zacatenco, C. P. 07738, México D. F., México. * Corresponding author. E-mail: jchimale@ipn.mx

 

Received January 14, 2015;
Accepted November 3, 2015.

 

Abstract

This article presents a local stability study for an endoreversible Chemical Reactor (ECR). The model consists of two particle reservoirs, one at high chemical potential μ1 and the other at low chemical potential μ2 (the terms "high" and "low" refer to the situation in which μ1 > μ2). There are two particle resistors (in this work for simplicity we take h1 = h2 = h), that restrict the particle flows N1 and N2. The net result is a particle flow drop from N1 to an intermediate particle reservoir N3 and from N4 to N2. From the local stability analysis it was concluded that the ECR is stable for every value of h, C1 and τ = nx/ny. After a small perturbation, the system declines to the steady state with two different relaxation times both being proportional to C, h and τ. Finally, when the power output in the steady state versus τ is plotted, it demonstrates how an increment of τ can improve the system stability. This suggests a compromise between the stability and the engine energetic properties driven by τ.

Keywords: endoreversible, chemical reactor, stability, steady state, power output.

 

Resumen

En este trabajo se presenta un análisis de estabilidad local de un Reactor Químico. El modelo consiste de dos almacenes de partículas uno a un potencial químico alto μ1 y el otro a un potencial químico bajo μ2 (los terminos "alto" y "bajo" se refieren a la situación en la que μ1 > μ2). Adicionalmente, existen dos resistencias (en este trabajo por simplicidad tomamos h1 = h2 = h), que restringen los flujos de las partículas N1 y N2. El resultado neto es una caida en el flujo de partículas desde N1 hacia un almacen intermedio de partículas N3 y de N4 a N2. A partir del análisis de estabilidad local, se puede concluir que el ECR es estable para cada valor de h, C1 y τ = nx/ny. Después de una pequeña perturbación, el sistema decae hacia un estado estacionario con cualquiera dos tiempos de relajación diferentes ambos proporcionales a C, h y τ. Finalmente, cuando graficamos la potencia de salida en el estado estacionario contra τ, encontramos que un incremento de τ puede mejorar la estabilidad del sistema. Esto sugiere un compromiso entre la estabilidad del sistema y las propiedades energéticas del mismo manejados por τ.

Palabras clave: endoreversibilidad, reactor químico, estabilidad, estado estacionario, potencia de Salida.

 

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Acknowledgements

The authors wish to thank "Consejo Nacional de Ciencia y Tecnología" (CONACyT), "Comisión de Operación y Fomento de Actividades Académicas del Instituto Politécnico Nacional" (COFAA-IPN, project number 20151704) and "Estímulos al Desempeño de los Investigadores del Instituto Politécnico Nacional" (EDI-IPN), for the support given for this work.

 

References

Angulo-Brown, F., Santillán, M., Calleja-Quevedo, E. (1995). Thermodynamic optimality in some Il Nuovo Cimento D 17, 87-90.         [ Links ]

Bejan, A. (1988). Advanced Engineering Thermodynamics; Wiley, New York.         [ Links ]

Chimal-Eguia, J., Barranco-Jiménez, M., Angulo-Brown, F. (2006). Stability analysis of an endoreversible heat engine with Stefan-Boltzmann heat transfer law working in maximum-power-like regime. Open Systems & Information Dynamics 13, 43-53.         [ Links ]

Chimal-Eguia, J.C., Reyes-Ramírez, I., Guzmán-Vargas, L. (2007). Local stability of an endoreversible heat engine working in an ecological regime. Open Systems & Information Dynamics 14, 411-         [ Links ]424.

Curzon, F.L. and Ahlborn, B. (1975). Efficiency of a Carnot engine at maximum power output. American Journal of Physics 43, 22-28.         [ Links ]

De Vos A., (1991). Endoreversible Thermodynamics and Chemical Reactions. Journal of Chemical Physics 95. 4534-4540.         [ Links ]

Díaz-Hernández, O., Páez-Hernández, R., Santillán, M. (2010). Thermodynamic performance vs. dynamic stability in an enzymatic model. Physica A 389, 3476-3483.         [ Links ]

Guzmán-Vargas, L., Reyes-Ramírez, I., Sánchez-Salas, N. (2005). The effect of heat transfer laws and thermal conductances on the local stability of an endoreversible heat engine. Journal of Physics D: Applied Physics 38, 1282-1291.         [ Links ]

He, J., Miao, G., Nie, W. (2010). Local stability analysis of an endoreversible Carnot refrigerator. Physica Scripta 82, 025002.         [ Links ]

Huang, Y., Sun, D., Kang, Y. (2007). Local stability analysis of a class of endoreversible heat pumps. Journal of Physics D: Applied Physics 102.         [ Links ]

Huang, Y., Sun, D. (2008). The effect of cooling load and thermal conductance on the local stability of an endoreversible refrigerator. International Journal of Refrigeration 31, 483-489.         [ Links ]

Huang, Y., Sun, D. (2008). Local stability analysis of a non-endoreversible heat pump. Journal of Non-Equilibrium Thermodynamics 33, 61-74.         [ Links ]

Huang, Y., Sun, D. (2008). Local stability analysis of a non-endoreversible refrigerator. Applied Thermal Engineering 28, 1443-1449.         [ Links ]

Huang, Y., Sun, D., Kang, Y. (2009). Local stability characteristics of a non-endoreversible heat engine working in the optimum region. Applied Thermal Engineering 29, 358-363.         [ Links ]

Huang, Y. (2009). Local asymptotic stability of an irreversible heat pump subject to total thermal conductance constraint. Energy Conversion and Management 50, 1444-1449.         [ Links ]

Kitano, H. (2004). Biological robustness. Nature Reviews Genetics 5, 826-837.         [ Links ]

Nie, W., He, J., Yang, B., Qian, X. (2008). Local stability analysis of an irreversible heat engine working in the maximum power output and the maximum efficiency. Applied Thermodynamics Engineering 28, 699-706.         [ Links ]

Nie, W., He, J., Deng, X. (2008). Local stability analysis of an irreversible Carnot heat engine. International Journal of Thermal Sciences 47, 633-640.         [ Links ]

Nie, W., He, J., Zhou, F. (2007). Local stability analysis for optimal performance of an irreversible Carnot heat engine. Journal of Applied Science 25, 418-423 (in Chinese).         [ Links ]

Ondrechen, M.J., Stephen-Berry, R., Andresen, B. (1980). Thermodynamics in finite time: A chemically driven engine. The Journal of Chemical Physics 72, 5118-5124.         [ Links ]

Ondrechen, M.J., Andresen, B., Stephen-Berry, R. (1980). Thermodynamics in finite time: Processes with temperatures-dependent chemical reactions. The Journal of Chemical Physics 73, 5338-5843.         [ Links ]

Páez-Hernández, R., Angulo-Brown, F., Santillán, M. (2006). Dynami thermodynamic optimization in a non-endoreversible Curzon-Ahlborn engine. The Journal of Chemistry Physics 31, 173-188.         [ Links ]

Páez-Hernández, R., Santillán, M. (2008). Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex. Physica A 387, 3574-3582.         [ Links ]

Páez-Hernández, R., Ladino-Luna, D. and Portillo-Díaz, P. (2011). Dynamic properties in an endoreversible Curzon-Ahlborn engine using a van der Waals gas as working substance. Physica A 390, 3275-3282.         [ Links ]

Páez-Hernández, R., Portillo-Díaz, P., Ladino-Luna, D. (2012). Local stability analysis of a Curzon-Ahlborn engine considering the Van der Waals equation state in the maximum ecological regime. 26-29, June. Perugia, Italy, ECOS2012 - the 25th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems.         [ Links ]

Rubin, H.M. (1979). Optimal configuration of a class of irreversible heat engines I. Physical Review A 19, 1272-1275.         [ Links ]

Santillán, M., Mackey, M.C. (2008). Dynamic stability versus thermodynamic performance in a simple model for a Brownian motor. Physical Review E 78(6 Pt 1), 061-122.         [ Links ]

Santillán, M., Maya, G., Angulo-Brown, Curzon-Ahlborn-Novikov engine working in a maximum-power-like regime. Journal of Physics D: Applied Physics 34, 2068-2072.         [ Links ]

Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos with applications to Physics, Biology, Chemistry and Engineering, Addison-Wesley Publishing Company.         [ Links ]

Villanueva-Marroquin, J., Barragan, D. (2009). Analysis of entropy production in a thermal engine powered by a nonlinear chemical system. Revista Mexicana de Ingeniería Química 8, 145-152.         [ Links ]

Wu, X.H., Chen, L.G. and Sun, F.R. (2011). Local stability of an endoreversible heat pump working at the maximum ecological function. Chinese Journal of Engineering Thermophysics 32, 1811-1815 (in Chinese).         [ Links ]

Wu, X.H., Chen, L., Ge Y., Sun, F. (2012). Local stability of an endoreversible heat pump with linear phenomenological heat transfer law working in an ecological regime. Scientia Iranica, Transactions B: Mechanical Engineering 19, 1519-1525.         [ Links ]

Wu, X.H., Chen, L., Ge, Y., Sun, F. (2015). Local stability of a non-endoreversible Carnot refrigerator working at the maximum ecological function. Applied Mathematical Modelling 39, 1689-170.         [ Links ]

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