Mathematical Analysis of Discontinuous Rectification Columns at Pilot Scale Based on the Continuous Stable States Concept and MESH Equations
Keywords:PSRK method, Thomas algorithm, UNIFAC model, UNIQUAC model, Wang-Henke algorithm
Mathematical analysis and simulation of a discontinuous rectification column was performed using an operational strategy during the start-up before reaching a pseudo-stable state in discontinuous operation. The mathematical model was formulated focusing on the equilibrium state (ES) and implementing MESH equations (M: Mass balance, E: Equilibrium thermodynamics, S: Stoichiometry relations, H: Enthalpy or heat balance) to provide solutions using the Thomas method and the Wang-Henke algorithms internally coupled to the Fourth Order Runge-Kutta method. The results were validated with experimental data from a distillation column at a pilot scale using an ethanol-water system with an equilibrium behavior described by the UNIQUAC Functional-group Activity Coefficients (UNIFAC) and Predictive Soave-Redlich-Kwong (PSRK) thermodynamic models with a global error of 1.84%. The molar ethanol concentrations presented deviations from the mathematical model predictions from 1.51% to 0.02%, with a global mean error of 0.48%. A mean error of 0.055% was obtained for the temperature profile of the column, thus demonstrating the effectiveness of the solution and its convergence capacity. The solution based on the Thomas method and the Wang-Henke algorithms coupled to the Runge-Kutta method made it possible to describe the behavior and variables of all stages of the distillation column. Operation at total reflux from start-up avoids wasting product and allows for the stabilization of the state variables, such as temperature and molar composition.
M. D. López-Ramírez, F. O. Barroso-Muñoz, J. Cabrera-Ruiz, J. G. Segovia-Hernández, H. Hernández-Escoto, S. Hernández, “Some insights in experimental studies on the start-up operation of a reactive dividing wall column,” Chemical Engineering and Processing-Process Intensification, vol. 159, e108211, Feb. 2021. https://doi.org/10.1016/j.cep.2020.108211
S. Elguea, L. Prata, M. Cabassuda, J. M. Le Lann, J. C´ezeracb, “Dynamic models for start-up operations of batch distillation columns with experimental validation,” Computers and Chemical Engineering, vol. 28, no. 12, pp. 2735–2747, Nov. 2004. https://doi.org/10.1016/j.compchemeng.2004.07.033
I. Thomas, B. Wunderlich, S. Grohmann, “Pressure-driven dynamic process simulation using a new generic stream object,” Chemical Engineering Science, vol. 225, e115171, Apr. 2020. https://doi.org/10.1016/j.ces.2019.115171
J. R. González-Velasco, M. A. Gutierrez-Ortíz, J. M. Castresana-Pelayo, J. A. Gonzalez-Marcos, “Improvements in batch distillation start-up,” Industrial & Engineering Chemistry Research, vol. 26, no. 4, 745–750, Apr. 1987. https://doi.org/10.1021/ie00064a020
L. Wang, P. Li, G. Wozny, S. Wang, “A start-up model for simulation of batch distillation starting from a cold state,” Computers & Chemistry Engineering, vol. 27, no. 10, pp. 1485–1497, Oct. 2003. https://doi.org/10.1016/S0098-1354(03)00094-2
E. Yamal, O. Martínez, “Simulación dinámica de una torre de destilación de platos perforados,” Revista Ingeniería UC, vol. 16, no. 1, pp. 65-70. Apr. 2009
E.J. Henley, D. J. Seader, Separation operations by Equilibrium Stages in Chemical Engineering, UItah, United State, Ed. Reverte S.A., 1997
M. Markowsky, S. Alabrudzinski, S. Storczyk, “Heat and mass exchanger model for hybrid heat integrated distillation systems (HHIDiS),” Applied Thermal Engineering, vol. 174, no. 25, e115249, Jun. 2020. https://doi.org/10.1016/j.applthermaleng.2020.115249
M. Chai, M. Yang, R. Qi, Z. Chen, J. Li, “Vapor-liquid equilibrium (VLE) prediction for dimethyl ether (DME) and water system in DME injection process with Peng-Robinson equation of state and composition dependent binary interaction coefficient,” Journal of Petroleum Science and Engineering, vol. 211, e110172, 2022. https://doi.org/10.1016/j.petrol.2022.110172
J. Jaubert, R. Privat R, “Relationship between the binary interaction parameters (kij) of the Peng–Robinson and those of the Soave–Redlich–Kwong equations of state: Application to the definition of the PR2SRK model,” Fluid Phase Equilibria, vol. 295, no. 1, pp. 26–37. Aug. 2010. https://doi.org/10.1016/j.fluid.2010.03.037
E. Boonaert, A. Valtz, C. Coquelet, “Vapour-liquid equilibria of n-butane and ethyl mercaptan: Experiments and modeling,” Fluid Phase Equilibria, vol. 504, e112335, Jan. 2020. https://doi.org/10.1016/j.fluid.2019.112335
J. M. Smith, H. C. Vann Ness, M. M. Abbott, Introducción a la termodinámica en Ingeniería Química, 7ª Ed. Mexico DF, McGraw Hill, 2007
E. Jara, D. Collado, M. De la Cruz, V. C. M. Vivas, “Dynamic simulation of bioethanol in batch régimen,” Tecnia, vol. 21, no. 1, pp. 56-72. Jun. 2011. https://doi.org/10.21754/tecnia.v21i1.95
L. Wanga, W. Gunter, S. Wang, “A startup model for simulation of batch distillation starting from a cold state,” Computers & Chemical Engineering, vol. 27, no. 10, pp. 1485-1497, Oct. 2003. https://doi.org/10.1016/S0098-1354(03)00094-2
M. A. Mueses, F. Machuca-Martínez, “A Solution of the Rachford-Rice Equation for Multiphase Systems by Using the Newton-Raphson Method, Broyden Parameter and the Negative Flash,” Información Tecnológica, vol. 21, no. 4, pp. 3-10, Feb. 2010. https://doi.org/10.4067/S0718-07642010000400002
R. H. Perry, Manual del Ingeniero Químico, 6ª Ed., Tomo IV, Mexico DF, McGraw Hill, 1994
F. S. Laganier, J. H. Le Lann, X. Joulia, B. Koehret, “Simultaneous modular dynamic simulation: Application to Interconnected Distillation Columns,” Computers & Chemical Engineering, vol. 17, no. S1, pp. 287-297, 1993. https://doi.org/10.1016/0098-1354(93)80241-E
J. Albet, J. M. Le Lann, X. Joulia, B. Koehret, “Evolutions et tendances en simulation de colonnes de rectification discontinue,” The Chemical Engineering Journal, vol. 54, no. 2, pp. 95-106, Jun. 1994. https://doi.org/10.1016/0923-0467(93)02815-E
S. Domenech, G. Muratet, M. Enjalbert, “Commandes en Temps Minimal d’une Rectification Discontinue,” The Chemical Engineering Journal, vol. 9, no. 2, pp. 125-135, 1975. https://doi.org/10.1016/0300-9467(75)80004-9
S. Aly, L. Pibouleau, S. Domenench, “Traitement par une méthode d’éléments finis de modelès de colonnes de rectification discontinue à garnissage,” The Canadian Journal of Chemical Engineering, vol. 65, no. 6, pp. 991-1003, Dec. 1987. https://doi.org/10.1002/cjce.5450650615
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Copyright (c) 2022 Jennyfer Diaz-Angulo, Alfonso Barbosa-Meza, Fiderman Machuca-Martínez, Miguel-Ángel Mueses
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