Jaime Romero González, Jorge Luis Garcia Alcaraz, Gilberto Velázquez Angulo, Aidé Aracely Maldonado Macías, Ismael Canales Valdivieso, Jaime Romero Rodríguez, Rosana Ramírez Martínez



La bioadsorción dinámica en columnas de lecho fijo con biomasas naturales ha adquirido gran importancia en la separación y recuperación de componentes de mezclas acuosas. Una etapa fundamental en el diseño de estos sistemas de separación es la modelación de la transferencia de masa. El presente trabajo fundamente ampliamente y muestra de manera detallada una metodología rápida para la solución numérica de las ecuaciones en derivadas parciales que describe el proceso de transferencia de masa y modelan el complejo proceso de bioadsorción del Cr(VI) mediante la aplicación de columnas de lecho fijo. La metodología descrita se basa en la transformación de las ecuaciones originales del tiempodominio en el dominio de Laplace, donde se lleva a cabo la integración numérica y posterior transformación inversa numérica de la solución final. Los resultados obtenidos mediante el modelo generado mediante esta técnica muestran una gran similitud con los resultados experimentales. Lo que valida la aplicación del modelo propuesto.

Palabras clave: Modelación, transferencia de masa, bioadsorcion, Cr(VI), transformadas
de Laplace

Palabras clave

Modelación; transferencia de masa; bioadsorcion; Cr(VI); transformadas

Texto completo:



Abramowitz M. and Stegun I. 1970. Handbook of Mathematical Functions, Dover Publications, Inc., New York.

Acosta, I., X. Rodríguez, C. Gutiérrez y M.G. Moctezuma-Zarate. 2004.

Biosorption of Chromium (VI) from aqueous solutions onto fungal biomass, Bioinorganic Chemistry Applications: 2 (1,2) 1-7.

Álvarez, S.G., M. Maldonado, M. Gerth, y P. Kuschk, 2004. Caracterización de agua residual de curtiduría y estudio del lirio acuático en la recuperación de Cromo, Inf. Tecnol: 15 (3), 75-80.

Atkinson, B.W. Bux F. and Kasan Hc. 1998. Considerations for application of biosorption technology to remediate metalcontaminated industrial effluents. Elsevier Science, Vol 24, No 2, pp. 129-135.

Ataie-Ashtiani, B., Lockington and D.A.,Volker, R.E. 1999. Truncation errors in finite difference models for solute transport equation with first-order reaction. Journal of Contaminant Hydrology 35, 409-428.

Bishnoi, N. R.; Bajaj, M.; Sharma, N.; Gupta, A. 2004. Adsorption of Cr(VI) on activated rice husk carbon and activated alumina. Bioresource Technol., 91 (3), 305-307.

Bohart, G. and Adams, E.Q. 1920. Some aspects of the behavior of charcoal with respect to chlorine. Journal of American Chemical Society 42, 523-544.

Brian, B.F., Zwiebel, I and Artigue, R. S. 1987. Numerical Simulation of Fixed- Bed Adsorption Dynamics by the Method of Lines, AIChE symp. Series, 83 (259), 80-86.

Campos, J., M. Martínez-Pacheco y C. Cervantes. 1995. Hexavalent chromium reduction by a chromate-resistant Bacillus spstrain, Antonie van Leeuwenhoek: 68, 203-208.

Carslaw, H.S. & Jaeger, J.C. 1959. Conduction of Heat in Solids. London: Oxford at the Clarendon Press.

Chen, T.L. and Hsu J.T. 1987. Prediction of Breakthrough Curves by the

application of fast fourier transform, AIChE Journal, 33 (8) 1387-1390.

Cervantes, C., J. Campos-García, S. Devars, F. Gutiérrez-Corona, H. Loza-Tavera, J.C. Torres-Guzmán y R. Moreno-Sánchez. 2001. Interactions of chromium with microorganisms and plants, FEMS Microbiology Review 25, 333-347.

Clark, R.M. 1987. Evaluating the cost and performance of field-scale granular actived carbon systems. Environmental Science and Technology 21, 573-580.

Cotton, F.A. y G. Wilkinson. 1980. Advanced Inorganic Chemistry, 4a Ed. Chichester, Uk; John Wiley&Sons. Gardea-Torresdey, J.L., Tiemann,

K.J., Armendáriz, V., Bess-Oberto, L., Chianelli, R.R., Rios, J., Parsons

J.G. and Gamez G. 2000. Characterization of Cr(VI) binding and reduction to Cr(III) by the agricultural byproducts of Avena monida

(Oat) biomass. Journal of Hazardous Materials 80, 175- 88.

Garg, V. K., Gupta, R., Kumar, R. and Gupta, R. 2004. Adsorption of chromium from aqueous solution on treated sawdust. Bioresource

Technology 92: 79–81. Hamed, A.M. 2002. Theorical and experimental study on the transient adsorption characteristics of a vertical packed porous bed. Renewable Energy 27, 525-541.

Hossain, M.A. 1999. Modeling advectivedispersive transport with reaction: an accurate explicit finite difference model.

Applied Mathematics and Computation 102, 101-108.

Hossain, M.A. and M.E. Barber. 2000. Optimized Petrov-Galerkin Model for Advective-Dispersive Transport, Applied Mathematics and Computation, 115:1-10.

Hossain, M.A. and M.R. Taha. 2000. Simulating Advective-Dispersive Transport by Finite Elements: Criteria for Accuracy of an Explicit Runge-Kutta Method. Applied Mathematics and Computation, 112:309-316.

Johnson, G.W. and Kapner, R.S. 1990. The dependence of axial dispersion on non-uniform flows in bed of uniform packing.Chemical

Engineering Science 45, 3329-3339.

Kraft, A. y Zuber A. 1978. On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions, Chem. Eng. Sci. 33, 1471-1480.

Kratochvil, D., Pimentel, P. and Volesky, B. 1998. Removal of trivalent and hexavalente chromium by seaweed biosorbent. Environmental Science and Technology 32, 2693-2698.

Lindstrom F.T., Haque R., Freed V.H. and Boersma L. 1967. Theory on the movement of some herbicides in soils, Linear diffusion and convection of chemicals in soils, Environ. Sci. Technol. 1, pp. 561–565.

Lehmann, M., Zouboulis, A.I. and Matis, K.A. 2001. Modelling the adsorption of metals from aqueous solution on geothite fixedbeds. Environmental Pollution 113, 121-128.

Losi, M.E., C. Amrhein, y W.T. Frankenberger. 1994. Environmental

biochemistry of Chromium, Rev Environ Contam Toxicol: 136, 91-131.

Mabbett, A., Y. Ping, J. Peter, G. Farr, y L. Macaskie. 2004. Reduction of Cr (VI) by “palladized” biomass of Desulfovibrio desulfuricans ATCC 29577, Biotechnology and Bioengineering, 87 (1), 104-109.

McLean, J. y T.J. Beveridge. 2001. Chromate reduction by a

pseudomonad isolated from a site contaminated with chromated copper arsenate, Appl Environ Microbiol: 67, 1076-1084.

Ogata, A., and R.B. Banks. 1961. A solution of the differential equation of longitudinal dispersion in porous media, United States Geological Survey,

Professional Paper No. 411-A.

Parker J.C. y van Genuchten, M.Th. 1984. Flux-Averaged and Volume-Averaged Concentrations in Continuum Approaches to Solute Transport . Water. Resour. Res., 20, 866-872 .

Raghavan, N.S., and Ruthven, D.M. 1983. Numerical Simulation of a Fixed-Bed Adsorption Column by Method of Ortogonal Collocation, AIChE Journal, 29 (6) 922-925

Ramírez-Ramírez, R., C. Calvo- Méndez, M. A. Avila-Rodríguez, P. Lappe, M. Ulloa, R. Vázquez-Juárez y J.F. Gutiérrez-Corona. 2004. Cr(VI) reduction in a Chromate-resistant strain of Candida maltosa isolated from the leather industry, Antonie van Leeuwenhoek: 85, 63-68.

Ruthven D.M. 1985. Principles of adsorption and Adsorption Process, John Wiley and Sons.

Rasmuson, A. and Neretnieks, I., 1980 Exact solution of a model fro diffusion in particles and longitudinal dispersion in packed beds, AIChE Journal 29(4), 686-690.

Romero-González J., Cano-Rodríguez I, Walton J.C., Peralta-Videa J.

R., Rodríguez E.y Gardea-Torresdey J. L.. 2005. A model to describe the adsorption and reduction of Cr (VI). From an aqueous solution by agave lechuguilla biomasa. Revista Mexicana de Ingenieria Quimica vol. 4 , 261-272

Serrano, S.E. 2001. Solute transport under nonlinear sorption and decay. Water Research 35, 1525-1533. Sag, Y. and Aktay, Y. 2001.

Application of equilibrium and mass transfer model to dynamic removal of Cr(VI) ions by Chitin in packed column reactor. Process Biochemistry 36, 1187-1197.

Sauty J.P. 1980. An analysis of hydrodispersive transfer in aquifers, Wat. Resour. Res. 16 (1), pp. 145–158 Van Zee, G., Veenstra, R. and de Graauw, J. 1995. Axial dispersion in packed fiber beds. The Chemical Engineering Journal and the Biochemical Engineering Journal, 58, 245-250.

Van Genuchten, M.Th. 1981. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-ordey decay. Journal of Hydrology 49, 213-233.

Van Genuchten, M. Th. and Alves W. J.. 1982. Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation. United States Department of Agriculture, Agricultural Research Service, Technical Bulletin 1661.

Veglio, F., Beolchini, F. 1997. Removal of toxic metals by biosorption: a review. Hydrometallurgy, 44, 301-316. Viti, C., A. Pace, y L. Giovenneti.

Characterization of Cr(VI)-resistant bacteria isolated from Chromiumcontaminated soil by tannery activity, Current Microbiology: 46, 1-5.

Volesky, B. 2001. Detoxification of metal-bearing effluents: Biosorption for the next century Hydrometallurgy 59 (2-3) , 203- 216.

Volesky, B. 2003 Sorption and Biosorption, BV Sorbex, Montreal, Canada.

Yang, r.T. 1987. Gas separation by adsorption processes, Butter-worths series in Chemical Enginnering.

Zhang, H., Cheng, D. 2000. Mathematical model for a fixed bed

adsorptive reactor. Carbon 38, 877-880.

Zouboulis, A.I., K.A. Kydros y K.A. 1995. Matis. Removal of hexavalent

Chromium anions from solutions by pyrite fines, Wat Res: 29 (7), 1755-1760.

Enlaces refback

  • No hay ningún enlace refback.

Copyright (c) 2017 CULCyT

Licencia de Creative Commons
Este obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial 4.0 Internacional.

Responsable de la última actualización de este número: Raúl Alfredo Meza González. Fecha de la última modificación, 15 de enero de 2020.

Las opiniones expresadas por los autores no necesariamente reflejan la postura del editor de la publicación. Los contenidos e imágenes de la publicación estan sujetos a una licencia CC 4.0 internacional BY NC. 

 Licencia de Creative Commons