Upscaled model for dispersive mass transfer in a tubular porous membrane separator
Modelo escalado para la transferencia dispersiva de masa en un separador tubular por membrana porosa
F.J. Valdés-Parada1, J.A. Ochoa-Tapia1, E. Salinas-Rodríguez1*, S. Gómez-Torres1 and M.G. Hernández2
1 Departamento de Ingeniería de Procesos e Hidráulica, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 col. Vicentina, C.P. 09340, México D.F., México. *Corresponding author. E-mail: sabe@xanum.uam.mx.
]]> 2 Departamento de Ciencias Básicas, Área de FAMA, Universidad Autónoma Metropolitana-Azcapotzalco.
Received November 22, 2013.
Accepted January 25, 2014.
Abstract
In this work, the steady-state mass transfer of a non-reactive species in a tubular separator involving a porous membrane is studied. This type of equipment has received considerable attention in the literature since it can be used for gas-gas separation processes. In specific, in this work we are interested in studying transport of oxygen from an air current to a pure helium flow. The air is transported in the annular region, whereas the helium is flowing in countercurrent within the inner compartment of the system. The membrane is permeable to gases in different proportions; however, only oxygen is assumed to constitute a dilute solution in both regions of the system. To derive the mathematical model, we averaged the pointwise equations in the system cross-section generating a system of two ordinary differential equations representing non-equilibrium mass transfer in each region of the system. These upscaled equations are written in terms of effective-medium coeffcients that capture the essential features from the pointwise transport and are predicted from the solution of the associated closure problem. To evaluate the predictive capabilities of the model, we compared the concentration profiles with those from solving the pointwise equations. The influence of the membrane permeability to oxygen transfer is studied and we found a close correspondence between the pointwise and upscaled models.
Keywords: mass transfer, tubular membrane separator, oxygen transfer, non-equilibrium model, upscaling.
Resumen
]]> En este trabajo, se estudia la transferencia de masa en estado estacionario de una especie no reactiva en un separador tubular que involucra una membrana porosa. Este tipo de equipo ha recibido considerable atención en la literatura ya que puede usarse en procesos de separación gas-gas. En específico, en este trabajo estamos interesados en estudiar el transporte de oxígeno de una corriente de aire hacia un flujo de helio puro. El aire es transportado en la región anular, mientras que el helio fluye a contracorriente en el compartimiento interno del sistema. La membrana es permeable a los gases en diferentes proporciones; sin embargo, se supone que sólo el oxígeno forma una solución diluida en ambas regiones del sistema. Para desarrollar el modelo matemático, se promediaron las ecuaciones puntuales en la sección transversal del sistema, lo que da lugar a un sistema de dos ecuaciones diferenciales ordinarias representando la transferencia de masa de no equilibrio en cada región del sistema. Estas ecuaciones escaladas están escritas en términos de coeficientes de medio efectivo que capturan las características esenciales del transporte puntual y se predicen a partir de la solución del problema de cerradura asociado. Para evaluar las capacidades predictivas del modelo, se compararon los perfiles de concentración con los que resultan de resolver las ecuaciones puntuales. Se estudió la influencia de la permeabilidad de membrana sobre la transferencia de oxígeno y encontramos una cercana correspondencia entre los modelos puntual y escalado.Palabras clave: transferencia de masa, separador tubular de membrana, transferencia de oxígeno, modelo de no equilibrio, escalamiento.
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgments
FVP expresses his gratitude to Fondo Sectorial de Investigación para la educación from CONACyT (Project number: 12511908; Arrangement number: 112087) for the financial aid provided. MGH is thankful to PROMEP for the scholarship provided.
References
Abdel-Jawad M.M., Gopalakrishnan S., Duke M.C., Macrossan M.N., Smith Schneider P., Diniz da Costa J.C. (2007). Flow fields on feed and permeate sides of tubular molecular sieving silica (MSS) membranes. Journal of Membrane Science 299, 229-235. [ Links ]
Bowen T.C., Noble R.D., Falconer J.L. (2004). Fundamentals and applications of pervaporation through zeolite membranes. Journal of Membrane Science 245, 1-33. [ Links ]
Bird R.B., Stewart W.E., Lightfoot E.N. (2007). Transport Phenomena, second edition, Wiley. [ Links ]
Chandesris M. and Jamet D. (2007). Boundary conditions at a fluid-porous interface: An a priori estimation of the stress jump coeffcients. International Journal of Heat and Mass Transfer 50, 3422-3436. [ Links ]
Coronas J., Santamaría J. (1999). Catalytic reactors based on porous ceramic membranes. Catalysis Today 51, 377-389. [ Links ]
Cushman J. (1997). The Physics of Fluids in Hierarchical Porous Media: Angstroms to Miles, Springer. [ Links ]
Faucheux V., Audier M., Rapenne L., Pignard S. (2008). Fabrication of thin and dense nanocrystalline membranes on porous substrates. Journal of Materials Processing Technology 204, 248-254. [ Links ]
Freeman B., Yampolskii Y., Pinnau I. (2008). Materials Science of Membranes for Gas and Vapor Separation, Wiley. [ Links ]
Gascon J., Kapteijn F., Zornoza B., Sebastián V., Casado C., Coronas J. (2012). Practical approach to zeolitic membranes and coatings: State of the art, opportunities, barriers, and future perspectives. Chemistry of Materials 24, 2829-2844. [ Links ]
Gray W.G. (1975). A derivation of the equations for multiphase transport. Chemical Engineering Science 30, 229-233. [ Links ]
Hernández M.G., Salinas-Rodríguez E., Gómez S., Roa-Neri J.A.E., Rodríguez R.F. (2012). Membranas zeolíticas y sus principales aplicaciones. Materiales Avanzados 18, 9-18. [ Links ]
Hussain A., Seidel-Morgenstern A., Tsotsas E. (2006). Heat and mass transfer in tubular ceramic membranes for membrane reactors. International Journal of Heat and Mass Transfer 49, 2239-2253. [ Links ]
Jiang Q., Faraji S., Slade D.A., Stagg-Williams S.M. (2011). Chapter 11 -A Review of Mixed Ionic and Electronic Conducting Ceramic Membranes as Oxygen Sources for High-Temperature Reactors, In: S. Ted Oyama and Susan M. Stagg-Williams, Editor(s), Membrane Science and Technology, Elsevier, Volume 14, Pages 235-273. [ Links ]
Kumar V.S., Hariharan K.S., Mayya K.S., Han S. (2013). Volume averaged reduced order Donnan Steric Pore Model for nanofiltration membranes. Desalination 322, 21-28. [ Links ]
Li S., Jin W., Huang P., Xu N., Shi J., Lin Y.S. (2000). Tubular lanthanum cobaltite perovskite type membrane for oxygen permeation. Journal of Membrane Science 166, 51-61. [ Links ]
Liang F., Jiang H., Schiestel T., Caro J. (2010). High-purity oxygen production from air using Perovskite hollow fiber membranes. Industrial and Engineering Chemistry Research 49, 9377-9384. [ Links ]
McLeary E.E., Jansen J.C., Kapteijn F. (2006). Zeolite based films, membranes and membrane reactors: Progress and prospects. Microporous and Mesoporous Materials 90, 198-220. [ Links ]
Rebollar-Perez G., Carretier E., Moulin P. (2010). Aplicaciones de la permeación de vapor: El tratamiento de compuestos orgánicos volátiles de origen antropogénico. Revista Mexicana de Ingeniería Química 9, 67-77. [ Links ]
Taylor G.I. (1953). Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 219, 186-203. [ Links ]
Taylor G.I. (1954). Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 225, 473-477. [ Links ]
Wang H., Cong Y., Yang W. (2003). Investigation on the partial oxidation of methane to syngas in a tubular Ba0.5Sr0.5Co0.8Fe0.2O3 − δ membrane reactor. Catalysis Today 82, 157-166. [ Links ]
Wang H., Wang R., Tee Liang D., Yang W. (2004). Experimental and modeling studies on Ba0.5Sr0.5Co0.8Fe0.2O3 − δ (BSCF) tubular membranes for air separation. Journal of Membrane Science 243, 405-415. [ Links ]
Whitaker S. (1999). The Method of Volume Averaging, Kluwer academic publishers. [ Links ]
Whitaker S. (2009). Chemical engineering education: making connections at interfaces. Revista Mexicana de Ingeniería Química 8, 1-33. [ Links ]
Wood B.D. (2009). Taylor-Aris dispersion: An explicit example for understanding multiscale analysis via volume averaging. Chemical Engineering Education 43, 29-38. [ Links ]
Wood B.D., Valdés-Parada F.J. (2013). Volume averaging: Local and nonlocal closures using a Green's function approach. Advances in Water Resources 51, 139-167. [ Links ]
Zhu X., Sun S., He Y., Cong Y., Yang W. (2008). New concept on air separation. Journal of Membrane Science 323, 221-224. [ Links ]
]]>