Unstationary film model for the determination of absolute gas-liquid kinetic rate constants: ozonation of Acid Red 27, Acid Orange 7, and Acid Blue 129

A method for the determination of absolute kinetic rate constants is proposed using an unstationary film model. This methodology avoids the experimental determination of parameters like the enhancement factor or the Hatta number which are usually model-dependent. The mathematical model is general for gas-liquid systems with irreversible second order reactions. An optimization procedure based on artificial neural networks is used to estimate the initial guess of the parameters and the subsequent application of Gauss-Newton algorithm for the final nonlinear parameter estimation. The model is tested with the ozonation reaction of Acid Red 27, Acid Orange 7 and Acid Blue 129. The second-order kinetic rate constants for the direct reaction with O3 are 1615±93, 609±83, and 49±2M−1s−1, respectivelyJF acknowledges the support of the doctoral fellowship from the Universitat Politecnica de Valencia (UPV-PAID-FPI-2010-04).Ferre Aracil, J.; Cardona Navarrete, SC.; López Pérez, MF.; Abad Sempere, A.; Navarro-Laboulais, J. (2013). Unstationary film model for the determination of absolute gas-liquid kinetic rate constants: ozonation of Acid Red 27, Acid Orange 7, and Acid Blue 129. Ozone: Science and Engineering. 35(6):423-437. https://doi.org/10.1080/01919512.2013.815104S423437356Biń, A. K. (2006). Ozone Solubility in Liquids. Ozone: Science & Engineering, 28(2), 67-75. doi:10.1080/01919510600558635Cardona, S. C., López, F., Abad, A., & Navarro-Laboulais, J. (2010). On bubble column reactor design for the determination of kinetic rate constants in gas-liquid systems. The Canadian Journal of Chemical Engineering, 88(4), 491-502. doi:10.1002/cjce.20327Chang, C. S., & Rochelle, G. T. (1982). Mass transfer enhanced by equilibrium reactions. Industrial & Engineering Chemistry Fundamentals, 21(4), 379-385. doi:10.1021/i100008a011Dachipally, P., & Jonnalagadda, S. B. (2011). Kinetics of ozone-initiated oxidation of textile dye, Amaranth in aqueous systems. Journal of Environmental Science and Health, Part A, 46(8), 887-897. doi:10.1080/10934529.2011.580201Danckwerts, P. V., & Lannus, A. (1970). Gas-Liquid Reactions. Journal of The Electrochemical Society, 117(10), 369C. doi:10.1149/1.2407312Das, A. K., & Das, P. K. (2009). Bubble Evolution through a Submerged Orifice Using Smoothed Particle Hydrodynamics: Effect of Different Thermophysical Properties. Industrial & Engineering Chemistry Research, 48(18), 8726-8735. doi:10.1021/ie900350hFerrell, R. T., & Himmelblau, D. M. (1967). Diffusion coefficients of nitrogen and oxygen in water. Journal of Chemical & Engineering Data, 12(1), 111-115. doi:10.1021/je60032a036Gerlach, D., Alleborn, N., Buwa, V., & Durst, F. (2007). Numerical simulation of periodic bubble formation at a submerged orifice with constant gas flow rate. Chemical Engineering Science, 62(7), 2109-2125. doi:10.1016/j.ces.2006.12.061Glasscock, D. A., & Rochelle, G. T. (1989). Numerical simulation of theories for gas absorption with chemical reaction. AIChE Journal, 35(8), 1271-1281. doi:10.1002/aic.690350806Gomes, A. C., Nunes, J. C., & Simões, R. M. S. (2010). Determination of fast ozone oxidation rate for textile dyes by using a continuous quench-flow system. Journal of Hazardous Materials, 178(1-3), 57-65. doi:10.1016/j.jhazmat.2010.01.043Gupta, P., Al-Dahhan, M. H., Duduković, M. P., & Mills, P. L. (2000). A novel signal filtering methodology for obtaining liquid phase tracer responses from conductivity probes. Flow Measurement and Instrumentation, 11(2), 123-131. doi:10.1016/s0955-5986(99)00025-4Hoigné, J., & Bader, H. (1983). Rate constants of reactions of ozone with organic and inorganic compounds in water—I. Water Research, 17(2), 173-183. doi:10.1016/0043-1354(83)90098-2Jamialahmadi, M., Zehtaban, M. R., Müller-Steinhagen, H., Sarrafi, A., & Smith, J. M. (2001). Study of Bubble Formation Under Constant Flow Conditions. Chemical Engineering Research and Design, 79(5), 523-532. doi:10.1205/02638760152424299Johnson, P. N., & Davis, R. A. (1996). Diffusivity of Ozone in Water. Journal of Chemical & Engineering Data, 41(6), 1485-1487. doi:10.1021/je9602125King, C. J. (1966). Turbulent Liquid Phase Mass Transfer at Free Gas-Liquid Interface. Industrial & Engineering Chemistry Fundamentals, 5(1), 1-8. doi:10.1021/i160017a001Ledakowicz, S., Maciejewska, R., Perkowski, J., & Bin, A. (2001). Ozonation of Reactive Blue 81 in the bubble column. Water Science and Technology, 44(5), 47-52. doi:10.2166/wst.2001.0248Lewis, W. K., & Whitman, W. G. (1924). Principles of Gas Absorption. Industrial & Engineering Chemistry, 16(12), 1215-1220. doi:10.1021/ie50180a002Lopez, A., Benbelkacem, H., Pic, J. ‐S., & Debellefontaine, H. (2004). Oxidation pathways for ozonation of azo dyes in a semi‐batch reactor: A kinetic parameters approach. Environmental Technology, 25(3), 311-321. doi:10.1080/09593330409355465Meldon, J. H., Olawoyin, O. O., & Bonanno, D. (2007). Analysis of Mass Transfer with Reversible Chemical Reaction†. Industrial & Engineering Chemistry Research, 46(19), 6140-6146. doi:10.1021/ie0705397Navarro-Laboulais, J., Cardona, S. C., Torregrosa, J. I., Abad, A., & López, F. (2006). Structural identifiability analysis of the dynamic gas–liquid film model. AIChE Journal, 52(8), 2851-2863. doi:10.1002/aic.10901Navarro-Laboulais, J., Cardona, S. C., Torregrosa, J. I., Abad, A., & López, F. (2008). Practical identifiability analysis in dynamic gas–liquid reactors. Computers & Chemical Engineering, 32(10), 2382-2394. doi:10.1016/j.compchemeng.2007.12.004Rapp, T., & Wiesmann, U. (2007). Ozonation of C.I. Reactive Black 5 and Indigo. Ozone: Science & Engineering, 29(6), 493-502. doi:10.1080/01919510701617959Tanaka, M., Girard, G., Davis, R., Peuto, A., & Bignell, N. (2001). Recommended table for the density of water between 0  C and 40  C based on recent experimental reports. Metrologia, 38(4), 301-309. doi:10.1088/0026-1394/38/4/3Tizaoui, C., & Grima, N. (2011). Kinetics of the ozone oxidation of Reactive Orange 16 azo-dye in aqueous solution. Chemical Engineering Journal, 173(2), 463-473. doi:10.1016/j.cej.2011.08.014Von Gunten, U. (2003). Ozonation of drinking water: Part I. Oxidation kinetics and product formation. Water Research, 37(7), 1443-1467. doi:10.1016/s0043-1354(02)00457-

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.Comment: 22 pages, 1 figure, submitted to Japan Journal of Industrial and Applied Mathematic

Dynamic Analysis of Unidirectional Pressure Infiltration of Porous Preforms by Pure Metals

Unidirectional pressure infiltration of porous preforms by molten metals is investigated numerically. A phenomenological model to describe fluid flow and transport phenomena during infiltration of fibrous preforms by a metal is formulated. The model describes the dynamics of the infiltration process, the temperature distribution, and solid fraction distribution. The numerical results are compared against classical asymptotic analyses and experimental results. This comparison shows that end effects may become important and render asymptotic results unreliable for realistic samples. Fiber volume fraction and initial temperature appear as the factors most strongly influencing infiltration. Metal superheating affects not only the length of the two-phase zone but also the solid fraction distribution in the two-phase zone. The effect of constant applied pressure, although significant on the infiltration velocity, is almost negligible on the two-phase zone length and on solid fraction distribution. When the initial preform temperature is below the metal melting point, and constant pressure is applied under adiabatic conditions, the flow ceases when sufficient solidification occurs to obstruct it. A comparison with literature experiments proves the model to be an efficient predictive tool in the analysis of infiltration processes for different preform/melt systems