IJRRAS 18 (3) ● March2014 www.arpapress.com/Volumes/Vol18Issue3/IJRRAS_18_3_07.pdf 1 KINETIC ANALYSIS OF AROMATIZATION OF N-HEXANEON PLATINUM/ALUMINA CATALYST USING THE TIKHONOV REGULARIZATION TECHNIQUE OyinlolaRukayat Oresegun 1 , AramideAdenike Adesina 1 & Alfred Akpoveta Susu 2 1 Department of Chemical & Polymer Engineering, Lagos State University, Epe, Lagos, Nigeria 2 Department of Chemical Engineering, University of Lagos, Lagos, Nigeria E-mail: lollykee@yahoo.com; ajeigbearamide@yahoo.com; poveta_susu@yahoo.com ABSTRACT Tikhonov regularization, which is a new technique for converting time-concentration data into concentration- reaction rate data, was applied to the kinetic analysis of n-hexane aromatization on Platinum/Alumina Catalyst.The technique was used for the conversion of the experimental concentration-time data to rate-concentration data. Due to the ill-posed nature of the problem of obtaining of reaction rates from experimental data, conventional methods will lead to noise amplification of the experimental data. Hence, Tikhonov regularization technique is preferably employed because it is entirely independent of reaction rate models and it also manages to minimize noise amplification, thus, leading to more reliable results. The kinetic parameters obtained by the application of the Nelder-Mead simplex optimization technique to formulated mechanistic models was used to discriminate among rival kinetic models based upon physicochemical criteria and thermodynamic tests to give the rate of conversion of adsorbed hexene-1 to adsorbed methylcyclopentane when hydrogen is adsorbed as a bi-molecular specie as the rate determining step. Keywords: Tikhonov regularization technique; Nelder-Mead simplex method; Hexane reforming; Mechanistic kinetic models; Kinetic and equilibrium parameters. 1. INTRODUCTION In the investigation of the kinetics of chemically reacting systems, it is often necessary to convert experimental time-concentration data into concentration-reaction rate data in order to determine the kinetic parameters of postulated reaction rate models.A variety of procedures has been developed to perform this task. For otherreactions it may be possible to deduce the rate constants by examining the initial slope of the time-concentration data. Another approach is to modify or simplifythe kinetic model if this can be physically justified. A more general technique is to treat the rate equations as ordinary differential equations. These equations are integratedto give the concentration of the reactants and products as a function of time with the rate constants appearing as unknown parameters. These parameters are then adjusted tominimize the deviation of the computed time-concentrationprofile from its experimentally observedcounterpart. Integration of simple rate equations can be performedanalytically leading to simple expressions for the time- concentration profiles. However, for many rate equations analytical solution cannot be foundandthey have to be integratednumerically. Determination of the rate constants to minimize the deviation from experimental data becomes correspondingly more complicated to the extent that they cannot be determined to a reasonable degree of accuracy. Therefore, if inappropriate methods are used, the conversion procedure becomes an ill-posed problemin the sense thatthe noise in the original data will be amplified leading to unreliable results. Hadamard [9] defined a linear problem to be well posed if itsatisfies the following three requirements: (a) existence,(b) uniqueness, and (c) stability. A problem is said to beill-posed if one or more of these requirements are not satisfied.Yeow et al. [3]showed that Tikhonov regularization is a reliable procedure for processing the time- concentration data of reaction kinetics. This procedure has been successful in keeping noise amplification under control and meets the important requirement that it does not require the assumption of a model to describe the original experimental data.This procedure was first used by Yeow and Taylor [4] for obtaining velocity profiles from various experimentally measured velocity data. Yeowet. al. [3] carried out further application of the procedure to reactions ranging from first order reactions to chain reactions involving a number of intermediate steps with rate equation of the rate determining process. Omowunmi and Susu [5] used the Tikhonov regularization technique in converting the concentration-time data for n-eicosane pyrolysis data procured by Susu and Kunugi [6] to generate the kinetic parameters for this homogeneous autocatalytic chain reaction. In addition, Omowunmi and Susu [7] also used the same technique in determining the kinetic parameters for the reforming of n-heptane, n-heptene and 3- methylhexane on Pt/Alumina catalyst.