Estimation of heat transfer parameters in a trickle-bed reactor using differential evolution and orthogonal collocation

A new non-sequential technique is proposed for the estimation of effective heat transfer parameters using radial temperature profile measurements in a gas–liquid co-current downflow through packed bed reactors (often referred to as trickle bed reactors). Orthogonal collocation method combined with a new optimization technique, differential evolution (DE) is employed for estimation. DE is an exceptionally simple, fast and robust, population based search algorithm that is able to locate near-optimal solutions to difficult problems. The results obtained from this new technique are compared with that of radial temperature profile (RTP) method. Results indicate that orthogonal collocation augmented with DE offer a powerful alternative to other methods reported in the literature. The proposed technique takes less computational time to converge when compared to the existing techniques without compromising with the accuracy of the parameter estimates. This new technique takes on an average 10 s on a 90 MHz Pentium processor as compared to 30 s by the RTP method. This new technique also assures of convergence from any starting point and requires less number of function evaluations.

[1]  B. Finlayson The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[2]  D. D. Perlmutter Stability of chemical reactors , 1972 .

[3]  W. E. Stewart,et al.  Solution of boundary-value problems by orthogonal collocation , 1995 .

[4]  R. Hughes,et al.  Simulation of an adiabatic packed bed reactor , 1974 .

[5]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[6]  Vern W. Weekman,et al.  Heat transfer characteristics of concurrent gas-liquid flow in packed beds , 1965 .

[7]  Rainer Storn,et al.  Differential Evolution-A simple evolution strategy for fast optimization , 1997 .

[8]  W. E. Stewart,et al.  Computational models for cylindrical catalyst particles , 1973 .

[9]  Michael P. Polis,et al.  Identification of parameters in distributed systems : a symposium of the American Automatic Control Council , 1974 .

[10]  L. Padmanabhan,et al.  Use of orthogonal collocation methods for the modeling of catalyst particles—II analysis of stability , 1974 .

[11]  Gabriel Wild,et al.  Heat transfer in a packed bed reactor with cocurrent downflow of a gas and a liquid , 1996 .

[12]  Forman S. Acton,et al.  Numerical methods that work , 1970 .

[13]  Simant R. Upreti,et al.  Optimal design of an ammonia synthesis reactor using genetic algorithms , 1997 .

[14]  R. Moros,et al.  A genetic algorithm for generating initial parameter estimations for kinetic models of catalytic processes , 1996 .

[15]  Bruce A. Finlayson,et al.  Transient chemical reaction analysis by orthogonal collocation , 1970 .

[16]  J. Villadsen,et al.  Solution of differential equation models by polynomial approximation , 1978 .

[17]  Laxmidhar Behera,et al.  Differential Evolution Based Fuzzy Logic Controller for Nonlinear Process Control , 1999, Fundam. Informaticae.

[18]  L. Young,et al.  Axial Dispersion in Nonisothermal Packed Bed Chemical Reactors , 1973 .

[19]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[20]  B. Finlayson Nonlinear analysis in chemical engineering , 1980 .

[21]  Bruce A. Finlayson,et al.  Packed bed reactor analysis by orthogonal collocation , 1971 .

[22]  L. Hellinckx,et al.  A new method for the estimation of parameters in differential equations , 1974 .

[23]  D. Wolf,et al.  Estimating rate constants of heterogeneous catalytic reactions without supposition of rate determining surface steps — an application of a genetic algorithm , 1997 .

[24]  Michel Crine Heat transfer phenomena in trickle-bed reactors , 1982 .

[25]  T. Edgar,et al.  Estimation of heat transfer parameters in a packed bed , 1976 .

[26]  Vito Specchia,et al.  HEAT TRANSFER IN TRICKLE-BED REACTORS , 1979 .

[27]  B. Finlayson,et al.  Orthogonal collocation on finite elements , 1975 .

[28]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[29]  Gilbert F. Froment,et al.  FIXED BED CATALYTIC REACTORS—CURRENT DESIGN STATUS , 1967 .

[30]  Alan H. Karp,et al.  A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides , 1990, TOMS.