| The problem of diffusion and reaction in a nonisothermal finite cylindrical catalyst pellet is modeled in the absence (Dirichlet problem) or presence (Robin problem) of external transport resistances. Prater analysis is used to relate the concentration and temperature profiles inside the catalyst. Green's function method is applied to transform the resulting partial differential equation into a Fredholm integral equation. A modified Green's function method is developed to accelerate the convergence of the partial eigen series. It was shown for both the Dirichlet and Robin problems that, the rate of convergence of the eigen series is enhanced by an order of two.; The resulting integral equations are solved by a Newton-Kantorvich iteration scheme to obtain the concentration profiles inside the catalyst. Effectiveness factors are calculated for various nonlinear reaction rate forms. Parameters considered include the Prater, Arrhenius, Sherwood and Nusselt numbers.; Carbon deactivation of 0.5 wt% Ru/(gamma)-Al(,2)O(,3) catalyst is studied using a Berty reactor-GC set up. The experimental variables were--temperature 473(DEGREES)K-573(DEGREES)K; pressure 2 atm-6 atm; weight hourly space velocity 0.85 hr('-1),16.5 hr('-1); H(,2)/CO feed ratio 3,2 and synthesis time 0.5 hr-5 hr. Carbon deposited in a synthesis run is measured by integrating the methane evolution curve during catalyst reduction at 723(DEGREES)K in H(,2).; Significant amounts of carbon were deposited, increasing to several monolayers during a 5 hr synthesis period. Methanation rate decreased as synthesis continued, while, the selectivity for C(,2)-C(,4) hydrocarbons showed a maximum during the initial stages of deactivation.; The kinetic data could be correlated by assuming both hydrogen assisted CO dissociation and hydrogenation of surface carbon to be rate determining. The turnover numbers for methanation(N(,CH(,4))) and carbon deposition(N(,C/Ru)) are given by N(,CH(,4)) = {lcub}8.94 x 10('9)exp(-22500/RT)P(,CO)P(,H(,2))/(1 + 9.56p(,CO))('2){rcub}exp(-1.2c),s('-1); N(,C/Ru) = {lcub}3.45 x 10('6)exp(-16600/RT)p(,CO)('2)/(1 + 9.56p(,CO)){rcub}exp(-0.76c),s('-1). |
