Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation

The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic non-zero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t^{-1/4} and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found.Comment: 8 pages, 7 figure

PARAMETER ESTIMATION IN MULTIRESPONSE MODELS

This article identifies a new Old English poetic motif, ‘The Departure of the Hero in a Ship’, and discusses the implications of its presence in Beowulf, the signed poems of Cynewulf and Andreas, a group of texts already linked by shared lexis, imagery and themes. It argues that the Beowulf-poet used this motif to frame his work, foregrounding the question of royal succession. Cynewulf and the Andreas-poet then adapted this Beowulfian motif in a knowing and allusive manner for a new purpose: to glorify the church and to condemn its enemies. Investigation of this motif provides further evidence for the intertextuality of these works

Methane Steam Limitations and Reforming: II. Diffusional Reactor Simulation

Given the intrinsic kinetics, the tortuosity factor of a Ni/MgAI,O, catalyst was determined under reaction conditions by minimizing the sum of squares of residuals of the experimental and the simulated conversions. The parallel cross-linked pore model with uncorrelated pore size distribution and orientation was used in the calculation of the effective diffusivities. A modified collocation method was used to obtain the partial pressure profiles of the reacting components in the catalyst pellet. The simulation of the experimental reactor during the optimization of the tortuosity factor also yielded the effectiveness factors of the reactions. The results of the simulation of an industrial steam reformer are also discussed

KINETICS OF SLURRY PHASE FISCHER-TROPSCH SYNTHESIS

This report covers the fourth year of a research project conducted under the University Coal Research Program. The overall objective of this project is to develop a comprehensive kinetic model for slurry-phase Fischer-Tropsch synthesis (FTS) employing iron-based catalysts. This model will be validated with experimental data obtained in a stirred-tank slurry reactor (STSR) over a wide range of process conditions. The model will be able to predict molar flow rates and concentrations of all reactants and major product species (water, carbon dioxide, linear 1- and 2-olefins, and linear paraffins) as a function of reaction conditions in the STSR. During the fourth year of the project, an analysis of experimental data collected during the second year of this project was performed. Kinetic parameters were estimated utilizing product distributions from 27 mass balances. During the reporting period two kinetic models were employed: a comprehensive kinetic model of Dr. Li and co-workers (Yang et al., 2003) and a hydrocarbon selectivity model of Van der Laan and Beenackers (1998, 1999) The kinetic model of Yang et al. (2003) has 24 parameters (20 parameters for hydrocarbon formation, and 4 parameters for the water-gas-shift (WGS) reaction). Kinetic parameters for the WGS reaction and FTS synthesis were estimated first separately, and then simultaneously. The estimation of these kinetic parameters employed the Levenberg-Marquardt (LM) method and the trust-region reflective Newton large-scale (LS) method. A genetic algorithm (GA) was incorporated into estimation of parameters for FTS reaction to provide initial estimates of model parameters. All reaction rate constants and activation energies were found to be positive, but at the 95% confidence level the intervals were large. Agreement between predicted and experimental reaction rates has been fair to good. Light hydrocarbons are predicted fairly accurately, whereas the model underpredicts values of higher molecular weight hydrocarbons. Van der Laan and Beenackers hydrocarbon selectivity model provides a very good fit of the experimental data for hydrocarbons up to about C{sub 20}. However, the experimental data shows higher paraffin formation rates in C{sub 12}-C{sub 25} region which is likely due to hydrocracking or other secondary reactions. The model accurately captures the observed experimental trends of decreasing olefin to paraffin ratio and increasing {alpha} (chain growth length) with increase in chain length

KINETICS OF SLURRY PHASE FISCHER-TROPSCH SYSTHESIS

This report covers the third year of this research grant under the University Coal Research program. The overall objective of this project is to develop a comprehensive kinetic model for slurry phase Fischer-Tropsch synthesis (FTS) on iron catalysts. This model will be validated with experimental data obtained in a stirred tank slurry reactor (STSR) over a wide range of process conditions. The model will be able to predict molar flow rates and concentrations of all reactants and major product species (H{sub 2}O, CO{sub 2}, linear 1- and 2-olefins, and linear paraffins) as a function of reaction conditions in the STSR. During the reporting period we utilized experimental data from the STSR, that were obtained during the first two years of the project, to perform vapor-liquid equilibrium (VLE) calculations and estimate kinetic parameters. We used a modified Peng-Robinson (PR) equation of state (EOS) with estimated values of binary interaction coefficients for the VLE calculations. Calculated vapor phase compositions were in excellent agreement with experimental values from the STSR under reaction conditions. Occasional discrepancies (for some of the experimental data) between calculated and experimental values of the liquid phase composition were ascribed to experimental errors. The VLE calculations show that the vapor and the liquid are in thermodynamic equilibrium under reaction conditions. Also, we have successfully applied the Levenberg-Marquardt method (Marquardt, 1963) to estimate parameters of a kinetic model proposed earlier by Lox and Froment (1993b) for FTS on an iron catalyst. This kinetic model is well suited for initial studies where the main goal is to learn techniques for parameter estimation and statistical analysis of estimated values of model parameters. It predicts that the chain growth parameter ({alpha}) and olefin to paraffin ratio are independent of carbon number, whereas our experimental data show that they vary with the carbon number. Predicted molar flow rates of inorganic species, n-paraffins and total olefins were generally not in good agreement with the corresponding experimental values. In the future we'll use kinetic models based on non-constant value of {alpha}