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This paper deals with the analysis of transient kinetic data obtained in the Thin-Zone (TZ) configuration of the Temporal Analysis of Products (TAP) reactor. The Y-procedure that reconstructs the reaction rate and gas composition in the catalytic zone with no assumptions on the reaction mechanism ( Yablonsky et al., 2007 ) was applied to irreversible adsorption with coverage-dependent kinetic coefficients. We have used the Y-Procedure analysis to develop a novel framework for the interpretation of non-steady-state kinetic data. This framework was illustrated by multiple numerical examples concerning irreversible adsorption, and by experimental data corresponding to oxygen adsorption on polycrystalline platinum. The total concentration of active sites was estimated as 6 × 10 − 7 mol / g cat . It was found that for the surface coverage up to 0.8, kinetics followed the dissociative adsorption model with an intrinsic adsorption constant of 1.12 × 10 6 m 3 / mol / s . Kinetic parameters estimated via the Y-procedure agreed well with the values obtained via the moment analysis. The methodology developed in this paper will guide the systematic application of the Y-Procedure analysis to more complex catalytic systems.

We obtain a general formula for reactant conversion in diffusion–reaction TAP systems over single non-porous catalyst particles as a product of two terms: α = P H × K . The first term, P H , is a purely geometric factor dependent only on the shape of the reactor and the shape and position of the catalyst particle, interpreted as the probability that an individual molecule of reactant will hit the catalyst before leaving the reactor. The second term, K = k τ H / ( 1 + k τ H ) , is a geometrical/chemical term involving the kinetic constant k and a transport characteristic (residence time in the catalyst zone, τ H ). Both P H and τ H can be effectively calculated for any given reactor-particle configuration. Our formula greatly extends the validity of a formula given in Shekhtman et al. [1999. Thin-zone TAP-reactor—theory and application. Chem. Eng. Sci. 54, 4371–4378] for thin-zone TAP-systems. It is derived by a probabilistic analysis of the residence time of individual molecular trajectories in chemically active regions. Our results are based on the theory previously developed in our paper [Feres, R., Yablonsky, G.S., Mueller, A., Baernstein, A., Zheng, X., Gleaves, J., 2009. Probabilistic analysis of transport-reaction processes over catalytic particles: theory and experimental testing. Chem. Eng. Sci. 64, 568–581].

We developed a probabilistic theory of transport–reaction processes over various types of configurations of catalytic particles, particularly for a single particle. The theory describes a single pulse–response experiment which is similar to the single pulse temporal analysis of products (TAP) experiment. The analysis is based on the general theory of Brownian motion with “killing” and the Feynman–Kac formula. Different diffusion–reaction problems, particularly the problem “diffusion–very fast reaction” (infinite rate reaction), have been analyzed. In the latter case, the probability for a reactant to be converted equals a purely geometric characteristic, namely, the probability for a reactant molecule to hit at least one catalyst particle in a configuration of particles. Solving a boundary value problem, the probability of conversion can be found as a function of the apparent kinetic parameter. Based on experimental data on exit flow and conversion this parameter can be extracted. Experimental data in studies of CO oxidation over a single particle of Pt catalyst show a qualitative agreement with data from computational experiments based on the developed probabilistic theory. For two-particle catalyst configurations, it was found computationally a non-trivial dependence of the reactant conversion on some geometric characteristics, especially the distance between particles. A distance was found for which conversion is highest.

The paper presents a new method to extract the chemical transformation rate from reaction–diffusion data with no assumption on the kinetic model (“kinetic model-free procedure”). It is a new non-steady-state kinetic characterization procedure for heterogeneous catalysts. The mathematical foundation of the Y-procedure is a Laplace-domain analysis of the two inert zones in a TZTR followed by transposition to the Fourier domain. When combined with time discretization and filtering the Y-procedure leads to an efficient practical method for reconstructing the concentration and reaction rate in the active zone. Using the Y-procedure the concentration and reaction rate of a non-steady state catalytic process can be determined without any pre-assumption regarding the type of kinetic dependence. The Y-procedure is the basis for advanced software for non-steady state kinetic data interpretation. The Y-procedure can be used to relate changes in the catalytic reaction rate and kinetic parameters to changes in the surface composition (storage) of a catalyst.

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

Thin-zone TAP reactor is presented as a basis of the new state-by-state transient screening approach which has been proposed by the authors for non-steady-state kinetic characterization of industrial catalysts. The general thin-zone TAP reactor model is described, and its mathematical status is justified analytically. It is shown that this model provides high enough accuracy to be applicable in the wide conversion interval (up to 90%), which is an important advantage of this approach compared with the traditional differential reactor.

A general theory of multi-response state-defining experiments for a multi-zone temporal analysis of products reactor, is developed using the Laplace transform and a generalization of the transfer matrix formalism previously introduced for single-response experiments. The theory provides a unified approach to multi-response modelling and an efficient means to compute the actual profiles of gases and surface species concentration in the reactor, as well as the values of the outlet fluxes numerically, using e.g. fast fourier transform. We investigate the kinetic/mathematical conditions under which explicit expressions for the moments of the outlet fluxes and series expansions for their transient values can be obtained. Several important examples are analyzed in detail, leading to simple criteria of instantaneousness for different reactants within a catalytic mechanism. In the case of thin-zone reactors, the criteria are significantly simplified, with equality (within experimental error) of “shifted residence times” of reactants being proposed as the criterion of instantaneousness. This is illustrated for the oxidation of propene on a vanadium oxide catalyst.

This paper presents a new strategy, “state-by-state transient screening”, for kinetic characterization of states of a multicomponent catalyst as applied to TAP pulse-response experiments. The key idea is to perform an insignificant chemical perturbation of the catalytic system so that the known essential characteristics of the catalyst (e.g. oxidation degree) do not change during the experiment. Two types of catalytic substances can be distinguished: catalyst state substances, which determine the catalyst state, and catalyst dynamic substances, which are created by the perturbation. The general methodological and theoretical framework for multi-pulse TAP experiments is developed, and the general model for a one-pulse TAP experiment is solved. The primary kinetic characteristics, basic kinetic coefficients, are extracted from diffusion–reaction data and calculated as functions of experimentally measured exit-flow moments without assumptions regarding the detailed kinetic mechanism. The new strategy presented in this paper provides essential information, which can be a basis for developing a detailed reaction mechanism. The theoretical results are illustrated using furan oxidation over a VPO catalyst.

The thin-zone TAP reactor (TZTR) model of a multi-pulse experiment is computationally validated based on a more general three-zone reactor model. The analysis is focused on the uniformity of gaseous and surface concentrations in the catalyst zone, which is a key property of TZTR model. It is shown that if the TZTR model is valid for the first pulse in a multi-pulse experiment then it is valid for all subsequent pulses. For a typical reactor packing (the ratio of the thin-zone thickness to the length of reactor is 1/30) and with the first pulse conversion up to 97%, the gaseous and surface concentration profiles can be considered uniform and characterized by their spatial average values only. The reaction rate in the catalyst zone may also be characterized by its spatial average value and directly related to the spatial average gaseous and surface concentrations, in the same way as an elementary rate is related to concentrations. As a result of these unique characteristics, the TZTR may be considered a “perfectly-mixed” reactor even at high conversion.

The rigorous three-dimensional theory for a TAP (Temporal Analysis of Products) Knudsen pulse response experiment is developed for the combined diffusion and reaction cases for multi-zone packing, in order to determine the domain of validity of the commonly used one-dimensional model. The analysis is based on a specific modification of the transfer matrix formalism previously introduced for one-dimensional TAP-reactor models. The outlet flux can be written as a sum of three independent terms: one corresponding to the one-dimensional solution, a term accounting for axially symmetric radial nonuniformity, and a term needed for a fully three-dimensional model. The theory provides a method for estimating the accuracy of the one-dimensional model and for finding the domain of its validity. The theory is illustrated by the diffusion-only case for a one-zone reactor. It is shown that the one-dimensional model is valid for aspect ratios L/R>3.5.

A general theory of single-pulse state-defining experiments for a multi-zone TAP (temporal analysis of products) reactor, is developed using the Laplace transform formalism; the theory gives explicit expressions for the moments of the outlet flux, series expansions for the transient values of this flux, and offers an efficient means to compute the actual profiles of gas concentration in the reactor and the values of the outlet flux numerically, using e.g. Fast Fourier Transform. The central concept of the theory is the global transfer matrix equation, which determines completely the dynamic behavior of the reactor. Using efficient computer algebra methods, the theory generates previous theoretical results reported in the literature for all the known TAP–reactor configurations, and yields new results related to the reversible adsorption/reaction–diffusion case and the thin-zone case. It can be used for further theoretical studies in the area of diffusion/reaction dynamics.

A new reactor model for TAP pulse response experiments called a ‘thin-zone reactor’ is developed and applied to irreversible adsorption/reaction and reversible adsorption. In a thin-zone reactor, concentration gradients across the catalyst bed can be neglected, and diffusion and chemical reaction can be separated. The expressions for kinetic parameters for a thin-zone reactor can be calculated using moments, and are much simpler than the expressions for a one-zone or a three-zone reactor. The thin-zone model is particularly useful for investigating fast chemical reactions, since the extent of reaction can be controlled by the thickness and position of the catalyst zone. The expression for conversion in the case of irreversible adsorption/reaction in a thin-zone reactor is governed by a relationship that is analogous to the expression for first-order reaction in a CSTR. Moment based ‘fingerprints’ are defined for irreversible adsorption, reversible adsorption, and diffusion. The thin-zone model is used to determine kinetic parameters for the oxidation of propene over a VPO catalyst.