Temperature response to reactant concentration perturbations in a packed‐bed reactor

Unsteady‐state operations are known to enhance the performance of some packed‐bed reactor systems. However, negative effects of this type of operation should not be neglected. Temperature excursions developed during transients may accelerate some deactivation mechanisms, reducing catalyst lifetime and selectivity. Temperature response to perturbations in reactant concentration was studied for CO oxidation over Pt/Al₂O₃ in a packed‐bed reactor. Experiments were conducted in the CO concentration range for which multiple steady states are observed. Temperature and concentration profiles in the packed‐bed reactor at steady state were found to depend on the dynamic history of the reactor prior to the steady‐state condition.     

Influence of cycle parameters on periodically operated fluidised bed reactor for CH4 autoreforming

Autothermal reforming of CH₄ has been studied under both periodic and steady state conditions. The investigation was conducted over Co–NiO in a fluidised bed reactor at 873 K and 101.32 kPa. Cycle periods of 1–40 min were used whilst the cycle split, S_ox (with respect to the O₂-rich cycle) was varied from 0.1 to 0.9. Generally, CH₄ oxidation stimulated CO formation, however, steam reforming yielded predominantly CO₂ and H₂. Although O₂-rich cycling (S_ox≥0.5) was detrimental to H₂ formation, H₂O-rich cycling resulted in a 15% improvement in steady state H₂ formation. Theoretical as well as experimental investigations pointed to a resonant frequency of about 6.7 mHz for CH₄ oxidation to produce super steady state H₂ yields. By periodic operation, it is possible to tune H₂/CO ratios over the range 2.5–7 for the same feed composition. Interestingly, S_ox=0.1 yielded the highest ratios, whereas the lowest ratios were attained at S_ox=0.9. Periodic composition cycling introduces a more flexible approach to reactor operation — H₂/CO can be easily modulated by varying the cycle parameters — compared to steady state operation.     

Effect of gas feed flow and gas composition modulation on activated carbon performance in phenol wet air oxidation

Modulation of gas feed composition (air/N₂ cycling) and gas feed flow (on-off air cycling) was investigated in the catalytic wet air oxidation of phenol over activated carbon (AC). Fifty hours lasting experiments were conducted in a laboratory trickle bed reactor at 140-160 °C, 2 bar of oxygen partial pressure and different splits and periods to determine the set of cycling parameters that optimise the periodic reactor operation. To follow the dynamic behaviour of the phenol oxidation, temperature and conversion were continuously monitored by means of computerised data acquisition and automatic liquid sampling. Several long term tests over 144 h were also run using both periodic operating strategies to compare the activity and stability of AC with those obtained in a steady state operation at otherwise same conditions. The results show that, depending on the selection of split and period, modulation of the gas phase significantly improves the stability of AC compared to steady state operation, thereby performing a superior long term phenol conversion.     

Performance Enhancement by Unsteady‐State Reactor Operation: Theoretical Analysis for Two‐Sites Kinetic Model

Theoretical analysis of the reactor performance under unsteady‐state conditions was carried out. The reactions are described by two kinetic models, which involve the participation in catalytic reaction of two types of active sites. The kinetic model I assumes the blocking of one of the active sites by a reactant, and the kinetic model II suggests a transformation of active sites of one type into another under the influence of the reaction temperature. The unsteady‐state conditions on the catalyst surface are supposed to be created (i) by forced oscillations of temperature and concentration in the reactor inlet (periodic operation of reactor) and (ii) by catalyst circulation between two reactors in a dual‐reactor system (spatial regulation). The influence of various parameters like concentration of reactant, cycle split, length of period of forced oscillations, temperatures and the ratio of catalyst volumes in the dual‐reactor was investigated with respect to the yield of the desired product. It is shown that for both cases of unsteady‐state conditions (periodic reactor operation as well as in a dual‐reactor system), a mean reaction rate predicted by the kinetic model I was up to two times higher than the steady‐state value. The kinetic model II shows a 20 % increase of the selectivity towards the desired product.     

A stochastic treatment of unimolecular reactions in an unsteady state continuous flow system

A stochastic approach, namely a continuous time Markov chain (Markov process), is employed to analyze and model, in a unified fashion, both the kinetics of unimolecular reactions and mixing accompanied by flow in a continuous flow reactor under an unsteady state operation; the results reduce to those under the corresponding steady state operation in the limit as t→∞. This approach can be applied to both the time homogeneous and heterogeneous processes. The transitional distributions of the number of molecules of each type inside the reactor as well as at the exit are formulated. The treatment leads to the general expressions for the transient internal and exit age distributions of molecules in the flow reactor. The life time distribution of molecules under steady state is also derived. The statistical basis of the residence time distribution theory for flow reactors is clarified. The approach is illustrated with two examples.     

Modelling FCC units under steady and unsteady state conditions

A FCC phenomenological‐based model is presented in this study. This model accounts for the behaviour of the riser, the stripper and the regenerator. Both the reactor and the regenerator are incorporated in the model using detailed reaction kinetics. Catalyst regeneration allows for both catalytic and non‐catalyzed combustion of CO to CO₂. Overall, the model is constituted by a set of ordinary differential equations, relatively easy to solve and suitable for steady and unsteady state simulation of FCC units. The proposed model avoids, as much as possible, empirical expressions being suitable for simulation of industrial FCC units and process control studies.     

Reaction rate hysteresis in the hydrotreating of thiophene in wide‐ and narrow‐pore catalysts during temperature cycling

The influence of capillary condensation of reagents in porous catalysts for hydrodesulfurization at temperatures below 195°C and at pressures around 0.95 MPa was investigated experimentally and by modelling. The rate of reaction of thiophene in a solution of n‐heptane was studied in steady and dynamic modes over two Ni‐Mo/γ‐Al₂O₃ mesoporous catalysts with mean pore diameters differing by 2.6‐fold. Pronounced rate hysteresis was observed under thermal cycling for the narrow‐pore catalyst, but less so for the wide‐pore catalyst. The process was modelled for a mixed‐flow reactor under steady and dynamic conditions by means of the Kelvin equation and introducing two kinetic models for liquid and vapour phase to estimate the concentration of reactant in both phases. The model exhibited good agreement with hysteresis results.     

OPERATION POLICIES FOR A GAS—LIQUID STIRRED TANK REACTOR

The operation of a gas-liquid stirred tank reactor is simulated, including batch operation, steady and unsteady state, continuous operation and cyclic variable volume operation. A pseudo first order reaction is considered. Analytical expressions for the enhancement factor of gas absorption rate are derived for each case, and productivity obtainable under different operation policies is evaluated. Results obtained are shown graphically for specific cases for the purpose of demonstrating the influence of some of the parameters on the system

The equations as presented can be easily extended to other kinetics, and serve as a useful guide for optimum operational policies in a gas-liquid stirred tank reactor.     

Modeling and optimization of the cyclic steady state operation of adsorptive reactors

Adsorptive reactors(AR),in which an adsorptive functionality is incorporated into the catalytic reactors,offer enhanced performance over their conventional counterparts due to the effective manipulation of concentration and temperature profiles.The operation of these attractive reactors is,however,inherently unsteady state,complicating the design and operation of such sorption-enhanced processes.In order to capture,comprehend and capitalize upon the rich dynamic texture of adsorptive reactors,it is necessary to employ cyclic steady state algorithms describing the entire reaction-adsorption/desorption cycle.The stability of this cyclic steady state is of great importance for the design and operation of adsorptive reactors.In this paper,the cyclic steady state of previously proposed novel adsorptive reactor designs has been calculated and then optimized to give maximum space–time yields.The results obtained revealed unambiguously that an improvement potential of up to multifold level could be attained under the optimized cyclic steady state conditions.This additional improvement resulted from the reduction of the regeneration time well below the reaction-adsorption time,which means,in turn,more space–time yield.     

OPERATION POLICIES FOR A GAS—LIQUID STIRRED TANK REACTOR

The operation of a gas-liquid stirred tank reactor is simulated, including batch operation, steady and unsteady state, continuous operation and cyclic variable volume operation. A pseudo first order reaction is considered. Analytical expressions for the enhancement factor of gas absorption rate are derived for each case, and productivity obtainable under different operation policies is evaluated. Results obtained are shown graphically for specific cases for the purpose of demonstrating the influence of some of the parameters on the system

The equations as presented can be easily extended to other kinetics, and serve as a useful guide for optimum operational policies in a gas-liquid stirred tank reactor.     

Adsorption/desorption models: How useful for predicting reaction rates under cyclic operation

A computational study is reported of the behaviour of three catalytic reaction models containing conventional adsorption, desorption, and surface reaction steps under conditions of forced composition cycling in a mixed reactor. The models contained varying degrees of non-linearity. With long cycle periods, the time-average rate of reaction asymptotically approached the quasi-steady state. Time-average rate behaviour was found to be bounded by the asymptotes of quasi-steady state rate under slow cycling, and the relaxed steady state under rapid cycling. It is concluded that the approach used until now to model catalytic reactions is very likely inadequate to describe the dynamics of forced cyclic operation observed in a number of experimental systems     

The effects of oscillatory feeding of CO and O2 on the performance of a monolithic catalytic converter of automobile exhaust gas: a modelling study

A monolithic catalytic converter of automobile exhaust gas was modelled in order to assess the effects of oscillatory feeding on the performance of the reactor with respect to CO oxidation by O₂. Simulations were performed with an oscillating feed composition of CO and O₂. The influence of frequency, amplitude, phase angle and ratio of reactants in the feed on the time average CO conversion was investigated. An improvement relative to the steady state conversion of 10% maximum is obtained at temperatures below the light-off temperature, at frequencies below 0.1 Hz and an amplitude of 15%. The reverse effect is obtained from temperatures slightly above the light-off temperature upwards. These effects are strongest when CO and O₂ oscillate in counterphase. The explanation for this effect is given in terms of strongly changing surface coverage during cycling of the feed concentrations.     

Forced temperature cycling of a catalyst layer and its application to propylene oxidation

In this study, a new reaction device suited for forced temperature cycling was developed. This device has a heating element in the reaction tube, and forced temperature cycling was realized by operating this element intermittently. The energy needed for the operation was about 20 W, which is much less than that required to operate reactors used in previous studies of temperature cycling. This reactor was used to examine the effect of periodic operation on the oxidation of propylene. It was found that the conversion under periodic conditions was higher than that observed under steady state. In addition, the reaction system approached a relaxed steady state as the cycle time was reduced to 1 s. The effect of forced temperature cycling on propylene oxidation was successfully demonstrated.     

Stady‐state and Dynamical Simulation of an Autothermal Gasoline Reformer

Detailed numerical simulation is an important tool for the analysis, development and optimization of new reactor systems. In this contribution results of steady‐state and dynamic simulations of a hydrogen production system for mobile applications based on gasoline are presented. The system consists of an autothermal reformer, a high temperature shift reactor and a countercurrent heat exchanger for heat integration. The simulations are based on 1‐D, multiphase, dynamic models, which are solved with the simulation tool PDEX‐Pack. Firstly steady‐state and dynamic simulations of the autothermal reformer alone are presented. Concentration and temperature profiles in the reformer under different operation conditions are discussed and possibilities to improve the performance are assessed. Dynamic simulations of load change and cold start show the fast dynamic response of the reformer due to its low thermal mass. Simulations of the coupled system underline the impact of the heat exchanger design for the system performance, especially under dynamic conditions. Finally dynamic simulations of a possible cold start strategy for the system are discussed.     

实验室绝热反应器的开发和设计

在绝热反应器中进行工程动力学的研究是一种有益的方法。本文介绍了实验室绝热反应器的设计方法及其结构。实验测定了反应器的绝热效果，并计算了在操作条件改变后，反应器的非稳态传热情况。计算结果表明，对本实验装置操作条件获得重新稳定所需时间为０．８４７ｈ。     

Evaluation of the potential of periodically operated reactors based on the second order frequency response function

A new, fast and easy method for analysing the potential for improving reactor performance by replacing steady state by forced periodic operation is presented. The method is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs). The second order frequency response function, which corresponds to the dominant term of the non-periodic (DC) component, G₂(ω, −ω), is mainly responsible for the average performance of the periodically operated processes. Based on that, in order to evaluate the potential of periodic reactor operation, it is enough to derive and analyze G₂(ω, −ω). The sign of this function defines the sign of the DC component and reveals whether a performance improvement by cycling is possible compared to optimal steady state process. The method is used to analyze the periodic performance of a continuous stirred tank reactor (CSTR), a plug flow tubular reactor (PFTR) and a dispersive flow tubular reactor (DFTR), after introducing periodic changes of the input concentrations. A homogeneous, n-th order reaction is studied under isothermal conditions.     

Development and simulation studies of an unsteady state biofilter model for the treatment of cyclic air emissions of an α‐pinene gas stream

This paper describes the development and simulation of an unsteady state biofilter model used to predict dynamic behaviour of cyclically‐operated biofilters and compares it with experimental results obtained from three, parallel, bench‐scale biofilters treating both periodically fluctuating concentrations and constant concentrations of an α‐pinene‐laden gas stream. The dynamic model, using kinetic parameters estimated from the constant concentration biofilter, was able to predict the performance of cyclic biofilters operating at short cycle periods (ie, in the order of minutes and hours). Steady state kinetic data from a constant concentration biofilter can be used to predict unsteady state biofilter operation. At a 24 h cycle period, the dynamic model compared well with experimental results. For long cycle periods (ie, hours and days), removal efficiency decreased after periods of non‐loading: the longer the period of non‐loading, the poorer the biofilter's performance at the re‐commencement of pollutant loading. At longer time scales the model did not effectively predict transient behaviour, as adsorption and changes in kinetic parameters were not accounted for. Modelling results showed that similar biofiltration performance for the cyclic and constant concentration biofiltration of α‐pinene is expected for biofilters operating solely in the first order kinetics regime. Poorer performance for cyclic biofilters following Monod kinetics spanning the entire kinetics range is expected as the cycle amplitude increases. The most important parameters affecting the performance of a cyclically‐operated biofilter with short cycle periods are: amplitude of cyclic fluctuations, C_{g, max}/C_g, relative value of the half‐saturation constant in the Monod expression, K_s, and effective diffusivity of α‐pinene in the biofilm, D_e. Copyright © 2005 Society of Chemical Industry     

In situ perpetual regeneration of a Ni-faujasite methanation catalyst

A prolonged lifetime of a Ni-faujasite methanation catalyst and a stable rate of methanation can be achieved by operating the fluidized catalyst bed under unsteady state conditions. A higher rate of methanation is accompanied by a shift in selectivity compared to a steady state operation due to an enhanced disproportionation of CO.     

The kinetics of methanol oxidation on a supported Pd model catalyst: molecular beam and TR-IRAS experiments

Combining a multi-molecular-beam approach and in situ time-resolved IR reflection absorption spectroscopy (TR-IRAS), we investigate the kinetics of methanol oxidation on a well-defined supported Pd model catalyst. The model catalyst is prepared under ultra-high-vacuum (UHV) conditions by Pd deposition onto a well-ordered Al₂O₃ film grown on NiAl (110). In previous studies, this system has been characterized in detail with respect to its geometric and electronic structure and its adsorption properties. Crossing molecular beams of methanol and oxygen on the sample surface, we systematically probe the rate of total methanol oxidation to CO₂ as a function of surface temperature and reactant fluxes. The results are compared with equivalent experiments for the related CO oxidation reaction. Pronounced differences are observed in the kinetics of the two processes, both under steady state and under transient conditions. The dissimilarities can be related to the dehydrogenation step of methanol, which is found to be strongly inhibited at high oxygen coverage. At low oxygen fluxes, CO is formed as the main product of methanol decomposition. Via a three-beam isotope-exchange experiment combined with TR-IRAS, the kinetics of CO formation is investigated as a function of reactant fluxes and surface temperature. Mean-field simulations of the kinetics are performed in a two-step procedure. First, the kinetics of CO oxidation is described, both under steady state and transient conditions. In a second step the microkinetic model is extended to include the formation of CO formed by methanol dehydrogenation. A comparison with the experimental data indicates that the transient kinetics cannot be fully described by a mean-field approach.