A sequential approach to modeling catalytic reactions in packed-bed reactors

A sequential modeling approach is proposed to simulate catalytic reactions in packed-bed reactors. The hydrogenation of alpha-methylstyrene and wet oxidation of phenol are selected as studied cases. The modeling scheme combines a reactor scale axial dispersion model with a pellet scale model. Without involving any fitting parameters, such an approach accounts for the non-linear reaction kinetics expression and different types of pellet-liquid wetting contact. To validate the developed modeling scheme and the parallel approach reported in the literature, the experimental observations for hydrogenation of alpha-methylstyrene to cumene have been employed. The predicted results by both approaches agree reasonably with the experimental data for both gas- and liquid-limited reaction. The proposed sequential approach was also used to simulate the dynamic performance of the reactor and pellets for the catalytic wet oxidation of aqueous phenol over a newly developed but rapidly deactivated catalyst (MnO₂/CeO₂). The simulation results for the catalytic wet oxidation process by both approaches were compared. The simulation describes the time evolution of the catalyst stability at different pellet points along the reactor axis. The performance of trickle beds and packed bubble columns over a range of operating conditions were also investigated, and packed bubble columns were found to achieve higher phenol conversion at the cost of more rapid catalyst deactivation.     

Forced unsteady-state processes in heterogeneous catalytic reactors

The main techniques of studying and designing heterogeneous catalytic processes under forced unsteady-state operation (FUSO) are discussed in this review. Topics included are: a) why FUSOs are theoretically more efficient than conventional steady-state processes?; b) how can a FUSO be devised?; c) reverse-flow operation; d) partial oxidation in a circulating fluidized bed; e) processes that could be attractive under FUSO at a commercial scale, but reasons why this has not been successfully accomplished; f) FUSO systems that have not been used on a commercial scale, such as reaction chromatography, input composition cycling, input temperature cycling, and g) what could be done to encourage use of FUSOs by industry? This review demonstrates the large amounts of data that have been collected on processes proposed for FUSO. Translating these efforts into commercial success becomes possible only when researchers understand thoroughly the fundamentals of the FUSO system they are working on. An overview of past and current research suggests that a catalytic process performed optimally under FUSO will never be less efficient than an optimal steady-state process.     

Development and analysis of heterogeneous catalytic processes and reactors

A retrospective review and a review of the current state are given for the problem of the development and analysis of heterogeneous catalytic processes and reactors. Advanced approaches to the study of kinetics and the engineering design of catalytic reactions are discussed. The advantages and drawbacks of the main types and structures of industrial catalytic reactors are demonstrated by the examples of present-day catalytic processes and reactors for basic organic and petrochemical synthesis. The operation of several industrial catalytic reactors is analyzed in order to clarify the causes of deterioration of design performance and/or to find ways for the process intensification in operating plants.     

A heterogeneous one-dimensional model for non-adiabatic fixed bed catalytic reactors

A heterogeneous one dimensional model which takes separately into account the heat transfer through the solid and fluid phases is introduced. The response of this model is compared with that of the heterogeneous two-dimensional model, and a very good agreement, especially at mild conditions, is obtained. Its performance is better than previous one dimensional models and the deviations are explained in tenns of the operative conditions and of the value of dimensionless groups. Conditions at which the different one and two-dimensional models are recommended to be used are presented.     

Modelling forced periodic operation of catalytic reactors

The kinetic adsorption/desorption or AD models used to predict product selectivities obtained through forced-feed concentration cycling have been re-examined. Selectivity improvement results from model structure and nonlinear rates of reaction. The relaxed-steady state bound to periodic operation was found to be predictable from steady state rates for the kinetic model used. Adsorption/desorption models predict no rate improvement for periodic operation. Also they fail to predict experimental observations that are now fairly extensive.     

Challenges for the periodic operation of trickle-bed catalytic reactors

Since the earliest publications just over a decade ago, the literature on periodic operation of trickle beds has grown rapidly. There are now over 30 published papers. Two applications, flow and feed composition modulation, for control of hot spots in large-scale reactors are sufficiently advanced for full-scale implementation if that has not already taken place. Models are now available that are capable of representing the time-average performance of periodically operated trickle beds, but these are not detailed enough to reproduce all of the transient behavior observed. Much about performance under periodic operation remains to be discovered. Research challenges are discussed under separate types of periodic operation: flow interruption, flow augmentation for hot spot control, feed composition modulation for hot spot control and to improve rate and/or to modify selectivity, and flow variation for enlargement of the pulse flow regime.     

A program package for simulation of heterogeneous catalytic reactions in ideal reactors

A new interactive program package for kinetic simulations is presented. With the package arbitrary heterogeneous catalytic reaction sequences can be simulated in gradientless, differential and integral plug-flow reactors. The underlying numerical algorithms are presented and tested with realistic heterogeneous catalytic systems: decomposition of N₂O and oxidation of CO. The program package can be used in kinetic research and in reactor simulations.     

Periodic operation of transport reactors for catalytic reactions

Based on plug flow of gas and catalyst particles and concentration dependent deactivation kinetics, the performance of transport reactors under a periodic (rectangular pulse) inlet concentration is analysed for improvement in conversion and extent of catalyst decay. The effects of reaction and deactivation orders, reaction and deactivation constant groups, and γ (cycle split) on the performance of the reactors are evaluated theoretically. For reaction orders greater than one, periodic operation improves conversion. Resonance behaviour is observed for certain combinations of parameters. For identical operating conditions vertical upflow, downflow and horizontal flow reactors are compared. Conversion in upflow reactors is higher than that in either horizontal flow or downflow reactors. However, catalyst decay is the least in downflow reactors.     

Some problems in the design of Ziegler-type catalytic reactors

Since the discovery of the remarkable properties of the Ziegler heterogeneous stereoregulating catalysts, an enormous amount of effort has been expended on investigating the mechanisms of such reactions. By comparison, the design of industrial scale reactors has not been discussed so widely. Nevertheless, as an example of the complex interactions between physical and chemical processes, it offers a considerable challenge to the techniques which have been developed over the past few years in reactor design. This paper reviews the present state of knowledge in this area and indicates where basic data are required. It also considers the potential benefits of some of the techniques being developed for control and optimisation of such systems.     

Application of the pseudoadiabatic operation to catalytic fixed bed reactors case of the orthoxylene oxidation

This is a further contribution to establish the crucial interest of appropriately considering the influence of a non-boiling cooling flow when modeling and operating exothermal multitubular catalytic reactors. Particularly, the characteristics of a condition named “pseudoadiabatic operation” (PO) where the maximum temperature appears at the reactor exit is analysed. The purpose of the present study is to illustrate the peculiarities of the PO and their significance for the design and operation of orthoxylene oxidation multitubular catalytic reactors.     

A simple additivity relation for analysis of heterogeneous catalytic reactors with first order reaction

An isothermal heterogeneous reactor with first order kinetics is characterized by two virtual maximum efficiencies, $\text{N}$_kin and $\text{N}$_tr, which are readily determined from the appropriate kinetic and transport parameters. The actual efficiency of the reactor, which is related to the conversion, X, by X = 1?e^?$\text{N}$, can be accurately approximated as $\text{N}$^?1 = $\text{N}$^?1_tr + $\text{N}$^?1_kin. The overall additivity relation offers a simple approach either to predict the conversion or to extract the kinetic or transport parameters when the reactor behavior is affected by both reaction and diffusion.     

Integrated approach for the intensification of heterogeneous catalytic processes

The integrated approach for the design of solid catalysts for process intensification is presented addressing simultaneously different levels of scale and complexity involved in the development starting from the molecular/nano-scale of the active phase optimization up to the macro-scale of the catalytic reactor design. The feasibility of this approach is demonstrated through case studies carried out in our group.     

A rigorous approach to photochemicals reactors

The modelling of photochemical reactors has been rigorously treated describing the radiation field within the realm of radiant energy transfer. This kind of approach causes a heavy integro-differential problem to arise any time the reacting species is the absorbing one while the differential nature of the model equations is maintained in the case of photosensitized reactions in a purely absorbing medium. An annular photoreactor has been considered for this last situation and the influence on the absorption process of the most parameters has been investigated for both the cases of a reactor shielded and unshielded by a reflector.     

Optimal temperature policies for catalytic transport reactors under periodic operation

The influence of inlet gas concentration cycling on the optimal temperature policy of catalytic transport reactors is studied theoretically. The model considered is based on plug flow of gas and catalyst particles with negligible interand intra-particle diffusional resistances and concentration dependent deactivation kinetics. To utilise the concentration of the reactant and the activity of the deactivating catalyst fully a proper temperature sequence along the reactor is needed. Thus, a general optimal temperature policy using the continuous minimum principle is derived for the reactor under periodic operation. The model equations are solved analytically for gas concentration, activity and temperature profiles. Resonance behaviour (maximum in conversion with pulse width) is obtained using the optimal temperature policy for certain sets of parameters. The effects of activation energy groups, reaction and deactivation constant groups and inlet temperature on the optimal temperature policy under periodic operation are evaluated. In all cases an improvement in conversion with the optimal temperature policy under periodic operation over that with an isothermal policy under periodic operation is obtained. A suboptimal policy, comprising constant temperature over different reactor sections, which is useful for implementation purposes is also discussed.     

A novel approach for describing mixing effects in homogeneous reactors

The Liapunov–Schmidt technique of classical bifurcation theory is used to spatially average the convection–diffusion–reaction (CDR) equations over smaller time/length scales to obtain low-dimensional two-mode models for describing mixing effects due to local diffusion, velocity gradients and reactions. For the cases of isothermal homogeneous tubular, loop/recycle and tank reactors, the two-mode models are described by a pair of coupled balance equations for the mixing-cup (C_m) and spatial average (〈C〉) concentrations. The global equation describes the variation of C_m with residence time (or position) in the reactor, while the local equation expresses the coupling between local diffusion, velocity gradients and reaction at the local scales, in terms of the difference between C_m and 〈C〉. It is shown that the two-mode models have many similarities with the classical two-phase models of heterogeneous catalytic reactors with the concept of transfer between phases being replaced by that of exchange between the two-modes. It is also shown that when the local Damköhler number (ratio of local diffusion to reaction time) is small, the solution of two-mode models approaches the exact solution of full CDR equations, while for fast reactions the two-mode models retain all the qualitative features of the latter. Examples are provided to illustrate the usefulness of these two-mode models in predicting micromixing effects on homogeneous reactions.     

On the use of adsorption/desorption models to describe the forced periodic operation of catalytic reactors

A model, of the adsorption/desorption type, is used to examine the behavior of a catalytic reaction system during forced cycling of the feed compositio     

Remarks upon the modelling of heterogeneous catalytic reactors – the single fluid-solid cases

To our benefit, the modelling of fluid-solid catalyzed reaction-reactor systems has long been the keen concern of Hanns Paul Hofmann. In the light of his instruction we remark upon key aspects of modelling for the (a) fixed bed (b) fluid bed and (c) moving bed/transport line reactors. There emerges from such analyses a properly renewed awareness of the need for a more sophisticated respect for reliable physical-chemical data. As Hanns has taught us, our models are no btter than our data.     

A systematic approach for the design of UV reactors using computational fluid dynamics

A wide variation exists in the geometries of UV reactors, which results in completely different hydrodynamics and therefore large differences with respect to the disinfection and oxidation performance. Among the large number of reactor types, it is not known beforehand which reactor type has the best performance with respect to disinfection or oxidation, and if such a reactor is the best reactor out of all the possible reactor designs. In this research, a systematic approach for the design of UV reactors is followed that makes use of computational fluid dynamics (CFD) modeling. To that end, the inactivation of Bacillus subtilis and degradation of atrazine was determined for a wide range of UV systems by means of CFD. The efficacy of UV systems was evaluated and improvements were made by taking measures that increase the mean dose and/or narrow the dose distribution, such as placing mirrors, enhancing the mixing and placing reactors in series. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A novel approach to scheduling multipurpose batch plants using unit‐slots

Several models for scheduling multipurpose batch plants exist in the literature. The models using unit‐specific event points have shown better solution efficiency on various literature examples. This article presents a novel approach to scheduling multipurpose batch plants, which uses unit‐slots instead of process‐slots to manage shared resources such as material storage. We develop two slightly different models that are even more compact and simpler than that of Sundaramoorthy and Karimi, Chem Eng Sci. 2005;60:2679–2702. Although we focus on material as a shared resource, our multi‐grid approach rationalizes, generalizes, and improves the current multi‐grid approaches for scheduling with shared resources. Our models allow nonsimultaneous transfers of materials into and out of a batch. We show by an example that this flexibility can give better schedules than those from existing models in some cases. Furthermore, our approach uses fewer slots (event‐points) on some examples than even those required by the most recent unit‐specific event‐based model. Numerical evaluation using literature examples shows significant gains in solution efficiency from the use of unit‐slots except where the number of unit‐slots required for the optimal solution equals that of process slots. We also highlight the importance of constraint sequencing in GAMS implementation for evaluating mixed‐integer linear programming based scheduling models fairly. © 2009 American Institute of Chemical Engineers AIChE J, 2010