The prediction of the performance of packed-bed catalytic reactors in the air-oxidation of o-xylene

The kinetics of the catalytic air-oxidation of o-xylene to phthalic anhydride over various commercial V₂O₂ and TiO₂-V₂O₂ catalysts are extended and a model derived which correctly predicts the temperature and yield profiles in a quasi-isothermal fixed-bed reactor of commercial dimensions. The model predicts the relative freedom from thermal “run-away” of commercial fixed-bed reactors and is used to demonstrate the possibilities of operation at elevated Xylene concentrations.In what follows, XH, TA, PI and PA refer to o-xylene o-tolualdehyde, phthalide and phthalic anhydride respectively, sometimes abbreviated to A, B, C and D.     

Estimating spectral properties of the thermal instability in packed-bed reactors

In response to transient perturbations, the packed-bed reactor (PBR) can exhibit dynamic thermal instability in the form of resonant amplification of process disturbances. Based on linearized PBR model we derive estimates of the resonance frequency, the frequency range where amplification takes place and the maximum amplification. We also discuss the velocity of perturbation waves and how nonlinearity of reactor response to finite-size perturbations limits the amplification predicted by the linear analysis.     

Global-coupling induced temperature patterns on top of packed-bed reactors

Infrared thermography was used to study the formation and dynamics of hot zones on top of a shallow packed bed reactor in which CO was oxidized by spherical Pd/Al₂O₃ catalytic pellets. The impact of global coupling between the gas on top of the bed and the catalyst was studied by changing the residence time of the gas. The global coupling had a strong impact on the selection, dynamics and stability of the observed hot zone motions (breathing, anti-phase and rotation).     

On the dynamical instability of packed-bed reactors in the presence of catalyst deactivation

Due to the thermal instability of the packed-bed reactor running an exothermic reaction, unsteady-state operation (for example a fluctuating inflow temperature) can result in a variety of thermal responses. These include the amplification of input temperature perturbations and high-temperature pre-extinction waves. Catalyst deactivation adds further dynamical features to these scenarios. We explore them numerically, using a first-order exothermic reaction and a pseudo-homogeneous (single phase) model of the PBR together with a first-order deactivation model of the catalyst. At low deactivation rate, moving hot spots are found, as well as a non-uniform activity profile of the catalyst. At high deactivation rate, however, high-temperature waves (so-called pre-extinction waves) are followed by the complete extinction of the reactor. The amplification of input temperature perturbations is generally enhanced by the presence of catalyst deactivation. Finally, a power-law model is derived numerically that predicts the resonance frequency for amplification as a function of operating parameters.     

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.     

Imaging of hydrocarbon reactions in zeolite packed-bed reactors using positron emission profiling

The ability of positron emission profiling (PEP) to measure concentration profiles of molecules labelled with positron-emitting nuclei, such as ¹¹C, ¹³N, and ¹⁵O, inside chemical reactors has been demonstrated for the system n-hexane–Pt/H-zeolites under conditions typical of the hydroisomerization reaction. Data obtained in the absence of reaction were first measured and used to model mass transport processes in these biporous, packed-bed reactors. Images obtained under conditions where injected, labelled pulses underwent reaction revealed that the products did not exit the reactor and thus demonstrated the need for in situ measurement. Such experiments should provide a valuable new tool in the study of transient, initial phenomena so often of importance in heterogeneous catalysis, such as “preconditioning” and deactivation. This revised version was published online in July 2006 with corrections to the Cover Date.     

A computational method for determination of the mass-transfer coefficient in packed-bed immobilized enzyme reactors

A computational method was developed that determined the mass-transfer coefficient k_L or the volumetric mass-transfer coefficient k_La in packed-bed immobilized enzyme (IME) reactors. To study the performance of this method, two experimental systems were considered where an enzyme was immobilized on a non-porous support surface (surface-IME system) or within a porous support (pore-IME system). The values of k_L and k_La determined in these packed-bed IME reactor systems were successfully expressed in terms of the substrate concentration at the reactor inlet and the liquid flow rate. Furthermore, the correlations obtained for k_L and k_La were used to calculate the unconverted fractions of substrate at the reactor outlet. Comparison showed that the calculated results were in satisfactory agreement with the experimental values.     

Mathematical analysis of the performance of a packed-bed coimmobilized bioreactor

A model has been developed to describe the performance of a packed-bed coimmobilized biochemical reactor. Each step in the consecutive reaction is assumed to follow Michaelis—Menten type kinetics. The model includes all the limiting steps controlling the rate of reaction and the additional effect of axial dispersion of bulk liquid. The model equations are solved by the explicit finite difference method from the transient to steady-state condition. The effects of various parameters of physical importance on the reactor performance are discussed.     

Application of metallic foams in electrochemical reactors of the filter-press type: Part II Mass transfer performance

This paper focuses on mass transfer characteristics of classical filter-press electrochemical reactors without membranes. In the tested configuration, the working electrode consists of a lane plate with a sheet of foam and the counter-electrode consists of a plane plate with a turbulence promoter. The global mass transfer coefficients of the two electrodes have the same order of magnitude. Moreover, a comparison with literature data shows that their values remain in the range of those previously presented. Due to the high specific surface area of the foam used (A _ve, = 6400 m^–1), the ratio of the surface area of the working electrode to that of the counter electrode is 15. The electroreduction of ferricyanide has been carried out to test the performance of this configuration. The value of the final conversion has been compared to that calculated from mass transfer coefficients and surface areas of the electrodes.List of symbols A _ve dynamic specific surface area of the foam: surface area per volume of material (m^–1) - A_ve dynamic specific surface area of the electrode consisting of a plate and a sheet of foam: surface area per volume of electrode (m^–1) - A _vs static specific surface area (m^–1) - C _in ferricyanide concentration at the inlet of the cell (mol m^–3) - C _out ferricyanide concentration at the outlet of the cell (molm^–3) - D diffusion coefficient (m² s^–1) - d _h equivalent hydraulic diameter, dh = 2lh (l + h)^–1 (m) - F Faraday number (C mol^–1) - h channel thickness (m) - I limiting diffusion current (A) - I _{c a} final limiting diffusion current intensity at the anode (A) - I _cf final limiting diffusion current intensity at the cathode (A) - k _a mass transfer coefficient at the anode (m s^–1) - k _c mass transfer coefficient at the cathode (ms^–1) - k _d mass transfer coefficient (m s^–1) - l channel width (m) - n number of electrons in the electrochemical reaction - Q _v volumetric flow rate in the channel (m³ s^–1) - Re Reynolds number, Re = U ₀ d _h v ^–1 - S active surface area of the electrode (m²) - S _a surface area of the anode (m²) - S _c surface area of the cathode (m ²) - S _c Schmidt number, Sc = v D ^–1 - Sh Sherwood number, Sh = k _d D _h/D - U ₀ superficial velocity (m s^–1) - V volume offered to fluid flow in the volumic electrode (m³) - V volume of one tank reactor in the cascade (m³) - X conversion - X _f final conversion Greek letters porosity - v kinematic viscosity (m² s^–1) - density (kg s^–1) - residence time in a continuous stirred tank reactor = /Q _v (s)     

Mass transfer in fluidised bed electrochemical reactors

Electrochemical mass transfer experiments involving the cathodic deposition of copper from aqueous solutions containing H₂SO₄ have been performed for two distinct cases. (a) Determination of mass transfer rates at a plane wall electrode in the presence of a fluidized bed of inert particles (glass beads). In this work bed height, bed size and fluidization conditions have been varied and a correlating equation:

is suggested as applying over the range

Comparison is made with mass transfer data of several other authors, revealing considerable variance. (b) Determination of mass transfer rates between electrolyte and particles within an active bed of fluidized conducting copper particles. Analysis of the data yields a correlating equation:

in the range

This compares very well with another source for electrolytic fluidized bed mass transfer, but is somewhat lower than other equations for particle to fluid non-electrolytic mass transfer.     

Developments in separator technology for electrochemical reactors

Some of the most important electrochemical processes are performed in so-called “divided cells”. These take their name from the presence of a separator dividing the cell into an anodic and a cathodic compartment, with the purpose of improving product purity and current efficiency. One can distinguish two main classes of separators, according to the physico-chemical constitution and mode of action, ie porous diaphragms and ion-selective membranes. This review outlines the developments accompanying the progress of materials science, to meet the ever more exacting requirements of electrochemical engineering in several fields, such as chlorine-caustic production and water electrolysis.     

Hydrogen peroxide production in trickle-bed electrochemical reactors

A trickle bed electrochemical reactor has been developed for the production of dilute alkaline peroxide solutions by reduction of oxygen. Oxygen gas and sodium hydroxide flow concurrently downward through a cell which consists of a thin packed cathode bed of graphite particles separated from the anode plate by a porous diphragm. Current flows perpendicular to the flow of electrolyte. The effects of current density, oxygen pressure and flow rate, electrolyte concentration and flow rate, graphite particle size, bed thickness and length were investigated. In 2 M NaOH peroxide solutions of 0.8 M have been produced at 60% efficiency with current densities of 1200 A m^–2 and cell voltages of 1.8 V. A bipolar cell stack consisting of five cells has been tested.     

Improvements to the marker pulse technique of characterizing electrochemical reactors

In the marker-pulse method of characterizing electrochemical reactors, unwanted coupling often occurs between the marker and detector electrodes. This makes the transient response hard to analyse and the continuous cross-correlation of input and output signals virtually impossible. The origins of the problem have been investigated and methods of minimizing the effect are described which produce clean transients and acceptable correlograms.     

Transversal moving-front patterns: Criteria and simulations for two-bed and cylindrical shell packed-bed reactors

We show that a moving-front solution in a cylindrical shell packed-bed catalyzing a first-order activated reaction may bifurcate into transversal patterns when Pe_C/Pe_T<ΔT_ad/ΔT_m, i.e. when the ratio of the mass to heat Pe numbers is smaller than the ratio of the adiabatic to maximal temperature rises. This coincides with the previous condition of transversal patterns to emerge in stationary fronts [Pe_C/Pe_T<1 [Viswanathan, G., Bindal, A., Khinast, J., Luss, D., 2005. Stationary transversal hot zones in adiabatic packed-bed reactors. A.I.Ch.E. Journal 51, 3028-3038]] and extends the bifurcations condition to the case of moving fronts. The novel condition cannot be satisfied in a downstream propagating front (ΔT_m/ΔT_ad>1), but for an upstream propagating front (toward the cold reactor inlet) ΔT_m/ΔT_ad<1 and the symmetry breaking can be obtained within a feasible domain of operating conditions (Pe_C/Pe_T>1). It was also assumed that the axial and the transversal Pe numbers vary consistently, i.e. κ_C=Pe_C⊥/Pe_C=κ_T=Pe_T⊥/Pe_T. A similar condition was also obtained using a simplified model composed of two 1-D beds with heat and mass exchange between them.Bifurcation diagram showing domains of transversal patterns is constructed using a learning two-bed model. These predictions are verified by direct numerical simulations of the continuous 2-D cylindrical shell model showing various types of moving transversal patterns within a feasible domain of the state parameters with Pe_C>Pe_T. In the case of varying ratio (κ_C≠κ_T) the pattern domain can be significantly extended toward larger Pe_C/Pe_T.     

Dual substrate limitations in upflow packed-bed biofilm reactors — a theoretical study

The performance of an upflow packed-bed biofilm reactor has been analyzed under dual substrate limitation conditions. The numerical solution of the proposed equations defining the system has been obtained for a wide range of operating conditions for a case of practical significance involving glucose and oxygen as dual substrates. The results show that the inlet glucose concentration defines the limiting substrate at a position near the inlet of the reactor. For inlet glucose concentrations up to 300 mg/l, glucose acts as the limiting substrate. However, for inlet concentrations of 400 mg/l of glucose or higher, oxygen assumes the role of the limiting substrate at that position. For all other positions in the reactor, glucose acts as the limiting substrate, irrespective of its inlet concentration. Extensive computations were performed in order to define regions where glucose, oxygen or both are limiting. The predicted results have been found to be in agreement with the theoretical criteria, proposed in the literature, of determining the limiting substrate.     

Evaluation and improvement of dynamic optimality in electrochemical reactors

A systematic approach for the dynamic optimization problem statement to improve the dynamic optimality in electrochemical reactors is presented in this paper. The formulation takes an account of the diffusion phenomenon in the electrode/electrolyte interface. To demonstrate the present methodology, the optimal time-varying electrode potential for a coupled chemical-electrochemical reaction scheme, that maximizes the production of the desired product in a batch electrochemical reactor with/without recirculation are determined. The dynamic optimization problem statement, based upon this approach, is a nonlinear differential algebraic system, and its solution provides information about the optimal policy. Optimal control policy at different conditions is evaluated using the best-known Pontryagin's maximum principle. The two-point boundary value problem resulting from the application of the maximum principle is then solved using the control vector iteration technique. These optimal time-varying profiles of electrode potential are then compared to the best uniform operation through the relative improvements of the performance index. The application of the proposed approach to two electrochemical systems, described by ordinary differential equations, shows that the existing electrochemical process control strategy could be improved considerably when the proposed method is incorporated.     

Mass-transport problems and some design concepts of electrochemical reactors

Electrochemical cells, designed to operate with reactants at low concentrations, require special provisions to be made for enhancement of mass transport of the reactants to the electrode surface. The different concepts for doing this in industrial or large-scale cells are reviewed. Examples are given of cells and processes in which these ideas have been used. A comprehensive literature survey of the quantitative relationships pertaining to the different configurations is given. The various cell designs are compared on a quantitative basis, usingi _lim, and some advantages and disadvantages are discussed.     

Modeling of a packed-bed electrochemical reactor for producing glyoxylic acid from oxalic acid

A two-dimensional reactor model was established for a packed-bed electrochemical reactor with cooled cathode (PERCC) for producing glyoxylic acid from oxalic acid based on the system's reaction kinetics, mass conservation equation, and the equation of charge conservation in terms of solution-cathode potential to describe the distributions of glyoxylic acid concentration and electrolyte potential in the cathode compartment of the PERCC. The equation for a circulating mixer was also presented to account for the accumulation of glyoxylic acid in the catholyte of a batch electroreduction process. Using the orthogonal collocation approach, the partial differential equations of the model could be converted into sets of algebraic equations and be numerically solved. The effects of operating temperature, conductivity of catholyte, operating cathode potential, and volumetric flow rate of the catholyte on the current efficiency and concentration of glyoxylic acid were simulated and discussed, with emphasis on the current densities generated from main and side reactions. The model was used in a batch operation process and a continuous operation process, with the predicted results being generally in good agreement with the experimental data for both the cases.     

Numerical assessment of diffusion-convection-reaction model for the catalytic abatement of phenolic wastewaters in packed-bed reactors under trickling flow conditions

Computational fluid dynamics (CFD) modeling of trickle-bed reactors with detailed interstitial flow solvers has remained elusive mostly due to the extreme CPU and memory intensive constraints. Here, we developed a comprehensible and scalable CFD model based on the conservative unstructured finite volume methodology to bring new insights from the perspective of catalytic reactor engineering to gas-liquid-solid catalytic wet oxidation. First, the heterogeneous flow constitutive equations of the trickle bed system have been derived by means of diffusion-convection-reaction model coupled within a Volume-of-Fluid framework. The multiphase model was investigated to gain further evidence on how the effect of process variables such as liquid velocity, surface tension and wetting phenomena affect the overall performance of high-pressure trickle-bed reactor. Second, as long as the application of under-relaxation parameters, mesh density, and time stepping strategy play a major role on the final corroboration, several computational runs on the detoxification of liquid pollutants were validated accordingly and evaluated in terms of convergence and stability criteria. Finally, the analysis of spatial mappings for the reaction properties enables us to identify the existence of relevant dry zones and unveil the channeling phenomena within in the trickle-bed reactor.     

Approximate analytical design procedures for plug flow electrochemical reactors

Approaches to the approximate design of plug flow electrochemical reactors are described. In one approach the local reactor voltage balance is combined with the associated material balance to give a single variable equation for the reactor residence time. Other approaches consider qualitatively situations when potentiostatic or galvanostatic conditions may be used as approximations to constant voltage operation.