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• Axial thermowells change the void fraction and cause flow by-passing in fixed beds. • For phthalic anhydride synthesis, thermowells displace hot-spots downstream. • Axial thermowell measurements can underestimate hot-spot temperatures. • Temperature errors do not always decrease with thermowell size, due to local effects. The present study analyses the thermowell system for monitoring temperatures in a fixed bed catalytic reactor for the highly exothermic partial oxidation of o-xylene to phthalic anhydride. Particle-resolved computational fluid dynamics (CFD) simulations are presented for the cases of randomly-packed spheres inside cylindrical tubes with tube-to-particle diameter ratios (N) of 3.96, 5.96 and 7.99. Results are obtained for each N value for cases with inner thermowell radius to outer tube radius ratios of 0.0 (no thermowell), 0.05, 0.1 and 0.2. Comparisons of radial void fraction and axial velocity profiles, axial pressure drop and axial temperature profiles under reaction conditions are presented. The presence of the thermowell did change the mass and heat transfer and reaction inside and around the particles, especially at the bed center. The configurations of catalyst particles were rearranged, leading to changes in voidage, flow and temperature profile. The axial temperature profiles from the thermowells differed from the profiles in the undisturbed beds. [ABSTRACT FROM AUTHOR]

Abstract: Maleic anhydride (MA) is an important chemical intermediate, which is mainly produced by the highly exothermic partial oxidation of n‐butane in fixed bed reactors. Production of maleic anhydride is limited by problems of temperature control and loss of selectivity. Here we present three‐dimensional resolved‐particle computational fluid dynamics (CFD) simulations of n‐butane partial oxidation in a randomly packed bed of 807 spherical catalyst particles. We used a semi‐empirical two‐site surface mechanism from the literature and obtained distributions of temperature, gas phase species, and surface species in the bed. The local selectivity patterns are strongly controlled by the changes in the gas phase flow field, the temperature in the fixed bed, and the weakly adsorbed oxygen surface coverage fraction (λO) profiles inside the particles. Most of the selectivity loss due to product combustion happens in the interior of the catalyst particles, as opposed to the production of MA, which is mainly in the near‐surface layers. We observed loss of selectivity and yield in the centre of the bed at increased bed depths, because of the temperature increase and decrease in gas phase oxygen there. The simulations show sharp λO gradients inside the particles. Near the cooled tube wall λO is strongly affected by the temperature, while at the bed centre gas phase oxygen diffusion limitations contribute to a depleted oxygen surface resulting in lower selectivity. [ABSTRACT FROM AUTHOR]

Resolved-particle 3-D computational fluid dynamics (CFD) simulations are presented of endothermic steam methane reforming in a random packed bed of 807 spherical catalyst particles at a tube-to-particle diameter ratio of N = 5.96 with constant wall heat flux. The fluid flow field is fully coupled to the temperature and species distributions inside the particles. This enables simulation of diffusion, conduction and reaction inside the catalyst particles, as opposed to only surface reactions. The results illustrate 3-D distributions of flow, temperature, species and reaction rates inside a 0.7 m length of packed tube. These show large variations on near-wall particle external surfaces, and non-symmetric distributions inside the catalyst particles on cross-sections through the bed. The detailed CFD approach allows statistical analysis of the particle-to-particle reaction rate variations, the correlation of rate with location in the bed, and the intrinsic variability of radial temperature and species mass fraction profiles. Comparisons to a 1-D reactor tube heterogeneous effective medium model showed that axial profiles of cross-sectional average temperature, species and velocity could not be reproduced using particle-fluid heat and mass transfer coefficients estimated from non-reacting simulations in the same tube. Comparisons to a 2-D reactor tube heterogeneous effective medium model showed good agreement with axial profiles if radial local void fractions and axial velocities were included in the model. Improved agreement with radial temperature profiles resulted from the model with a radially-varying effective radial thermal conductivity. [ABSTRACT FROM AUTHOR]

An implementation of a simplified microkinetics model in three-dimensional computational fluid dynamics (CFD) simulations of an ethylene oxide fixed-bed reactor is proposed. An existing microkinetics model in the literature is simplified to a model with general rate expressions to reduce the complexity of the computations. It then is coupled with CFD simulations of flow in the fixed bed and transport inside the catalyst particles. Illustrative CFD simulations are carried out in a randomly packed bed of 120 spherical particles, which take into account surface species under steady-state conditions in the particles. The proposed approach represents a practical method to integrate simplified surface chemistry with a realistic-scale fixed bed for more in-depth analysis. It is shown that the surface coverages can be greatly affected by the surrounding flow conditions; furthermore, the effects of transport limitations, products, and different inlet compositions on the ethylene oxide selectivity are studied. [ABSTRACT FROM AUTHOR]

A method is developed to couple microkinetics with fluid flow in a fixed bed and transport inside the catalyst particles using computational fluid dynamics. Initially, the microkinetics model is solved for a wide range of different temperatures, and partial pressures. Next, reaction rates are mapped into quadratic multivariate splines. Splines coefficients are then imported into our user-defined function, and consequently the reaction rates are evaluated at each iteration simultaneously with the CFD simulations. This method has been applied to our solid particle model to investigate the effects of fluid flow, transport and elementary reaction steps on each other for ethylene and methanol partial oxidations. Reaction rates of all elementary steps as well as species surfaces sites and compositions are evaluated inside the particle. The suggested method can couple complex reaction mechanisms with detailed CFD simulations without increasing the computational time compared with global kinetics methods. [ABSTRACT FROM AUTHOR]

A newvelocity-based approach to fixed bed radial heat transferis presented. Axial and radial velocity components were averaged fromdetailed 3D computational fluid dynamics (CFD) fixed bed simulationsof computer-generated beds of spheres and used to model radial thermalconvection. The convection terms were coupled with a radially varyingstagnant bed thermal conductivity in a 2D pseudocontinuum fixed-bedheat transfer model. The usual effective radial thermal conductivity krand apparent wall heat transfer coefficient hwwere not used, and there were no adjustableparameters. The radial and axial temperature variation predicted bythe velocity-based model agreed well with the angular-averaged temperaturesfrom the detailed 3D CFD simulations over the range 80 ≤ Re≤ 1900 and for N= 3.96, 5.96,and 7.99. [ABSTRACT FROM AUTHOR]

Abstract: For the conduction mode of heat transfer in a fixed bed, we have carried out an evaluation of whether the most widely-used equations for the overall stagnant bed effective thermal conductivity ke 0, the Zehner–Schlünder cell model, can be used on a pointwise basis to obtain local values of ke 0(r) using the local bed voidage, ε(r). A three-dimensional computational fluid dynamics (CFD) model of an annular test bed of spheres with tube-to-particle diameter ratio equal to four was constructed to obtain the local void fraction, and solved for the radial temperature profiles. Comparisons to a one-dimensional pseudo-continuum model with ke 0(r) gave good agreement for a range of values of solid thermal conductivity, establishing that the Zehner–Schlünder cell model can be used in local models of fixed-bed heat transfer. [Copyright &y& Elsevier]

Abstract: In the development of meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds of spheres, particle–particle and wall–particle contact points often present difficulties. We give results for drag coefficient (C D ) and heat flow (Q) for flow past sphere–sphere and wall–sphere contact points, focusing on higher flow rates typical of industrial steam reformers (500

Abstract: CFD simulations of heat transfer in fixed beds of spheres were validated by comparison to experimental measurements in a pilot-scale rig. The comparisons were made for particle Reynolds numbers in the range 2200

An interpretation of the state-of-the-art in modelling radial heat transfer in fixed bed catalytic reactors is presented. The persistence of the classical kr- hw model is discussed, problems with typical approaches to obtaining and analysing experimental heat transfer data to get kr and hw are explained, current correlations for kr are evaluated and the contentious history of hw is elaborated. A brief discussion of alternatives to the kr- hw approach and their pros and cons is attempted, and the review is concluded by a look at computational fluid dynamics (CFD) in fixed bed radial heat transfer modelling. © 2011 Canadian Society for Chemical Engineering [ABSTRACT FROM AUTHOR]

Abstract: To develop and validate meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds, a single particle is often used as a test case. We present results for drag coefficient (C D) and heat transfer Nusselt number (Nu) for flow past a sphere, focusing on high flow rates typical of industrial steam reformers (400< Re <20,000). Over this range, good predictions of C D were obtained using large eddy simulation (LES) to capture vortex shedding and wake dynamics, with a mesh refined downstream from the sphere. The small time-steps and high cell count required make this too expensive for fixed beds. Nu can be accurately calculated using a Reynolds-averaged Navier–Stokes (RANS) method with shear-stress transport (SST) k–ω closure provided the mesh at the particle surface is fine enough and covers most of the boundary layer. Single sphere simulations of heat transfer are more useful for fixed bed mesh development than drag coefficient calculations. [Copyright &y& Elsevier]

• Particle-resolved CFD (PRCFD) fixed-bed simulations run for exothermic reaction. • 1-D model over predicts temperature, conversion of reactants in ethylene oxidation. • Varying voidage, velocity in 2-D model not better than using constant values. • 2-D model requires accurate radial heat transfer parameters for exothermic reaction. • Different temperature fields in endo-, exothermic cases require different models. Particle-resolved 3-D computational fluid dynamics (PRCFD) simulations of highly exothermic ethylene partial oxidation in a fixed bed were made to evaluate heterogeneous pseudo continuum reaction engineering models. The ethylene oxidation results were compared to a previous study (Dixon, Chem. Eng. Sci., 168 , 156–177 (2017)) of endothermic steam methane reforming (SMR). The 1-D pseudo continuum reactor model predicted too high a reaction rate compared to the PRCFD simulations. Unlike the endothermic SMR, manipulation of the fluid-particle heat and mass transfer coefficients did not improve agreement. For the 2-D pseudo continuum reactor model, agreement was not helped by the inclusion of radial voidage and velocity profiles, but was improved by the radial heat transfer model, again in contrast to SMR. These results arose from the differences between heating from the strong heat flux applied to the tube wall, and from the weaker heat source supplied by reaction in the main fixed bed. [ABSTRACT FROM AUTHOR]

• Transient resolved-particle CFD used for simulations of ethylene oxidation. • Dynamic behavior of hot-spots under wrong-way response and reactor start-up. • A decrease in feed temperature causes a temporary increase in outlet temperature. • Moving heat wave along the tube is simulated for reactor shut-down and start-up. • Local transient interactions between fluid flow and reacting pellets are shown. Fixed-bed reactors are widely used for large-scale, heterogeneously-catalyzed gas-phase reactions, such as steam reforming, selective hydrogenations and partial oxidations. These reactions have strong heat effects; exothermic reactions can exhibit "hot-spots", while endothermic reactions require a large supply of heat. Steady-state reactor analysis does not give the whole picture; when dynamics are considered then hot-spots, extinction waves and "wrong-way" behavior (increased downstream temperature following inlet feed temperature decrease) can result. We investigate here the interactions between the local pellet-scale dynamic responses, and the bed-scale global fields, using computational fluid dynamics (CFD). This method allows detailed simulation of the fluid around the catalyst, coupled to transport and reaction inside it. To date, reactor dynamics have been based on simplified reactor models. We have developed a methodology to use 3D detailed models to investigate local dynamic hot-spot formation and wrong-way responses to inputs and their connections to bed-scale flow and transport. [ABSTRACT FROM AUTHOR]

Highlights • Flux-dependent model developed for effective diffusivity in CFD calculations. • Anisotropic diffusivity tensor needed to allow non-constant flux ratios. • Choice of diffusivity model is more important for longer diffusion paths. • Resolved-particle 3D simulations show differences between models. • Small changes in a single pellet can be significant under extreme conditions. Abstract The implementation of multicomponent diffusion in porous catalyst particles into resolved-particle fixed bed computational fluid dynamics (CFD) presents challenges. Usually an isotropic effective diffusivity is employed for each species, which includes molecular diffusion, Knudsen diffusion and viscous flow. To obtain this quantity, constant and isotropic molar flux ratios are assumed. In fixed bed models, pellets composed of isotropic materials are situated in non-isotropic fluid-phase gradients in the bed, which call the assumptions into question. In this paper we present an extended model using a non-isotropic effective diffusivity tensor, which allows evaluation of the flux assumptions. The method is illustrated for resolved particle steady-state CFD simulations of ethylene oxidation in small test beds of spheres and four-hole cylinders. Comparisons to the original constant molar flux ratio model are made, which show that the flux changes affect reaction, species and temperature profiles in the particles, and are stronger in particles with longer diffusion paths. Larger differences between results from the two diffusion models are also seen when the effective diffusivity is decreased by reducing porosity and increasing tortuosity, typical of a reaction system where deactivation increases by carbon deposition. [ABSTRACT FROM AUTHOR]