In this work, the role of hydrodynamics in an industrial-scale packed-bed catalytic reactor with a low tube/ particle diameter ratio (d t /d p ∼ 3) and the role of redox dynamics of the catalyst surface together with the use of a catalyst activity profile are assessed on the heat transport during the partial oxidation of o-xylene on a V 2 O 5 /TiO 2 catalyst. Temperature and concentration observations at different steady-state conditions are used to test the modeling approach, and reasonably good predictions are obtained when (1) the information contained in the heat-transport parameters, estimated from a boundary layer approximation to the hydrodynamics in the absence of chemical reactions [Ind. Eng. Chem. Res. 2007, 46 (23), 7426-7435], is used in the reactor model and (2) the redox catalyst dynamics, included in the reaction kinetics, is used, together with an empirical catalyst activity profile.

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This work describes a heat-transfer study conducted in two beds of low tube/particle diameter ratio (d t/d p ≈ 3) with almost the same diameter but different lengths, packed with catalyst spheres, operating in quasi-adiabatic and nonadiabatic modes. The operation in the short bed in a quasi-adiabatic mode provided independent sets of experiments to estimate the effective thermal conductivity at various Reynolds numbers. This information was transferred successfully to model the short and long beds operating in a nonadiabatic mode. The modeling compares the classical approach to model heat transfer in a packed bed with no hydrodynamics, against those which include the hydrodynamics and a radial voidage profile, as well as the boundary layer approximation of this model. Modeling results showed that very similar predictions of radial and axial temperature profiles are obtained in all cases, making it difficult to discriminate between both model approaches.

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Lithium-ion batteries (LiBs) have gained a worldwide position as energy storage devices due to their high energy density, power density and cycle life. Nevertheless, these performance parameters are yet insufficient for current and future demands diversifying their range of applications, and competitiveness against other power sources. In line with the materials science, the optimization of LiBs, first, requires an in-depth characterization and understanding of their determining steps regarding transport phenomena and electrode kinetics occurring within these devices. Experimental and theoretical studies have identified the solid-state diffusion of Li+ into the composite cathode material as one of the transport mechanisms limiting the performance of LiBs, in particular at high charge and discharge rates (C-rates). Nowadays, there is however ambivalence to characterize this mass transport mechanism using the diffusion coefficient calculated either by electrochemical techniques or ab initio quantum chemistry methods.  This contribution revisits conventional electrochemical methodologies employed in literature to estimate mass transport diffusivity of LiBs, in particular using LiFePO4 in the cathode, and their suitability and reliability are comprehensively discussed. These experimental and theoretical methods include Galvanostatic and Potentiostatic Intermittent Titration Technique (GITT and PITT), Electrochemical Impedance Spectroscopy (EIS), Cyclic Voltammetry (CV) and ab initio quantum chemistry methods. On the one hand, experimental methods seem not to isolate the diffusion mechanism in the solid phase; thus, obtaining an unreliable apparent diffusion coefficient (ranging from 10–10 to 10–16 cm2 s−1), which only serves as a criterion to discard among a set of LiBs. On the other hand, atomistic approaches based on ab initio, density functional theory (DFT), cannot yet capture the complexity of the local environments involved at this scale; in consequence, these approaches have predicted inadequate diffusion coefficients for LiFePO4 (ranging from 10–6 to 10–7 cm2 s−1) which strongly differ from experimental values. This contribution, at long last, remarks the factors influencing diffusion mechanisms and addresses the uncertainties to characterize this transport mechanism in the cathode, stressing the needs to establish methods to determine the diffusion coefficient accurately, coupling electrochemical techniques, ab initio methods, and engineering approaches based on modeling.

In the last decade it has been a special interest to incorporate the hydrodynamics in packed bed reactor models. This seems to be important in the case of highly exothermic partial oxidation reactions normally performed in packed beds with low tube/particle diameter ratio (dt/dp< 5) because of the large void distributions in the radial and axial directions, which have a direct impact on the magnitude of radial, angular and axial profiles of the velocity field, and consequently on both, the temperature and concentration profiles in the catalytic reactor. A successful reactor model needs an adequate hydrodynamic description of the packed bed, and for this reason several models additionally incorporate empirical expressions to describe radial voidage profiles, and use viscous (Darcy) and inertial (Forchheimer) terms to account for gas-solid interactions, via Ergun's pressure drop equation. In several cases an effective viscosity parameter has also been used with the Brinkman's viscous term. The use of these various approaches introduce some uncertainty in the predicted results, as to which extent the use of a particular radial voidage expression, or the use of an effective viscosity parameter, yield reliable predictions of measured velocity profiles.In this work the predictions of radial velocity profiles in a packed bed with low tube to particle diameter ratio from six hydrodynamic models, derived from a general one, are compared. The calculations show that the use of an effective viscosity parameter to predict experimental data can be avoided, if the magnitude of the two parameters in Ergun's equation, related to viscous and inertial energy losses, are re-estimated from velocity measurements, for this particular packed bed. The predictions using both approaches adequately fit the experimental data, although the results are analyzed and discussed.