Johannes G. Khinast

Impact of drying on the catalyst profile in supported impregnation catalysts

Abstract The impact of drying conditions and system properties on the final catalyst profile in supported impregnation catalysts is studied. A model is developed, which accounts for convective flow in the liquid phase, multi-component diffusion of the metal in the liquid phase, metal adsorption on the porous support, and heat transport. Transport of the gas and liquid phase are described by the dusty gas model and Darcys law, respectively. Transport of charged particles (dissolved metal and its ion counterpart) in the liquid solution, i.e., the convective and diffusive ion transport, are modeled by the Nernst–Plank equation. Metal adsorption on the porous support is modeled by a Langmuir adsorption isotherm. It was shown that in the case of strong adsorption, drying does not affect the final metal profile. In such cases, the profile is mainly determined during impregnation. In the case of weak metal adsorption, drying strongly impacts the final catalyst distribution. Accumulation of the metal at the external particle surface (egg-shell profile) becomes significant with increasing drying rate, since convective flow towards the surface is the dominant transport mechanism. Egg-shell catalysts are also obtained, if the permeability of the support is very high, or if the liquid solution has low viscosity. If metal back-diffusion is strong, the metal is transported towards the particle center, leading to uniform or decreasing egg-yolk catalysts. A dimensional analysis of the model equations showed that the final catalyst profile is determined by three dimensionless groups, which describe the relative strength of convection, diffusion, and adsorption. Maps were computed that show regions of different catalyst profiles. Therefore, knowledge of these three dimensionless groups allows the prediction of the final catalyst profile.

Reactive mass transfer at gas-liquid interfaces: impact of micro-scale fluid dynamics on yield and selectivity of liquid-phase cyclohexane oxidation

The impact of single-bubble wake dynamics on the reaction-enhanced mass transfer and on the yield and selectivity of the cyclohexane oxidation reaction was studied using a two-dimensional CFD-reaction model that was developed by our group. Temperature and the concentrations of the (desired) intermediate and (undesired) final products of this autocatalytic reaction were the parameters of this study. Two bubble types were studied: (a) a circular bubble with closed wake, and (b) an elliptical bubble with an unsteady, vortex-shedding wake. The main results of our work are: (1) Film theory over-predicts reaction-enhanced mass transfer since the assumption of an average film thickness is not justified. In order to study fast reaction systems on a reactor scale using coarse-grid CFD codes, a full bubble model, or correlations based on it, should be incorporated as a sub-grid micro model. (2) The bubble wake does not contribute to mass transfer in systems where reaction rates are low. For fast reactions, the local mass transfer rate in the wake can increase by several thousand percent. (3) Vortex shedding causes qualitatively different mixing since patches rich in the dissolved gas are quickly convected away from the bubble. Bubbles that cause vortex shedding will lead to a significantly higher conversion per volume than spherical bubbles. (4) Parallel–consecutive reactions with a high liquid-phase reactant concentration and with reaction rates that depend in an identical way on the dissolved gas concentration, are not micro-mixing sensitive in terms of selectivity. Since bubble shapes and sizes can be controlled by changing operating and design parameters, the yield of this reaction can be controlled.

Efficient bifurcation analysis of periodically-forced distributed parameter systems

Abstract Changes in the qualitative features of the bifurcation diagrams or the dynamic features of forced periodic systems occur at singular points, which satisfy certain defining conditions. The loci of these singular points may be constructed by a continuation procedure and used to bound parameter regions with qualitatively different features. When the model of a forced periodic system is a set of partial differential equations, construction of these loci may require extensive computational time, making this task often impractical. We present here a novel, very efficient numerical method for construction of these loci. The procedure uses Frechet differentiation to simplify the determination of the defining conditions and the Broyden inverse update method to accelerate the iterative steps involved in the shooting method. The procedure is illustrated first by construction of a map of parameter regions with qualitatively different bifurcation diagrams for an adiabatic reverse-flow reactor (RFR), the direction of feed to which is changed periodically. We then construct a map of parameter regions in which a cooled RFR has qualitatively different dynamic features. Both maps reveal surprising features.

Mass-transfer enhancement by static mixers in a wall-coated catalytic reactor

Abstract Using CO oxidation in a wall-coated tubular reactor, the enhancement of radial mass transfer by a static mixer was investigated. Experiments were conducted at various flow rates, CO concentrations and temperatures. Flow rates were chosen such that the flow remains in the laminar regime. Several effects were observed: light-off occurred at higher temperatures for higher flow rates and higher CO concentrations. Lower conversions were obtained for higher flow rates. In general, measured conversions were higher with the static mixer, compared to an empty tube under mass-transfer limited conditions. An expression for the Sherwood number, Sh =2+0.059 Re , was calculated for the system with static mixers. Our study demonstrates that the performance of wall-coated reactors can be significantly enhanced using static mixers. This reactor may be a new tool for reaction engineers, e.g., to replace catalyst-pellet-filled tubes in multi-tubular reactors to suppress hot-spot formation or for heterogeneously catalyzed viscous liquid-phase reactions.

Adaptive multiscale solution of dynamical systems in chemical processes using wavelets

Abstract Most chemical processes occur at different spatial and temporal scales such as turbulence or chromatographic separations. Irregular features, singularities and steep changes emerge, which require solution procedures that can resolve these varying scales in the most efficient manner. Wavelets with their multiresolution analysis properties have the potential to express the solution from the coarsest to the finest scale with minimal effort. In this paper, a dynamically adaptive algorithm for solving PDEs in simple geometry using Wavelet–Galerkin (WG) discretization is presented. The algorithm is applied to a convection-diffusion problem and a reverse flow reactor. Using the residual and/or the absolute value of the wavelet coefficients as a measure of error, the algorithm could track the moving fronts and irregularities and sequentially refine the solution in the partial domain of interest. Also, it enables solving a coupled set of PDEs at different resolutions, exploiting the differences in differential operator stiffness. Issues regarding stability of multiresolution analysis for high Peclet number and the treatment of non-linearities are discussed.

Enantioselective Hydrogenations with Chiral Titanocenes

In this review article chiral titanocenes and their application for the enantioselective hydrogenations of different unsaturated compounds are discussed, with a special emphasis on the kinetics and the practicality of the developed systems. The nature of enantioselectivity and the hydrogenation mechanisms are reviewed as well. Catalyst immobilization and the different immobilization techniques are examined.

Mass transfer and chemical reactions in reactive deformable bubble swarms

A hybrid numerical/experimental technique was developed for the study of the impact of the multiphase hydrodynamics on mass transfer and chemical reactions at deformable interfaces. Different material properties and flow conditions can yield flows with qualitatively different mass transfer and transport characteristics. As many (bio-) reaction systems exhibit sensitivity to mass transport in general, and mixing specifically, it is possible to control their product distribution by tailoring the system parameters.

Synthesis of a novel ethylene-bis(tetrahydroindenyl) ligand containing a functionalized four-carbon tether

Abstract In this work we present an efficient synthesis of a novel ethylene-bis(2-methyl-tetrahydroindenyl) ligand, 2b , containing a tethered functional group. The tethered functional group may enable heterogenization of the homogeneous ligand on various solid supports. This strategy is the first attempt of incorporating a functional tether into a bridged metallocene ligand without disrupting the ethane bridge and represents a new approach to heterogenizing metallocene ligands. A practical synthesis was achieved by selective alkylation of the starting material and the Pauson–Khand cyclization. In addition, this strategy offers a new synthetic pathway for the preparation of the ethylene-bis(2-methyl-tetrahydroindenyl) ligand, 1b .

Efficient Bifurcation Analysis of Forced Periodic Processes

A numerically efficient procedure is described for computing the loci of bifurcation points separating parameter regions with qualitatively different dynamics and bifurcation diagrams of spatially distributed and periodically forced processes. The numerical method combines shooting, Broyden’s Jacobian update, continuation and direct Frechet differentiation of the PDEs describing the system. The reverse-flow reactor is used to illustrate the application of the numerical procedure.

The boiling slurry reactor : Axial dispersion model

Abstract We use a mathematical model that accounts for axial dispersion in both the gas and liquid phases to study the dynamics of a special configuration of a boiling slurry reactor (BSR). It is fed by a nonvolatile liquid reactant, a solvent, and a gaseous reactant and its effluent consists only of a gas. The proposed BSR configuration offers two important advantages over conventional slurry reactors, i.e., complete conversion of the liquid reactant and no need for expensive solid–liquid separation. Additionally, internal cooling devices are not needed since the reactor is cooled by evaporation of the solvent and the liquid products. The results generated by the dispersion model are compared with those of a well-mixed CSTR model. High dispersion — typical of a large diameter commercial scale reactor operating at high superficial gas velocity — leads to a reactor behavior similar to a well-mixed CSTR. Reduced backmixing does not change the qualitative reactor behavior dramatically, although temperature and concentration gradients increase, as expected. At low feed temperatures and very low axial dispersion no steady-state is reached since the reaction does not ignite at the bottom of the column. An increase of the feed temperature will stabilize the operation. A unique feature of this BSR is the possible existence of fill-up and dry-up states at which the reactor volume changes monotonically while the other state variables remain unchanged. The fill-up state will lead to spillover unless the feed and/or initial conditions are properly adjusted.