J.A.M. Kuipers

Multiscale modeling of gas-fluidized beds

Numerical models of gas-fluidized beds have become an important tool in the design and scale up of gas-solid chemical reactors. However, a single numerical model which includes the solid-solid and solid-fluid interaction in full detail is not feasible for industrial-scale equipment, and for this reason one has to resort to a multiscale approach. The idea is that gas-solid flow is described by a hierarchy of models at different length scales, where the particle-particle and fluid-particle interactions are taken into account with different levels of detail. The results and insights obtained from the more fundamental models are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (engineering) scale. Our multi-scale approach involves the lattice Boltzmann model, the discrete particle model, and the continuum model based on the kinetic theory of granular flow. In this chapter we give a detailed account of each of these models as they are employed at the University of Twente, accompanied by some illustrative computational results. Finally, we discuss two promising approaches for modeling industrial-size gas-fluidized beds, which are currently being explored independently at the Princeton University and the University of Twente.

Gas-particle interactions in dense gas-fluidised beds

The occurrence of heterogeneous flow structures in gas-particle flows seriously affects gas?solid contacting and transport processes in dense gas-fluidized beds. A computational study, using a discrete particle method based on Molecular Dynamics techniques, has been carried out to explore the mechanisms underlying the formation of heterogeneous flow structures. Based on energy budget analyses, the impact of non-linear drag force on the flow structure formation in gas-fluidized beds has been examined for both ideal particles (elastic collision, without inter-particle friction) and non-ideal particles (inelastic collision, with inter-particle friction). Meanwhile, the separate role of inter-particle inelastic collisions, accounted for in the model via the restitution coefficient (e) and friction coefficient (?), has also been studied. n nIt is demonstrated that heterogeneous flow structures exist in systems with both non-ideal particle-particle interaction and ideal particle-particle interaction. The heterogeneous structure in an ideal system, featured with looser packing, is purely caused by the non-linearity of the gas drag: the stronger the non-linearity of the gas drag force with respect to the voidage, the more heterogeneous flow structures develop. A weak dependence of drag on the voidage produces a homogenous flow structure. Collisional dissipation dramatically intensifies the formation of heterogeneous flow structures after the system equilibrium breaks. Quantitative comparisons of flow structures obtained by using various drag correlations in literature will also be reported

Experimental validation of granular dynamics simulations of gas-fluidised beds with homogeneous inflow conditions using Positron Emission Particle Tracking

A hard-sphere granular dynamics model of a two-dimensional gas-fluidised bed was experimentally validated using Positron Emission Particle Tracking (PEPT). In the model the Newtonian equations of motion are solved for each solid particle while taking into account the particle?particle and particle?wall collisions. The gas phase hydrodynamics is described by the spatially averaged Navier?Stokes equations for two-phase flow. A quasi two-dimensional (i.e. narrow) bed of 0.185-m width and 0.4-m height with homogenous inflow conditions at 1.5 umf was chosen as a test case. Glass particles (?p=2435 kg/m3) with diameters ranging from 1.25 to 1.5 mm were used as the bed material. The collision parameters required in the simulation were obtained from separate, independent measurements. In the PEPT experiment, the motion of a single tracer particle in the bed was tracked for 1 h. In the simulation, the motion of 15,000 particles was tracked for 45 s. The simulation data were time-averaged over 45 s for each particle and subsequently ensemble-averaged over all the particles in the simulation. The comparison was made on the basis of averaged velocity maps, occupancy plots and speed histograms. The results showed good agreement between experiment and simulation when the measured values for the collision parameters were used. When collisions were assumed to be fully elastic and perfectly smooth the agreement was much worse.

Gas Dispersion and Bubble-to-Emulsion Phase Mass Exchange in a Gas-Solid Bubbling Fluidized Bed: A Computational and Experimental Study

Knowledge of gas dispersion and mass exchange between the bubble and the emulsion phases is essential for a correct prediction of the performance of fluidized beds, particularly when catalytic reactions take place. Test cases of single rising bubble and a bubbling fluidized bed operated with a jet without a chemical reaction were studied in order to obtain fundamental insights in the prevailing mass transfer phenomena. Numerical simulations were carried out to predict the dispersion of tracer gas using a two-fluid model based on Kinetic Theory of Granular Flow (KTGF). The simulations of a single-bubble rising through an incipiently fluidized bed revealed that the assumptions often made in phenomenological models in the derivation of correlations for the mass transfer coefficient, mainly that the bubble diameter remains constant and that the tracer concentration is uniform in the bubble, are not valid. The predicted bubble-to-emulsion phase mass transfer coefficient showed good agreement with the estimated values from the literature correlations assuming additive convection-diffusion transport for different bubble sizes and different particle sizes, indicating the importance of the convective distribution even for relatively small particles. Experiments were carried out to measure the steady state concentration profiles of a tracer gas in a pseudo two-dimensional bubbling fluidized bed operated with a jet. The simulated steady state concentration profiles of the tracer gas agreed well the experimental measurements. The radial convection of the gas is significantly influenced by the bubble x91throughflowx92 and therefore depends upon the particle and bubble size. The experimental comparison of theoretical results was extended to study the influence of the jet velocity and the particle diameter on the radial dispersion of the tracer gas in the bed.

Supercritical shallow granular flow through a contraction: experiment, theory and simulation

Supercritical granular flow through a linear contraction on a smooth inclined plane is investigated by means of experiments, theoretical analysis and numerical simulations. The experiments have been performed with three size classes of spherical glass beads, and poppy seeds (non-spherical). Flow states and flow regimes are categorized in the phase space spanned by the supercritical Froude number and the minimum width of the contraction. A theoretical explanation is given for the formation of steady reservoirs in the contraction observed in experiments using glass beads and water. For this purpose, the classical, one-dimensional shallow-water theory is extended to include frictional and porosity effects. The occurrence of the experimentally observed flow states and regimes can be understood by introducing integrals of acceleration. The flow state with a steady reservoir arises because friction forces in the reservoir are much smaller than in other parts of the flow. Three-dimensional discrete-particle simulations quantitatively agree with the measured granular flow data, and the crucial part of the theoretical frictional analysis is clearly confirmed. The simulations of the flow further reveal that porosity and frictional effects interact in a complicated way. Finally, the numerical database is employed to investigate the rheology in a priori tests for several constitutive models of frictional effects.

Modelling of a reverse flow catalytic membrane reactor for the partial oxidation of methane

Gas-To-Liquid (GTL) processes have great potential as alternative to conventional oil and coal processing for the production of liquid fuels. In GTL-processes the partial oxidation of methane (POM) is combined with the Fischer-Tropsch reaction. An important part of the investment costs of a conventional GTL-plant is related to cryogenic air separation. These costs could be substantially reduced by separating air with recently developed oxygen perm-selective perovskite membranes, which operate at similar temperatures as a POM reactor. Integration of these membranes in the POM reactor seems very attractive because oxygen reacts at the membrane surface resulting in a high driving force over the membrane increasing the oxygen permeation.Because the POM-reaction is only slightly exothermic, the natural gas and air feed have to be preheated to high operating temperatures to obtain high syngas yields and because the Fischer-Tropsch reactor operates at much lower temperatures, recuperative heat exchange is essential for an air-based POM process. External heat transfer at elevated temperatures is expensive and therefore recuperative heat exchange is preferably carried out inside the reactor, which can be achieved with the reverse flow concept. To combine the POM reaction, air separation and recuperative heat exchange in a single apparatus a novel, multi-functional reactor is proposed, called the Reverse Flow Catalytic Membrane Reactor (RFCMR). In this reactor a relatively uniform temperature profile should be established at the membrane section and the temperature fronts should be located in the inert in- and outlet sections.To study the RFCMR concept, reactor models have been developed assuming a shell-and-tube geometry, based on models that are commonly used to describe conventional reverse flow reactors. Simulations of the novel reactor concept revealed that a small amount of methane has to combusted on the air side to create the reverse flow behaviour. Also a small amount of steam has to be injected distributively along the perovskite membrane section to maintain the centre of the reactor at nearly isothermal conditions. With these modifications it was found that the desired temperature profile could indeed be created in the RFCMR and that high overall syngas yields can be achieved.

Large-Eddy simulation of a particle-laden turbulent channel flow

Large-eddy simulations of a vertical turbulent channel flow with 420,000 solid particles are performed in order to get insight into fundamental aspects of a riser flow The question is addressed whether collisions between particles are important for the ow statistics. The turbulent channel ow corresponds to a particle volume fraction of 0.013 and a mass load ratio of 18, values that are relatively high compared to recent literature on large-eddy simulation of two-phase ows. In order to simulate this ow, we present a formulation of the equations for compressible ow in a porous medium including particle forces. These equations are solved with LES using a Taylor approximation of the dynamic subgrid-model. The results show that due to particle-uid interactions the boundary layer becomes thinner, leading to a higher skin-friction coefcient. Important effects of the particle collisions are also observed, on the mean uid prole, but even more o on particle properties. The collisions cause a less uniform particle concentration nand considerably atten the mean solids velocity prole.

Radial distribution of ions in pores with a surface charge

A sorption model applicable to calculate the radial equilibrium concentrations of ions in the pores of ion-selective membranes with a pore structure is developed. The model is called the radial uptake model. Because the model is applied to a Nafion sulfonic layer with very small pores and the radial uptake model is based on the assumption that continuum equations are applicable, the model is used near its limits of fundamental validity. However, the results indicate that the calculated profiles with the radial uptake model are realistic and similar to literature results (e.g. [J.R. Bontha, P.N. Pintauro, J. Phys. Chem. 96 (1992) 7778; J.R. Bontha, P.N. Pintauro, Chem. Eng. Sci. 49 (1994) 3835]). The membrane microstructure parameters (surface charge density and pore diameter) have been determined by fitting the sorption of sodium as predicted by the radial uptake model to the sorption of sodium as predicted by the so-called modified Pitzer model [J.H.G. Van der Stegen, A.J. van der Veen, H. Weerdenburg, J.A. Hogendoorn, G.F. Versteeg, Fluid Phase Equilibria 157 (1999a) 181]. This modified Pitzer model has proven to be able to predict volume averaged sorption of ions in a sulfonic membrane layer. Via the introduction of a component dependent correction factor in the radial uptake model, the sorption of ions other than sodium could also be fitted to the volume averaged sorption data as predicted by the modified Pitzer model. The correction factors were in the order of magnitude of 0.05–10, and dependent on the concentration of sodium. The necessity of the application of correction factors for the ions other than sodium may have been induced by the assumption that: n• the applicability of continuum equations in the model is justified and/or; n• the activity coefficients in the radial uptake model are equal to unity. nIt was observed that due to the preferential sorption of iron near the pore wall, the pore surface charge could be shielded, resulting in a decrease of the preferential selectivity of the membrane for sodium. However, such a phenomenon does not occur in the operating range of the chloralkali process, where the sorption of iron inside the membrane is proportional to its external concentration.

Chapter 23 Multi-level computational fluid dynamics models for the description of particle mixing and granulation in fluidized beds

Publisher Summary To model gas-fluidized bed granulation processes, a multi-level modeling approach has been adopted in this chapter. The idea of this approach is to use different levels of modeling, each level developed to study phenomena that occur at a certain length scale. Information obtained at the level of small length scales can be used to provide closure information at the level of larger length scales. The interaction between the gas and the particles is another important aspect in the continuum and the Discrete Element Model (DEM), which requires closures. There are a number of semi-empirical closure relations available, which despite their widespread application contain a large uncertainty, rendering accurate prediction of the overall bed behavior difficult. Techniques, such as the lattice Boltzmann model (LBM) can be used to validate and eventually improve these closure relations. In LBM the flow around small ensembles of particles can be modeled without making prior assumptions, hence gas-particle interactions can be quantified. This chapter focuses on the levels of the DEM and the continuum model. A detailed theoretical description of these models is given and the predictive capabilities of these models are illustrated here with a few examples.

Gas-liquid reactor / separator: dynamics and operability characteristics

A comprehensive mathematical model is developed to simulate gas?liquid reactor in which both, reactants as well as products enter or leave the reactor in gas phase while the reactions take place in liquid phase. A case of first-order reaction (isothermal) was investigated in detail using the dynamic model and numerical bifurcation tools. Strong coupling between reaction kinetics and product removal rate was found to lead to complex dynamic (including over-flow/dry-up or oscillatory) behaviour. Key parameters controlling operability and dynamic characteristics were identified. Operability maps of the reactor/separator are presented. The model and results discussed will be useful for design and operation of industrial reactor/separators.