K Kornelis Rietema

The effect of interparticle forces on the stability of gas-fluidized beds - I.Experimental evidence

The stability theory for homogeneous fluidized beds presented earlier is reviewed. This theory is based on the concept of the elasticity of the bed structure as a consequence of interparticle forces. It is shown that this theory explains the effect of gas viscosity and gravity. It is further shown that the elasticity modulus is increased by gas adsorption to the solid surface at elevated pressure and, thus, explains the effect of gas pressure on bed expansion. The theory is compared with experimental results obtained with fluidization of fresh cracking catalyst and polypropylene by different gases and at gas pressures up to 15 bar. It is further shown that the elasticity modulus can be used to correlate bed expansion and bubble size during heterogeneous fluidization. The stability theory of Foscolo and Gibilaro is criticized and rejected on the basis of serious mistakes made in their theoretical derivation.

Effects of pressure and type of gas on particle-particle interaction and the consequences for gas—solid fluidization behaviour

Abstract The fluidization behaviour of cracking catalyst has been studied up to pressures of 15 bar with different fluidization gases (Ar, N 2 , H 2 ). A number of parameters of both the homogeneous and heterogeneous fluidized bed has been examined experimentally. The experimental results reveal that the minimum fluidization velocity (U mf ) is independent of the pressure. The bubble point velocity (U bp ) and the maximum bed expansion (H bp ) at this velocity increase with increasing pressure. This also holds for the dense phase voidage (e d ) and the dense phase gas velocity (U d ) in the bubbling bed. The bubble size decreases drastically with increasing pressure. However, the above-mentioned parameters are also strongly dependent on the type of fluidization gas used. The cohesion constant of the powder was measured, using a tilting bed technique. The results reveal that the cohesion constant increases with increasing pressure. Analysis of the results of adsorption measurements of the different gases to the solid reveals for the adsorption as well as for the cohesion and for the beu expansion the same pressure dependence. It is believed that the gas adsorption influences the cohesion between the particles and hence the elasticity modulus introduced by Rietema and Mutsers [1,2]. The increasing elasticity modulus with increasing pressure also explains the increasing bed expansion with pressure.

The effects of interparticle forces on the stability of gas-fluidized beds—II. Theoretical derivation of bed elasticity on the basis of van der Waals forces between powder particles

In Part I of this series it was shown, on the basis of elasticity of the bed structure, that a fluidized powder bed can be stable. It was also suggested that the origin of the elasticity is to be found in the existence of interparticle forces. These interparticle forces are the subject of the present paper. The van der Waals forces between the two neighbouring particles are discussed, while the effect of particle deformation is calculated. Starting from the interparticle forces at the asperities, a model is derived that describes the demndence of the elasticitv modulus on the characteristics of the particle bed as, e.g., the bed porosity, the pa-kicle diameter and the coordination number.

Drying granular solids in a fluidised bed—II The influence of diffusion limitation on the gas—solid contacting around bubbles

When diffusion inside the solid particles which are dried in a fluidised bed can not be neglected this internal diffusion can be accounted for by two mechanisms: (a) the long term response which describes the gradual build up of a concentration profile inside the solid particles as function of the total drying time, and (b) the short term response which describes the generation of a thin concentration boundary layer inside the particles during the passage of these particles through the cloud of a rising bubble. Both mechanisms can be analyzed separately and are included in a final model which can be conceived as a further development of the model presented in Part I.

Gas transfer from bubbles in a fluidized bed to the dense phase — II. Experiments

Abstract An experimental check was made upon the theory given in Part I. Cracking catalyst was used as a solid and differently adsorbed tracer gases were used. In a two-dimensional fluidized bed bubbles were formed underneath a gauze cap, while solid flowed along the bubble at the corresponding bubble velocity. Tracer injections provided the value for the transfer coefficient. In three-dimensional beds of 18 and 90 cm dia. large traced gas bubbles were injected. Tracer concentration was detected at certain heights. From the decrease the transfer coefficient was calculated. In the 90 cm bed the transfer coefficient was also calculated from residence time distribution measurements when the dense phase was perfectly mixed. It shows, that the two-dimensional bubble confirms the theory. For three-dimensional bubbles the transfer is higher than theoretically predicted, especially when the dense phase is expanded.

A theoretical study on the influence of gas adsorption on interparticle forces in powders

Using data from the literature and some additional experiments it is investigated whether the interparticle forces in general and more specifically the cohesion between particles are influenced by the physisorption of gases. In this otherwise theoretical study the force to be applied to a particle to obtain a specific distance from a plane is derived from the total energy of the system of particle and plane. This energy consists of three terms: molecular interaction energy between the particle and the plane; elastic energy due to deformation of the particle; and adsorption energy of the gas. It is concluded that gas adsorption may indeed quite heavily influence the interparticle forces and cohesion (increase up to a factor of 3). The degree of influence is determined by the type of gas and the gas pressure.

Performance of a large-cone-angle hydrocyclone—I: Hydrodynamics

Abstract As opposed to “normal” hydrocyclones, large-cone-angle hydrocyclones can be used to separate solids with equal free-fall velocities but with different densities. One of the applications of these cyclones is the recovery of heavy minerals from sand. In order to investigate the hydrodynamical behaviour of such a cyclone the following experiments have been carried out on two cyclones of diferent dimensions: determination of solids distribution at steady state operation; measurement of the residence time distribution of the liquid; pressure gradient and pressure drop measurements. From the experimental results it follows that at the bottom a bed of suspended solids rotates, which more or less seems to be fluidized. Similar to the derivation of an expression of the pressure gradient in a one-phase vortex flow from the Navier-Stokes equation, an expression of the pressure gradient in such a solid-liquid vortex flow has been obtained from two-phase momentum equations. From this theory it follows that in the rotating bed a secondary solids flow has to occur; solids are moving towards the centre at the bottom and away from the centre at the top.

The effect of interstitial gas on milling

Abstract In a research program on the influence of interstitial gas on the handling of fine powders, particle diameter less than 100 μm, the effect on milling is also investigated. The influence of the interstitial gas is exhibited through the drag force, due to velocity differences, which the gas exerts on the solid particles of the powder. These forces strongly influences the behavior of the powder. Our investigations of milling showed that the milling parameters, i.e. the specific rates of breakage and the breakage parameter, were dependent on the powder flow behavior. Two extremes were the regime of free-flowing powder, where the rate of breakage was high and the grinding of the individual particles was rather ineffective, and the regime in which the powder did not flow at all, where the rate of breakage was low, but where the grinding of the single particles was rather fine.

Continuous sedimentation theory: Effects of density gradients and velocity profiles on sedimentation efficiency

Abstract A theory is presented on continuous sedimentation. In case the solids concentration is small and uniformly distributed over the inlet height, the theory predicts independent sedimentation efficiencies on velocity distributions in a longitudinal vertical plane. A velocity profile in a horizontal plane on the other hand will have a negative effect on the efficiency. Experiments, carried out on a laboratory-scale model, have shown that even smal density differences in the basin can have a significant effect on the velocity distribution. The measured efficiencies are in good agreement with the theory

The effect of interstitial gas on milling. Part 2

Abstract In a previous paper results were presented on the effect of interstitial gas on the milling characteristics of one specific fine powder in a ball mill. This second paper gives more data on two other powders, cracking catalyst and hematite, together with those on the powder used in the earlier experiments, quartz sand. The effects found are similar for each of the three powders: increasing gas pressure or viscosity of the gas or both inside the mill increases the rate of breakage and decreases the fineness of the daughter particles of a milling event. The overall milling speed or production rate as well as the ultimate fineness of the product are both improved by increasing pressure or viscosity. On the basis of these results a comparison is made with wet milling. It appears that pressurized milling, pressure around 10 bar, is a good alternative for the milling of fine powders.