Mass transfer in trickle-bed reactors at low reynolds number

Mass transfer rates were determined in a 3.4 cm i.d. trickle-bed reactor in the absence of reaction by absorption measurements and in presence of reaction. Gas flow rates were varied from 0-100 l/h and liquid flow rates from 0-1.5 l/h. The catalyst particles were crushed to an average diameter of 0.054 and 0.09 cm. Mass transfer coefficients remained unaffected by change in gas flow rate but increased with liquid rate. The data from absorption measurements were evaluated with predictions based upon plug-flow and axial dispersion model. Mass transfer coefficients were found greater in case of axial dispersion model than that of plug-flow model specially at low Reynolds number (Re₁ < 1).Hydrogenation of α-methylstyrene to cumene using a Pd/Al₂O₃ catalyst was taken as a model reaction. Intrinsic kinetic studies were made in a laboratory-stirred-autoclave. Mass transfer coefficients were determined using these intrinsic kinetic data from the process kinetic measurements in trickle-bed reactor. Mass transfer coefficients under reaction conditions were found to be considerably higher than those obtained by absorption measurements.Correlations were suggested for predicting mass transfer coefficients at low Reynolds number.The gas to liquid mass transfer coefficients for lower gas and liquid flow rates were determined in a laboratory trickle-bed reactor. The effect of axial dispersion on mass transfer was considered in order to evaluate the experimental data. Three correlations were formulated to calculate the mass transfer coefficients, which included the effect of liquid loading, particle size and the properties of the reacting substances. The gas flow rate influences the gas to liquid mass transfer only in the region of low gas velocities. In the additional investigations of gas to liquid mass transfer without reaction in trickle-bed reactor, the mass transfer coefficients were determined under reaction conditions and the intrinsic kinetics was studied in a laboratory scale stirred autoclave with suspended catalyst. A few correlations are formulated for the mass transfer coefficients. A comparison with the gas-liquid mass transfer coefficient obtained by absorption measurements showed considerable deviations, which were illustrated phenomenologically.     

Solids motion at horizontal tube surfaces in a large gas-solid fluidized bed

The motion of fluidized particles at the surface of 38 mm diameter horizontal tubes, immersed in a 1.2 m square bed of silica sand (U_mf = 0.3 m/s), fluidized at 0.9 m/s has been observed using photographic techniques (200 fps). It is shown that the solids motion is different for centrally located tubes and those adjacent to a side wall. Data on particle velocity and surface contact are presented and the degree of particle contact at various zones around the tube circumference is shown to vary in a similar manner to published localized heat transfer rates.     

Estimation of the particle diffusivity in a liquid-solids fluidized bed based on a stochastic model

A simple method was developed for estimating the particle diffusivity or mixing coefficient in a liquid-solids fluidized bed from the variance (dispersion) of the number of particles in a given section of the bed during relaxation in the bed expansion. This variance was estimated from the pressure drop history above the location of the pressure sensor recorded continuously after the stepwise disturbance in the velocity of the fluidizing medium. The method has been verified by comparing the particle diffusivities obtained by the present method with the available data obtained by other methods.     

The effect of pore diffusion on the dissolution of porous mixtures

When a suspended solid dissolves in acid, the dissolved ions can diffuse further into the suspension. In many cases, these diffusing ions will effect precipitation of the same solid that was initially dissolved. This effect, which depends on a non-linear solubility, can usually be successfully predicted by assuming that the process is diffusion controlled. The predictions depend on diffusion and dissolution proceeding in parallel, and so represent an extension of earlier analyses where diffusion and reaction occurred sequentially.     

The forces on obstacles suspended in flowing granular materials

Measurements have been made of the forces on obstacles suspended in a flowing granular medium. It was found that the forces on vertical cylinders whose top surfaces protruded above the top of the granular medium showed substantial agreement with the predictions of Janssen's method. However the forces on horizontal surfaces within the material were an order of magnitude greater than those predicted by Janssen's method. This is attributed to the formation of a stress discontinuity ahead of the obstacle.     

Specular reflection in radiant heat transport across a spherical void

The emissivity factor for radiant heat transport across a spherical void with specular surfaces in a conducting solid is derived. To calculate the emissivity factor, the probability of all possible paths for radiation are formulated and summed. Emissivity factors for the diffuse and specular limits are compared. The resulting temperature dependence of void space radiation for several typical oxide materials is discussed.     

Effect of size and shape of catalyst microparticles on pellet pore structure and effectiveness

Catalyst pellets with bidisperse pore structure were simulated by packed bed of microporous ion exchange resin (sulfonated styrene-divinylbenzene copolymer) and inert glass particles. Inert particles of different size and shape were used to modify the shape and volume of transport macropores (voids between the particles).Tortuosities of pellets were obtained from the experimentally measured effect of internal diffusion on the rate of catalytic methanol dehydration.Analysis of results shows that in the region of strong internal diffusion influence the highest pellet effectiveness is achieved for equal-size spherical microparticles. To ensure optimum macropore structure even in the transition region between the kinetic region and the region of strong diffusion influence, volume of transport macropores has to be reduced by combination of appropriately-sized spherical catalyst microparticles.     

Drag and mass transfer in non-newtonian flows through multi-particle systems at low reynolds numbers

An approximate solution for the motion of an assemblage of solid spheres moving through a power-law fluid at low Reynolds numbers is obtained using HapThe theoretical predictions based on Kuwabara's zero-vorticity cell model are very similar to those based on Happel's model. An approximation technique     

Asymptotic analysis of single pore gas-solid reactions

The single-pore model for gas-solid reactions proposed by Ramachandran and Smith[1] is used to develop exact, closed-form solutions for the concentrati pore radius and conversion profiles in a long, narrow pore for both cylindrical and slab geometries. For relatively large values of the Thiele modulus, the solutions portray the asymptotic behavior of the reaction scheme in a finite pore. The cases of incomplete conversion associated with pore closure low initial porosities and complete conversion associated with a moving reaction zone at high initial porosities are analyzed. It is shown that the asy results provide very accurate estimates of the overall conversion in applications involving large pore diffusional resistance or fast reactions. The se of the conversion to various physicochemical parameters is also examined. The asymptotic results show good agreement with experimental data for gas-sol     

Migration of suspended particles in plane stationary ultrasonic field

The time-averaged motion of microscopic particles in plane stationary sound fields is investigated. A generalized kinetic theory of particle migration in which the effect of particle diltusion is taken into account is formulated and the particle distributions at the rather early stage and after a sufficient sound irradiation are derived analytically from the theory. It is found that the nodal change of particle concentration of microscopic polystyrene latex dispersions is well predicted by the present theory, independently of the particle size, the sound frequency and the energy density of sound. The condition of formation of the Kundt's tube striation is also characterized theoretically.     

Lateral migration of spherical particles in porous flow channels: application to membrane filtration

Lateral migration of spherical rigid neutrally buoyant particles moving in a laminar flow field in a porous channel is induced by an inertial lift force (tubular-pinch effect) and by a permeation drag force due to convection into the porous walls. The analysis of Cox and Brenner [7], for the particle motion in a nonporous duct is extended to include the effect of the wall porosity. Criteria are established under which the inertial and permeation drag force in the lateral direction can be vectorially added. Particle trajectories and concentrations profiles are calculated for a plane Poiseuille flow with one porous wall. For particles with radius of 1 μm, inertial and permeation drag forces are of comparable size under flow conditions often met in ultra- and hyperfiltration of dilute suspensions. For smaller particles the permeation drag force dominates.     

The onset of blob motion in a random sphere packing caused by flow of the surrounding liquid

Entrapped liquid blobs in the pore space of a packing of equal spheres were made visible by matching the refractive index of the spheres with that of the bulk fluid filling the pore space. By pumping bulk fluid through the surrounding pore space an experimental determination of the curvature difference between the ends of the blobs at the onset of mobilisation was made. This was repeated for blobs with special histories. The probability of blob movement was calculated. Good agreement between the theory and experiments was found.     

A visual study of particle deposition and reentrainment during depth filtration of hydrosols with a polyelectrolyte

A new experimental apparatus was developed to observe and photographically record the process of particle deposition and pore-clogging during deep bed filtration of sols in a model porous medium. Runs were made for twelve different sets of conditions, using three different pH values and four different concentrations of a commercial cationic polyelectrolyte. All other conditions were kept constant. In most cases of practical interest, it was observed that the main mechanism through which deposited particles alter the geometry of the flow channels is throat-clogging. In the case of weakly unstable hydrosols, clogging occurs either by gradual constriction of a throat or by sudden blocking caused by a reentrained cluster. In the case of agglomerated hydrosols, throat-clogging is caused by growing pillar-like deposits and by sudden blocking. Throat-clogging causes profound changes in the local flow pattern, which in turn result in an increase of the local capture efficiency and a decrease of the local flow rate. Throat-clogging leads systematically to the formation of deposits resembling “pendants”, “pouches” and cascades of pendants and pouches. In the case of hydrosols with reversed charge (due to polymer overdosing) a checkerboard pattern of deposition develops. These observations explain the initial increase of deep bed filtration efficiency and the following monotonic decrease. They also explain the drastic decrease of permeability caused by only small amounts of deposited matter.     

Particle—particle interaction force in a dilute gas—solid system

An experiment to measure pressure drop and solids velocities in a dilute pneumatic conveying pipe has been designed and constructed. A model based on momentum balance over particles has been developed to translate pressure drop and solids velocities data into an expression for particle—particle interaction. A correlation for particle—particle interaction with the relative velocity of 7 to 16 m/s has been developed. This correlation describes our experimental data within the 20% deviation.     

Solid particle mixing in a continously operated fluidized bed reactor

In a bench-scale fluidized bed reactor, 20cm in dia., residence time distribution of solid particles (d_p, = 137μm) were measured by the radionuclide technique (²⁴Na₂C0₃) in the absence and in the presence of the chemical reaction 2NaHCO₃→Na₂C0₃+C0₂+H₂O. The residence time distributions were evaluated by a backflow cascade model by nonlinear optimization. The radial and logitudinal concentration profile of NaHCO₃ in the emulsion phase of the reactor were measured during steady-state operation. The solid is well-mixed.The connection of the measured bubble properties with the longitudinal solid dispersion coefficient and the use of the Haines-King-Woodburn model allow     

Equations for predicting growth or dissolution rates of spherical particles

Approximate analytical solutions to the transport equations describing the heat or mass transfer-controlled growth or dissolution of an isolated sphere are discussed and critically evaluated. The predictions of these equations are compared with finite-difference and similarity solutions. Recommendations are presented for using particular analytical expressions to evaluate the radius-time behavior of the spherical particle for various ranges of the two dimensionless groups of the problem.     

Effect of particle size distribution on adsorption kinetics in stirred batch systems

The effect of different particle size distributions (PSD's) on kinetic behavior in stirred-batch adsorption systems was investigated by numerically modeling the uptake of p-nitrophenol from aqueous solution by granular activated carbon in a well-stirred batch type of environment. Four different Gaussian PSD'S, two different log-normal PSD's and one case of uniform particle size were studied. The model accounted for both external and internal mass transfer resistances, and for the highly nonlinear equilibrium relation which characterizes the p-nitrophenol/activated carbon system. All isotherm parameters and “base-case” kinetic parameters were experimentally determined values (from the literature). The kinetic parameter values were varied in some cases to assess their influence. Moreover, both infinite-bath and finite-bath situations were evaluated. The modeling results show that the different particle size distributions did not generally give kinetic behavior widely different from the uniform particle size case when an infinite bath was assumed. However, for the more realistic case of a finite bath, the different PSD's gave significantly more distinctive results, especially for fractional mass uptake values greater than about 0.7. It is concluded that, in finite bath experiments, the nature of the adsorbent PSD must be accounted for in interpreting data obtained at fractional mass uptake values greater than about 0.7, unless the adsorbent PSD is reasonably nar