Pressure drop in two phase cocurrent upward flow in packed beds: Air/non-newtonian liquid systems

New data on the two phase pressure drop for the concurrent upflow of air-liquid (Newtonian and non-Newtonian) mixtures through packed beds of spherical and non-spherical particles are presented. The results for single phase flows and for the air-Newtonian liquid mixtures have been used both to gauge the overall accuracy of the present experimental methods and to evaluate the validity of the predictive expressions available in the literature. The two phase pressure drop has been measured as a function of the liquid and gas flow rates, column diameter and the power law model constants. Depending upon a suitable combination of the gas and liquid fluxes and the power law index, the two phase pressure drop may be less than its value for the flow of liquid alone. A simple expression is proposed which correlates the present set of experiments (nearly 500 data points) with satisfactory levels of accuracy over the following ranges of conditions: 0.54 ≤ n ≤ 1; 0.001 ≤ Re_L^* ≤ 50; 3.7 ≤ Re_G ≤ 177 and 0.9 ≤χ (Lockhart-Martinelli parameter) ≤ 104.     

Slow non-newtonian flow through packed beds: Effect of zero shear viscosity

The slow non-Newtonian (inelastic) flow through packed beds of mono-size spherical particles has been simulated by solving the equations of motion numerically. The inter-particle interactions have been modelled by using a simple cell model. Theoretical estimates of pressure, friction and total drag coefficients as function of the pertinent physical (l≥n≥ 0.2; 0.3 ≤ e ≤ 0.5) and kinematic parameters (0.01 ≤ '≤ 100) for a fixed value of Reynolds number {Re = 0.001) have been obtained. The theoretical predictions reported herein have been validated using the suitable experimental results available in the literature, and the importance of including the zero shear viscosity in analyses for the creeping flow problems is convincingly demonstrated.     

Determination of thermal parameters of non-spherical particles in a packed bed from svstem response analysis in the time domain

The thermal conductivity and the particle-to-fluid heat-transfer coefficient for peanut-shaped polyester particles in a packed bed were determined simultaneously using the pseudo-random binary noise sequence (PRBNS) response technique. The modified Dispersion-Concentric (D-C) model was applied to beds packed with the non-spherical particles. A time domain method, using the convolution integral, was developed for removing the effects of the bed ends and the transducer time lag on the experimental responses. Parameter estimation was performed in the time domain, using a simplex method to fit the thermal response calculated from the parametric D-C model to the experimental response curve. The particle-to-fluid heat transfer coefficient in the bed was determined to be 106 W/m². K at an interstitial fluid velocity of 2.0 m/s. The thermal conductivity of polyester was 0.22 W/m. K at 313 K.     

Prediction of minimum velocity and minimum bed pressure drop for gas-solid fluidization in conical conduits

Experimental investigations have been carried out for spherical and non-spherical particles using beds comprised of single-sized particles and mixtures in the size and particle density ranges of 439 to 1524 μm and 1303 to 4948 kg/m³, respectively. Five conical fluidizers with varying apex angles of 8.86, 14.77, 19.60, 32.0 and 43.2 degrees were used. Experimental values of minimum velocity and bed pressure drop with air as the fluidizing medium have been compared with their respective values obtained from different models available in the literature. Deviations for each chosen model have been presented.     

Hydrodynamics of shallow,conical spouted beds

Experiments were conducted with shallow beds, in the presence of atomizing air injected into the base, under the following conditions: Particles — urea, sulphur coated urea, polyethylene, polyformaldehyde and polystyrene; particle diameters (d_p) – 2.1 to 2.8 mm; cone angle – 60°; cylindrical bed diameter (D) – 0.24 and 0.45 m; bed height (H) – 0.24 to 0.40 m; orifice diameter (d_i) – 21 to 35 mm; main spouting air (Q_s) ≤ 37 L(actual)/s; atomizing air (Q_a) ≤ 0.87 L(actual)/s. The minimum spouting velocity is well represented by: U_ms = 13.5 (2gH)^0.5 (d_p/D')^1.17 (D'_i/D')^0.372 (H/D')^?0.148 [(τ_p - τ)/τ]^0.289 where D' and D'_i denote the modified column and orifice diameter, respectively. Q_a, which affects D'_i, significantly influenced the air velocity in the spout, but not the pressure profiles in the annulus. Morgan and Littman's (1980) correlation could be adapted to predict the experimental pressure profiles in the annulus.     

Dynamics of gas–solid fluidised beds with non-spherical particle geometry

Fluidised beds play an important role in physical and chemical engineering processing. Understanding the granular motion within these beds is essential for design, optimisation and control of such processes. Motion on the particle scale is difficult to measure experimentally, making computational simulations invaluable for determining the dynamics within such systems. Computational models which have had the greatest success at capturing the full range of dynamics are coupled discrete element model and Navier–Stokes solvers, based on a pressure-gradient-force formulation. However, most discrete element models assume spherical geometry for the particles. Particle shape in many important industrial processes, such as catalysis and pyrolysis, is often non-spherical. We present a re-formulation of the pressure-gradient force model, based on a modified pressure correction method, coupled to a discrete element model with non-spherical grains. The drag relations for the coupling are modified to take into account the grain shape and cross-sectional area relative to the local gas flow. We show that grain shape has a significant effect on the dynamics of the fluidised bed, including increased pressure gradients within the bed and lower fluidisation velocities when compared to beds of spherical particles. A model is presented to explain these effects, showing that they are due to both decreased porosity within the bed as well as the relative particle cross-sectional area creating a greater net drag over the bed. Our findings will be of interest from an applied standpoint as well as showing fundamental effects of particle shape on coupled fluid and granular flow.     

A STUDY OF SPINLINE DYNAMICS USING ORTHOGONAL COLLOCATION

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Drying of Sodium Acetate in a Pulsed Fluid Bed Dryer

Sodium acetate crystals obtained from the reaction of acetic acid with sodium hydroxide are usually dried in rotary or fluidized beds. In this study, a batch pulsed fluid bed dryer with a 0.18 m² cross‐sectional area was used in an attempt to reduce energy consumption and increase productivity. Drying curves of sodium acetate were determined for different conditions: inlet air temperature of 65 and 80 °C and pulsation frequency of 0 rpm (conventional fluidized bed), 500 and 900 rpm (pulsed fluid bed). A 2² factorial design was used to analyze the results. The intermittent flow helped to break agglomerates and provided better contact between particles and the gas. Drying rates were higher under pulsed fluidization when compared to conventional fluidization. Conventional fluidized bed drying consumed 2.5 times more energy at 80 °C. The influence of temperature on the drying rate was also evident.     

Combined forced and free convection flow past a horizontal flat plate

The problem of simultaneous forced and free convection flow of a Newtonian fluid past a hot or cold horizontal flat plate is investigated by means of numerical solutions of the full equations of motion and thermal energy subject only to the Boussinesq approximation. These solutions span the parameter ranges 10 ≤ Re ≤ 100, 0.1 ≤ Pr ≤ 10, and –2.215 ≤ Gr/Re^5/2 ≤ 2.215 where Re, Pr, and Gr are based on the ambient free stream fluid properties and the overall plate length l. When Gr > 0, the boundary flow near the plate surface is accelerated relative to the corresponding forced convection flow, with a resulting increase in both the local skin friction and heat transfer coefficients. When Gr < 0, the boundary flow is decelerated, the local skin friction and heat transfer are decreased, and the flow actually separates for Gr/Re^5/2 < –0.8 when Pr = 0.7. In the latter circumstance, an increasing degree of upstream influence is observed as Gr/Re^5/2 is further decreased.     

Experimental and numerical investigation of structure and hydrodynamics in packed beds of spherical particles

In chemical industry, flows often occur in nontransparent equipment, for example in steel pipelines and vessels. Magnetic resonance imaging is a suitable approach to visualize the flow, which cannot be performed with classical optical techniques, and obtain quantitative data in such cases. It is therefore a unique tool to noninvasively study whole‐field porosity and velocity distributions in opaque single‐phase porous media flow. In this article, experimental results obtained with this technique, applied to the study of structure and hydrodynamics in packed beds of spherical particles, are shown and compared with detailed computational fluid dynamics simulations performed with an in‐house numerical code based on an immersed boundary method‐direct numerical simulation approach. Pressure drop and the radial profiles of porosity and axial velocity of the fluid for three packed beds of spheres with different sizes were evaluated, both experimentally and numerically, in order to compare the two approaches. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1896–1907, 2018     

Bubble behavior in corrugated‐wall bubbling fluidized beds—Experiments and CFD simulations

A new concept to harness bubble dynamics in bubbling fluidization of Geldart D particles was proposed. Various geometrical declinations of a cold‐prototype corrugated‐wall bubbling fluidized bed were compared at different flow rates (U_g) to conventional flat‐wall fluidized bed using high‐speed digital image analysis. Hydrodynamic studies were carried out to appraise the effect of triangular‐shaped wall corrugation on incipient fluidization, bubble coalescence (size and frequency), bubble rise velocity, and pressure drop. Bubble size and rise velocity in corrugated‐wall beds were appreciably lower, at given U_g/U_mb, than in flat‐wall beds with equal flow cross‐sectional areas and initial bed heights. The decrease (increase) in size (frequency) of bubbles during their rise was sustained by their periodic breakups while protruding through the necks between corrugated plates. Euler‐Euler transient full three‐dimensional computational fluid dynamic simulations helped shape an understanding of the impact of corrugation geometry on lowering the minimum bubbling fluidization and improving gas distribution. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Mathematical modeling of polyethylene terephthalate pyrolysis in a spouted bed

A model has been developed for pyrolysis of polyethylene terephthalate (PET) in a spouted bed reactor based on the conservation equations for heat, mass, and momentum transports. A spouted bed has been constructed and the kinetic parameters have been obtained within the temperature range of 723–833 K, using two particle size ranges, (0.1–1.0) × 10^?3 and (1.0–3.0) × 10^?3 m. The model' predictions for the radial distributions of temperature and concentration confirm the excellent mixing of particles. Thus, spouted beds are appropriate equipments for performing kinetic studies of PET pyrolysis. The inlet gas temperature and the mass of PET highly affect PET conversion. The amount of inert particles has a negligible effect on the conversion and it can be reduced as far as a stable spouting is preserved. The gas flow suffices to eliminate the external heat and mass‐transfer limitations. It can be reduced to the minimum value to decrease the energy consumption. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1900–1911, 2015     

Residence time distribution in a packed bed bioreactor containing porous glass particles: Influence of the presence of immobilized cells

An experimental investigation of the liquid phase residence time distribution (RTD) in a packed bed bioreactor containing porous glass particles is presented. For Re < 1, intraparticle forced convection is negligible and only diffusion, characterized by an effective diffusion coefficient, must be considered to describe the mass transfer process between the extraparticle and the intraparticle fluid phase. For Re > 1, the mass transfer rate becomes dependent on the liquid flow rate, indicating the existence of intraparticle convection. A model including axially dispersed flow for the external fluid phase and an ‘apparent’ effective diffusivity that combines diffusion and convection, predicts experimental RTD data satisfactorily. Yeast cells immobilized inside the porous glass beads did not affect the mass transfer rate at low biomass loading. At high biomass loading (0·02 g yeast cells g^?1 carrier), the mass transfer rate between the extraparticle and intraparticle fluid phase was significantly decreased. Comparison of the RTD data from experimets performed in the presence and absence of cells in the external fluid phase revealed that the mass transfer rate is influenced by the cells immobilized inside the porous particles and not by the cells present in the external fluid phase.     

Fluidization Characteristics in Micro‐Fluidized Beds of Various Inner Diameters

The fluidization characteristics of quartz sand and fluid catalytic crack (FCC) catalyst particles in six micro‐fluidized beds with inner diameters of 4.3, 5.5, 10.5, 15.5, 20.5, and 25.5 mm were investigated. The effects of bed diameter (D_t), static bed height (H_s), particles and gas properties on the pressure drop and minimum fluidization velocity (u_mf) were examined. The results show that the theoretical pressure drops of micro‐fluidized beds deviated from the experimental values under different particles and gas properties. The possible reason is due to an increase in bed voidage under smaller bed diameters. The equations for conventional fluidized beds did not fit for micro‐fluidized beds. u_mf increased with decreasing D_t. When the ratio of H_s to D_t ranged from 1:1 to 3:1, u_mf was characterized by a linear equation with H_s, while the slope of the equation u_mf versus H_s decreased with increasing D_t. In this paper, D_t/d_p and H_s/d_p were defined as dimensionless variables and a new equation was developed to predict u_mf in micro‐fluidized beds under the present experimental conditions.     

Flow through beds of perfusive particles: effective medium model for velocity prediction within the perfusive media

The effective medium model is a modified model for flow through beds of perfusive particles. This model accounts for the advantages in the existing models and eliminate most of their disadvantages. This model consists of a perfusive particle surrounded by a hypothetical envelope that has fluid only. This envelope is surrounded by a swarm of perfusive particles with permeability equal to the bed permeability. The analytical solution has been obtained by solving Brinkman’s equation in the swarm and the perfusive particle and Navier–Stokes equation for creeping flow in the envelope. This model has proven to converge to the existing models. Where, the proposed model is more general. The validity of this model has been tested through the relation between its parameters, where a relation has been derived through the macroscopic and microscopic force balances on a perfusive bed and a single perfusive particle, respectively. The analysis shows that the result from the effective medium model is in a good agreement with the available experimental data for overall bed permeability.     

A numerical study of the accelerating motion of a dense rigid sphere in non-newtonian power law fluids

The equations of motion of an accelerating sphere falling through non-Newtonian fluids with power law index n in the range 0.2 ≤ n ≤ 1.8 were integrated numerically using the assumption that the drag on the sphere was a function of both power law index and terminal Reynolds number, Re_t For 10^?2 ≤ Re_t ≤ 10³ both dimensionless time and distance travelled by the sphere under transient conditions showed a much stronger dependence on the flow behaviour index, n, for shear-thinning than for shear-thickening fluids. The form of this dependence is investigated here. Furthermore, results in four typical shear-thinning fluids suggested a strong correlation between the distance and time travelled by the sphere under transient conditions and the value of the fluid consistency index. The analysis reported herein is, however, restricted to dense spheres falling in less dense fluids, when additional effects arising from the Basset forces can be neelected.     

Particle-resolved simulation of packed beds by non-body conforming locally refined orthogonal hexahedral mesh

The traditional fixed-bed reactor design is usually not suitable for the low tube-to-particle diameter ratios (N=D/d < 8) where the local phenomena of channeling near the wall and backflow in the bed are dominant. The recent "solid particle" meshing method is too complicated for mesh generation, especially for non-spherical particles in large random packed beds, which seriously hinders its development. In this work, a novel high-fidelity mesh model is proposed for simulation of fixed bed reactors by combining the immersed boundary and adaptive meshing methods. This method is suitable for different shapes of particles, which ingeniously avoids handling the complex "contact point" problem. Several packed beds with two different shapes of particles are investigated with this model, and the local flow in the bed is simulated without geometrical simplification. The predicted pressure drop across the fixed bed and heat transfer of the single particle are in good agreement with the corresponding empirical relations. Compared with spherical particles, the packed bed packing with pentaphyllous particles has lower pressure drop and better heat/mass transfer performance, and it shows that this method can be used for the screening of particle shapes in a fixed bed.     

Liquid-Solid mass transfer in a slurry bubble column and a gas-liquid-solid three-phase fluidized bed

Mass transfer coefficients between particles and liquids in a slurry bubble column and a three-phase fluidized bed containing small size particles were obtained with two mass transfer systems: (1) K⁺ –Na⁺ ion-exchange in cation-exchange resin bead beds, including anion-exchange resin beads as inert particles; (2) zinc dissolution by HCl in zinc-plated glass bead beds, and in beds of non-plated glass beads. Operating parameters were gas velocity, liquid velocity, particle diameter, and particle concentration. The dependence of mass transfer coefficients on these parameters is discussed from the viewpoint of the energy supplied into the systems. Correlations of the experimental data using dimensionless groups are compared to previous correlations.     

Numerical determination of fluid-to-particle mass and heat transfer coefficients in packed bed reactors

A method based on particle-resolved CFD is built and validated, to calculate the fluid-to-particle mass and heat transfer coefficients in packed beds of spheres with different tube-to-particle diameter ratios (N) and of various particle shapes with N = 5.23. This method is characterized by considering axial dispersion. The mass and heat transfer coefficients increase by 5%–57% and 9%–63% after considering axial dispersion, indicating axial dispersion should be included in the method. The mass and heat transfer coefficients are reduced as N decreases. The catalyst particles without inner holes show higher mass and heat transfer coefficients than the ones with inner holes, because of unfavorable fluid flow in inner holes. The bed of trilobes has the highest mass and heat transfer coefficients, being 85% and 95% higher than the one of spheres. This work provides a versatile method and some useful guidance for the design of packed bed reactors.