Mass transfer during the removal of dissolved heavy metals from wastewater flows in fluidized beds of ion exchange resins

A fluidized bed of cation exchange resin was used for the removal of cupric ions from a simulated wastewater effluent consisting of copper sulphate solution. Variables investigated were: superficial liquid velocity, particle diameter, bed height and copper sulphate concentration. These variables were studied with respect to their effect on the solid-liquid mass transfer coefficient. The coefficient was found to increase with increasing superficial liquid velocity. Increasing particle diameter, bed height and copper sulphate concentration were found to reduce the mass transfer coefficient. The experimental data can be correlated by the equation valid for the following conditions: 0.23 < Re₁ < 2.27; 0.52 < ? < 0.87; 0.0127 < d_p/d < 0.0417 and 0.0095 < d_p/L < 0.125.     

Effect of Drag–Reducing Polymers on the Rate of Liquid-Solid Mass Transfer in Fixed Beds of Spheres under Forced Convection Conditions

The effect of drag–reducing polymers on the rate of liquid – solid mass transfer in a packed bed reactor under forced convection conditions was studied by measuring the rate of diffusion–controlled dissolution of copper spheres in acidified chromate solutions. The variables investigated were superficial liquid velocity, sphere diameter, bed height, and polymer concentration. The mass transfer coefficient was found to increase with increasing superficial liquid velocity. Increasing both sphere diameter and bed height were found to decrease the mass transfer coefficient. Polymer addition was found to decrease the rate of mass transfer by an amount ranging from 29.2 to 56.9% depending on superficial liquid velocity and polymer concentration. Mass transfer data were correlated in absence and in the presence of drag–reducing polymer, using the following equations, respectively: J_d = 3.71Re^–0.54 and, J_d = 2.5 Re^–0.61where J_d is mass transfer J-factor and Re is the Reynolds number.     

Effect of gas sparging on the rate of mass transfer at fixed beds of horizontally stacked screens

Rates of mass transfer at air sparged fixed beds of stacked screens were measured by an electrochemical technique. Variables studied were air superficial velocity, physical properties of the solution and bed thickness. The liquid mass transfer coefficient was found to increase with air superficial velocity up to a certain point and then remain almost constant with further increase in velocity. The increase in the mass transfer coefficient as a result of air sparging ranged from 2.8 to 10 times the natural convection value depending on the operating conditions. Increasing bed thickness was found to decrease the mass transfer coefficient at a given air superficial velocity. Mass transfer data at fixed beds were correlated by the equation: j = 0.268 (Re · Fr)^?0.25 (L/d)^?0.35. For a single horizontal screen the data were correlated by the equation: j = 0.275 (Re · Fr)^?0.21.     

Effect of Drag‐Reducing Polymer on the Rate of Cementation of Copper Ion on Zinc Pellets

The effect of Polyox WSR‐301 drag‐reducing polymer on the rate of cementation of copper from copper sulfate solution over packed beds of zinc pellets was investigated. The mass transfer coefficient was found to increase with increasing superficial liquid velocity for solution free of polymer. The mass transfer data were correlated in the absence of drag‐reducing polymer, using the following equation J_d = 12.55 Re^–0.5 for the conditions 10 < Re < 1970 and 1265 < Sc < 1393. In the presence of polymer, starting from a Reynolds number (Re) 550, the rate of mass transfer was found to decrease by an amount ranging from 7.5 to 51 % depending on Re and polymer concentrations. The percentage decrease in the rate of mass transfer increased with increasing Re, passed through a maximum at Re = 1400 and then decreased rapidly with further increase in Re.     

Solid‐Liquid Mass Transfer at Gas Sparged Tube Bundles

The solid‐liquid mass transfer characteristics of an in‐line tube bank immersed in a gas‐liquid bubble column were investigated by measuring the rate of diffusion‐controlled dissolution of copper surface in acidified dichromate solution. Variables studied were the number of rows in the tube bank, physical properties of the solution, and nitrogen flow rate. The mass transfer coefficient was found to increase with increasing nitrogen flow rate. Increasing the number of rows in the tube bank was found to decrease the mass transfer coefficient. The data were correlated for the following conditions: 0.0021 < Fr.Re < 0.1603, 1 < N_r < 5 and 850 < Sc < 1370 by the equation J = 0.15 ( Fr.Re )^–0.15. Comparison was made between the present mass transfer data and previous heat and mass transfer studies conducted in packed and empty bubble columns.     

Gas holdup,bubble size distribution,and mass transfer in an airlift reactor with ceramic membrane and perforated plate distributor

The airlift reactor is one of the most commonly used gas–liquid two-phase reactors in chemical and biological processes. The objective of this study is to generate different-sized bubbles in an internal loop airlift reactor and characterize the behaviours of the bubbly flows. The bubble size, gas holdup, liquid circulation velocity, and the volumetric mass transfer coefficient of gas–liquid two-phase co-current flow in an internal loop airlift reactor equipped with a ceramic membrane module (CMM) and a perforated-plate distributor (PPD) are measured. Experimental results show that CMM can generate small bubbles with Sauter mean diameter d₃₂ less than 2.5 mm. As the liquid inlet velocity increases, the bubble size decreases and the gas holdup increases. In contrast, PPD can generate large bubbles with 4 mm < d₃₂ < 10 mm. The bubble size and liquid circulation velocity increase as the superficial gas velocity increases. Multiscale bubbles with 0.5 mm < d₃₂ < 10 mm can be generated by the CMM and PPD together. The volumetric mass transfer coefficient k_La of the multiscale bubbles is 0.033–0.062 s⁻¹, while that of small bubbles is 0.011–0.057 s⁻¹. Under the same flow rate of oxygen, the k_La of the multiscale bubbles increases by up to 160% in comparison to that of the small bubbles. Finally, empirical correlations for k_La are obtained.     

Gas‐Liquid Mass Transfer in Fibrous Bed Reactor with Counter‐Current Liquid Recycle

In this work, the gas‐liquid mass transfer in a lab‐scale fibrous bed reactor with liquid recycle was studied. The volumetric gas‐liquid mass transfer coefficient, k_La, is determined over a range of the superficial liquid velocity (0.0042–0.0126 m.s^–1), gas velocity (0.006–0.021 m.s^–1), surface tension (35–72 mN/m), and viscosity (1–6 mPa.s). Increasing fluid velocities and viscosity, and decreasing interfacial tension, the volumetric oxygen transfer coefficient increased. In contrast to the case of co‐current flow, the effect of gas superficial velocity was found to be more significant than the liquid superficial velocity. This behavior is explained by variation of the coalescing gas fraction and the reduction in bubble size. A correlation for k_La is proposed. The predicted values deviate within ± 15 % from the experimental values, thus, implying that the equation can be used to predict gas‐liquid mass transfer rates in fibrous bed recycle bioreactors.     

Mass transfer characteristics of low H/D bubble columns

The mass transfer characteristics of 0.2, 0.6 and 1.0 m diameter bubble columns having a low height to diameter ratio (0.6 < H/D < 4) and operated at low superficial gas velocities (0.01 < V_G < 0.08 m/s) were investigated. Different types of spargers were used to study their effect on the column performance. The values of effective interfacial area, a , and volumetric mass transfer coefficient, k_L a , were measured by using chemical methods. The values of a and k_L a were found to vary from 40 to 420 m²/m³ of clear liquid volume and from 0.01 to 0.16 s^?1, respectively, in the range of V_G, and V_L covered in this investigation. The value of the liquid-side mass transfer coefficient, k_L, was found to vary from 3 × 10^?4 to 7 × 10⁴ m/s. The effect of the physical properties of the system on the values of a was also investigated. The height to diameter ratio and the column diameter did not have significant effect on the values of gas holdup, a and k_L a . It was found that the sparger design is not of critical importance, provided multipoint/multiorifice gas spargers are used. The comparative performance of bubble columns having low H/D with horizontal sparged contactors and tall bubble columns has been considered.     

Bed-to-wall heat transfer characteristics in a circulating fluidized bed

The bed-to-wall heat transfer coefficients were measured in a circulating fluidized bed of FCC particles (d_p = 65 μm). The effects of gas velocity (1.0–4.0 m/s), solid circulation rate (10–50 kg/m²s) and particle suspension density (15–100 kg/m³) on the bed-to-wall heat transfer coefficient have been determined in a circulating fluidized bed (0.1 m-ID x 5.3 rn-high). The heat transfer coefficient strongly depends on particle suspension density, solid circulation rate, and gas velocity. The axial variation of heat transfer coefficients is a strong function of the axial solid holdup profile in the riser. The obtained heat transfer coefficient in terms of Nusselt number has been correlated with the pertinent dimensionless groups     

Solid–liquid mass transfer in a gas sparging contactor equipped with a tube of circular fins

The solid–liquid mass transfer rate at a stack of circular fin surfaces in a gas sparging contactor was investigated. A diffusion-controlled dissolution technique of copper in an acidified chromate solution was employed. Variables studied included the number of actively exposed fins ranging from 5 to 20, pertinent physical properties of the solution, and air superficial velocity. Experimental data showed that the rate of the diffusion-controlled mass transfer increases with increasing superficial air velocity and decreases with increasing chromate solution acid concentration. Moreover, at relatively low superficial air velocity, increasing the number of actively exposed fins results into a continuous increase in the mass transfer coefficient. At relatively higher superficial air velocity, however, the mass transfer coefficient decreases in the 5–10 range of actively exposed fins and then reverts to increase in the 15–20 range. An empirical correlation relating the mass transfer j factor to Re_g, Fr, and a dimensionless height defined as the ratio of the height of actively exposed fins to the column equivalent diameter was developed based on the data generated in this study, with ±6.45% average deviation.     

Electrochemical wall mass transfer in liquid particulate systems

Ionic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion-controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100. The developed fluidization mass transfer coefficient for 41 < D_T/d_p < 105 were correlated by i_D E = 0.274 Re_H^?0.38 for 10 < Re_H <1600 and by J_D E = 0.455 Re_H^?0.44 for 16.7 < D_T/d_p < 27 and 50 < Re_H < 3500. Re_H is the hydraulic Reynolds number = d_H up/μ_E and d_H is D_T E/[1 + (3/2) ((1–E)) (D_T/d_p)). The distinct effect of D_T/d_p ratio is attributed to wall effects and the non-particulate behaviour of the fluidized bed for D_T/d_p < 27. Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given Re_H.     

Electrodeposition from a fluidized bed electrolyte. II. Effects of bed porosity and particle size

Mass transfer from a fluidized bed electrolyte containing inert particles has been found to depend on bed porosity and particle size. The optimum porosity was found to vary from 0.52 – 0.57 with decreasing particle size but mass transport increased with particle size.A mass transfer entry length effect was observed on the cylindrical cathode but its position within the bulk of the bed was found not to be critical, thus indicating that the hydrodynamic entry length was small. The limiting current density was found to vary as (d _e/L _e)^0.15 whered _e is the annular equivalent diameter andL _e the electrode length.List of symbols Re_I modified Reynolds No. =U _o d _p /v(1–) - Re_II particle Reynolds No. =U _o d _p /v - Re_O sedimentation Reynolds No. =U _i d _p v (constant value) - Re_t terminal particle Reynolds No. =U _t d _p /v - Sc Schmidt No. =v/D - St_I modified Stanton No. =k _L /U _o - C _b bulk concentration, M cm^–3 - D diffusion coefficient, cm² s^–1 - d _t tube diameter, mm - d _e electrode equivalent diameter, mm - d _p particle diameter, mm - bed porosity - zF Faradaic equivalence - cd current density - i _L limiting current density, mA cm^–2 - i _LO limiting current density in the absence of particles - k _L mass transfer coefficient, cm s_–1 - L _e electrode length, mm - m, n constants or indices - v kinematic viscosity, cm² s^–1 - U _o superficial velocity, cm s^–1 - U _i sedimentation velocity, cm s^–1     

Gas‐Liquid Mass Transfer in a Bench‐Scale Trickle Bed Reactor used for Benzene Hydrogenation

The gas‐liquid mass transfer coefficients (MTCs) of a trickle bed reactor used for the study of benzene hydrogenation were investigated. The Ni/Al₂O₃ catalyst bed was diluted with a coarse‐grained inert carborundum (SiC) particle catalyst. Gas‐liquid mass transfer coefficients were estimated by using a heterogeneous model for reactor simulation, incorporating reaction kinetics, vapor‐liquid equilibrium, and catalyst particle internal mass transfer apart from gas‐liquid interface mass transfer. The effects of liquid axial dispersion and the catalyst wetting efficiency are shown to be negligible. Partial external mass transfer coefficients are correlated with gas superficial velocity, and comparison between them and those obtained from experiments conducted on a bed diluted with fine particles is also presented. On both sides of the gas‐liquid interface the hydrogen mass transfer coefficient is higher than the corresponding benzene one and both increase significantly with gas velocity. The gas‐side mass transfer limitations appear to be higher in the case of dilution with fine particles. On the liquid side, the mass transfer resistances are higher in the case of dilution with coarse inerts for gas velocities up to 3 · 10^–2 cm/sec, while for higher gas velocities this was inversed and higher mass transfer limitations were obtained for the beds diluted with fine inerts.     

Experimental Study on Flow Behavior in a Gas‐Solid Fluidized Bed for the Methanol‐to‐Olefins Process

A cold model experimental system is established to investigate the flow behavior in a gas‐solid fluidized bed for the methanol‐to‐olefins process catalyzed by SAPO‐34. The system comprises a gas distributor in a F 300 × 5000 mm acrylic column, double fiber optic probe system and a series of cyclones. The experiments are carried out under conditions of atmospheric pressure and room temperature with different superficial velocities (0.3930–0.7860 m s^–1) and different initial bed heights (600–1200 mm). The effects of radial distance, axial distance, superficial gas velocity, and initial bed height on the solid concentration and particle velocity in the bed are discussed. The time‐averaged solid concentration and rising particle velocity profiles under different conditions are obtained. The results show that an increase in the value of r/R or initial bed height results in an increase in the solid concentration but a decrease in the rising particle velocity in the dense phase area, while improvement of the superficial gas velocity has a negative influence on the solid concentration but results in an increase in the rising particle velocity.     

Effect of temperature on slug properties in a gas fluidized bed

In order to understand the effect of temperature on slug properties, the onset velocity of slugging, slug rising velocity and slug frequency have been measured by a differential pressure method in an electrically heated gas fluidized bed of 0.1 m i.d. and height of 1.97 m and, with respect to variations in gas velocity (U_mf∼0.15 m/s) and temperature (25-400 °C). Air was used as fluidizing gas and fluid catalytic cracking (FCC) catalyst particle (Geldart's group-A particle, d_p=0.071 mm, ρ_p=1600 kg/m³) as bed material. The minimum slugging velocity was found to increase a little with bed temperature. The qualitative change in minimum slugging velocity was found to agree with the inverse of minimum fluidizing velocity as temperature was varied. As the bed temperature increased, slug frequency was found to decrease a little, whereas slug rising velocity increased. A correlation between slug rising velocity and bed temperature was proposed.     

Wall-to-bed heat transfer characteristics of spout-fluid beds

Wall-to-bed heat transfer characteristics have been investigated in a rectangular spout-fluid (S–F) bed segment column (20 cm length, 5 cm width and 50 cm height) utilizing glass beads (D_p = 0.254, 0.388 and 0.461 mm) and air as fluid. Results indicate that h values in the S–F bed increase with increasing air mass velocity and particle diameter, and decrease with increasing bed height. Under identical flow conditions h values in the S–F bed were about 30% more than for the corresponding fluidized bed.     

IONIC MASS TRANSFER IN THREE-PHASE FLUIDIZED BEDS IN THE PRESENCE OF DISC PROMOTERS

Three-phase fluidized beds have wide applications in process industries. The present investigation is carried out to identify the enhancement of ionic mass transfer coefficients due to the presence of a disc promoter in a three-phase fluidized bed. A diffusion-controlled electrode reaction—reduction of ferricyanide ion—was employed to obtain mass transfer coefficient data. The mass transfer coefficient data were obtained by varying the geometric variables of the disc promoter (disc diameter, disc spacing) and dynamic variables (superficial liquid velocity, superficial gas velocity). The effect of particle diameter was also investigated. The investigations revealed that the mass transfer coefficients were enhanced with decreased disc spacing, increased disc diameter, increased superficial gas velocity, increased superficial liquid velocity, and increased particle diameter.     

Mass transfer at rough gas-sparged electrodes

Rates of mass transfer were measured by the limiting current technique at a smooth and rough inner surface of an annular gas sparged cell in the bubbly regime. Roughness was created by cutting 55°V-threads in the electrode normal to the flow. Mass transfer data at the smooth surface were correlated according to the expression j = 0.126(Fr Re)^–0.226 Surface roughness of peak to valley height ranging from 0.25 to 1.5 mm was found to have a negligible effect on the mass transfer coefficient calculated using the true electrode area. The presence of surface active agent (triton) in the solution was found to decrease the mass transfer coefficient by an amount ranging from 5% to 30% depending on triton concentration and superficial air velocity. The reduction in the mass transfer coefficient increased with surfactant concentration and decreased with increasing superficial gas velocity.Nomenclature a constant - A electrode area (cm²) - C _p specific heat capacity Jg^–1 (K^–1) - C ferricyanide concentration (m) - d _c annulus equivalent diameter, (d _o – d _i) (cm) - d _o outer annulus diameter (cm) - d _i inner annulus diameter (cm) - D diffusivity of ferricyanide (cm²s^–1) - e peak-to-valley height of the roughness elements (cm) - e ⁺ dimensionless roughness height (eu ^*/) - f friction coefficient - F Faraday constant (96 500 Cmol^–1) - g acceleration due to gravity (cm s^–2) - h heat transfer coefficient (J cm^–2 s K) - I _L limiting current (A) - K mass transfer coefficient (cm s^–1) - K thermal conductivity (W cm^–1 K^–1) - V _g superficial air velocity (cm s^–1) - Z number of electrons involved in the reaction - Re Reynolds number (_L V _g d _e/) - J mass or heat transfer J factor (St Sc ^0.66) or (St Pr ^0.66), respectively - St Stanton number (K/V _g for mass transfer and h/C _p V _g for heat transfer) - Fr Froude number (V _g ² /d _e g) - Sc Schmidt number (/D) - Pr Prandtl number (C _p/K) - PL solution density (g cm^–3) - kinematic viscosity (cm²s^–1) - gas holdup - u ^* friction velocity = V _L(f/2) - diffusion layer thickness (cm) - solution viscosity (gcm^–1 s^–1)     

Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Thermal inefficiency model for determination of the bed-to-gas heat transfer coefficients with effectiveness factor in a fluidised bed

Process operations often involve the physical interaction of a gas and a solid phase. Fluidised bed heat transfer can be characterised by limited space–time (τ) on the basis of particle volume in the bed. As aimed in this study, a thermal inefficiency model (TIM) was developed using a pseudo-steady-state heat balance, i.e., equating the electrical power input to the rate of heat transfers from the bed to the gas. A bench-scale fluidised bed (105 × 200 mm) was operated for obtaining the gas temperature profiles. Temperature data were used for extracting the bed-to-gas heat transfer coefficients (h_BG) with effectiveness factors (η) from the TIM. Fluidised bed experiments at low temperature range (290–473 K) were conducted avoiding excessive instrumentation and time. Compressed dry air entered the bed through a distributor of a 200-mesh brass sieve and fluidised the single charge of alumina particles (1.3 kg) with a mean diameter approximately 250 μm. The superficial gas velocity was changed from 0.085 to 0.469 m s^− 1. The bed-to-gas heat transfer coefficients (h_BG0×η₀) at initial bed hight and thermal inefficiency constants (k_I) were calculated from the intercept and slope of the linear form of the TIM, respectively. The agreement between the experimental and predicted values of gas temperatures confirmed by the TIM. The latter may be successfully used to design fluidised beds for, e.g., drying or combustion.