Mass transfer in agitated vessels: energetic aspects

This paper deals with the experimental determination of the mass transfer rates between the liquid of an agitated vessel and a spherical particle immersed in a reactor. The spatial distribution of the mass transfer coefficients is obtained using an electrochemical method and the influence of the most pertinent hydrodynamic parameters (impeller speed and fluid residence time inside the vessel) is deduced from experimental results. The study considers the two limiting cases of mechanical agitation alone and agitation induced by the liquid jets generated by the feed nozzles. It is shown that knowledge of the specific power dissipated per unit mass of fluid can be useful for the theoretical prediction of the mass transfer rates.Nomenclature D molecular diffusion coefficient - d _p particle diameter - D _i impeller diameter - D _v vessel diameter - E hydrodynamic parameter defined in Equation 8 - H vessel height - k mass transfer coefficient - l characteristic length in Equation 2 - M mass of liquid in the vessel - N rotational speed of agitator - N _p specific power number - P specific power delivered - Q _v volumetric flow rate of the feed fluid - S area for fluid injection - (Sc) =v/D = liquid Schmidt number - (Sh) =kd _p /D kl/D = Sherwood number - U local fluid velocity - V vessel volume - x vertical distance between the bottom of vessel and the measuring point - coefficient in Equation 2 - kinematic viscosity - fluid density - =V/Q _v = residence time in vessel     

Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables

A hierarchical and computationally efficient mathematical model was developed to explain the polymerization of high-density polyethylene (HDPE) in an isothermal, industrial, continuous stirred tank slurry reactor (CSTR). A modified polymeric multi-grain model (PMGM) was used. Steady-state macroscopic mass balance equations were derived for all species (namely, monomer, solvent, catalyst and polymer) to obtain the final particle size and the required monomer and solvent input rates for a given catalyst input and the reactor residence time. The interphase mass transfer coefficients were calculated for the industrial CSTR using the operating data on the reactor. The present model was tuned with some data on an isothermal industrial reactor and the simulation results were compared with data on another set of industrial reactor. The comparison revealed that the present tuned model is capable of predicting the productivity and the polymer yield at various catalyst feed rates and the mean residence times. The effects of variation of two operating variables (catalyst feed rate and mean residence time) on the productivity, the polymer yield, the polydispersity index (PDI) and the operational safety were analyzed. The present study indicated that an optimal value of the reactor residence time (for maximum productivity per catalyst particle) exists at any catalyst feed rate.

     

Application of metallic foams in electrochemical reactors of filter-press type Part I: Flow characterization

The aim of the present paper is to investigate the application of nickel foam electrodes in classical filter-press type electrochemical cells. For this purpose the ElectroSynCell®, commercialized by Electrocell AB, has been used. The interest of using metallic foams linked to a classical plane plate is to improve the performance of the electrochemical cell by increasing the electrode surface area. Moreover, for some industrial applications it is possible to use the cell without a membrane. In the proposed configuration, the working electrodes consist of metallic foam linked to a plane plate and the auxiliary electrode is simply a plane plate. The imbalance between the surface areas of working and auxiliary electrodes allows operation with a single hydraulic circuit. This paper, focuses on the study of residence time distribution and pressure drop in order to compare the flow behaviour with that in a classical configuration. A model for the reactive zone of the cell is also given.Notation D _ax axial dispersion coefficient (m2 s^–1) - ER root mean square error - F(s) transfer function in Laplace domain - I number of continuous stirred tank reactors in the first cascade (model of the two cascades) - J number of continuous stirred tank reactors in the second cascade (model of the two cascades) - L length of the path in the reactor (m) - P pressure drop (Pa) - Pe _r Peclet number of reactor - Q _v volumic flow rate (m³ s^–1) - _s mean residence time (s) - u interstitial velocity (m s^–1) - U _o mean superficial velocity (m s^–1) - X(t) experimental signal at the inlet of the reactor - Y(t) experimental signal at the outlet of the reactor - Y _ca1(t) calculated signal at the outlet of the reactor Greek letters porosity of the duct in the reactor - standard deviation - ₁ mean residence time in the first cascade (s) - ₂ mean residence time in the second cascade (s)     

Radiation-induced polymerization of ethylene in pilot plant. III. Heavy-phase recycling process

Radiation-induced polymerization of ethylene using aqueous tert-butyl alcohol as medium was carried out in a large-scale pilot plant with a 50-liter central source-type reactor at a pressure of 105 to 395 kg/cm², temperature of 30° to 80°C, mean dose rate of 4.5 × 10⁴ to 1.9 × 10⁵ rads/hr, ethylene feed rate of 5.5 to 23.5 kg/hr, and medium feed rate of 21 to 102 l./hr. The space–time yield and molecular weight of the polymer were in the range of 4.7 to 16.8 g/l.-hr and 1.3 × 10⁴ to 8.9 × 10⁴, respectively. The space–time yield and molecular weight increased with mean residence time at 30°C, whereas at 80°C they became almost independent of the time. The space–time yield increased with pressure and dose rate, slightly decreased with temperature, and was maximum at ethylene molar fraction of 0.5. The polymer molecular weight increased with pressure and ethylene molar fraction, and decreased with dose rate and temperature. The total amount of deposited polymer on the reactor wall, source case wall, and scraping blades was usually less than 1 kg, which was negligibly small for the analysis of polymerization. Continuous discharge of the polymer slurry and production of fine-powder polyethylene were successfully carried out. In the central source-type reactor, a dose rate of 1.9 × 10⁵ rads/hr was obtained with a ⁶⁰Co source of ca. 12 kCi.     

Longitudinal mixing in horizontal rotary drum reactors

The longitudinal mixing of sodium carbonate (soda) (mean particle size 137 μm) has been investigated in a laboratory horizontal rotary drum reactor 250 mm in diameter and 600 mm long. The distributions of residence times have been estimated by means of a pulse of a small amount of sodium bicarbonate. The concentration of the tracer at the reactor discharge has been evaluated by thermal decomposition of the samples and by measuring their weight loss.The hold-ups, the mean residence times and the variances of the distribution of residence times were evaluated as a function of the rotational speed of the reactor and the feed rate of the particles. By applying a dispersion model, the Peclet numbers were evaluated from the standardized variances and plotted as a function of the feed rate and rotational speed. The mean residence time of the particles was calculated by means of an extended model of Vahl and Kingma. They correspond with the experiments.     

Mixing and Crystallization Kinetics in Gas‐liquid Reactive Crystallization

A study of gas‐liquid reactive crystallization for CO₂‐BaCl₂‐H₂O system was performed in a continuous flow crystallizer. The influences of mixing on the crystallization kinetics of barium carbonate crystals were investigated. The mixing parameters are stirrer speed, feed concentration, gas‐flow rate, pH of solution, addition rate of NaOH solution, and mean residence time. Under pH‐stat operation, the crystallization mechanism can be assessed by the addition rate of NaOH solution, which acts as an indicator for the absorption rate of carbon dioxide. Assuming a size‐independent agglomeration mechanism, the nucleation rate, growth rate and agglomeration kernel can be obtained, simultaneously, at steady state, by the method of moments. Evidence shows that feed concentration, feed rate, gas‐flow rate, and stirrer speed have a significant influence on the nucleation rates and mean particle sizes. This shows the effect of micromixing. The crystallization mechanism tends to be reaction limited when the feed concentration of barium chloride solution is higher than 5 mM, while at lower stirrer speeds and feed concentrations, the mechanism tends to be both mixing and reaction controlled. The growth rate depends on the mean supersaturation value and the pH of the solution and the mass‐transfer resistance cannot be completely eliminated in this work. For a monodispersal collision model, in the viscous sub‐range of turbulence, the agglomeration kernel can be expressed as β ∝ d^{3 –1/4}, showing a low efficiency of collision. The result is also demonstrated by the agglomeration kernel expression. Comparison with a liquid‐liquid‐mixing reactive crystallization system is also discussed.     

Paste Residence Time in a Spouted Bed Dryer. IV: Effect of the Inert Particle Size Distribution

The residence time distribution and mean residence time of a 10% sodium bicarbonate solution that is dried in a conventional spouted bed with inert bodies were measured with the stimulus-response method. Methylene blue was used as a chemical tracer, and the effects of the paste feed mode, size distribution of the inert bodies, and mean particle size on the residence times and dried powder properties were investigated. The results showed that the residence time distributions could be best reproduced with the perfect mixing cell model or N = 1 for the continuous stirred tank reactor in a series model. The mean residence times ranged from 6.04 to 12.90 min and were significantly affected by the factors studied. Analysis of variance on the experimental data showed that mean residence times were affected by the mean diameter of the inert bodies at a significance level of 1% and by the size distribution at a level of 5%. Moreover, altering the paste feed from dripping to pneumatic atomization affected mean residence time at a 5% significance level. The dried powder characteristics proved to be adequate for further industrial manipulation, as demonstrated by the low moisture content, narrow range of particle size, and good flow properties. The results of this research are significant in the study of the drying of heat-sensitive materials because it shows that by simultaneously changing the size distribution and average size of the inert bodies, the mean residence times of a paste can be reduced by half, thus decreasing losses due to degradation.     

CFD-DPM-based numerical simulation for char gasification in an entrained flow reactor: Effect of residence time distribution

The rate of conversion during gasification of char particles depends on the type of reagents, the concentration of reactants, and reactor temperature, among many other parameters; however, the overall conversion depends on the residence time distribution (RTD) of the particles in the reactor. The objective of the present work is to investigate the influence of gasifying agents, their concentration, and reactor wall temperature on the RTD of the char particles. The aim also includes studying the effect of mean residence time on the overall char conversion during gasification of Victorian brown coal in an entrained flow reactor. Two gasifying reagents, namely, CO₂ and H₂O, are selected in the present study. A discrete particle model (DPM) is coupled with computational fluid dynamics (CFD) to simulate the solid phase dynamics. Gasification is modelled using a lumped approach. The mean residence time of the solid char particles, determined using three different methods, is observed to increase with the CO₂ concentration and wall temperature but decrease in the H₂O environment. The longer residence time leads to higher overall char conversion in a CO₂ environment despite the higher reactivity of H₂O compared to CO₂ as a gasifying reagent.     

Modelling of simultaneous methanogenesis and denitrification in an upflow packed-bed biofilm reactor

The performance of an upflow packed-bed biofilm reactor was investigated by considering simultaneous methanogenesis and denitrification reactions under step and sinusoidal variations of feed concentration and temperature. For simultaneous step inputs of 20 mg dm⁻³ of NO₃⁻—N and 60 mg dm⁻³ of methanol, the proposed model shows that major conversion of both the substrates takes place in the first half of the reactor. However, when the inlet concentration of methanol is subjected to sinusoidal variation, while that of NO₃⁻—N is maintained stepwise, the exit concentration of both methanol and NO₃⁻—N follow a sinusoidal response. On the other hand, when the inputs are reversed (methanol stepwise and NO₃⁻—N sinusoidal), the response exhibits similar behaviour. For sinusoidal variation of feed temperature the exit concentration profiles of both substrates also follow a sinusoidal pattern. For methanol, the mean steady state conversion under sinusoidal variation is higher than the corresponding steady state concentration when feed temperature is constant at 30°C. The model predictions are in good agreement with the experimental data available in the literature. ©1997 SCI     

Radiation-induced polymerization of ethylene in pilot plant. IV. Kinetic analysis

The kinetics of the radiation-induced polymerization of ethylene in a flow system using tert-butyl alcohol aqueous solution as a medium were studied. The polymerization was carried out in a large-scale pilot plant with a 50-liter central source-type reactor at various mean residence times and does rates under constant pressure of 300 kg/cm², temperature of 30°C, and ethylene molar fraction of ca. 0.4. The reaction mixture in the reactor was back-mixed flow from the residual polymer concentration in the reactor. The results of the polymerization were analyzed by kinetic treatment based on a reaction mechanism with both first-and second-order terminations for the propagating radical. The apparent rate constants, except for that of second-order termination (k_t2), were consistent with those determined by small-scale batch experiments. The k_t2 is 20 to 40 times larger than that in the batch experiments. The k_t2 increases with decrease in mean residence time and with agitation, probably because of mobility of the propagating radical.     

Continuous Methanolysis of Palm Oil Using a Liquid–Liquid Film Reactor

A system for the continuous methanolysis of palm oil using a liquid–liquid film reactor (LLFR) was developed and characterized. This reactor is a co-current, constant diameter (0.01 m), custom-made packed column where the mass transfer area between the partially miscible methanol-rich and vegetable oil-rich phases is created in a non-dispersive way, without the intervention of mechanical stirrers or ultrasound devices. An increase in contact area between phases enhances reaction rate while the absence of small, dispersed droplets of one phase into the other diminishes the settling time at the end of the reaction. In this study variations on the concentration of catalyst (sodium hydroxide), flow rate of palm oil and normalized length of the reactor (L/L _max) were explored, keeping constant both the methanol to oil molar ratio and the temperature of the reaction (6:1 and 60 °C). The best experimental results with a reactor of 1.26 m (L/L _max = 1.0) showed a conversion of palm oil of 97.5% and a yield of methyl esters of 92.2% of the theoretical yield, when the mass flow rate and the residence time of the palm oil were 9.0 g min⁻¹ and 5.0 min, respectively. To determine the mean residence time and the degree of axial mixing in the reactor, a residence time distribution (RTD) study was performed using a step-function input. The dispersion model appears to fit well the RTD experimental data.     

Experimental Study on Ozone Synthesis via Dielectric Barrier Discharges

The characteristics of ozone generation using a dielectric barrier discharge reactor were investigated experimentally. Results indicate that ozone concentration increases with increasing applied voltage and gas residence time. In addition to applied voltage, ozone generation rate varies with reactor configuration as well. Optimum ozone generation rates can be reached at the specific gas residence time for a given applied voltage and gas composition. At the same applied voltage, the reactor with a single dielectric barrier results in a higher ozone generation rate in comparison with the reactor having double dielectric barriers. Given a constant N₂/O₂ ratio in the feed gas, NO_x concentration increases as applied voltage and gas residence time increase. Results indicate that maximum NO_x concentration is reached when the N₂/O₂ ratio of feed gas is 4.     

The effect of radical desorption on the particle size distribution in vinyl acetate emulsion polymerization

The effect of free radical desorption is studied by using a mathematical model of particle size distribution in continuous emulsion polymerization. By comparing the theoretical prediction with experimental data, the value of D_o for the vinyl acetate (VAc) system is best chosen as 0.19 × 10^?7 cm²/h. The effect of radical desorption as well as mean residence time on the absolute particle size distribution, total concentration of polymer particles, conversion, and average number of radicals per polymer particle are analyzed by the model proposed.     

Attrition of Victorian brown coal during drying in a fluidized bed

Analyzing the attrition of Victorian brown coal during air and steam fluidized bed drying, the change in particle size distribution over a range of initial moisture contents (60% to 0%) and residence times (0 to 60 minutes) was determined. Dried at a temperature of 130°C with a fluidization velocity 0.55 m/s and an initial particle size of 0.5–1.2 mm, both fluidization mediums show a shift in the particle size distribution between three and four minutes of fluidization, with a decrease in mean particle size from 665 µm to around 560 µm. Using differential scanning calorimetry (DSC), the change in particle size has been attributed to the transition between bulk and non-freezable water (approximately 55% moisture loss) and can be linked to the removal of adhesion water, but not to fluidization effects. This is proved through the comparison of air fluidized bed drying, steam fluidized bed drying, and fixed bed drying—the fixed bed drying is being used to determine the particle size distribution as a function of drying. The results show the three drying methods produce similar particle size distributions, indicating that both fluidization and fluidization medium have no impact upon the particle size distribution at short residence times around ten minutes. The cumulative particle size distribution for air and steam fluidized bed dried coal has been modeled using the equation P_d = A₂ + (A₁ ? A₂)/(1 + (d/x₀)^p), with the resultant equations predicting the effects of moisture content on the particle size distribution. Analyzing the effect of longer residence times of 30 and 60 minutes, the particle size distribution for steam fluidized bed dried coal remains the same, while air fluidized bed dried coal has a greater proportion of smaller particles.     

Effect of residence time spectrum in the oligomerisation of isobutene from mixed butenes

The influence of the residence time spectrum on the conversion, selectivity and product composition in the oligomerisation of isobutene from mixed butenes in a continuous stirred-tank reactor was studied at a temperature of 65 °C and impeller Reynolds number in the range of 36 × 10⁴ to 67 × 10⁴. The average residence time and its spectrum affected the conversion of olefins in the feed gas, the selectivity and the octene yields. It was established that for best yields of 2,4,4-trimethyl pent-1-ene obtained from the mixed butenes feed, the residence time spectrum should be as narrow as possible. The results indicate that for good yield and selectivity in iso-octene production from a C₄ olefin fraction, Reynolds number of mixing of around 68 × 10⁴ or slightly higher would be most desirable.     

Performance of bipolar trickle reactors

The performance of the bipolar trickle reactor has been studied using the electrochemical tracer technique. The theoretical equations for a semi-infinite dispersion model have been fitted to the experimental responses for the reactor with and without electrochemical reaction. Hydrodynamic parameters and reaction rate constants for copper deposition as functions of both the film Reynolds number and the dimensions of the bipolar trickle reactor have been derived and are interpreted in this paper.List of Symbols (Bo) Bodenstein number (uL _p/D) - C amplitude of the response curve (dimen sionless) - C ⁰ area under the response curve (mol cm^–3 s) - D dispersion coefficient (cm²s^–1) - h film thickness (cm) - k/h first order reaction rate constant (s^–1) - L length of the reactor (cm) - L _p length of the ring (cm) - n _r number of rings in a single layer - (Pe) Peclét number (uL/D) - (Re)_f film Reynolds number - r _i,r _o inner and outer radii of the ring (cm) - t time (s) - u mean liquid velocity (cm s^–1) - v volumetric liquid velocity (cm³ s^–1) - residence time (s) - kinematic viscosity (cm²s^–1)     

Preparation of Fe-Si Nanoparticles in Furnace Aerosol Reactor

Crystalline Fe-Si alloy particles ranging from 37 to 150 nm in diameter were produced by thermal decomposition of a mixture of Fe(CO)₅ and SiH₄ in a furnace aerosol reactor. The reactor was made of alumina, 2.4 cm in diameter and 100 cm in length. The operating variables were reactor temperature (800–1400°C), the Fe(CO)₅ concentration (2.5 × 10^?5 to 1.5 × 10^?4 moI/I), the molar ratio of Fe(CO)₅ to SiH₄ (100:0 to 50:50), and the residence time (2.5–10s). The primary particle size increased with reactor temperature increase and decreased when the Si content of the precursor was increased. The sintering of the particles within the agglomerates was an important factor in determining the primary particle size, and the sintering was inhibited by the silicon. The spatial variation of particle morphology was observed by in situ deposition of particles on a TEM grid. At 7 cm from the reactor inlet, nonagglomerated spherical particles encapsulating several smaller iron particles were found. The spherical structure were destroyed downstream to form agglomerates.     

Emulsion polymerization kinetics and reactor design. IV. Continuous-flow operation with recycling

A new mathematical model with a correction for radical capturing efficiency in a continuous emulsion polymerization with recycle flow has been proposed. These performance equations predict the conversion as well as molecular weight distribution of the polymer product during the continuous-flow operation. Experimental results obtained with vigorous mixing associated with a premixer are in best agreement with the theoretical prediction. In certain situations, the recycling provides a means for obtaining a higher degree of back-mixing with a normal flow reactor. However, it is difficult to obtain a high conversion of monomer by a continuous emulsion polymerization operation even with a long residence time. Theoretical and experimental average degrees of polymerization of polymer leaving the reactor are progressively displaced toward smaller values with greater mean residence time. According to the calculations based on our kinetic model the ratio M?_w/M?_n in the continuous emulsion polymerization remains constant regardless of mean residence time.     

Decolorization of organic dyes by Irpex lacteus in a laboratory trickle‐bed biofilter using various mycelium supports

BACKGROUND: Dyes used in textile industries and released to their wastewaters are serious ecological problems as they are hard to degrade by common means used in wastewater treatment plants. White‐rot fungi can biodegrade textile dyestuffs using their extracellular enzyme system. However, it is difficult to keep them in functional form in conventional wastewater treatment systems, because of their specific nutritional and physiological requirements. Selection of a suitable bioreactor type and mode of operation are crucial for successful implementation of white rot fungi in waste water treatment processes. RESULTS: Both Remazol Brilliant Blue R (RBBR) and Reactive Orange 16 (RO16) were decolorized efficiently in the trickle‐bed reactor. A degree of decolorization exceeding 80% was achieved within 2 days with all mycelium carriers and both dyes. In reactors packed with plastic kitchen scourers and luffa sponge slices the decolorization degree reached 90% within 2 days. The initial rate of decolorization of RBBR dye was notably higher than the rate of RO16 decolorization. The lowest liquid hold‐up value (1–1.5%) was achieved in the reactor packed with the plastic kitchen scourers, the largest hold‐up value (3–5%) was observed in the reactor filled with luffa sponge. The longest mean retention time, 430 s, was achieved in the reactor with the luffa carrier at a liquid flow rate of 6.81 cm³ min^?1; the shortest mean retention times (10–20 s) were achieved in the reactor filled with the plastic kitchen scourers. Broad liquid residence time distributions were observed in tracer experiments at all volumetric flow rates. CONCLUSIONS: The ability of I. lacteus to secrete laccase and manganese peroxidase enzymes in a trickle‐bed bioreactor with three mycelium carriers was proved and quantified experimentally. The decolorization capability of the I. lacteus mycelium was only marginally influenced by the kind of carrier used. Basic operational characteristics of the reactor—residence times, axial dispersion and liquid hold‐up—were determined at various liquid flow rates. Copyright © 2009 Society of Chemical Industry     

Radiation-induced polymerization of ethylene in a pilot plant. II. Development of wet-wall process

Radiation-induced polymerization of ethylene using tert-butyl alcohol aqueous solution as a medium was carried out in a pilot plant with 10 liter reactor at pressures of 100 to 400 kg/cm², ethylene feed rates of 1.2 to 11.8 kg/hr, medium feed rates of 0 to 100 liter/hr, dose rates of 0.6 × 10⁵ to 1.4 × 10⁵ rad/hr, and at room temperature. The space-time yield and molecular weight of polymer were in the range of 1.2 to 16.7 g/liter hr and 6 × 10³ to 2 × 10⁵, respectively. The space-time yield and molecular weight increased with pressure and mean residence time. The space-time yield was the maximum at an ethylene molar fraction of 0.5. The produced polymer was continuously taken out from the high-pressure system as a slurry. The amount of deposited polymer to the reactor wall was markedly decreased, and five full days continuous operation was successfully performed with the space-time yield of 13.5 g/liter hr.