Particle suspension and mass transfer rates in agitated vessels

This paper reviews and presents new information on three aspects of the behaviour of suspended solid particles in agitated tanks. The first is the minimum rate of stirring N required to keep the particles just suspended (JS) against their tendency to settle to the bottom of the tank. The second is the rate of mass transfer from suspended particles. The third is the relation between these two rates, that is, between N_JS and the corresponding mass transfer coefficient k_LJS.Theoretical and practical aspects of these three problems are discussed here, and it is shown that, starting from basic turbulence theory, one can predict N_JS as a function of particle concentration c.The reported constancy of the experimental k_LJS when the tank geometry is widely varied follows from the theoretical equations of the present paper.     

Particle liquid mass transfer in stirred tanks

Mass transfer coefficients were determined for 1/8 inch diameter spherical particles suspended in stirred aqueous iodine solutions. Particle density was adjusted to within 5% of the liquid density. For these particles, suspended in a covered and fully baffled vessel, the effect of impeller speed (200-600 rpm), system Schmidt number (770-11, 300) and impeller type (fan disk turbine, propeller and 45° paddle and turbine) on the mass transfer coefficient, was examined. A dimensionless group correlation using the impeller blade tip velocity represent the data with an average deviation of 8% and a maximum deviation of 27%. N_sh = 2 + 0.109 Because the particles used in the present study are considerably different from the tablets, beads and crystals that have been used previously, the coefficients of this study are a strict test of existing correlations. Partial agreement of coefficients and recent correlations was observed, but no single correlation can be recommended. Considerable discussion of the many aspects of Harriott's method of correlation also is presented.     

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     

Experimental Studies on Suspension of Solid Particles in a Low‐Shear Stirred Vessel

A low‐shear stirred vessel was explored. Experimental studies on the suspension of solid particles in solid‐liquid and gas‐solid‐liquid systems were conducted to examine the performance of this new reactor. The method based on the power number curve was modified to determine the critical impeller speeds required for just complete off‐bottom suspension of solids under non‐gassed (N_js) and gassed conditions (N_jsg) in this reactor, and a PC‐6A fiber‐optic probe for the measurement of solid distribution was used to complementarily validate this method. A more homogeneous flow field was gained with a draft tube installed, so that the standard deviations of average shear rate and maximal shear rate are reduced. The modified power consumption method can determine N_js and N_jsg, and the values of N_js with a draft tube are much lower than those without it. N_jsg increases slightly with increasing gas flow rate, and N_jsg with a higher solid weight fraction is larger in this lower‐shear reactor.     

Unsuspended mass of solid particles in stirred tanks

An original technique for the determination of the fraction of unsuspended solid particles at agitation speeds smaller than N_js, is proposed. The technique is based on the “twin-systems” concept and is completed by a suitable tracing and detection technique for the solid phase. Results obtained with a fully baffled tank stirred by a Rushton turbine impeller show that the fraction of solids never leaving the tank bottom can be simply correlated to the ratio between agitation speed and Zwietering's complete suspension speed. It is shown that at agitator speeds of about 80% of Zwietering's complete suspension speed, practically all particles but a few, are already suspended. This finding implies that large energy and installation cost savings can be achieved, with respect to current design practices, without significantly affecting the solid-liquid mixing performance.     

Gas‐liquid mass transfer in low‐ and medium‐consistency pulp suspensions

The volumetric gas—liquid mass transfer coefficient (k_La) was measured for low‐ and medium‐consistency pulp suspensions using the cobalt‐catalyzed sulfite oxidation technique. Mass transfer rates were measured in a high‐shear mixer for a range of operating parameters, including the rotor speed (N = 10 to 50 rev/s), gas void fraction (X_g = 0.10 to 0.40) and fibre mass concentration (C_m = 0.0 to 0.10). k_La measurements were compared with the macroscale flow regime in the vessel (characterized using photographic techniques) and correlated with energy dissipation, gas void fraction and suspension mass concentration in the mixer. We found that gas‐liquid mass transfer was significantly reduced in pulp suspensions, even for low suspension concentrations. Part of this reduction was associated with dissolved components leached from the fibres into the liquid phase. This could account for reductions in k_La of up to 30% when compared with distilled water. The fibres further reduced k_La, with the magnitude of the decrease depending on the fibre mass concentration. Correlations were developed for k_La and compared with results available in the literature.     

Influence of polyethylene oxide on absorption of carbon dioxide into aqueous <Emphasis Type="Italic">N</Emphasis>-methyldiethanolamine solution

Carbon dioxide was absorbed into aqueous polyethylene oxide (PEO) solution containing N-methyldiethanolamine (MDEA) in a flat-stirred vessel to investigate the effect of non-Newtonian rheological behavior of PEO on the chemical absorption rate of CO₂, where the reaction between CO₂ and MDEA was assumed to be a first-order reaction with respect to the concentration of CO₂ and MDEA, respectively. A unified correlation equation containing the Deborah number, which reflects the viscoelastic properties of a non-Newtonian liquid, was used to obtain the volumetric liquid-side mass transfer coefficient of carbon dioxide in aqueous PEO solution. The elastic properties of PEO accelerated the absorption rate of CO₂ compared with that of a Newtonian liquid based on the same values of viscosity.     

Gas–liquid interfacial area and mass transfer coefficient in a co‐current down flow contacting column

The gas–liquid interfacial area and mass transfer coefficient for absorption of oxygen from air into water, aqueous glycerol solutions up to 1.5% (w/w) and fermentation medium containing glucose up to a 3% concentration were determined in a co‐current down flow contacting column (CDCC; 0.05 m i.d. and 0.8 m length). Experimental studies were conducted using various nozzle diameters at different gas and re‐circulation liquid rates. Specific interfacial area (a) is determined from the fractional gas hold‐up (ε_G) and the average bubble diameter (d_b). Once the interfacial area is determined, the volumetric mass transfer coefficient (k_La) is then used to evaluate the film mass transfer coefficient in the CDCC. The effects of operating conditions and liquid properties on the specific interfacial area were investigated. The values of interfacial area in air–aqueous glycerol solutions and fermentation media were found to be lower than those in the air–water system. As far as experimental conditions were concerned, the values of interfacial area obtained from this study were found to be considerably higher than those of the literature values of conventional bubble columns. The penetration theory is used to interpret the film mass transfer coefficient and results match the experimental k_L data reasonably well. Copyright © 2006 Society of Chemical Industry     

Mass transfer of carbon dioxide in aqueous colloidal silica solution containing <Emphasis Type="Italic">N</Emphasis>-methyldiethanolamine

The absorption rate (R _A ) of carbon dioxide was measured into an aqueous nanometer sized colloidal silica solution of 0–31 wt% and N-methyldiethanolamine of 0–2 kmol/m3 in a flat-stirred vessel for the various sizes and speeds of at 25 °C and 0.101 MPa to obtain the volumetric liquid-side mass transfer coefficient (k _L a) of CO₂. The film theory accompanied by chemical reaction between CO₂ and N-methyldiethanolamine was used to estimate the theoretical value of absorption rate of CO₂. An empirical correlation formula containing the relationship between k _L a and rheological property of the aqueous colloidal silica solution was presented. The value of R _A in the aqueous colloidal silica solution was decreased by the reduction of k _L a due to elasticity of the solution.     

Mass Transfer Characteristics in a Rotor‐Stator Reactor

Mass transfer characteristics in a rotor‐stator reactor in terms of the overall volumetric mass‐transfer coefficient (K_xa) using the N₂‐H₂O‐O₂ system were investigated. The effects of various operating parameters including rotation speed, liquid volumetric flow rate, and gas volumetric flow rate on K_xa were systematically examined, and a gas‐liquid mass transfer model was established to predict K_xa. Results reveal that K_xa increased with higher rotation speed, liquid volumetric flow rate, and gas volumetric flow rate. The results also confirm that the predicted values of K_xa were in agreement with the experimental values with deviation within 15 %. The results contribute to a better understanding of mass transfer characteristics in rotor‐stator reactors.     

Absorption of CO2 by aqueous triethanolamine (TEA) solutions in a high shear jet absorber

CO₂ diluted with N₂ was absorbed by aqueous triethanolamine (TEA) solutions in a jet absorber consisting of a high pressure stainless steel vessel with a pressure nozzle at the top. The gas mixture and the aqueous solution were passed simultaneously, through the pressure nozzle into the absorber. Due to the high shear imparted to the liquid very fine droplets were produced, which resulted in a very high interfacial area and rapid mass transfer. CO₂ was absorbed rapidly by the TEA solution. The effects of gas and liquid flow rates, solution concentration and CO₂ partial pressure on CO₂ loading per unit mole of TEA and the overall mass transfer coefficient were examined. CO₂ loading per mole of TEA increased with gas flow rate and decreased with liquid flow rate and solution concentration. The overall mass transfer coefficient was found to increase with gas and liquid flow rates. Both the CO₂ removal per mole of TEA and the overall mass transfer coefficient were found to be a strong function of power dissipated at the nozzle.     

Tribological properties of polyimide coatings filled with PTFE and surface‐modified nano‐Si3N4

Polyimide (PI) coatings filled with PTFE and nano‐Si₃N₄ were prepared by a spraying technique and successive curing. Nano‐Si₃N₄ particles were modified by grafting 3‐aminopropyltriethoxysilane to improve their dispersion in the as‐prepared coatings. Friction and wear performances and wear mechanisms of the coatings were evaluated. The results show that the incorporations of PTFE and modified nano‐Si₃N₄ particles greatly improve the friction reduction and wear resistance of PI coating. The friction and wear performance of the composite coating is significantly affected by the filler mass fraction and sliding conditions. PI coating incorporated with 20 wt % PTFE and 5 wt % modified nano‐Si₃N₄ displays the best tribological properties. Its wear rate is more than one order of magnitude lower and its friction coefficient is over two times smaller than that of the unfilled PI coating. Differences in the friction and wear behaviors of the hybrid coatings as a function of filler or sliding condition are attributed to the filler dispersion, the characteristic of transfer film formed on the counterpart ball and the wear mechanism of the coating under different sliding conditions. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40410.     

Mass transfer and hydrodynamic characteristics of a high aspect ratio self-ingesting reactor for gas-liquid operations

The mass transfer performance of a gas-liquid self-ingesting stirred reactor is reported both for coalescing and non-coalescing systems. The vessel features are a high aspect ratio and a rather narrow multiple-impeller draft tube, through which the gas phase is ingested and led down to the vessel bottom, where it is finely dispersed into the liquid rising in the annular portion of the vessel. Comparison is made between k_La values determined by several variants of the dynamic method, among which pure oxygen absorption in a previously de-gassed liquid phase. Results show that the gas-liquid mass transfer coefficient values obtained with the last approach are remarkably larger than those measured with all other techniques in which nitrogen is initially dissolved in the liquid phase. Possible reasons behind this discrepancy are discussed.The gas-liquid mass transfer performance of the investigated gas inducing contactor is finally compared with literature data on other self-inducing/ingesting devices. Comparison results encourage further development of the investigated apparatus.     

Bubble size and mass transfer coefficients in dual-impeller agitated reactors

The study relates to the mass transfer and the bubble size in a non standard vessel equipped with various dual-impeller combinations. The effects of the rotational speed, gas flow rate, impeller type and diameter are investigated. The volumetric mass transfer coefficient k_La and the bubble size d_bs were studied. The liquid side mass transfer coefficient k_L and the volumetric interfacial area a were estimated separately. A comparison has been made with some existing correlations.     

Improved mass transfer and biodegradation rates of naphthalene particles using a novel bead mill bioreactor

One of the main challenges in the treatment of polycyclic aromatic hydrocarbons (PAHs) in controlled bioreactors is the hydrophobicity and low solubility of these compounds in the aqueous phase, resulting in appreciable mass transfer limitations within the bioreactor. To address this challenge, we have developed a modified roller bioreactor (Bead Mill Bioreactor) in which inert particles are used to improve mass transfer from the solid phase to the aqueous phase. Experimental results with naphthalene as a model PAH and Pseudomonas putida as a candidate bacterium indicate that both the mass transfer rate from the solid phase to liquid phase and the biodegradation rate in the Bead Mill Bioreactor (BMB) were significantly higher than those in a conventional roller bioreactor (20‐fold and 5.5‐fold, respectively). The enhancement of mass transfer was dependent on the type, size and volumetric loading of the inert particles, as well as concentration of particulate naphthalene. The highest mass transfer coefficient (k_La = 2.1 h^?1) was achieved with 3 mm glass beads at a volumetric loading of 50% (particle volume/working volume) with 10 000 mg dm^?3 particulate naphthalene. The maximum biodegradation rate of naphthalene attained in the bead mill bioreactor (59.2 mg dm^?3 h^?1 based on the working volume and 118.4 mg dm^?3 h^?1 based on the liquid volume) surpasses most other rates published in the literature and is equivalent to values reported for more complex bioreaction systems. The bead mill bioreactor developed in the present work not only enjoys a simple design but shows excellent performance for treatment of PAHs suspended in an aqueous phase. This fundamental information will be of significant value for future studies involving soil‐bound PAHs. Copyright © 2005 Society of Chemical Industry     

Untersuchung der CO2‐Absorptionskinetik in wässrigen Lösungen von N,N‐Diethylethanolanmin und N‐Ethylethanolamin

N‐Ethylethanolamine (EEA) and N,N‐diethylethanolamine (DEEA) represent promising alkanolamines for CO₂ removal from gaseous streams, as they can be prepared from renewable resources. In this work, the reaction rate constant for the reaction between CO₂ and EEA and the liquid‐side mass transfer coefficient were determined from the absorption rate measurements in a blend comprising DEEA, EEA and H₂O. A stirred‐cell reactor was applied for the absorption studies, whereas a zwitterion mechanism for EEA and a base‐catalyzed hydration mechanism for DEEA were used to describe the reaction kinetics.     

A Langrangian Study of Solids Suspension in a Stirred Vessel by Positron Emission Particle Tracking (PEPT)

A technique of Positron Emission Particle Tracking (PEPT) was used to obtain information on the flow behavior of coarse particles suspended in pseudoplastic liquids agitated by axial‐hydrofoil Lightnin impellers A320 and A410. PEPT enables the position of a 600 μm radioactive particle tracer inserted inside one of the suspended particles to be detected many times per second and its full trajectory followed inside the vessel. Particle trajectory analysis yielded information on particle circulation, velocity distribution, and spatial occupancy. The minimum speed for complete particle suspension, N_js, was also determined. The well‐known Zwietering correlation failed to predict the measurements by a substantial margin, suggesting that it is inadequate for viscous non‐Newtonian liquids.     

Gas-liquid mass transfer in “dead-end” autoclave reactors

Gas-liquid volumetric mass transfer coefficients, (k_La), have been obtained for “dead-end” autoclave reactors operated in two different modes: (a) gas introduced into the gas phase, and (b) gas introduced through a dip-tube in the liquid. Three different methods of k_La determination have been compared. Effects of agitation speed, impeller diameter, gas to liquid volume ratio (V_g/V_L), position of the impeller and reactor size on k_La have been investigated. The k_La data were found to be correlated as: k_La = 1.48 × 10^?3 (N)^2.18 (V_g/V_L)^1.88 (d_I/d_T)^2.16 (h₁/h₂)^1.16 The critical speed of surface breakage, at which transition from the surface convection to the surface entrainment regime occurs, was also determined for different impeller positions, impeller diameters and gas to liquid volume ratios.     

Gas—Liquid Mass Transfer Coefficient in Stirred Tank Reactors

Volumetric gas—liquid mass transfer coefficient (k_La) data available in the literature for larger tanks (T = 0.39 m to 2.7 m) have been analyzed on the basis of relative dispersion parameter, N/N_cd. It was observed that at a given superficial gas velocity (V_G), k_La values were approximately the same irrespective of geometric configuration (size of the tank, type and size of the impellers, type of the sparger, etc.) at a particular N/N_cd. A single correlation based on N/N_cd is presented which shows satisfactory agreement with the k_La data of different workers.     

Gas-side mass transfer coefficients in a falling film microreactor

Gas–liquid mass transfer in a falling film microreactor (FFMR) with 29 microchannels (0.6 mm width each) was investigated. CO₂ was absorbed from a CO₂/N₂ gaseous mixture into a NaOH aqueous solution and the liquid-side mass transfer coefficient and the gas-side mass transfer coefficient were measured. The influence of gas concentration on the value of gas-side mass transfer coefficient has been discussed.