INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

ESTIMATION OF EFFECTIVE SHEAR RATE FOR AERATED NON-NEWTONIAN LIQUIDS IN AIRLIFT BIOREACTOR”“

Effective shear rate is one of the indispensable parameters for the design of aerobic fermentors using a viscous non-Newtonian system. The estimation of effective shear rate in airlift loop bioreactors has been investigated with liquid circulation velocity. An empirical correlation of effective shear rate in airlift loop reactors is proposed.

γ_eπ= 3.26-3.51 ; 10²U_G + 1.48 10⁴U²_G

It is found that the effective shear rate is lower in airlift reactors than in bubble columns. This equation can be used for the cultivation of cells sensitive to shear stress.     

EFFECTS OF GEOMETRY ON HYDRODYNAMICS IN EXTERNAL-LOOP AIRLIFT REACTORS

Experimental investigations were carried out in model external-loop airlift reactors. Two reactors of laboratory scale (riser liquid height ranged between 1.16-1.56 m, riser diameter 0.03 m, A_D/A_R ratio between 0.111-1,000, total liquid volume V_T = (1.189-2.446).10^-3m³) and pilot-plant scale (riser liquid height of 4.4 and 4.7 m, respectively, riser diameter 0.200 m, A_D/A_R ratio of 0.1225 and 0.040 m, total liquid volume, V_T = (0.144-0.170) m³) were used.

The influences of reactor geometry characterized by some parameter as: A_D/A_R ratio, liquid height in riser and downcomer and liquid height in gas separator, together with the amount of introduced air, on the basic hydrodynamic design parameters: gas holdup and liquid circulation velocity were analysed.

The influence of gas sparger design on gas holdup and liquid velocity was found to be negligible.

The experimental liquid circulation velocity was correlated using a simplified form of the energy balance in airlift reactors, valid for external-loop airlift reactors with almost complete phase separation at the top.

An original dimensionless correlation for gas holdup prediction involving superficial velocities of gas and liquid, cross sectional areas, dispersion height, riser diameter, as well as Froude number, was obtained.     

MULTIPHASE HYDRODYNAMICS AND SOLID-LIQUID MASS TRANSPORT IN AN EXTERNAL-LOOP AIRLIFT REACTOR—A COMPARATIVE STUDY

The solid-solid mass transfer performance of an external-loop airlift reactor was measured by dissolution of benzoic acid coated on nylon-6 particles, and the hydrodynamics of the gas-liquid-solid multiphase system in the airlift reactor were investigated. The solid-liquid system was designed to simulate the micro-carrier culture of animal cells, and some typical suspensions of immobilized enzyme particles.

The solid-liquid mass transfer coefficient remained constant below a superficial air velocity of 0.04 ms^-1 for the particles examined, but increased rapidly with further increase in gas velocity. Solids loading (0.3-3.5% w/w) did not affect the mass transfer coefficient in turbulent flow.

The mass transfer coefficient was correlated with energy dissipation rate in the airlift reactor. The mass transfer coefficient in stirred vessels, bubble columns, fluidized beds, and airlift reactors was compared.

Over an energy dissipation Reynolds number of 4-400, the solid-liquid mass transfer coefficient in the airlift device was comparable to that obtainable in fluidized beds. The performance of the airlift was distinctly superior to that of bubble columns and stirred tanks.     

STEAM CONDENSATION IN A VERTICAL CORRUGATED DUCT

An experimental investigation was made on the condensation of water steam in a vertical corrugated duct. The data have been correlated as follows

Co=5.11Re^-0.431 150 ≤ Re ≤ 350 Co = 0.034311Re^-0.425350 ≤Re ≤l000

The vertical corrugated duct is constructed of two corrugated plates with corrugation inclination angles of β = 0 and β = 45° respectively (relative to the overall flow direction).

The condensation heat transfer coefficient in the corrugated duct is more than two times higher than that of bulk condensation on a vertical plate. A physical model was proposed to explain the heat transfer enhancement. Attention was also paid to the effect of exit steam velocity on the heat transfer during partial condensation. It was demonstrated that the heat transfer in the corrugated duct was strongly affected even at a low exit velocity, which was different from the case of bulk condensation on a vertical plate. Experimental apparatuses and the method for examining their reliability are described in detail.     

FIBRE OPTIC AND CAPACITANCE PROBES IN TURBULENT FLUIDIZED BEDS

In the present study, local flow properties are investigated in pilot plant scale fluidized bed reactors using both fibre optic and capacitances probes. Measurements are conducted at ambient as well as at 150°C. The system used is air and spent FCC particles (mean particle diameter: 65pm). The static bed height is 1.6 m. Bubbling and turbulent regimes (V = 0.40 and 0.70 m/s) are investigated in two 0.3 and 0.5 m ID columns.

Bubble fraction under the bubbling regime and at room temperature, measured using fibre optic and capacitance probes, are in good agreement. However, in the turbulent regime, fibre optic probes are prone to underestimate the bubble fraction while capacitance sensors tend to overestimate it. These discrepancies between fibre optic and capacitance measurements increase with temperature.

Using capacitance probes, a prevalent flat bubble rise velocity profile is measured. This is assigned to the relatively slow response, to the size and to the geometry of the capacitance probes. Overall this gives an underestimation of the bubble frequency and an overestimation of the bubble contact time and the bubble contact length.

Due to the high fibre optic probe sensitivity, care should be taken in the interpretation of signals. Overestimation of bubble frequency leads to underestimation of both bubble contact times and bubble contact lengths.     

A GENERALIZED BUBBLE RISE VELOCITY CORRELATION

A generalized bubble rise velocity correlation is developed to cover the range of conditions:

liquid-phase density = 45.1 to 74.7 lb/ft³,

liquid-phase viscosity = 0.233 to 59 cP., and

interfacial tension = 15 to 72 dynes/cm

The gas-phase is air and the bubble size ranged from 1.2 to 15 mm. The developed correlation is based upon new dimensionless groups which contain the parameters affecting bubble rise velocity as well as their interaction, The correlation is independent of flow regimes and applicable for Reynolds numbers from 0.1 to 10⁴. It is in good agreement with work appearing in the literature.     

Drying Sawdust in a Pulsed Fluidized Bed

The objective of this work was the experimental and theoretical study of sawdust drying, in batch and continuous experiences, using a pulsed fluidized bed dryer.

In the batch experiences, a 2³ factorial design was used to determine the kinetics of drying, the critical moisture content, and the effective coefficients of both diffusivity and heat transfer, all of them as a function of the velocity and temperature of the air, the speed of turning of the slotted plate that generates the air pulses in the dryer, using sawdust with 65% moisture in each run.

In the continuous operation, a 2³ factorial design was used to study the effect of the solid flow and the velocity and temperature of the air on both the product moisture and the distribution of residence times. In order to determine these last ones, digital image processing was used, utilizing sawdust colored by a solution of methylene blue as tracer.

The statistically significant factors were the velocity and the temperature of the heating air, for both the continuous and batch operations. Although the speed of turn of the slotted plate was not significant, it was observed that the air pulses increased the movement of particles, facilitating its fluidization, especially at the beginning of drying.

The heat transfer coefficients were adjusted according to the equation Nu = 0.0014 Re_p^1.52, whose standard deviation of fit is 0.145.

The period of decreasing rate was adjusted to several diffusivity models, giving the best fit the simplified variable diffusivity model (SVDM). The curve of distribution of residence times was adjusted using the model of tanks in series, with values between 2.6 and 5 tanks.     

A MONTE-CARLO APPROACH TO THE INTERPRETATION OF BUBBLE PROBE SIGNALS IN FREELY BUBBLING FLUID BEDS†

The interpretation of the signals generated by a double probe may be done by the three characteristic times method:

t₁ the time duration of the pulses;

t₂ the time shift between the signals of the two probes;

t₃ the time interval between two pulses on one channel.

Each of these times is largely dispersed and the corresponding histograms may be constructed.

The present work is a trial to go over from the time histograms to physical properties of the bubbles combining a Monte-Carlo simulation and a flexible simplex optimisation procedure.

As a result, the percentage of oblique bubbles cutting just one level, the bubble size distribution, the average velocity-size relation, and the individual dispersion around it may be defined.

The procedure is finally applied to experimental results obtained with a light probe in a fluid bed of glass beads.     

ACETIC ACID AS AN OXYGEN CARRIER BETWEEN TWO PHASES FOR EPOXIDATION OF OLEIC ACID

Acetic acid was found to be an effective oxygen carrier for epoxidation of oleic acid. The reaction model of oleic acid epoxidation in the two-phase reaction system was systematically analyzed and the rate determining step was experimentally identified.

The results indicated that the rate of oxidation of the unsaturated acid was independent of the concentration of oleic acid and depended on the mixing rate and the rate of formation peracetic acid which in turn depended on the concentration of acetic acid, strength of acid catalyst and the oxygen source, hydrogen peroxide. In the region of reaction control, the rate equation of epoxidation was found to be

$

where k = 2.98 × 10^-2 M^-2 min^-1 at temperature of 35^°C.     

RIBBING INSTABILITY OF A TWO-ROLL COATER: NEWTONIAN FLUIDS

Data are presented for the critical conditions at which the ribbing instability appears on the surface of a Newtonian liquid film emerging from the nip between two rotating rolls. Data are obtained over two decades in Capillary number (Ca = μU/σ) for values of H₀/R in the range 3 × 10^-3 to 5 × 10^-2. The critical Capillary number is found to be given by the expression

$

Data are compared to the predictions that follow from a theory due to Savage, and agreement is found to be poor.     

TRANSITION OF FLOW REGIME IN FLUIDIZED BEDS WITH SLANTING BLADE BAFFLES

A flow model is proposed to investigate the transition of flow regime from bubbling to turbulent fluidization postulating that the flow in the emulsion phase follows the Richardson-Zaki equation.

Void fraction of the whole bed ε_f and the mean velocity of bubbles U_b were measured in fluidized beds of 0.3 and 0.5 m ID, in which slanting blade baffles were positioned. Mo-catalyst, silica gel, sand and glass beads with size between 135-443 μm were fluidized by air.

Void fraction of the emulsion phase ε _e was calculated on the basis of the above model. Correlating ε _e with superficial gas velocity U_ƒ, we found that ε _e was very close to ε _mƒ in the bubbling regime and that e, increased with increasing U_ƒ in the turbulent regime.

Calculated values of the volume fraction of bubble phase δ were correlated with U_ƒ, from which apparent transition point from bubbling to turbulent regime was estimated. Combining information obtained, transition of flow regime in the above type of fluidized beds is discussed     

Particle Adhesion in Model Systems: 16. Barium Sulfate Particles on Glass and Protein Surfaces

The adhesion phenomena of monodispersed barium sulfate (BaSO₄) particles on gelatin-coated glass beads were evaluated using the packed column technique and compared with the same system in the absence of the protein.

Multilayer deposition was observed with the uncoated glass beads at pH 4, 5 and 6, while at pH 9, which is above the isoelectric point (pH ∼ 6) of BaSO₄ particles, monolayer deposition took place, even though the BaSO₄ particles and glass beads bore the same sign of charge. At pH = 10, no uptake was observed on the glass beads, but the addition of 10^-4 mol dm^-3 BaCl₂ induced multilayer deposition due to the adsorption of the Ba²⁺ cation on BaSO₄ particles, which causes a reversal of their charge to positive.

The formation of multilayers was found to occur over a much wider pH range on the gelatin coated glass beads.

BaSO₄ particles deposited in multilayers could not be removed from either glass beads or gelatin-coated glass beads by rinsing the loaded column with solutions of pH 11.5, but could be detached from monolayers on glass beads only.     

AXIAL DISPERSION OF LIQUID IN MOBILE-BED CONTACTING

Axial dispersion of liquid in Mobile-Bed Contacting (MBC) was investigated employing transient-response technique with impulse input of NaCI tracer. Experiments were performed in a 0.195 m ID column. Three different packing diameters (15, 19.5 and 32 mm) and three different static bed heights (0.1, 0.195 and 0.3 m) were used. Gas flow rate was varied between 3.02 and 4.05 kg/m²/s and liquid flow rate from 2.4 to 10.4 kg/m²/s.

Transfer function analysis of data yielded that Peclet number was practically independent of liquid and gas flow rates and static bed height but depended on packing size only. A simple correlation for Peclet number was developed     

BUBBLE FORMATION IN A TRANSVERSE HORIZONTAL LIQUID FLOW

Over a wide range of liquid velocities, gas emitted from an orifice forms a cylinder or jet of gas which disrupts by varicose instability to generate bubbles. Data is presented which extends the previous use of this model by Silberman (1957).

At liquid velocities low enough to be comparable with bubble rise velocity, bubbles are formed discretely at the orifice. Mathematical models indicate that the value of hydrodynamic mass that is effective in the horizontal direction in delaying bubble release lies between 0 and 0.5 times the displacement. The value of 0.5 is a useful predictive guide up to the point where jetting occurs and the instability model predicts a smaller bubble.     

EXPERIMENTAL OBSERVATIONS OF FLUIDIZED BEDS AT ELEVATED PRESSURES

The object of the work described here was to elucidate the effects of operation under pressure on the physical behaviour of gas fluidized beds. Extensive measurements of various bubble properties such as size, shape and rise velocity in beds of coarse powders (mean particle diameters of 184 μm and 450μm) operated at pressures of up to 81 bar were made by photographing the images created by irradiation of the bed with X-rays, and analysing the bubble silhouettes thereby obtained. Most of the results presented here are averages of some 200 individual measurements.

Experimental evidence to support the following picture of the effect of pressurization on the behaviour of freely bubbling gas fluidized beds is presented. Both bubble interaction (tendency to coalesce) and the incidence of bubble splitting increase with increasing pressure; the two are intimately connected. The nett results are a decrease in bubble size with increasing pressure over most of the pressure range and an increase in the tendency for bubbles to distribute non-uniformly in a radial direction. This latter tendency probably causes gross solids circulation in the bed, and this in turn leads to higher bubble rise velocities than those observed for single bubbles under similar conditions. The splitting mechanism accounting for the decrease in bubble size was found to be intrusion of the wake into the bubble void by the flow of gas through the wake region of a leading bubble during pair coalescence.

An updated review of other published work relating to the subject of experimental observations of the effects of pressure on gas fluidized beds is included in the form of a table.     

PREDICTION OF GAS-PHASE HOLDUP IN A BUBBLE COLUMN

Hydrodynamic properties of bubble columns play a significant role in many chemical and biochemical processes. Recent theoretical and experimental work conducted by Krishna et al. (1991, 1994), and Wilkinson et al. (1992) have been examined in conjunction with a bubble column and data for the air-water system operating at ambient conditions. The bubble column is 0.108 m in internal diameter, has a 1.70 m tall test section, and is equipped with a perforated plate distributor having 91 holes of 0.8 mm diameter. The data are taken for five values of the slumped water column height in range from 0.79 to 1.15 m, and for superficial air velocities up to about 0.4 m/s.

The data accord to the qualitative aspects of Krishna et al. model but lead to different values of the bubble swarm rise velocity, and superficial transition air velocity characterizing the transition from homogeneous bubbly flow regime to heterogeneous churn-turbulent flow regime. The quantitative reproduction by the model expressions of these recent works of the experimental data is poor. This may be partly attributed to the geometry of the column, diameter and distributor design.

The qualitative features of Krishna et al. model for the two regimes are confirmed by the present data. For quantitative predictions of gas-phase holdup, a new model is proposed in which the large bubble flow in the churn-turbulent regime is formulated following the drift-flux theory. The proposed theory and experimental data are in good agreement.     

A CONTINUUM ANALYSIS OF SURFACE TENSION IN NONEQUILIBRIUM SYSTEMS

The intermolecular forces that cause surface tension in multiphase systems at equilibrium give rise to pressure gradients in nonequilibrium systems. The present paper treats such systems within a framework of thermodynamics and continuum mechanics and uses a generalization of the conceptual experiment of Rowlinson and Widom which applies to systems with curved interfaces and to nonequilibrium situations where the phase interfaces are not fully developed. The pressure tensor has a component p_n acting in the direction normal to the concentration gradient and a component p_t acting in the plane tangent to the surface of constant concentration where

P_n —P_t = k(∇c)² The concentration gradient causes an additional volumetric force not present in homogeneous fluids

Here, k.- is the gradient energy parameter appearing in the Landau-Ginzburg functional, c is the concentration of the key component, ₁, and R₂ are the principal radii of curvature for the surface of constant constration, n is a unit vector normal to that surface, and ∇, is the gradient along the surface. The volumetric force generates pressure gradients in systems with curved interfaces at equilibrium or can drive flow in nonequilibrium situations.     

FREE CONVECTIVE DRAFT INDUCED BY THERMAL AND CONCENTRATION GRADIENTS INSIDE AN ISOTHERMAL, VERTICAL CYLINDER†

Laminar, free convective flow through a vertical cylinder induced by the thermal and concentration buoyancy forces is investigated. The numerical studies involve development of a steady-state, two-dimensional heat and mass transfer model for the moist air core of the vertical tube. The stream function-vorticity method is employed to simplify the governing, coupled conservation equations which were then numerically solved by the successive over-relaxation (SOR) and alternating direction implicit ((ADI) methods.

A graphical correlation was found between dimensionless flow rate and dimensionless tube length as a function of the buoyancy force ratio N = Gr/Grc. Excellent agreement was obtained for the dimensionless flow rale results with those of Davis and Perona¹⁶ and Kageyama and Izumi¹³ for the case when only the-thermal buoyancy force is considered.

The combined buoyancy force from thermal and species diffusion provides larger local Nusselt Nu and local Sherwood Sh numbers relative to the case when just one buoyancy force is accounted for. Both local Nu and local Sh are seen to asymptotically approach a constant value as flow develops.     

THERMAL CONDUCTIVITY OF GASEOUS AMMONIA IN THE TEMPERATURE RANGE 358-925 K.

Thermal conductivity of research grade pure ammonia gas has been measured by the column method at pressures of 12.9, 26.5, and 45.0 kN/m² over the temperature range 358 to 925 K. The maximum probable error of measurement is 1.5% at 874 K and it increases in magnitude as the temperature decreases. At 405 K, it is about 4.8%. The experimental data are correlated by the following cubic polynomial in temperature:

k(T)=5.237× 10^-3 + 5.179 × 10^-4 T + 8.404 × 10^-7 T² + 1.557 × 10^-10 T³.

Here k is in mW/cm-K and T is in K.

The experimental values are compared with three kinetic theory expressions for thermal conductivity of polyatomic gases in conjunction with the Stockmayer (12-6-3) potential. It is concluded that none of the theories can accurately predict the thermal conductivity of ammonia and probably of polar gases in general. The diffusion coefficient characterizing the transport of vibrational energy is computed as a function of temperature and on the basis of experimental data and the theory due to Ahtye. It has been long known that the transfer of energy by polyatomic and polar molecules is quite complex because of the presence of internal degrees of freedom and the possibility of resonant energy transfer in the latter (Hirschfelder, Curtiss and Bird, 1964).