Gas, liquid, and solid holdups

A three-phase slurry reactor is characterized by the holdup of the three phases, satisfying the equation 

A review of earlier studies on gas, liquid, and solid holdups in a three-phase slurry reactor is given by Ostergaard.97 Kato54 studied the effects of gas velocity, particle size, the amount of solids and liquid in the bed, and the density of the solids on the gas holdup. The gas holdup [defined as volume of gas/(volume of gas + volume of liquid)] decreased with increasing particle size and amount of solids in the bed, and with the decreasing nominal gas velocity. 

Ostergaard and Michelsen104 measured the gas holdup in beds of 0.25-, 1-, and 6-mm glass particles using a radioactive tracer technique. They found that hG °c Uqg, where U0G is the superficial gas velocity, and n took values of 0.88, 0.78, and 0.93, respectively, for three particle sizes. The solid-free bubble-column gave n = 1.05. They also found that, in the solid-free system and in beds of 6-mm particles, the gas holdup decreased with increasing liquid flow rate whereas in beds of 0.25- and 1-mm particles, the gas holdup increased with increasing liquid flow rate. 

Michelsen and Ostergaard82 extended the study of Ostergaard and Michelsen104 to a wider range of flow rates and other system conditions. The data were obtained in a 15.2-cm-i.d. and 11-m-tall concurrent-upflow air-water-sol id system. The RTD of both the gas and liquid phases were measured by a radioactive tracer 

Adlington and Thompson1 reported that the presence of solids had little influence on gas holdup below nominal gas velocities of about 1.5 cm s 1. At higher gas velocities, the gas holdup was decreased by the solids but was relatively independent of the solids particle size. Viswanathan et al.140 found that, in an air-water sy stem, the gas holdup in beds of small particles (0.649-, or 0.928-mm glass beads) was lower than in a solid-free system, whereas the gas holdup in beds of large particles (4-miti glass beads) was higher than in a solid-free system. 

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The hydrodynamic parameters that are required for stirred tank design and analysis include phase holdups (gas, liquid, and solid) volumetric gas-liquid mass-transfer coefficient liquid-solid mass-transfer coefficient liquid, gas, and solid mixing and heat-transfer coefficients. The hydrodynamics are driven primarily by the stirrer power input and the stirrer geometry/type, and not by the gas flow. Hence, additional parameters include the power input of the stirrer and the pumping flow rate of the stirrer. 

Hydrodynamic parameters that are required for bubble column design and analysis include phase holdups (gas, liquid, and solid for... 

Phases gas-liquid, liquid-liquid, gas-liquid and solid (bio). Intermediate reaction rates. High capacity, high conversion in both gas and liquid phases. Intensive dispersion of gas in liquid. Large number of plates gives plug flow. Some flexibility in varying liquid holdup and exchange heat via cods on plates, d = 40-100 0.6 < Ha < 3. 

Dp, catalyst density) and the hydrodynamic parameters (gas, liquid and solid dispersion coefficients, catalyst settling velocity, gas holdup, gas-liquid interfacial area, liquid-solid mass transfer coefficient). The influence of these parameters on the catalyst concentration, reaction rate and conversion is indicated by the arrows. As the gas velocity varies with the conversion, the hydrodynamic parameters, while depending on the gas velocity, will be influenced by the conversion as well. This causes also a modification of the catalyst concentration profile in the reactor. 

In the continuum (Euler-Euler)-type formulation, the gas, liquid, and solid phases are assumed to be continuum and the volume-averaged mass and momentum equations (see Table 6.10) are solved for each phase separately to predict the pressure, phase holdup, and phase velocity distributions. As a result of time and volume averaging, additional terms appear in the momentum conservation equations. These additional terms need closure models and such unclosed terms are highlighted in Table 6.10. 

Small bubbles and flow uniformity are important for gas-liquid and gas-liquid-solid multiphase reactors. A reactor internal was designed and installed in an external-loop airlift reactor (EL-ALR) to enhance bubble breakup and flow redistribution and improve reactor performance. Hydrodynamic parameters, including local gas holdup, bubble rise velocity, bubble Sauter diameter and liquid velocity were measured. A radial maldistribution index was introduced to describe radial non-uniformity in the hydrodynamic parameters. The influence of the internal on this index was studied. Experimental results show that The effect of the internal is to make the radial profiles of the gas holdup, bubble rise velocity and liquid velocity radially uniform. The bubble Sauter diameter decreases and the bubble size distribution is narrower. With increasing distance away from the internal, the radial profiles change back to be similar to those before contact with it. The internal improves the flow behavior up to a distance of 1.4 m. 

The structure of wakes behind the gas bubbles affects several aspects (such as holdup, gas-liquid mass transfer, etc.) of three-phase fluidized-bed behavior. The magnitude and composition of such wakes are still not known with any certainty. Wake holdups have been estimated from experimental measurements of gas and solid holdups. It is commonly assumed that the bed can be divided into three regions a liquid fluidized region, a gas-bubble region, and a bubble-wake region and that the bubbles and their wakes travel at the same velocity. Different investigators have, however, assumed different values of hws the ratio of solids holdup in the wake to the solids holdup in the liquid fluidized region. Different methods have been used to calculate wake holdups from the experimental... 

Gas-liquid For large liquid holdup, slow reactions that are kinetically controlled reactions that require long residence times and low viscosity liquids. Preferred if large gas volumes needed or if the liquid vol > 40 m OK for high pressure. Cocurrent surface area 50-400 m /m Downflow surface area 20-1000 m /m. Ha < < 0.3 and = 4000-10000. Can handle solids. Incurs a high pressure drop. Gas-liquid-catalytic solid Surface area 50-350 m /m. ... 

Unique for CSTR Phases liquid, gas-liquid, hquid-liquid, hquid-catalytic solid, gas-liquid-catalytic solid, gas-liquid -biosohd. Capacity 0.0001-100 L/s and usually > 0.4 L/s volumes 1-1000 000 L. Autothermal reactions. Usually if the concentration of reactants is low, and need low concentration of reactants for selectivity. CSTR is larger and more expensive than PFTR. For multiphase, STR are characterized by high liquid holdups holdup of the reactive phase is important if the reaction is slow Ha < 1 phase ratio is easy to control. Adiabatic, CSTR usually gives higher productivity for exothermic reactions than for STR batch or PFTR. Use for large capacity, otherwise batch. Heat recovery is easier in CSTR than in a batch STR. 

Gas holdup (or gas fraction or void fraction) is defined as the volumetric fraction occupied by the gas phase in the total volume of a two- or three-phase mixture. It is one of the most important parameters characterizing gas-liquid and gas-liquid-solid hydrodynamics, because it not only gives the volume fraction of... 

It is evident from Figure 7A.4 that the power number attains a constant value in the turbulent region. For the case of two- (gas-liquid) and three-phase (gas-liquid-solid) systems, additional parameters that represent the gas- and solid-phase holdups have an important bearing on the power required. Hence, these are also included. The effects of introduction of gas and solid phases on the power number are discussed... 

Padial et al. [91] performed qualitative simulations of three-phase flow in a draff tube bubble column and compared the overall gas volume fraction and liquid circulation time for gas-liquid and gas-liquid-solid systems. Michele and Hempel [92] simulated flow air bubbles and PMMA particles (300 pm, 10 vol%) dispersed in water for superficial gas velocities in the range of 0.02-0.09 m/s. They compared their predictions with measured overall gas holdup and only a qualitative agreement... 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

Bubble-column slurry operations are usually characterized by zero net liquid flow, and the particles are held suspended by momentum transferred from the gas phase to the solid phase via the liquid medium. The relationships between solids holdup and gas flow rate is of importance for design of bubble-column slurries, and some studies of this aspect will be reviewed prior to the discussion of transport phenomena. 

Roy et al. (R3) define the critical solids holdup as the maximum quantity of solids that can be held in suspension in an agitated liquid. They present measurements of this factor for various values of gas velocity, gas distribution, solid-particle size, liquid surface tension, liquid viscosity, and a solid-liquid wettability parameter, and they propose the following two correlations in terms of dimensionless groups containing these parameters ... 

Kato (K3) reported gas holdup as a function of gas velocity, particle size, amount of solids and liquid in the bed, as well as of density of solids, for the system described in Section V,C. The holdup, defined as the ratio between the gas volume and the sum of gas and liquid volumes, increased with increasing nominal gas velocity to a maximum value ranging from 0.40 to 0.75 reached for gas velocities of from 10 to 20 cm/sec. The gas holdup decreased with increasing particle size and with increasing amounts of solids in the bed. 

Viswanathan et al. (V6) measured gas holdup in fluidized beds of quartz particles of 0.649- and 0.928-mm mean diameter and glass beads of 4-mm diameter. The fluid media were air and water. Holdup measurements were also carried out for air-water systems free of solids in order to evaluate the influence of the solid particles. It was found that the gas holdup of a bed of 4-mm particles was higher than that of a solids-free system, whereas the gas holdup in a bed of 0.649- or 0.928-mm particles was lower than that of a solids-free system. An attempt was made to correlate the gas holdup data for gas-liquid fluidized beds using a mathematical model for two-phase gas-liquid systems proposed by Bankoff (B4). 

Measurement of the expansion of a gas-liquid fluidized bed provides a measure of the holdup of solids or of the corresponding combined holdup of gas and liquid. From such measurements, the holdup of liquid may be calculated if the gas holdup has been determined independently. 

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