Gas dispersion and solid suspension in mechanically stirred reactors are commonly used in many industry processes because of their unmatched flexibility and under-controlled fluid dynamics. During the last decade, more and more researchers have focused on the study of gas dispersion in stirred tanks with multiple impellers because the increase of the reactor scale causes the height-diameter ratio of vessels could be as large as 2 or 3. Moreover, the optimum design of the diameter for the multi-impeller becomes more and more important for the large scale industrial reactors such as the volume up to 800 m³. In such huge gas-liquid reactors, the manufacturing and operational costs are closely related to the optimal design of the impeller, especially the diameter of impellers. Given the same power input of the reactors, the impellers with smaller diameter have higher rotational speed and less shaft torque compared with the larger diameter impellers. As a result, the size of the gearing box, mechanical seals, impeller shaft are determined by the choice of the impeller diameter, which becomes very important in the design of large scale reactors. Thus, more research is needed to obtain the relationship between gas holdup and agitator geometrical parameters for the purpose of the optimized design of agitators.

The objectives of this work include:

1. The diameter optimization for a triple-impeller agitator in a gas-liquid stirred tank;

2. Gas dispersion and solid suspension of a triple-impeller agitator with optimized diameter in a three-phase stirred tank.

1. Diameter optimization of a triple-impeller agitator

All the experiments were carried out in a stainless steel full baffled, dished-bottom cylindrical tank with internal diameter T=0.48 m and a filled aspect ratio H/T=1.66. The impeller configuration consisted of a six parabolic blade disk turbine (PDT) below two down-pumping narrow blade hydrofoil propellers (CBY), identified as PDT+2CBY. Impellers with diameters of 0.30T, 0.33T, 0.37T, and 0.40T were used. Air and deionized water were used as the gas and liquid phase. The total gas rates ranged from 5 to 59 m³·h^-1, and the corresponding superficial gas velocity V_S were from 0.0078 to 0.092 m·s^-1. The power consumption was calculated from the torque and rotational speed of the shaft measured with a torque transmitter and a portable tachometer, respectively. The gas holdup was calculated from the changes in liquid level measured by a calibrated Krohne radar probe.

1.1 Relative power demand.

The introduced gas causes the gassed power consumption decreases compared with the ungassed power input. Define the relative power demand (RPD) as the ratio of the gassed to ungassed power input. In all triple impellers with different D/T, the RPD decreases with the increase of either gas flow number (Fl_G=Q_g/ND³) or Froude number (Fr=N ²D/g). Both the cavities behind the impeller blade and the gas recirculation can affect the power consumption in the aerated stirred tank. After the gas is introduced into the tank, it is dispersed mainly by the bottom impeller and sent to other regions. Part of the gas may flow with the liquid and re-enter the impeller region instead of running out of the liquid surface. As the impeller diameter increases, the blockage area of the impeller increases, forcing more gas to re-circulate to the impeller region and leading to the decrease of power consumption at a given gas flow rate and agitation speed.

The regressive correlation of RPD is shown as, RPD=0.521Fl_G^-0.093Fr^-0.10(D/T)^-0.154 (R²=0.953). The negative exponent of D/T reflects the reduced aerated agitation power at larger impeller diameter as discussed above. Moreover, the absolute exponent of D/T is larger than that for gas flow number and Froude number, which means that D/T has greater effect on RPD than Flow number and Froude number.

1.2 Gas Holdup.

The gas holdup in stirred tanks is an important factor for the design and scale-up of gas-liquid stirred-tank reactors. For its strong influence on the mass transfer, gas hold-up has been a very important research subject in an aerated stirred tank.

When the power input and V_S increase, the total gas holdups increase simultaneously. However, the effects of D/T on total gas holdups are various for different V_S. When the superficial gas velocity is low (V_S=0.0078 m·s^-1), an increase of D/T leads to an obvious increase of total gas holdup at a given power input. The total gas holdup of system with D/T =0.40 is obviously higher than others which are almost the same at given power inputs. However, when V_S becomes higher as 0.025 m·s^-1, the total gas holdups in all systems are almost the same. When V_S reaches the high level as 0.05 and 0.092 m·s^-1, the total gas holdup of the system with D/T =0.33 becomes higher than other D/T’s. For a given power input, the smaller impeller combination can have higher agitation speed and higher shear rate, leading to more chances to break up bubbles. At high V_S, the system with D/T=0.33 gets a reasonable balance between the gas recirculation and shear rate, leading to the highest gas holdup eventually. It should be noticed that all experiments were carried out above the complete dispersion impeller speed corresponding to the specific gas rate.

A quantitative equation of gas holdup could be obtained as, ε=0.441P_m^0.272V_S^0.459(D/T)^-0.195 (R²=0.954).

Among four D/T of 0.30, 0.33, 0.37, and 0.40, triple impellers PDT+2CBY with D/T =0.33 is recommended for the industrial application of gas-liquid stirred reactors.

2. Solid suspension and gas dispersion of PDT+2CBY with optimized D/T=0.33

The tripe-impeller combination with the optimized D/T of 0.33 was used to investigate the solid suspension and gas dispersion properties in a gas-liquid-solid three phase stirred tank, where glass beads with average diameter of 100 μm and density of 2500 kg·m^-3 were used as the solid phase. The volumetric solid concentrations C_V were 3%, 6%, 10%, 15%.

2.1 Solid suspension in sparged systems

The critical suspension agitation speeds for ungassed two-phase and G-L-S three-phase systems were determined by visual observation method and identified as N_JS and N_JSG, respectively. With the increase of the solid concentration, the ungassed N_JS increases as the rule of N_JS∝C_V^0.075. With the introduction of gas, the effect of solid concentration on N_JSG becomes smaller than that in ungassed two-phase system and the exponent for C_V in three-phase system reduces to 0.03-0.055 corresponding to different gas flow rates.

With the introduction of gas into the solid suspension system, both N_JSG and the corresponding critical specific power consumption P_mJSG increases with the increasing of V_S, approximately obeying the linear increasing rule. The quantitative regression results are N_JSG=N_JS+(50-58)V_S and P_mJSG=P_mJS+(4.0-4.8)V_S corresponding to different solid concentrations, where N_JS and P_mJS are the critical suspension speed and specific power consumption in two-phase system, respectively. Namely, N_JS=4.5-5.1 s^-1 and P_mJS=0.11-0.17 W·kg^-1, corresponding to C_V from 3% to 15%.

2.2 Gassed Power Demand.

The relative power demand RPD curves were measured at the fully solid suspension and gas dispersion conditions, implying that all agitation speeds were higher than N_JSG and the complete gas dispersion speed. Similar as the rules in gas-liquid system, RPD in three-phase system also decreases with the increase of either the gas flow rate or the agitation speed, correspondingly to the flow number Fl_G or Froude number Fr, respectively. With the addition of more glass beads into the system, RPD decreases a little, but not always monotonic decreasing with the increase of C_V.

The quantitative equation of RPD could be obtained as RPD=0.569Fl_G^-0.151Fr^-0.156(1+C_V)^-0.015 (R²=0.943), where the exponent of (1+C_V) is negative, implying the decreasing tendency of RPD with the increase of C_V. However, the absolute value of only 0.015 indicates the effect of C_V on RPD is nearly neglectable.

2.3 Gas Holdup

Same as the rule in gas-liquid system, the gas holdups in three-phase system also increase with the increasing of either the power consumption or the gas flow rate. With the addition of solids in the system, the total gas holdup decreases with the increasing of C_V at the given power consumption and superficial gas velocity. When more solids are introduced in the systems, the apparent viscosity of the slurry becomes larger and the surface tension, which helps in stabilize the bubble, also becomes larger. As a result, the collision and coalescence of bubbles might dominate the break-up of them. Thus, as more particles are suspended in the tank, the higher rise velocity of the resulting larger bubbles will itself lead to a reduced gas holdup.

The quantitative equation of gas holdup could be obtained as, ε=0.760P_m^0.276V_S^0.525(1+C_V)^-1.06  (R²=0.967).

Keywords: solid suspension, gas holdup, power consumption, gas-liquid-solid system, triple impellers, stirred reactors