Mechanical power requirements of gas‐liquid agitated systems

Abstract

The power requirements for mechanical agitation of liquids have been investigated extensively, since this parameter is an important criterion for scaling-up stirred reactors, and it also relates to the overall mass transfer coefficient. There is only a limited number of useful correlations for its estimation such as those of Oyama and mechanical power input in nonaerated, agitated non-Newtonian liquids in a turbulent regime also varied with i V as indicated by Calderbank and Moo-Young (1959). It could thus be generalized that the power consumption for mixing in turbulent regime is proportional to N3 for both Newtonian and non-Newtonian fluids. Endoh (1955), Michel and Miller (1962), klark and Vermeulen (1963), Pharamond et al. (1975), and a recent contribution of Hassan and Robinson ( 1977). Oyarna and Endoh (1955) introduced the correlation of the gassed-to-ungassed mechanical mixing power ratio with the aeration number, The new correlating procedure of Michel and Miller (1962) cannot be reliably applied to large scale equipment and also failed at extreme values of gas ilow rate. It is also not applicable for prediction of the effect of surfactants on the mixing power input. The correlation by Pharamond et al. (1975) is restricted to correlating only their experimental data developed with six-blade turbine impellers. The correlations of Clark and Vermeulen (1963) and Hassan and Robinson (1977) appear to have the most merit, since they use the impeller Weber number and measured gas holdup. The correlation of Clark and Vermeulen (1963), however, was developed with unusual method of gas sparging, using a perforated plate covering the entire bottom of the vessel. The correlation of Hassan and Robinson (1977) may vary with different tank sizes and requires the measurement of the gas holdup which is somewhat inconvenient for applications involving fermentation broths. All aforementioned correlations are restricted to Newtonian fluids.In order to improve the accuracy of estimating the mixing power input, an empirical correlation for predicting the gassed-to-ungassed power ratio is suggested as follows: EXPERIMENTAL RESULTS AND DISCUSSIONFor the experimental work reported herein, a modified strain-gauge dynamometer ( Aiba et al., 1973) was employed to measure the torque of a rotating impeller shaft. The air flow rate to the tank was measured by a rotameter. The fully baffled stirred tank contained one single-hole orifice sparger. The stirred-tank geometry and ranges of operating variables of the mixed system are given in Figure 1. The physicochemical properties of liquid solutions used in this study are given in Table 1. Power Requirement in Nongassed SystemIt was confirmed here that the mechanical power input of turbulent Newtonian liquids in nonaerated, agitated, fully baffled tank varied with the cube of the impeller rotational speed. The power number N p was found to be equal to 6.14 for a six-blade turbine. This agrees well with the work of Rushton et al. Power Requirement in Gassed SystemThe experimental resul...

Role of sparger design in mechanically agitated gas‐liquid reactors. Part I: Power consumption

“… 23. shows that the variation of the power number with impeller speed is similar in the 0.57 and 1.5 m i.d.…”

“…vessels, respectively, which are lower thaii those observed by Mihel and Miller [22], Luong and Volesk! [23], Hassan and Robinson [lo] and Hughmark [24]. These investigators determined the exponent as -0.24, -0.38, -0.38, and -0.25, respectively.…”

Quantification of power consumption and oxygen transfer characteristics of a stirred miniature bioreactor for predictive fermentation scale‐up

“…Although Koloini et al (1989) reported that Hughmark's correlation predicted higher values for power input compared to their experimental data, in the case of the miniature bioreactor this correlation also slightly under estimates the power input compared to the measured values, especially at higher stirrer speeds. Finally the Luong and Volesky (1979) correlation based on the use of dimension- Table I. Summary of the most commonly reported gassed to un-gassed power consumption correlations ( P g /P ug ) for smaller scale stirred vessels Hughmark (1980) 0.16-1 Flat blade turbine 1 0.33 less groups and Newtonian fluids, is seen to greatly over predict the measured values and is unsuitable.…”

“…The values determined for the constants C, a, and b from Equation (7) were 0.22, 0.35, and 0.52 respectively as shown in Table II. Cui et al (1996); (^) Luong and Volesky (1979); (*) Mockel et al (1990). Experimental measurements as shown in Figure 2.…”

Bioprocess scale‐up: quest for the parameters to be used as criterion to move from microreactors to lab‐scale

“…Such modifications included taking into account the number and type of impellers and reactor dimensions, among others. 99,100,101 Along with the use of predictive correlations, power consumption may be determined experimentally through the use of electrical or calorimetric measurements, or through the use of dynamometers, torquemeters and strain gauges. 87 In bench-and pilot-scale bioreactors typically used for the fermentation of bacteria and fungal micro-organisms, the power consumption ranges from 1 to 3 kW m −3 .…”