Backmixing flow rates

Normally the backmixing flow rates Lb and Gb are defined in terms of constant backmixing factors, at = Lb/L and ttc = Gb/G. The mass balance equations then appear in the form... 

Ratio Backmixing flow rate/Forward flow rate = Rb = 1.18... 

Aiba (A3), Fox and Gex (F8), Kramers, Baars and Knoll (K15), Metzner and Taylor (MIO), Norwood and Metzner (N3), Van de Vusse (V5) and Wood et al. (W12) have studied flow patterns and mixing times. In addition, Brothman et al. (B22), Gutoff (G9), Sinclair (S16) and Weber (W3) analyzed flow in a stirred tank in terms of the recycle flow model of Fig. 23F. This model corresponds to the draft-tube reactor, and with sufficiently large recycle rate the performance prediction of this model approximates backmix flow. 

Velocity as a function of radial position Mean velocity in a packed bed based on empty tube Unit step function Volumetric flow rate Volume of vessel Volume of backmix flow region... 

Backmix flow reactor or continuously stirred tank reactor. The conversion rate is lower than for plug-flow reactors because the reagent is immediately diluted on being introduced into the reactor. Many flow reactors, e.g. tubular reactors, and especially in the turbulent regime are in this class. 

A fluidized bed can be made fully mixed by providing suitable baffles or by using a stirrer. A stirrer fluidized bed reactor of this design has been used by Trotter (1960). Shah etal. 911) examined the pressure drop and the gas-phase backmixing in a stirred fluidized bed. They found that the pressure drop through a solid bed below incipient fluidization decreased with an increase in stirrer speed. The torque on the stirrer under the same conditions increased with an increase in stirrer speed. Both pressure drop and torque on the stirrer remained essentially independent of both gas flow rate and stirrer speed once the incipient fluidization conditions were reached. The gas phase backmixing coefficient remained essentially independent of stirrer speed once the incipient... 

The residence-time distribution in the liquid phase of a cocurrent-upflow fixed-bed column was measured at two different flow rates. The column diameter was 5.1 cm and the packing diameter was 0.38 cm. The bed void fraction was 0.354 and the mass flow rate was 50.4 g s l. The RTD data at two axial positions (which were 91 cm apart in Run 1 and 152 cm apart in Run 2) are summarized in Table 3-2. Using the method of moments, estimate the mean residence time and the Peclet number for these two runs. If one assumes that the backmixing characteristics are independent of the distance between two measuring points, what is the effect of gas flow rate on the mean residence time of liquid and the Peclet number Hovv does the measured and the predicted RTD at the downstream positions compare in both cases ... 

The differences in tm and Pe are partly caused by the difference in Lp. As one may expect, the increase in gas flow rate increases the backmixing. The RTD at the downstream positions predicted from the estimated parameters are compared with the measured ones in Figs. 3-17 and 3-18. As shown, the agreement is fair for both runs. 

Similar to tray columns, packed columns operated at high gas velocities causes backmixing, and low gas velocities reduce the mass transfer rate. If the gas velocity is too high, the column will flood. In addition, at low liquid flow rates the packing will not wet completely, resulting in a reduction in mass-transfer. Another problem is the tendency for the liquid to channel. To minimize this effect, redistributors have to be installed every 5 to 10 m (16.4 to 30.5 ft) [23] to even out the liquid flow. 

Figure 5.2 shows the influence of dead volume and connection design on the peak distortion and dead time of the HPLC unit. Three runs were performed with the same flow rate and sample size (injection time 2 s). The straight black line describes the elution profile of a tracer in an optimal system with small dead volume and optimal connections. In the next example one of the tube connections was insufficient because, within the connector, the tube endings did not touch and a small dead volume is formed. The dashed line shows the new elution profile. A poor connection results in higher backmixing and, thus, peak distortion. This effect should be kept in mind for systems with many connections. 

In this example of a five-stage extraction column with backmixing, proportional plus integral control of the exit raffinate concentration is to be achieved by regulating solvent flow rate. 

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