Backmix flow

Allowing for the additional backmixing flow contributions, the component balance equation for the two phases in stage n of the cascade are now... 

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... 

Allowing for the backmixing flow contributions in the inflow and outflow terms, the continuity equations for each phase, in stage n, are given by... 

Vary the backmixing flows for each phase separately and notice the effect of changes in conditions between plug flow and full backmixing on the performance of the extractor. 

Figure 5.193. The response of the cascade for a ten-fold increase in the backmixing flows EL and EG.

Continuous-flow stirred tank reactor (CSTR), based on backmix flow,... 

The fluid inside each vessel is perfectly mixed (backmix flow, BMF), and hence its properties are uniform at any time, because of efficient stirring. 

A stirred-tank flow reactor may be single-stage or multistage. As an ideal backmix flow reactor, it is referred to as a CSTR or multistage CSTR this is treated in Chapter 14. Nonideal flow effects are discussed in Chapter 20. 

Ideal flow is introduced in Chapter 2 in connection with the investigation of kinetics in certain types of ideal reactor models, and in Chapter 11 in connection with chemical reactors as a contrast to nonideal flow. As its name implies, ideal flow is a model of flow which, in one of its various forms, may be closely approached, but is not actually achieved. In Chapter 2, three forms are described backmix flow (BMF), plug flow (PF), and laminar flow (LF). 

TYPES OF IDEAL FLOW, CLOSED AND OPEN VESSELS 13.2.1 Backmix Flow (BMF)... 

Backmix flow (BMF) is the flow model for a CSTR, and is described in Section 2.3.1. BMF implies perfect mixing and, hence, uniform fluid properties throughout the vessel. It also implies a continuous distribution of residence times. The stepwise or discontinuous change in properties across the point of entry, and the continuity of property behavior across the exit are illustrated in Figure 2.3. 

All patterns of flow other than plug and backmix flow may be called nonideal flow patterns because for these the design methods are not nearly as straightforward as those for the two ideal flow patterns. The methods of treating nonideal patterns either have only recently been developed or are yet to be developed. 

In real vessels flow is usually approximated by plug or backmix flow however, for proper design, the departure of actual flow from these idealizations should be accounted for. Here we intend to consider these nonideal flow patterns to characterize them, to measure them and to use this information in design. 

Names have been associated with different types of flow patterns of fluid in vessels. First of all, we have the two previously mentioned ideal flow patterns, plug flow and backmix flow. Flow in tubular vessels ap-... 

Dispersion models, as just stated, are useful mainly to represent flow in empty tubes and packed beds, which is much closer to the ideal case of plug flow than to the opposite extreme of backmix flow. In empty tubes, the mixing is caused by molecular diffusion and turbulent diffusion, superposed on the velocity-profile effect. In packed beds, mixing is caused both by splitting of the fluid streams as they flow around the particles and by the variations in velocity across the bed. 

In the preceding section we discussed the dispersion model which can account for small deviations from plug flow. It happens that a series of perfectly mixed tanks (backmix flow) will give tracer response curves that are somewhat similar in shape to those found from the dispersion model. Thus, either type of model could be used to correlate experimental tracer data. 

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. 

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