Meso-mixing

A fast reaction can already occur at the point of addition, where the meso-mixing can be slower than the micro-mixing. The meso-mixing concerns a length-scale between macro- and micro-mixing. There are differences between the... 

The evaluation of diazotization reactions [41], which were carried out in Kenics and Sulzer SMXL mixers, provide a possible access to this parameter determination. For small throughputs and high viscosities the yield of the desired product was determined by micro-mixing. The power dissipation of 85-90% in both mixers indicated, that the engulfment model for micro-mixing prevailed. Faster micro- and meso-mixing was achieved in the Sulzer mixers, because larger pressure drops were also present in them, see Fig. 8.11 and 8.12. 

Characteristic time of meso-mixing (mixing at the expense of exchange between large turbulent flows and being inside of them little flows) is calculated by ratio ... 

Figure 3.19. The values of characteristic times of turbulent mixing Tturb (1), micro-mixing Xmicro (3-6), and meso-mixing Xmeso (2) in dependence on reaction mixture movement rate V. The values of dynamic viscosity 0,001 (3), 1 (4), 10 (5), 50 (6) Pa-sec. d = 0,025m, p = 1000 kg/m, Vc = 4 m/sec.

Figure 3.23. Dependence of characteristic time of meso-mixing Tmeso on apparatus diameter dc and linear rate of reaction mixture movement Vc. Y = 45°, dd / dc = 2, Ls / da = 3.

When a liquid flow is introduced into a stirred reactor, such as in semi-batch or in fully continuous operation, the mixing of this flow with the reactor contents may be critical, particularly in turbulent flow conditions. This effect is known as meso-mixing. The incoming liquid forms a jet that is surrounded by a turbulent stream of liquid that circulates in the reactor. The jet will be broken up from the outside into small lumps of liquid these will deform and become engulfed by the surrounding liquid (Baldyga and Bourne, 1992, Baldyga et al., 1993). 

There are as yet no generally accepted theories that describe the meso-mixing with sufficient accuracy. We should distinguish between two situations ... 

The meso mixing time is the time needed for turbulent diffusion to transport matter acrosss a distance on the order of the diameter of the feeding tube d ... 

Combination of the last two equations leads to the following relation for estimating the meso-mixing time ... 

It was shown above that local values of the specific energy dissipation e (= T e) vary considerable across the reactor. The ratio r is highest in the impeller region, particularly in the flow leaving the impeller. Obviously, it is best to introduce the feed there. Meso-mixing times could be at least 3 times shorter than when the feed is introduced into the bulk of the liquid. 

There is one restriction in applying eq. (4.12) the meso-mixing time cannot be smaller than the micro-mixing time (the lowest value of eqs. (4.9) or (4.10)). 

For those situations that the parameter (p will be > 1, the meso-mixing time can be estimated as follows ... 

In this situation the meso-mixing time would be reduced when the inlet tube diameter is increased, if thereby

[Pg.70]

This will generally guarantee the same micro-mixing time on the larger scale. However, the meso-mixing time, that is usually critical, may go up with the scale of the reactor. As long as the parameter

tube diameter is increased proportional to other linear dimensions to the power 2/3. 

When (p would become > 1, multiple feed tubes may be advisable. When still (p > 1 on scale-up, the meso-mixing time will increase. 

As was pointed out on p. 60, micro- and meso-mixing are not really different processes in laminar flow. We will consider them as one. 

Note the similarity between eq. (4.18) and eq. (4.12), for the meso-mixing time in turbulent flow. In laminar flow, meso- and micro-mixing are identical. So we see that the ratio of meso-mixing times in laminar and turbulent flow in the same stirred vessel with the same power input can be estimated from... 

Micro- (or meso-) mixing rates are at best moderate. In the case of rapid reactions (virtually all solution polymerizations) the reaction rates will be determined to a large extent by micro-mixing. 

The meso-mixing time for reactant A can be compared with the reaction time, which... 

Reaction rate constants can vary enormously, depending on the type of reaction and the reaction conditions. Concentrations can vary also, even wiAin a reactor, so reaction times will vary widely in practice, say from 10 to 10 s. Consequently, reaction times can be much greater or much smaller than meso-mixing times. 

A third characteristic time (in the case of continuous reactors) is the mean residence time T. In liquid phase processes this is usually much greater than the meso-mixing time, and for rapid reactions it usually is also much greater than the reaction time. (The situation of rapid gas-phase reactions carried out in reactors with very short residence times is a special case that is not treated here). It is generally useful to make the following broad distinction in average values of the characteristic times for a given reactor ... 

Situation I was discussed in Chapter 3. Situations II and m will be discussed in the next sections. Note that both situations can occur in laminar and in turbulent flow conditions. In the following we shall concentrate primarily on the meso-mixing in continuous stirred tank reactors (CSTR), since the mixing effects in these reactors are relatively simple to visualize. The effect of meso-mixing on reactions in semi-batch reactors will be discussed thereafter. 

Zones a and b may be called entrance zones, zone c the mixed or exit zone. The relative volumes of these zones depend entirely on the conditions. In turbulent flow, zones a and b are limited to very small volumes close to the entrance ports of the reactants, while the bulk of the reactor is made up by zone c. The existence of the entrance zones is related to the finite rate of meso-mixing (see section 4.22A) the higher this rate, the smaller the entrance zones. Micro-mixing takes place throughout the reactor. 

---