Definition of draft tube
The tube diameter is 30-50% that of the vaporization space. The distance from the bottom of the tube to the bottom of the vat is equal to the diameter DT of the draft tube. In order to alleviate the vortex effect, the distance from the top of the tube to the free surface of the liquid considered as at rest is equal to DT/2. In the work of Oldshue (p. 479, [OLD 83]), we find the plan of a draft tube. To reduce the drop in pressure, it is advisable to “round” the lower part of the tube by fitting it with an external ring made with a tube of diameter DT/4.
The draft tube fitted with a marine impeller is capable of a significant recirculation flow. This flow must meet two conditions:
- avoiding dividing the crystals, that is, ensuring that their retention time does not vary according to size:
Vc: useful volume of the crystallizer (m3)
Q : recirculated flow (m3.s-1);
- avoiding supersaturation heterogeneities, that is, ensuring that the composition of the liquor is the same throughout the crystallization body:
AT: fictive variation of temperature between 0.5 and 1°C pB: slurry density (kg.m-3)
CB: thermal capacity of the slurry (J.kg-1.°C-1)
W: thermal power injected into the crystallizer (W).
The clean liquor is extracted from the upper part of the clarification zone, which avoids attrition of the crystals by the pump. The liquor leaving the exchanger is injected at the base of the crystallizer, that is, near the large crystals (maximum crystal surface) that grow by absorbing the supersaturation, which avoids excessive nucleation.
A reasonable value for slurry velocity in the draft tube is 2 m/s. The liquid rises in the tube.
Figure 4.3. A crystallizer with a draft tube and vaporization (Swenson)
The impeller, of the marine type with three vanes, is placed on the lower part of the tube (at a third of its height).
According to the classic formula, the flow created by an impeller at a pitch equal to p is:
A: cross-section of the draft tube (m2)
N: rotation speed (rev.s-1)
p: impeller pitch (often equal to its diameter) (m)
This equation provides the impeller rotation speed.
To ensure correct homogeneity and avoid unscheduled decantation, the speed at the end of each vane must be greater than 3 m.s-1. This speed must not exceed 7 m.s-1 for brittle crystals and can reach 10 m.s-1 for resistant particles. In order to diminish the shear at the end of the vanes, we leave a clearance of 2-3 cm between the impeller and the tube wall. The impeller’s position in the tube is not significant; however, if we wish to correct an unscheduled decantation that occurs during a stoppage, the impeller should preferably be placed on the lower part as mentioned earlier in this chapter.
According to Oldshue’s formula [OLD 83], the pressure loss created by circulation is:
AP: pressure drop (Pa) pB: density of slurry (kg.m-3)
V: velocity in tube (m.s-1).
The energetic yield n of a marine impeller operating in these conditions is approximately 20%, so that the shaft power is:
Pa: shaft power (W).
The power number NP can then be assessed. Indeed:
This value is greater than the value of 0.43 for an impeller operating without a draft tube. However, the tube has the advantage of orientating the circulation vertically, which effectively neutralizes the decantation effect due to gravity.
If vaporization occurs, the top of the draft tube must be 30 cm below the liquid level to avoid splashes and contamination on the wall of the vaporization space.
In some cases, magma can be particularly viscous. Here, its viscosity is given by Bruhns’ formula [BRU 96]:
pM and pLM: viscosities of magma and the mother liquor (Pa.s)
фт: volume fraction of solid in the magma
9max: maximum value of фт (complement to 1 of resting crystals porosity)
For near-equidimensional crystals (with their three main dimensions of the same order), we take ф™х = 0.6
This expression is not applicable for particles below 50 nm.
For plates, we take ф™х # 0.20
For fibers, we take 0.01 < ф^ < 0.05
The above is only applicable for magmas that are not too viscous, such as those present in most crystallizers. In such cases, we use the pressure drop formulae for pipes both for the draft tube and for the thermal exchanger. Therefore, we have:
This is not the case in sugar refineries where, at 40°C, and for C sugar (after useful production), we can have:
The formula above gives 96 Pa.s, while the viscosity of magma can reach 1,000 Pa.s (though this is simply an apparent viscosity as magma is no longer Newtonian).