# Friction on the tube wall

The pressure drop in a tube is expressed by:

1

Hence, the friction stress:

Moreover, for two different tubes:

For an exchanger tube, the friction coefficient f is given by: With:

Example.- [1] [2]

3) Friction stress:

The friction on the pilot exchanger tube wall is weaker, which will lead to the apparition of crusting if it can form. Inversely, if the pilot tubes remain clean, we can be certain that the tubes of the industrial exchanger will also remain clean.

# How should the blockages in the pilot be avoided?

The operation of a pilot is inevitably punctuated by stoppage periods during which crystals can decant rapidly wherever they may be. In the presence of a saturated mother liquor, the sediment can, in certain cases, become resistant in the space of a few minutes. Thus, horizontal pipes are to be avoided. Only vertical pipes or pipes inclined at 45° should be used. Moreover, the exchanger itself should be of the vertical variety.

Valves must, as far as possible, be direct passage valves and must always be placed on the high points of pipes. In particular, control valves can close in a brief instant, which can be enough to cause a blockage if the solid accumulates around the valve.

Valves should be of a nominal diameter equal to (and not less than) that of the pipe.

During a stoppage, slurry decants to the low points of the pipes and the solid accumulates there. Accordingly, at each of these points, a cleaning liquor (often hot water) injection pipe should be fitted. The exit of this liquor is at a high point.

We will not return to slurry velocity in the exchanger tubes. However, the velocity in the tubes must be between 1.5 and 3 m.s-1. Indeed, we can accept a higher velocity in a pilot, even if this entails the erosion of the pipe wall.

These walls are not made to endure for more than several months. A well- planned pilot test should last for 3 weeks.

# Conclusion

If we set the interior diameter and the number of tubes in the pilot exchanger, the rest should follow naturally, particularly the volume of the crystallizer.

Of course, we should retain the following parameters in the industrial installation:

• - the crystal content in the slurry;
• - the residence time in the crystallizer;
• - the renewal velocity of the crystallizer volume by flow through the exchanger;
• - the temperature at various points in the installation.

• [1] Industrial tubes: And if we transport water:
• [2] Pilot tubes: