Thickener design and control are currently aspects of active research. One of the research groups is AMIRA project 266. Google and read the published papers from the research team. Gladman, Usher and Scales reported "performance enhancement" factors between static tests and actual thickener performance of typical 5 to 20 but factors up to 100 was observed depending on the material. In short there is no "one size fit all" answer to your question. Other thickener research were done in South America and Germany with collaboration between the parties.

No mathematical way will be able to correctly size a High rate thickener. There is nothing more accurate than testwork being carried out by experts in the field. When I say correclty sized I mean both from operational and capex point of view.

Agreeing completely. I would like to add that the Hi-Rate sizing based on test work I have practiced kept always in consideration the old and valid rule of the 1,0 m mud hight of average density in the cylindrical part of the tank.

I conducted bench to thickener pilot scale test work on a wide range of materials. The procedure uses a dynamic rig rather than cylinders and in my experience gives much better results. We found a significant improvement in under flow density, reduced thickener size etc when compared to cylinder work which is very conservative. Raked cylinder work is an improvement. Overflow clarity can look great in cylinder work but much worse in dynamic too eg mineral sand slimes.

No magic bullet system, even Outotec dynamic at bench scale is probably a bit pessimistic. That's why the taller 190mm rigs were built to test realistic bed depths.

Test work is the key, CSIRO and AMIRA P266 coming up with great info but still can't just put numbers into a formula.

Your comments summarize the point but experience will show that the rise rate of the clear water and the area required to handle the solids settle are the critical factors in sizing the high rate thickeners. When the solids settled fast, lesser area will be required and how fast it is possible to rake them to center without disturbing the solids that keep on settling in the same ares is a major factor. But then at the same time, water that rises through to the top should not be at too high velocities so that it disturbs the settling of the finer particles.Ideal will be to opt for dynamic testing simulating the feed at specific solids percentage and continuously withdrawing the solids settled and varying the dosages of the flocculants and then determine the size.

Agree with your comments, testwork will provide the accurate solids loading and rise rates. A good thickeners provider like us will find the equilibrium and design the smallest thickener performing as needed.

The size of the basic thickener, and feed well dimensions like diameter & depth, even the rake torque and drive sizing is not the hard part. The hard part is getting the full scale unit to deposit the thickened slurry evenly and uniformly and ensure that there are no spurious eddy currents rushing around in the quiescent zone. The feed system needs to arrest the energy of the incoming feed, mix the floculants correctly ensuring adequate & optimal contact time with the right amount of dilution and low shear mixing to form good flocs, Then it must channel these flocs downwards without segregation or classification. WesTech EvenFlo technology is arguably the only design that really looks the same on the P266 models as it does in practice, and they perform in a huge range of flow rates. Take a closer look at EvenFlo next time you want a settler, be it high rate or paste. Pilots scale testing available globally at competitive rates.

I believe each of the various methods of testing have their merit, although I believe they have evolved over the years. Having worked for Outotec for a number of years, I started off as a test engineer for the first 3-4 years performing many dynamic tests at operations and research facilities alongside static tests. In many cases, with higher SG ores or concentrates, the results would not widely vary, but the dynamic tests would be more insightful for the more difficult ores (laterite, ores with fines or clays, polymetallic, low sg materials, hydroxides or sludges) because in these cases, the rise rate and height of the fluidized zone would sometimes be the rate limiting factor for sizing that thickener. These aspects are difficult to measure in static tests.

One aspect that I believe is paramount in thickener testwork (static or dynamic) is to identify the correct flocculant prior to commencing thickener testwork. I would recommend having a flocculant supplier or expert perform testwork as they have the most experience with their range of products. Using the wrong flocculant can greatly influence the testwork results and ultimately the size of the HRT. 

Related to this topic is https://www.911metallurgist.com/water-treatment-tailings/sizing-a-high-rate-thickener/

Also see https://www.911metallurgist.com/blog/how-to-size-a-thickener