3. Thickener Design

Overflow Quality and Thickener Depth

The depth of a thickener depends on the rate of settling of the solids. The objective is a clear overflow solution. Even so, very fine solids might still be present. Flocculation is the process of particles coming together. Hence the growth of a floc requires interaction of two particles. This then may be expected to obey second order kinetics,

\[\ce{\frac{dC}{dt} = -kC^2} \tag{30}\]

where C is the concentration of particles, k is the rate constant for flocculation and t is time. Rearranging,

\[\ce{-\frac{dC}{C^2} = k\,dt} \tag{31}\]

This may be integrated over the limits C0 to C and 0 to t,

\[\ce{-\int_{C_0}^{C} \frac{dC}{C^2} = k \int_{0}^{t} dt} \tag{32}\]

Then,

\[\ce{\frac{1}{C} = kt + \frac{1}{C_0}} \tag{33}\]

The overflow quality is indicated by 1/C = Z. When C is small, the overflow is largely free of solids and 1/C is large. The volumetric flow rate of slurry is designated Q0, e.g. m3/hr. The residence time in the thickener is volume / flow rate,

\[\ce{t = \frac{Q_0}{A h}} \tag{34}\]

where A is the thickener surface area and h is the depth. Then,

\[\ce{Z = \frac{1}{C} = \frac{kAh}{Q_0} + \frac{1}{C_0}} \tag{34}\]

If k is large then h can be small to achieve a given quality. But, if k is small, i.e. flocculation is slow, then h must be large to achieve the same quality.

Surface Area Determination

In order to determine the required surface area for a thickener settling tests are performed. These involve mixing up a slurry of the required solids with varying additions of flocculant. The mixture is poured into a large graduated cylinder (e.g. 1 L) and inverted several times to ensure it is well mixed. Then it is allowed to stand for about a day. As the solids fall a definite interface appears. Above is clear solution. Below is a bed of slurry. Theinterface drops over time as the solids settle. A plot of slurry bed depth with time is the settling curve. This may be analyzed by a number of methods that involve geometric constructions to estimate the required thickener area per unit flow rate. The methods vary widely, some over-estimating and some under-estimating the required area. In practice it is better to over-estimate than under-estimate. Mineral processing textbooks may be consulted for details of the methods.