## Overflow Level

CONCENTRATION (GMS/L)

Figure 18. Shows effect of underflow rate on thickening capacity.

The curves of concentration as a function of depth in the compression zone are essentially vertical displacements of each other and are similar to those observed in batch sedimentation. When the sludge rakes operate, they essentially break up a semirigid structure of concentrated sludge. Generally, this action extends to several inches above the rakes and contributes to a more concentrated underflow. The required height of the compression zone may be estimated from experiments on batch sedimentation. The first batch test should be conducted with a slurry having an initial concentration equivalent to that of the top layer of the compression zone during the period of constant rate settling. This is referred to as the critical concentration. The time required for the sample slurry to pass from the critical concentration to the desired underflow concentration can be taken as the retention time for the solids in the continuous operation. The underlying assumption here is that the solids concentration at the bottom of the compression zone in the continuous thickener at any time is the same as the average concentration of the compression zone in the batch unit and at a time equal to the retention time of the solids in the continuous thickener. Hence, it is assumed that the concentration at the bottom of the thickener is an implicit function of the thickening time. The retention time is obtained from a batch test by observing the height of the compression zone as a function of time. The slope of the compression curve is described by the where Z, Z„ are the heights of compression at times t and infinity, respectively, and k is a constant that depends on the specific sedimentation system. Integrating this where Zc is the height of the compression zone at its critical concentration. This expression is the equation of a straight line and normally is plotted as log[(Z -ZJ/(Z0 - ZJ] versus time, where Z0 is the initial slurry concentration.Jf batch tests are performed with an initial slurry concentration below that of the critical, the average concentration of the compression zone will exceed the critical value because it will consist of sludge layers compressed over varying time lengths. A method for estimating the required time to pass from the critical solids content to any specified underflow concentration can be done as follows:

1. Extrapolate the compression curve to the critical point or zero time.

2. Locate the time when the upper interface (between the supernatant liquid and slurry) is at height Z'0, halfway between the initial height, Z0, and the extrapolated zero-time compression zone height, Z'0. This time represents the period in which all the solids were at the critical dilution and went into compression. The retention time is computed as t - tc, where t is the time when the solids reach the specified underflow concentration. The procedure is illustrated in Figure 19. It is recommended that you determine the required volume for the compression zone to be based on estimates of the time each layer has been in compression. The volume for the compression zone is the sum of the volume occupied by the solids plus the volume of the entrapped fluid. This may be expressed as:

where Q = solids mass feed per unit time; At = t - tc = retention time; rr^ = mass of liquid in the compression zone; m, = mass of solids in the compression zone.

This expression is based on our earlier assumption that the time required to thicken the sludge is independent of the interface height of the compression zone. An approximate solution to this expression can be obtained if we assume mj/ms to be constant, i.e., an average mass ratio in the thickening zone from top to bottom. Then,

More reliable results can be obtained by assuming average conditions over divided parts of the compression zone. That is, the above expression can be applied to divisions of the compression zone and the total volume obtained by the sum of these calculations. Try some of the problems in the section on Questions for Thinking and Discussing to strengthen your understanding of the principles covered.

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