## Volume Fraction Of Liquid In Slurry

Figure 16. Settling factor for hindered settling.

OVERFLOW LEVEL

Figure 17. Plot of concentration versus height in a continuous sedimentation device. Curve (1) - low feedrate; Curve (2) - high feed rate.

Sedimentation equipment is designed to perform two operations : to clarify the liquid overflow by removal of suspended solids and to thicken sludge or underflow by removal of liquid. It is the cross section of the apparatus that controls the time needed for settling a preselected size range of particles out of the liquid for a given liquid feed rate and solids loading. The area also establishes the clarification capacity. The depth of the thickener establishes the time allowed for sedimentation (i.e., the solid's residence time) for a given feed rate and is important in determining the thickening capacity. The clarification capacity is established by the settling velocity of the suspended solids. Sedimentation tests are almost always recommended when scaling up for large settler capacities. By means of material balances, the total amount of fluid is equal to the sum of the fluid in the clear overflow plus the fluid in the compacted sludge removed from the bottom of the thickener. The average vertical velocity of fluid at any height through the thickener is the volumetric rate passing upward at that level divided by the unit's cross section. Note that if the particle settling velocity is less than the upward fluid velocity, particles will be entrained out in the overflow, resulting in poor clarification. For those size particles whose settling velocity approximately equals that of the upward fluid velocity, particles remain in a balanced suspension, i.e., they neither rise nor fall, and the concentration of solids in the clarification zone

Figure 17. Plot of concentration versus height in a continuous sedimentation device. Curve (1) - low feedrate; Curve (2) - high feed rate.

increases. This eventually results in a reduction of the settling velocity until the point where particles are entrained out in the overflow.

The thickener must be designed so that the settling velocity of particles is significantly greater than the upward fluid velocity, to minimize any increase in the solids concentration in the clarification zone.

Solids concentration varies over the thickener's height, and at the lower levels where the solution is dense, settling becomes retarded. In this region the upward fluid velocity can exceed the particle settling velocity irrespective of whether this condition exists in the upper zone or not. Figure 17 illustrates this situation, where curve II denotes a higher feed rate. A proper design must therefore be based on an evaluation of the settling rates at different concentrations as compared to the vertical velocity of the fluid. If the feed rate exceeds the maximum of the design, particulates are unable to settle out of the normal clarification zone. Hence, there is an increase in the solids concentration, resulting in hindered settling. The result is a corresponding decrease in the sedimentation rate below that observed for the feed slurry. The feed rate corresponding to the condition of just failing to initiate hindered settling represents the limiting clarification capacity of the system. That is, it is the maximum feed rate at which the suspended solids can attain the compression zone. The proper cross-sectional area can be estimated from calculations for different concentrations and checked by batch sedimentation tests on slurries of increasing concentrations. You will find some problems in the section on Questions for Thinking and Discussing that illustrate the need to check the thickener's calculated area against concentrations at various points in the vessel (including both the clarification and thickening zones)._Figure 18 shows the effect of varying the underflow rate on the thickening capacity. In this example, the depth of the thickening zone (compression zone) increases as the underflow rate decreases; hence, the underflow solids concentration increases, based on a constant rate of feed.

3E 3

OVERFLOW LEVEL

3E 3

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.

LINE

IF SLIGHT

CORRECTION

APPLIED

Figure 19. Extrapolation of sedimentation data to estimate time for critical concentration.

LINE

IF SLIGHT

CORRECTION

APPLIED

Figure 19. Extrapolation of sedimentation data to estimate time for critical concentration.

There are commercially available clarifier simulation software for comprehensive (2D) analyzes of wastewater treatment processes in circular and rectangular clarifiers. With these software, you can predict processes like:

• distribution of sludge in the settler

• flow streamlines in the settler

• vertical and horizontal flow velocities

• vertical and horizontal flow velocities

• sludge concentration in the effluent

• return sludge concentration

• total mass of sludge in the settler

Different processes like eddy turbulence, bottom current, stagnation of flows, and storm-water events can be simulated, using either laminar or turbulent flow model for simulation. All processes are displayed in real-time graphical mode (history, contour graph, surface, etc.); you can also record them to data files. Thanks to innovative sparse matrix technology, calculation process is fast and stable: a large number of layers in vertical and horizontal directions can be used, as well as a small time step. You can hunt for these on the Web.

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