A. Design of a Thickener

With the use of the batch sedimentation data collected from the column with slurry of

concentration 100g/L CaCO3, the continuous thickener parameters calculated were as follows:

Table 5. Continuous Thickener Design Parameters

Feed concentration (g CaCO3/L) 100

Feed rate (kg dry solids/hr) 30000

Underflow concentration (g CaCO3/L) 350

Thickener Cross-sectional Area 455.8957 m2

Diameter of Cylindrical Thickener (D) 24.10 m

Volume of Compression Zone 240.1858 m3

Height of Compression Zone 0.5268 m

Total Height of the Thickener (H) 2.2032 m

The unit area requirement for a certain concentration may be calculated using Equation

1 (Perry,2008).

⁄ ⁄

Equation 1

Where a is the unit area, is the concentration at the interfacial velocity and is the

concentration of the underflow. From the unit areas calculated, the largest value is used for the

calculation of the cross-sectional area of the thickener. Theory holds that for any specific

sedimentation set up, there exists a critical concentration which limits the settling rate of solids

in the fluid (Perry, 2008). Thus, in designing thickeners, the settling rates at different

concentration are considered to ensure that the area of the thickener is sufficient for satisfactory

clarification of the overflow and concentration of the underflow. A rate limiting layer is identified

and is used as the basis for the calculations. This layer corresponds to the layer in the

sedimentation set up that has the lowest capacity for the passage of the solid particles (Foust,

1980) and thus requires the largest area.

Table 6. Unit Area at Different Concentrations

Time, tl (min) Concentration of Slurry,

cl (g/cm3) Settling Velocity, vl

(cm/min) Unit Area, a (cm2 min/g)

10 0.1000 1.3000 5.4942

30 0.1057 1.0767 6.1348

40 0.1232 0.7625 6.9006

50 0.1542 0.4520 8.0227

60 0.1754 0.3250 8.7494

70 0.1935 0.2536 9.1179

90 0.2140 0.2011 9.0277

108 0.2329 0.1681 8.5443

120 0.2481 0.1479 7.9306

138 0.3756 0.0622 -3.1306

150 0.4505 0.0357 -17.8768

From the calculated values, the largest unit area is 9.1179 cm2 min/g. To solve for the final

thickener area, Equation 2 is used.

Equation 2

where is the mass feed rate of dry solids per unit time.

The volume required for the compression zone in the continuous thickener is given by

Equation 3 (Brown, 1950). This is equal to the sum of the volume occupied by the solids plus

the volume of the associated fluids.

( )

∫

Equation 3

where V = the volume of the compression zone = mass of solids per unit time = time in which the solids have reached the desired underflow concentration =time when all solids at critical concentration go to compression L =mass of liquid in compression zone S =mass of solid in compression zone

With the assumption that the concentration of the solids in the compression zone of a

continuous thickener at any time is the same as the average concentration of the compression

zone of the batch test at time equal to the retention time of the solids in the continuous

thickener, then the time required for the slurry in the batch test to pass from the critical

concentration to the desired underflow concentration is the retention time of the solids in the

continuous thickener (Brown, 1950). The plot of the height of the interface of the supernatant

liquid and the slurry versus time may be described by Equation 4.

( )

( ) Equation 4

Where z is the height of the interface at time t and is the height at infinite time.

If the batch sedimentation basis has an initial slurry concentration at its critical concentration,

that is when t0 corresponds to which is the height of the compression zone at critical

concentration cc, then plotting ( )

( ) versus time would give a straight line. Since the initial

concentration of the slurry in the experimental batch sedimentation was not at cc, then tc is

determined by extrapolating the compression curve from the critical point to zero time and then

locating the time when the upper interface is at a height halfway between the initial slurry height

z0 and the extrapolated zero-time compression zone height z0’ (Brown, 1950). The tc obtained

from the batch test was 9.4 min from Figure--.

The density of the slurry is constant at 1.0831 g/cm3 as well as the feed rate at 30000

kg/hr. To obtain the volume of the compression zone, the area under the curve in Figure 10 is

obtained and values were inputted to Equation 3.

The height was obtained by dividing the volume of the compression zone to the area.

Height allowances for the bottom pitch of the thickener, storage capacity and for the

submergence of feed were added to the initial computed height (Foust, 1980) to get the total

height of the thickener. Suggested allowances are given below:

For the pitch of the bottom 0.3048-0.6096 m

For the storage capacity to cover interruptions

or irregularities in discharge 0.3048-0.6096 m

For submergence of feed 0.3048-0.9144 m