Water tools

Gravity thickener area from batch settling data

A thickener fails when the solids flux it must pass exceeds what the blanket can carry. Batch settling tests at several concentrations give the gravity flux curve; the underflow you want sets the limit.

Batch tests: concentration in g/L and initial interface velocity in m/h, one pair per line

Underflow concentrationg/L

Feed flowm³/h

Feed solidsmg/L

Thickener area

313m²

Limiting flux

7.66kg/m²·h

Limiting concentration

5.0g/L

Underflow flow

160m³/h

Underflow velocity

0.51m/h

Surface loading

12.77m/h

How it works

Each batch test gives the gravity flux at its concentration, and the underflow adds a bulk flux:

J_{s} = v_{s} (C) C J_{T} = (v_{s} + v_{u}) C v_{u} = \frac{J_{L}}{C_{u}}

(1)

The limiting flux is the intercept of the line from the underflow concentration tangent to the gravity flux curve, which in algebra is the minimum over the descending limb:

J_{L} = \min_{C} \frac{J_{s} (C) C_{u}}{C_{u} - C}

(2)

Q_{u} = \frac{Q_{i} C_{i}}{C_{u}} A = \frac{Q_{i} C_{i}}{J_{L}}

(3)

where

$J_{s}$: gravity solids flux, kg/m²·h
$v_{s} (C)$: interface settling velocity at concentration C, m/h
$C$: solids concentration, kg/m³
$J_{T}$: total flux, kg/m²·h
$v_{u}$: underflow velocity, m/h
$J_{L}$: limiting flux, kg/m²·h
$C_{u}$: underflow concentration, kg/m³
$Q_{u}$: underflow flow, m³/h
$Q_{i}$: feed flow, m³/h
$C_{i}$: feed solids, kg/m³
$A$: thickener area, m²

Effluent solids are neglected against the feed and underflow. If the applied loading exceeds the limiting flux the blanket rises and solids overflow. The velocities are interpolated between test points; the printed construction in practice is graphical, so expect a few percent of reading tolerance.

Gravity thickener area from batch settling data

How it works

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