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Water treatment sludge: mass from coagulant and solids, density and volume

Residuals are the coagulant's hydroxide plus the solids it captured plus whatever else was dosed. Their volume depends almost entirely on how much water they still hold.

Plant flowm³/d

Coagulant

Coagulant dosemg/L

Turbidity removedNTU

TSS per NTUmg/NTU1 to 2; about 1 below 10 NTU. Use measured TSS when you have it.

Polymer and other aidsmg/L

Sludge solids content%Settled alum sludge 0.1 to 4%; thickened 2 to 5%; dewatered 15 to 25%.

Volatile fraction of dry solids

Specific gravity of fixed solids

Temperature°C

Mass

Total dry solids

1,892kg/d

From the coagulant

337kg/d

From removed turbidity

1,512kg/d

From polymer and aids

43kg/d

Volume

Sludge volume

36.9m³/d

Share of plant flow

0.09%

Alum plants typically 0.05 to 0.15%; most of it from the basins.

Sludge specific gravity

1.028

Sludge density

1,027kg/m³

How it works

Dry solids add up from three sources, with the coagulant's contribution per kilogram dosed (alum 0.26, ferric sulfate 0.53, ferric chloride 0.66 on the anhydrous salt):

M = Q (f_{c o a g} D + T S S + X) T S S \approx 1.4 mg per NTU removed

(1)

The specific gravity of the sludge follows from its solids and their fixed and volatile parts, with water at 1.00:

\frac{1}{S_{s}} = \frac{f_{f i x e d}}{S_{f}} + \frac{f_{v o l}}{S_{v}} \frac{1}{S_{s l}} = \frac{P_{s}}{S_{s}} + (1 - P_{s})

(2)

V = \frac{M}{ρ_{w} S_{s l} P_{s}} \frac{V_{1}}{V_{2}} \approx \frac{P_{2}}{P_{1}}

(3)

where

$M$: dry solids, kg/d
$Q$: plant flow, m³/d
$f_{c o a g}$: kg of dry sludge per kg of coagulant
$D$: coagulant dose, mg/L
$T S S$: suspended solids removed, mg/L
$X$: polymer and other aids, mg/L
$S_{s}$: specific gravity of the dry solids
$f_{f i x e d}, f_{v o l}$: fixed and volatile fractions of the solids
$S_{f}, S_{v}$: specific gravity of fixed and volatile solids
$S_{s l}$: specific gravity of the sludge
$P_{s}$: solids content, fraction
$V$: sludge volume, m³/d
$ρ_{w}$: water density, kg/m³

Volume is governed by water content: thickening from 2% to 4% solids halves it. Washwater from filters carries a further 100 to 1,000 mg/L of solids at 2 to 5% of plant flow and is handled separately.

Water treatment sludge: mass from coagulant and solids, density and volume

How it works

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