Water tools

Minimum powdered activated carbon dose for a target effluent

Powdered carbon in a contactor can at best reach equilibrium with the water leaving it. That gives the lowest dose that could ever meet the target; the practical dose is well above it.

Influent concentrationµg/L

Target effluentµg/L

Freundlich K(mg/g)(L/mg)^(1/n)

Freundlich 1/n

Minimum PAC dose (equilibrium)

1.777mg/L

A floor, not a design value: real doses are often 10 to 100 times higher because contact time is short and natural organic matter competes.

GAC usage for the same water

0.804mg/L

PAC to GAC ratio

2.21

Depends only on 1/n and the removal: PAC sees the effluent concentration, a GAC bed sees the influent.

Confirm with jar tests at the plant's real contact time. The equilibrium dose assumes complete mixing and enough time to reach it.

How it works

Mass balance on a completely mixed contactor whose carbon leaves in equilibrium with the effluent:

D_{P A C} = \frac{C_{i n f} - C_{e f f}}{q_{e} (C_{e f f})} = \frac{C_{i n f} - C_{e f f}}{K C_{e f f}^{1 / n}}

(1)

D_{G A C} = \frac{C_{i n f}}{K C_{i n f}^{1 / n}} \frac{D_{P A C}}{D_{G A C}} = \frac{1 - C_{e f f} / C_{i n f}}{(C_{e f f} / C_{i n f})^{1 / n}}

(2)

where

$D_{P A C}$: minimum powdered carbon dose, g/L
$C_{i n f}, C_{e f f}$: influent and target effluent concentration, mg/L
$q_{e}$: equilibrium loading at the effluent concentration, mg/g
$K, 1 / n$: Freundlich constants
$D_{G A C}$: carbon usage of a granular bed for the same water, g/L

Powdered carbon behaves co-currently and a granular bed counter-currently, which is why the bed always uses less carbon for the same duty. For removals below about 95% and seasonal problems the powdered form can still be the economical choice. Jar-test dose-response curves on a log-log plot are independent of the starting concentration for a given water and carbon.

Minimum powdered activated carbon dose for a target effluent

How it works

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