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Chlorine residual decay from bench data, with temperature and CT

A chlorine residual does not stay put. Fit the decay from a dark bottle test, move it to the operating temperature, and see what residual and CT survive the contact time.

Residual measurements: time in h and chlorine in mg/L, one pair per line

Test temperature°C

Operating temperature°C

Activation energy of decaykJ/mol

Contact timeh

Decay

Decay constant at test temperature

0.1021/h

Decay constant at operating temperature

0.3851/h

Half-life at operating temperature

1.80h

At the contact time

Residual after the contact time

0.660mg/L

CT delivered over the contact time

48.3mg·min/L

CT if the residual did not decay

58.2mg·min/L

Dark-bottle constants do not transfer to open basins in sunlight, where the hypochlorite ion photolyses within tens of minutes.

How it works

C (t) = C_{0} e^{- k_{d} t} k_{d} = - \frac{\sum t_{i} \ln (C_{i} / C_{0})}{\sum t_{i}^{2}}

(1)

\ln k_{d, T_{2}} = \ln k_{d, T_{1}} + \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})

(2)

C T = \int_{0}^{t} C d t = \frac{C_{0}}{k_{d}} (1 - e^{- k_{d} t})

(3)

where

$C (t)$: residual after time t, mg/L
$C_{0}$: residual at time zero, mg/L
$k_{d}$: first-order decay constant, 1/h
$t_{i}, C_{i}$: measurement times and residuals
$E_{a}$: activation energy of the decay, J/mol
$R$: gas constant, 8.314 J/mol·K
$T_{1}, T_{2}$: test and operating temperature, K
$C T$: dose delivered over the contact time, mg·h/L

Simple first order is often the best model for natural organic matter demand; two-phase decay can be fitted with two parallel first-order terms when the data call for it. The decay constant depends on the starting residual, so test at the dose you will use. Combined chlorine can usually be held constant through a contactor; free chlorine and chlorine dioxide only at short times.

Chlorine residual decay from bench data, with temperature and CT

How it works

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