Chlorine Decay Constant from a Bottle Test
The first-order decay constant k from an initial and a measured residual over an elapsed time.
Example
You enter
- Initial free chlorine (mg/L) 2
- Measured residual after time (mg/L) 0.7358
- Elapsed time (hr) 10
You get
- Decay-rate constant k 0.1
- Half-life 6.9 hr
Checked against published worked examples from: EPA / AWWA.
Details, formula, and sources
Scopek = ln(C0 / C) / t, with the half-life. A residual falling 2.0 -> 0.7358 mg/L in 10 h gives k = 0.100 1/hr (a 6.9 h half-life). The field number that feeds the forward decay and booster-spacing model. Per EPA 815-R-02-020 and AWWA M14.
Formula or tableFirst-order decay C(t) = C0 x exp(-k x t) solved for the rate constant: k = ln(C0 / C) / t, from an initial residual C0 and a measured residual C over an elapsed time t (a distribution bottle test). Half-life = ln(2) / k.
Source and editionEPA 815-R-02-020 (Effects of Water Age on Distribution System Water Quality); AWWA M14.
Free accessepa.gov and awwa.org.
What governsEstimate. Operator of record and primacy agency govern.
API field namesinitial_mg_l, residual_mg_l, time_hr, decay_k_per_hr, half_life_hr
- Decay model bulk first-order C(t) = C0 e^(-kt)EPA 815-R-02-020 water-age model
- Measurement C is the residual measured after time t on the same water sample as C0AWWA M14 bottle-test method
- Typical k 0.05-0.20 1/hr depending on TOC and temperatureAWWA M14 / EPA water-age studies