Also in: Disaster Response and Recovery
Chlorine Residual Decay (First-Order)
First-order residual C(t) = C0 x exp(-k t), time to a target residual, and an optional booster distance.
Example
You enter
- Initial free chlorine (mg/L) 2
- Decay-rate constant k (1/hr) 0.1
- Elapsed time (hr) 10
- Target residual (mg/L) 0.2
You get
- Residual at elapsed time 0.73576
- Time to reach target 23.0259
Checked against published worked examples from: EPA / AWWA.
Details, formula, and sources
ScopePer EPA 815-R-02-020 and AWWA M14; 40 CFR 141.72(a)(4) and (b)(3) govern the extremity residual.
Formula or tableFirst-order decay C(t) = C0 x exp(-k x t). Time to target = ln(C0 / target) / k. Booster distance = distribution velocity x time-to-target (when a velocity is entered).
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, decay_k_per_hr, time_hr, target_mg_l, residual_mg_l, time_to_target_hr
- Decay model bulk first-order C(t) = C0 e^(-kt)EPA 815-R-02-020 water-age model
- Typical k 0.05-0.20 1/hr depending on TOC and temperatureAWWA M14 / EPA water-age studies
- Extremity target 0.2 mg/L default target; 141.72(b)(3) requires only a detectable residual in the system (0.2 mg/L is the entry-point minimum of 141.72(b)(2))EPA 40 CFR 141.72(b)(3)