Dose a closed loop and the chemical stays. Dose a cooling tower and it starts leaving immediately, because the tower is bleeding — and what bleeds out is treated water, at full strength. The question a service technician actually needs answered is: how long does a slug last?

$\text{HTI} = \dfrac{0.693\,V}{B}$ — H-T-I equals nought point six nine three, V over B. $\text{HTI}$ is the holding time index in hours, $V$ is the system volume in m³, and $B$ is the chemical-consuming loss in m³/h — the blowdown plus the drift, every route by which treated LIQUID leaves. Evaporation is deliberately not in it: vapour leaves the chemical behind.

The 0.693 is $\ln 2$, and it is there because the index is a half-life. Fresh water arriving dilutes what is there, so the concentration decays exponentially — it never reaches zero, it just halves, and halves again. HTI is the time to the first halving. Two HTIs leaves a quarter; three leaves an eighth. Skip the $\ln 2$ and you have calculated the time to bleed away one whole system volume instead, which over-states the half-life by about 44 % — always in the flattering direction.

You need $V$ before you can use any of this, and on most sites nobody has the drawings. Measure it: $V = R\,t$, where $R$ is the pump recirculation rate and $t$ the turnover time — how long a tracer takes to come back around. One unit of time, chosen and stated; the flow is usually per hour and the turnover in minutes, and sixty is a small number that has ruined a great many dosing calculations.

Do not confuse the two times. Turnover is minutes: how fast the pump mixes the system. HTI is tens of hours: how fast the bleed empties it of chemistry. They differ by a factor of a hundred or more, and the practical use is this — a non-oxidising biocide needs its kill time inside the holding time. If the slug half-lives away in six hours and the biocide needs twelve to work, the programme is a gesture, and the answer is to shut the bleed during the dose.