Hydraulic Retention Time Calculator

Background.

Every treatment tank is a bet on time. Bacteria need hours to strip dissolved organic matter from sewage, particles need time to settle in a clarifier, and a disinfectant needs contact time to kill pathogens. Hydraulic retention time is the first check on whether a tank gives the water enough of it: divide the volume of liquid in the tank by the rate at which water flows through, and you have the average time a parcel of water spends inside.

For a 750 m³ aeration basin fed at 25 litres a second, that comes to 30,000 seconds, a little over eight hours. Halve the tank or double the flow and the time halves too. That simple proportion is why operators watch retention time during storms: when inflow doubles, every tank downstream gives the water half as long, whether or not the process can keep up.

The figure is nominal, and the word matters. It assumes the whole volume is in play and the flow is steady. Real tanks have corners where water barely moves and fast lanes where an inlet jet runs almost straight to the outlet, so some water leaves well before the average while some lingers. Even in an ideally stirred tank, where every drop has the same chance of leaving at any moment, 63% of the water entering at one instant has gone within one retention time. Tracer tests measure how far a real tank departs from the nominal value.

Hydraulic retention time is also not the same as sludge age. In an activated sludge plant the biomass is settled out and pumped back, so solids stay for days while the water passes through in hours, and the two are controlled separately.

What is hydraulic retention time calculator?

Hydraulic retention time, written HRT or τ, is the volume of liquid in a tank or reactor divided by the volumetric flow passing through it. It has units of time and is the mean time water would spend in the vessel if the whole volume took part in the flow. Engineers use it to size and check aeration basins, clarifiers, septic tanks, digesters, ponds and contact tanks, usually alongside other loading measures. Its reciprocal, Q/V, is known as the dilution rate.

How to use this calculator.

1. 01Enter the liquid volume in cubic metres: the working volume up to the water surface, not the full tank including freeboard. For a rectangular tank, multiply length by width by water depth.
2. 02Enter the flow through the tank in cubic metres per second. A flow in m³ per day divides by 86,400, and a flow in litres per second divides by 1,000.
3. 03Decide which flow you are testing: the average daily flow for normal operation or the peak flow for the worst case.
4. 04Read the retention time in seconds and in hours, and treat it as the best case; most real tanks give much of the water less time than this.

The formula.

t = V / Q, with V in cubic metres and Q in cubic metres per second, so t comes out in seconds; dividing by 3,600 gives hours. The relationship is a balance: at steady flow the tank's contents are replaced once every V/Q seconds, so V/Q is also the mean age of the water leaving it, provided no part of the volume is cut off from the flow. Volume and flow carry equal and opposite weight: a 10% rise in flow cuts the time by about 9%, exactly as a 9% smaller tank would. The model is deliberately bare. It ignores how water moves inside the tank, so dead zones, short-circuiting, dispersion and stratification do not show up, and it assumes the flow is constant. It also says nothing about reactions; whether a given time is long enough depends on the process, which has its own design criteria.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed. (PRINT), reactor hydraulics.
2. [2]U.S. EPA, Wastewater Technology Fact Sheet: Sequencing Batch Reactors.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.