# Detention Time Calculator

Created by Gabriela Diaz
Reviewed by Purnima Singh, PhD and Adena Benn
Last updated: Sep 28, 2022

With Omni's detention time calculator, you'll be able to quickly determine a tank's or basin's detention time. In different equipment such as clarifiers, settling tanks, storage tanks, and reactors, the term detention or residence time is present. You might find this tool useful if you're studying any of these.

We invite you to keep reading to learn a bit about detention time, specifically:

• What detention time is;
• How to calculate detention time and its formula;
• An example calculation; and
• Detention time units for different types of equipment.

## What is detention time?

Detention time (DT), also known as retention time or residence time, refers to the average amount of time that a type of fluid is retained in a tank, reservoir, or system, from the moment it enters until it flows out. We can also see it as the time it would take to fill or empty a given system.

Different industries use this concept, from water and wastewater treatment plants and pharmaceutical industries to petrochemical facilities. In water and wastewater treatment, the terms detention or retention time are most generally used, while the term residence time is more common in petrochemical applications.

Given the broad range of applications, detention times can be greater or shorter. Detention time depends on the plant's size, which relates to the volume and flow rate associated with a specific system, the flow pattern (swirling, plug, slug, mist... ), and what this time is required for. For example:

• Detention time is an important parameter when referring to physical separation methods, such as sedimentation or settling, that allows the separation of liquids or solids from liquids by the difference in densities. Closer densities will require longer periods, while substances with distant densities can separate in shorter periods.
• Another scenario concerns allowing enough time for a chemical reaction to occur. This is the case with reactors, bioreactors, and mixing tanks.
• To ensure the proper functioning of other elements in the system. For example, some vessels and tanks must have a low liquid level (LLL) and a high liquid level (HLL) to maintain the net positive suction head (NPSH) of a pumping system downstream. The residence time defines these levels.

## How do I calculate detention time?

We can calculate the detention time by dividing the volume of the vessel or basin by the system's flow rate. This is the detention time formula:

DT = V / Q


Where:

• DT - Detention time in days (d) or hours (h);
• V - Volume in cubic feet (ft3) or gallons (gal); and
• Q - Volumetric flow rate in gallons per minute (gpm) or gallons per day (gpd).

These are the most commonly used units when calculating detention times and expressing volumes and flow rates. Nevertheless, we can express these quantities in any other adequate units. In fact, depending on the application, detention times can be from seconds to days. In the table below, you can find some examples of industrial equipment and typical detention time unit:

Equipment

Typical detention time unit

Flash mix chambers, hydrocyclones, distillation columns

Seconds (s)

Flocculation basins, two-phase and three-phase separators, deaerators

Minutes (min)

Sedimentation tanks or clarifiers, oxidation ditches, reactors

Hours (h)

Wastewater ponds, storage tanks

Days (d)

Similar to detention time, we find the term hydraulic retention time, which is mainly used for reactors or digesters.

## Detention time example calculation

For example, let's imagine that we'll like to calculate the detention time of an already existing and operating three-phase separator of volume 2100 ft3 and a flow rate of 15 MBPD (thousands of barrels per day):

1. To determine the residence time, all we have to do is substitute these values in the detention time formula introduced before:
$\quad \scriptsize \quad \text{DT} = \frac{V}{Q} = \frac{\text{2100 ft}^3}{\text{15 MBPD}}$
1. Notice that volumetric flow rate and volume units don't match. Flow rate is given in thousands of barrels per day (MBPD) and volume in cubic feet (ft3). We'll need to convert them to continue with the calculation.

In this specific case, we'll be converting barrels to cubic feet. Here the conversion factor is: 1 US barrel = 4.211 cubic feet.

We will also express the thousand (M) prefix into its scientific notation equivalent, 103.

\quad \scriptsize \quad \begin{align*} \text{DT} & = \frac{\text{2100 ft}^3}{\text{15 MBPD}} \times \frac{1 \text{ bbl}}{4.211 \text{ ft}^3} \\ \\ & = \frac{\text{2100 ft}^3}{63.165 \times 10^ 3 \frac{\text{ ft}^3}{\text{d}}} \end{align*}
1. After performing the corresponding numerical calculation, we get that the detention time is:
\quad \scriptsize \quad \begin{align*} \text{DT} & = 33.245 \times 10^{-3}\ \text{d} \\ & = 0.033245 \text{ d} \end{align*}
1. Since we're getting such a small number of time in days (0.033245 d), we'll convert this result into minutes for a more comprehensible value:
\quad \scriptsize \quad \begin{align*} \text{DT} &= 33.245 \times 10^{-3}\ \text{d} \times \frac{1440 \text{ min}}{1 \text{ d}} \\ &= 47.87 \text { min} \end{align*}

## How to use the detention time calculator

With Omni's detention time calculator, you'll be able to determine the detention time of any tank or vessel. To use the calculator:

1. On the first row, Volume (V), enter the volume of the tank, vessel, or basin.
2. Next, in the row below, Flow rate (Q), indicate the system's flow rate.
3. With these two values entered, the calculator will show you the detention time associated (Detention time (DT)).

## FAQ

### How do I calculate detention time in hours?

To calculate detention time (DT) in hours, you'll need to convert the unit's result from the DT formula into hours. Let's see with an example:

1. Imagine a tank with a capacity of 500 gals and a flow rate of 100 gpm.
2. To determine the DT, we use the formula:
DT = V / Q
3. Substitute the known values:
DT = 500 gal / 100 gpm
DT = 100 min
4. This result is given in minutes. To convert to hours, divide by 60 min:
DT = 100 min / (60 min / 1 h) = 1.67 h.

### What is the detention time of a primary clarifier?

Detention time in primary clarifiers is between 1 to 3 hours or 2.5 hours. Around 50% of the suspended solids will settle in 30 minutes, the other 10% after 1 hour and 70% can be achieved in 2 hours.

Gabriela Diaz
Volume (V)
cu ft
Flow rate (Q)
US gal/day
You can click on the Advanced mode to enter tank dimensions or check our tank volume calculator for a more accurate tank volume calculation.
Detention time
Detention time (DT)
hrs
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