Residence Time Calculator Documentation

What is residence time?

Residence time or Mean residence time is a quantity used in chemical reactors modeling and simulation. It is the average time that liquid spends in a vessel. It is calculated as the ratio of the reactor volume to the volumetric flow rate.

$$\tau = V/F_V$$

Where:

• $\tau$ - mean residence time, s
• $V$ - volume, $m^3$
• $F_V$ - volumetric flow rate, $m^3/s$

Residence time in ideal reactors

We can distinguish two types of ideal reactors: CSTR (Continuous Stirred Tank Reactor) and PFR(Plug Flow Reactor). In a CSTR, the fluid is perfectly mixed, resulting in uniform concentrations throughout the entire reactor volume. In a PFR, fluid particles flow along the reactor without any back-mixing. The mean residence time plays a crucial role in the modeling, simulation, and design of both reactor types.

The time reactants spend in a reactor influences the reactor's efficiency. For a first-order reaction in a CSTR, the substrate concentration in the effluent stream can be calculated using the following equation:

$$C_{A}=\frac{C_{Af}}{(1+\tau k)}$$

Where:

• $C_A$ - substrace concentration in the effluent stream, $mol A/m^3$
• $k$ - kinetic constant, $1/s$
• $C_{Af}$ - substrace concentration in the feeding stream, $mol A/m^3$

The relationship for first-order reaction in a PFR presents as follows:

$$C_{A}={C_{Af}} \cdot exp{(-k \cdot \tau)}$$