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CSTR Residence Time (Space Time)

Defines the average time a fluid element spends inside a continuous stirred-tank reactor, based on reactor volume and volumetric feed rate.

Written by the Vorzep Team

Chemical EngineeringReaction EngineeringReactor Design

CSTR Residence Time Calculatorτ = V / v₀ · Space Time

τ = V / v₀
V volume (L)  ·  v₀ volumetric flow rate (L/min)
⟹ τ⟷V, v₀
L
L/min
min
Units:
Solve for:
Residence Time—
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Residence Time—
Short (<1 min) Moderate (1–10 min) Long (10–60 min) Very Long (>60 min)
τ vs. v₀fixed V
τ(v₀) = V / v₀ Computed point
τ = V / v₀  ·  Volume in L, flow in L/min → time in minutes
tau = V / v0
CSTR Residence Time (Space Time)

Variables

SymbolQuantityUnit
tauSpace time / residence times
VReactor volumem3
v0Volumetric feed flow ratem3/s

What it means

Space time (or residence time) for a continuous stirred‑tank reactor (CSTR) is defined as the reactor volume divided by the volumetric flow rate at the inlet. It represents the average time the fluid elements stay inside the reactor. For an ideal CSTR, the residence time distribution is exponential, meaning that some elements leave quickly and others stay longer. Space time is a key design parameter: it determines the extent of reaction for a given kinetics. For a first‑order reaction, conversion is a function of the Damköhler number (k τ). In practice, the space time is used to size reactors and to compare performance across different scales. It is also used in the design of other continuous reactors (e.g., PFR) where the residence time is the same for all elements (plug flow). Understanding space time is essential for reactor design and for troubleshooting non‑ideal behaviour.

Worked example

CSTR Residence Time – Two Examples

Real‑World
Scenario: V = 10 m³, v₀ = 0.5 m³/s. Find residence time τ.
ParameterValue
V10 m³
v₀0.5 m³/s
1τ = V/v₀ = 10/0.5 = 20 s
Result τ = 20 s ✓ Adequate
Scenario: V = 5 m³, v₀ = 0.1 m³/s. Compute τ.
ParameterValue
V5
v₀0.1
1τ = 5/0.1 = 50 s
Result τ = 50 s ✓ Longer residence
Key insight: Residence time = V/v₀; longer τ usually gives higher conversion.

Common mistakes

  • Reactor volume V: The total volume of the reactor (liquid volume for CSTR).
  • Volumetric flow v₀: Inlet volumetric flow rate, assumed constant if density is constant.
  • Space time τ: The average residence time; units are time (e.g., min, s).
  • For variable density: If density changes, use the outlet or average flow rate; in ideal CSTR, volume is usually constant.
  • Space velocity: Is the inverse of space time (v₀/V).

Applications

Space time (residence time) for a CSTR is defined as τ = V / v₀, representing the average time a fluid element spends in the reactor. It is a key design parameter for continuous stirred‑tank reactors, influencing conversion and product distribution. Engineers use space time to size reactors, to compare different reactor configurations, and to predict performance at different flow rates. For a given reaction kinetics, a longer space time generally increases conversion but requires a larger reactor volume. Space time is also used in the design of bioreactors and in the analysis of plug flow reactors (where it is equivalent to the residence time). By understanding space time, professionals can optimise reactor size and operation.

  • Sizing of CSTRs for chemical and biochemical processes
  • Comparison of CSTR performance with other reactor types
  • Scale‑up and scale‑down of stirred reactors
  • Design of fermenters and biological reactors
  • Analysis of mixing and residence time distribution (RTD)