What is the difference between space time and residence time?

Space time (τ = V/v₀) is defined using the inlet volumetric flow rate v₀. Residence time (mean time a fluid element spends in the reactor) equals space time when fluid density is constant — the common case for liquid-phase reactions. For gas-phase reactions with changing moles, they differ.

Why does PFR require less volume than CSTR for the same conversion?

In a CSTR the entire reactor operates at the outlet (lowest) concentration, giving a lower reaction rate throughout. A PFR has a concentration gradient from inlet to outlet, so the average rate is higher, requiring less volume for the same conversion.

What is the Damköhler number?

Da = k·τ for first-order reactions (or k·C₀·τ for second-order). It is the ratio of the reaction rate to the convective transport rate. Da 10 means nearly complete conversion.

Are these formulas valid for reversible reactions?

No. The design equations used here assume irreversible reactions. For reversible reactions you would need to incorporate the equilibrium constant and back-reaction term.

What units should I use?

The calculator is unit-consistent: use any coherent system (SI or other) as long as you are consistent. For example, k in s⁻¹ (first-order) or L·mol⁻¹·s⁻¹ (second-order), C₀ in mol/L, v₀ in L/s, and V in L. The conversion X and Damköhler number are dimensionless.

Reactor Conversion Calculator

Calculate conversion, space time, and residence time for CSTR and PFR reactors with first-order or second-order kinetics.

Reactor Parameters

Reactor Type

Reaction Order

Rate Constant (k, s⁻¹)

Initial Concentration C₀ (mol/L)

Volumetric Flow Rate v₀ (L/s)

Reactor Volume V (L)

Results CSTR · 1st Order

Conversion X

—

dimensionless

Space Time τ

—

seconds

Damköhler Da

—

dimensionless

Conversion progress —

Additional Parameters

Outlet Concentration C —

Molar Feed Rate F₀ —

Outlet Molar Rate F —

Reaction Rate at Outlet —

Design Equation Used

Summary

This calculator handles the two most common ideal reactor models — the Continuous Stirred-Tank Reactor (CSTR) and the Plug Flow Reactor (PFR) — for first-order and second-order irreversible reactions. Enter your rate constant, feed concentration, volumetric flow rate, and reactor volume to instantly obtain conversion, space time, and Damköhler number.

How it works

Select the reactor type: CSTR (perfectly mixed) or PFR (plug flow).
Choose reaction order: first-order (rate = k·C) or second-order (rate = k·C²).
Enter the rate constant k, initial concentration C₀, volumetric flow rate v₀, and reactor volume V.
The calculator solves the design equation analytically for conversion X.
Space time τ = V/v₀ and Damköhler number Da are derived from the inputs.
Results update instantly; adjust any input to explore the design space.

Use cases

Size a CSTR or PFR for a target conversion in a chemical plant.
Compare the reactor volume required by CSTR vs PFR for the same conversion.
Determine space time and residence time for a known reactor volume.
Verify hand-calculated reactor design problems from textbooks.
Teach or study chemical reaction engineering concepts interactively.
Perform quick sensitivity analysis on rate constant or feed concentration.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu