Reactor Design Calculator (CSTR & PFR)

Size ideal isothermal reactors for a single irreversible reaction. Compute conversion, reactor volume, or space time for CSTR and PFR with first‑order or n‑th order kinetics.

CSTR Design

Ideal continuous stirred‑tank reactor, isothermal, single irreversible reaction \(A \rightarrow \text{products}\).

Units must match reaction order n.

For liquids, FA0 = v0CA0.

How this reactor design calculator works

This tool implements the classical design equations from chemical reaction engineering for ideal isothermal reactors with a single irreversible reaction \(A \rightarrow \text{products}\) and rate law \(r_A = -k C_A^n\).

It assumes constant density and volumetric flow (typical for liquid‑phase systems), no mass transfer limitations, and steady‑state operation.

CSTR design equations

For a continuous stirred‑tank reactor (CSTR), the concentration inside the reactor equals the outlet concentration. The mole balance at steady state is:

\[ F_{A0} - F_A + r_A V = 0 \] \[ F_A = F_{A0}(1 - X), \quad C_A = C_{A0}(1 - X) \]

Substituting and solving for the reactor volume:

\[ V = \frac{F_{A0} X}{-r_A} = \frac{F_{A0} X}{k C_A^n} = \frac{F_{A0} X}{k \left(C_{A0}(1 - X)\right)^n} \]

The space time (or residence time) is \(\tau = V / v_0 = V C_{A0} / F_{A0}\) when density is constant.

PFR design equations

For a plug flow reactor (PFR), concentration varies along the reactor length. The differential mole balance is:

\[ dF_A = r_A dV \quad\Rightarrow\quad F_{A0} dX = -r_A dV \] \[ V = F_{A0} \int_0^X \frac{dX}{-r_A} \]

For a first‑order reaction (\(n = 1\)) with constant volumetric flow:

\[ r_A = -k C_A = -k C_{A0}(1 - X) \] \[ V = \frac{F_{A0}}{k C_{A0}} \int_0^X \frac{dX}{1 - X} = \frac{F_{A0}}{k C_{A0}} \ln\left(\frac{1}{1 - X}\right) \]

The corresponding space time is \(\tau = V / v_0 = V C_{A0} / F_{A0}\).

Reaction order and rate constant units

The rate law is \(r_A = -k C_A^n\). The units of \(k\) depend on the reaction order:

  • Zero order (n = 0): \(r_A\) in mol/(L·s) ⇒ \(k\) in mol/(L·s)
  • First order (n = 1): \(k\) in 1/s
  • Second order (n = 2): \(k\) in L/(mol·s)

When you choose a reaction order in the calculator, make sure the units of \(k\) are consistent with that order.

When to use CSTR vs PFR

  • CSTR: good mixing, uniform temperature and concentration, easier temperature control.
  • PFR: higher conversion per unit volume for most reactions, especially first‑order and higher.

For a given set of kinetics and feed conditions, you can use this calculator to compare the required volume and space time for CSTR and PFR at the same target conversion.

Limitations and good practice

  • Single reaction only; side reactions and parallel/series networks are not modeled.
  • Isothermal operation; no energy balance or temperature gradients are included.
  • Ideal mixing (CSTR) and ideal plug flow (PFR); no back‑mixing or dispersion.
  • No catalyst deactivation or mass‑transfer limitations.

Use the results as a first sizing estimate or for homework and conceptual design. Detailed industrial design should always include full mass and energy balances, safety factors, and validation with pilot data where possible.

Reactor design FAQ