What it does
The same reaction can need very different reactor sizes depending on how the reactor is mixed. This tool works out, for one reaction A → products at a fixed temperature, the size of four ideal reactors:
- a CSTR (continuous stirred tank), where the whole tank sits at the exit concentration;
- a PFR (plug flow reactor, a long tube), where the concentration falls along the length;
- N equal CSTRs in series, which behave more and more like a PFR as N grows;
- a batch reactor at constant volume, for which the answer is a reaction time.
Choose the rate law: n-th order (−rA = k·CA^n, any order from 0 to 5), reversible first order A ⇌ B (the conversion cannot pass equilibrium, Xe = K/(1+K)) or a saturating law of Michaelis-Menten form, −rA = k·CA/(Km + CA). The rate constant is moved from a reference temperature to the reactor temperature with the Arrhenius equation. For gas-phase flow reactors, ε accounts for the change in the number of moles.
You can size the reactors for a target conversion or find the conversion a given volume (or batch time) reaches. The Levenspiel plot shows FA0/(−rA) against conversion: the CSTR volume is the rectangle, the PFR volume the area under the curve. A second chart shows conversion against volume for all three flow arrangements.
How to use it
- Pick the rate law and give the order, K or Km.
- Give k at a reference temperature, the activation energy and the reactor temperature, the feed concentration and ε (0 for liquids). Keep units consistent: concentrations in mol/L, volumes in L, and k in the units shown for your chosen time unit.
- Give the feed flow, the number of tanks for the series, and either the target conversion or the reactor volume and batch time.
Worked example
A made-up second-order liquid reaction, k = 0.15 L/(mol·min) at 50 °C with Ea = 60 kJ/mol, run at 60 °C: k rises to 0.2932 L/(mol·min). With CA0 = 1 mol/L and 10 L/min of feed, 80 % conversion needs a 136.4 L PFR but a 682.1 L CSTR, five times as big, because the CSTR works at the low exit concentration where the rate is slow. Three equal CSTRs in series need 230.7 L in all, and a batch reactor needs 13.64 min. Switching to “conversion from a given size”, a 200 L CSTR reaches 66.36 % and a 200 L PFR 85.43 %.
Tips
- For positive-order reactions the PFR is always the smallest flow reactor; for zero order the two are equal.
- A few tanks in series recover most of the PFR’s advantage; try 2, 3 and 5.
- With a reversible reaction, aim well below the equilibrium conversion: the size grows without limit as you approach it.
FAQ
Is the reactor isothermal? Yes. Heat effects are not included; a strongly exothermic reaction needs an energy balance as well (the mass and energy balance solver gives the adiabatic outlet temperature for a set conversion).
What about pressure drop or non-ideal mixing? Not included. Real reactors sit between the ideal CSTR and PFR; a residence time distribution study tells you where.
Where the numbers come from
- Design equations of ideal reactors (CSTR, PFR, batch, CSTRs in series), the Levenspiel plot, the Arrhenius equation and the volume-change factor ε: standard chemical reaction engineering, for example Fogler, Elements of Chemical Reaction Engineering, and Levenspiel, Chemical Reaction Engineering (methods only).
- The example rate constant, activation energy and feed are made up.
- Checked against an independent SciPy calculation (solve_ivp, quad and brentq) for five rate laws, written for the tests.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.