Choosing a reactor: batch, CSTR, PFR and fixed bed

01 / Introductory

First principles

A reactor is a controlled place for chemical transformation.

A batch vessel is charged, reacted and discharged in separate steps.

It suits changing recipes and smaller campaigns, but charging, cleaning and unloading contribute to the total cycle time.

A continuous stirred tank reactor (CSTR) is idealized as perfectly mixed: its outlet composition equals the tank composition.

A plug flow reactor (PFR) has no axial mixing in the ideal model; each fluid element changes composition as it travels.

A fixed bed holds solid catalyst while fluid flows through it.

Fixed bed and PFR describe different things: catalyst arrangement and an ideal flow pattern.

Real packed beds can deviate from plug flow.

02 / Applied

Worked example

Consider an irreversible liquid reaction A → B, isothermal, first order, constant density, with k = 0.20 min⁻¹, inlet volumetric flow q = 2.0 m³/min and desired conversion X = 0.80.

For a CSTR, steady accumulation is zero and inlet minus outlet consumption equals reaction: FA0 X = (−rA) V.

Substituting CA = CA0(1−X) gives τ = 20 min and V = qτ = 40 m³.

Integrating the PFR balance gives τ = −ln(0.20)/0.20 = 8.047 min and V = 16.094 m³.

A constant-volume batch takes the same ideal reaction time, but not the same production cycle.

The comparison assumes identical temperature and kinetics and excludes downtime and heat-transfer limits.

−rA = k CA
CSTR: τ = X / [k(1 − X)]
PFR: τ = −ln(1 − X) / k
Batch: t = −ln(1 − X) / k

03 / Advanced

Engineering decisions

Choose by product selectivity and safety before minimizing volume.

For this positive-order example, mixing fresh feed with depleted liquid reduces the CSTR rate; autocatalytic or competing reactions can reverse a simple volume ranking.

Series CSTRs can approximate plug flow, while recycle modifies concentration and temperature profiles.

Exothermic duty requires an energy balance, cooling capacity, runaway assessment and relief design.

A fixed bed needs a mass-based rate, catalyst effectiveness, deactivation and a pressure-drop model; do not put a volumetric rate into dFA/dW = r′A.

Test residence-time distribution and kinetic data before treating an ideal model as plant performance.

Sources

1. University of Michigan · Elements of Chemical Reaction Engineering, Chapter 2 ↗
2. MIT OpenCourseWare · 10.37 Chemical and Biological Reaction Engineering ↗