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Qwestrum Engineering360 · Chemical Engineering · Chemical Reaction Engineering

Non Isothermal Reactor Design

Non-isothermal design couples the mole balance to an energy balance, because temperature changes the rate through Arrhenius; adiabatic reactors follow a linear temperature-conversion path, and exothermic cooled CSTRs can exhibit multiple steady states.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Adiabatic operation: Q = 0, so temperature rises for an exothermic reaction
  • Multiple steady states are possible in an exothermic cooled CSTR
  • Ignition–extinction: intersection of heat-generation and heat-removal curves

Topic details

Introduction

This Levenspiel topic recognises that real reactors seldom stay at one temperature. You solve the mole and energy balances simultaneously, trace the adiabatic temperature rise with conversion, and analyse the intersection of heat-generation and heat-removal curves that determines the stable operating point and the risk of thermal runaway.

Key relations & formulas

FA0ΣθiCpi(T−T0)=(−ΔHR)FA0X+QF_{A0} Σ\theta_{i} C_{pi} (T - T_{0}) = (-\Delta H_{R}) F_{A0} X + Q
(CSTR energy balance)
dTdV=(−ΔHR)(−rA)(ΣFiCpi)\frac{dT}{dV} = (-\Delta H_{R})\frac{(-r_{A})}{(Σ F_{i} C_{pi})}
(PFR energy balance)
d(lnK)dT=ΔH§K1§(RT2)d\frac{(ln K)}{dT} = \frac{\Delta H^{§K1§}}{(R T^{2})}
(van’t Hoff — equilibrium constant vs T)

Notation and sign conventions

Relation 1 —
FA0ΣθiCpiF_{A0} Σ\theta_{i} C_{pi}
FA0ΣθiCpi(T−T0)=(−ΔHR)FA0X+QF_{A0} Σ\theta_{i} C_{pi} (T - T_{0}) = (-\Delta H_{R}) F_{A0} X + Q
(CSTR energy balance)
Write this relation with symbols exactly as in Chemical Reaction Engineering — Octave Levenspiel before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
dTdV=\frac{dT}{dV} =
dTdV=(−ΔHR)(−rA)(ΣFiCpi)\frac{dT}{dV} = (-\Delta H_{R})\frac{(-r_{A})}{(Σ F_{i} C_{pi})}
(PFR energy balance)
Write this relation with symbols exactly as in Chemical Reaction Engineering — Octave Levenspiel before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
dd
d(lnK)dT=ΔH§K1§(RT2)d\frac{(ln K)}{dT} = \frac{\Delta H^{§K1§}}{(R T^{2})}
(van’t Hoff — equilibrium constant vs T)
Write this relation with symbols exactly as in Chemical Reaction Engineering — Octave Levenspiel before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Temperature and conversion are linked two ways: conversion generates heat that changes temperature, and temperature changes the rate constant exponentially. For an adiabatic reactor all reaction heat stays in the stream, giving a straight energy-balance line on the temperature-conversion plane. In a cooled exothermic CSTR the S-shaped heat-generation curve can cross the straight heat-removal line at up to three points; the outer two are stable and the middle one unstable, which explains ignition (a small change tips the reactor to the hot state) and extinction. Endothermic reactions cool as they proceed, so heat must be supplied to sustain conversion.

Assumptions and validity limits

State assumptions explicitly before using any relation for non isothermal reactor design — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Reaction Engineering viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Reaction Engineering papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to non isothermal reactor design.
4. Use equation 1:
FA0ΣθiCpiF_{A0} Σ\theta_{i} C_{pi}
.
5. Use equation 2:
dTdV=\frac{dT}{dV} =
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Non Isothermal Reactor Design appears in chemical and pharma plants. In Indian chemical curricula this topic is tested because it connects theory to reactor design and kinetics.
GATE and semester exams often combine non isothermal reactor design with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use non isothermal reactor design?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students treat the rate constant as fixed while temperature changes, get the sign of ΔH_R wrong (endothermic versus exothermic), and overlook the possibility of multiple steady states. Forgetting to include the coolant duty Q in the CSTR energy balance is common.

Quick revision checklist

Before attempting non isothermal reactor design problems, confirm you can:
1. Adiabatic operation: Q = 0, so temperature rises for an exothermic reaction
2. Multiple steady states are possible in an exothermic cooled CSTR
3. Ignition–extinction: intersection of heat-generation and heat-removal curves
Revise the solved examples in Chemical Reaction Engineering — Octave Levenspiel and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Adiabatic temperature rise

Problem

An exothermic reaction (−ΔH_R = 80 kJ/mol) reaches X = 0.5. Feed heat capacity per mole of A is ΣθC_p = 200 J/mol·K. Find the adiabatic ΔT.

Solution

ΔT = (−ΔH_R)X/ΣθC_p = (80000 × 0.5)/200 = 200 K. The large rise flags the need for cooling or staged feed.

Conceptual check — Non Isothermal Reactor Design

Problem

In a Reaction Engineering semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of non isothermal reactor design." What should a complete answer include?

Exams & GATE

Levenspiel Ch. 17–19 — plot rate vs T at fixed conversion.

📖 Standard books (India)

  • Chemical Reaction Engineering — Octave Levenspiel

    Read: Syllabus unit

    Reactor design and kinetics

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