Reactor Sizing And Kinetics

Reactor Sizing and Kinetics

Overview

Isothermal liquid-phase reactor design equations from first principles:

• Arrhenius fit (A, Ea) from temperature / rate-constant data.
• CSTR / PFR / batch volume or time for nth-order kinetics (analytical).
• N equal-sized CSTRs in series for 1st-order kinetics.
• Numerical PFR for any user-defined rate law (Langmuir-Hinshelwood,

Michaelis-Menten, reversible reactions).

Prerequisites

1. uv available.
2. On first use, the script writes LICENSE_NOTIFICATION.txt.

When to Use

• Sizing a CSTR, PFR, or batch reactor for a known rate law.
• Fitting A and Ea from experimental data at multiple temperatures.
• Comparing CSTR-in-series vs single PFR for a target conversion.

Don't use for

• Non-isothermal design (no energy balance — would need a coupled T(z) or

T(t) solver).

• Heterogeneous catalysis with pore diffusion (Thiele modulus, effectiveness

factor not covered).

• Multiple parallel reactions where selectivity matters (extension needed).
• Polymerization moments / chain-length distribution work.
• Bioreactors with cell death / inhibition (use a specialised model).

Utility Scripts

• uv run scripts/reactor.py arrhenius --temperatures 298,308,318,328 --k-values 1.2e-3,2.4e-3,4.8e-3,9.5e-3 --output /tmp/arr.json
• uv run scripts/reactor.py cstr --C0 1000 --conversion 0.9 --flow 0.001 --k 5e-4 --order 1 --output /tmp/cstr.json
• uv run scripts/reactor.py pfr --C0 1000 --conversion 0.9 --flow 0.001 --k 5e-4 --order 2 --output /tmp/pfr.json
• uv run scripts/reactor.py batch --C0 1000 --conversion 0.9 --k 5e-4 --order 1 --output /tmp/batch.json
• uv run scripts/reactor.py series --C0 1000 --conversion 0.95 --flow 0.001 --k 5e-4 --N 3 --output /tmp/series.json

Procedure

1. Fit the rate constant if you have temperature data: arrhenius.
2. Pick reactor type from process needs:

• CSTR: tight T control, easy fouling cleanout, lower conversion per

volume for positive-order kinetics.

• PFR: higher conversion per volume for positive-order; flow regime

matters (turbulent assumed in the simple formulas).

• Batch: small / specialty / multi-product.

1. Compute volume or time at the design conversion.
2. Sensitivity: re-run with +10%/-10% in k to bracket uncertainty in

the rate constant.

1. Compare against any pilot data; the analytical formulas assume perfect

mixing (CSTR) or plug flow (PFR), neither of which is exact in industry.

Pitfalls

• Using a single-temperature k for a reactor that operates over a 20 K

range. Fit A, Ea and evaluate k(T) at the design temperature.

• Confusing reaction order with stoichiometry. The order in the rate law

is empirical; do not assume it equals the stoichiometric coefficient.

• Reporting reactor volume without stating whether it is liquid volume,

total vessel volume, or void volume in a packed bed.

• Using pfr_volume_nth_order for a system where back-mixing matters

(low Re, large vessel). Real reactors are between CSTR and PFR.

• Using cstr_volume_nth_order for very high conversions with positive

order kinetics — the volume blows up as conversion → 1.

• Forgetting that batch time excludes load / unload / cleaning time.
• Treating R^2 from the Arrhenius fit as a substitute for prediction

intervals; with three points an excellent R^2 is not the same as a defensible A.

• Forgetting that real CSTRs in series do not behave like a single PFR

even at large N because of finite mixing in each vessel.

Fallback Strategies

• For arbitrary rate laws (Langmuir-Hinshelwood, Michaelis-Menten,

reversible reactions), use the pfr-numeric --rate-fn subcommand which accepts a Python expression in C (e.g. 0.5*C/(1+0.1*C)).

• For non-isothermal design, surface to the user that this skill does not

cover it; they should set up a coupled ODE solver.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/design_equations.md — derivations.
• Fogler, Elements of Chemical Reaction Engineering.
• Levenspiel, Chemical Reaction Engineering.

Anti-Patterns

• Picking PFR over CSTR purely because PFR "is more efficient"; ignoring

fouling, cleaning, and control implications.

• Citing reactor volume without the rate constant used.
• Using textbook k without checking units consistency in the rate law.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.