Ethanol Product Inhibition in Batch Fermentation

Batch Setup

Initial sugar (S₀) 200 g/L

Fermentation temperature 32 °C

Strain ethanol tolerance (P_max) 90 g/L

Inhibition sharpness (n) 1.0

Batch State

Biomass X Sugar S Ethanol P

Elapsed time

0.0 h

Growth rate μ

0.000 /h

Biomass X

1.0 g/L

Sugar S

200 g/L

Ethanol P

0.0 g/L

Yield vs. theoretical

0 %

How it works

Saccharomyces cerevisiae ferments glucose to ethanol and CO₂ anaerobically, but the ethanol it makes is itself a poison to the cell membrane. Growth rate follows Monod kinetics on sugar, multiplied by a Levenspiel product-inhibition term that shuts growth down as ethanol approaches the strain's tolerance limit:

μ(S,P) = μmax(T) · S/(Ks+S) · max(0, 1 − P/Pmax)ⁿ

dX/dt = μ·X − kd·X            (biomass)
dS/dt = −(μ/Yxs)·X − ms·X     (sugar consumed)
dP/dt = Yps · (−dS/dt)        (ethanol formed, Yps ≈ 0.46 g/g)

Theoretical max (Gay-Lussac): 0.511 g ethanol / g glucose

Initial sugar (S₀) — more feedstock means more potential ethanol, but only until P reaches P_max and growth stalls; excess sugar can be left unfermented.
Temperature — μmax(T) peaks near 32-33 °C for typical brewing/fuel-ethanol strains and falls off on both sides (a Gaussian response), so a batch run too cold or too hot ferments slower.
Strain ethanol tolerance (P_max) — industrial and engineered strains tolerate far more ethanol than wild yeast; raising it lets the batch reach a higher final titer before self-poisoning stops growth.
Inhibition sharpness (n) — how abruptly growth collapses as P approaches P_max: low n gives a gradual slowdown, high n gives a near-cliff cutoff.

Real-world relevance: this product-inhibition ceiling is exactly why fuel-ethanol plants distill continuously or use fed-batch feeding instead of one huge batch — driving sugar loading past what the strain's P_max can clear just leaves unconverted sugar and wastes feedstock.

Lag phase

Yeast cells CO₂ bubbles

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