Bioreactor Fermentation Simulator

Stirred-Tank Bioreactor

Dilution rate D 0.15 h⁻¹

Feed substrate S₀ 20 g/L

Aeration kLa 150 h⁻¹

Temperature 37 °C

Growth rate μ–

⚠ Washout: D exceeds μmax·S₀/(Ks+S₀) — biomass is being diluted out faster than it can grow.

Biomass X

–

Product P

–

Dissolved O₂

–

Biomass X (g/L) Substrate S (g/L) Product P (g/L)

How it works

The tank is modelled as a well-mixed continuous stirred-tank reactor running unstructured Monod growth kinetics with double substrate/oxygen limitation, plus Luedeking-Piret product formation — the same equations used to design real fermenters for insulin, antibiotics, ethanol and enzymes:

μ = μmax(T) · S/(Ks+S) · DO/(Ko+DO)
dX/dt = (μ − D)·X
dS/dt = −μX/Yxs − msX + D(S₀−S)
dP/dt = αμX + βX − D·P
dDO/dt = kLa·(100−DO) − μX/Yxo
μmax(T) = μmax0 · exp(−(T−37)²/128)

Dilution rate D — feed/outflow rate per reactor volume in continuous (chemostat) mode. Above the critical dilution rate D꜀ = μmax·S₀/(Ks+S₀), cells wash out faster than they can divide and biomass collapses to zero even though feed keeps flowing — a real, load-bearing failure mode in industrial continuous culture.
Feed substrate S₀ — glucose concentration entering the vessel. Sets the steady-state biomass ceiling (X꜀ₛ ≈ Yxs·(S₀−S꜀ₛ)) but very high S₀ + high D pushes the system toward washout sooner in relative terms.
Aeration kLa — the volumetric oxygen transfer coefficient (how fast the sparger + impeller can resupply dissolved O₂). If oxygen uptake by growing cells (μX/Yxo) outpaces kLa's resupply, dissolved oxygen collapses and throttles μ through the DO/(Ko+DO) term — the classic "oxygen-limited fermentation" every scale-up engineer fights.
Temperature — μmax follows a Gaussian response peaking near 37 °C (mesophilic organism); too cold slows metabolism, too hot denatures enzymes — both cut growth rate.

Cell colour tracks instantaneous μ (yellow = slow/lag, green = fast exponential growth, grey = stalled or washing out); bubble rate tracks kLa; the liquid tint darkens toward amber as product P accumulates, the way a real fermentation broth changes colour as metabolites build up.

Cells — lag phase Cells — exponential growth Cells — stalled / washing out

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