Bioreactor Fermentation Simulator (Monod Kinetics)

Bioreactor

Initial substrate S₀ 20 g/L

Aeration (k_La) 150 h⁻¹

Feed rate (dilution D) 0.10 h⁻¹

Sim speed 8 h/s

Time

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Growth rate μ

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Biomass X

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Substrate S

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Product P

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Dissolved O₂

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How it works

The culture's specific growth rate follows the Monod equation, saturating toward μmax as substrate becomes plentiful and additionally throttled by how much oxygen is dissolved in the broth:

μ = μmax · S/(Ks+S) · DO/(Ko+DO)
dX/dt = μX − D·X
dS/dt = −μX/Yxs + D·(Sf−S)
dP/dt = (α·μ + β)·X − D·P
dDO/dt = k_La·(DOsat−DO) − qO2·X − D·DO

Biomass X, substrate S and product P are integrated forward every frame with a fixed-step RK4 solver — nothing here is a scripted animation. D (the feed dilution rate) is zero in batch mode; switching to fed-batch continuously bleeds fresh concentrated substrate (Sf) into the vessel while simultaneously diluting X, S and P, exactly as a real fed-batch fermenter mass balance requires.

Initial substrate S₀ — starting sugar/nutrient concentration; more substrate supports a longer exponential phase before it runs out (batch mode).
Aeration (k_La) — the oxygen mass-transfer coefficient. Too low and dissolved oxygen collapses under respiration demand, which throttles μ through the DO/(Ko+DO) term even while substrate is abundant — a real oxygen-limited fermentation.
Feed rate (D) — only active in fed-batch mode; higher D delivers substrate faster but also washes out biomass and product faster through dilution, so there is a real trade-off, not a free lunch.
Product P — follows Luedeking-Piret kinetics: partly growth-associated (α·dX/dt, e.g. a primary metabolite made only while cells divide) and partly non-growth-associated (β·X, made continuously by resting cells too).

Real-world relevance: this is the same coupled-ODE model (Monod + Luedeking-Piret + oxygen-transfer balance) process engineers use to design and control industrial fermenters for antibiotics, enzymes, biofuels and single-cell protein.

Biomass X Substrate S Product P Dissolved O₂