MY SIMULATOR

Stirred-Tank Bioreactor

Oxygen transfer, Monod growth and fed-batch.

INTERACTIVE 3D

t 0.0 hX 0 g/LS 0 g/LDO 0 %kLa 0 /hFPS 0

GROWTH RATE0 /h

DISSOLVED O20 %

STIRRING POWER0 W/m3

TIME SPEED⏱2 h/s

Stirred-Tank Bioreactor Lab: Oxygen Transfer, Monod Growth & Fed-Batch

A 10-litre glass bioreactor with two impellers, an air sparger and a feed line. Choose the agitation, the air flow, the temperature and the feeding, and watch how fast oxygen can be supplied, how low the dissolved oxygen falls and how the culture grows.

Educational simulation of a generic, harmless production culture. Constants are illustrative model values. This is not a protocol: nothing here tells you how to run a real fermentation.

Scenario

Operation mode

Settings

Reactor report

Biomass and substrate

Dissolved oxygen and stirring

Oxygen supply and demand

Missions

Independent numerical checks

Also run outside the browser: node src/check.js (oxygen-transfer transient against the exponential, carbon balance with maintenance, chemostat steady state against the washout formula, quasi-steady dissolved oxygen, monotonic kLa and gassed power).

Model values and simplifications: perfectly mixed liquid, two pitched-blade impellers with a power number of 1.3 [check against a source], gassed power from a Michel-Miller type correlation [check against a source], kLa from the coalescing-medium van’t Riet correlation [check against a source], oxygen solubility from a fresh-water polynomial [check against a source], one carbon source, one oxygen-and-carbon dual-Monod organism with illustrative yields. No pH, foam, heat balance, CO₂ or gas-phase depletion. The rotation of the impellers and the speed of the bubbles in 3D are shown slowed down and bubbles and cells are drawn much bigger than real.

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Hero / Impeller / Sparger / Top buttons (keys 1-4) move the camera; Space pauses.
Sliders: stirrer speed, air flow (vvm = litres of air per litre of liquid per minute), temperature, share of oxygen in the gas, feed rate and feed concentration, starting biomass and sugar (these two restart the run).
The coloured column on the side shows the dissolved oxygen (red = starved, blue = well supplied). The DO controller button lets a PI controller raise the stirrer speed when the oxygen falls below 40 %.
The time-speed slider sets how many hours of culture pass in one second.

The science

Oxygen transfer. Oxygen enters the liquid from bubbles at the rate OTR = k_La (C* − C), where C* is the saturation concentration (about 7–9 mg/L for air-saturated water, lower when it is warmer) and k_La is the volumetric transfer coefficient. Without cells, C approaches C* as 1 − e^{−k_La t}.

What sets kLa. More stirring power per volume and more air both help: k_La = 0.026 (P_g/V)^0.4 v_s^0.5 (SI units, one empirical correlation). Stirring power without air is P₀ = N_p ρ N³ D&sup5;; bubbles reduce it to a gassed power P_g < P₀.

Growth (Monod). μ = μ_max(T) · S/(K_S + S) · C/(K_C + C): the cells slow down when sugar or oxygen is scarce. Biomass obeys dX/dt = μ X − D X, substrate dS/dt = −(μ/Y_XS + m) X + D (S_f − S) with dilution rate D = F/V.

Oxygen balance. dC/dt = k_La (C* − C) − OUR − D C with OUR = (μ/Y_XO + m_O) X. A dense culture can use more oxygen than the reactor can deliver, so C falls toward zero and growth becomes oxygen-limited, almost linear in time.

Modes. Batch: no feed. Fed-batch: a concentrated feed adds volume and substrate without removing cells. Chemostat: feed in equals harvest out, so at steady state μ = D, S* = K_S D/(μ_max − D); if D exceeds μ_max the culture is washed out.

Not modelled: pH, foam, heat of reaction, CO₂, bubble-size distribution and coalescence, mixing time and gradients, shear damage, by-products.