kLa Simulator — Gassing-Out
How to use: pick a scenario or set the true kLa, saturation C*, oxygen demand (OUR) and probe response time, then press Run. Watch DO crash then recover, and see kLa back-calculated live from the curve. Background: how to calculate kLa.
Scenario preset
True kLa (h⁻¹)100
Saturation C* (mmol/L) ?0.21
Oxygen demand OUR (mmol/L/h) ?0
Probe response time τ (s) ?4
Starting DO (% sat)90
Playback speed
—
h⁻¹ — kLa back-calculated from the curve
Dynamic gassing-out determination
100
True kLa
—
Probe-lag error
—
Live OTR (mmol/L/h)
Gas-out phase (N₂ / aeration off) Gas-in phase (air on, recovery) Probe-measured DO (lagged)
—
Steady-state DO (supply = demand)
—
OTRmax = kLa · C*
Film theory — the O₂ driving force
C* (saturation) Gas / bubble Liquid film Bulk liquid (CL) OTR = kLa (C* − CL)
Oxygen crosses the stagnant liquid film by diffusion. The vertical gap between the dashed C* line and the falling profile is the driving force C* − CL. As the culture recovers, CL rises, the gap shrinks, and OTR falls — until it just meets demand.
OTR vs OUR — where oxygen supply meets demand
Dissolved O₂ (% saturation) Rate (mmol/L/h) OTR = kLa(C*−CL) OUR (demand)

The dynamic gassing-out method, made visual

This kLa simulator runs the classic dynamic gassing-out method on screen so you can see, rather than just read about, how the volumetric oxygen mass transfer coefficient (kLa) is determined. Dissolved oxygen is first driven down — by sparging nitrogen in a cell-free vessel, or simply by switching off aeration and letting cells consume it — and then air is switched back on. The dissolved-oxygen probe traces the recovery, and kLa is back-calculated live from the shape of that curve.

The recovery of a cell-free system follows CL(t) = C*(1 − e−kLa·t). Taking logs linearises it: a plot of ln(C* − CL) against time is a straight line of slope −kLa, which is exactly how the number is read off in practice. The simulator fits that slope on the revealed part of the curve so you watch the estimate converge as more data arrives. Crucially, it also reproduces the single biggest source of error in the method: dissolved-oxygen probe response time. A slow probe lags the true signal, the measured recovery looks gentler than it is, and the fitted kLa comes out too low. Increase the probe τ slider and watch the back-calculated value drift below the true value.

The oxygen transfer rate itself is OTR = kLa (C* − CL), the product of the coefficient and the driving force. The film-theory panel animates that driving force as the gap across the stagnant liquid film, and the OTR-vs-OUR panel shows where transfer capacity meets a culture's oxygen uptake rate. When demand (OUR = qO2 × X) exceeds the maximum transfer rate OTRmax = kLa · C*, the culture becomes oxygen-limited and dissolved oxygen collapses toward zero. To predict kLa from vessel geometry and agitation instead of measuring it, use the OTR & kLa estimator; to size the impeller power that drives kLa, see the Reynolds number calculator, and for moving a validated kLa between scales, the scale-up calculator.

Further reading

Related Tools & Articles

OTR & kLa Estimator
Predict kLa from vessel geometry, agitation and sparge with Van't Riet / Büchs correlations.
How to Calculate kLa
The methods, formulas and pitfalls behind oxygen mass transfer measurement.
Off-Gas Analyzer (OUR / CER / RQ)
Turn exhaust-gas readings into oxygen uptake, CO₂ evolution and respiratory quotient.
Scale-Up Calculator
Hold kLa, P/V or tip speed constant when moving between bioreactor scales.

Frequently Asked Questions

What is the dynamic gassing-out method for kLa?

The dynamic gassing-out method is the most common experimental way to determine the volumetric oxygen mass transfer coefficient (kLa). Dissolved oxygen is driven down — by sparging nitrogen in a cell-free vessel, or by switching off aeration and letting cells consume it — then air is switched back on and the DO recovery curve is recorded. For a cell-free system the recovery follows CL(t) = C*(1 − e−kLa·t), so kLa is obtained from that curve. It needs only a DO probe and the existing gas supply.

How do you calculate kLa from a gassing-out curve?

Linearise the recovery. Rearranging CL(t) = C* − (C* − CL0)e−kLa·t gives ln(C* − CL) = ln(C* − CL0) − kLa·t. Plotting ln(C* − CL) against time gives a straight line of slope −kLa. In practice you fit the middle 20–80% of the recovery by linear regression, which is exactly what this simulator does on the revealed curve.

Why does probe response time bias the measurement?

A DO probe responds like a first-order sensor with a time constant τ of a few to tens of seconds, so it lags the true dissolved oxygen. The measured recovery looks slower than reality and the fitted kLa comes out too low. The error is worst when τ is comparable to the mass-transfer time constant 1/kLa — i.e. in high-kLa vessels. Use a fast probe or deconvolve the probe dynamics. Raise the probe τ slider here to see the fitted value drop below the true value.

Static vs dynamic kLa method — what's the difference?

The static (sodium sulphite oxidation) method measures kLa chemically at steady state without cells. The dynamic gassing-out method measures it from the transient DO response to a step change in aeration and can run with or without cells. The dynamic method is faster and non-destructive but is sensitive to probe lag; the sulphite method avoids probe dynamics but uses a non-biological liquid whose bubble-coalescence behaviour differs from real broth.

How does OTR relate to kLa?

OTR = kLa (C* − CL). kLa sets the slope — more oxygen transfers per unit driving force (C* − CL). The maximum, at CL = 0, is OTRmax = kLa · C*. Raising agitation or sparge raises kLa; raising head pressure raises C*.

When is my culture oxygen-limited?

When OUR = qO2 × X exceeds OTRmax = kLa · C*. At steady state DO settles where supply equals demand: DOss = 100% × (1 − OUR / (kLa · C*)). If OUR > kLa · C*, that is negative and DO collapses toward zero. Fix it by raising kLa (agitation, sparge), raising C* (head pressure, O₂ enrichment), or lowering OUR.