Dynamic oxygen reoxygenation kLa fit calculator

What this calculation answers

During ideal reoxygenation, the driving difference between saturation and measured dissolved oxygen becomes smaller as oxygen rises. Plotting concentration directly against time does not produce the straight line used by the simple dynamic transfer model.

This page fits the logarithm of oxygen deficit against elapsed time. The negative fitted slope is the apparent volumetric mass-transfer coefficient kLa under constant-saturation, no-consumption assumptions.

The Integrated reaction order fit calculator compares integrated reaction orders. This reoxygenation fit assumes a known constant saturation and regresses the logarithmic oxygen deficit.

Use the right input conventions

Enter one fixed saturation concentration and at least three time/concentration readings. Each measured concentration must be strictly below saturation because the logarithm of a nonpositive deficit is undefined.

All concentrations must use the same unit, and all times one consistent elapsed-time unit. A slope derived from minutes gives kLa per minute; the calculator cannot infer hours or seconds from the numbers alone.

Interpret the result

The table compares observed and fitted log deficits. R squared is computed in that transformed coordinate, so it does not minimize squared concentration errors or establish uniform concentration measurement uncertainty.

The fitted intercept also gives an extrapolated initial oxygen concentration. It can be negative for imperfect data and is retained as a diagnostic model extrapolation rather than asserted to be a physically measured starting value.

Work through the example

With saturation eight and concentrations following eight minus eight times exp of minus 0.5t, readings at times zero, one and two form an exact straight line after transformation.

The recovered kLa is 0.5 per entered time unit, R squared is one and the extrapolated initial concentration is zero. These known values make the example an inspectable model check rather than a parameter guess.

Where the model stops

The model excludes oxygen uptake, probe lag, changing saturation and incomplete mixing. A positive fitted reoxygenation coefficient is required; a rising log deficit is incompatible with this stated scenario.

The fit does not recommend aeration or agitation settings and does not estimate confidence intervals. Use a model and measurement procedure appropriate to the actual vessel and oxygen-transfer experiment.