Drybench Bioreactor.
kLa calculator, Van 't Riet correlation
Calculate kLa from power per volume and superficial gas velocity, with the correlation's valid range stated, or enter your measured kLa.
kLa from Van 't Riet's correlation for a stirred vessel with Rushton turbines, with Hughmark's gassed power. Its range is stated beside the answer, and a value outside it is marked extrapolated, never hidden.
kLa
106 per hour
Gassed power per volume 1,890 W/m³; superficial gas velocity 0.00307 m/s; Pg/P0 0.5.
Inside Van 't Riet's and Hughmark's ranges. Unverified: Van 't Riet's range not yet checked against Van 't Riet 1979.
This empirical correlation does not supply a prediction interval for your vessel or broth. Yawalkar et al. 2002 report substantial deviations for some conditions. Enter a measured kLa in the app if you have one.
The coalescing coefficients are read from Yawalkar et al. 2002 (Table 2). The non-coalescing coefficients and the approximate domain are cited to Van 't Riet 1979 but not yet read against a clean copy of the paper, so they are marked Unverified. Np=5 is a nominal default for standard fully baffled Rushton geometry in the turbulent regime (approximately Re ≥20,000); this app does not compute Reynolds number or rheology. Summing impeller powers and extrapolating to a broth require calibration.
kLa = K · (Pg/V)^α · vs^β · 3600
= 0.026 · (1,890 W/m³)^0.4 · (0.00307 m/s)^0.5 · 3600 ≈ 106 per hour
The correlation at your vs, 0.00307 m/s
Dashed line: extrapolated, the correlation outside Van 't Riet's approximate range of Pg/V
Your inputs through the correlation, not a measurement
Tank diameter T, impeller diameter D and the liquid height H (your volume over the tank's cross-section) are drawn to scale with one another; the drawing's size is not, and the tank's height, the impeller's position and spacing, the sparger and the baffles (assumed by Np 5, not drawn) are schematic; their sizes and positions do not enter the calculation. Van 't Riet's correlation for coalescing broth as this calculator evaluates it, kLa = 0.026·(Pg/V)^0.4·vs^0.5 (SI, kLa per second; Yawalkar et al. 2002, Table 2). The curve is the correlation, not measurements; your vessel and broth may differ substantially. The dashed line is outside Van 't Riet's approximate range of Pg/V; the answer above lists every range your inputs are checked against.
Limits
- Teaching and estimation model, not a validated process model.
- The rescue cascade stays within the agitation, gas-flow and oxygen-enrichment limits you enter, and ignores cooling capacity, vessel pressure and gas-safety limits. Oxygen enrichment near flammable solvents or vapours is a fire and explosion hazard. Do not run a vessel from these outputs without your own engineering review.
A simulation, not a forecast. Every output follows from the model equations and the parameters you entered. It is a teaching and estimation model, not a validated process model, and not a prediction for any real strain, vessel or process.