kLa predicted via Van't Riet (1979) empirical correlation. Gassed P/V accounts for dynamic cavity formation and aeration number (Fl_G). Multi-impeller agitation incorporates an empirical n^0.5 enhancement factor.
Oxygen transfer from sparged gas bubbles to the liquid broth is the universal rate-limiting step in aerobic biomanufacturing. Because oxygen exhibits poor aqueous solubility ($C^* pprox 7 ext{–}8 ext{ mg/L}$ at 37°C), maintaining culture viability requires maximizing the volumetric mass transfer coefficient ($k_L a$, hr⁻¹).
The volumetric mass transfer coefficient is predicted using classical empirical correlations developed by Van 't Riet and modified for bioprocess broths:
Where $P_g/V$ is the gassed agitation power per unit volume ($ ext{W/m}^3$), $v_s$ is the superficial gas velocity ($ ext{m/s}$), and the coefficients $lpha, eta, \gamma$ reflect coalescing vs non-coalescing fluid electrolyte characteristics.
| Broth Chemistry / Vessel Type | Alpha (α) | Beta (β) | Gamma (γ) | Typical kLa (hr⁻¹) |
|---|---|---|---|---|
| Deionized Water (Coalescing) | 0.026 | 0.40 | 0.50 | 40 – 120 |
| Fermentation Broth (Non-coalescing) | 0.002 | 0.70 | 0.20 | 150 – 500 |
| Mammalian Microcarrier Broth | 0.0015 | 0.60 | 0.30 | 15 – 45 |
| Viscous Mycelial Fermentation | 0.0008 | 0.80 | 0.15 | 30 – 100 |
This calculator is maintained by the simulation engineers at BioFlo Bioprocess Engineering. We specialize in industrial bioreactor design, computational fluid dynamics (CFD) modeling, oxygen mass transfer optimization, and custom digital twin development for pharmaceutical fermentation plants.