The volumetric oxygen uptake rate (OUR, mmol O₂ L⁻¹ h⁻¹) is: $OUR = q_{O_2} \cdot x$, where $q_{O_2}$ is the specific oxygen consumption rate (mmol O₂ g⁻¹ biomass h⁻¹) and $x$ is biomass concentration. At steady state, OUR must equal the oxygen transfer rate (OTR): $OTR = k_La(C^* - C_L)$, where $k_La$ is the volumetric mass transfer coefficient and $C^*$ is the dissolved oxygen saturation concentration.