When and why do gradients of the gas phase composition and pressure affect liquid-gas transfer?

Gas bubbles are introduced in water to absorb or strip volatile substances in a variety of unit operations, for example during (waste)water treatment. To calculate the transfer rate of substances between the liquid phase and the gas phase, different assumptions have been made in literature regarding the gas phase composition and hydraulic pressure, which both vary along the reactor height. In this study, analytical expressions were derived for the total (macroscopic) liquid-gas transfer rate, using either the complete gradients of the mole fraction and pressure (comprehensive approach) or a uniform value, for one or both of them. Simulations with the comprehensive model were performed to understand the effect of the type of volatile substance and of the reactor design and operating conditions on the total liquid-gas transfer rate. These effects were found to be highly interactive and often non-linear. Next, the simulation results of the comprehensive model were compared with those from models that assume either a uniform mole fraction or a uniform pressure in the complete reactor volume. This illustrated that for soluble substances, the mole fraction gradient strongly affects the total liquid-gas transfer rate, while the pressure gradient became only important under operating conditions that promote stripping (i.e., for a high concentration in the liquid phase and low concentration in the inlet gas). For very poorly soluble substances, the pressure became more important under conditions that promote absorption. These results on the importance of the mole fraction and pressure gradients remained equally valid when explicitly considering a typical variation of the volumetric overall transfer coefficient (K_La) along the reactor height. Finally, a simple and fast procedure was made available through a spreadsheet to select appropriate simplifying assumptions in reactor or plant-wide models. By applying the procedure to oxygen (O₂), carbon dioxide (CO₂), methane (CH₄), nitrous oxide (N₂O) and nitrogen gas (N₂) in an aerobic biological wastewater treatment reactor, it was demonstrated that some common simplifications can lead to significant errors, for which corrections were proposed.