Oxygen Transfer Process in Liquid Media

Oxygen Transfer Model Equation

• xQO2 represents the rate of oxygen consumption by microorganisms in the system.
• kLa represents the volumetric mass transfer coefficient, quantifying the efficiency of oxygen transfer between the gas phase and the liquid phase.
• dCL / dt = kLa(C-CL) – xQO2* accurately represents the change of dissolved oxygen concentration over time.
• (C - CL)* signifies the driving force for oxygen transfer, representing the difference between the oxygen saturation concentration (C*) and the actual dissolved oxygen concentration (CL).

Dynamic Gassing Out Method

• The slope of the line AB in the dynamic gassing out method typically represents the kLa value.

Factors Affecting Oxygen Transfer

• CO2 in bubbles decreases oxygen transfer rate.
• Oxygen concentration in the bubble is directly proportional to the oxygen transfer rate.
• Factors affecting the rate of oxygen diffusion include temperature, pressure, and the nature of the membrane.
• Contribution to oxygen transfer resistance can be neglected in the bulk liquid if there's a high level of agitation.
• Significant oxygen transfer resistance is evident when agitation is low or the liquid viscosity is high.
• Diffusion through the bubble boundary layer is characterized by a rapid decrease in concentration due to the large surface area of the bubble.
• Cell intraparticle resistance is influenced by the presence of cell walls and internal structures.
• Transfer through the bulk liquid contributes resistance to oxygen transfer due to factors like convection currents.
• Stalled impeller conditions lead to larger bubbles in a liquid-gas system.

kLa and Gas-Liquid Systems

• Factors impacting kLa in a gas-liquid system include agitation, sparger design, and liquid properties.
• The inlet flow rate ratio (QL/QG) is directly proportional to the gas holdup.
• Factors that impact oxygen transfer rate in a gas-liquid system include kLa, (C*-CL), and xQO2.
• Increased stirrer speed improves oxygen transfer rate by creating smaller bubbles and increasing gas holdup.
• Sparger characteristics like orifice size, shape, and material significantly influence kLa.
• The number of impellers on a stirrer shaft impacts kLa, with more impellers potentially increasing kLa due to better mixing.
• Flooded impellers in liquid-gas systems lead to decreased oxygen transfer due to reduced gas holdup and inefficient mixing.

Oxygen Transfer Theories

• Two-film theory suggests that mass transfer occurs through two stagnant films at the gas-liquid interface.
• Penetration theory states that mass transfer occurs by penetration of the gas into the liquid, creating a concentration gradient that drives diffusion.
• Mass transfer coefficient in penetration theory is directly proportional to the square root of the molecular diffusivity.
• Surface age distribution function in surface renewal theory represents the distribution of time that a surface element has been exposed to the bulk fluid.

Oxygen Transfer and Bioprocessing Engineering

• Oxygen transfer is vital in bioprocessing because it provides the oxygen needed for microbial growth and metabolism.
• Exposure time in penetration theory represents the duration a fresh surface element is exposed to the bulk liquid.
• Two-film and penetration theories are distinct in their descriptions of the mass transfer mechanism, but both focus on film resistance and concentration gradients.
• Molecular diffusion in mass transfer involves the movement of molecules from areas of higher concentration to lower concentration.
• Co in the equations represents the oxygen concentration.

Oxygen Uptake Rate (OUR)

• OUR is represented by the equation X = μ (C_o) X
• At steady-state, OTR = OUR.
• $u_{max}$ signifies the maximum specific growth rate of microorganisms.
• $dC_o/dt$ represents the rate of change in oxygen concentration over time.
• $Y_o$ represents the yield of biomass per unit of oxygen consumed.
• Monod constant $K_o$ represents the oxygen concentration at which the specific growth rate is half its maximum value.
• $dC_o/dt = k_L a (C_o^ - C_o) - X$* describes the balance between oxygen transfer rate and oxygen uptake rate.