Transport Phenomena in Bioprocess System PDF

Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering TRANSPORT PHENOMENA IN BIOPROCESS SYSTEM...

Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering TRANSPORT PHENOMENA IN BIOPROCESS SYSTEM (Written Report) Submitted by: Bugay, Crizha Ann B. De Mesa, John Nhilsan I. Montalban, Mark Anthony Salvador, Andrea R. Tinaja, Emanuel Jay L. Submitted to: Engr. Denvert C. Pangayao, PhD CHE 0412-1 Biochemical Engineering Page 1 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Table of Contents I. Introduction 3 II. Learning Objectives 3 III. Gas-Liquid Mass Transfer in Cellular Systems 3 IV. Determination of Oxygen Transfer Rates 18 V. Determination of KLa values 31 VI. Factors Affecting KLa values in bioreactor 44 a. Degree of Agitation 50 b. Medium Culture Rheology 51 VII. Effects of Foam and Anti-foam on Oxygen Transfer 56 VIII. References 68 CHE 0412-1 Biochemical Engineering Page 2 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering I. Introduction As the biological systems grow larger from molecular through cellular to fluid volumes containing million or billions of cells per milliliter, the movement of nutrients, gases, and other substances becomes more complex. Sources and sinks of entities such as nutrients, cells, and metabolic products become further separated in space and the probability increases that some physical-transport phenomena, rather than a chemical rate, will influence or even dominate the overall rate of solute processing in the reaction volume under consideration. II. Learning Objectives At the end of the discussion, students will be able to understand transport phenomena in bioprocess systems, specifically:  Understand the principles of gas-liquid mass transfer in cellular systems.  Identify methods and approaches for determining oxygen transfer rates in bioreactor systems.  Explain the importance of the volumetric mass transfer coefficient (KLa) and its role in characterizing oxygen transfer efficiency.  Identify the factors influencing oxygen transfer efficiency and their impact on cell culture performance.  Evaluate the effects of foam formation and the addition of anti-foam agents on oxygen transfer efficiency. III. Gas-Liquid Mass Transfer in Cellular Systems Transport Phenomena in Bioprocess Transport phenomena is the study of how different substances, such as fluids, heat, or particles, move during chemical or biochemical processes. It is governed by fundamental principles and laws of transport. Understanding this is key to designing and operating bioprocesses CHE 0412-1 Biochemical Engineering Page 3 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering or biochemical plants efficiently. The term "transport phenomena" in chemical engineering covers the areas of momentum transfer (fluid mechanics), mass, and energy or heat transfer processes.  Momentum transport – also referred to as fluid dynamics. It encompasses momentum in fluids such as blood circulation in the body and mixing in bioreactors  Mass transport – also known as mass transfer, pertains to the movement of various chemical species themselves. Examples include oxygen transport from bubbles to aerobic microorganisms.  Energy or heat transport – also known as heat transfer, involves the movement of different forms of energy within a system. This includes processes like reactor sterilization and temperature control in bioreactors. Mass Transfer in Bioprocess In biochemical processes, the rate at which reactions occur is often influenced by how substances are transferred between different phases, such as gases, liquids, and solids. This concept is called mass transfer which refers to the movement of matter from one point to another due to concentration gradient in the system. Mass transfer in bioprocesses is significant as the movement of substances whether in gas absorption, humidification, leaching, adsorption, or liquid-liquid extraction determines how fast reactions proceed. When designing a fermenter, ensuring adequate mixing is essential. The primary goals of mixing in fermentation are to disperse air bubbles, suspend microorganisms (or animal and plant tissues), and enhance heat and mass transfer within the medium. Very little mixing is needed during fermentation to simply mix the medium while microbes consume nutrients because the majority of nutrients are very soluble in water. Dissolved oxygen, on the other hand, is an exception since it is highly necessary for the growth of aerobic bacteria but is relatively insoluble in a fermentation medium. For instance, in a fermentation broth, oxygen absorption into the liquid often determines the rate of aerobic fermentation where microorganisms need oxygen to metabolize nutrients and grow. Oxygen transfer is crucial for microbial metabolism as CHE 0412-1 Biochemical Engineering Page 4 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering microorganisms consume it rapidly, requiring continuous replenishment. If the supply of oxygen is insufficient, the concentration in the broth can decrease, leading to cell damage or death. Therefore, oxygen transfer is a critical limiting factor in aerobic fermentation systems. To address this, engineers utilize aeration to maintain high oxygen levels in the broth. However, it's not only about introducing oxygen into the liquid but also necessary to ensure that enough oxygen reaches the cells. Mass transfer often occurs against concentration gradients, and it's important to differentiate between passive and active transport mechanisms.  Passive transport - also called downhill transport. It occurs naturally as substances move from areas of higher to lower concentration.  Active transport – also called uphill transport. It requires energy and is commonly observed across biological membranes. Oxygen Transport from a Gas Bubble to Inside a Cell Transferring a sparingly soluble gas, usually oxygen, from a source like a rising air bubble to a liquid phase like liquid hydrocarbons (used in hydrocarbon fermentation) containing cells involves overcoming a series of transport resistances. The magnitude of these resistances is affected by factors that determine the efficiency of gas transfer in the system. These factors include the hydrodynamics of the bubble or droplet, temperature, cellular activity and density, the composition of the solution, interfacial phenomena, and other variables. Transport Resistances 1. Diffusion from bulk gas to gas-liquid interface. 2. Movement through gas-liquid interface. 3. Diffusion of the solute through the relatively unmixed liquid region adjacent to the bubble into the well-mixed bulk liquid. CHE 0412-1 Biochemical Engineering Page 5 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 4. Transport of the solute through the bulk liquid to a second relatively unmixed liquid region surrounding the cells. 5. Transport through the second unmixed liquid region associated with the cells. 6. Diffusive transport into the cellular floc, mycelia, or soil particle. 7. Transport across cell envelope and to intracellular reaction sites. Figure 1 illustrates the resistances present in the transport process of gas into a cell. If organisms are in the form of individual cells rather than aggregates, the sixth (6th) resistance does not occur throughout the transfer. Microbial cells also tend to adsorb at the gas-liquid interface, causing the diffusion of solute oxygen to only pass through the unmixed liquid region and not in the bulk liquid. Hence, the oxygen concentration in the bulk liquid may not always represent the actual oxygen supply available to the cells. This behavior is also observed with sparingly soluble substrates like hydrocarbons, where cells cluster around droplets, affecting substrate diffusion. Figure 1. Schematic Diagram of Steps Involved in Transport of Oxygen from a Gas Bubble to Inside a Cell CHE 0412-1 Biochemical Engineering Page 6 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Gas-liquid Interaction The way gas and liquid interact in a bioreactor is influenced by fluid motions, whether caused naturally by rising or falling bubbles or by external forces like mechanical stirring. Their physical configurations when in contact can be classified as freely rising, falling particles, fluid, and mechanically agitated. Distinguishing these motion types is complicated because natural convection and forced mixing may contribute equally to gas-liquid contact. This indicates the importance of studying hydrodynamics and mass transfer, as these factors affect how oxygen and nutrients reach the cells. In laboratory settings, a shaker apparatus provides sufficient mixing for cultivating microorganisms in flasks or test tubes. The rotary or reciprocating motion of the shaker ensures gentle mixing and surface aeration. For larger-scale fermenters—whether bench, pilot, or production scale— mechanical agitation is commonly used, with or without aeration. A popular choice for this is the radial-flow Figure 2. Rushton Turbine impeller, specifically the flat-blade disk turbine, also known as the Rushton turbine. This impeller pushes the liquid outward from the turbine blades toward the vessel's walls, where the flow splits upward and downward, eventually circulating back to the impeller. In contrast, axial flow impellers such as propellers and pitched blade paddles create a downward flow toward the tank bottom, which then circulates upward along the sides. The Rushton turbine has an advantage in preventing gas short-circuiting along the drive shaft by directing the gas through its discharge jet. CHE 0412-1 Biochemical Engineering Page 7 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering (a) (b) Figure 4. Rushton 90° Mixing Figure 3. Flow Pattern from (a) Radial Impeller and (b) Axial Impeller Diffusion in Liquid and Gas Aerobic fermentation is an important application of mass transfer in bioprocessing systems. Understanding the mass transfer in biochemical engineering is important as a continuous oxygen supply is essential for cell growth and metabolic activity. The transfer of substrates from a gas bubble to a cell's organelle involves diffusion, which plays a central role in describing this process. Molecular diffusion refers to the movement of molecules within a mixture due to concentration differences, where molecules naturally move from areas of high concentration to low concentration. If the concentration gradient is maintained by continuously adding material to the high concentration area and removing it from the low concentration area, diffusion will continue. This principle is commonly used in mass transfer operations and reaction systems. CHE 0412-1 Biochemical Engineering Page 8 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Figure 5. Diffusion Fick's Law governs diffusion in mass transfer. It states that the mass flux of a component is directly proportional to the concentration gradient (dC/dz). For example, a mass transfer of component A occurs across the z-direction which can be written as 𝑑𝐶 𝐽 ∝ (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1) 𝑑𝑧 In order to remove the proportionality sign, a constant is multiplied on the right-hand side of equation 1, giving the actual Fick’s law equation as follows: 𝑑𝐶 𝐽 = −𝐷 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2) 𝑑𝑧 If component A is not in motion, the molar flux of component A can be expressed as 𝐶 𝐷𝐶 𝑁 = (𝑁 + 𝑁 ) − 𝐷 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 3) 𝐶 𝑑𝑧 where: 𝐷 = 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐴 𝑖𝑛𝑡𝑜 𝐵 𝑜𝑟 𝑏𝑖𝑛𝑎𝑟𝑦 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐴 𝐶 = 𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠 𝐴 𝑎𝑛𝑑 𝐵 𝑁 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐴 𝑜𝑟 𝑚𝑜𝑙𝑎𝑟 𝑓𝑙𝑢𝑥 𝑜𝑓 𝐴 𝑁 = 𝑚𝑜𝑙𝑎𝑟 𝑓𝑙𝑢𝑥 𝑜𝑓 𝐵 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑜 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 CHE 0412-1 Biochemical Engineering Page 9 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝑑𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑟 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑐𝑜𝑛𝑐𝑒𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝐴 𝑤𝑖𝑡ℎ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑧 𝑑𝑧 The first term on the right-hand side of equation 3 refers to the flux due to the bulk flow while the second term denotes the diffusion. For dilute solution of A, 𝑁 ≈𝐽 Diffusivity Diffusion correlations in liquids are less reliable than those in gases because the kinetic theory of liquids is less developed than that of gases. Among the various correlations available, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most commonly applied for dilute solutions of nonelectrolytes (equation 13). However, when the solvent is water, Skelland (1974) suggests using the correlation formulated by Othmer and Thakar in 1953 (equation 14). (𝜉𝑀 ). 1.173 × 10 𝑇 𝐷° =. (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 4) 𝜇𝑉 1.112 × 10 𝐷° = (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 5) 𝜇. 𝑉. The preceding two correlations are not dimensionally consistent; therefore, the equations are for use with the units of each term as SI unit as follows: 𝑚2 𝐷° = 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐴 𝑖𝑛 𝐵, 𝑖𝑛 𝑎 𝑣𝑒𝑟𝑦 𝑑𝑖𝑙𝑢𝑡𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛, 𝑠 𝑘𝑔 𝑀 = 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐵, 𝑘𝑚𝑜𝑙 𝑇 = 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, °𝐾 𝑘𝑔 𝜇 = 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦, 𝑠 𝑚 𝑚3 𝑉 = 𝑠𝑜𝑙𝑢𝑡𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝑎𝑡 𝑛𝑜𝑟𝑚𝑎𝑙 𝑏𝑜𝑖𝑙𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡, 𝑘𝑚𝑜𝑙 𝑚3 0.0256 𝑓𝑜𝑟 𝑜𝑥𝑦𝑔𝑒𝑛 [𝑆𝑒𝑒 𝑃𝑒𝑟𝑟𝑦 𝑎𝑛𝑑 𝐶ℎ𝑖𝑙𝑡𝑜𝑛 (𝑝. 3 − 233, 1973)𝑓𝑜𝑟 𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑣𝑒 𝑡𝑎𝑏𝑙𝑒] 𝑘𝑚𝑜𝑙 CHE 0412-1 Biochemical Engineering Page 10 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝜉 = 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑠𝑜𝑙𝑣𝑒𝑛𝑡 2.26 𝑓𝑜𝑟 𝑤𝑎𝑡𝑒𝑟, 1.9 𝑓𝑜𝑟 𝑚𝑒𝑡ℎ𝑎𝑛𝑜𝑙, 1.5 𝑓𝑜𝑟 𝑒𝑡ℎ𝑎𝑛𝑜𝑙, 1.0 𝑓𝑜𝑟 𝑢𝑛𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑠𝑜𝑙𝑣𝑒𝑛𝑡𝑠, 𝑠𝑢𝑐ℎ 𝑎𝑠 𝑏𝑒𝑛𝑧𝑒𝑛𝑒 𝑎𝑛𝑑 𝑒𝑡ℎ𝑦𝑙 𝑒𝑡ℎ𝑒𝑟. Sample Problem Estimate the diffusivity for oxygen in water at 25°C. Compare the predictions from the Wilke-Chang and Othmer-Thakar correlations with the experimental value of 2.5×10−9 m2/s (Perry and Chilton, p. 3-225, 1973). Convert the experimental value to that corresponding to a temperature of 40°C. Solution: Oxygen is designated as component A, and water, component B. The molecular volume of oxygen, 𝑉 , is 0.0256. The association factor for water 𝜉 is 2.26. The viscosity of water at 25°C is 8.904 × 10 𝑠 (CRC Handbook of Chemistry and Physics, p. F-38, 1983). In Eq. 4, (𝜉𝑀 ). 1.173 × 10 𝑇 𝐷° =. 𝜇𝑉 1.173 × 10 [2.26(18)]. 298 𝟗 𝒎𝟐 𝐷° = = 𝟐. 𝟐𝟓 × 𝟏𝟎 (8.904 × 10 ). (0.0256). 𝒔 In Eq. 5, 1.112 × 10 𝐷° = 𝜇. 𝑉. 1.112 × 10 𝟗 𝒎𝟐 𝐷° = = 𝟐. 𝟐𝟕 × 𝟏𝟎 (8.904 × 10 ). (0.0256). 𝒔 CHE 0412-1 Biochemical Engineering Page 11 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering If we define the error between these predictions and the experimental value as ( 𝐷° ) − ( 𝐷° ) % 𝑒𝑟𝑟𝑜𝑟 = × 100 ( 𝐷° ) The resulting errors are -9.6 % and -9.2% for equations 13 and 14, respectively. Since the estimated possible error for the experimental value is ±20 percent (Perry and Chilton, p. 3-225, 1973), the estimated values from both equations are satisfactory. ° Wilke-Chang correlation suggests that the quantity is constant for a given liquid system. Though this is an approximation, we may use it to estimate the diffusivity at 40°C. Since the viscosity of water at 40°C is 6.529×10−4 kg/m s from the handbook, 8.904 × 10 313 𝑚 𝐷° 𝑎𝑡 40°𝐶 = 2.5 × 10 = 3.58 × 10 6.529 × 10 298 𝑠. If we use the correlation formulated by Othmer and Thakar, 𝐷° 𝜇 is constant, 8.904 × 10 𝑚 𝐷° 𝑎𝑡 40°𝐶 = 2.5 × 10 = 3.52 × 10 6.529 × 10 𝑠 Mass-Transfer Coefficient For a gas–liquid diffusion, the mass flux of solute on the gas side may be written as 𝑞 𝑁 = ∝ (𝐶 − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 6) 𝐴 In order to remove the proportionality sign, a constant is introduced giving the equation 𝑞 𝑁 = = 𝑘 (𝐶 − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 7) 𝐴 CHE 0412-1 Biochemical Engineering Page 12 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering where: 𝑞 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑖𝑛 𝑔𝑎𝑠 𝑝ℎ𝑎𝑠𝑒 𝐴 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑢𝑙𝑘 𝑝ℎ𝑎𝑠𝑒 𝑔𝑎𝑠 𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 𝑘 = 𝑔𝑎𝑠 − 𝑠𝑖𝑑𝑒 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 Likewise, for a solute undergoing gas–liquid diffusion, the mass flux on the liquid side may be written as 𝑞 𝑁 = = 𝑘 (𝐶 − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 8) 𝐴 where: 𝑞 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑖𝑛 𝑙𝑖𝑞𝑢𝑖𝑑 𝑝ℎ𝑎𝑠𝑒 𝐴 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑏𝑢𝑙𝑘 𝑝ℎ𝑎𝑠𝑒 𝑙𝑖𝑞𝑢𝑖𝑑 𝐶 = 𝑐𝑜𝑛𝑐𝑒𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 𝑘 = 𝑙𝑖𝑞𝑢𝑖𝑑 − 𝑠𝑖𝑑𝑒 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 It is evident that 𝑁 = 𝑁. Substituting equation 7 and 8, we get 𝑘 (𝐶 − 𝐶 ) = 𝑘 (𝐶 − 𝐶 ) 𝑘 (𝐶 − 𝐶 ) = (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 9) 𝑘 (𝐶 − 𝐶 ) CHE 0412-1 Biochemical Engineering Page 13 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Figure 6. Concentration profile near a gas–liquid interface and an equilibrium curve From equation 9, the slope of the graph 𝐶 versus 𝐶 is. It is difficult to evaluate 𝐶 and 𝐶 ; therefore, one cannot easily determine the mass-transfer coefficients on either side. The equation looks as follows: 𝑁 = 𝑁 = 𝐾 (𝐶 − 𝐶 ∗ ) = 𝐾 (𝐶 ∗ − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 10) where 𝐶 ∗ and 𝐶 ∗ are the gas-side concentration and liquid phase concentration, respectively. Due to the identical mass-transfer rates, we can write 𝐾 (𝐶 ∗ − 𝐶 ) = 𝑘 (𝐶 − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 11) 1 (𝐶 ∗ − 𝐶 ) (𝐶 ∗ − 𝐶 ) + (𝐶 − 𝐶 ) 1 (𝐶 ∗ − 𝐶 ) = = = + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 12) 𝐾 𝑘 (𝐶 − 𝐶 ) 𝑘 (𝐶 − 𝐶 ) 𝑘 𝑘 (𝐶 − 𝐶 ) Since 𝑘 (𝐶 − 𝐶 ) = 𝑘 (𝐶 − 𝐶 ), the entire denominator of the second term can be modified, Hence, equation 10 can also be written as 1 1 (𝐶 ∗ − 𝐶 ) 1 1 = + = + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 13) 𝐾 𝑘 𝑘 (𝐶 − 𝐶 ) 𝑘 𝑘 𝑀 CHE 0412-1 Biochemical Engineering Page 14 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Equation 13, thus, relates 𝐾 , 𝑘 , 𝑎𝑛𝑑 𝑘. 𝑀 is the slope. In similar manner, one can prove 1 1 𝑚 = + (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 14) 𝐾 𝑘 𝑘 Here, 𝑚 can be obtained as a slope joining (𝐶 ∗ , 𝐶 ) and (𝐶 , 𝐶 ). where: 𝐾 = 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑖𝑛 𝑔𝑎𝑠 𝑝ℎ𝑎𝑠𝑒 𝑘 = 𝑔𝑎𝑠 𝑝ℎ𝑎𝑠𝑒 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑘 = 𝑙𝑖𝑞𝑢𝑖𝑑 𝑝ℎ𝑎𝑠𝑒 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑚 = 𝑠𝑙𝑜𝑝𝑒 𝑗𝑜𝑖𝑛𝑖𝑛𝑔 (𝐶 ∗ , 𝐶 ) 𝑎𝑛𝑑 (𝐶 , 𝐶 ) Mechanism of Mass Transfer There are numerous processes available to explain the interphase mass transfer and the most well-known ones are two-film theory, penetration theory, and surface renewal theory.  Two-film theory The two-film theory explains that mass transfer occurs due to molecular diffusion, with a fluid film or mass transfer boundary layer that forms wherever there is contact between two phases. In this theory, it is assumed that all of the resistance to mass transfer is concentrated in a thin film, or layer, adjacent to the phase boundary. Also, that transfer occurs within this film by steady-state molecular diffusion alone and that outside this film, in the bulk fluid, the level of mixing or turbulence is so high that all composition gradients are wiped out. The thickness of this hypothetical film is in the range 0.01-0.1mm for liquid phase transports and in the range of 0.1-1mm for gas-phase transport. It is a valuable model for understanding mass transfer between phases, where solute moves from the bulk of one phase to the phase boundary, and then from the interface into the bulk of the second phase. Mathematically, it states that the mass transfer coefficient (kL) is inversely proportional to the film thickness (δ) and directly proportional to the diffusivity (DAB). CHE 0412-1 Biochemical Engineering Page 15 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝐷 𝑘 = (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 15) δ (a) (b) Figure 7. Two-film Theory  Penetration theory The penetration theory, developed by Higbie in 1935, assumes that turbulent eddies move from the bulk of fluid to the interface, where they remain for a specific exposure time, denoted as t0. During this time, unsteady-state molecular diffusion allows the solute to penetrate the eddy while it is at the interface. Unlike the two-film theory, the penetration theory predicts that the mass transfer coefficient (kL) is directly proportional to the square root of molecular diffusivity (DAB) and inversely proportional to the exposure time (t0). 𝐷 𝑘 =2 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 16) 𝜋𝑡 CHE 0412-1 Biochemical Engineering Page 16 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering (b) (a) Figure 8. Penetration Theory  Surface renewal theory In 1951, Danckwerts modified Higbie’s penetration theory for the liquid phase mass transfer. The modified theory is widely known as the surface renewal theory. The surface renewal theory states that a portion of the mass-transfer surface is replaced with a new surface by the motion of eddies near the surface assuming that the liquid elements at the interface are being randomly swapped by fresh elements from bulk and each of the liquid elements at the surface have the same probability of being substituted by a fresh element. Similar to the penetration theory, the mass transfer coefficient is directly proportional to the square root of diffusivity. The mathematical expression of the surface renewal theory is as follows: 𝑘 = 𝑠𝐷 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 17) where: 𝑠 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑟𝑒𝑛𝑒𝑤𝑎𝑙 𝑟𝑎𝑡𝑒 CHE 0412-1 Biochemical Engineering Page 17 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Figure 9. Surface Renewal Theory All these theories require knowledge of one unknown parameter, the effective film thickness (δ), the exposure time (𝑡 ), or the fractional rate of surface renewal (𝑠). Little is known about these properties, so as theories, all three are incomplete. However, these theories help us to visualize the mechanism of mass transfer at the interface and also to know the exponential dependency of molecular diffusivity on the mass-transfer coefficient. IV. Determination of Oxygen Transfer Rates In aerobic culture, cells take in oxygen from the liquid. Therefore, the rate at which oxygen moves from gas to liquid is important, especially in dense cell cultures with a high demand for dissolved oxygen. The equation for the rate of oxygen transfer from gas to liquid is: 𝑁 = 𝑘 𝑎(𝐶 ∗ − 𝐶 ) (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 18) where: 𝑁 = rate of oxygen transfer per unit volume of fluid ⋅ 𝑘 = liquid-phase mass transfer coefficient 𝑎 = gas-liquid interfacial area per unit volume of fluid CHE 0412-1 Biochemical Engineering Page 18 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝐶 = oxygen concentration in the broth 𝐶 ∗ = oxygen concentration in the broth in equilibrium with the gas phase The 𝐶 ∗ is called the saturation concentration or solubility of oxygen in the broth. This is the maximum possible concentration of oxygen that the liquid can hold based on the current gas composition, temperature, and pressure. The difference between the maximum possible oxygen concentration and the actual oxygen concentration in the liquid(𝐶 ∗ − 𝐶 ) shows the concentration-difference driving force for mass transfer. Oxygen dissolves in aqueous solutions at less than 10 ppm at room temperature and pressure, which gets used up quickly in aerobic cultures. To keep oxygen levels steady, it has to be constantly replaced by sparging. Since actively respiring cells can use up all the oxygen in just a few seconds, oxygen needs to be transferred from the gas to the liquid 10 to 15 times per minute. However, because oxygen has low solubility, the concentration difference driving oxygen transfer remains small. Fermenter designs must consider these factors to ensure effective oxygen transfer. Factors Affecting Cellular Oxygen Demand The rate at which cells use oxygen in fermenters determines how fast oxygen needs to move from the gas to the liquid. Several factors affect the oxygen demand: (1) cell species, (2) culture growth phase, and (3) nature of the carbon source provided in the medium. In batch culture, the rate at which cells use oxygen changes over time. There are two main reasons for this: First, as the culture progresses, the concentration of cells increases, so the total rate of oxygen used depends on the cell count. Second, the specific oxygen uptake rate, which defines how much oxygen each cell consumes, also changes and is usually at its maximum during the early phases of cell growth. It is defined by the equation: 𝑄 =𝑞 𝑥 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 19) CHE 0412-1 Biochemical Engineering Page 19 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering where: 𝑄 = oxygen uptake rate per volume of broth ⋅ 𝑞 = specific oxygen uptake rate ⋅ 𝑥 = cell concentration Figure 10 below shows the typical profiles of 𝑄 , 𝑞 , and x during batch culture of microbial, plant, and animal cells, where ○ represents the oxygen uptake rate, represents the specific oxygen uptake rate, and represents the cell concentration. (a) Streptomyces aureofaciens (b) Catharanthus roseus CHE 0412-1 Biochemical Engineering Page 20 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering (c) Mouse-mouse hybridoma cells Figure 10. Variations in the oxygen uptake rate, the specific oxygen uptake rate, and the cell concentration x (K) during batch culture of microbial, plant, and animal cells The demand for oxygen 𝑞 in an organism mainly depends on its biochemical characteristics and nutritional environment. However, when the dissolved oxygen level in the medium drops below the critical oxygen concentration 𝐶 , the specific rate of oxygen uptake also becomes dependent on the oxygen concentration in the liquid 𝐶. If 𝐶 is above 𝐶 , 𝑞 remains constant and does not depend on 𝐶. If 𝐶 falls below 𝐶 , 𝑞 increases linearly with oxygen concentration. To prevent oxygen limitations and ensure cell metabolism, the dissolved oxygen concentration in the fermenter must always be above 𝐶 , which typically ranges from 5% to 10% of air saturation. Maintaining sufficient oxygen levels (𝐶 >𝐶 ) is more challenging for organisms with higher 𝐶 values compared to those with lower 𝐶 values. The dependence of the specific oxygen uptake rate versus the oxygen concentration in the broth is shown in the figure below: CHE 0412-1 Biochemical Engineering Page 21 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Figure 11. Relationship between the specific rate of oxygen consumption by cells and dissolved oxygen concentration The choice of substrate in fermentation also affects the oxygen demand. Glucose is consumed more quickly than other sugars, resulting in higher oxygen uptake rates. Oxygen needs for cell growth and product formation also depend on the substrate's reduction degree, with higher reduction requiring more oxygen. Therefore, specific oxygen uptake rates are generally higher for cultures using alcohol or alkanes compared to carbohydrates. Table 10.1 shows typical maximum 𝑞 and 𝑄 values for different organisms, with plant and animal cells typically requiring less oxygen than microbial cells. CHE 0412-1 Biochemical Engineering Page 22 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering At steady state in a fermenter, there can be no accumulation of oxygen; thus, the rate of oxygen transfer from bubbles must equal the rate of oxygen consumption by the cells. This relationship can be described by the equation below and can be obtained by making 𝑁 = 𝑄. 𝑘 𝑎(𝐶 ∗ − 𝐶 ) = 𝑞 𝑥 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 20) CHE 0412-1 Biochemical Engineering Page 23 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering where 𝑘 𝑎 characterizes the oxygen transfer capability of the fermenter. A small 𝑘 𝑎 indicates limited oxygen delivery to the cells. Changes in mass transfer conditions can be predicted using this equation; for instance, increasing 𝑘 𝑎 while keeping cell metabolism constant will raise the dissolved oxygen concentration 𝐶 , while an increase in oxygen consumption will lower 𝐶 , if 𝑘 𝑎 remains unchanged. Additionally, the maximum cell concentration supported by the fermenter's oxygen transfer system can be estimated using the formula: 𝑘 𝑎 ⋅ 𝐶∗ (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 21) 𝑥 = 𝑞 indicating that maximum oxygen transfer occurs when the dissolved oxygen concentration 𝐶 is zero. If the maximum cell concentration (𝑥 ) calculated using the oxygen transfer equation is lower than what is needed for the process, the oxygen transfer rate (𝑘 𝑎) must be improved. Note that 𝒙𝒎𝒂𝒙 is a theoretical maximum that can only be reached if all other cultures' conditions are favorable and with sufficient time and substrates. Comparing 𝑥 values from mass and heat transfer calculations helps evaluate their effectiveness in aerobic fermentation. If 𝑥 from mass transfer is low while heat transfer is high, mass transfer is likely the limiting factor for biomass growth. Conversely, if both values are greater than the desired concentration, heat and mass transfer are adequate. Although the equation above is useful, operating culture systems at zero dissolved oxygen is not advisable, as the specific oxygen uptake rate depends on oxygen concentration. With that, to maintain 𝑪𝑨𝑳 > 𝑪𝒄𝒓𝒊𝒕 in the fermenter, the minimum 𝑘 𝑎 is required. This can be determined by the equation: 𝑞 𝑥 (𝑘 𝑎) = (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 22) (𝐶 ∗ − 𝐶 ) CHE 0412-1 Biochemical Engineering Page 24 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Sample Problem (pg. 392 from Doran) A strain of Azotobacter vinelandii is cultured in a 15 𝑚 stirred fermenter for alginate production. Under current operating conditions, 𝑘 𝑎 is 0.17 𝑠. The solubility of oxygen in the broth is approximately 8 × 10. a) The specific rate of oxygen uptake is 12.5 ⋅. What is the maximum cell concentration supported by oxygen transfer in the fermenter? b) The bacteria suffer growth inhibition after copper sulphate is accidentally added to the fermentation broth just after the start of the culture. This causes a reduction in the oxygen uptake rate to 3 ⋅. What maximum cell concentration can now be supported by oxygen transfer in the fermenter? Given: 𝑘 𝑎 = 0.17 𝑠 𝑘𝑔 𝐶 ∗ = 8 × 10 𝑚 (a) 𝑞 = 12.5 ⋅ (b) 𝑞 = 3 ⋅ Required: 𝑥 =? Solution: (a) 𝑘 𝑎 ⋅ 𝐶∗ 𝑥 = 𝑞 𝑘𝑔 0.17 𝑠 8 × 10 𝑚 𝑥 = 𝑚𝑚𝑜𝑙 1ℎ 1𝑔𝑚𝑜𝑙 32𝑔 1𝑘𝑔 12.5 𝑔 ⋅ ℎ 3600𝑠 1000 𝑚𝑚𝑜𝑙 1 𝑔𝑚𝑜𝑙 1000𝑔 CHE 0412-1 Biochemical Engineering Page 25 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝑔 0.001 𝑚 𝑥 = 12240 𝑚 1𝐿 𝒈 𝒙𝒎𝒂𝒙 = 𝟏𝟐. 𝟐𝟒 𝑳 The maximum cell concentration supported by oxygen transfer in the fermenter is 12.24 (b) 𝑘 𝑎 ⋅ 𝐶∗ 𝑥 = 𝑞 𝑘𝑔 0.17 𝑠 8 × 10 𝑚 𝑥 = 𝑚𝑚𝑜𝑙 1ℎ 1𝑔𝑚𝑜𝑙 32𝑔 1𝑘𝑔 3 𝑔 ⋅ ℎ 3600𝑠 1000 𝑚𝑚𝑜𝑙 1 𝑔𝑚𝑜𝑙 1000𝑔 𝑔 0.001 𝑚 𝑥 = 51000 𝑚 1𝐿 𝐠 𝐱𝐦𝐚𝐱 = 𝟓𝟏 𝐋 The maximum cell concentration supported by oxygen transfer in the fermenter after addition of copper sulphate is 51. CHE 0412-1 Biochemical Engineering Page 26 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Measuring Dissolved Oxygen Concentration Dissolved oxygen concentration (𝐶 ) in fermenters is measured using a dissolved oxygen electrode, which comes in two common types: galvanic and polarographic electrodes. Both types have a membrane that is permeable to oxygen, separating the fermentation fluid from the electrode. Figure 12. Diffusion of oxygen from the bulk liquid to the cathode of an oxygen electrode. From the figure above, as oxygen diffuses through the membrane to the cathode, it reacts to generate a current between the anode and cathode, which is proportional to the oxygen partial pressure in the broth. These electrodes contain an electrolyte solution that must be replenished periodically, and steam-sterilizable probes can be inserted directly into fermentation vessels for continuous monitoring. Proper placement of the probe is necessary to avoid direct bubble contact, which can distort the readings. Regular calibration of the probes is important to address fouling from cells, electronic noise from air bubbles, and signal drift. The measurement of oxygen concentration in the probes is based on mass transfer processes, specifically the diffusion of oxygen across the membrane and electrolyte solution. This diffusion can introduce a time delay in the electrode's response to sudden changes in dissolved oxygen levels. However, this delay does not impact applications where dissolved oxygen levels change slowly during cell culture. In addition to standard electrodes, microprobes are available, which have smaller cathodes and lower oxygen consumption, resulting in quicker responses. It’s CHE 0412-1 Biochemical Engineering Page 27 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering important to note that both galvanic and polarographic electrodes measure the oxygen tension or partial pressure rather than the actual dissolved oxygen concentration. To convert this tension into concentration, the solubility of oxygen at the specific temperature and pressure must be known. Estimating Oxygen Solubility The concentration difference (𝐶 ∗ − 𝐶 ) drives oxygen mass transfer, making it necessary to accurately know the solubility (𝐶 ∗ ) to avoid errors in this difference. Table 10.2 provides important solubility values for oxygen in water at different temperatures and atmospheric pressures, but these values may not be directly applicable to bioprocessing systems due to variations in dissolved materials and gas composition during fermentation. CHE 0412-1 Biochemical Engineering Page 28 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering  Effect of Oxygen Partial Pressure Henry's law states that the solubility of oxygen is directly proportional to the mole fraction of oxygen in the gas phase and the total gas pressure. The equation 𝑝 = 𝑝 ⋅𝑦 = 𝐻𝐶 ∗ and Henry's constant values in Table 10.2 can be used to calculate the solubility of oxygen in water as a function of these variables.  Effect of Temperature The solubility of oxygen decreases as the temperature rises. The following formula has been used to correlate the values of solubility of oxygen from air in pure water between 0°C and 36°C as shown in Table 10.2: 𝐶 ∗ = 14.161 − 0.3943 𝑇 + 0.007714 𝑇 − 0.0000646 𝑇 where 𝐶 ∗ is oxygen solubility ( ), and T is temperature in °𝐶.  Effect of Solutes Tables 10.3 and 10.4 show how the solubility of oxygen in water can be affected by the presence of solutes like salts, acids, and sugars. These findings show that adding ions and sugars, which are typically needed in fermentation media, reduces the solubility of oxygen. An empirical correlation between the effects of cations, anions, and sugars and the proper values of oxygen solubility in water has been established by Quicker et al. and values for Hi and Kj are listed in Table 10.5. 𝐶∗ log = 0.5 𝐻 𝑧 𝐶 + 𝐾 𝐶 𝐶∗ where: 𝐶∗ = oxygen solubility at zero solute concentration 𝐶 ∗ = oxygen solubility in the presence of solutes 𝐻 = constant for ionic component i 𝑧 = charge (valence) of ionic component i CHE 0412-1 Biochemical Engineering Page 29 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 𝐶 = concentration of ionic component i in the liquid 𝐾 = constant for nonionic component j 𝐶 = concentration of nonionic component j in the liquid CHE 0412-1 Biochemical Engineering Page 30 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering V. Determination of KLa values Mass Transfer Correlations for Oxygen Transfer kLa is considered as the mass transfer coefficient. This coefficient is very dependent on the fluid properties and prevailing hydrodynamic conditions. The value of the mass transfer coefficient, kLa, in fermenters is influenced by fluid properties (like density and viscosity) and flow conditions. Studies have attempted to link kLa with factors such as liquid density, oxygen diffusivity, bubble size, and fluid velocity, using empirical equations based on past experimental data. These equations theoretically allow us to predict k La values under different conditions. However, in practical, biological systems, the accuracy of these equations is limited. One reason is that fermentation media contain various additives (like substrates, salts, cells, etc.) that complicate oxygen transfer by changing bubble surface chemistry. Most kLa correlations were developed using air in pure water, but additives in fermentation liquids significantly alter kLa, making it difficult to adjust for these variations. CHE 0412-1 Biochemical Engineering Page 31 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Another issue is that the available surface area for oxygen transfer is often reduced by substances that accumulate at the bubble surface in fermentation broths. This "blanketing" effect makes it hard to predict kLa accurately. Scaling up to industrial fermenters adds further complications. Unlike laboratory reactors with high turbulence throughout, industrial fermenters have limited turbulence, mostly around the impeller, with slower flow in other areas. This difference means lab-derived kLa equations usually overestimate oxygen transfer in large fermenters. Despite these limitations, there is agreement in the literature on the general form of kLa equations and how reactor conditions affect kLa. The most successful correlation for dimensional equation is in the form: (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 23) where kLa is the oxygen transfer coefficient, PT is the total power dissipated, VL is the liquid volume, uG is the superficial gas velocity. In fermenters, the term PT captures all the hydrodynamic effects of flow and turbulence on bubble dispersion and the mass transfer boundary layer. The total power used in the system combines power from stirring (in a gassed environment) and, if significant, the power from gas expansion. The formula used to relate PT and kLa is independent of the stirrer or sparger design, meaning that the power input determines kLa regardless of the stirrer type. Constants A, α, and β have different roles: α and β usually range between 0.2 and 1.0 and don't change much with broth properties, while A varies widely depending on liquid composition and the properties of the culture, like coalescence and cell content. Because α and β are generally less than 1, increasing kLa by raising air flow or power input becomes less effective and more costly as inputs grow. For non-Newtonian and viscous fluids, this modified equation can be applied: CHE 0412-1 Biochemical Engineering Page 32 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 24) Mass Transfer Correlations for Oxygen Transfer Due to the challenges in using equations to predict kLa in bioreactors, oxygen transfer coefficients are often measured experimentally. However, this approach has its own difficulties. For accurate results, the conditions during measurement should closely match those in the actual fermenter. Various methods for measuring kLa have been reviewed in research. Oxygen Balance Method The steady-state oxygen balance method is a reliable way to estimate kLa and can determine it from a single measurement. A key benefit is that it can be used while the fermenter is in normal operation. However, it relies heavily on precise measurements of the gas composition, flow rate, pressure, and temperature at both the inlet and outlet. If measurements are inaccurate, errors as high as ±100% can occur. This method involves measuring the oxygen levels in the gas entering and exiting the fermenter to establish a mass balance at steady state. (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 25) where NA is the volumetric flow rate of oxygen transfer, VL, is the liquid volume in fermenter, FG is the volumetric gas flow rate, CAG is the gas-phase concentration of oxygen with subscripts I and o representing inlet and outlet respectively. Incorporating the ideal gas law, the equation becomes: (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 26) CHE 0412-1 Biochemical Engineering Page 33 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering In estimating kLa using the steady-state oxygen balance method, R is the gas constant, ρAG is the oxygen partial pressure in the gas, and T is the temperature. Because the oxygen levels in the gas entering and exiting the fermenter are often quite similar, their difference is small, which can introduce errors. To reduce this error, ρAG is typically measured with a high-sensitivity method, like mass spectrometry, and the gas temperature and flow rate are measured carefully. Once the oxygen transfer rate (NA) is calculated, and the dissolved oxygen level in the broth CAL is measured, kLa can be determined. The kLa value will depend on factors like stirrer speed, air flow rate, and broth properties. The oxygen balance method for estimating kLa relies on a few key assumptions: 1. The liquid phase is well mixed, meaning a single value of dissolved oxygen CAL represents the entire broth. This assumption works well in smaller vessels with high stirring power but may not hold in large fermenters, especially with viscous broths. 2. The gas phase is well mixed, allowing the bubble gas composition to match that of the outlet gas stream. This is more achievable in small, highly agitated vessels with efficient gas recirculation, typical of lab-scale fermenters. In large vessels, however, bubbles have longer residence times, and gas mixing is less uniform. 3. Pressure is constant throughout the vessel, which is generally true in small vessels. But in large, tall fermenters, hydrostatic pressure can vary significantly from top to bottom, impacting oxygen transfer analysis. These assumptions are best met in lab-scale fermenters but become less reliable in large- scale fermenters. CHE 0412-1 Biochemical Engineering Page 34 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Sample Problem: A 20-liter stirred fermenter containing Bacillus thuringiensis is used to produce a microbial insecticide. The oxygen balance method is applied to determine kLa. The fermenter operating pressure is 150 kPa, and the culture temperature is 30°C. The oxygen tension in the broth is measured as 82% using a probe calibrated to 100% in situ using water and air at 30°C and 150 kPa. The solubility of oxygen in the culture fluid is the same as in water. Air is sparged into the vessel; the inlet gas flow rate measured outside the fermenter at 1 atm pressure and 22°C is 0.23 L s−1. The exit gas from the fermenter contains 20.1% oxygen and has a flow rate of 8.9 L min−1. a) Calculate the volumetric rate of oxygen uptake by the culture. b) What is the value of kLa? Solution: (a) 150 kPa = 1.48 atm 1 𝑁 = [(1.636 × 10 ) − (1.456 × 10 )]𝐿 𝑎𝑡𝑚 𝐾 𝑠 0.082057 𝐿 𝑎𝑡𝑚 𝐾 𝑔𝑚𝑜𝑙 (20 𝐿) 𝟓 𝑵𝑨 = 𝟏. 𝟏 × 𝟏𝟎 𝒈𝒎𝒐𝒍 𝑳 𝟏 𝒔 𝟏 (b) 𝑃 𝑌 (1.48 𝑎𝑡𝑚)0.201 𝐶∗ = 𝐶∗ = 8.05 × 10 𝑔𝐿 = 0.0114 𝑔𝐿 𝑃 𝑌 (1 𝑎𝑡𝑚)0.2099 1.48 𝑎𝑡𝑚 𝐶 = 0.82 8.05 × 10 𝑔𝐿 = 9.77 × 10 𝑔𝐿 1 𝑎𝑡𝑚 32 𝑔 1.1 × 10 𝑔𝑚𝑜𝑙 𝐿 𝑠 ∗ 1 𝑔𝑚𝑜𝑙 𝑘 𝑎= 0.0114 𝑔𝐿 − 9.77 × 10 𝑔𝐿 𝟏 𝒌𝑳 𝒂 = 𝟎. 𝟐𝟐 𝒔 CHE 0412-1 Biochemical Engineering Page 35 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering The oxygen balance method is less effective for cultures with low cell growth and oxygen uptake rates, such as plant and animal cell cultures or aerobic waste treatment. With slow oxygen uptake, the difference in oxygen levels between the inlet and outlet gases becomes very small, leading to high error rates. In such cases, alternative methods for measuring kLa are needed. Dynamic Method The dynamic method for estimating kLa involves measuring changes in dissolved oxygen using an oxygen electrode after altering aeration conditions in the fermenter. This approach uses unsteady-state mass balance equations to determine kLa and is more affordable than the steady- state method, as it requires less expensive equipment. Additionally, it doesn’t depend on knowing the oxygen solubility CAL and works well in small, lab-scale fermenters. While simple and easy to perform, the dynamic method can yield inaccurate results if certain factors aren’t carefully controlled. These include the response time of the oxygen electrode, the impact of liquid boundary layers near the probe, and gas dynamics within the vessel. Simple Dynamic Method The simple dynamic method for estimating kLa works well under certain assumptions: 1. Well-Mixed Liquid: The liquid must be well mixed so that the oxygen concentration measured at one point represents the entire vessel. This is easier with small, vigorously stirred fermenters but can be challenging with larger ones with viscous broths. 2. Fast Electrode Response: The dissolved oxygen electrode's response time should be much shorter than 1/ kLa. 3. High Stirrer Speed: The stirrer speed must be high enough to eliminate liquid boundary layers around the oxygen probe. 4. Negligible Gas Phase Effects: Gas-phase dynamics (like gas mixing and hold-up) should not significantly affect the measurement. CHE 0412-1 Biochemical Engineering Page 36 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering If any of these assumptions are violated, the method may yield inaccurate kLa values, and alternative methods should be considered. To measure kLa using this method:  The fermenter is stirred and sparged to maintain a constant dissolved oxygen concentration CAL.  At a specific time t0, the broth is deoxygenated by either sparging nitrogen or stopping the air flow, allowing the culture to consume available oxygen.  The air is then introduced back into the broth, and the increase in CAL is recorded over time using a dissolved oxygen probe.  It's crucial to keep the oxygen concentration above a critical level Ccrit to ensure that the rate of oxygen uptake by the cells remains constant.  The dissolved oxygen concentration will eventually stabilize, reflecting a balance between oxygen supply and consumption. Two oxygen concentrations CAL1 and CAL2 are measured at times t1 and t2, respectively, to develop an equation for kLa based on the experimental data. Figure 13. Variation of dissolved oxygen concentration CHE 0412-1 Biochemical Engineering Page 37 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering During the reoxygenation step, the system is unsteady. The rate of change in oxygen concentration can be represented as: Where qOx is the oxygen consumption rate. When CAL = CAL then dCA/dt = 0. Integrating the resulting expression would be: (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 27) Figure 14. kLa value based on dynamic method CHE 0412-1 Biochemical Engineering Page 38 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Electrode Response Time and Liquid Boundary Layers The dynamic method for measuring the mass transfer coefficient (kLa) estimates changes in dissolved oxygen levels after altering aeration conditions in a fermenter. However, challenges can arise if the oxygen electrode is slow to respond to increases in oxygen concentration during reoxygenation. If the electrode's response is slower than the actual increase in oxygen, the recorded levels will reflect the probe's characteristics rather than the real changes in the fermenter. Therefore, measuring the electrode response time is crucial in the dynamic method. Additionally, a liquid boundary layer can develop at the probe's surface, impacting the response time. The presence of this layer depends on flow conditions, liquid properties, and the rate of oxygen consumption; it may be negligible in low-viscosity fluids like water but can significantly affect measurements in viscous fermentation broths. Figure 15. Development of a liquid film at the surface of the oxygen probe CHE 0412-1 Biochemical Engineering Page 39 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering To assess the electrode response time (τE), tests should be performed under conditions similar to those used for kLa measurements. The probe is initially placed in a nitrogen-sparged vessel (0% oxygen) and quickly moved to the fermenter (constant dissolved oxygen concentration). The response is recorded over time, especially at different stirrer speeds. As the stirrer speed increases, the probe's response time decreases, indicating thinner boundary layers. At sufficiently high stirrer speeds, the response stabilizes, reflecting only the electrode's characteristics. The response is often modeled as first-order kinetics, with τE defined as the time taken to reach 63.2% of the total change in dissolved oxygen. Commercially available electrodes typically have response times ranging from 10 to 100 seconds, while faster electrodes can respond in 2 to 3 seconds. Figure 16. Typical electrode response curves after a step change in dissolved oxygen tension at different stirrer speeds In viscous broths, achieving the same testing conditions as in water may not be feasible, making it challenging to estimate response time accurately. For the dynamic method to be valid, τE must be significantly shorter than 1/ kLa. If the response time is longer, it could introduce errors in measuring kLa. The method only works effectively when liquid boundary layers are eliminated, which can be validated using high stirrer speeds. If either assumption regarding response time or boundary layers is not met, the dynamic method may not provide accurate measurements of kLa. CHE 0412-1 Biochemical Engineering Page 40 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Gas-phase Dynamics Gas-phase dynamics refer to the changes in gas dispersion properties over time, such as bubble size, number, and gas composition, which can significantly impact the measurement of the mass transfer coefficient (kLa). In the dynamic method for measuring kLa, alterations in aeration conditions can quickly change the inlet gas flow rate and composition. However, these changes do not immediately affect the gas hold-up and bubble composition in the liquid. It takes time for the gas phase to adjust to a new steady state, which can affect the oxygen transfer driving force, making the kLa values variable during measurement. Two common methods for deoxygenating culture broth prior to measuring kLa are nitrogen sparging and de-gassing. 1. Nitrogen Sparging: Nitrogen is introduced into the broth to lower the dissolved oxygen levels. After this, when air is switched back in, the gas composition in the bubbles gradually changes from nitrogen-rich to air. During this transition, the measured dissolved oxygen concentration (CAL) reflects this changing gas-phase composition. 2. De-gassing: This method involves stopping the air supply to let the cells consume the existing oxygen. The volume of gas hold-up decreases as bubbles escape. When aeration resumes, the gas hold-up must stabilize before kLa becomes consistent. Until this stabilization occurs, the CAL values will be influenced by the gas hold-up changes. Both deoxygenation strategies create transient gas-phase conditions that can affect the accuracy of kLa measurements, even in small fermenters. For instance, in systems with high stirrer power, gas-phase dynamics can have a more significant effect, as bubbles may recirculate and take longer to flush out. Comparisons of kLa values obtained from both methods can indicate whether gas dynamics are influencing the results. If the values are similar, it suggests that the gas-phase changes occur quickly enough relative to oxygen transfer rates, improving confidence in the measurement technique. CHE 0412-1 Biochemical Engineering Page 41 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Sample Problem: A stirred fermenter is used to culture hematopoietic cells isolated from umbilical cord blood. The liquid volume is 15 liters. The simple dynamic method is used to determine kLa. The air flow is shut off for a few minutes and the dissolved oxygen level drops; the air supply is then reconnected at a flow rate of 0.25 l s-1. The following results are obtained at a stirrer speed of 50 rpm. When steady state is established, the dissolved oxygen tension is 78% air saturation. In separate test experiments, the electrode response to a step change in oxygen tension did not vary with stirrer speed above 40 rpm. The probe response time under these conditions was 2.8 s. When the kLa measurement was repeated using nitrogen sparging to deoxygenate the culture, the results for oxygen tension as a function of time were similar to those listed. Estimate kLa. Solution: 78 − 50 ln (78 − 66) 𝑘 𝑎= = 0.056 𝑠 (20 − 5)𝑠 Modified Dynamic Method When the response of a dissolved oxygen electrode is slow, or if liquid boundary layers and gas-phase dynamics cannot be controlled, the simple dynamic method for measuring the mass transfer coefficient (kLa) is not suitable. Sterilizable electrodes often have long response times, and using fast, non-sterilizable electrodes in non-sterile conditions can be impractical. Additionally, eliminating liquid boundary layers can be challenging, especially in viscous fluids, and stirring speeds may need to be limited to avoid damaging sensitive cultures. If gas-phase dynamics are significant, they can greatly skew kLa measurements, sometimes by more than 100%. CHE 0412-1 Biochemical Engineering Page 42 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering To address these issues, several modified methods have been developed. These modifications incorporate mass transfer processes affecting electrode response and liquid film resistance into the models used to estimate kLa. One effective approach is to normalize the dissolved oxygen data based on observed effects from the electrode, liquid film, or gas mixing. Accounting for gas-phase dynamics is particularly complex, but it can be done by estimating gas concentrations over time and location within the model equations. A noteworthy variation is the dynamic pressure method, where a change in aeration conditions is achieved by adjusting the fermenter pressure instead of changing the gas composition. By temporarily closing the gas outlet and then constricting it during sparging, a pressure increases of about 20% can be applied. This method avoids issues with changing gas- phase compositions and gas hold-up that the simple dynamic method encounters. However, changes in bubble size after a pressure shift can complicate measurements, and the oxygen probe must be able to withstand pressure variations. Sulphite Oxidation This method measures kLa by oxidizing sodium sulfite to sulfate with a catalyst like Cu²⁺ or Co²⁺. While the sulfite method has been widely used, its results vary unpredictably with operating conditions and often yield higher kLa values compared to other techniques. Because salt solutions are involved, bubble size can be influenced by changes in coalescence properties, making the results less applicable to actual fermentation broths. As a result, the use of this method is generally discouraged. CHE 0412-1 Biochemical Engineering Page 43 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering VI. Factors Affecting KLa values in bioreactor Bioreactors are widely used to cultivate cells relevant to biotechnology and other bioprocesses. The volumetric mass transfer coefficient (kLa) is frequently used to compare the effectiveness of bioreactors and as an important scale-up factor. Cells are susceptible to changes in the culture's ambient conditions, such as aeration, agitation, nutrients, and pH. When the values of the liquid-phase solute diffusivity, DO2, are changed, the values of kL and a', as well as the parameters that determine the thickness of the mass-transfer resistance zone near bubble and droplet surfaces, such as resistance at the gas-liquid interface and continuous phase viscosity, c, are also affected. With shear, the liquid's "viscosity" might change. The parameters often rely on the system under consideration (i.e., on the bioreactor design). A particular set of parameters can only be used in a system that closely resembles the one from which they were initially created because the parameter values may drastically vary for different stirrers and tank geometries. The remaining factors affecting the kLa values are discussed in this section. A. Estimation of Diffusivities Compared to gas kinetic theory, liquid kinetic theory is substantially less developed. As a result, the association between liquid diffusivities and gases is less reliable. Among the known correlations for diluted solutions of nonelectrolytes, the Wilke-Chang correlation (Wilke and Chang, 1955) is the one that is most frequently used:. 1.173 × 10 (𝑥 𝑀) 𝑇 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 28) 𝐷° = 𝜇𝑉. When the solvent is water, the Othmer and Thakar correlation (1953) is recommended: 1.112 × 10 𝐷° = (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 29) 𝜇. 𝑉. CHE 0412-1 Biochemical Engineering Page 44 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering where: 𝐷 ° − diffusivity of A in B in a very dilute solution, m2/s 𝑀 – solute’s molecular weight, kg/kmol 𝑉𝑚 – molecular volume of solute at boiling point, m3/kmol 𝜇𝑙 – liquid viscosity, Pa-s 𝑇 – temperature, K The parameter 𝑥𝑎 represents the association factor for the solvent of interest; association factor for the solvent: 2.26 for water, 1.9 for methanol, 1.5 for ethanol, 1.0 for unassociated solvents, such as benzene and ethyl ether. The diffusion coefficient varies with ionic strength and solute concentration, which affects solution viscosity. A high solvent viscosity can result in a significant decrease in the mass transfer coefficient. As long as the solute-solvent interactions remain unchanged in the latter case, the relationship: 𝐷1𝜇𝑐1𝑇1 = 𝐷𝑟𝑒𝑓𝜇𝑐,𝑇𝑟𝑒𝑓 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 30) provides a useful scale for correcting changes in solution viscosity from a constant- temperature reference point, such as pure water. Sample Problem Estimate the diffusivity coefficient for ethanol in water at (a) 25°C using the Wilke-Chang correlation and the Othmer-Thakar correlation. Solution: (From CRC Handbook of Chemistry and Physics, p. F-38, 1983) A: Ethanol 𝜇𝑙 @ 25℃ = 1.1 × 10−3 𝑘𝑔/(𝑚 ∙ 𝑠) B: Water 𝑥𝑎 = 2.26 𝑉𝑚 = 0.0256 𝑚3 /𝑘𝑚𝑜𝑙 CHE 0412-1 Biochemical Engineering Page 45 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering (a) using Wilke-Chang correlation:. 1.173 × 10 (𝑥 𝑀) 𝑇 𝐷° = 𝜇𝑉. ° 1.173 × 10 (2.26 × 18). × 298 𝐷 = = 𝟏. 𝟖𝟐𝟕𝟓 × 𝟏𝟎 𝟗 𝒎𝟐 /𝒔 1.1 × 10 × 0.0256. (b) using Othmer-Thakar correlation: 1.112 × 10 𝐷° = 𝜇. 𝑉. 1.112 × 10 𝐷° = = 𝟏. 𝟖𝟎𝟏𝟓 × 𝟏𝟎 𝟗 𝒎𝟐 /𝒔 (1.1 × 10 ). × 0.0256. B. Ionic Strength Ionic strength can be referred to as the measurement of the total concentration of ions in the solution, weighted by ion charge. It is denoted by 𝜇. The greater the magnitude of the charge, the greater the magnitude of the concentration, and thus the greater the ionic strength. The concentration itself does not have an impact on the external mass transfer coefficient, but the overall kinetics is largely influenced by this factor. This influence becomes more pronounced at lower concentrations because the internal mass transfer process slows down. Generally, the efficiency and mass transfer coefficients decreased considerably at low surfactant concentrations but remained relatively constant at higher concentrations. The precise dissection of the effects of ionic strength into all relevant components appears to be a challenging task. Newtonian fluids are examined to determine the physical absorption outcome. / 𝑃 𝐹 𝜌. 𝐷 (𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 31) 𝐾 𝑎 = λ( ) ( ) ( / ) 𝑉 𝐴 𝜎. 𝜇 CHE 0412-1 Biochemical Engineering Page 46 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering where: 𝐾𝐿𝑎 – volumetric mass transfer coefficient, s-1 𝑉𝑙 – liquid volume, ft3 𝑃𝑎 – power during operation, (ft-lbf)/min 𝐹𝑔 – flow rate, ft3/s 𝐴 – reactor’s cross-section perpendicular to the flow rate, ft2 C. Surface-Active Agents Many biochemicals are amphipathic, meaning they contain hydrophilic and hydrophobic moieties that tend to concentrate on gas-liquid and liquid-liquid interfaces. Cells release substances like polypeptides throughout different fermentation phases, which can act like surfactants and occasionally cause containers with aerated air to foam. Chemical antifoam additions also have an impact on interfacial resistances to mass transfer, though usually in the opposite direction as surfactants do. In comparison to pure water, smaller bubbles were observed to be generated in the surfactant solutions due to a drop in the liquid's surface tension. Surfactants significantly increased mixing time and gas hold-up while decreasing oxygen mass transfer coefficient and liquid circulation velocity. Moreover, surfactants spontaneously adsorb at the phase interface, reducing the surface tension relative to its initial value and the interfacial free energy. The interfacial area per volume a' is expected to increase when the values of Dsauter and Dc decline. This tendency for the a' to increase is lessened by the impact of surfactant films on the mass transfer coefficient kL. A macromolecular film that has been absorbed creates a stagnant, rigid interface. The two mechanisms described below are likely to be responsible for the decrease in kL: CHE 0412-1 Biochemical Engineering Page 47 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering 1. The ease of liquid movement near the interface is reduced due to the decreased mobility of the interface; thus, the variety of mass-transfer theories based on estimating exchange rates of small fluid elements between the surface and the bulk will predict a decreased mass transfer coefficient. 2. Like the cell membrane itself, the molecular film is expected to contribute to a resistance of its own, which may cause a departure from the presumed gas-liquid equilibration in the plane of the interface. The addition of 10 parts per million (ppm) of sodium lauryl sulfate (SLS) resulted in a 56 percent decrease in kL, which is the rate of oxygen transfer, compared to pure water. At higher surfactant concentrations, a constant or plateau value of kL was consistently observed. The surface area per volume a' gradually increased across the entire range of SLS concentrations, ranging from 0 to 75 ppm, with the lowest kLa' value occurring at approximately 10 ppm of surfactant. In a turbine aerator, it has been noted that the product kLa' consistently rises with the addition of surfactant. When examining the data for the ratio of a' (with surfactant) to a' (without surfactant) and comparing it to the corresponding ratio for the product kLa', an interesting trend emerges. For instance, when 4.0 parts per million of sodium dodecyl sulfate was added, a' increased by a substantial 400 percent, whereas kLa' only experienced an increase of approximately 15 percent. This suggests a considerable reduction of about 71 percent in the value of kL. The decline seen in both datasets is consistent with findings from previous research. In the case of several poorly soluble gases, the typical stable kL values reached after adding surfactants coincide with reductions of around 60 percent in kL. This underscores the importance of using these correlations as useful approximations, but it is advisable to substitute them with experimental values obtained from more relevant equipment whenever feasible. CHE 0412-1 Biochemical Engineering Page 48 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering D. Effects of Electrolytes Most of the kLa data published are gathered through physical absorption or desorption using clean water. It is common knowledge that mechanical force-generated bubbles in electrolyte solutions are considerably smaller than those in pure water. This can be explained by a decrease in the rate of bubble coalescence caused by an electrostatic potential at the surface of aqueous electrolyte solutions. And using the same apparatus, gas rate, and stirrer speed, the sulfite oxidation process produces higher kLa values in aerated stirred tanks than physical absorption into pure water. In this regard, the values of kLa in culture media may be closer to those obtained by the sulfite oxidation method than to those produced by trials with pure water. This is because culture media typically contain some electrolytes. E. Presence of Cells The physical presence per se of microbial cells in the broth will affect the kLa values in bubbling-type fermenters. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in: (i) an unaerated stirred tank with a known free gas–liquid interfacial area. (ii) a bubble column; and (iii) an aerated stirred tank. Data acquired with scheme (i) showed that the kL values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and kLa values were decreased somewhat with increasing cell concentrations, due to increased bubble sizes. CHE 0412-1 Biochemical Engineering Page 49 of 68  Pamantasan ng Lungsod ng Maynila (University of the City of Manila) College of Engineering and Technology Department of Chemical Engineering Degree of Agitation Agitating the fermentation broth ensures uniform air distribution within the medium. When you blend a solution, you introduce energy into the system. Higher power input leads to smaller bubbles, thereby increasing the interfacial area. Consequently, the mass transfer coefficient is expected to be influenced by both the power input per unit volume of the fermentation broth and the gas's superficial velocity. The general correlation for this is as follows: 𝑃