Mass Transfer PDF

Mass transfer MIC 321-Basic Bioprocess Engineering Oxygen transfer rate Sukanya Phuengjayaem, PhD. Department of Microbiology, Faculty of Science, KMUTT  > To get the knowledge of mass tran...

Mass transfer MIC 321-Basic Bioprocess Engineering Oxygen transfer rate Sukanya Phuengjayaem, PhD. Department of Microbiology, Faculty of Science, KMUTT  > To get the knowledge of mass transfer > To understand the oxygen transfer process > To explain the oxygen transfer Objective model (kLa) > To apply knowledge for calculation in the fermentation process and scale up MIC 321-BASIC BIOPROCESS ENGINEERING 2  AGENDA PRINCIPLE OF MASS TRANSFER OXYGEN TRANSFER PROCESS OXYGEN Gas-liquid system o o Liquid-Liquid system TRANSFER MODEL AND OXYGEN UPTAKE RATE o Liquid-Solid system Calculation of k La Factors affecting Co*-Co o Gas-Solid system OXYGEN TRANSFER FACTORS AFFECT PROCESS THE OXYGEN There are a possible 8 steps TRANSFER RATE during DO transfer from a o Factors affecting the rising gas bubble into a volumetric oxygen transfer fluid containing cells. coefficient (k L) o Factors affecting the interfacial 3 MIC 321-BASIC BIOPROCESS ENGINEERING area (a) Principle of mass transfer Mass transfer of molecules from different concentration phases: 1. Gas-liquid system 2. Liquid-Liquid system 3. Liquid-Solid system 4. Gas-Solid system MIC 321-BASIC BIOPROCESS ENGINEERING  For example: Oxygen is typically supplied as gas and the oxygen in the Mass bubble must be transferred from the gaseous state to the liquid state before it is accessible to the cells. transfer What is important? Oxygen transfer to cell in fermenter https://www.cytivalifesciences.com/en/us/solutions/bioprocessing/knowledge- center/7-factors-that-affect-oxygen-transfer-to-cells-in-bioreactors  Mass transfer process Mass transfer is defined as “the movement of mass” What is important? For example: For the reaction to occur, the catalyst must meet the reactant by mixing -- > they are moving. The movement of molecules within a phase or between phases is referred to as mass transfer. Mass transfer is essential in “fermentation technology” MIC 321-Basic Bioprocess Engineering  How about Example of Mass transfer Water being flowed Dispersion of sulfur oxide Coffee maker machine through a pipe release from power plant Air moving by fan or air conditioning system Drying of material Transfer of vapor into dry air MIC 321-BASIC BIOPROCESS ENGINEERING 7  1. Mass transfer: Gas-liquid system Aeration is a common gas–liquid contacting operation where compressed air is introduced to the bottom of a tank of liquid water through small-orifice dispersers, such as perforated pipes, porous sparger tubes, or porous plates. These dispersers produce small bubbles of gas that rise through the liquid. Often, rotating impellers break up the bubble swarms and disperse the bubbles throughout the liquid volume. Gas–liquid mass-transfer processes induced by aeration include absorption and stripping. In gas absorption, a solute in the aeration gas is transferred from the gas to the liquid. Plate towers. (Welty L. et al, 2020) MIC 321-Basic Bioprocess Engineering  1. Mass transfer: Gas-liquid system Two–film model Schematic representation of concentration profiles Aerated stirred tank (Welty L. et al, 2020). in gas–liquid assuming two film models. (Kashid, M. MIC 321-Basic Bioprocess Engineering N., et al., 2011) 1. Mass transfer: Gas-liquid system GAS–LIQUID MASS TRANSFER IN STIRRED TANKS The figure shows a correlation for the nonaerated, non vortexing agitation of a Newtonian fluid, providing a reasonable approximation for estimating the nonaerated power input P. Power number vs. Reynolds number for impellers immersed in single- phase liquids (Welty L. et al, 2020). 1. Mass transfer: Gas-liquid system The power input per unit liquid volume (P/V) is a When complex function of impeller diameter (di), impeller rotation rate (N, revolutions per time), Po is Power number. impeller geometry, liquid viscosity, liquid density, and aeration rate. PG is the gage pressure. V is liquid volume (m3) The impeller Reynolds number is defined as ugs is the superficial velocity of the gas flowing through the empty vessel in units of m/s. Pg/V is the power consumption of the aerated and the Power number Po is defined as vessel per unit liquid volume in units of W/m3. N is the impeller rotation rate. di is a complex function of impeller diameter 2. Mass transfer: Liquid-Liquid system Film –penetration model Liquid–liquid systems are used in processes such as emulsion polymerization, phase transfer catalysis, homogenous catalyst screening, enzymatic reactions, extraction, precipitation, crystallization, and cell separation. Schematic representation of concentration profiles in liquid- liquid systems assuming a combined film-penetration model. 3. Mass transfer: Liquid-Solid system Liquid−solid mass-transfer coefficients can be obtained by two experimental methods. In the first method, the dissolution of soluble particles in a liquid is measured and the mass balance equation is used to derive the mass-transfer coefficient, which is equivalent to the external mass transfer. Figure Illustration of diffusion steps of the adsorbate for liquid–solid adsorption (Inglezakis, V. J., et al., 2020).  4. Mass transfer: Gas-Solid system Gas-Solid Systems: Reactions Involving One Gas The following derivation, based on Langmuir’s theory of unimolecular adsorption layer, is made on the assumption that (i) the solid surface has a fixed number of adsorption sites, (ii) the properties of all adsorption sites are the same, (iii) each site can hold only one adsorbed molecule, Silicon-glass microreactor with magnification of the (iv) the heat of adsorption is independent of the copper particle bed area (overall chip size: 23 mm × 23 mm, copper particle size: 53–63 μm) (Cao et al., 2021). adsorption sites. The Transport Diffusivities Mass diffusion occurs in liquids and solids, as well as in gases. Extremely small particles suspended in a fluid are subjected to Brownian motion which is random movement due to collisions with fluid molecules. Thus, such small particle may become impacted upon the filter fibers. Diffusion is more significant in the filtration of gases than in the filtration of liquids. The solution-diffusion model from different concentrations. Fick’s law of diffusion Mass transfer Fick’s law of diffusion Mass transfer Analogous of Fourier’s law of heat conduction Valid gas for gas mixtures, and liquid solutions and solid solutions Empirical law, based on experimental evidence Fick’s law of diffusion Theory of Transport Diffusion 1. Film Theory 2. Penetration theory 3. Surface renewal theory Mass transfer from one phase 1. The Surface renewal theory is 1. The penetration theory explains to another involves three the mutual exchange of steps: the mass transfer in the liquid an element from a penetrated 1. Solute is transported phase during gas absorption. interfacial region and a well- from bulk of one phase to mixed bulk region 2. It has been applied to turbulent interface. flow and many other investigators. 2. This transfer occurs at a rapid 2. Diffusion of solute occurs rate where the exchange zone across the interface. 3. When the diffusing component behaves like a thick film 3. Transport of solute to penetrates only a short distance bulk of second phase. 3. The surface is based on the into the phase of interest because function and application, and of its rapid disappearance through success of the Penetration Theory chemical reaction or relatively short contact time. Film Theory Two phase theory states: Lewis & Whitman Basic concept – the resistance to diffusion can be considered equivalent to that in stagnant film of a certain thickness Two stagnant film exist on both side of interface Mass transfer through these films occurs by Molecular diffusion No resistance to solute transfer exists A schematic showing the concept of mass transfer model based on the two-film theory (Chikukwa, A., et across the interface separating the phases al., 2012). Resistances in fluid are the only resistances. Penetration theory Penetration theory assumes that turbulent eddies travel from the bulk of the phase to the interface, where they remain for a constant exposure time (te). The solute is assumed to penetrate into a given eddy during its stay at the interface by unsteady-state molecular diffusion. This model predicts that the mass-transfer coefficient is directly proportional to the square root of molecular diffusivity. Schematic illustration of the penetration theory (Cussler, 1997). K = Gas transfer coefficient (m/s) L Surface renewal theory Surface renewal theory (Danckwerts, 1951) proposes that there is an infinite range of ages for elements of the surface and the surface age distribution function φ(t) can be expressed as When φ(t) = surface age distribution function σ surface tension (kg/s2) s = fractional rate of surface renewal, s-1 Schematic illustration of the surface renewal theory (Danckwerts, 1951) t = exposure time for the penetration theory, s Theory of Transport Diffusion Models for convective mass-transfer coefficients (dilute systems)  Oxygen transfer process MIC 321-BASIC BIOPROCESS ENGINEERING 22 Mass transfer: Oxygen transfer Most enzymes, antibiotics, biochemicals, Why do we need to learn diagnostics, and therapeutics are produced about Oxygen transfer? using aerated bioreactors. There are very few commercially essential products produced by the anaerobic Aerobic fermentation is the primary method fermentation process, for example, organic of product formation in bioprocess. acid bacteria.  Oxygen transfer Problem: Oxygen is poorly soluble in water. For example: Sucrose is soluble up to 600 g/L The solubility of oxygen at 4 ºC in pure water is only 8 mg/L NOTE: The solubility of oxygen decreases with increasing temperature and concentration of solutes in the solution.  Oxygen transfer rate is a key factor in bioprocess For Glutamic acid fermentation: 3 Glucose + 2O2 + NH3 --- > Glutamic acid + CO2 + 3 H2O Glucose Oxygen Amount of substrate needed for 180 g 48 g production of 1 mole of glutamic acid Solubility 450 g/L 7 mg/L MIC 321-BASIC BIOPROCESS ENGINEERING 25  The oxygen transfer process How can fermentation systems be designed to maximize dissolved oxygen concentration in bioreactors? The supplied oxygen is often the rate-limiting step in aerobic fermentation and satisfying oxygen demands, especially for the operating of an industrial-scale fermentation system. Oxygen transfer involves the moment of oxygen from the gas phase to the liquid phase. How oxygen moves from a bubble to microorganism cells. Oxygen transfer from gas bubble to cells Oxygen transfer occurs when there is non-uniformity in DO concentration in a fluid resulting in a concentration gradient. The concentration gradient causes transport of DO from a region of high concentration to a region of low concentration. Oxygen transfer process Step 1: Diffusion through the bubble to the gas-liquid interface Transport through the interior of the gas bubble. Diffusion through the bubble to the gas-liquid interface. In fact, gas molecules move so quickly Air bubble that they are evenly distributed throughout the bubble. The contribution to oxygen transfer resistance is negligible. Oxygen transfer process Step 2: Diffusion across the gas-liquid interface - Movement through a gas-liquid interface. - This step will be very rapid if the oxygen concentration in the bubble is high. - High oxygen concentrations in the bubble will push the oxygen molecules across the interface into the boundary layer.  Oxygen transfer process Step 2: - If the medium is rich in carbon dioxide, then CO2 CO2 CO2 will be pushed into the bubble. - If the bubble is rich in CO2 and contains a O2 O2 low concentration of oxygen, then the rate of oxygen transfer out of the bubble will be slow or zero. O2 rich bubble - Contribution to oxygen transfer resistance is negligible. Oxygen transfer process Step 3: Diffusion through the bubble boundary layer - Diffusion through the relatively stagnant liquid film surrounding the gas bubble to the bulk liquid - The movement of solutes through the boundary layer is slow because solutes must move through the liquid by diffusion. - Contribution to oxygen transfer resistance is significant resistance. Oxygen transfer process Step 4: Transfer through the bulk liquid. - Contribution to oxygen transfer resistance is negligible only in turbulent and less viscous media. - Many factors will affect the rate of diffusion of oxygen, including temperature, the concentration of oxygen in bulk liquid, saturation concentration of oxygen in a bubble, size of the molecule, viscosity of the medium. Oxygen transfer process Step 5: Transfer through the relatively stagnant liquid film surrounding the cells. - Contribution to oxygen transfer resistance is negligible only if the cells are much smaller than the oxygen bubbles. Step 6: Movement through a liquid-cell interface. - Contribution to oxygen transfer resistance is negligible. 6  Oxygen transfer process Step: 7 Diffusion through cell intraparticle resistance. - If individual cells are dispersed in the fluid rather than in clumps (as is the case here), the resistance due to diffusion through the cell clump becomes negligible (Doran, 1995). - Contribution to oxygen transfer resistance is the magnitude of resistance related to the cell clump size. Step 8: Movement across the cell membrane - Contribution to oxygen transfer resistance is negligible due to the small distances involved  Oxygen transfer model MIC 321-BASIC BIOPROCESS ENGINEERING 35 Modelling the volumetric oxygen transfer coefficient kLa For modelling the kLa coefficient it was set the oxygen balance for an aerobic batch bioreactor, as shown in equation below: 𝑑𝐶 ( 𝑑𝑡 ) = OTR - OUR 𝑑𝐶 where is the oxygen accumulation rate in the liquid phase. 𝑑𝑡 OTR is the oxygen transfer rate from gas to liquid. OUR is the oxygen uptake rate. It was employed the dynamic method for estimating the kLa on the above equation, and using the recommendations given by Doran (2013) it was obtained the expression shown in following: 𝑑𝐶 ( 𝑑𝑡𝐿)= kLa(CL*-CL) - NA  The oxygen transfer model When bulk mixing levels are high and 𝑑𝐶𝐿 suspended cell cultures are involved, the = 𝑘𝐿 𝑎 𝐶𝐿∗ − 𝐶𝐿 − 𝑁𝐴 𝑑𝑡 rate-limiting step will be the diffusion of oxygen though the bubble boundary layer where (Step 3) CL = the oxygen concentration in the liquid (ppm) Thus, it is possible to use the interphase CL* = the saturation concentration of the oxygen transfer equation to describe the oxygen (ppm) oxygen transfer rate (OTR): NA = the oxygen desorption rate for cellular demand (ppm/s) MIC 321-BASIC BIOPROCESS ENGINEERING t = the time (s) COURSE TITLE 37  The oxygen transfer model Oxygen concentration at the gas-liquid interface (C 0 *) Oxygen concentration in solution at saturation (C L*) There is no probe small enough to directly measure the average dissolved oxygen concentration at the gas-liquid interface (C0*). The value of C0* can be approximated by “indirect methods” During the aeration of an uninoculated fermenter, the dissolved oxygen concentration will eventually reach a steady value equivalent to the maximum solubility of oxygen in the liquid (CL*). MIC 321-BASIC BIOPROCESS ENGINEERING COURSE TITLE 38  The oxygen transfer model At steady state The value is also approximately equal to CL*, as can be seen as follow: Since 𝑑𝐶𝐿 = 𝑘𝐿 𝑎 (𝐶𝐿∗ − 𝐶𝐿 ) 𝑑𝑡 At steady state 𝑑𝐶𝐿 =0 𝑑𝑡 Therefore 𝐶𝐿∗ − 𝐶𝐿 COURSE TITLE 39  The oxygen transfer model Dissolved oxygen concentration ,C L (mg/L) C L = C L* In a sparged, uninoculated reactor, the dissolved oxygen concentration will eventually equal the saturation concentration. Time (min) MIC 321-BASIC BIOPROCESS ENGINEERING COURSE TITLE 40  The oxygen transfer model The maximum solubility of oxygen in a fluid can also be estimated using “Henry’s equation” - CL* is the maximum solubility of oxygen 𝑃0 in the liquid. 𝐶𝐿∗ = 𝐻0 - P0 is the partial pressure of oxygen in the gas phase. - H0 is Henry’s constant. MIC 321-BASIC BIOPROCESS ENGINEERING COURSE TITLE 41  The oxygen transfer model The volumetric oxygen transfer coefficient (k L) and The gas-liquid interfacial area per unit volume (a) Since it is not possible to accurately measure the total interfacial area of the gas bubbles (a), kL and (a) are combined into single team, referred to kLa The kLa represents the oxygen transfer rate per unit volume. There are several methods of measuring kLa. 1. Sulfite oxidation 2. Static method 3. Dynamic method MIC 321-BASIC BIOPROCESS ENGINEERING COURSE TITLE 42  THE OXYGEN TRANSFER MODEL 1. Sulfite oxidation technique The oxygen-transfer rates is determined by the oxidation of sodium sulfite solution. This technique does not require the measurement of dissolved oxygen concentrations. Based on the rate of conversion of a 0.5 M solution of sodium sulfite to sodium sulfate in the presence of a copper or cobalt catalyst: Na2S03 + 0.502 --- > Na2S04 MIC 321-BASIC BIOPROCESS ENGINEERING 43  THE OXYGEN TRANSFER MODEL Sulfite oxidation technique As oxygen enters solution it is immediately consumed in the oxidation of sulfite, so that the sulfite oxidation rate is equivalent to the oxygen-transfer rate. Since the dissolved oxygen concentration, is zero then the kLa may then be calculated from the equation: dCL/dt = OTR= kLa.C* kLa = OTR/C* where OTR is the oxygen transfer rate The volumes of the thiosulphate titrations are plotted against sample time and the oxygen transfer rate may be calculated from the slope of the graph. MIC 321-BASIC BIOPROCESS ENGINEERING 44  THE OXYGEN TRANSFER MODEL 2. Static method (Oxygen-balance method) The oxygen concentration of the solution is calculated by balance the oxygen in a gas-liquid contactor which the different oxygen flow rate between entrances of the inlet and outlet must be equal to the rate of transfer of oxygen to the liquid. Then using the equation as NA = kLa (CL* – CL) Where NA is the total amount of gas (oxygen) absorbed by the system per unit of time and per volume. 𝜐𝐺 𝐶𝐴𝐺 𝑖𝑛 − 𝜐𝐺 𝐶𝐴𝐺 𝑜𝑢𝑡 NA = 𝑉 Where CAV is oxygen concentration in aqueous phase. V is liquid volume. 𝜐𝐺 is volumetric gas flow rate. 45  THE OXYGEN TRANSFER MODEL 3. Dynamic Method OTR = dCL / dt = kLa(C*-CL) – xQO2 Where, x is the concentration of biomass. QO is the specific respiration rate (mmoles of oxygen g-l biomass h- I). The term xQO is given by the slope of the line AB in Figure Dynamic gassing out for the determination of kLa values. Aeration was terminated at point A and recommenced at point B. MIC 321-BASIC BIOPROCESS ENGINEERING 46  THE OXYGEN TRANSFER MODEL 3. Dynamic Method 𝑑𝐶𝐿 = 𝑘𝐿 𝑎 (𝐶𝐿∗ − 𝐶𝐿 ) 𝑑𝑡 𝐶𝐿∗ − 𝐶0 ln ∗ (𝐶𝐿 −𝐶𝐿 ) or integral, given that the kLa value is time-independent (𝐶∗𝐿 −𝐶0 ) ln ∗ kLa 𝐶𝐿 −𝐶𝐿 𝑘𝐿 𝑎 = 𝑡2 −𝑡1 (C∗L −C0 ) ln ∗ = k L a (t 2 − t1 ) CL −CL 𝑡2 − 𝑡1 y = mx + c MIC 321-BASIC BIOPROCESS ENGINEERING 47  THE OXYGEN TRANSFER MODEL 3. Dynamic Method 0.03 0.025 E ffec t of d i fferent a g it at ion r a t e a n d 0.02 La (s ) -1 a e r atio n r a t e o n k L a kLak(s-1) 0.015 0.01 0.005 0 300 450 600 Ni (rpm) 0.5 vvm 1 vvm 1.5 vvm MIC 321-BASIC BIOPROCESS ENGINEERING 48  THE OXYGEN TRANSFER MODEL A DVA N TAGES DI S A DVA NTAGES The dynamic gassing-out method has the A major limitation in the operation of the technique advantage over the previous methods of is the range over which the increase in dissolved determining the k La during an actual oxygen concentration may be measured. fermentation and may be used to determine It may be difficult to apply the technique during a k La values at different stages in the process. fermentation which has an oxygen demand close to The technique is also rapid and only requires the supply capacity of the fermenter. the use of a dissolved-oxygen probe, of the Both the dynamic and static methods are also membrane type. unsuitable for measuring k La values in viscous systems. MIC 321-BASIC BIOPROCESS ENGINEERING 49 Factors affect the Oxygen Transfer Rate MIC 321-BASIC BIOPROCESS ENGINEERING 50  Effecting factors of oxygen transfer rate Factors affecting k L - The size of the boundary layer is determined by - The volumetric oxygen transfer coefficient (kL) the level of mixing. represents the rate at which oxygen molecules - The diffusivity of the molecule through the move through the boundary layer to the liquid. boundary layer is determined by - Medium viscosity - The value of kL can be increased by reducing - Temperature the size of the boundary layer increases the rate - Increasing temperature also reduces the medium at which molecules travel through the boundary viscosity, but it will also decrease the solubility of layer. oxygen. M I C 3 2 1 - B A S I C B I O P R O C E S S E N G I NCE O ERU IRNSGE T I T L E 51 MIC 321-BASIC BIOPROCESS ENGINEERING 51 Factors affecting the interfacial area (a) Effecting factors of oxygen transfer rate 11 Factors 1. Size of bubble 2. Gas Hold-up 3. Impeller design and stirrer speed 4. Sparger characteristics 5. Properties of the liquid or medium 6. Temperature 7. Pressure 8. Cell phenomenal 9. Antifoaming agents 10. Air flow rate 11. Power input to agitator MIC 321-BASIC BIOPROCESS ENGINEERING 52 Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 1. Size of bubble When gas bubble size decreases, surface area and gas residency time increases, causing bubbles to stay in the culture longer. Thus, there is a greater opportunity for oxygen to release mass transfer into the cell culture medium. An increase in this oxygen residence time improves kLa. Effecting factors of oxygen transfer rate Factors affecting 4 V = 3 𝜋𝑅3 3 4 = n x V = 𝜋𝑟 3 the interfacial area (a) 4 3 V= 4 3 𝜋(1.5) = 14.14 mm3 V = 27 x 𝜋(0.5) = 27x0.52 3 1. Size of bubble 3 = 14.14 mm3 Bubble size plays a major role in determining the total interfacial area. The smaller the bubble size -- > the larger the interfacial area. Smaller bubble sizes can be achieved using appropriate design, operated gas sparging systems, agitation systems. A= 4𝜋𝑅2 A = 27x4𝜋𝑟 2 = 28.26 mm2 = 84.82 m2 Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 2. Gas hold-up The gas holdup is an important variable for the εG = 0.125 (QL/QG)-1.04 estimation of the pressure drop and the specific interfacial area. It is calculated from the number of bubbles and kLa = 0.101Pw0.443εG 0.459 bubble size, assuming that the number of bubbles seen from above is exactly the number actually existing in the entire channel height. At constant QL gas holdup Where εG = gas hold-up increases with increasing QG. kLa is overall mass transfer coefficient (1/s) It is observed that gas holdup depends significantly on the inlet flow rate ratio QL/QG and it can be correlated Pw is power consumption (W/m3) according to Equation: QG is volumetric gas flow rate (ml/min) QL is volumetric liquid flow rate (ml/min) Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 2. Gas hold-up Variation in gas hold-up with flow rate ratio in vertical orientation for different water flow rates (ml/min): Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 3. Impeller design and stirrer speed Impeller design for the maximization of oxygen transfer rates typically produces high shear conditions. The high shear conditions are used to reduce the bubble size. Factors such as operating cost, the capital cost of the agitation system, and the sensitivity of the cells to shear will determine the impeller diameter and Type of impeller and mixing profile. (Buffo, M. M., 2016) diameter and stirrer speed used in practice. Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 3. Impeller design and stirrer speed Flooded impeller If the agitation speed is too low or the air flow is too high, then a phenomenon known as a flooded impeller will be occurred. This leads to the formation of large bubbles and poor oxygen transfer efficiencies. Flooded impeller Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 3. Impeller design and stirrer speed Increasing stirrer speed improves kLa. However, very low sparging rates, increasing the gas flow is generally considered to exert only a minor influence on kLa. Increasing number of impeller on stirrer shaft does not improve kLa. The quantity of gas passing through the upper Gas-liquid flow regimes in agitated vessels (Lins Barros, P., et al., 2022). impellers is small compared with the lower one. Effecting factors of oxygen transfer rate 4. Sparger characteristics kLa values will vary widely with sparger characteristics, including number, pore size, and surface area, because these factors affect bubble size, gas velocity, and flow rates. The sparger design also plays an important role determining bubble size. In air-lift and bubble column reactors, the sparger hole size is the sole determinant of the size of the stirrer. To maximize the efficiency of bubble breakup, the sparger is normally designed as the holes are directly under the impeller blades. Different kinds of spargers: a) single nozzle sparger, b) ring sparger, and c) micro sparger (Sakuma 2001). Effecting factors of oxygen transfer rate 5. Properties of the liquid or medium Doran, P. M. (1995) During cell culture, small bubbles collide and coalesce to form larger bubbles, decreasing surface area (a) and subsequently kLa. Be aware of reported kLa values in which high salt concentrations are used, because this can prevent bubble coalescing. Cells, proteins and other molecules which adsorb at gas-liquid interfaces interfacial blanketing reduces contact area between gas and liquid. Solutes : oxygen solubility is decreased by the ions and sugars normally added to fermentation media. It is 5-25% lower than in water.  Effecting factors of oxygen transfer rate 6. Temperature Doran, P. M. (1995) Increasing temperatures inversely affects both the volumetric mass transfer coefficient and oxygen solubility in culture Between 0-36 °C medium. Oxygen solubility in pure water falls with increasing CL* = 14.161 – 0.3943T + 0.007714T2 – 0.0000646T3 temperature (i.e., -0.5 × 10-3 kg/m-3 between 30°C and 35°C ). When Above 40 °C, solubility of O2 drops significantly, adversely CL* = oxygen solubility (mg/L) T = temperature in °C affect CL* and kL It is important to note the temperature conditions from vendor-supplied characterization data. Effecting factors of oxygen transfer rate 7. Pressure The adding back pressure to the system affects on the gas hold-up and other hydrodynamic parameters. This is important in gas-liquid systems. The gas is compressible, and solubility can be affected by pressure. Pressure drop increases with inlet superficial gas velocity and two-phase Reynolds number. At a given liquid flow rate, the two-phase pressure drop is greater than that of single-phase. This reflects the additional pressure drop that is present in this type of flow with bubbles moving through a continuous liquid phase. Not only friction of single-phase due to the walls is present, but also, friction for each bubble flowing in water, breakup of bubbles dissipating energy, and impact of bubbles against obstacles throughout the reactor causing pressure loss.  Effecting factors of oxygen transfer rate 8. Cell phenomenal Cell species: In batch culture, the rate of O2 uptake varies with time, and also specific O2 uptake rate Qo = qox When Qo = oxygen uptake rate per volume of broth (gg-1s-1) qo = specific oxygen uptake rate (gg-1s-1) x = cell concentration (g/l) Culture growth phase : As cell density increases during the exponential phase, OUR increases until OTR becomes a limiting rate, as determined by the mass transfer of oxygen into the bulk liquid. Morphology: complex morphology as a lower transfer rates Phases of cell growth in fermentation process https://www.cytivalifesciences.com/en/us/solutions/bioprocessing/knowl edge-center/7-factors-that-affect-oxygen-transfer-to-cells-in-bioreactors  Effecting factors of oxygen transfer rate 8. Cell phenomenal Table Critical dissolved oxygen levels for a range of microorganisms Temperature Critical dissolved oxygen Organism (°C) concentration (mmoles/dm3) Penicillium chrysogenum 24 0.022 E. coli 37 0.008 Saccharomyces sp. 30 0.004 Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 9. Detergent and antifoam Detergent and oil substance have dramatic effects on bubble size. Both these agents are surface active agents. They affect the surface tension properties of the liquid. However, their effects on oxygen transfer are dramatically different. Karakashev, S. I., & Grozdanova, M. V. (2012). Foams and antifoams. Advances in colloid and interface science, 176, 1-17. Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 9. Detergent and antifoam Detergents and detergent like molecules typical have a hydrophobic and hydrophilic end. They tend to accumulate in the bubble-liquid interface and thus cover the bubbles. The hydrophobic end will face the bubble (as bubble are full of air which is hydrophobic). Charged groups on the detergents cause The hydrophilic end will face the liquid. bubbles to repel and prevent coalescence. https://exovio.de/about/ Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 9. Detergent and antifoam Antifoam agent include vegetable oils and silicone oils. Vegetable oils are often used by the cells as a substrate. Silicone oils are biologically inert and can cause problems in downstream processing, but more effective antifoaming agents than vegetable oils. Antifoaming agents act by binding up detergents and thus preventing them from aggregating around bubbles. https://www.dow.com/en-us/product-technology/pt- antifoams/pg-antifoams-antifoams-defoamers-food.html Effecting factors of oxygen transfer rate Factors affecting The accumulation of antifoam at the bubble surface leads the interfacial area (a) to an increased tendency for bubbles to coalesce. In fact, high hydrophobicity of the antifoams increases the 9. Detergent and antifoam attraction between the bubbles. Entry of contaminating organisms and blockage of outlet gas lines. Liquid and cells trapped in the foam represent a loss of bioreactor volume. Fragile cells can be damaged by collapsing foam. Antifoam affect the surface chemistry of bubbles and their https://stillana.ru/th/holidays/what-do-the-soap-bubbles- tendency to coalesce and have a significant effect on kLa. make-up-the-composition-of-the-solution-the-recipe-for- large-soap-bubbles/ Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 9. Detergent and antifoam Antifoaming agents are used to influence surface tension, resulting in reduced bubble coalescence and foaming so the number of bubbles has decreased. However, this principle does not always lead to increases in OTR wherein antifoam also reduces bubble mobility, which subsequently With addition of antifoam Without addition of antifoam reduces the kLa. Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 9. Detergent and antifoam Because antifoams accumulate around bubbles, they block the movement of oxygen through the interfacial boundary. Without addition of antifoam Excess antifoam Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 10. Air flow rate For example: Higher oxygen availability drives kLa increases. - High air flow rates can cause cell damage Increasing oxygen supply to a bioreactor due to shear forces. drives this availability and can be controlled by - Excessive foam might also be generated, modifying concentration (air vs O2 enrichment) requiring a high concentration of antifoam that and volumetric flow. Although high kLa values could hinder downstream processing. are desirable, it is important to consider the - Higher air flow rates require a larger exhaust actual operating conditions and implications to filter area, driving consumable cost increases. cell viability and associated process costs. Effecting factors of oxygen transfer rate Factors affecting the interfacial area (a) 11. Power input to agitator In microbial fermentation, agitation Where is needed at a higher power input to K is a constant, Pu is the power required in the ungassed vessel, disperse air bubbles and to increase d is the impeller(s) diameter, oxygen transfer efficiency. Q is the volume of air supplied per minute per volume of the liquid in the vessel for which the unit is often referred to as vvm. **The constant term in this equation is strictly dependent on the geometry of the tank and impeller(s) and the operational conditions. Factors affect the Oxygen Transfer Rate and Uptake Rate MIC 321-BASIC BIOPROCESS ENGINEERING 74 Oxygen transfer process Oxygen transfer rate (OTR): Oxygen uptake rate (OUR): the amount of oxygen (in grams or moles) the amount of oxygen (in grams or moles) transferred from gas to liquid per units of time consumed by the cells per units of time and of and of liquid volume. This is the rate at which liquid volume. This is the rate at which oxygen is oxygen can be delivered to the biological utilized by the microorganism. system; - Factors affecting CL*- CL Gas pressure and oxygen partial pressure Henry’s law Henry’s law may also express the equilibrium solubility of gas-liquid systems. C0* > equals the concentration of oxygen in the gas-liquid interface > equal to saturation concentration of oxygen in the reactor The value of a medium’s Henry’s constant for oxygen is dependent on the concentration of salts and temperature. The partial pressure of oxygen in the gas phase is the 𝑃0 fraction of the total gas pressure which can be 𝐶𝐿∗ = 𝐻0 contributed to oxygen. When - CL* is the maximum solubility of oxygen in the liquid For example, if air contains 21% oxygen, then the partial - P0 is the partial pressure of oxygen in the gas phase and pressure of oxygen in air at 1 atm is 0.21 atm. - H0 is Henry’s constant  Factors affecting C L*- CL The equilibrium concentrations of oxygen in water, CIA,eq, as functions of temperature for air Henry’s “Law” constants at 20 ℃ for Where some common gases in water. xA is the mole fraction of A in solution. CIA, eq is the equilibrium concentrations of oxygen in water. MWA is molecular weight. CW is the concentration of the water. Oxygen-saturated concentrations in water in contact with air. MIC 321-BASIC BIOPROCESS ENGINEERING 77 Factors affecting C L*- CL Example: If we assume that oxygen makes up approximately 20.5% of air, the partial pressure of the oxygen at atmospheric pressure (1 atm) is 0.205 atm. The liquid mole fraction of oxygen at 0 ºC is readily calculated through use of Henry’s “Law” constant at that temperature from previous Table. MIC 321-BASIC BIOPROCESS ENGINEERING 78 Factors affecting C L*- CL Liquid height An alternative method of increasing Po is to increase the total pressure in the bubbles. For example, the partial pressure of oxygen in the air at 10 atm is 2.1 atm as compared to 0.21 atm in the air at 1 atm. One method of increasing the pressure in a reactor would be to pressurize the whole fermenter. MIC 321-BASIC BIOPROCESS ENGINEERING 79 Factors affecting C L*- CL Liquid height An alternative method of increasing Po is to increase the height of the fermentor. The hydrostatic pressure at the base of a column of liquid increases with the height of the columns according to the following equation: Pbase = gh + 1 atmosphere where Pbase = the pressure at the base of the reactor (Pa)  = density of liquid (g/cm3) g = gravitational acceleration (9.8 m/s2) h = the height of the reactor One atmosphere = 101,000 Pa or 1 atm = 101 kPa MIC 321-BASIC BIOPROCESS ENGINEERING 80  Factors affecting C L*- CL Liquid height Pre sen ce o f solutes Ce l l ul ar activity The total pressure acting on a gas The presence of salts and sugars will The more significant dissolved oxygen bubble will be higher at the base of the decrease the solubility of oxygen and concentration gradient between the column than at the surface. thus decrease the value of CL* interfacial boundary and the bulk liquid the rate of oxygen transfer will be higher. There are two ways of increasing the value of CL*-CL to increase the value of CL * and to decrease the value of CL MIC 321-BASIC BIOPROCESS ENGINEERING 81  Factors affecting C L*- CL From oxygen transfer equation, Manipulating the value of CL to maximize the 𝒅𝑪 oxygen transfer rate is not an appropriate 𝑶𝑻𝑹 = = 𝒌𝑳 a(𝑪∗𝑳 -CL) 𝒅𝒕 option as it would also have a negative effect If CL* and ka are constant, then the maximum rate of n biomass productivity designing and oxygen transfer will be occurred when Co is zero. operating the fermenter to obtain high values of CL* is a much more practicable solution. If CL = 0, then OTR = kLa CL* MIC 321-BASIC BIOPROCESS ENGINEERING 82  OXYGEN AS A GROWTH-LIMITING NUTRIENT Specific growth rate the Monod model is based on the observation Oxygen that growth rate is determined by the limited growth Growth not limited by oxygen concentration of the growth limiting substrate 𝜇𝑚𝑎𝑥 𝑆 𝜇= 𝐾𝑆 + 𝑆 Critical oxygen concentration Where Oxygen concentration µ is known as the specific growth rate (h-1). µmax is maximum specific growth rate (h-1). Monod relationship between the dissolved oxygen KS is a system coefficient. concentration and the specific growth rate of an organism. S is substrate concentration. 83  OXYGEN AS A GROWTH LIMITING NUTRIENT The growth-limiting substrate may be the carbon and energy source or maybe a nutrient such as a nitrogen compound. Therefore, the following kinetic equations can be used to describe growth under oxygen-limited conditions. 𝑑𝑋 𝜇𝑚𝑎𝑥 𝐶𝑜 Where = 𝑑𝑡 𝐾𝑜 + 𝐶𝑜 Co = the concentration of oxygen µm = the maximum specific growth rate 𝑑𝐶𝑜 1 𝜇𝑚𝑎𝑥 𝐶𝑜 Yo = the biomass yield from oxygen =. X 𝑑𝑡 𝑌𝑜 𝐾𝑜 +𝐶𝑜 Ko = the Monod constant for oxygen uptake MIC 321-BASIC BIOPROCESS ENGINEERING 84  OXYGEN AS A GROWTH-LIMITING NUTRIENT Oxygen Uptake Rate (OUR) The dissolved oxygen concentration in a reactor is determined by the balance between the oxygen 1 𝜇𝑚𝑎𝑥 𝐶𝑜 transfer rate (OTR) and oxygen uptake rate (OUR) 𝑂𝑈𝑅 =. X 𝑌𝑜 𝐾𝑜 +𝐶𝑜 𝑑𝐶0 1 𝜇𝑚𝑎𝑥 𝐶𝑜 =. X 𝑑𝑡 𝑌𝑜 𝐾𝑜 +𝐶𝑜 Where µ is known as the specific growth rate (h-1). 𝑑𝐶0 1 𝜇𝑚𝑎𝑥 𝐶𝑜 = 𝑘𝐿 𝑎 𝐶𝑜∗ − 𝐶𝑜 −. X µmax is maximum specific growth rate (h-1). 𝑑𝑡 𝑌𝑜 𝐾𝑜 +𝐶𝑜 KS is a system coefficient. Co is oxygen concentration. MIC 321-BASIC BIOPROCESS ENGINEERING 85 Oxygen as a growth limiting nutrient OTR = OUR 𝑑𝐶0 1 𝜇𝑚𝑎𝑥 𝐶𝑜 Steady-state = 𝑘𝐿 𝑎 𝐶𝑜∗ − 𝐶𝑜 −. X 𝑑𝑡 𝑌𝑜 𝐾𝑜 +𝐶𝑜 analysis 𝑑𝐶0 =0 𝑑𝑡 The movement of oxygen from a 1 𝜇𝑚𝑎𝑥 𝐶𝑜 bubble through the bulk liquid of 𝑘𝐿 𝑎 𝐶𝑜∗ − 𝐶𝑜 =. X 𝑌𝑜 𝐾𝑜 +𝐶𝑜 a cell can be thought of as a continuous process. The kLa should be maintained to ensure that the growth of a given concentration of biomass is not oxygen limited. Alternatively, this equation Oxygen enters the bulk liquid could be used to estimate the concentration of biomass at which a population and is removed by the cells. will become oxygen limited, assuming a constant kLa is maintained. MIC 321-BASIC BIOPROCESS ENGINEERING  References 1. Bailey, J. E., and Ollis, D. F. (1986). Biochemical Engineering Fundamentals. 2nd edition, McGraw-Hill, Singapore. 2. Berenjian, A. (Ed.). (2019). Essentials in fermentation technology. Springer. 3. Buffo, M. M., Corrêa, L. J., Esperança, M. N., Cruz, A. J. G., Farinas, C. S., & Badino, A. C. (2016). Influence of dual-impeller type and configuration on oxygen transfer, power consumption, and shear rate in a stirred tank bioreactor. Biochemical Engineering Journal, 114, 130-139. 4. Cao, E., Radhakrishnan, A. N., Hasanudin, R. B., & Gavriilidis, A. (2021). Study of Liquid–Solid Mass Transfer and Hydrodynamics in Micropacked Bed with Gas–Liquid Flow. Industrial & Engineering Chemistry Research, 60(29), 10489- 10501. 5. Danckwerts, P. V.,.Significance of Liquid-Film Coefficients in Gas Absorption,. Ind. Eng. Chem. 43 (1951):1460.1467. 6. Doran, P.M. (2013) Bioprocess Engineering Principles. 2nd edition. Academic Press, London. 7. Inglezakis, V. J., Balsamo, M., & Montagnaro, F. (2020). Liquid–solid mass transfer in adsorption systems—An overlooked resistance?. Industrial & Engineering Chemistry Research, 59(50), 22007-22016. 8. Ruston, J. H., Costich, E. W. and Everett, H. J. (1950) Chem. Eng. Prog.,46, 467. MIC 321-BASIC BIOPROCESS ENGINEERING 87  References 9. Kashid, M. N., Renken, A., & Kiwi-Minsker, L. (2011). Gas–liquid and liquid–liquid mass transfer in microstructured reactors. Chemical Engineering Science, 66(17), 3876-3897. 10. Lins Barros, P., Ein-Mozaffari, F., & Lohi, A. (2022). Gas Dispersion in Non-Newtonian Fluids with Mechanically Agitated Systems: A Review. Processes, 10(2), 275. 11. Sakuma H., ‘Hakkōsō’ (Fermenter), in Baioindasutorii kyōkai hakkō to taisha kenkyūkai, ed., Hakkō handobukku (Fermentation Handbook) (Tokyo: Kȳoritsu shuppan, 2001), pp. 485–90. 12. Shuler, M. L., Kargi, L. Bioprocess Engineering: Basic Concepts. (2002). Upper Saddle River, NJ: Prentice-Hall. 13. Simpson, R., Sastry, S.K. (2013). Chemical and Bioprocess Engineering – Fundamental Concepts for First-Year Students. Springer, New York. 14. Welty, J., Rorrer, G. L., & Foster, D. G. (2020). Fundamentals of momentum, heat, and mass transfer. John Wiley & Sons. MIC 321-BASIC BIOPROCESS ENGINEERING 88  If you have any question, please feel free to ask me via: Thank you Sukanya Phuengjayaem, PhD E mail: [email protected] Sci 5 th floor, room 513, Department of Microbiology, KMUTT Tel: 02-4708897 MIC 321-Basic Bioprocess Engineering 89