94 Fermentation and Biochemical Engineering Handbook 5.0 FERMENTER COOLING When designing a fermenter, one primary consideration is the removal ofheat. There is a practical limit to the square feet of cooling surface that can be achieved from a tank jacket and the amount of coils that can be placed inside the tank. The three sources ofheat to be removed are from the cooling of media after batch sterilization, from the exothermic fermentation process and the mechanical agitation The preceding topic about the design of a continuous sterilizer empha sized reduced turnaround time, easier media sterilization, higher yields and one speed agitator motors. The reduced turnaround time is realized because the heat removal after broth sterilization is two to four times faster in a continuous sterilizer than from a fermenter after batch sterilization. The cooling section of a continuous sterilizer is a true countercurrent design Cooling a fermenter after batch sterilization is more similar to a cocurrent heat exchang Assuming that all modern large scale industrial fermentation plants sterilize media through a continuous sterilizer, the heat transfer design of the fermenter is only concerned with the removal of heat caused by the mechani- cal agitator(if there is one)and the heat of fermentatio ese data can be obtained while running a full scale fermenter. The steps are as follows 1. Heat Loss by Convection and radiation a. Perry's Handbook: [14 ∪=1.8 Btu/hr/F/ft No insulation; if tank is insulated determine proper 6. Calculate tank surface area =A C. Temp. of Broth=T1 d. Ambient Air Temp =T2 Q1=UA(T1·T2)=Btu/hr
94 Fermentation and Biochemical Engineering Handbook 5.0 FERMENTER COOLING When designing a fermenter, one primary consideration is the removal of heat. There is a practical limit to the square feet of cooling surface that can be achieved from a tank jacket and the amount of coils that can be placed inside the tank. The three sources of heat to be removed are from the cooling of media after batch sterilization, from the exothermic fermentation process, and the mechanical agitation. The preceding topic about the design of a continuous sterilizer emphasized reduced turnaround time, easier media sterilization, higher yields and one speed agitator motors. The reduced turnaround time is realized because the heat removal after broth sterilization is two to four times faster in a continuous sterilizer than from a fermenter after batch sterilization. The cooling section of a continuous sterilizer is a true countercurrent design. Cooling a fermenter after batch sterilization is more similar to a cocurrent heat exchanger. Assuming that all modern large scale industrial fermentation plants sterilize media through a continuous sterilizer, the heat transfer design of the fermenter is only concerned with the removal of heat caused by the mechanical agitator (if there is one) and the heat of fermentation. These data can be obtained while running a full scale fermenter. The steps are as follows: 1. Heat Loss by Convection and Radiation a. Perry's Handbook:[14] U = 1.8 Btu/hr/"F/ft2 (No insulation; if tank is insulated determine proper constant .) b. Calculate tank surface area =A c. Temp. of Broth = Tl d. Ambient Air Temp. = T, Q, = uA (Tl - T2) = Btukr
Fermentation Design 95 Convection and radiation depend upon whether the tanks are insulated or not, and the ambient air temperatu especially during the winter. Measurements of convection and radiation heat losses are, on average, 5% or less of total heat of fermentation(winter and uninsulated tanks) 2. Heat Loss by Evaporatio a. If fermenters have level indicators, theaverage evapo- ation per hour is easily determined b. Calculate pounds of water/hour evaporated from psychometric charts based on the inlet volume and humidity of air used, and at the broth temperature The exhaust air will be saturated, Determine heat of vaporization from steam tables at the temperature of the broth= HEy= Btu/lb Q2=HEy X(b water evap/hr)=Btw/hr Evaporation depends upon the relative humidity of the compressed air, temperature of the fermentation broth and the aeration rate. It is not uncommon that the loss ofheat by evaporation is 15 to 25%ofthe heat of fermentation. Modern plants first cool the com- pressed air then reheat it to 70-80%relative humidity based on summertime air intake conditions. Conse- quently, in winter the air temperature and absolute humidity of raw air are very low and the sterile supply will be much lower in relative humidity than summer conditions. Therefore in the winter more water is evaporated from the fermenters than in the summer. ( Water can be added to the fermenter or feeds can be made more dilute to keep the running volume equal to summer conditions and productivity in summer and winter equal) 3. Heat Removed by refrigerant a. This is determined by cooling the broth as rapidly as possible 5%F below the normal running temperature
Fermentation Design 95 Convection and radiation depend upon whether the tanks are insulated or not, and the ambient air temperature, especially during the winter. Measurements of convection and radiation heat losses are, on average, 5% or less of total heat of fermentation (winter and uninsulated tanks). 2. Heat Loss by Evaporation a. Iffermenters have level indicators, the average evaporation per hour is easily determined. b. Calculate pounds of waterhour evaporated from psychometric charts based on the inlet volume and humidity of air used, and at the broth temperature. The exhaust air will be saturated. Determine heat of vaporization from steam tables at the temperature of the broth = HEV = Btu/lb. Q2 = HEV x (lb water evaphr) = Btuh Evaporation depends upon the relative humidity of the compressed air, temperature of the fermentation broth and the aeration rate. It is not uncommon that the loss of heat by evaporation is 15 to 25% ofthe heat of fermentation. Modern plants first cool the compressed air then reheat it to 70-80% relative humidity based on summertime air intake conditions. Consequently, in winter the air temperature and absolute humidity of raw air are very low and the sterile air supply will be much lower in relative humidity than summer conditions. Therefore, in the winter more water is evaporated from the fermenters than in the summer. (Water can be added to the fermenter or feeds can be made more dilute to keep the running volume equal to summer conditions and productivity in summer and winter equal.) 3. Heat Removed by Refrigerant a. This is determined by cooling the broth as rapidly as possible 5°F below the normal running temperature
96 Fermentation and Biochemical Engineering Handbook and then shutting off all cooling. The time interval is then very carefully measured for the broth to heat up to re(△ T and time) b. Assume specific heat of broth= 1.0 Btu/lb-F c. Volume of broth by level indicator (or best estimate) Q3=SpHt. x broth vol.×8345×△T÷ time(hr) 23= Btu/hr 4. Heat Added by Mechanical Agitation a. Determine or assume motor and gear box efficiency about 0.92) 6. Measure kw of motor Q4=kW×3415× efficiency=Btu/hr 5. Heat of Fermentation=AH, g1+Q2+g3-4=MH The heat of fermentation is not constant during the course of the fermentation. Peaks occur simultaneously with high metabolic activity Commercial fermentation is not constant during the course of the fermenta tion. Commercial fermentations with a carbohydrate substrate may have peak loads of 120 Btu/hr/gal. The average AH, for typical commercial fermentations is about 60 Btu/hr/gal. The average loss of heat due to evaporation from aeration is in the range of 10 to 25 Btu/hr/gal. Fermenta tions with a hydrocarbon substrate usually have a much higher AHf than carbohydrate fermentations. Naturally, most c determine the△Hr for each product, especially after each major medium revision. (Typically, data are collected every eight hours throughout a run to observe the growth phase and production phase. Three batches can be averaged for a reliable AHf.) In this manner, the production department can give reliable data to the engineering department for plant expansions
96 Fermentation and Biochemical Engineering Handbook and then shutting off all cooling. The time interval is then very carefully measured for the broth to heat up to running temperature (AT and time). b. Assume specific heat of broth = 1 .O BtuAb-OF c. Volume of broth by level indicator (or best estimate) = gal Q3 = Sp.Ht. x broth vol. x 8.345 x AT + time (hr) 4. Heat Added by Mechanical Agitation a. Determine or assume motor and gear box efficiency b. Measure kW of motor (about 0.92) Q4 = kW x 3415 x efficiency = Btuihr 5. Heat of Fermentation = AHf e, + Q2 + Q3 - Q4 = AHf The heat of fermentation is not constant during the course of the fermentation. Peaks occur simultaneously with high metabolic activity. Commercial fermentation is not constant during the course of the fermentation. Commercial fermentations with a carbohydrate substrate may have peak loads of 120 Btu/hr/gal. The average AHf for typical commercial fermentations is about 60 Btu/hr/gal. The average loss of heat due to evaporation from aeration is in the range of 10 to 25 BtuMgal. Fermentations with a hydrocarbon substrate usually have a much higher Mf than carbohydrate fermentations. Naturally, most companies determine the AHr for each product, especially after each major medium revision. (Typically, data are collected every eight hours throughout a run to observe the growth phase and production phase. Three batches can be averaged for a reliable AHf.) In this manner, the production department can give reliable data to the engineering department for plant expansions
ermentation Desigh The following is how the heat transfer surface area could be designed for a small fermenter. The minimum heat transfer surface area has been alculated(based on the data below)and presented in Table 2 Assume S/S fermenter capacity 30,000gal Agitator 15hp/1,000gal Heat of fermentation(peak) 100 Btu/hr/gal Heat of agitation 38 Btu/hr/gal Heat transfer. U coils 120 Btu/hr/sq ft Heat transfer, u jacket 80 tw/hr sq ft No Btu lost in evaporation Chilled water supply 50°F Chilled water return 60°F Broth temperature(28C) Table 2. The heat Transfer Surface Area(ft2)Required for Tank with Coils onl Jacket Only Mechanical agitation Air agitation onl 150 After the heat transfer surface area requirements are known, various shaped(height to diameter)tanks should be considered. Table 3 illustrates parameters of 30,000 gallon vessels of various h/d ratios
Fermentation Design 9 7 The following is how the heat transfer surface area could be designed for a small fermenter. The minimum heat transfer surface area has been calculated (based on the data below) and presented in Table 2. Assume: S/S fermenter capacity Agitator Heat of fermentation (peak) Heat of agitation Heat transfer, U coils Heat transfer, U jacket Safety factor Chilled water supply Chilled water return Broth temperature (28°C) Table 2. The Heat Transfer 30,000 gal 15 hp/ 1,000 gal 100 Btu/hr/gal 38 Btu/hr/gal 120 Btu/hr/sq A 80 Btu/hr sq A No Btu lost in evaporation 50°F 60°F 82°F Surface Area (A2) Required for Tank with: Coils Only Jacket Only Mechanical agitation 200 Air agitation only 150 5 6 After the heat transfer surface area requirements are known, various shaped (height to diameter) tanks should be considered. Table 3 illustrates parameters of 30,000 gallon vessels of various WD ratios
98 Fermentation and Biochemical Engineering Handbook Table 3. Maximum Heat Transfer Surface Area Available(ft?)on 80% of the Straight Side H/d F(it) D (ft) Jacket Coils* 27313.79381,2 2.5 31.7 12.71,0101,340 35811.91,0701,400 3.5 1,455 43.4 10.81,1801,150 *Coil area is based on 3. 5 inch o d, 3. 5 inch spacing between helical coils and 12 inches between the tank wall and the center line of the coil It can be seen by comparing Tables I and 2 that if mechanical agitation is used and a jacket is desired, then additional internal coils are required. the intermal coils can be vertical, like baffles, or helical. Agitation experts state that helical coils can be used with radial turbines if the spaces between the coil loops are I to 1.5 pipe diameters. Once helical coils are accepted, Why use a jacket at all? Reasons in favor of coils (in addition to the better heat transfer coefficient)are 1. Should stress corrosion cracking occur(due to chlorides in the cooling water), the replacement of coils is cheaper than the tank wall and jacket 2. The cost of a fermenter with helical coils is cheaper than a jacketed tank with internal coils 3. Structurally, internal coils present no problems with continuous sterilization However ifbatch sterilization is insisted upon, vertical coils are one solution to avoiding the stress between the coil supports and tank wall created when cooling water enters the coils while the broth and tank wall are at 120C. notice that the method of medi sterilization batch or continuous. is related to the fer menter design and the capital cost
98 Fermentation and Biochemical Engineering Handbook Table 3. Maximum Heat Transfer Surface Area Available (ft2) on 80% of the Straight Side H/D F (ft) D (ft) Jacket Coils* 2 27.3 13.7 938 1,245 2.5 31.7 12.7 1,010 1,340 3 35.8 11.9 1,070 1,400 3.5 39.7 11.3 1,130 1,455 4 43.4 10.8 1,180 1,150 *Coil area is based on 3.5 inch o.d., 3.5 inch spacing between helical coils and 12 inches between the tank wall and the center line of the coil. It can be seen by comparing Tables 1 and 2 that if mechanical agitation is used and ajacket is desired, then additional internal coils are required. The internal coils can be vertical, like baffles, or helical. Agitation experts state that helical coils can be used with radial turbines if the spaces between the coil loops are 1 to 1.5 pipe diameters. Once helical coils are accepted, Why use ajacket at all? Reasons in favor of coils (in addition to the better heat transfer coefficient) are: 1. Should stress corrosion cracking occur (due to chlorides in the cooling water), the replacement of coils is cheaper than the tank wall and jacket. 2. The cost of a fermenter with helical coils is cheaper than a jacketed tank with internal coils. 3. Structurally, internal coils present no problems with continuous sterilization. However, if batch sterilization is insisted upon, vertical coils are one solution to avoiding the stress between the coil supports and tank wall created when cooling water enters the coils while the broth and tank wall are at 120°C. Notice that the method of media sterilization, batch or continuous, is related to the fermenter design and the capital cost
Fermentation Design 6.0 THE DESIGN OF LARGE FERMENTERS (BASED ON AERATION 6. 1 Agitator effectiveness Laboratory scale work frequently reports aeration rates as the volume of air at standard conditions per volume of liquid per minute, or standard cubic feet of air per hour per gallon. Production engineers realized that the scale-up of aeration for a large range of vessel sizes was by superficial linear elocity (SLV), or feet per second. Large scale fermenters, for energy savings in production equipment, use air-agitated fermenters. The cost savings are not apparent when comparing the cost of operating a fermenter agitator to the cost of the increased air pressure required. However, when the total capital and operating costs of fermentation plants (utilities included) for the two methods of fermentation are compared, the non-mechanically agitated fer- menter design is cheaper. The questions are, How much mixing horsepower is available from aeration, versus how much turbine horsepower is effective r aeration and mixing? D N. millerlll of DuPont, describing his results of scale-up of an agitated fermenter states, both Ki a and gas hold-up increase with an increasing gas rate and agitator speed. Gas sparging is the stronger'effect and tends to be increasingly dominant as gas rate increases At superficial gas velocities, 0.49 ft/sec and higher, very little additional mass transfer improvement can be gained with increased mechanical energy input. "Otto Nagel and associates 2) found in gas-liquid reactors that the mass transfer area of the gas in the liquid is proportional to the 0. 4 power in the energy dissipation. Thus for a 50 hp agitator, 12 hp directly affects the mass transfer area of oxygen. The upper impellers mainly circulate the fluid and contribute very little to bubble dispersion and oxygen transfer. Most of the agitators power is spent mixing the fluid. Tounderstand mixing theories see Brodkey, Danckwerts, Oldshue or other texts. 3)The primary function of mixing for aerobic fermentations is to increase the surface area of ai bubbles(the interfacial surface area)to minimize the bubble diameter. The fermenter is not the same as a chemical reactor where first and second order reactions occur between soluble reactants. The dissolution rate of oxygen into fermentation broth is controlled by diffusion. The consumption of soluble oxygen by the organism is an irreversible reaction and unless sufficient oxygen diffuses across the air- liquid surface area, the fermentation will cease aerobic metabolism. Methods offorcing more air into solution are more interfacial surface area, more air/oxygen, higher air pressure, reduced cell volume, or controlling metabolism by reduced carbohydrate feed rates
Fermentation Design 99 6.0 THE DESIGN OF LARGE FERMENTERS (BASED ON AERATION) 6.1 Agitator Effectiveness Laboratory scale work frequently reports aeration rates as the volume of air at standard conditions per volume of liquid per minute, or standard cubic feet of air per hour per gallon. Production engineers realized that the scale-up of aeration for a large range of vessel sizes was by superficial linear velocity (SLV), or feet per second. Large scale fermenters, for energy savings in production equipment, use air-agitated fermenters. The cost savings are not apparent when comparing the cost of operating a fermenter agitator to the cost of the increased air pressure required. However, when the total capital and operating costs of fermentation plants (utilities included) for the two methods of fermentation are compared, the non-mechanically agitated fermenter design is cheaper. The questions are, How much mixing horsepower is available from aeration, versus how much turbine horsepower is effective for aeration and mixing? D. N. Miller[”] of DuPont, describing his results of scale-up of an agitated fermenter states, “both &a and gas hold-up increase with an increasing gas rate and agitator speed. Gas sparging is the ‘stronger’ effect and tends to be increasingly dominant as gas rate increases. At superficial gas velocities, 0.49 Wsec and higher, very little additional mass transfer improvement can be gained with increased mechanical energy input.” Otto Nagel and associates[12] found in gas-liquid reactors that the mass transfer area of the gas in the liquid is proportional to the 0.4 power in the energy dissipation. Thus for a 50 hp agitator, 12 hp directly affects the mass transfer area of oxygen. The upper impellers mainly circulate the fluid and contribute very little to bubble dispersion and oxygen transfer. Most of the agitator’s power is spent mixing the fluid. (To understand mixing theories see Brodkey, Danckwerts, Oldshue or other texts.[I3]) The primary function of mixing for aerobic fermentations is to increase the surface area of air bubbles (the interfacial surface area) to minimize the bubble diameter. The fermenter is not the same as a chemical reactor where first and second order reactions occur between soluble reactants. The dissolution rate of oxygen into fermentation broth is controlled by diffusion. The consumption of soluble oxygen by the organism is an irreversible reaction and unless sufficient oxygen diffuses across the air-liquid surface area, the fermentation will cease aerobic metabolism. Methods of forcing more air into solution are: more interfacial surface area, more aidoxygen, higher air pressure, reduced cell volume, or controlling metabolism by reduced carbohydrate feed rates
100 Fermentation and Biochemical Engineering Handbook Not all of these options are practical because of shear, foaming and control devices 6.2 Fermenter Height The height-to-diameter(H/D)ratio of a fermenter is very important fo oxygen transfer efficiency. Tall, narrow tanks have three major advantages compared to short, squat fermenters. Bubble residence time is longer in taller vessels than shorter ones. The air pressure is greater at the sparger resulting in higher dissolved oxygen in taller vessels. The third advantage is shown in Table 4, namely that for a vessel of constant volume, as the Hd ratio increases, the volume of air required is reduced even though the superficial linear velocity remains constant. At the same time, bubble residence time and sparger air pressure increase. For larger volume fermenters, even greater vertical heights are used. the conclusion is that fermenter height is the most important geometrical factor in fermenter design. Conversely, shorter vessels need more air and/or more mechanical agitation to effect the same mass transfer rate of oxygen. The majority of industrial fermenters are in the h/d ange of 2-3. The largest sizes are about 10 liters It is thought that the cost of compressing air sufficient for air agitation alone is prohibitive. However, as seen in Table 5, if the fermenters are tall, the power consumption is less than for short squat tanks. Careful selection of compressors with high efficiencies will keep power costs at a minimum Table 4. Effect of Air Requirements on Geometric Fermenter Design Bubble parser H/D F D scfm Residence Time Pressure 227313.73,522 335811.92,683 160 43410.82,219 1.6 194 Constant: 30,000 gal tank; 24, 000 gal run vol: 0. 4 fU/sec SLV
100 Fermentation and Biocltemical Engineering Handbook Not all of these options are practical because of shear, foaming and control devices. 6.2 Fermenter Height The height-to-diameter (WD) ratio of a fermenter is very important for oxygen transfer efficiency. Tall, narrow tanks have three major advantages compared to short, squat fermenters. Bubble residence time is longer in taller vessels than shorter ones. The air pressure is greater at the sparger resulting in higher dissolved oxygen in taller vessels. The third advantage is shown in Table 4, namely that for a vessel of constant volume, as the WD ratio increases, the volume of air required is reduced even though the superficial linear velocity remains constant. At the same time, bubble residence time and sparger air pressure increase. For larger volume fermenters, even greater vertical heights are used. The conclusion is that fermenter height is the most important geometrical factor in fermenter design. Conversely, shorter vessels need more air and/or more mechanical agitation to effect the same mass transfer rate of oxygen. The majority of industrial fermenters are in the H/D range of 2-3. The largest sizes are about 10' liters. It is thought that the cost of compressing air sufficient for air agitation alone is prohibitive. However, as seen in Table 5, if the fermenters are tall, the power consumption is less than for short squat tanks. Carehl selection of compressors with high efficiencies will keep power costs at a minimum. Table 4. Effect of Air Requirements on Geometric Fermenter Design Bubble Sparger WDF D scfm Residence Time Pressure 2 27.3 13.7 3,522 1 12.3 3 35.8 11.9 2,683 1.3 16.0 4 43.4 10.8 2,219 1.6 19.4 Constant: 30,000 gal tank; 24,000 gal run vol; 0.4 ft/sec SLV
Fermentation Design 101 Table 5. Air Compressor Horsepower per Fermenter 30 compressor compressor H/D scfm 2 3.522 429 609 2,693 327 2,219 Constant: 30,000 gal tank; 24,000 gal run vol; 0. 4 ft/sec SLV Note: Basis of hp is( 8 hp)/(0. 7) 6.3 Mixing Horsepower by Aeration The theoretical agitation effect of aeration alone can be easily calcu ted. There are two separate forces, the first caused by the free rise of bubbles. The bubbles rise from the sparger at a pressure equal to the hydrostatic pressure of the liquid and as they rise to the surface, the gas bubble pressure remains in constant equilibrium with the hydrostatic pressure above it until it escapes from the liquid surface, The temperature of the air in the bubble is equal to the fermentation temperature and remains constant due to heat transfer from the fermentation broth. These conditions describe an isothermal expansion of gas; gas pressure and gas volume change at constant temperature. Using the formula from Perry and Chilton, 4 the theoretical horsepower for the isothermal expansion of air can be calculated 436P In 1.000 scfm where: PI is the hydrostatic pressure(absolute) P2 is the(absolute) pressure above the liquid Figure 8 shows the curves at different superficial linear velocities and the relationship ofhorsepower to height ofliquid in a fermenter. These curve are the mixing energy (power per unit volume) released by rising bubbles to the liquid
Fermentation Design IO1 Table 5. Air Compressor Horsepower per Fermenter 30 psig 50 psig compressor compressor m sch (hP) (hP) 2 3,522 429 609 3 2,693 327 464 4 2,2 19 270 3 84 Constant: 30,000 gal tank; 24,000 gal run vol; 0.4 Wsec SLV. Note: Basis of hp is (8 hp)/(0.7) 6.3 Mixing Horsepower by Aeration The theoretical agitation effect of aeration alone can be easily calculated. There are two separate forces, the first caused by the free rise of bubbles. The bubbles rise from the sparger at a pressure equal to the hydrostatic pressure ofthe liquid and as they rise to the surface, the gas bubble pressure remains in constant equilibrium with the hydrostatic pressure above it until it escapes from the liquid surface. The temperature of the air in the bubble is equal to the fermentation temperature and remains constant due to heat transfer from the fermentation broth. These conditions describe an isothermal expansion ofgas; gas pressure and gas volume change at constant temperature. Using the formula from Perry and Chilt~n,['~I the theoretical horsepower for the isothermal expansion of air can be calculated. p2 1,000 sch 4 hp = 4.36P2 In - where: P, is the hydrostatic pressure (absolute) P, is the (absolute) pressure above the liquid Figure 8 shows the curves at different superficial linear velocities and the relationship ofhorsepower to height ofliquid in a fermenter. These curves are the mixing energy (power per unit volume) released by rising bubbles to the liquid
HORSEPOWER/1000 GAL RISE OF BUBBLES AT CONSTANT LINEAR VELOCIT P2=147PS|A sR 0 2FT/SEC 03FT/SEC0. FT/SECos FT /SECO.6 FT SEC\0.7 FT.\OB FT SE sesss HP/1000 GALS Figure 8. Isothermal bubble rise curve horsepower/1000 gal
102 Fermentation and Biochemical Engineering Handbook 'C w
Fermentation Design 103 Thus in a fermenter 1. The horsepower per 1000 gallons(P/n) can be increased by adding more air 2. The effect of aeration scale-up by superficial linear velocity(SLV) is not proportional to(P/n). However, by using these curves scale-up at constant(/n) can be used to determine the required SLv. Experience indicates that the P/v relationship is not affected by non-Newtonian fluids below 6000 cps 4. If the air temperature at the bottom of the fermenter is less than the liquid temperature, there is a gain in P/v. This is due to the fact that at a lower temperature, the air density is greater, and heat is transferred from the broth to the bubbles(isothermal expansion) resulting inmore work(P/n 5. If the fermenter vent valve is restricted to increase the pressure above the broth, it has the effect of reducing P/n, but oxygen transfer increases due to the greater partial pressure of oxygen There have been reports of air dispersion with improved oxygen transfer using static mixers attached to the air ring. Two papers on static mixers were given by Smith and Koch at the Mixing(Engineering Founda tion)Conference in Rindge, NH(1977). Additional papers can be found in the waste treatment field There is additional energy to be gained from aeration. In order for the air to enter a tank below the liquid surface, the pressure in the sparging device must exceed the static head pressure. Thus the mass of air has a determinable velocity through the orifices of the sparger. The force exerted against the liquids F=M2/2g. Thatis, for a fixed mass flow rate of air, the force varies as the velocity squared. The velocity of air through a nozzle is a function of the(absolute) pressure ratio on each side of the orifice, and it can be increased to sonic velocity. The time of flow through an orifice is so short there is no heat transferred from the broth to the air and the air temperature drops. The expansI ion of air at sonic velocity is isentropic(adiabatic). The horsepower obtained by the isentropic expansion ofair(at any pressure ratio)is(see Perry and Chilton )u
Fermentation Design 103 Thus in a fermenter: 1. The horsepower per 1000 gallons (P/v) can be increased by adding more air. 2. The effect of aeration scale-up by superficial linear velocity (SLV) is not proportional to (PlV). However, by using these curves scale-up at constant (PR) can be used to determine the required SLV. 3. Experience indicates that the PN relationship is not affected by non-Newtonian fluids below 6000 cps apparent viscosity. 4. If the air temperature at the bottom of the fermenter is less than the liquid temperature, there is a gain in PN. This is due to the fact that at a lower temperature, the air density is greater, and heat is transferred from the broth to the bubbles (isothermal expansion) resulting in more work (Pm or kinetic energy imparted to the broth by turbulence. 5. If the fermenter vent valve is restricted to increase the pressure above the broth, it has the effect of reducing PN, but oxygen transfer increases due to the greater partial pressure of oxygen. There have been reports of air dispersion with improved oxygen transfer using static mixers attached to the air ring. Two papers on static mixers were given by Smith and Koch at the Mixing (Engineering Foundation) Conference in Rindge, NH (1 977). Additional papers can be found in the waste treatment field. There is additional energy to be gained from aeration. In order for the air to enter a tank below the liquid surface, the pressure in the sparging device must exceed the static head pressure. Thus the mass of air has a determinable velocity through the orifices of the sparger. The force exerted against the liquid is F=@/2g. That is, for a fixed mass flow rate of air, the force varies as the velocity squared. The velocity of air through a nozzle is a function of the (absolute) pressure ratio on each side ofthe orifice, and it can be increased to sonic velocity. The time of flow through an orifice is so short there is no heat transferred from the broth to the air and the air temperature drops. The expansion of air at sonic velocity is isentropic (adiabatic). The horsepower obtained by the isentropic expansion of air (at any pressure ratio) is (see Perry and Chilton.)[14]:
