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]: