Post Mixing Optimization and Solutions
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Parameter
Symbol
Units
Explanation of parameters
alpha a [-] Factor that describes the ratio of kLa in the media as compared to the kLa in water/air under identical conditions of power and gas flow rate.
1/(w/T) (wBAF/T)-1 [-] Inverse of the baffling ratio.
A A Constant in the kLa equation.  A is a function of Theta, viscosity factor, and kLa-factor.
Coil surface area ACOIL m2 Heat transfer surface area.
Cross sectional area of tank ACS m2 This is the area of the circular cross section of the cylindrical part of the reactor, tank, vessel, or fermenter. This is the metric unit.
Cross sectional area of tank ACS ft2 This is the area of the circular cross section of the cylindrical part of the reactor, tank, vessel, or fermenter. American units.
B B Exponent on P/V.
Baffle type(=BAF): BAF Style of baffle: Straight standard, F, D, Beaver-Tail, special or none. Could also be hollow for heat transfer.
Percent baffled BAF% % Percent of baffling. 100% NB = 0.4
Recommended % of normal baffles BAF%REC % Based on viscosity, this factor states what the recommended baffle width (in % or standard) should be for Rushton Turbines.
Henzler Baffle Factor for Mixing BFHENZLER,MIX [-] Henzler baffle factor for mixing.
Henzler Baffle Factor for power BFHENZLER,P [-] Henzler Baffle Factor for Power
Baffle Power Factor * Swirl Factor BFiSFi [-] Baffle Power Factor * Swirl Factor for the i-impeller.
Oldshue Baffle Factor for Power BFOLDSHUE,P [-] Oldshue Baffle Factor for Power.
Oldshue Baffle Factor for power BFOLDSHUE,P [-] Oldshue Baffle Factor for Power
C C   Exponent on F or vsg.
c*(Head Space) with reaction c*ACTUAL,TOP ppm Actual c* at the top of the reactor, tank, vessel, or fermenter, which is in equilibrium with the off-gas concentration of oxygen.
c*(H2O,O2) at 1 bar and temp c*H2O/O2 ppm c-star of clean water/oxygen (in air) at 1 bar and process temperature
c*(H2O,O2)(bottom) c*H2O/O2,BOT ppm c* of clean water/oxygen (in air) at the bottom and process temperature
c*(H2O,O2)(i) c*H2O/O2,i ppm c* of clean water/oxygen (in air) at i-impeller and process temperatur
c*(H2O,O2)(mid-depth) c*H2O/O2,MD ppm c* of clean water/oxygen (in air) at mid-depth and process temperature
c*(H2O,O2)(sparge) c*H2O/O2,SP ppm c* of clean water/oxygen (in air) at the sparge and process temperature
c*(H2O,O2)(Head Pressure) c*H2O/O2,TOP ppm c* of clean water/oxygen (in air) at head pressure and process temperature
c*(LnMean) c*LnMean ppm Log mean average of c* from the bottom of the reactor, tank, vessel, or fermenter (oxygen inlet) to the top of the reactor, tank, vessel, or fermenter (oxygen outlet)
Coil type(=COIL): COIL   Style of coil. Examples: None, helical coils, vertical coils, vertical plate coils or other.
Ungassed COV/D COVi,0 /Di [-] Ratio: Distance above an impeller to the liquid surface (coverage) to impeller diameter when the reactor, tank, vessel, or fermenter is ungassed for the i-impeller.
Gassed COV/D COVi,G /Di [-] Ratio: Distance above an impeller to the liquid surface (coverage) to impeller diameter when the reactor, tank, vessel, or fermenter is gassed for the i-impeller.
Chem Scale CSi ft/min ChemScale: A term from Chemineer to show the intensity of agitation for the i-impeller.
Coil swept diameter dCOIL mm For helical coils: CL of coil to shaft center times 2; For vertical coils and vertical plate coils: inner and outer swept diameters.
Hole diameter dHOLE mm For pipe sparge: hole diameter = pipe diameter. For ring sparge: diameter of the holes where the gas (air) comes out.
Disk diameter(i) di,DISK mm Diameter of the i-disk of a Rushton-type impeller. Only valid for impellers with a disk.
d(disk)/D di,DISK/Di [-] Ratio: Disk diameter to impeller diameter for the i-impeller.
Hub diameter(i) di,HUB mm Diameter of the hub of the i-impeller. This is the metal that holds the impeller onto the shaft.
d(hub)/d(disk) di,HUB /di,DISK [-] Ratio: Hub diameter to disk diameter for the i-impeller.
Manway diameter dMW mm The inner diameter of the manway. If there is no manway, the inner diameter of the tank. This is useful when determining the maximum size impeller that can be put into the tank.
Pipe diameter dPIPE, SP mm Inner diameter of the sparge pipe.
Coil pipe diameter dPIPE,COIL mm For helical and vertical pipes: Outer diameter of pipes; For vertical plate coils: overall thickness of the plates.
Shaft diameter(bottom) dSHAFT,BOT mm If there is a step down in shaft size, this is the diameter near the lowest impeller.
Bottom Shaft d/T dSHAFT,BOT/T [-] Ratio: Shaft diameter near the bottom of the reactor, tank, vessel, or fermenter above the steady bearing to tank diameter.
Shaft diameter(middle) dSHAFT,MID mm If the shaft is stepped down in size, this is the diameter of the shaft in the middle of the reactor, tank, vessel, or fermenter. If there is only one step down, this in irrelevant.
Middle Shaft d/T dSHAFT,MID/T [-] Ratio: Shaft diameter in the middle of the reactor, tank, vessel, or fermenter to tank diameter.
d(shaft)/d(disk) dSHAFT,T /di,DISK [-] Ratio: Shaft diameter to impeller disk diameter for the i-impeller.
Shaft diameter(top) dSHAFT,TOP mm Diameter of the shaft near the entry to the reactor, tank, vessel, or fermenter.
Top Shaft d/T dSHAFT,TOP/T [-] Ratio: Shaft diameter near the top of the reactor, tank, vessel, or fermenter (near seal) to tank diameter.
Swept CL diameter dSP mm CL=Center Line. For ring sparge: Center diameter of the sparge. For pipe: distance from pipe opening to shaft center times 2.
D(sparge)/D(bottom) dSP/DB [-] Ratio: Sparge diameter to bottom impeller diameter. For a pipe it is the outlet diameter.
Bottom head thickness DBOT mm Thickness of the bottom dish. Often found on data describing the ASME pressure testing of the tank.
Impeller diameter(i) Di mm Swept diameter of the i-impeller.
D/T Di/T [-] Ratio: Impeller diameter to tank diameter for the i-impeller
Mass transfer driving force DFLnMean ppm The log mean driving force of the oxygen mass transfer
DO [% of Saturation] DO % Dissolved Oxygen in percent of the saturated value.
DO at 1 bar pressure and temp DO1,t ppm Dissolved Oxygen in parts per million at 1 bar and process temperature.
DO(actual) at pressure and temp DOMD,t ppm Dissolved Oxygen in parts per million at mid-depth pressure and temperature.
DO(Sat) at 1 bar and temp DOSAT ppm Dissolved oxygen concentration at saturation at 1 bar, process temperature and process media.
dZ(i) dZi mm Liquid depth of an impeller zone above and below the i-impeller for the i-impeller.
dZ(i)/T dZi /T [-] Ratio of the impeller zone liquid depth to tank diameter for the i-impeller.
Gas Hold-up eG [%] The amount of volume increase due to the sparging of the media with air. This does not include a stable foam layer.
Gas Hold-up (Post) eG,POST % Gas hold-up according to Post.
Gas Hold-up Smith eG,SMITH % Gas hold-up according to Smith.
Gas Hold-up Whitton eG,Whitton % Gas hold-up according to Whitton.
Motor efficiency effMOTOR % Motor efficiency. The standard value can be found on the nameplate. Best is to acquire a motor curve for each system from the vendor.
Superficial gas velocity (mid-depth) FMD ft/min The actual superficial gas velocity at mid-depth at operating conditions, assuming no consumption of oxygen, in American units.
Superficial gas velocity (sparge) FSP ft/min The actual superficial gas velocity at sparge-depth at operating conditions, assuming no consumption of oxygen, in American units.
Superficial gas velocity (mid-depth) F'MD,ft/s ft/s The actual superficial gas velocity at mid-depth at operating conditions, assuming no consumption of oxygen, in American units.
Superficial gas velocity (sparge) F'SP,ft/s ft/s The actual superficial gas velocity at sparge-depth at operating conditions, assuming no consumption of oxygen, in American units.
Fr(i) Fri [-] Froude Number for the i-impeller. It is usually used to determine the affinity to vortexing.
Henry (Water/O2)=f(temperature) HH2O/O2 bar/ppm Henry coefficient for water/oxygen in air.
Blade height(i) hi mm Height of each blade of the i-impeller. For Smith Turbines, hydrofoils, and pitched bladed turbines use projected height of the blade (z-dimension).
Hub height(i) hi,HUB mm Height of the hub of the i-impeller.
h/D hi/Di [-] Ratio: Blade height to impeller diameter for the i-impeller.
standard h/D hi/Di,STD [-] h/D of a standard impeller of this type for the i-impeller.
Amperes IMOTOR Amps Motor amperes can be found on the nameplate.
Overall Interstage mixing efficiency factor IEFAVG (x) This is a factor that describes the rate of mixing exchange between impellers. This number represents an overall average of all impellers in the reactor, tank, vessel, or fermenter. A more precise model contains individual factors for each pair of impellers. Whereas Rushton Turbines (RT) will have a high number, axial foil hydrofoils will have a very low number. The lower the number the faster the mixing.
Impeller Type(=i): IMPi   Type of impeller.
Design k-factor KFi % Ratio of the power under gassed conditions as compared to ungassed conditions at the same impeller speed for the i-impeller. There is no overall k-factor as there is for SF, because each impeller has different characteristics.
Literature k-factor KFLIT,i % Literature k-Factor for Rushton Turbines for the i-impeller.
Impeller design kLa kLaIMP hr-1 Mass transfer coefficient kLa (of the impeller design)
Required process kLa kLaPROC hr-1 Mass transfer coefficient kLa (of the process)
Baffle length LBAF mm Vertical distance from the bottom of the baffle to the top of the baffle.
L(baffle)/T LBAF/T [-] Ratio: Length of a baffle to tank diameter.
Coil length LCOIL mm Total length of coil pipe.
Shaft length LSHAFT mm For top entry, inside length of shaft from head to the bottom of the shaft. For bottom entry, from bottom to top of shaft. This is the total length of the shaft within the reactor, tank, vessel, or fermenter.
Ungassed torque Mdi,0 in lbs Ungassed torque of the impeller for the i-impeller.
Gassed torque Mdi,G in lbs Gassed torque of the impeller for the i-impeller.
Ungassed Total Torque MdTOT,0 Nm The sum of all individual impeller torques.
Ungassed Total Torque MdTOT,0 in lbs The sum of all individual impeller torques.
Torque MdG MdTOT,G Nm This is the sum of the individual impeller torques.
Torque MdG MdTOT,G in lbs This is the sum of the individual impeller torques.
Torque nameplate MdMOTOR Nm Motor torque.
Number of baffles nBAF [-] Number of baffles in the reactor, tank, vessel or fermenter.
Number of coil bundles nCOIL [-] Bundles are groups of similar coil structures.
Number of holes nHOLE [-] For pipe sparge: number = 1; for ring sparge: number of holes for the gas (air) to come out.
Number of blades(i) ni,BLADES [-] Number of blades of the i-impeller.
Number of impellers nIMP [-] Number of impellers on the shaft.
Number of pipes nPIPE [-] Number of pipes in each bundle.
Impeller Speed N RPM Rotational speed of the impellers.
Maximum impeller speed NMAX RPM Maximum impeller speed. Often this is at 60 Hz on the frequency drive for variable speed drives. Some drives may run at higher frequencies. For a two-speed motor, this is the higher speed. This is the same as the typical speed for fixed speed drives.
Minimum impeller speed NMIN RPM Minimum speed that the agitator can be run at. It is not 1 for variable speed drives. For a two-speed motor, this is the lower speed. This is the same as the typical speed for fixed speed drives.
Maximum Motor Speed NMOTOR RPM Output motor speed.
Typical impeller speed NTYP RPM Typical impeller speed, which is process specific for variable speed drives or the speed of a fixed speed drive.
World Nae for current dispersion for the bottom impeller NaeB,W % World definition of Aeration Number for the current dispersion of the bottom impeller.
World Nae for a flooded dispersion for the bottom impeller NaeB,W, FLOODED % World definition of Aeration Number for the transition of flooded to intermediate dispersion for the bottom impeller.
World Nae for a great dispersion for the bottom impeller NaeB,W, GREAT % World definition of Aeration Number for the transition of intermediate to well dispersed (great) dispersion for the bottom impeller.
LIGHTNIN Nae for a flooded dispersion NaeL,FP,i % Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.
LIGHTNIN Nae for current dispersion NaeL,i % Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.
LIGHTNIN Nae for a great dispersion NaeL,WD,i % Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.
World Nae for a flooded dispersion NaeW,FP,i % World definition Aeration number for the transition between intermediate and flooded gas dispersion at impeller i conditions for the i-impeller.
World Nae for current dispersion NaeW,i % World definition Aeration number at impeller i conditions for the i-impeller.
World Nae for a great dispersion NaeW,WD,i % World definition Aeration number for the transition between intermediate and well dispersed (Great) gas dispersion at impeller i conditions for the i-impeller.
NB (Baffle Number) NB [-] Baffle number. Describes the relative area of resistance to flow.
Np0 Npi,0 [-] Ungassed power number for the i-impeller.
Np(g) Npi,G [-] Gassed power number (operating conditions) for the i-impeller.
Nq Nqi [-] Flow Number. Dimensionless fluid flow rate for the i-impeller.
Off-bottom impeller ratio OBB /DB [-] Ratio: Bottom impeller off-bottom to bottom impeller diameter
Baffle off-bottom OBBAF mm OB= Off Bottom. Vertical distance from the lowest point of the baffle to the inner bottom of the reactor, tank, vessel, or fermenter.
Steady bearing off-bottom OBBOT,SB mm Height of the center of the bottom steady bearing or limit ring from the tank bottom.
Coil off-bottom OBCOIL mm Off Bottom distance to bottom of coils.
Off-Bottom of dip tube OBDIP mm Distance of the outlet of a dip tube to the bottom of the tank.
Off-bottom(i) OBi mm Off bottom distance from the inner center bottom of the tank to the vertical midpoint of the i-impeller. For Rushton Turbines it is to the disk centerline.
Int. steady bearing off-bottom OBINT,SB mm Height of the center of the intermediate steady bearing or limit ring from the tank bottom.
Sparger CL off-bottom OBSP mm For pipe sparge: Off bottom distance to center of opening; For ring sparge: Off bottom to center of pipe.
OB(sparge)/D OBSP/DB [-] Ratio: Off bottom distance of the sparge to bottom impeller diameter
OB(sparge)/D(sparge) OBSP/DSP [-] Ratio: Off bottom distance of the sparge to sparge diameter
Measured OTR OTR mmol O2/L hr Oxygen Transfer Rate is the rate of transfer of oxygen as a result of the dispersion of gas from the impellers.
Design OTR OTR IMP gr/L/hr Oxygen Transfer Rate based on impeller characteristics
OTR (based on N and QG) OTR N,QG mmol/L/hr Oxygen Transfer Rate based on given N and QG
Process OTR OTR PROC gr/L/hr Oxygen Transfer Rate based on process characteristics
Baffle off-wall OWBAF mm OW= Off Wall. Horizontal space between the tank sidewall and the side of the baffle closest to the wall.
P(bottom) >pBOT bar Total pressure at the bottom
BackPressure pBP bar This is the additional pressure above the station pressure that is put into the reactor, tank, vessel, or reactor.
P(i) pi bar Total pressure at the i-impeller
P(mid-depth) pMD bar Total pressure at mid-depth
P(sparge) pSP bar Total pressure at the sparge
Station Pressure pSTAT bar This is the true atmospheric pressure on the outside of the reactor, tank, vessel or fermenter during a recorded run. This is different from the reported barometric pressure. The barometric pressure is corrected down to sea level from the actually measured station pressure. It is important to know the distance above sea level to achieve the station pressure if only the barometric pressure is known.
P(Head Pressure) pTOP bar Total pressure at the top of the tank
Measured Power P kW The measured power draw at the motor.
Ratio of measured/calc Power P/ PTOT,G [-] How does the measured power compare to the calculated operating power?
Ungassed Power Pi,0 kW Ungassed power consumption of the impeller, metric units for the i-impeller.
Ungassed Power Pi,0 Hp Ungassed power consumption of the impeller, American units for the i-impeller.
Gassed Power Pi,G kW Gassed power consumption of the impellers, metric units for the i-impeller.
Gassed Power Pi,G Hp Gassed power consumption of the impeller, American units for the i-impeller.
Iso-thermal expansion Power/Volume(mid-depth) PIEG,MD/ VLIQ kW/m3 Based on the power per volume given off to the fluid of the rising gas bubbles at mid-depth.
Iso-thermal expansion Power/Volume(mid-depth) PIEG,MD /VLIQ Hp/kgal Based on the power per volume given off to the fluid of the rising gas bubbles at mid-depth. (kgal = 1000 US gallons)
Iso-thermal expansion Power/Volume(sparge) PIEG,SP/ VLIQ kW/m3 Based on the power per volume given off to the fluid of the rising gas bubbles at spage-depth.
Iso-thermal expansion Power/Volume(sparge) PIEG,SP /VLIQ Hp/kgal Based on the power per volume given off to the fluid of the rising gas bubbles at sparge-depth. (kgal = 1000 US gallons)
Motor Power PMOTOR Hp American units of the motor power.
Maximum Impeller Power PMAX kW Maximum power drawn. Often this is at 60 Hz on the frequency drive. Some drives may run at higher frequencies. This is at NMAX.
Minimum impeller power PMIN kW Minimum power that the agitator can be run at. This is at NMIN.
Motor HP nameplate PMOTOR kW Motor power can be found on the nameplate.
Motor Power PMOTOR kW Metric units of the motor power.
Motor P / V total PMOTOR/VTOT kW/m3 Theoretical P/V when the motor is running full out and the reactor, tank, vessel, or fermenter is completely full.
Ungassed total shaft power PTOT,0 kW Total power imparted from the impellers to the fluid with no aeration.
Ungassed total shaft power PTOT,0 Hp Same as PTOT,0, but in American units.
Ungassed power per unit ungassed volume PTOT,0/VLIQ kW/m3 Self-explanatory.
Ungassed power per unit ungassed volume PTOT,0/ VLIQ Hp/kgal Self-explanatory. This is 1/5 of the metric unit. (kgal = 1000 US gallons)
Total operating shaft power PTOT,G kW Total power imparted from the impellers to the fluid under actual operating conditions. If there is no aeration this is the same as the ungassed total shaft power.
Gassed total shaft power PTOT,G Hp Same as PTOT,G, but in American units.
Ratio of calc/measured powers PTOT,G/P [-] How does the calculated operating power compare to the measured power?
Power Ratio Imp/Gas at mid-depth PTOT,G/PIEHP,MD [-] Ratio total impeller power to gas expansion power based on conditions at reactor, tank, vessel, or fermenter mid-depth.
Power Ratio Imp/Gas at the sparge PTOT,G/PIEHP,SP [-] Ratio total impeller power to gas isothermal expansion power based on conditions at the sparge pipe or ring.
Gassed power per unit ungassed volume PTOT,G/VLIQ kW/m3 Self-explanatory.
Gassed power per unit ungassed volume PTOT,G/ VLIQ Hp/kgal Self-explanatory. This is 1/5 of the metric unit. (kgal = 1000 US gallons)
Typical impeller power PTYP kW This is often process specific. This is a typical power draw at NTYP.
Typical maximum head pressure PTYP,BP bar Typical head pressure put on the reactor, tank, vessel, or fermenter.
PF(D2) PF(D2)i [-] Proximity Factor for D2 flow patterns for the i-impeller.
PF(D3) PF(D3)i [-] Proximity Factor for D3 flow patterns for the i-impeller.
PF(R1 and R2) PF(R1,R2)i [-] Proximity Factor for R1 and R2 flow patterns for the i-impeller.
PF(U3and U2) PF(U2,U3)i [-] Proximity Factor for U2 and U3 flow patterns for the i-impeller.
Proximity Factor PFi [-] Proximity Factor. A relative value of ungassed power based on geometrical location of an impeller in a tank compared to a standard location for the i-impeller.
Ungassed Power Split PSi,0 % Ungassed Power Split. % of total power for this impeller for the i-impeller.
Gassed Power Split PSi,G % Gassed Power Split. % of total power for this impeller for the i-impeller.
Top Impeller power split PSi,G % Percentage of the total power being consumed by the i-impeller.
O2 vol. feed rate/volume qO2,IN nm3/L/hr Volume specific volumetric flow rate of pure oxygen in the feed at normal conditions
Coolant rate QCOIL kg/hr Flow rate through the heat exchanger coils.
Gas Flow Rate QG nm3/hr The flow rate of the gas (for example air) into the reactor, tank, vessel or fermenter under normal conditions (1 bar and 20oC).
Gas Rate Maximum QG,MAX nm3/hr The maximum normal gas rate you can put through the sparge pipe or ring.
gas flow rate(normal) QG,nLPM nLPM Gas flow rate under standard conditions converted to Liters per Minute.
gas flow rate(standard) QG,SCFH SCFH Gas flow rate under standard conditions converted to cubic feet per hour.
gas flow rate(standard) QG,SCFM SCFM Gas flow rate under standard conditions converted to cubic feet per minute.
QG(mid-depth) QG,MD,aLPM aLPM Actual gas flow rate at mid-depth under operating conditions, assuming no consumption of oxygen.
QG(mid-depth) QG,MD,m3/hr m3/hr Actual gas flow rate at mid-depth under operating conditions, assuming no consumption of oxygen.
QG(mid-depth) QG,MD,m3/min m3/min Actual gas flow rate at mid-depth under operating conditions, assuming no consumption of oxygen.
QG(mid-depth) QG,MD ACFM Actual gas flow rate at mid-depth under operating conditions, assuming no consumption of oxygen.
QG(sparge) QG,SP,aLPM aLPM Actual gas flow rate at sparge-depth under operating conditions, assuming no consumption of oxygen.
QG(sparge) QG,SP,m3/hr m3/hr Actual gas flow rate at sparge-depth under operating conditions, assuming no consumption of oxygen.
QG(sparge) QG,SP,m3/min m3/min Actual gas flow rate at sparge-depth under operating conditions, assuming no consumption of oxygen.
QG(sparge) QG,SP ACFM Actual gas flow rate at sparge-depth under operating conditions, assuming no consumption of oxygen.
Gas flow rate at the impeller Qi,G ALPM Actual gas flow rate at the impeller assuming no consumption of oxygen for the i-impeller.
Gas flow rate at the impeller Qi,G ACFM Actual gas flow rate at the impeller assuming no consumption of oxygen for the i-impeller.
Flooded Minimum Gas Flow Rate Qi,FLOODED ALPM Minimum gas flow rate that begins flooding for the i-impeller.
Well Dispersed Maximum Gas Flow Rate Qi,GREAT ALPM Maximum gas flow rate that is still considerd well dispersed for the i-impeller.
Q(LIQ): Liquid flow rate QLIQ,i m3/hr Liquid flow rate generated directly from the impeller for the i-impeller.
Q(LIQ): Liquid flow rate QLIQ,i GPM Liquid flow rate generated directly from the impeller for the i-impeller.
O2 vol. feed rate QO2,IN nm3/hr Volumetric flow rate of pure oxygen in the feed at normal conditions
Bottom dish/knuckle radius rBOT mm The radius of the bottom dish and the radius of the bottom dish segment (knuckle) closest to the straight side. This info is found on tank drawings.
Top Dish/Knuckle radius rTOP mm The radius of the top dish and the radius of the top dish segment (knuckle) closest to the straight side. This info is found on tank drawings.
Gear Ratio RGEAR [-] Ratio of the motor speed to output impeller speed. This is often found on the nameplate or drawings from the vendor.
Ratio kW/(Volts*Amps/1000) RP/VI [-] This is a calculated value of the Motor HP nameplate, Volts and Amps of the motor. This ratio is fairly constant among brands and can be used to determine a value if one of the three other parameters are missing.
Re Rei [-] Reynolds Number. A dimensionless number that discribes the turbulence for the i-impeller.
Coil spacing sCOIL mm For helical and vertical pipes: Space between pipes; For plate coils, space between plates if in bundles.
Impeller spacing Si   mm Spacing (distance) between the i-impeller and the one below it.  The "spacing" of the bottom impeller is the OB.
S/D Si /Di [-] Ratio: Impeller spacing to impeller diameter for the i-impeller.
S(sparge)/D SSP/DB [-] Ratio: Space (distance) between the sparge and the bottom impeller to the impeller diameter.
SEff (automatic input) initial assumption to calc c*(top) SEff % Stripping Efficiency: The amount of oxygen stripped from the oxygen feed.
SEff calculated SEffCALC % Calculated SEff derived from a mass balance.
Overall Avg. Swirl&Viscosity Factor SFAVG [-] This factor is needed when the unaerated measured power and the calculated power do not match. In order to keep it simple, I have combine the two factors into one. Viscosity factors are generally >1 (except for Rushton Turbines) when Re (Reynolds Number) < 2000. Swirl factors are generally < 1, because coils and real baffles may not achieve the desired fully baffled condition. In the case of reactors, tanks, vessels or fermenters with more than 4 standard baffles, SF > 1.
Swirl&Viscosity Factor SFi [-] SF for the i-impeller. Under normal circumstances SFi = SFAVG unless there are geometrical differences to the rest of the reactor, tank, vessel, or fermenter.
Motor Service Factor SFMOTOR % Service factor of the motor. This value can be found on the nameplate.
Sparger type(=SP): SP   Description of the device that injects air or gas into the reactor, tank, vessel, or fermenter, such as pipe or ring, or rotating pipes.
Temperature t C Temperature at operating conditions inside the reactor, tank, vessel, or fermenter.
Outlet temperature tCOIL, OUT C Temperature exiting the coils.
Inlet temperature tCOIL,IN C Temperature entering the coils.
Stage MixTime(95%) ti,MIX s Stage mixing time for a 95% Degree of Mixing for the i-impeller.
Desired blending time tMIXDES s Desired overall mixing time in the tank.
Tank diameter T mm Inner diameter of the reactor, tank, vessel, or fermenter.
Tip Speed TSi m/s Tip Speed. Peripheral speed of the impeller blade tips for the i-impeller.
v(sparge exit velocity) vSP,EXIT m/s Actual exit gas velocity from the sparge pipe or sparge holes.
v(sparge exit velocity) vSP,EXIT ft/s Actual exit gas velocity from the sparge pipe or sparge holes, American units.
v(sparge pipe velocity) vSP,PIPE m/s Actual gas velocity through the pipe feeding the sparger.
v(sparge exit velocity) vSP,EXIT ft/s Actual exit gas velocity from the sparge pipe or sparge holes.
70% of the total fermenter volume. V70 Liters Volume when the reactor, tank, vessel, or fermenter is 70% full.
Volume of the baffles VBAF Liters Displacement volume of the baffles.
Bottom head volume VBOT Liters Volume of the bottom head.
ASME dish volume VBOT,a Liters Volume of an ASME bottom dish.
Other dish volume VBOT,o Liters Volume of a dish not matching any of the standards.
Semi-Elliptical dish volume VBOT,s Liters Volume of a semi-elliptical bottom dish.
Flat head volume VBOT.f Liters Volume of a flat bottom head.
Coil Volume VCOIL Liters Displacement volume of the coils.
Displacement Volume of Internals VDISP Liters Displacement volume of all internals in the reactor, tank, vessel, or fermenter.
Gassed liquid volume VG Liters Volume of gassed liquid in the reactor, tank, vessel, or fermenter.
Ratio: Gassed liquid volume to total tank volume. VG/ VTOT [%] Percent of total gassed volume.
Ungassed liquid volume VLIQ Liters Volume of ungassed liquid in the reactor, tank, vessel, or fermenter.
Ratio: Ungassed liquid volume to total tank volume. VLIQ/ VTOT [%] Percent of total ungassed volume.
Listed volume VLIST Liters Volume according to the tank vendor or listed on the tank drawings.
Volts VMOTOR Volts Motor volts can be found on the nameplate.
Dish volume for other dishes Vo Liters For dish shapes labeled as o (other), the actual volume of the dish or head.
Shaft Volume VSHAFT Liters Volume of the shaft within the reactor, tank, vessel, or fermenter.
Straight side volume VSS Liters Volume of the cylindrical portion of the reactor, tank, vessel, or fermenter.
Top head volume VTOP Liters Volume of the top head.
ASME dish volume VTOP,a Liters Volume of an ASME top dish.
Other dish volume VTOP,o Liters Volume of a dish not matching any of the standards.
Semi-Elliptical dish volume VTOP,s Liters Volume of a semi-elliptical top dish.
Flat head volume VTOP.f Liters Volume of a flat top head.
Total fermenter volume VTOT Liters Volume when the reactor, tank, vessel, or fermenter is completely full.
Typical volume at end VTYP, Liters Typical volume of the reactor, tank, vessel, or fermenter at the end of a run.
Typical volume at beginning VTYP,0 Liters Typical volume of the reactor, tank, vessel, or fermenter at the beginning of a run.
Typical gassed volume VTYP,G Liters This is process specific and will vary from process to process. This does not include foam height. This reflects typical values.
Superficial gas velocity (mid-depth) vsgMD m/min The actual superficial gas velocity at mid-depth at operating conditions, assuming no consumption of oxygen, in metric units.
Superficial gas velocity (mid-depth) vsgMD,m/s m/s The actual superficial gas velocity at mid-depth at operating conditions, assuming no consumption of oxygen, in metric units.
Superficial gas velocity (mid-depth) vsgMD,m/s m/s The actual superficial gas velocity at mid-depth at operating conditions, assuming no consumption of oxygen, in metric units.
Superficial gas velocity (sparge) vsgSP m/min The actual superficial gas velocity at sparge-depth at operating conditions, assuming no consumption of oxygen, in metric units.
Superficial gas velocity (sparge) vsgSP,m/s m/s The actual superficial gas velocity at sparge-depth at operating conditions, assuming no consumption of oxygen, in metric units.
Superficial gas velocity (sparge) vsgSP,m/s m/s The actual superficial gas velocity at sparge-depth at operating conditions, assuming no consumption of oxygen, in metric units.
vvm (normalized) vvm min-1 Volume of gas per minute per volume of liquid in the reactor, tank, vessel, or fermenter under standard conditions
vvm(i) vvmi min-1 Actual average gas rate for the i-impeller
vvm(mid-depth) vvmMD min-1 The actual vvm at mid-depth at operating conditions, assuming no consumption of oxygen.
vvm(sparge) vvmSP min-1 The actual vvm at sparge-depth at operating conditions, assuming no consumption of oxygen.
Width of baffles wBAF mm Distance from the side closest to the shaft to the side closest to the tanks wall.
Recommended wB wBAF,REC mm Self-explanatory. Assumes standard wBAF/T is 0.1 for water and determines wBAF.
w(baffle)/T wBAF/T [-] Baffling ratio: Width of the
baffles to tank diameter.
Recommended wB/T wBAF/TREC [-] Self-explanatory. Assumes standard is 0.1 for water.
Blade width(i) wi,BLADES mm Width of the blade of the i-impeller = distance of blade closest to the shaft to the blade farthest out from shaft.
w/D wi/Di [-] Ratio: Blade width to impeller diameter for the i-impeller.
Media Weight WLIQ kg Weight of the fluid media inside the reactor, tank, vessel, or fermenter.
O2 mass feed rate WO2,IN grO2/hr Mass flow rate of pure oxygen in the feed
O2 mass feed rate/volume wO2,IN grO2/L/hr Volume specific mass flow rate of pure oxygen in the feed at normal conditions
O2 Inlet Concentration yO2,IN Vol% Concentration of the oxygen in the gas feeding the reactor, tank, vessel, or fermenter through the gas-sparging device.
Oxygen Outlet Concentration yO2,OUT Vol% Concentration of the oxygen in the gas exiting the reactor, tank, vessel, or fermenter through the exhaust or condensor.
Bottom head height zBOT mm Height from bottom of the bottom dish to the flange. If welded, till the straight side starts.
ASME dish height zBOT,a mm Height of an ASME bottom dish.
Flat head height zBOT,f mm Height of a flat bottom head.
Other dish height zBOT,o mm Height of a dish not matching any of the standards.
Semi-Elliptical dish height zBOT,s mm Height of a semi-elliptical bottom dish.
Coil height zCOIL mm Height of coil from lowest point of the coils to the highest point of the coils.
Straight side height zSS mm Height of the straight side of the reactor, tank, vessel, or fermenter.
Overall tank height zTOT mm The total height of the reactor, tank, vessel, or fermenter consisting of the straight side and the height of the bottom and upper heads
Aspect ratio of the tank zTOT/T [-] Aspect ratio: Height to width ratio.
Top head height zTOP mm Height from top of the top dish to the flange. If welded, till the straight side starts.
ASME dish height zTOP,a mm Height of an ASME top dish.
Flat head height zTOP,f mm Height of a flat top head.
Other dish height zTOP,o mm Height of a dish not matching any of the standards.
Semi-Elliptical dish height zTOP,s mm Height of a semi-elliptical top dish.
Gassed liquid height ZG mm Height of gassed liquid in the reactor, tank, vessel, or fermenter.
Ratio: Gassed liquid level to tank diameter. ZG/T [-] Aspect ratio of the gassed liquid.
Ungassed liquid height ZLIQ mm Height of ungassed liquid in the reactor, tank, vessel, or fermenter.
Ratio: Ungassed liquid level to total tank height. ZLIQ/ ZTOT [%] Percent of total ungassed liquid height.
Ratio: Ungassed liquid level to tank diameter. ZLIQ/T [-] Aspect ratio of the ungassed liquid.
Typical liquid level at end ZTYP, mm Typical liquid level of the media in the reactor, tank, vessel, or fermenter at the end of a run.
Typical liquid level at beginning ZTYP,0 mm Typical liquid level of the media in the reactor, tank, vessel, or fermenter at the beginning of a run.


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