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 |
A’CS |
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%º
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 |
BFi·SFi |
[-] |
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) |
F’MD |
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) |
F’SP |
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 |
Md’i,0 |
in lbs |
Ungassed torque of the impeller for the i-impeller. |
| Gassed torque |
Md’i,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 |
Md’TOT,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 |
Md’TOT,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 |
P’i,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 |
P’i,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) |
P’IEG,MD /V’LIQ |
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) |
P’IEG,SP /V’LIQ |
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 |
P’MOTOR |
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 |
P’TOT,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 |
P’TOT,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 |
P’TOT,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 |
P’TOT,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) |
Q’G,SCFH |
SCFH |
Gas flow rate under standard conditions converted to cubic feet per hour. |
| gas flow rate(standard) |
Q’G,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) |
Q’G,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) |
Q’G,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 |
Q’i,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 |
Q’LIQ,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 |
[-] |
Reynold’s 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 (Reynold’s 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) |
v’SP,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) |
v’SP,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 tank’s 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. |
