1/(w/T)

(wBAF/T)^-1

[-]

Inverse of the baffling ratio.

A

A

Constant in the k_La equation.  A is a function of Theta, viscosity factor, and k_La-factor.

Coil surface area

A_COIL

m2

Heat transfer surface area.

Cross sectional area of tank

A_CS

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.

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BF_HENZLER,MIX

[-]

Henzler baffle factor for mixing.

Henzler Baffle Factor for power

BF_HENZLER,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

BF_OLDSHUE,P

[-]

Oldshue Baffle Factor for Power.

Oldshue Baffle Factor for power

BF_OLDSHUE,P

[-]

Oldshue Baffle Factor for Power

C

C

Exponent on F or vsg.

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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 temperature

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

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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

COV_{i,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

COV_{i,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

CS_i

ft/min

ChemScale: A term from Chemineer to show the intensity of agitation for the i-impeller.

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d_COIL

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

d_HOLE

mm

For pipe sparge: hole diameter = pipe diameter. For ring sparge: diameter of the holes where the gas (air) comes out.

Disk diameter(i)

d_i,DISK

mm

Diameter of the i-disk of a Rushton-type impeller. Only valid for impellers with a disk.

d(disk)/D

d_i,DISK/D_i

[-]

Ratio: Disk diameter to impeller diameter for the i-impeller.

Hub diameter(i)

d_i,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)

d_i,HUB /d_i,DISK

[-]

Ratio: Hub diameter to disk diameter for the i-impeller.

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d_MW

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

d_{PIPE, SP}

mm

Inner diameter of the sparge pipe.

Coil pipe diameter

d_PIPE,COIL

mm

For helical and vertical pipes: Outer diameter of pipes; For vertical plate coils: overall thickness of the plates.

Shaft diameter(bottom)

d_SHAFT,BOT

mm

If there is a step down in shaft size, this is the diameter near the lowest impeller.

Bottom Shaft d/T

d_SHAFT,BOT/T

[-]

Ratio: Shaft diameter near the bottom of the reactor, tank, vessel, or fermenter above the steady bearing to tank diameter.

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d_SHAFT,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

d_SHAFT,MID/T

[-]

Ratio: Shaft diameter in the middle of the reactor, tank, vessel, or fermenter to tank diameter.

d(shaft)/d(disk)

d_SHAFT,T /d_i,DISK

[-]

Ratio: Shaft diameter to impeller disk diameter for the i-impeller.

Shaft diameter(top)

d_SHAFT,TOP

mm

Diameter of the shaft near the entry to the reactor, tank, vessel, or fermenter.

Top Shaft d/T

d_SHAFT,TOP/T

[-]

Ratio: Shaft diameter near the top of the reactor, tank, vessel, or fermenter (near seal) to tank diameter.

Swept CL diameter

d_SP

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)

d_SP/D_B

[-]

Ratio: Sparge diameter to bottom impeller diameter. For a pipe it is the outlet diameter.

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D_BOT

mm

Thickness of the bottom dish. Often found on data describing the ASME pressure testing of the tank.

Impeller diameter(i)

D_i

mm

Swept diameter of the i-impeller.

D/T

D_i/T

[-]

Ratio: Impeller diameter to tank diameter for the i-impeller

Mass transfer driving force

DF_LnMean

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

DO_1,t

ppm

Dissolved Oxygen in parts per million at 1 bar and process temperature.

DO(actual) at pressure and temp

DO_MD,t

ppm

Dissolved Oxygen in parts per million at mid-depth pressure and temperature.

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DO_SAT

ppm

Dissolved oxygen concentration at saturation at 1 bar, process temperature and process media.

dZ(i)

dZ_i

mm

Liquid depth of an impeller zone above and below the i-impeller for the i-impeller.

dZ(i)/T

dZ_i /T

[-]

Ratio of the impeller zone liquid depth to tank diameter for the i-impeller.

Gas Hold-up

e_G

[%]

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)

e_G,POST

%

Gas hold-up according to Post.

Gas Hold-up Smith

e_G,SMITH

%

Gas hold-up according to Smith.

Gas Hold-up Whitton

e_G,Whitton

%

Gas hold-up according to Whitton.

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eff_MOTOR

%

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.

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Fr_i

[-]

Froude Number for the i-impeller. It is usually used to determine the affinity to vortexing.

Henry (Water/O2)=f(temperature)

H_H2O/O2

bar/ppm

Henry coefficient for water/oxygen in air.

Blade height(i)

h_i

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)

h_i,HUB

mm

Height of the hub of the i-impeller.

h/D

h_i/D_i

[-]

Ratio: Blade height to impeller diameter for the i-impeller.

standard h/D

h_i/D_i,STD

[-]

h/D of a standard impeller of this type for the i-impeller.

Amperes

I_MOTOR

Amps

Motor amperes can be found on the nameplate.

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IEF_AVG

(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):

IMP_i

Type of impeller.

Design k-factor

KF_i

%

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

KF_LIT,i

%

Literature k-Factor for Rushton Turbines for the i-impeller.

Impeller design k_La

k_La_IMP

hr^-1

Mass transfer coefficient k_La (of the impeller design)

Required process k_La

k_La_PROC

hr^-1

Mass transfer coefficient k_La (of the process)

Baffle length

L_BAF

mm

Vertical distance from the bottom of the baffle to the top of the baffle.

L(baffle)/T

L_BAF/T

[-]

Ratio: Length of a baffle to tank diameter.

Coil length

L_COIL

mm

Total length of coil pipe.

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L_SHAFT

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

Md_TOT,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 Md_G

Md_TOT,G

Nm

This is the sum of the individual impeller torques.

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Md^’_TOT,G

in lbs

This is the sum of the individual impeller torques.

Torque nameplate

Md_MOTOR

Nm

Motor torque.

Number of baffles

n_BAF

[-]

Number of baffles in the reactor, tank, vessel or fermenter.

Number of coil bundles

n_COIL

[-]

Bundles are groups of similar coil structures.

Number of holes

n_HOLE

For pipe sparge: number = 1; for ring sparge: number of holes for the gas (air) to come out.

Number of blades(i)

n_i,BLADES

[-]

Number of blades of the i-impeller.

Number of impellers

n_IMP

[-]

Number of impellers on the shaft.

Number of pipes

n_PIPE

[-]

Number of pipes in each bundle.

Impeller Speed

N

RPM

Rotational speed of the impellers.

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N_MAX

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

N_MIN

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

N_MOTOR

RPM

Output motor speed.

Typical impeller speed

N_TYP

RPM

Typical impeller speed, which is process specific for variable speed drives or the speed of a fixed speed drive.

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Nae_B,W

%

World definition of Aeration Number for the current dispersion of the bottom impeller.

World Nae for a flooded dispersion for the bottom impeller

Nae_{B,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

Nae_{B,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

Nae_L,FP,i

%

Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.

LIGHTNIN Nae for current dispersion

Nae_L,i

%

Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.

LIGHTNIN Nae for a great dispersion

Nae_L,WD,i

%

Same as world Nae but with the inclusion of Nq (Lightnin method) for the i-impeller.

World Nae for a flooded dispersion

Nae_W,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

Nae_W,i

%

World definition Aeration number at impeller i conditions for the i-impeller.

World Nae for a great dispersion

Nae_W,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.

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NB

[-]

Baffle number. Describes the relative area of resistance to flow.

Np0

Np_i,0

[-]

Ungassed power number for the i-impeller.

Np(g)

Np_i,G

[-]

Gassed power number (operating conditions) for the i-impeller.

Nq

Nq_i

[-]

Flow Number. Dimensionless fluid flow rate for the i-impeller.

Off-bottom impeller ratio

OB_B /D_B

[-]

Ratio: Bottom impeller off-bottom to bottom impeller diameter

Baffle off-bottom

OB_BAF

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

OB_BOT,SB

mm

Height of the center of the bottom steady bearing or limit ring from the tank bottom.

Coil off-bottom

OB_COIL

mm

Off Bottom distance to bottom of coils.

Off-Bottom of dip tube

OB_DIP

mm

Distance of the outlet of a dip tube to the bottom of the tank.

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OB_i

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

OB_INT,SB

mm

Height of the center of the intermediate steady bearing or limit ring from the tank bottom.

Sparger CL off-bottom

OB_SP

mm

For pipe sparge: Off bottom distance to center of opening; For ring sparge: Off bottom to center of pipe.

OB(sparge)/D

OB_SP/D_B

[-]

Ratio: Off bottom distance of the sparge to bottom impeller diameter

OB(sparge)/D(sparge)

OB_SP/D_SP

[-]

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 Q_G)

OTR _N,QG

mmol/L/hr

Oxygen Transfer Rate based on given N and Q_G

Process OTR

OTR _PROC

gr/L/hr

Oxygen Transfer Rate based on process characteristics

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OW_BAF

mm

OW= Off Wall. Horizontal space between the tank sidewall and the side of the baffle closest to the wall.

P(bottom)

p_BOT

bar

Total pressure at the bottom

BackPressure

p_BP

bar

This is the additional pressure above the station pressure that is put into the reactor, tank, vessel, or reactor.

P(i)

p_i

bar

Total pressure at the i-impeller

P(mid-depth)

p_MD

bar

Total pressure at mid-depth

P(sparge)

p_SP

bar

Total pressure at the sparge

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p_STAT

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)

p_TOP

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/ P_TOT,G

[-]

How does the measured power compare to the calculated operating power?

Ungassed Power

P_i,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

P_i,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)

P_IEG,MD/ V_LIQ

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