Credits: Pharmacalc.blogspot.com 
Hello readers, wishing you a very happie day for all of you,
Today i gonna demonstrate a way to Scale up Agitator, which is the main Hero in operations like Reaction, Extractions etc.
A wrong selection of agitator will leads to unimaginable situations, which cannot be tolerated in Pharma industries. Without a proper agitator there lacks efficiency in some operations which will impact the yield of product manufacturing directly/indirectly.
Before going into this topic directly i would like you to have some basic knowledge related to the terms that were used in this topic.
Difference Between Agitation and Mixing?
Agitation is the process of keeping a mixture that has been mixed in the proper mixed state required for the 'end' product.
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Mixing refers to the actual stirring of different liquids and/or materials to blend them together into an end product or mixture. Once this mixture is 'mixed' it may require agitation to keep the mixture in the proper 'mixed' state.
What is an Agitator?
An agitator is an piece of equipment which is used for mixing operations, it can be used inside reactors, drying equipment's, extraction equipment's etc.
What are the types of Agitator and What is its significance?
For this, read here: Types of Agitators and their Significance
What is the Basic principle involved in selecting an Agitator?
The basic principle involved in agitator selection is the power number resemblance as like in small scale.
What is Scale of Agitation?
Generally Agitation Scale is nothing but intensity of agitation, this Scale of agitation can be classified based on range of values
Scale of Agitation Range Values and their Significance over Agitation :
If Scale of Agitation is 1, then the effect of agitation is Mild, and this could be affordable when the operation is a crystallisation, that too if its a supersaturated Crystallisation.
If Scale of Agitation is 3, then the effect of agitation is Normal, this is most probably used for the Dryer's.
If Scale of Agitation is 6, then the effect of agitation is Vigorous, this means the mass that need to be stirred is somewhat denser but the bulk density will be not much.
If Scale of Agitation is 10, then the effect of agitation is Violent, this is applicable for the mass where there is need for extraction of product in between layers, and also the settling time during this extraction should be higher than regular cases.
If you have understood the above things clearly you are ready for next step, if not any queries feel free to ask.
Agitation ScaleUp:
For this We need some basic Data of Small Scale process like Vessel dia ( T1), Liquid level ( Z1 ), Liquid Density ( rho ), Liquid Viscosity ( myu ), Shaft Speed ( N1 ), Type of Agitator, D/T ration.
If you can gather all this data then our mission can be completed in minutes. And one major input we need to know is How Many times we need to ScaleUp.
ScaleUp ratio Calculation:
The Cubth Root value ratio of Large scale batch volume to small scale batch volume is ScaleUp ratio.
S = ( V2 / V1 ) ^ (1/3).
Shaft Speed Scaling have to be done based on the Scaling exponent, which depends upon the way of Scale up.
Scaleup to be done based on equaling atleast one of the following parameters,
1. Reynolds number
2. Power number.
3. Froude's number,
4. Shaft Speed,
5. Tip Speed.
The Scaling exponent will differs for all these 5, and they were tabulated below.
PARAMETER  SCALING EXPONENT 

Reynolds Number

2

Tip Speed

1

Power per Volume

2/3

Froude Number

1/2

Shaft Speed

0

And now there holds a relation between the scaling exponent and the shaft speed.
n/3 n
N2 = N1 x ( V1 / V2 ) = N1 x ( 1 / R )
So, Based on the Value obtained from the above relation we can calculate the following, if needed.
Reynolds number, Froude Number, Power per Volume, Pumping Rate, Pumping Velocity, Scale of Agitation.
Reynolds Number: Nre = D x D x N x rho / myu.
Tip Speed: Ts = 3.141 x D x N
Froude Number: Nfr = Nq x N x ( D ^ 3 )
Power Per Volume : P / V = Np x rho x ( N^3 ) x ( D^5 )
Pumping Rate: Q = Ts x ( 0.785 x ( T ^ 2 ) )
Pumping Velocity: Vs = Q / A.
Scale of Agitation : R = Pumping Velocity(Ft/min) / 6
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The Values for Flow Number Nq and Power Number Np can be found from the below tables.
For Example, i'll give you a sample case, with inputs as T1 = 250 mm, Z1 = 300 mm, N1 = 600, D / T = 0.4, water as solvent. and i wish to do scale up 100 times to the small scale.
Now, Lets start the show.
Scale Up ration, R = ( V2/ V1) ^(1/3) = ( 100 )^(1/3) = 4.64,
This scale up, i wish to do with equaling power / volume, so my scaling exponent is 2/3.
So RPM calculation, N2 = N1 x ( 1 / R )^n = 600 x ( 1 / 4.64 )^(2/3) = 216,
Reynold's number calculation, Nre = D^2 x N x rho / myu = 774264,
Tip Speed, G= pi x D x N = 5.24,
Flow number, Nq = 0.68 [For PBT, refer to the agitator curves above],
Pumping Rate, Q = Nq x N x D^3 = 0.24 m/sec,
Power Number, Np = 1.37 [for PBT],
Power required, P = Np x rho x N^3 x D^5 = 1.37 KW,
Power per Volume, P / V = 0.93 KW / Cu.m,
Bulk velocity, Vc = 4 x Q / ( 3.141 x Teq^2) = 0.2 m /sec,
Scale of Agitation, S = Vc / 0.03048 = 6.56
So, our Scale of Agitation need to be Vigorous.
That's it Cheers..........!!!!
Any queries happy to help,
Comments are Most appreciated....!!
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About The Author
Small query..
ReplyDeleteSo Np,Nq values depend on type of agitator or there is any relation b/w Re number,Np,Nq..xplain me briefly.
We r calc power req and for P/V calc..which volume hav to be taken(Scaleup volume i•e 100times factor) so determine me V,m3 in P/V calc.
Need Significance of bulkvelocity Vc ?? Finally scale of agitation formula Vc/? Please clear my tiny doubts.. cheerz tnx fr da informative post..
Np value depends upon the agitator, and the Nq value depends upon both reynolds number and agitator, and while calculating the power per volume, we need to consider the respective cases, for small scale, p/v calculation involves the small scale batch volume and same the case of scale up too, the intensity of agitation depends upon the bulk velocity as the velocity increases the scale of agitation increases, and actually the bulk velocity will be 6 times the scale of agitation and the bulk velocity will be in ft/min, so this 6 times will vary based on the units as if ft/min varies.
ReplyDeleteStill any queries, very happy to clear them.......!!
sir, can you please let me know the value of D you have taken and how did you get it in calculating the reynolds number in above calculation
ReplyDeleteD is dia of impeller
Deletesir, i am asking for numerical value of D which you used in calculating reynolds no
Delete0.463 m
DeleteHow can we increase the bulk density during crystallization stage. I mean which type of agitator we shud take.. PBT(clockwise or anti) ,gate,flat disk ..temp during centralization is 10deg.reactor moc is ss. Present bd is. 35 .future expected is. 48
ReplyDeletehow to decide constant power to volume and constant tip speed during scale up .
ReplyDeletehave to decide on what basis we are scalling up, thats our choice.
DeleteRegards,
AJAY K
could you please explani D units in Nre, rho? myu? and units
ReplyDeletebest regards,
Dheeraj
D is meters, rho is Kg/Cu.m, Myu is Kg/m.sec
DeleteRegards,
AJAY K
what is ment by pumping velocity is that velocity in reactor or somthing else? what is pumping rate. confused with that two please Explain
ReplyDeletepumping velocity is something what the impeller generates to reduce the pressure over the bottom mass, you can physically observe that the pressure exerted by the reaction mass over the bottom dish will reduce under agitation.
DeletePumping capacity(pumping rate) is what we can calculate from pumping velocity.
Regards,
AJAY K
I'll explain you in a simpler fashion, An impeller rotates reaction mass in a reactor like a pump that generates fluid motion throughout the tank, this pumping action propagates through out the tank by momentum transfer.
DeleteThe volumetric flowrate leaving the impeller blades is called pumping flowrate/rate.
Regards,
AJAY K
Thankyou..
ReplyDelete