# Pharma Engineering

For Engineer By An Engineer

• ## Friday, 13 May 2016 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.

How to Select a Condenser?
How to Calculate the Energy of Steam?

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 Scale-Up.

Scale-Up ratio Calculation:

The Cubth Root value ratio of  Large scale batch volume to small scale batch volume is Scale-Up 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.

Scale-up 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, Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.

1. Small query..
So 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..

2. 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.

Still any queries, very happy to clear them.......!!

3. 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

1. D is dia of impeller

2. sir, i am asking for numerical value of D which you used in calculating reynolds no

3. 4. How 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

5. how to decide constant power to volume and constant tip speed during scale up .

1. have to decide on what basis we are scalling up, thats our choice.

Regards,
AJAY K

6. could you please explani D units in Nre, rho? myu? and units

best regards,
Dheeraj

1. D is meters, rho is Kg/Cu.m, Myu is Kg/m.sec

Regards,
AJAY K

7. what is ment by pumping velocity is that velocity in reactor or somthing else? what is pumping rate. confused with that two please Explain

1. pumping 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.

Pumping capacity(pumping rate) is what we can calculate from pumping velocity.

Regards,
AJAY K

2. 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.

The volumetric flowrate leaving the impeller blades is called pumping flowrate/rate.

Regards,
AJAY K

8. 9. 10. There is another factor that comes into action.
that is Njs or just off bottom suspension.
could you please explain that with a practical example.

1. Dear Rajeev,

Yes, its true, surely it will have impact during stirring,
It is well explained here:
https://www.hindawi.com/journals/ijce/2012/945314/

Regards,
AJAY K

11. I observe that in your example, you scaled-up by 100 times, and the impeller rotation speed (from your calculations) must go down with scale-up. But by intuition, I believe if one has a larger batch, then the impeller rotation speed must be higher since it is required to agitate a lot more liquid than in the initial case. Am I right? Please explain.

Thanks,
Vembha.

1. Dear Vembha,

Happie to hear from you,
Basically there are many ways to scale-up,
1. Geometric scale-up - based on L/D ratio,
2. Dynamic scale-up, in this case we may vary RPM.

In Dynamic scale-up, we have to look after the P/V ratio as constant.

Regards,
AJAY K

12. This comment has been removed by the author.

13. dear sir which type of agitator used for drying in anfd with out failure of partical size and free folw

14. dear sir
which type of agitator used for anfd with out failure free flow of the dried materiel.and failure of partical size .plz give best suggestion

1. Hii Mohan,

There is no specific name for that agitator, it will be referred as a propeller / S shaped agitator. Particle size depends on the solids concentration in the reaction mass which is filtered and the agitation pattern that is preferred during isolation stage. ANFD agitator wont attribute that much to particle size.

As there will be two different pattern like cut and press mode which can be used to maintain consistency.

Best Regards,
AJAY K

15. Mr.Ajay, when you are explaining a concept from starting to ending you are going in detailed steps, but when it came to calculation part you used some values and finally said hence proved like that. It is better maintain that clarity at the ending also, as we are not understanding what are the numerical values you have considered. I'm totally confused.

In one comment you said diameter of impeller considered as 0.463m from where you got this value, I'm not understanding. Can you give me the clarity.? Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.