Batch Size selection for Scale-up & Feasibility Study

Hiii all, back after a long time .....!!!

Because of my stringent schedules, Can't check the comments and sorry for not replying to those, Apart from that i'm quite happy as followers were getting increased day to day, in parallel it was desperate as i'm not getting any author requests. 

Anyway, recently i've received a mail from a Process Engineer working in one of the top Pharma company, his name is Mr. Ram Prakash, and the query is, 

"How to select a batch size during scale up ? As mostly management is not interested in going for green field projects, how to select a appropriate batch size ?"

So, as per me the query is slightly a common issue, because in the early stages of process engineering during learning about scale-up techniques there will be lots and lots of things, but while coming to implementation, a process engineer should always think in company's favour and the decision that is taken should be in company's interest. As management always want high returns with low investments.

Rookie Process Engineer's may not accept this, but after gaining some experience one should accept it.

Also Read: 

How to calculate theoretical boil up in a reactor ? 

How to select pump, motor and line sizings required for pumping ?

Anyway, i'll explain you clearly with basic calculations and a general case study.

Usually Scale-up shall be done based on 5 parameters, those are:

1) Equating power per unit volume,

2) Equating Reynold's number,

3) Equating Tip speed,

4) Equating Shaft speed,

5) Equating Froude's number.

For additional information based on above mentioned parameters, Please visit: 
https://pharmacalc.blogspot.in/2015/05/api-scaleup-calculations.html

Scale-up's are most common in industries with certain amount of risk. Always there will be a some risk under every task, But a process engineer is treated as a true professional when the executed scale-up get succeeded with calculated risk. For that there may be many ways, out of which Power per unit volume is a basic and traditional path. Everyone knows that, but mostly not applied practically . 

Mostly the equipment selection shall be done based on availability (no offense to anyone). But the scale-up batch size selection most probably rests with a process engineer. And the available chance need to be capitalised properly.

Lets start with a case study, Consider a reaction and we need to scale it up.

Let it be some condensation / dehydration reaction. 

and initially the reaction [35 Kg batch size] is carried out in a 500 L SSR in small scale.

2000 L SSR is available for Scale-up,  Agitator remains the same as PBT.

Below is the Calculation :

Parameters	UOM	Values	Formulae
Reactor Capacity (REV)	L	500	-
Batch Size (B)	Kg	35	-
Reaction mass volume (RV)	L	265.3	7.6 volumes
% Occupancy (O%)	-	53.06	REV/V
Cylindrical height  (H)	m	0.865	-
Reactor ID  (D)	m	0.815	-
L/D	-	1.06134969	H/D
Agitator Dia (d)	m	0.46	-
% sweep (S%)	-	56.4417178	(d/D)*100
Torispherical Volume (Tv)	m3	0.04817956	0.089x(D^3)
Cylindrical Volume (Cv)	m3	0.45102538	0.785x(D^2)xH
Volume in Cylindrical section (Rcv)	m3	0.26525182	(Rv-Tv)/1000
Cylindrical height of Rxn. Mass (Rh)	m	0.50871378	Rcv/(0.785x(D^2))
L/D for RM	-	0.62418868	Rh/D
Agitator type	-	PBT	-
Np	-	5	-
RPM	-	96	-
RPS (N)	rps	1.6	RPM/60
Density of the Rxn. Mass ®	Kg/m3	780	-
P	J/S	329.013496	Np x r x (N^3) x (D^5)
P	KW	0.3290135	P/1000
V	m3	0.2653	Rv/1000
P/V	KW/m3	1.24015641	P/V

So as per the batch size of 35 Kg, the power per unit volume is 1.24 KW/Cu.m.

To learn how Height and Dia of reactor is calculated, follow below link:
http://pharmacalc.blogspot.com/2016/03/how-to-find-reactor-heat-transfer-area.html

To learn how to determine the volume occupied in a torispherical dish, follow below link:http://pharmacalc.blogspot.com/2016/03/how-tocalculate-volume-occupied-by.html

Now, we need to consider some random batch sizes, [ kindly don't ask me how to consider those random too, that depends on our common sense],

and perform the same calculation like we have done for 35 Kg batch size,

Parameters	UOM	Values							Formuale
Capacity	L	2000							-
Batch Size	Kg	70	80	90	95	100	110	120	-
Reaction mass volme	L	530.6	606.4	682.2	720.1	758	833.8	909.6	7.6 volumes
% Occupancy	-	26.53	30.32	34.11	36.01	37.9	41.69	45.48	REV/V
Cylindrical height	m	1.79	1.79	1.79	1.79	1.79	1.79	1.79	-
Reactor ID	m	1.4	1.4	1.4	1.4	1.4	1.4	1.4	-
L/D	-	1.28	1.28	1.28	1.28	1.28	1.28	1.28	H/D
Agitator Dia	m	0.56	0.56	0.56	0.56	0.56	0.56	0.56	-
% sweep	-	40	40	40	40	40	40	40	(d/D)*100
Torispherical Volume	m3	0.244	0.244	0.244	0.244	0.244	0.244	0.244	0.089x(D^3)
Cylindrical Volume	m3	2.754	2.754	2.754	2.754	2.754	2.754	2.754	0.785x(D^2)xH
Volume in Cylindrical section	m3	0.53	0.606	0.682	0.72	0.758	0.834	0.909	(Rv-Tv)/1000
Cylindrical height of Rxn. Mass	m	0.345	0.394	0.443	0.468	0.492	0.542	0.591	Rcv/(0.785x(D^2))
L/D for RM	-	0.25	0.28	0.32	0.33	0.35	0.39	0.42	Rh/D
Agitator type	-	PBT	PBT	PBT	PBT	PBT	PBT	PBT	-
Np	-	5	5	5	5	5	5	5	-
RPM	-	96	96	96	96	96	96	96	-
RPS (N)	rps	1.6	1.6	1.6	1.6	1.6	1.6	1.6	RPM/60
Density of the Rxn. Mass	Kg/m3	780	780	780	780	780	780	780	-
P	J/S	879.76	879.76	879.76	879.76	879.76	879.76	879.76	Np x r x (N^3) x (D^5)
P	KW	0.88	0.88	0.88	0.88	0.88	0.88	0.88	P/1000
V	m3	0.53	0.61	0.68	0.72	0.76	0.83	0.91	Rv/1000
P/V	KW/m3	1.66	1.45	1.29	1.22	1.16	1.06	0.97	P/V

After performing the calculation, it is clear that power per unit volume of only three batch sizes 90, 95, 100 Kgs were comparable to that of standard, and remaining four batches were out of bounds.

So, the conclusion is that if we are proceeding with 2000 L SSR, 90 Kgs, 95 KGs, 100 Kgs batch size is preferable and can be proceeded with calculated risk.

That's it....!!!

For automated Calculator follow the below link and download the spread sheet.

Reference Screen:

DOWNLOAD HERE

If any queries pl do comment or use contact me page.

Pl feel free to comment / contact.

Comments are most appreciated......!!!

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About The Author

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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.
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