Scale-Up Calculator Tutorial - mcc- · PDF fileTutorial for Scale-Up Calculator, Version 2.0 Page 2 of 24 compaction variables for such a press, please contact MCC for more

Tutorial for Scale-Up Calculator, Version 2.0 Page 1 of 24

Scale-Up Calculator Tutorial The MCC Tableting Calculator Press speed is a major factor in tableting, and yet the commonly used measures of press speed (such as RPM, tablets per hour, dwell time, linear speed, etc.) do not take into account significant differences in press and tooling geometry, press deformation, tablet thickness, or depth of fill. Scale-up of tableting process involves shorter die feeding times (can affect tablet weight), smaller consolidation times (may lower compactibility), and faster ejection (can create cracks or lamination). At the same production rate, duration of tableting events depends on roll diameter, pitch circle diameter, number of stations, punch geometry, length of feed frame and the angle of ejection ramp. On the other hand, the speed of various tableting events becomes a limiting factor in press productivity. However, the same consolidation time will, most probably, ensure the same tablet quality, or, at least, bring the process to a close proximity of the target. To properly scale-up a formulation based on consolidation time: During a new formulation development, evaluate the minimum consolidation time

at which tablets of a satisfactory quality can be produced (i.e. the maximum compaction speed).

Calculate at what speed (RPM) different production presses can offer the

minimum satisfactory consolidation time, and what tablet output can be expected from different presses at that speed.

Algorithms and formulas of the MCC Tableting Calculator are based on extensive list of published papers and on our own investigations into the geometry and dynamics of tableting. Some sources are listed in Tableting.pdf in the c:\sc folder created on your computer after software installation (you will need an Adobe Acrobat Reader to access this file). We suggest that you read this file in its entirety before proceeding with this tutorial. Please note that sometimes the resulting fields are blank. Than means that not all press parameters are available in the database for calculations. If you need to calculate

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compaction variables for such a press, please contact MCC for more information. We will try to find the missing press parameters and update the database. In the reports, when a calculated field is blank, this may also mean that the press can not reach the requested velocity (e.g., it is outside the range of attainable speeds for this particular tablet press). The Tableting Calculator Algorithms

Consolidation time Ts calculation are based on geometrical parameters such as roll diameter, pitch circle diameter, punch geometry, depth of fill and in-die tablet thickness. Calculation formulas are based on the analysis of Rippie and Danielson (1981)

and represent extension of work by Muños Ruiz et al, (1992). Calculation of vertical punch displacement Zs during consolidation time is based

on depth of fill Hf and in-die thickness Hi. Calculations of Consolidation time Ts take into account a correction for press

deformation if the rate of deformation is known. A new, more accurate expression for dwell time calculation takes into account

the rotational motion of the punches. A proper formula to calculate decompression (relaxation) time is used for

estimation of all periods of the compaction event and the entire contact time. Definitions Feeding Time, Tf. Time when the die is fed with powder. Consolidation (Solidification) Time, Ts. The portion of Contact Time when punches are changing their vertical position in reference to the rolls decreasing the distance between their tips. Dwell Time, Td. The portion of Contact Time when punches are not changing their vertical position in reference to the rolls. Decompression (Relaxation) Time, Tr. The portion of Contact Time when punches are changing their vertical position in reference to the rolls increasing the distance between their tips before losing a contact with the rolls. Compression Time, Tp. The portion of Contact Time before the decompression period begins (Tp = Ts + Td). Contact Time, Tc. Time when both punches are moving having their tips in contact with the material that is being compacted, and their heads are in contact with the pressure rolls (Tc = Ts + Td + Tr). Ejection Time, Te. Time when the tablet is being ejected from the die


Total Time, Tt. Time required to produce one tablet on a press (including time between tablets). Feeding Efficiency Factor Ef = Tf/Tt, where Tf is a feeding time. Consolidation Efficiency Factor Es = Ts/Tt, where Ts is the time required to perform work of consolidation. Ejection Efficiency Factor Fe = Te/Tt, where Te is the time required to eject a tablet. About “Dwell Time” Dwell time is defined as a portion of the contact time when punches are not changing their vertical position with respect to the rolls, that is, when a flat portion of the punch head is in contact with the rolls. Note that dwell time (unlike contact time) as defined does not depend on the roll diameter. The notion of dwell time is largely misused or misunderstood. In fact, it should be used as a yardstick, a measure of linear (that is, tangential or angular) velocity and therefore it will depend on the punch geometry. The speed comparisons based on the dwell time assume that the punch has a flat head. The velocity then is the dwell time divided by the length of that flat portion. For the same linear velocity, the smaller is the punch head flat, the smaller is the dwell time. To everyone’s surprise, dwell time for dome-shaped punch heads is practically zero by definition, regardless of press linear velocity or RPM. That is why, compared to dwell time, linear velocity is a better measure of press speed. Calculations of dwell time in the MCC Tableting Calculator are based on a length of a punch head flat. By default, this value is conventionally set at 9.3 mm (R3, radius of the punch head flat = 4.65 mm). Since the flat portion is surrounded by a curvature, some published sources use different values. You can change the length of the flat portion of the punch head by adjusting the R3 parameter on the MCC Tableting Calculator screen. How to use the MCC Tableting Calculator for scale-up In order to properly scale-up a strain-rate sensitive formulation, you have to match not only force and tooling, but consolidation time (the most important factor), dwell time (linear speed) and contact time (depends on roll diameter) as well. In their seminal paper, Muñoz Ruiz et al. (1992) have described a failed attempt to scale-up a particular granulation from Korsch PH106 to Manesty Betapress. The failure was “surprising since the scale-up of the product from a single punch machine to a 6 station Korsch Pharmapress was conducted without any evidence of compaction problems”. The granulation turned out to be strain-rate sensitive, and further analysis indicated that “it is not possible to obtain the same dwell times” on the Korsch PH106 and Manesty Betapress. Let us use the MCC Tableting Calculator to forecast such scale-up problems. The easy way to learn the basics is to use the Tableting Calculator Wizard. It is self-explanatory.


To follow the problem as outlined in the above mentioned paper, use the Wizard as follows: At Step 1, select Korsch PH106 6-station press from the list of tablet presses. At Step 2, make sure the “Match” radio buttons indicate “Td”, that is, the Tableting Calculator is set to match dwell time, or linear speed. Note that your choices are mimicked on Panel 1 of the Tableting Calculator. At Step 3, move the speed slider all the way to the right to indicate the highest value, namely, 32,400 TPH, or 90 RPM, or 471 mm/sec horizontal punch velocity (linear speed). At Step 4, select Manesty Betapress 16 station press. Note that your choice is mimicked on Panel 2 (“The Matching Panel”) of the Tableting Calculator. Finish the Wizard and look at the panels. For clear comparison, on both panels set R3 = 4.65, d = 0.015, F = 3.0, Hf = 6 mm, Hi = 3 mm (these parameters affect either Consolidation time, or Dwell Time, or both). For the Korsch PH106 press, the Panel 1 on the left indicates Consolidation Time Ts = 31.4 ms, Dwell Time Td = 19.8 ms, Relaxation Time Tr = 18.2 ms, and Contact Time Ts = 69.3 ms.


Note that “?data” means missing data (in this case, missing information on the feed frame and ejection). Now, on the Matching Panel 2, the Manesty Betapress 16 station machine is selected.


In general, each time you click on Panel 2, the program will try to match the selected parameter (e.g., dwell time) between the primary press (Panel 1) and secondary press (Panel 2). The same 19.8 ms dwell time (same Horizontal Velocity or linear speed) for Betapress corresponds to 37,751 TPH, or 39.3 RPM, which is almost the lower limit of Betapress speed. Thus, the lowest speed of Betapress can match the highest Korsch PH106 speed in terms of dwell time, but this is highly impractical. Other compaction values are: Ts = 36.6 ms, Td = 19.8 ms (matching the Korsch), Tr = 21.4 ms, Tc = 77.8 ms. Even at this matching speed, the tablets would probably be somewhat harder on the Betapress because of a larger contact time.


To enable a comparison mode on the Panel 2, click on the Match Mode check box. The speed slider appears and the Panel title is changed to “The ‘Compare’ Panel”.


If we increase the Betapress speed on Panel 2 to more realistic 60,000 TPH = 62.5 RPM (by moving the speed slider), the Td is reduced to 12.4 ms that no Korsch PH106 can produce. Therefore, a proper scale-up of a product from Korsch PH106 to Betapress is not theoretically possible in terms of dwell time or linear speed, or consolidation times of compaction.


Now, switch to Panel 1 and select Betapress 16 stations at 62.5 RPM. Hit “Report” button to produce an Excel report listing all tablet presses at a fixed Td = 12.4.


A blank cell or “?data” in the report indicates lack of data in the database. If the value of Td is not equal to 12.4, it means that this particular press cannot reach the desired speed (either the press is too slow or too fast).

How to use the MCC Tableting Calculator to compare productivity of tablet presses When you have to select a tablet press, you can use the MCC Tableting Calculator to compare press output at the same consolidation time Ts that is the most crucial part of the compression cycle. For example, on Panel 1, select Fette PT 2090 IC 36 station press and move the speed slider to produce 100,000 TPH (that would correspond to 46.3 RPM or 20.2 ms consolidation time). As before, we set R3 = 4.65, d = 0.015, F = 3.0, Hf = 6 mm, Hi = 3 mm (these parameters affect either Consolidation time, or Dwell Time, or both).


Set the “Match” radio buttons to indicate “Ts”, that is, the Tableting Calculator is set to match consolidation times of different tablet presses. Now, on Panel 2, select Kikusui Libra2 36 single sided station press to obtain Ts = 20.2 (that would correspond to 90,000 TPH or 41.7 RPM).


One would be inclined to admit that PT 2090 is more efficient (Consolidation Efficiency Factor Es = 0.56) than Libra 2 (Es = 0.51). Note that Es is defined as the ratio of Consolidation Time Ts to total time required to produce a tablet. Now, switch to the “Match Mode” and select Kikusui Pegasus 1036 36 station press on Panel 2. You will see that, for the same consolidation time of 20.2 ms (108,669 TPH, 50.3 RPM), the Pegasus press makes more tablets and is more efficient (Es = 0.61) than the Fette 2090.


You can also set the “Match” radio buttons to indicate “Td + Ts” to see on Panel 2 the matching Pegasus speed (52.1 RPM), corresponding to Ts + Td = 29.6 ms.


This option will allow the MCC Tableting Calculator to match the sum of consolidation and dwell times of different tablet presses, and to produce a corresponding Excel report:

A blank cell or “?data” in the report indicates lack of data in the database. If the value of Ts + Td is not equal to 29.6, it means that this particular press cannot reach the desired speed (either the press is too slow or too fast). Yet another matching parameter may be the Av, the Average Punch Vertical Velocity per unit horizontal displacement that, some say, may be a good descriptor of a compaction event. We offer the Av calculation for completeness. However, based on our experience, we are of the opinion that Ts + Td is best suited for scale-up or product transfer. How to use the MCC Tableting Calculator to compare consolidation times of tablet presses For a fixed press output, some presses are better than others in terms of consolidation time Ts. For example, let us compare two different presses at the same production output. As before, we set R3 = 4.65, d = 0.015, F = 3.0, Hf = 6 mm, Hi = 3 mm (these parameters affect either Consolidation time, or Dwell Time, or both).


At the speed of 200,000 TPH (27.3 RPM), Fette PT 3090 IC 61 station press shows Ts = 20.6 ms.


while Korsch PH336 at the same 200,000 TPH (92.6 RPM) shows Ts = 11.0 ms. Obviously, for the same production output, tablets made on Fette 3090 will be somewhat harder than on Korsch 336.

How to use the MCC Tableting Calculator to select the best production press Obviously, many factors are involved in press selection. One of such factors should be suitability to a compaction task and productivity. Let us say that product development has established that a minimum of 22 ms of consolidation and dwell time is required for your formulation to make a decent tablet. Set the “Match” radio buttons to indicate “Ts + Td”, that is, the Tableting Calculator is set to match the sum of consolidation and dwell times of different tablet presses.

On Panel 1, select, for example, a Kilian TX 30A tablet press, and move the speed slider to get Ts + Td = 22 ms (this corresponds to 73.2 RPM). Hit “Report” button to produce an Excel report listing all tablet presses at a fixed Ts + Td.


A blank cell or “?data” in the report indicates lack of data in the database. If the value of Td is not equal to 22.0 ms, it means that this particular press cannot reach the desired speed (either the press is too slow or too fast).

From the report, it will be evident, for example, that the Ts + Td = 22 ms can be reached by Kikusui Gemini 1545 at 257,840 TPH (Td = 10.2 ms), and by Fette 2090 36 station press at 134,300 TPH (Td = 7.0 ms). It means that Gemini will make more tablets at the same consolidation + dwell time with a larger dwell time. If the press you have does not appear in the table, let us know, and we will update the data base for you.


The MCC Granulation End-Point Calculator

Algorithms and formulas of the MCC End-Point Calculator are based on an extensive list of published papers and on our own investigations into the geometry and dynamics of granulation. Some sources are listed in “Wet Granulation.pdf” in the c:\sc folder created on your computer after software installation (you will need an Adobe Acrobat Reader to access this file). We suggest that you read this file in its entirety before proceeding with this tutorial. Special attention should be devoted to the chapter entitled “Practical Considerations for End-Point Determination and Scale-Up”. The paper is published in the Encyclopedia of Pharmaceutical Technology by Francis and Taylor (2006). Another reference is: Michael Levin (ed)., Pharmaceutical Process Scale-Up, Second Edition, Taylor & Francis (2006).

The calculator has 4 main functions:

1. Calculate Net Impeller Power 2. Calculate Newton Power Number 3. Calculate Wet Mass Viscosity 4. Calculate Fill Ratio

How to use the MCC End-Point Calculator to calculate Net Impeller Power

Calculate Net Impeller Power, which is the target quantity for scale up, given wet mass density ρ, wet mass viscosity η, fill ratio h/d ~ m Vb / ρ, setup speed n, blade radius R, as well as the slope "a" and intercept "b" from the regression equation of the form

Ne = b * (Re * Fr * h/d)a

where Ne is Newton (power) number: Ne = P / (ρ n3 d5) Fr is Froude number: Fr = n2 d / g Re is Reynolds number Re = d2 n ρ / η For example, for ρ = 600 kg/m3, η = 0.0021 Pa*s (at Viscosity Factor = 7.40E-04), h/d = 0.539, n = 500 RPM, R = 0.11 m, a = -0.72, b=4.5, the end-point values are calculated to be (click “Calculate Net Impeller Power” button): Reynolds Number = 28809.5 Froude Number = 0.779 Newton Power Number = 36.3 Target Net Impeller Power = 203.2


How to use the MCC End-Point Calculator to calculate Newton Power Number

Recalculate Newton Power Number Ne, given Net Impeller Power ΔP (enter value in the appropriate field at the lower right corner), impeller speed n, blade radius R, and wet mass density ρ. This may be useful if you have established an end point in terms of some Net Impeller Power ΔP, and would like to reproduce this end point on the same mixer at a different speed or wet mass density (keeping the target Newton Power Number Ne).


For example, without changing anything from the preceding example, enter 350 into the “Enter Net Impeller Power” window and click “Calculate Net Impeller Power” button. The end-point values are calculated to be:

Reynolds Number = 28809.5

Froude Number = 0.779

Target Net Impeller Power = 350.0 (W)

Newton Power Number = 62.6


How to use the MCC End-Point Calculator to calculate Wet Mass Viscosity

Calculate wet mass viscosity η given Net Impeller Power ΔP (enter value in the appropriate field at the lower right corner), blade radius R and impeller speed n, using the following equations:

ΔP = 2π Δτ * n η = ϕ * Δτ / (n * R3)

where Δτ is the net torque required to move wet mass, n is the speed of the impeller, R is the blade radius, and ϕ is mixer specific "viscosity factor" relating torque and dynamic viscosity (note: ϕ can be established empirically by running a mixer with water that has dynamic viscosity η = 1 and measuring torque).

For example, if the “viscosity factor” for your specific mixer was found to be 0.000625, click “Enter New Viscosity Factor” and enter the number. For n = 400 RPM, R = 0.4 m, enter 385 into the “Enter Net Impeller Power” window and click “Calculate Viscosity” button. The results are calculated to be: Net Power = 385 W Wet Mass Viscosity calculated as 0.06597 Pa * s using Viscosity Factor = 6.25E-04


How to use the MCC End-Point Calculator to calculate Fill Ratio

Calculate Fill Ratio, given powder weight, granulating liquid density (1000 kg/m3 for water), rate of liquid addition, time interval for liquid addition, and bowl volume Vb. If liquid is added at once, then, instead of rate of liquid addition and time interval for liquid addition, enter liquid volume. The calculations are performed using the idea that the fill ratio h / d (wet mass height to blade diameter) is proportional to V / Vb, and wet mass volume V can be computed as

V = m / ρ


where m is the mass (weight) of the wet mass and ρ is the wet mass density. Now, the weight of the wet mass is computed as the weight of powder plus the weight of added granulating liquid. The latter, of course, is calculated from the rate and duration of liquid addition and the liquid density.

For example, using powder weight m=1.2 kg, liquid density ηL = 1000 kg/m3, bowl volume Vb = 4 l, rate of liquid addition = 21 ml/min, time of liquid addition = 270 s, and leaving the liquid volume field blank, press “Calculate Fill Ratio” button to see the following result: Fill Ratio 0.539 Note that this value now became visible in the “Fill Ratio” field ready to be used for other calculations.


Alternatively, if water was added all at once, you can enter liquid volume = 94.5 ml (leaving rate and time of liquid addition fields blank) and, clicking “Calculate Fill Ratio” button, see the same result.

______________________________________________________________________ Disclaimer: Although an utmost diligence was used to compile press and mixer-granulator data, human errors may happen. Please bear in mind that MCC will not be legally responsible for any such errors in calculations. Copyright © 2006-2012 Measurement Control Corporation (MCC).

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Scale-Up Calculator Tutorial - mcc- · PDF fileTutorial for Scale-Up Calculator, Version 2.0 Page 2 of 24 compaction variables for such a press, please contact MCC for more