(344d) Application of Johanson Model Calibrated With Instrumented Roll Data for Roller Compaction Process Development and Scale Up

Roller compaction is a dry
granulation process used to convert powder blends into free flowing
agglomerates.  During scale up or transfer of roller compaction process, it is
critical to maintain comparable ribbon densities at each scale in order to achieve
similar tensile strengths and subsequently similar particle size distribution
of milled material. Similar ribbon densities can be reached by maintaining
analogous normal stress applied by the rolls on ribbon for a given gap between
rolls.  Johanson (1965) developed a model to predict normal stress based on
material properties and roll diameter. However, the practical application of 
Johanson model to estimate normal stress on the ribbon is limited due to its
requirement of accurate estimate of nip pressure i.e., pressure at the nip
angle.  Another weakness of Johanson model is the assumption of a fixed angle
of wall friction that leads to use of a fixed nip angle in the model. 

To overcome the above mentioned
limitations, a novel approach was developed using roll force equations based on
a modified Johanson model in which the requirement of pressure value at nip
angle was eliminated.  An instrumented roll on WP120 roller compactor (See
Figure 1) was used to collect normal stress data (P1, P2, P3) measured at three
locations across the width of a roll, as well as gap and nip angle data on
ribbon for placebo and various active blends along with corresponding process
parameters.  The sensor # 1 is located towards the inner edge of the roll and
records normal stress P1, the sensor # 3 is located towards the outer edge of
the roll and records normal stress P3, and the middle sendor records normal
stress P2. 

The nip angles were estimated
directly using experimental pressure profile data of each run.  Example of nip
angle calculation for one of the placebo runs is provided in Figure 2.  The
angle between intersection of tangents to ascending and descending portions of
pressure peak with the base line was used as a nip angle.

The equations (1) and (2) below show
the roll force (RF) as a function of gap (S), nip angle (α), roll diameter
(D), roll width (W), and pre blend compressibility (K).

Pm (i.e. P2) is maximum normal stress
at the center of the roll width.

And F is defined as

Roll diameter (D) is 120 mm for WP120
compactor.  The compressibility (K) is determined from the reciprocal of the
slope of initial linear portion of the logarithmic plot of density as a
function of pressure data obtained in uniaxial compaction.  The roll force equation of Johanson
model was validated using normal stress, gap, and nip angle data of the placebo
runs.

The calculated roll force values (i.e.
Johanson model) compared well with those determined from the vendor supplied
roll force equation (3) provided for the Alexanderwerk^® WP120 roller
compactor.

Subsequently, the calculation was
reversed to estimate normal stress (Pm or P2) and corresponding ribbon
densities as a function of gap and roll pressure.  A set of calibration runs
are conducted for a given preblend using 2^2 factorial with gap and roll
pressure as two factors.  In absence of such data, a set of runs with different
combinations of gap and roll pressure can be used.  A calibration set of 3 or
more runs is ideal for this purpose. 

The purpose of calibration runs are
as follows.  In our research (Nesarikar et al. 2012), we have shown that the
normal stress values recorded by side sensors P1 and P3 were lower than normal
stress values recorded by the middle sensor P2.  This is attributed to
heterogeneity of feeding pressure in the last flight of the feed screw and this
has also been previously reported in the literature (Simon et al. 2003).  In
addition, using FEM simulations, Cunningham et al. (2010) also showed that the
normal stress and relative density decreased near the ribbon edges due to side
seal friction, resulting in variation of relative density across ribbon width. 

The variation of normal stress across
ribbon width leads to variation of ribbon density.  Use of Johanson model
without taking into account the normal stress variation can over predict the
ribbon density as ribbon density will be calculated using Pm (or P2) alone. 
Therefore, modeling approach we used takes into account the normal stress
variation across ribbon width to avoid over prediction of ribbon densities. 

The typical assumed normal stress
profile across ribbon width for a roller compactor with a single feed screw
system is shown in Figure 3.  As shown in Figure 3, Pe is normal stress at the
ribbon edge.  x1 is the distance from the center on both sides over which P2
(i.e Pm) is effective.  The experimental ribbon density data of calibration set
is used to determine x1 and Pe values. Note that sensors 1 and 3 are located
6.75 mm each from the roll edge.  True density and pressure-porosity data of
pre blend is used to calculate densities corresponding to normal stress at each
location on the ribbon.  Once density profile across ribbon width is obtained,
trapezoidal rule is used to estimate area under curve for calculating average
ribbon density. 

The model predicted ribbon densities
of the placebo runs compared well with the experimental data.  The placebo
model also predicted with reasonable accuracy the ribbon densities of active A,
B, and C blends prepared at various combinations of process parameters.  Example
of prediction for ribbon densities of active B batches is shown in Figure 4. 
Active B was a low drug load ( <= 5% w/w) formulation.

We have also successfully demonstrated the extension of this
model to scale up from Alexanderwerk® WP120 to WP200 unit.  The scale up
approach presented in this work is not limited to WP200 and can be applied to
any other roller compactor since the model inputs; gap and RFU are machine
independent parameters.  Example of scale up from Alexanderwerks WP120 to WP200
for the active C batches is shown in Table 1.

References

1)      
Cunningham J., Winstead D., Zavaliangos A. 2010.  Understanding
variation in roller compaction through finite element-based process modeling. 
Computers and Chemical Engineering.  34, 1058-1071.

2)      
Johanson, J. R., 1965.  A rolling theory of granular solids.  ASME, J.
Applied Mechanics Series E 32 (4), 842-848.

3)       Nesarikar V,
Vatsaraj N., Patel C., Early W., Pandey P., Sprockel O., Gao Z., Jerzewski R.,
Miller R., Levin M.  Instrumented Roll
Technology for the Design Space Development of Roller Compaction Process. 
International Journal of Pharmaceutics. 426 (2012) 116-131

4)       Nesarikar V, Patel
C., Vatsaraj N., Early W., Pandey P., Sprockel O., Jerzewski R., Roller
compaction process development and scale up using Johanson model calibrated
with instrumented roll data.  International Journal of Pharmaceutics. 436(2012)
486-507.

5)      
Simon O. and Guigon P., 2003, Correlation between powder-packing
properties and roll press compact heterogeneity, Powder Tech. 130, 257-264.