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.