# (94g) Blend Uniformity Prediction Based on Discrete Element Method

#### AIChE Annual Meeting

#### 2018

#### 2018 AIChE Annual Meeting

#### Particle Technology Forum

#### Modeling of Particulate Systems

#### Monday, October 29, 2018 - 9:48am to 10:06am

Prediction

of Blend Uniformity by utilizing Discrete Element Method simulation

Shuichi

Tanabe^{1, 2, 3}, Srikanth R. Gopireddy^{1}, Shuichi Ando^{2},

Hidemi Minami^{2}, Nora A. Urbanetz^{1}, Regina Scherlieb^{3}

1

Pharmaceutical Development, Daiichi Sankyo Europe GmbH, Pfaffenhofen 85276,

Germany

2

Formulation Technology Research Laboratories, Daiichi Sankyo Co., Ltd.,

Hiratsuka 2540014, Japan

3

Department of Pharmaceutics and Biopharmaceutics, Kiel University, Grasweg 9a,

24118 Kiel, Germany

This

work presents the prediction of the probability density distribution of blend

uniformity of a binary granular blend using Discrete Element Method (DEM). Sample

Blend Uniformity (BU), i.e., %SD of the active ingredient concentration in samples

taken from various locations of bulk blend, was evaluated to assure the quality

of finished drug product such as content uniformity. There exists three key

factors in BU analysis (BUA) for assuring homogeneity of the bulk blend, and

these include (1) particle size of components in the blend, (2) the sampling

regimen that defines sampling locations and the number of samples taken from

each sampling location, and (3) the acceptance criteria. The acceptable ranges

of the particle size of the components at a given sampling regimen and

acceptance criteria can be confirmed based on experiments. However, as

resources are limited it is practically difficult to conduct comprehensive

experiments to identify the physical propertiesf allowable ranges in commercial

scale, which makes the gedge of failureh setting difficult and conservative in

manufacture. With the increasing computational capabilities over the last

years, computationally intensive in-silico experiments using DEM are becoming

an important tool to understand production processes such as blending. The

advantage of DEM compared to other simulation techniques is that it is able to

capture the trajectory of each and individual particle in the system through

Newton's equation of motion, by calculating the new positions and velocities of

the particles based on the forces acting on it at a defined time step. The

forces acting on each particle which may be due to particle-particle or

particle-wall contacts or the non-contact forces such as gravity, cohesion,

etc. enter as source terms in the equation of motion (Zhu et al., 2007). Herein

this study aims at predicting the sample BU at a given combination of key

factors based on DEM simulation, and thus selecting the appropriate sampling

regimen.

The

blending process of a binary granular blend (active : placebo = 14 : 86 w/w%)

using a 50 L bin blender is considered. After filling of more than 50% of total

placebo granules the active granules are filled into the blender. Following to

the active granule filling the remaining portion of the placebo granules are

filled, result in a sandwich like filling. Blender rotation speed is 6 rpm, the

Froude number is 0.02. Both granules are mono-sized (180 micrometre in

diameter) having a spherical shape and no cohesiveness. In order to keep the

simulation time reasonably low, upscaling of particle size and downscaling the

blender geometry were applied. This decreases the computational time as less

particles are involved. At a given blending time, the blend is divided into *M*

equivalent mass spaces as sampling locations. Each of these *M* sampling

locations is sub-divided into *N* equivalent mass spaces. The mass present

in one of those *M *x *N* mass spaces is assumed to be a sample. Sample

BU is calculated using only those samples taken according to a sampling

regimen, i.e., 1 sample each from 10 (*M* = 10) locations (10x1). The 10x1

sampling regimen at *N *= 8 will have 10^{8} ways of sampling

resulting in 10^{8} sample BU values giving the probability density

distribution of the sample BU. In total, 14 DEM simulations were performed having

different particle size expansion level (F_{PS} = 3, 5, 7), blender

geometry reduction level (F_{G} = 0.05, 0.1, 0.2), and number of samples

in a sampling location (*N = 4 and 8*) of a same blend. The equation below

has been derived that allows the prediction of the sample BU of an actual blend

in a given blender based on the DEM simulation which was performed with

enlarged particles and reduced blender geometry.

*BU _{S1}*/

*BU*

_{S2}= (

*PN*/

_{S2}*PN*)

_{S1}^{0.5}

Here

*PN*_{S1} and *PN*_{S2} are the number of particles

in a sample of the DEM condition 1 and 2, respectively. Root mean square error

normalized by the mean (nRMSE) was calculated based on the equation by

considering the sample BU at (F_{PS}, F_{G}) = (5, 0.1), *N*

= 8, 25% fill level as a reference.

Qualitative

and quantitative prediction of sample BU probability density distribution in a

binary blend was successfully demonstrated, which have not been addressed

previously. The sample BU was decreased gradually until 60 to 80 sec, and reached

a plateau state after 80 to 100 sec (8 to 10 rotations) of blending. The powder

blending dominated by diffusion was also observed visually in the snapshots of

the time-series DEM simulation. The blending pattern shown at 100 s (10

rotations of blending), shows that blending is complete, and any further

blending may not be necessary. At the plateau state the probability density

distribution of the sample BU was normally distributed, which is a reasonable

approximation of a binomial distribution for a complete random mixture of a

binary blend. The mean sample BU became small as the number of particles in a

sample increase as reported in the previous study (Muzzio et al., 2002). The

sample BU probability density distribution with 10x1, *N* = 4 having ca.

3200 particles in a sample was smaller than those with 1x10, *N* = 8

having ca. 1600 particles in a sample, while they have overlapping portion. The

relative standard deviation (RSD) of the sample BU was constant regardless of

the mean sample BU in a given blend. The sample BU of the blends was

successfully predicted where the nRMSE was 0.2, suggesting a feasible prediction

accuracy. The number of particles in a sample was considered to be a critical

parameter in predicting the mean sample BU based on DEM results. Therefore, quantitative

sample BU probability density distribution prediction of a given blend having different

physical properties of granules should be possible at a similar prediction

accuracy considering the principle of DEM. Further verification studies will be

performed for blends having a particle size distribution and cohesiveness.

With

the proposed DEM simulation a sophisticated in-silico design of experiments for

setting proven acceptable ranges can be performed, which has been considered

practically difficult to perform in experiment due to limited resources. The DEM

simulation will provide not only the mean sample BU that will be obtained in

experiments but also the

probability density distribution, which will provide a forecast of the

possibility to pass/fail the acceptance criteria for sample BU. A detailed visualization

enabled by simulation also reveals intriguing blending development, and helps

e.g. to identify the critical regions of blending thereby optimizing the

sampling locations. These in-silico

experiments would provide comprehensive understanding of the allowable particle

size range of components at a given sampling regimen and acceptance criteria,

which helps in setting a reliable gedge of failureh specification.

References

Muzzio,

F.J., Sudah, O.S. Coffin-Beach, D, 2002. Effects of blender rotational speed

and discharge on the homogeneity of cohesive and free-flowing mixtures. Int. J.

Phram. 247, 57-68

Zhu,

H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of

particulate systems: theoretical developments. Chem. Eng. Sci. 62, 3378–3396.