(557b) Continuous Mixing Technology: Residence Time Distribution Modeling

Continuous
Mixing Technology: Residence Time Distribution Modeling

Peter Toson¹, Eva Siegmann¹,
Martina Trogrlic¹, Dalibor Jajcevic¹, Johannes Khinast¹

&

Pankaj Doshi², Daniel Blackwood²,
Alexandre Bonnassieux², Mary T. am Ende²

¹ Research Center Pharmaceutical
Engineering, Inffeldgasse 13, 8010 Graz, Austria

² Worldwide Research and Development,
Pfizer Inc. Groton CT, USA

Keywords:
Pharmaceutical Manufacturing; Mixing; Process Design & Development

The
pharmaceutical industry is in the midst of a transformation from batch to
continuous production processes. There are several advantages of continuous
manufacturing which include better control of process parameters and product
quality as well as lower down-times compared to batch processing. One of the most
important unit operations in a continuous process is powder mixing.

An overview of
the Continuous Mixing Technology (CMT) design is given in Figure 1 (a). Multiple
feeders provide a constant inlet material flow to the CMT device. The top
region is a de-lumping zone that breaks up agglomerates that may have formed
upstream. The mixing happens in the bottom conical region of the CMT – the
mixing zone. The mass throughput is actively controlled by upstream feeders and
hold-up mass in the CMT is controlled by changing the exit valve opening.
Therefore, the mean residence time of particles in the mixer, which is defined
by ratio of hold up mass to mass throughput, is also constant. However,
discrete element method (DEM) simulations and tracer experiments have revealed
that even if the mean residence time (MRT) is actively controlled, the shape of
the residence time distribution (RTD) changes with different operating
conditions, e.g. impeller speeds and hold-up mass.

The RTDs are
described by a generalized model of n continuous stirred tank reactors
in series (n-CSTR). Whereas the standard tanks-in-series (TIS) model
only allows integer values of n, the residence time distribution formula
can be generalized to any positive, fractional value of n. DEM
simulations and tracer experiments showed that a typical value of n for
the CMT device is between 0.5 and 1.1. . A value of n=1 corresponds to
the ideal CSTR model with an exponential residence time distribution. Values n>1
describe over-mixing (just as the TIS model, but with finer granularity),
values n<1 describe under-mixing. A value of 0.5 is an indication of
short-circuiting in the mixing process indicated by an early peak in the RTD.
Thus, the value of n quantitatively describes the mixing quality. An
example fit with n=0.95 is shown in Figure 1 (b).

The analytical
RTD described by the generalized n-CSTR model is then used to describe the
response at the CMT outlet to upstream fluctuations in the feeder. Three kinds
of fluctuations in the input mass flow are considered:

1.      
general low-amplitude noise

2.      
short, high peaks in the mass flow, e.g. a
cohesive agglomerate falls off the feeder screw (feeder bearding)

3.      
long drifts in the feeder signal, e.g. if the
feeder controller switches to volumetric flow with an incorrect feed-factor and
slowly corrects the mass flow. This case is demonstrated in Figure 1 (c).

The mass flow at
the CMT outlet is calculated as a convolution integral of the input mass flow
and the residence time distribution of the CMT. From the outlet mass flows of
the individual components, it is possible to calculate whether or not the
resulting blend composition is still within content uniformity specifications.
Because different operating points result in different RTDs, it is possible to
link the results back to the operating conditions. Thus, RTD modeling helps to
define process operating space to ensure blend composition meet the specification.

Figure 1. (a) CMT
overview. (b) Comparison of the RTD obtained from discrete element method (DEM)
simulations (histogram), a fit with n=0.95 (black dotted line), and a tracer
experiment (green solid line). (c) Response of the CMT outlet to a feeder drift
under different process conditions. Although the feeder starts at 150% of the
target and takes 90s to correct the mass flow, the CMT is able to damp this
peak to 112%-115% of the target value, depending on the process conditions.