Modelling Approaches for Bio-Manufacturing Operations - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 96

characterise the energy dissipation profile. The damaging effects of this upon the
material can be replicated at bench scale e.g. by using shear devices to induce an
equivalent level of solids damage observed upon scale-up. Such strategies have
been employed in several studies, e.g. by Boychyn et al. [ 4 ]; Boulding et al. [ 2 ]
and Boychyn et al. [ 5 ], to improve the accuracy of scale-up predictions.
Other unit operations can also benefit from CFD, such as chromatography.
Determining the rate of mass transport in either the bulk fluid or the stationary
phases can be facilitated by CFD to solve equations such as the general rate model
in order to predict breakthrough and elution profiles [ 14 ]. Modelling uptake pro-
files can require access to data such as mass transfer equilibrium parameters or rate
coefficients; these can be used to calibrate the terms within the CFD models, and
normally such information will come from small-scale (lL or mL) experiments
(see Chap. 7 ). Computational fluid dynamics requires considerable experience
with the available commercial software packages to perform such types of analysis
and also far more processing power than is found in a conventional PC. This may
owe much to the need to perform repeated iterations of the same equations; e.g. the
solution to the general rate model [ 17 ] involves discretising the column dimen-
sions into a series of coordinate points and then numerically solving a large system
of ordinary differential equations. Hence as indicated above, it is important to
introduce simplifying assumptions wherever possible to ensure that the numerical
solution does not become intractable. Often, the nature of the operation (and
similar prior examples) can provide much valuable data about which mass
transport phenomena are the most significant and thus how the equations can be
simplified; For example, in cases where mass transfer inside the macropores of the
resin beads is known to be the dominating mass transport step, the pore diffusion
model of chromatography can be solved using CFD software. If, however, the
isotherm is sufficiently rectangular, then the shrinking core assumptions [ 42 ] may
be used to reduce the pore diffusion model into a simpler set of equations that may
be evaluated using a spreadsheet.
3.3 Factorial Design Models
One way to model a process is to use purely empirical data and to fit regression
models to the data values, and in principle this could be done in a custom manner
by an end-user in a spreadsheet or similar piece of software. In practice, it is more
common to use commercial factorial design software which assists with selection
of an experimental design, statistical data analysis and the generation of a
regression model accompanied by statistical parameters that indicate the quality of
fit between data and model. Choosing the most suitable regression model from the
many which may be suggested by the software requires some skill and in particular
may rely upon the understanding possessed by an end-user when interpreting the
fitness statistics. Before conducting a factorial design, it is necessary to have some
idea of which parameters are likely to be important, since this can be used to limit