(593ay) A Model-Based and a Multi-Objective Optimisation Framework for Incremental Scale-up of Bioreactors

A
model-based and a multi-objective optimisation framework for incremental
scale-up of bioreactors

Mauricio-Iglesias, Miguel¹; Sin, Gürkan²

CAPEC - 
Department of Chemical and Biochemical Engineering, Technical University
of Denmark, Søltofts Plads, Building 229, DK-2800 Kgs. Lyngby, Denmark

¹ mim@kt.dtu.dk;
²gsi@kt.dtu.dk

Scale-up is an important stage
in development and commercialization of new process technologies in many
industries, for production of chemicals such enzymes, antibiotics or materials
such as bioplastics. Moving a fermentation process from a lab-scale to a
commercial/production scale remains still challenging due to a number of
factors that affects biological response of cells to changing conditions from
cultivation. Scale-up problems
may arise then due to inadequate interphase mass
transfer, heat removal and non-uniform temperature and concentration gradients
in the reactor (Villadsen et al. 2011). As a result, many large-scale fermentation
processes give a lower yield than achieved in the laboratory.

Traditionally, scale-up problem is tackled using a step-wise
process development approach: from lab-scale to pilot-scale and ultimately to
production-scale by following certain empirical criteria based on dimensionless
numbers or ratios critical to performance of the process.  The difficulty with this approach lies in
several aspects as there is just a limited number of
empirical criteria than one can keep constant during the scale-up.
Additionally, the controlling conditions (bottleneck) may change at different
scales.

This contribution aims at developing a framework for
scale-up of bioreactors based on data and information translated into
quantitative knowledge using models.  The
framework allows using multiobjective scale-up
principles and various degree of models, from first-principles to empirical
(e.g. response surface type models based on experimental data) to hybrid models.

The proposed methodology is illustrated as a flowchart
in Figure 1 and assumes that a successful bioreactor design and operation
protocol has been developed at a lab/bench scale. The methodology consists of
the following steps:

1)      Definition
of objectives and constraints:
where the objective of the scaled-up operation is defined, including the
scaling-up factor. It is important to note that the goal of scaling-up is not
to reproduce the bench scale reactor at a larger scale but to accomplish the
objective defined. To this aim, the bioreactor configuration can be modified in
the large scale

2)      Model
development. Depending on
the available information and the goal of the process, a model with the
corresponding assumptions is formulated at the small scale and is assumed to be
translatable to the large scale. The model complexity can range from complete
first-principle model including the mass, heat and momentum balances and a
structured metabolic kinetic description to simple meta-models, e.g. obtained
from an experimental campaign response surface methodology.  

3)      Design
scale-up. Using the model
developed, the problem of design at a large scale is formulated as an
optimization to achieve the defined objective. If a full model is available,
the large scale design can be done without taking into account the bench scale
protocol. Otherwise, sensitivity analysis of the bench scale model is used to
determine the operating parameters that affect most the performance of the
reactor. In the vast majority of cases the scale-up will represent a trade-off
since not all the operation parameters/ratios can be kept constant. A multiobjective optimization is proposed as a systematic
method to carry out the scale up, hence keeping constant the most significant
operating conditions and parameters (according to the sensitivity analysis) and
whereas the least important ones can be varied. Hence, the use of multiobjective optimization together with an assessment of
the model in order to choose the most relevant phenomena for the process
provides a rational method for scale-up.  

4)      Scale-up
validation. The goal of
this step is to check whether the assumptions formulated in step 2 are
applicable at the new scale and thereby, the validity of the model and the
scale-up. The most spread and straightforward tool is the regime analysis of
all the phenomena taking place in the reactor. The limiting steps can be
therefore inferred and, the hypotheses used to build the model can be validated
(Sweere et al. 1986). Otherwise, a more complex model
is needed in order to properly describe the operation in the reactor, and the
hypotheses are reformulated.

5)      Evaluation. This step consists on checking whether
the objectives initially defined are actually fulfilled at the large scale. If
not, the model and/or the objectives may have to be redefined if the model
cannot capture the bioreactor description properly or if the defined objectives
are not feasible at large scale.

Figure
1. Methodology proposed for incremental
scale-up of bioreactors based on incremental model development

The methodology is illustrated step by step through a
case-study consisting on a bacterial fermentation scale-up (E. coli in a rich glucose environment, Villadsen et al. 2011 ) assuming
different levels of available information: i) a full
model, ii) a partial model consisting on mass balances and kinetic rates but
failing to include hydrodynamics and iii) a meta-model obtained from simulated
experimental data. The results using the methodology were benchmarked with
other widely used methods based on rules of thumbs (e.g. keeping the
power/volume ratio constant at all scales) and dimensional analysis (e.g.
keeping the Sherwood number constant at all the scales). The proposed
methodology was proven to provide a rational framework for scaling up,
considering both simple and complex models. 

References

Villadsen J. et al. (2011)
Bioreaction Engineering Principles. Springer Science

Sweere, A.P.J. Luyben,
K.C.A. M., Kossen, N.W.F..
(1986), Regime analysis and scale-down: tools to investigate the performance of
bioreactors, Enwyme Microb.
Technol. vol.9, 386