(421r) A Systematic Framework for Optimisation of Bioprocess Operation Under Uncertainty: A Lignocellulosic Ethanol Production Case Study

Optimization techniques
and methods are commonly used in the development and subsequent improvement of
chemical processes for the design, synthesis and operation. The optimization
problem has often been cast as multi-objective decision-making problem reflecting
an increasing awareness of the environmental and sustainable aspects in
addition to process economics of processes (Grossmann and Guillén-Gosálbez, 2010). While many mathematical programming techniques are available to solve process
optimization problems such as mixed-integer non-linear programming, dynamic
optimization, the
element of uncertainties in the optimisation problem is still a formidable
challenge. The uncertainties could be related to different sources such as technical
(untested process technology with risk of underperformance and lower yields),
operational conditions (particularly feedstock composition) as well as
economical factors (prices of feedstocks, utility and
products). These uncertainties then lead to uncertainties in the process
performance indices such as the predicted yield and unit operating cost. To
address these uncertainties, it is required to perform a formal uncertainty and
sensitivity analysis. Hence the objective of this paper is to develop and implement
a systematic framework for the optimization of bioprocesses under uncertainties
(see Figure 1). The framework is highlighted using lignocellulosic
bioethanol production under uncertainty, using several case studies for bioethanol
production previously presented in a publication covering diverse process
technology evaluations using a dynamic modeling approach (Morales-Rodriguez et
al., 2011).

Figure 1. Systematic framework for the
optimization of lignocellulosic bioethanol
production under uncertainty.

The
systematic framework for the optimization of bioprocesses starts with the
definition of the objective function. Secondly, followed by
the collection of data, identification and selection of mathematical models
(from open literature), generation and fine-tuning of new and existing
mathematical models, and design of integrated dynamic process models (i.e.
process flowsheets configuratoins)
to describe the system. In the third step, the uncertainty and
sensitivity analysis is performed to identify the critical process operational
variables and parameters in the system. The uncertainty analysis (using the
Monte-Carlo technique (step 3.a)) consists of: (i)
sampling of (uncertain) parameters (Latin Hypercube Sampling, LHS), (ii)
Monte-Carlo simulations with the sampled parameter values and (iii)
representation of uncertainty (e.g. mean, standard deviation, variance (Helton
and Davis, 2003). As far as sensitivity analysis is concerned (step 3.b.),
decomposition of the variance with respect to uncertain parameters is
performed, where, the standardized regression coefficient (SRC) method is
employed to determine the global sensitivity measure, b_i, which provides a
quantitative measure of how much each parameter contributes to the variance
(uncertainty) of the model predictions, used as basis to identify the most
critical parameters involved in the process. In the fourth step, a process
optimization study is carried out. Firstly the initial values for the
optimization variables are estimated by sampling based method (LHS sampling) to
provide good starting values to the optimization solver.  The objective function in the optimization
problem is formulated as stochastic variable due to uncertainties in the model.
Hence sampling based technique is used to calculate the mean of the objective
function, which is then solved in the outer loop by using an appropriate NLP
solver. In this study, a successive quadratic programming based (SQP) solver in
Matlab (fmincon) is used.
In step 5, a validation analysis is done in which one evaluates the performance
of the optimized process operation via comparison to data obtained in lab or
pilot-scale experiments. If the validation results are satisfactory, then the
systematic procedure will be terminated. Otherwise the procedure needs to be
iterated, either by reviewing the models used for the optimization or by
evaluating a different set of critical system parameters.

References

Grossmann, I.E., Guillén-Gosálbez,
G. (2010). Scope for the
application of mathematical programming techniques in the synthesis and
planning of sustainable processes. Computers and Chemical Engineering, 34,
1365-1376.

Sin, G., Gernaey, K.V., Neumann,
M.B., van Loosdrecht, M.C.M., Gujer, W. (2009).
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43, 2894-2906.

Helton, J. C., Davis, F. J. (2003). Latin hypercube sampling and the propagation
of uncertainty in analyses of complex systems.
Reliability Engineering & System
Safety, 81, 23?69.

Morales-Rodriguez,
R., Meyer, A.S. Gernaey, K.V. Sin, G. (2011). Dynamic Model-Based Evaluation of Process
Configurations for Integrated Operation of Hydrolysis and Co-Fermentation for Bioethanol Production from Lignocellulose.
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