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). Uncertainty analysis in WWTP model applications: A critical discussion using an example from design. Water Research, 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. Bioresource Technology, 102, 1174-1184.