Building high quality, validated, steady-state or dynamic mechanistic models of process systems is a key activity in process engineering for many applications such as model-based product and process design, control and optimisation. Such models invariably contain adjustable parameters that have to be estimated and need to be validated statistically [1]. One of the most important aspects in building a process model, which reproduces the physical behaviour of a system properly, is to identify mechanism and kinetics of the reactions involved. This is often complex and may require a considerable amount of experimental work and resources. Traditionally, this activity has been helped by statistical data analysis and black-box experiment design, but the recent advances in model-based experiment design make this technique a reliable tool to assist in these situations. After building an initial model, basing on Literature data or on results of preliminary experimental work, the structural and parametric information contained in this model can be used through model-based experiment design techniques to plan the new set of experiments. The aim is to obtain the most informative data, in a statistical sense, for use in parameter estimation and model validation minimising the experimental effort.

The aim of this paper is to present the validation of a model by means of model-based experiment design techniques, using a case study of practical interest: a biodiesel production process. The key issues of the procedure, required to go from a preliminary model (the parameters of which need to be validated statistically) to a final validated model suitable for an optimisation of the process, will be illustrated in this paper. The results of the parameter estimation, performed using the data of the optimal experiments suggested from the experiment design, and some preliminary results of the optimisation study will be presented here as a support of the approach proposed.

The case study chosen is the alkaline transesterification of refined rapeseed oil and methanol into biodiesel (using sodium methoxide as catalyst) under mild pressure conditions in a batch reactor. Starting from data from previous experimental work, a mathematical model was developed from first principles, but the available data did not allow a statistically significant estimation of the twelve kinetic parameters involved in the model [2]. Model-based experiment design was, therefore, used to plan the new set of experiments which, however, had to be carried out with the available experimental and analytical setup. This led to an interesting experiment design problem, which couples a complex reaction network (three consecutive and competitive reversible reactions) with many practical constraints and limitations of the apparatus (for example the non-isothermal conditions). All these restrictions, the high number of parameters to be estimated and the high correlations between them (highlighted by some preliminary studies) did not allow a set of experiments for the global estimation of all the parameters to be designed. The only realisable solution was to plan experiments for the estimations of individual, couple or group of three parameters with the others fixed at their values. The estimation of the individual parameters was performed successfully using the data of the six optimal experiments which were planned according to this procedure.

The global estimation of all the parameters was the last step required to validate the model and this goal was achieved successfully in two steps by linearizing the model equations which involve the parameters to be estimated (modified Arrhenius' equations). In this way, most of the parameters (8 out of 12) were identified with enough precision (t-tests satisfied) and the model was validated statistically (the 95%-χ² value was 45.33 for the first step and 58.34 for the second compared to a reference value of 49.8 and 60.5 respectively). These results improved the confidence in the reliability of the model, which was, therefore, used to achieve the final goal: the process optimisation in order to enhance the biodiesel yield.

References

[1] S.P. Asprey and S. Macchietto (2000). Statistical Tools for Optimal Dynamic Model Building. Computers and Chemical Engineering, 24, 1261-1267.

[2] G. Franceschini, A. Bertucco and S. Macchietto. Simulation and optimisation of a biodiesel production process. Presented at “Convegno GRICU 2004: Nuove Frontiere di Applicazione delle Metodologie dell'Ingegneria Chimica”, Porto d'Ischia (Napoli), 12-15 settembre 2004.

Keywords

Biodiesel, Model-based Experiment design, Parameter estimation, Kinetics Elucidation, Rapid Model Development, Model Validation, Dynamic Optimisation