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This paper presents a methodology for developing grey models of process systems, that is, models that, being based on fundamental principles and laws of nature, combine them with sub-models obtained from experimental data. The method follows two steps: the first one takes advantage of what is known, while the second uses the data and mixed-integer optimization algorithms to identify the structure and parameters of the remaining parts of the model. The method is illustrated in a challenging biotechnological process: the Acetone-Butanol-Ethanol (ABE) fermentation process.