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In this work, a methodology for the model-based identifiable parameter determination (MBIPD) is presented. This systematic approach is proposed to be used for structure and parameter identification of nonlinear models of biological reaction networks. Usually, this kind of problems are over-parameterized with large correlations between parameters. Hence, the related inverse problems for parameter determination and analysis are mathematically ill-posed and numerically difficult to solve. The proposed MBIPD methodology comprises several tasks: (i) model selection, (ii) tracking of an adequate initial guess, and (iii) an iterative parameter estimation step which includes an identifiable parameter subset selection (SsS) algorithm and accuracy analysis of the estimated parameters. The SsS algorithm is based on the analysis of the sensitivity matrix by rank revealing factorization methods. Using this, a reduction of the parameter search space to a reasonable subset, which can be reliably and efficiently estimated from available measurements, is achieved. The simultaneous saccharification and fermentation (SSF) process for bio-ethanol production from cellulosic material is used as case study for testing the methodology. The successful application of MBIPD to the SSF process demonstrates a relatively large reduction in the identified parameter space. It is shown by a cross-validation that using the identified parameters (even though the reduction of the search space), the model is still able to predict the experimental data properly. Moreover, it is shown that the model is easily and efficiently adapted to new process conditions by solving reduced and well conditioned problems.

This work presents the mathematical formulation of a nonlinear programming (NLP) model which optimizes simultaneously crude oil blending and operating conditions for a system of several crude oil distillation units (CDUs) at a Colombian refinery. The CDU system consists of three industrial units processing a blending of five extra-heavy crude oils and producing two commercial fuels, Jet-1A and Diesel. The NLP model involves typical restrictions (e.g., flow rate according to capacity of pumps, distillation columns, etc.) and the heat integration of streams from atmospheric distillation towers (ADTs) and vacuum distillation towers (VDTs) with the heat exchanger networks for crude oil preheating. A metamodeling approach is used so as to represent the ADTs. Preheating networks are modeled with mass, energy balances, and design equations of each heat exchanger. The NLP model has been implemented in GAMS using CONOPT as solver. Different cases are solved by the NLP model such that the optimal case with less profit increment had an economical benefit of 13% with respect to its case without optimization. In each optimal case the extra-heavy crude oils in the feed blending of each CDU required more severe operating conditions such as higher temperature of the crude oil at the entrance to the towers, greater flow rate of stripping steam at the bottom, and minor pressure of the tower tops

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Models are prone to errors, often due to uncertain parameters. For optimization under uncertainty, the larger the amount of uncertain parameters, the higher the computational effort and the possibility of obtaining unrealistic results. In this contribution it is assumed that not all uncertain parameters need to be regarded and focus should be laid on a subset. As a first step in the algorithm, a parameter estimation is carried out to determine expected values, followed by a linear-dependency analysis and a ranking of the uncertain parameters. Parameters with a high linear-dependency are fixed, while others are left uncertain. This is followed by a subset selection regarding the sensitivity of the parameters towards the model and towards a user-defined objective function. Thus, only parameters with the largest sensitivities are selected as uncertain parameters and considered for optimization under un