A simple approach to improve the robustness of equation-oriented simulators: Multilinear look-up table interpolators

doi:10.1016/j.compchemeng.2015.12.014

Computers & Chemical Engineering

Volume 86, 4 March 2016, Pages 1-4

https://doi.org/10.1016/j.compchemeng.2015.12.014 Get rights and content

Highlights

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A methodology using look-up tables in equation-oriented simulators is proposed.
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Nonlinear rigorous models replaced by look-up tables.
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Two distillation column trains and a hydrolysis reactor were chosen as examples.
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The accuracy of the look-up tables reached the imposed threshold.
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A bioethanol plant was successfully optimized using the methodology.

Abstract

Equation-oriented simulators have some advantages over the modular sequential ones, but improvements are still necessary to deal with nonlinearities, while preserving the robustness of the solver. Linear approximations and/or surrogate models can be used in place of nonlinear models, but the loss of predictive accuracy may be a drawback. An alternative to circumvent this problem is the use of grid-based look-up tables for interpolating responses from rigorous models. This methodology was integrated in an equation-oriented simulator (EMSO). A case study involving the production of bioethanol from sugarcane is used to demonstrate the robustness of this approach. Look-up tables replaced the models of two distillation column trains and of the cellulose hydrolysis reactor. These models were included into the global process and an optimization problem aiming at the maximum production of ethanol was successfully solved by a PSO algorithm varying the solid mass fraction in the hydrolysis reactor.

Introduction

Equation-oriented process simulators solve the system of equations simultaneously. Although useful when the number of recycle streams in the process is large, this approach prevents the implementation of strategies for circumventing local convergence problems (i.e., including ad hoc algorithms within the models of specific process units, the “modules” of the sequential modular simulators). According to Morton (2003), processes with awkward nonlinearity and high recycle complexity should be solved by equation-oriented simulators, provided their robustness undergoes some improvements. Nevertheless, while such generically robust solver is not available, some strategies can be developed to circumvent this bottleneck. As a general case, these strategies rely on simplifications of the models that constitute the chemical plant. However, these simplifications generally imply loss of accuracy and operational flexibility (Morton, 2003).

Here, an alternative approach is presented: using grid-based look-up tables to interpolate the results of previous offline simulations, for the process unit models whose nonlinearity was hindering the convergence of the simulations of the overall industrial plant. With this simple strategy, the accuracy of the simplified model (the interpolator) can be tuned, while still requiring low computational power (Nelles, 2001). As a proof of concept, an integrated first and second generation ethanol biorefinery was modeled, using both sugarcane and sugarcane leaves as feedstock. Two process sections, chosen for their characteristically nonlinear behavior, were used for testing the methodology: the distillation columns trains, which were simulated in steady-state, and the enzymatic hydrolysis reactor, which was simulated dynamically, with the results at the end of the batch run being considered in the global process simulations. In both cases, results obtained with this methodology were compared to the ones generated by the original phenomenological models. The look-up table interpolators were then coupled to the global process flowsheet, in order to evaluate the robustness of the approach.

Section snippets

Simulator

The simulator EMSO™ (Environment for Modeling Simulation and Optimization), used in this work, is equation-oriented. This simulator has an internal object-oriented modeling language that allows insertion of new models into its internal library. Moreover, it is possible to add plug-ins for running calculations which are not suitable for the equation-oriented approach; and new solvers may be linked as dynamic libraries as well (Soares and Secchi, 2003).

Grid-based look-up tables

Grid based look-up tables consist of a set

Results and discussion

Based on the accuracy criteria described in Section 2.2, a grid with 15 points (three inlet temperatures and five ethanol mass fractions) was used for approximating the behavior of the hydrous ethanol distillation column train. Fig. 2 presents the error distribution as a function of the two input variables (wine temperature and molar fraction of ethanol). Two output variables were selected as examples of the error distribution: the heat duty in the first column reboiler (the main energy

Conclusions

In this work, a methodology involving the use of grid-based look-up tables in equation-oriented simulators was developed. The methodology allowed the construction of simplified models that approximate nonlinear phenomenological models with a controllable accuracy, without the impairments in convergence caused by the rigorous models. As a demonstration of the capabilities of the methodology, an integrated first and second generation (1G–2G) ethanol production process (with 26,502 process

Acknowledgements

This work was financially supported by CAPES, CNPq and FAPESP (Proc. 09/13325-0 and 08/56246-0).

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NoteA simple approach to improve the robustness of equation-oriented simulators: Multilinear look-up table interpolators

Highlights

Abstract

Introduction

Section snippets

Simulator

Grid-based look-up tables

Results and discussion

Conclusions

Acknowledgements

Biochem Eng J

Comput Chem Eng

Comput Aided Chem Eng

Systematic methods of chemical process design

Simulation of ethanol production process from sugar and sugarcane bagasse aiming at process integration and energy production maximization

Note
A simple approach to improve the robustness of equation-oriented simulators: Multilinear look-up table interpolators