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Process flowsheet optimization with surrogate and implicit formulations of a Gibbs reactor

Sergio I. Bugosen, Carl D. Laird, Robert B. Parker

TL;DR

This study investigates convergence reliability in chemical process flowsheet optimization by comparing four formulations for a Gibbs reactor–containing ATR: full-space, ALAMO polynomial surrogates, neural network surrogates, and an implicit-function reformulation. The results show that ALAMO surrogates provide the most reliable and fastest convergence with small objective deviations, while the implicit formulation yields exact solutions with comparable solve times; neural surrogates offer substantial improvements over full-space but are less robust outside training ranges. The work highlights a trade-off between solution accuracy and computational effort and provides practical guidance on selecting reformulations for large, complex flowsheets. It also demonstrates how surrogate and implicit strategies can enhance convergence reliability in challenging nonconvex optimization problems in chemical engineering.

Abstract

Alternative formulations for the optimization of chemical process flowsheets are presented that leverage surrogate models and implicit functions to replace and remove, respectively, the algebraic equations that describe a difficult-to-converge Gibbs reactor unit operation. Convergence reliability, solve time, and solution quality of an optimization problem are compared among full-space, ALAMO surrogate, neural network surrogate, and implicit function formulations. Both surrogate and implicit formulations lead to better convergence reliability, with low sensitivity to process parameters. The surrogate formulations are faster at the cost of minor solution error, while the implicit formulation provides exact solutions with similar solve time. In a parameter sweep on an autothermal reformer flowsheet optimization problem, the full space formulation solves 33 out of 64 instances, while the implicit function formulation solves 52 out of 64 instances, the ALAMO polynomial formulation solves 64 out of 64 instances, and the neural network formulation solves 48 out of 64 instances. This work demonstrates the trade-off between accuracy and solve time that exists in current methods for improving convergence reliability of chemical process flowsheet optimization problems.

Process flowsheet optimization with surrogate and implicit formulations of a Gibbs reactor

TL;DR

This study investigates convergence reliability in chemical process flowsheet optimization by comparing four formulations for a Gibbs reactor–containing ATR: full-space, ALAMO polynomial surrogates, neural network surrogates, and an implicit-function reformulation. The results show that ALAMO surrogates provide the most reliable and fastest convergence with small objective deviations, while the implicit formulation yields exact solutions with comparable solve times; neural surrogates offer substantial improvements over full-space but are less robust outside training ranges. The work highlights a trade-off between solution accuracy and computational effort and provides practical guidance on selecting reformulations for large, complex flowsheets. It also demonstrates how surrogate and implicit strategies can enhance convergence reliability in challenging nonconvex optimization problems in chemical engineering.

Abstract

Alternative formulations for the optimization of chemical process flowsheets are presented that leverage surrogate models and implicit functions to replace and remove, respectively, the algebraic equations that describe a difficult-to-converge Gibbs reactor unit operation. Convergence reliability, solve time, and solution quality of an optimization problem are compared among full-space, ALAMO surrogate, neural network surrogate, and implicit function formulations. Both surrogate and implicit formulations lead to better convergence reliability, with low sensitivity to process parameters. The surrogate formulations are faster at the cost of minor solution error, while the implicit formulation provides exact solutions with similar solve time. In a parameter sweep on an autothermal reformer flowsheet optimization problem, the full space formulation solves 33 out of 64 instances, while the implicit function formulation solves 52 out of 64 instances, the ALAMO polynomial formulation solves 64 out of 64 instances, and the neural network formulation solves 48 out of 64 instances. This work demonstrates the trade-off between accuracy and solve time that exists in current methods for improving convergence reliability of chemical process flowsheet optimization problems.
Paper Structure (14 sections, 22 equations, 3 figures, 4 tables)

This paper contains 14 sections, 22 equations, 3 figures, 4 tables.

Table of Contents

  1. Abstract
  2. Introduction
  3. Background
  4. Full Space Formulation
  5. Surrogate Formulation
  6. Implicit Formulation
  7. Problem Statement
  8. Implementation
  9. Dataset Generation
  10. ALAMO surrogate
  11. Neural Network surrogate
  12. Implicit Function
  13. Results
  14. Conclusions

Figures (3)

  • Figure 1: Process Flow Diagram of the ATR process.
  • Figure 2: Incidence matrix of the square system corresponding to the Gibbs reactor.
  • Figure 3: Convergence status for each formulation. "Untrained region" indicates conversions above 0.95, the upper bound used for surrogate training data. The results indicate that while all three alternative formulations are more reliable than the full-space formulation, the ALAMO surrogate is the most reliable.