Two 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 an increased solve time. In a parameter sweep on the autothermal reformer flowsheet optimization problem, the full space formulation solves 30 out of 64 instances, while the implicit function formulation solves 49 out of 64 instances, the ALAMO polynomial formulation solves 64 out of 64 instances, and the neural network formulation solves 37 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.

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