  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.
