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.

翻译：提出了一种替代性化工流程优化数学表述方法，通过采用代理模型与隐式函数分别替换和移除描述难收敛吉布斯反应器单元操作的代数方程组。比较了全空间、ALAMO代理、神经网络代理及隐式函数四种数学表述在优化问题中的收敛可靠性、求解时间与解质量。代理模型与隐式函数表述均能提升收敛可靠性，且对过程参数敏感性较低。代理模型表述求解速度更快但存在微小解误差，隐式函数表述则能提供精确解且求解时间相当。在自热重整器流程优化问题的参数扫描测试中，全空间表述在64个实例中成功求解33个，隐式函数表述求解52个，ALAMO多项式表述求解64个，神经网络表述求解48个。本研究揭示了当前提升化工流程优化收敛可靠性的方法中，精度与求解时间之间存在的权衡关系。