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.

翻译：本文提出了两种用于优化化工流程的公式化方法，分别利用代理模型和隐函数来替代或移除描述难收敛吉布斯反应器单元操作中的代数方程。研究比较了全空间、ALAMO代理、神经网络代理和隐函数公式在优化问题中的收敛可靠性、求解时间和解质量。代理公式和隐函数公式均能实现更高的收敛可靠性，且对工艺参数的敏感度较低。代理公式以轻微解误差为代价获得更快的求解速度，而隐函数公式则能在增加求解时间的前提下提供精确解。在自热重整器流程优化问题的参数扫描中，全空间公式成功求解了64个案例中的30个，隐函数公式求解了49个，ALAMO多项式公式求解了64个，神经网络公式求解了37个。本研究揭示了当前提升化工流程优化问题收敛可靠性的方法中，精度与求解时间之间的权衡关系。