Process Operability
Process operability analysis asks whether a process design can reach a desired range of outputs given the inputs available to it. It is framed in terms of sets: the available input set (AIS), the achievable output set obtained by forward mapping, the desired output set (DOS), and the desired input set (DIS) obtained by inverse mapping from the DOS. It is used early in conceptual design, for example to size modular or intensified equipment. See also Inverse problems.
Operability sets by AD-based inverse mapping (2023)
Alves, Kitchin and Lima applied an inverse mapping method built on automatic differentiation and the implicit function theorem to the operability analysis of a direct methane aromatization membrane reactor (Alves et al. 2023). For a circular DOS covering 22.3 to 23 mg/h of benzene and 39.2% to 40% methane conversion, they traced the boundary of the DIS in tube length and tube diameter and found it to be non-convex. The result agreed with the established NLP-based operability approach to within about 0.02% while being about 2 to 19 times faster depending on how the NLP was warm-started and differentiated. Summary: alves2023.
Operability sets under uncertainty (2025)
Alves, Laird, Lima and Kitchin mapped correlated uncertainty between operability sets for a direct methane aromatization membrane reactor (Alves et al. 2025). A 95% ellipse of correlated tube and shell pressures in the expected disturbance set mapped forward to a nonconvex region of the achievable output set spanning more than 10% in methane conversion and about 20 mg/h in benzene production, which the authors use to argue for mapping correlated regions rather than only variable bounds. An output-space ellipse was also mapped inversely to the available input set (tube and shell flow rates) and validated against NLP-based inverse mapping in the Opyrability package. Summary: alves2025.