A new model formulation and solution strategy for the design and simulation of processes involving multistream heat exchangers (MHEXs) is presented. The approach combines an extension of pinch analysis with an explicit dependence on the heat exchange area in a nonsmooth equation system to create a model which solves for up to three unknown variables in an MHEX. Recent advances in automatic generation of derivative‐like information for nonsmooth equations make the method tractable, and the use of nonsmooth equation solving methods make the method very precise. Several illustrative examples and a case study featuring an offshore liquefied natural gas production concept are presented which highlight the flexibility and strengths of the formulation. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3390–3403, 2015

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This article presents new methods for robustly simulating process flowsheets containing nondifferentiable models, using recent advances in exact sensitivity analysis for nonsmooth functions. Among other benefits, this allows flowsheeting problems to be equipped with newly developed nonsmooth inside-out algorithms for nonideal vapor−liquid equilibrium calculations that converge reliability, even when the phase regime at the results of these calculations is unknown a priori. Furthermore, process models for inherently nonsmooth unit operations may be seamlessly integrated into process flowsheets, so long as computationally relevant generalized derivative information is computed correctly and communicated to the flowsheet convergence algorithm. These techniques may be used in either sequential-modular simulations or simulations in which the most challenging modules are solved using tailored external procedures, while the remaining flowsheet equations are solved simultaneously. This new nonsmooth flowsheeting strategy is capable of solving process simulation problems involving nonsmooth models more reliably and efficiently than the algorithms implemented in existing software, and, in some cases, allows for the solution of problems that are beyond the capabilities of classical approaches. As examples of the latter, it will be shown that the nonsmooth approach is particularly well-suited for highly accurate simulation of natural gas liquefaction processes, in which many nonsmooth modeling elements are present in combination with nonideal thermodynamic behavior and complex heat-transfer considerations.

Dynamic modeling of processes involving phase changes can be challenging due to changes in the model equations caused by appearance and disappearance of equilibrium phases. Dynamic simulation of these processes requires the ability to detect the change in the number of phases and adapt the model to the new phase regime on the fly. In this work, an easy‐to‐use nonsmooth model for dynamic simulation of processes with vapor‐liquid equilibrium is presented. The presented model does not introduce any auxiliary variables or equations, nor does it require solution of an optimization problem to determine the new phase regime during the dynamic simulation. It can therefore be used for comprehensive simulation of, e.g., distillation columns, where the number of phases present can change during startup and shutdown. The nonsmooth model is illustrated through examples of an evaporator and a distillation column. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3334–3351, 2016

Dependable algorithms for nonideal vapor–liquid equilibrium calculations are essential for effective process design, simulation, and optimization. Inside-out algorithms [BostonJ.BrittH. Boston, J. Britt, H. Comput. Chem. Eng.19782109] for flash calculations serve as the basis for many of the algorithms used by process simulation software due to their robustness with respect to initialization and inexpensive computational cost. However, if the specified flash conditions imply a single-phase result, the conventional inside-out algorithms fail, as the solution is constrained to obey equilibrium relationships, which are only valid in the two-phase region. These incorrect results can be postprocessed to determine the true single-phase solution; however, such approaches either carry a high computational cost or are heuristic in nature and vulnerable to failure (or both). Such attributes are undesirable in a process simulation/optimization problem where many flash calculations must be performed for streams where the phase regime at the solution is not known a priori. To address this issue, this article presents modifications of the classical inside-out algorithms using a nonsmooth equation system in the inner loop to relax equilibrium conditions when necessary, allowing reliable convergence to single-phase results. Numerical results for simulations involving several common flash types and property packages are shown, highlighting the capability of the new nonsmooth algorithms for handling both two-phase and single-phase behavior robustly and efficiently.