Reliable Flash Calculations: Part 1. Nonsmooth Inside-Out Algorithms

Abstract

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.

Multiple Steady States and Nonsmooth Bifurcations in Dry and Vaporless Distillation Columns

“…For instance, in Phase Regimes II, one of the flow rates is zero and the summation relationship in eq 5 is still satisfied. The explicitly nonsmooth approach has been successfully applied to perform flowsheet flash calculations 17 and model multi-stream heat exchangers with 16 and without 30 phase change.…”

“…On the other hand, recent advances in the automatic evaluation of generalized derivatives have opened up the possibility of creating explicitly nonsmooth algebraic models that can be directly solved with Newton-like methods. By introducing a single nonsmooth equation in terms of the mid function, which returns the median of its three arguments, Watson et al , have successfully reformulated the phase equilibrium problem for a single stage in order to perform flash calculations and model multistream heat exchangers with phase change. With an analogous approach, Sahlodin et al proposed a nonsmooth dynamic model for multistage distillation columns, formulated in terms of liquid and vapor molar holdups.…”

Deterministic global flowsheet optimization: Between equation‐oriented and sequential‐modular methods

“…This approach was used by Stuber and Barton 3 on the Rachford-Rice method for an ideal mixture without considering the energy balance, and by Watson 42 for a nonsmooth modification of the inside-out method. 43 However, this requires the use of methods for relaxation of implicit functions, 25,26 which is beyond the scope of this work. Furthermore, Watson 42 reports relatively weak resulting relaxations for the inside-out flash.…”

Work and heat integration—A new field in process synthesis and process systems engineering

“…Additional nonsmooth equations are included for correct phase detection of the process streams [88][89][90] . The resulting simulation model was applied to single mixed refrigerant (SMR) and dual mixed refrigerant (DMR) processes 91,92 (Vikse et al, 2018) using a nonsmooth Newton solver.…”