Fast and efficient chemical process flowsheet simulation by pseudo-transient continuation on inertial manifolds

Abstract

Process flowsheets are mathematical models that describe the steady-state operation of (petro)chemical processes and comprise large-scale systems of nonlinear algebraic equations. The solution of these systems (referred to as “flowsheet simulation”) is challenging for practically-relevant problems. Pseudo-transient continuation is a promising numerical approach for process flowsheet simulation, and has been shown to converge flowsheets reliably from a wider range of initial guesses compared to standard Newton-type methods. However, the pseudo-transient approach is more computationally demanding than flowsheet simulation with a Newton-type solver (assuming a good initial guess is available for the latter). Moreover, process flowsheet simulation with pseudo-transient continuation involves defining a set of dynamics in pseudo-time, and both convergence and computational efficiency can be highly dependent on the user-selected time constants that govern this dynamic behavior. In this work, we address these challenges with a novel algorithm for process flowsheet simulation based on a hierarchical, multiply-singularly perturbed formulation of pseudo-transient dynamics, and an associated cascade of quasi-steady-state assumptions. The algorithm replaces a subset of the differential equations of the reformulated model with algebraic quasi-steady-state conditions when the system approaches the inertial manifold defined by steady state of the respective dynamics. The proposed technique allows a seamless transition from pseudo-time integration to efficient algebraic solvers, and we prove that the method converges to the solution of the original algebraic system in a finite number of steps. Moreover, the time-scale decomposition of the pseudo-transient dynamics eliminates the need to explicitly set the time constants of the dynamics in each time scale. Using two prototype chemical process examples, we show that the proposed method significantly reduces the computational effort involved in pseudo-transient process flowsheet simulation.