Matias Vikse

Comparison of reformulations of the Duran-Grossmann model for Work and Heat Exchange Network (WHEN) synthesis

Abstract Work and Heat Exchange Networks (WHENs) have received increasing attention from both researchers and engineers during the last 5-10 years. The Duran-Grossmann model (Duran and Grossmann, 1986) can deal with heat integration problems with variable process streams. In WHENs, however, the identity of streams (hot/cold) can also change. Therefore, a revised Duran-Grossmann model applied to WHENs without knowing the identity of streams a priori is proposed. The revised Duran-Grossmann model consists of both binary variables and non-smooth functions. To facilitate the solution of the model, the non-smooth functions (max operators) can be reformulated in three ways. The first method is to reformulate the max operator using a Smooth Approximation (Balakrishna and Biegler, 1992). This function incorporates a small parameter, which may lead to either an ill- conditioned approximation or loss of accuracy if poorly chosen. The second method is using Explicit Disjunctions based on principles of the Duran-Grossmann model (Grossmann et al., 1998). To avoid using a max operator, disjunctions explicitly revealing the relationship between the stream inlet/outlet temperatures and pinch candidate temperatures are applied. The last method reformulates the max operator with Direct Disjunctions (Quirante et al., 2017). The max operator picks up the maximum value of two variables, thus it can be straightforward reformulated by a disjunctive programming approach. Even though these three reformulations of the Duran-Grossmann model have been previously investigated, considering uncertain stream identities applied to WHENs has not yet been reported. In this study, all the reformulations and models are implemented in the GAMS (Brooke et al., 1998) modelling framework. For a case study without isothermal streams, Smooth Approximation performs better than the other two formulations.

Robust Flash Calculations through Nonsmooth Inside-Out Algorithms

Abstract The ability to solve many important problems in process systems engineering is dependent on being able to perform vapor-liquid equilibrium (flash) calculations rapidly and consistently. The flash equations are particularly challenging to solve for non-ideal systems with many components, and many process simulators use some version of the inside-out algorithms ( Boston and Britt, 1978 ) for performing such calculations. However, these methods assume that the calculation result is always a two-phase mixture, which is not guaranteed outside of a range of input parameters that is not generally known a priori . This article continues the development of nonsmooth inside-out algorithms ( Watson et al., 2017 ) which retain the benefits of the original algorithms without the possibility of loss of reliability or performance when only a single phase is present. This article shows how this can be accomplished for the fixed pressure-entropy flash through the use of nonsmooth equations that relax the equilibrium constraints when necessary, automatically allowing convergence to either single-phase or two-phase solutions.