MINLP combined with the analytic hierarchy process for the design of chemical processes under uncertainty: Application to the synthesis of heat exchanger networks
Dauda Ibrahim, Gonzalo Guillen-Gosalbez*, Megan Jobson
Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, The Mill, Sackville Street, Manchester M13 9PL, United Kingdom
*Corresponding author Tel: +44(0) 1613068755, E-mail address: firstname.lastname@example.org
Chemical processes are traditionally designed under the assumption of fixed operating parameters (temperature, pressure, composition, flow rate, etc.), which reflect nominal conditions. During plant operation, however, it is likely that the process will undergo changes in the operating parameters. The question that arises then is whether the plant will be able to cope with these new conditions that may differ (sometimes significantly) from the nominal ones.
This paper introduces a new framework for the synthesis under uncertainty of chemical processes that combines mathematical programming with the analytic hierarchy process (AHP). At the design stage, our approach takes into account explicitly the most critical uncertainties that can affect the calculations. The final goal is to identify a robust design showing good performance in the space of uncertain parameters.
The framework proposed comprises four main steps. First, the main uncertainty sources are identified and described via probability functions. Monte Carlo sampling is then applied on these distributions in order to generate representative scenarios that will be used in the calculations. In step 2, an optimization model is solved for every such scenario in order to generate a set of potential designs behaving in different ways in the uncertain parameters space. In step 3, these designs are next evaluated against all the scenarios in terms of feasibility and profitability. A set of stochastic metrics are also calculated in this step, including the expected performance, worst case and level of feasibility in different operative constraints. In step 4, the analytic hierarchy process (AHP) is applied in order to identify the most economic, feasible and flexible process design among those generated in step 2. To this end, pairwise comparisons between the metrics calculated in step 3 are first carried out using the Saaty scale. The eigenvalues of the matrix of pairwise comparisons will then be used to calculate the weights to be attached to every metric. The designs generated in step 2 will then be sorted according to these weights.
The capabilities of our approach are illustrated through its application to the design of several heat exchanger networks (HENs), in which uncertain supply temperatures and heat capacity flow rates are considered. The problem is modelled as a multi-scenario MINLP based on the original formulation of Yee and Grossmann (1990). This MINLP is solved for every scenario, which reduces the complexity associated with the original model and avoids in turn potential convergence and feasibility problems resulting from the large number of variables and non-linear nature of the problem.
Keywords: Process design, Uncertainty, Flexibility, Optimisation, HEN, MINLP, AHP
See more of this Group/Topical: Process Development Division