Energy efficiency is one of the easiest and most cost effective ways to combat climate change. It is thus not surprising that improving energy efficiency is one of the objectives of the strategic plan of the US Department of Energy and of the framework program for research and innovation of the European Union.
Process integration is the system-oriented approach for the efficient use of energy and includes pinch analysis (Linnhoff et al. 1982) as well as a variety of mathematical programming models (Biegler et al. 1997). The main concept is that by exchanging heat between a hot (at a higher temperature) and cold process stream, the energy requirement of external utilities (e.g. steam, cooling water) is reduced twice. Process integration started with the optimal design of continuous processes and has been extended to the design and operation of batch plants (see review of Fernández et al. 2012).
In this work, we focus on direct heat integration in batch plants, which requires a pair of (hot, cold) streams to co-exist in time, at least partially. The difficulty is that to achieve the optimal synchronization (minimum utility consumption) significant production delays may be incurred (Vaklieva-Bancheva et al. 1996 and Adonyi et al. 2003). Halim and Srinivasan (2009) considered the bi-objective optimization problem but used a decomposition approach to reduce the complexity that caused their best schedule to feature both minimum makespan and utility usage. Not surprisingly, Seid and Majozi (2014) were able to find a better solution with a general model for direct and indirect heat integration in multipurpose batch plants. However, no tradeoff analysis is performed.
We now consider a novel industrial case study from a vegetable oil refinery that can be classified as a single stage multiproduct plant with parallel units. For this type of configuration, recent work by Castro et al. (2014a) has shown that orders of magnitude reduction in computational time can be obtained with a mixed-integer linear programming formulation derived from Generalized Disjunctive Programming (Raman and Grossmann 1994). More specifically, GDP facilitates the derivation of the complex timing constraints between interacting tasks. Another example can be seen in Castro et al. (2014b) involving the interaction of a processing task with constant electricity time periods (Nolde and Morari 2010).
The goal of having a computationally efficient formulation gains significance when switching from a single to a bi-objective approach. We rigorously tackle the bi-objective problem involved in the simultaneous optimization of product sequencing, timing and heat integration decisions. From the latter point of view, the new formulation can be seen as an extension of the simultaneous targeting and design model of Yee et al. (1990) for heat exchanger networks of continuous plants. An algorithm relying on the epsilon-constraint method (Guillén-Gosálbez et al. 2010) is used for generating the Pareto optimal points.
We show that problems with up to 46 hot and cold streams can be solved to optimality in reasonable time for the single objective of minimizing total energy consumption given tight bounds on makespan. There is a clear trade-off between the two conflicting objectives with potential savings due to heat integration ranging from 16% for the shortest production time to above 40%. Larger savings are however linked to significantly longer production times (doubled in one case) but this can be an interesting choice in plants operating well below their maximum capacity. There are multiple Pareto optimal solutions between the two extreme cases and adjacent solutions exhibit differences in product sequencing as well as heat exchange matches.
Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through the Investigador FCT 2013 program, grant SFRH/BDE/51346/2011 and projects PTDC/EQU-ESI/118253/2010 and UID/MAT/04561/2013.
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