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Long-term scheduling methods

Wu and Ierapetritou (2004) presented a method for the cyclic scheduling of batch plants for scheduling over long time horizons. The assumption was that for a long time horizon and for the case where task durations are much shorter in comparison, there exists a sub-schedule with a shorter time horizon which, if repeated, may achieve an overall production close to the production achieved when periodic scheduling is not considered. It involves obtaining an optimal cyclic schedule which is then repeated and therefore reduces the problem size. It may also be easier to implement practically. This method was based on the previous discrete time model of Shah et al. (1993b) and rather used the continuous time scheduling constraints of Ierapetritou and Floudas (1998), based on the STN representation. It was assumed that the plant operated under stable conditions and would also have stable product requirements. The resulting model was a MINLP which was solved using both DICOPT and BARON. Cyclic scheduling sacrifices some accuracy when compared to the direct solution of the scheduling problem, but this is balanced by the easier solution of a less complex scheduling problem. The cyclic scheduling model was later rewritten for use with the SSN representation and was  combined with wastewater minimisation constraints in order to minimise water usage over long time horizons in multipurpose batch plants (Nonyane & Majozi, 2012).

Heat integration in batch plants

Heating and cooling are unavoidable in many processing facilities, with operations where heat is generated and others where heat is required. It is because of this occurrence that heat integration becomes a possibility.
Heat integration in a batch process is complicated by the fact that it is constrained both by temperature and by time. Direct heat integration may be exploited when the heat source and heat sink processes are active over a common time interval. Alternately, indirect heat integration involves using a heat transfer fluid for storing energy and allows heat integration of processes regardless of the time interval. This is possible as long as the heat source process takes place before the heat sink process. This allows heat to be stored and then used later when required. The inclusion of heat storage instead of only direct heat integration leads to more flexibility in the process and therefore improved energy usage. In both cases, heat transfer may only take place if the thermal driving forces allow. When applying heat integration to batch plants, there will be a trade-off between scheduling, savings achieved from heat integration, heat exchanger design and capital investment. After applying heat integration, the overall profit of a plant may increase due to savings from reduced utility consumption even though there may be a decrease in production or an increase in capital expenditure.

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Pinch analysis adapted for batch plants

Early techniques for heat integration in batch processes were based on pinch analysis, which was originally developed for heat integration in continuous plants at steady state. However, hot and cold streams in batch plants are not continuously available. Variations of the technique for batch processes still appear in literature. The major drawback of these techniques is their reliance on a predefined schedule, which leads to suboptimal results.
Kemp and Deakin (1989a) presented work on cascade analysis for heat integration in batch plants. Energy targets were set using the time average model (TAM) and time slice model (TSM). Time-temperature cascade tables determined the extent of heat recovery between streams via direct heat integration and heat recovery between different time intervals via heat storage. A three-dimensional cascade plot was also used to visualise heat flows. Kemp and Deakin (1989b) carried out heat exchanger network design using the energy targets from the cascade analysis. Methods for rescheduling to improve direct heat integration opportunities were explored and assessed. Kemp and Deakin (1989c) applied the cascade techniques to a case study based on a specialty chemicals plant and large savings could be achieved using direct heat integration and heat storage.

1.1 Background
1.2 Problem statement and objectives
1.3 Scope
1.4 Structure
1.5 References
2.1 Introduction .
2.2 Operation of batch plants
2.3 Operational philosophies .
2.4 Scheduling in batch processes .
2.5 Time horizon representation
2.6 Flowsheet representation
2.7 Early mathematical methods for scheduling .
2.8 Short-term scheduling methods based on the STN
2.9 Short-term scheduling methods based on the RTN
2.10 Short-term scheduling method based on the SSN
2.11 Short-term scheduling methods based on the S-Graph approach .
2.12 More recent scheduling methods
2.13 Long-term scheduling methods
2.14 Heat integration in batch plants
2.15 Pinch analysis adapted for batch plants
2.16 Mathematical techniques using a predefined schedule
2.17 Simultaneous scheduling and heat integration approaches .
2.18 Specific heat integration applications
2.19 Heat storage
2.20 Wastewater minimisation in batch plants
2.21 Combined heat integration and wastewater minimisation
2.22 Conclusions
2.23 References
3.1 Introduction
3.2 Problem statement and objective
3.3 Mathematical model
3.4 Solution procedure
3.5 Case study I (Halim & Srinivasan, 2011) .
3.6 Case study II
3.7 Case study III
3.8 Conclusions
3.9 References
4.1 Introduction
4.2 Cyclic scheduling concepts .
4.3 Problem statement and objectives
4.4 Mathematical model .
4.5 Simple linear process
4.6 Multipurpose example
4.7 Industrial case study
4.8 Conclusions


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