Table 6.2 shows the investment costs related to the heat pump and the storage system. The payback time is evaluated without considering the cost of new heat exchangers and compared to the current situation. It is important to note that the heat recovery potential is here mainly realized by basic heat exchangers.
The possibility to include the annual investment costs in the objective function, enables to reduce the equipment size and therefore the payback time. The heat pump is smaller but works at full capacity except for two time slices where the evaporation unit does not work.
It is also interesting to analyze the problem size. Table 6.3 compares the number of constraints and variables and the computation time for the MILP problems.
Introducing a heat pump and the corresponding restricted matches (between heat pump and pro-cess) increases the number of constraints and variables and also the computation time. The
intro-142 CHAPTER 6. MULTI-PERIOD AND BATCH PROBLEMS
Table 6.2: Global multi-period multi-time slice results: Case 1 to Case 6
Unit Case1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 6 tot hp st hp st hp st 500 hp st 100 hp st 100
OpC [ke/year] 1177 1098 1169 1081 1082 1084 1084
InvChp [ke] 0 453 0 786 496 892 415
InvCst [ke] 0 0 455 703 495 214 184
P B [year] 0 5.7 56.5 15.5 10.5 12.0 6.5
AP [ke/year] 0 43 -28 -24 15 4 45
Table 6.3: Example problem size of period 1
MILP Problem Constraints Variables Computation time
Case 1 4671 4826 0.016 sec
Case 2 12683 11586 0.187 sec
Case 3 10496 10124 0.094 sec
Case 4 19918 18054 1.560 sec
duction of a storage system (Case 3) increases also the problem size. Consequently the problem size of Case 4 which integrates both the heat pump and the storage system becomes bigger. Especially the computation time is more than 8 times higher than in Case 2. Cases 5 and 6 have the same number of constraints and variables than Case 4. However, the computation time for data handling is not considered here and can be significantly higher (e.g. 1-2 hours for Case 4).
Case 1 could be compared to Case 1a, calculated with the time average approach in Table B.11.
The time average problem is solved in 0.062 seconds with 2187 constraints and 2005 variables. The multi-period multi-time slice approach needs one optimization for each period, the example of one period with 15 time slices is given in Table 6.3 (Case 1).
6.5 Conclusions
This chapter introduced the multi-period multi-time slice approach that is illustrated by a case study from the food industry. This approach can integrate non-continuous process operation and seasonal variations.
Results are presented on a multi-period real case study. The method seems to be promising to solve multi-period problems and the small saving potential can be explained by several facts. First the process of the case study in the current situation is already quite efficient. Nevertheless, the method showed that the saving potential is high especially through optimal heat recovery using simple heat exchangers.
Concerning heat pump integration, the temperature difference is big, since the technology repre-sentation has been chosen. It would be worth to study more in detail the main energy consumer, the evaporation unit. This has been done in Section 3.5.2.2, where the evaporation unit has been modified and a mechanical vapour re-compression unit replaces the thermal vapour re-compression.
Rather than taking the evaporation unit as a black box, saving potential can be exploited by modifying the evaporation unit to make it more efficient.
This complete approach is new and before going further, several problems have to be fixed: the number of constraints and variables and thus the problem size is increasing. The resolution time of the MILP is acceptable, but the required data handling to define the input problem takes significantly more time than for the pseudo multi-period approach. This depends of course on the number of time slices.
Finally, there is a need of more detailed results analysis and also the heat load distribution and the heat exchanger network has to be adapted, to be able to solve the complete problem. Especially for the process flexibility which is strongly linked to the heat exchange connections this is in an important topic. The intermediate heat networks of the previous chapter are therefore very useful to make the process operation independent from each other, since the heat exchange could be realized through the networks. Keeping in mind that the heat exchanger network is still too complex for mono-period problems, it will not be easy to compute the heat exchanger network for large scale multi-period multi-time slice systems.
The multi-period multi-time slice approach is a good way to evaluate the efficiency of industrial processes with batch or discontinuous operations where storage can play a role. It has been demon-strated that the pseudo multi-period approach presented in Chapter 3 gives similar values for the target, but does not provide information on the size of the storage tanks and on their operating conditions. However, since the obtained results are similar, both approaches are valid. The main advantage of the multi-time slice approach presented here is that the utility equipments sizing and storage units can be estimated from the beginning. The investment calculation is therefore more realistic.
It has been shown that the investment costs play an important role and have to be considered.
There are two possibilities. Either investment costs can be considered as a part of the objective function in the MILP formulation (e.g. Section 6.4.4.2) or the second possibility is to use the multi-objective optimization. The multi-objective optimization could thus characterize the trade-off between process operating and investment costs of heat recovery, storage and heat pumps and identify optimal solutions. It could be for example interesting to have continuous heat pump usage to increase their profitability.
Another open point is the optimization of the temperature levels of the storage tanks. One option
144 CHAPTER 6. MULTI-PERIOD AND BATCH PROBLEMS
could be to define a fine discretization of the temperature levels in the virtual storage system. The second option could be a non-linear optimization approach, based on a multi-objective optimization strategy as it has been developed for heat pump integration in Chapter 4. In the same way the temperature level of the storage tanks could be defined as the optimization variables.
Implementation
This chapter summarizes the implementation approach and gives a small overview on the tool that is developed and validated in this thesis.
Related publication: Approach: Bolliger et al. (2009).
7.1 Introduction
The design of energy conversion systems is based on models which describe the mass and energy balances for the different process units and their integration into the global system. These models generate the data needed to analyze the overall system efficiency and to establish performance indicators, using for example exergy analysis, process integration with pinch analysis or thermo-economic evaluation. The increasing complexity of the system, the highest degree of integration and the increasing number of energy conversion options together with the demand of applying different performance indicators require more systematic approaches. This chapter proposes a tool which systematically tackles the integrated system design by dissociating technology modeling from the methods for the analysis and the synthesis of integrated systems.
In recent years, research activity in energy conversion system analysis and design considers more and more complex systems, often composed by combining smaller sub-systems. The domain covers multiple system scales from equipment design (Palazzi et al., 2007) to process design (e.g. biomass conversion processes (Gassner and Mar´echal, 2009)) to industrial processes (e.g. industrial processes (Becker et al., 2011d)) and even urban systems (Mar´echal et al., 2008).
In order to address the problem of handling complex models, research recently focused on developing tools for exchanging information and allow the interoperability of modeling softwares. For exam-ple, The DOME platform (distributed object-based modeling environment) Kraines and Wallace (2003) implemented a model based co-current system design and engineering platform. It has been
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Mass Integration
Cost est im at ion - Grassroot - Engineering - Land - Maintenance - Operation
LCIA - CO2 - NOx - Hydrocarbons - Phosphates
Parameters Constants Variables Sets...
Technology Model System Integration Model
Analysis / synthesis Method Interfaces
Energy Integration
Figure 7.1: Schematic view of the separation of physical model from method analysis related data (Bolliger et al., 2009)
successfully applied to urban systems and allows to interconnect versatile sub-systems models using web services. The CAPE-OPEN Morales-Rodr´ıguez et al. (2008) initiative on the other hand has been developed by the process engineering community to allow the interoperability of flow-sheeting tools, unit models and thermodynamic packages. Although these methods give the opportunity to construct very complex models, most of the time they are only focused on the process flow-sheet calculation problem.
However, the design of the energy conversion systems requires the application of one or more analysis and synthesis methods in order to deduce the performance indicators and the information about the interactions between the various technologies of the global system. The major drawback of the existing approaches is that they do not separate energy and mass balances modeling from the system analysis and the synthesis methods. Models are built in one single block containing all the information. The reuse of the same models in different study contexts becomes therefore very difficult and often requires a partial recoding of the model.