Results analysis and discussion

6.4.3.1 Comparison with pseudo - multi-period

For the pseudo multi-period approach, the same case study has been used in Section 5.5.1. In order to prevent the heat exchange between non-simultaneous process operation, the concerned units are defined as sub-systems. Heat transfer units for the indirect heat recovery are not considered.

Unit Case 0 Case 1 Case 2 Case 3 Case 4

hp st hp st

OpC [ke/year] 1506 1177 1098 1169 1081

E_f [MWh/year] 34740 28566 25164 28349 24417

E_el [MWh/year] 2328 917 1792 919 1984

Qcw [GWh/year] n.a. 12 9 11 9

MCO2 [t/year] 7232 5855 5248 5811 5115

Ep [GJ/year] 183772 139359 134363 138400 133267

0 1 2 3 4 5 6 7

−50 0 50 100

Case

Savings [%]

CostFuel Electricity CO2 emissions Primary energy

Figure 6.4: Saving potential of the cheese factory with multi-period multi-time slice resolution

Therefore, the results of Case 1 (without storage and heat pump) are comparable to Case 1a (pseudo period approach) in Table B.11. The total operating cost with the pseudo multi-period approach and a cheese production of 12000 tons corresponds to 1174 ke per year and is almost the same than the result of the multi-period multi-time slice approach.

The electricity consumption is higher in the approach of pseudo multi-period. This is due to the restricted matches. As the multi-time slice approach allows the direct heat exchange between simultaneous process operations, it is not necessary to introduce restricted matches due to non-simultaneous operations. On the contrary, the time average approach imposes restricted matches between two process operations with different operating schedules, even if some of their process operations work simultaneously for one given time slice. Thus, for this given time-slice and these

136 CHAPTER 6. MULTI-PERIOD AND BATCH PROBLEMS

two process operations, the multi-time approach allows direct heat exchange while the time average approach imposes heat exchange restrictions. Since the restricted matches in the time average approach concern the streams needing refrigeration below the pinch point, the utilization rate and consequently the electricity consumption of the refrigeration cycle are slightly higher for the pseudo multi-period calculation.

Case 2 shows that the integration of a closed cycle R245fa heat pump can save almost 7% of the operating costs, whereas the pseudo multi-period approach predicts a saving potential of 10% of the operating costs.

To conclude this section, it is important to note that both approaches are valid and give similar results. The heat pump potential is however overestimated in the pseudo multi-period approach for this case study.

The advantage of the pseudo multi-period approach is that the size of the problem is smaller and less information (e.g. scheduling) is necessary. However the multi-period multi-time slice approach can evaluate the real size of equipments and the storage potential including the operation schedule of the time slices.

6.4.3.2 Storage between time slices in a period

As shown in Table B.11, the storage potential is relatively low in the example of the cheese fac-tory. As already mentioned in Section 5.5.1, the heat recovery potential between non-simultaneous process streams is rather low. The same conclusions are drawn when solving the multi-time slice problem.

However a small storage potential could be exploited and the optimal storage capacity can be calculated. Choosing a very high virtual amount of possible storage, the optimal heat storage amount can be optimized. This corresponds to 647 m³. Figure 6.5 shows the optimal storage distribution of Case 3. This seems to be very high and in the following (Section 6.4.4), it will be seen that the storage volume can be reduced, by choosing a smaller upper bound for the water content.

The first important fact to notice is that only temperature levels 2 & 3 are interesting for storage.

This means that heat is stored at 40 °C and after giving the stored heat to the process, the water is stored in the cold tank of 30 °C. The evaporation unit is not working in time slices 1 & 2, where the heat previously stored in tank 2 is used to satisfy a part of the hot utility at low temperature (< 40°C). It is also interesting to see that the hot tank 2 is filled only in time slices 14 and 1, just before the heat is needed, in order to avoid heat losses in the tank.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Figure 6.5: Storage distribution of Case 3 without heat pump integration

The utilization rate of utilities is also shown in Figure 6.5. The energy consumption of the boiler can be directly related to the operating hours of the evaporation unit. It is also shown that more cooling water is necessary when the evaporation unit is turned off.

6.4.3.3 Storage and heat pumps

From the energy efficiency point of view, the combination of storage and heat pump units can be particularly interesting. A heat pump can recover low grade heat to satisfy the needs of cold streams at higher temperature. The combination with storage units enables the heat recovery between hot and cold process demands that do not occur at the same time. Moreover, it increases the heat pump working hours and reduces its size, which leads to a higher profitability, especially if one considers that the use of an intermediate fluid and storage tank will be necessary to practically integrate the heat pump.

The storage distribution is shown on Figure 6.6 for Case 4 where the highest heat pump utilization rate is reached in time slice 12. At the same time storage tank 7 at 80°C is filled. This heat is then used in time slices 2 & 3. The result of Figure 6.6 seems not be satisfying, since the heat pump works only at partial load (around 40%), except for one time slice the heat pump is fully operated.

138 CHAPTER 6. MULTI-PERIOD AND BATCH PROBLEMS

Figure 6.6: Storage distribution of Case 4, including integration of a heat pump

To improve the results the investment costs related to storage units and new heat pumps will be considered in the next section.