*3.4. Feasibility of Using Zeotropic Mixtures*

Traditionally, the primary reason for using zeotropic mixtures as working fluids in ORC power systems is to utilize the temperature glide of phase change for temperature profile matching with sensible heat sources and sinks, with the aim of reducing the irreversibilities of the heat transfer processes. As indicated in the fluid comparison based on equal heat transfer area (see Figure 10), those benefits are highest when the heat transfer area is high. In the theoretical case of infinitely large counter-flow heat exchangers, it is possible for mixtures to reach higher capacities (lower mean temperature differences and higher *UA*¯ ) than pure fluids, since the temperature profiles achieve a better match with the sensible heat source and sink in the primary heat exchanger and the condenser. On the other hand, when the heat exchangers are small, the temperature differences in the heat exchangers are large and the *UA*¯ values are small. In this case, the performance increase due to the better temperature match achieved with zeotropic mixtures is limited and tends to be overcompensated by the degradation in heat transfer coefficient, as demonstrated in Section 3.1.4. This observation indicates that zeotropic mixtures are more likely to be economically feasible compared to pure fluids in applications where it pays off to invest in large heat exchangers. This is the case in geothermal applications, where a large investment is required for establishing the geothermal well. Astolfi et al. [45] demonstrated how their thermoeconomic optimization results for pure fluids in an ORC unit designed for utilizing geothermal heat, was affected by the investment required for the geothermal well. A variation of the geothermal well cost from zero to 12 Me resulted in an increase of the ORC unit cost (power block only) from 3.03 Me to 8.57 Me, and a reduction of the minimum pinch point temperature difference of

the condenser from 2.5 ◦C to 0.43 ◦C. Similarly, it is more likely that zeotropic mixtures achieve higher economic performance than pure fluids, when the cost of the heat exchangers is low.

It is also worthwhile considering zeotropic mixtures for other reasons than the temperature profile matching capabilities. By including zeotropic mixtures in the fluid screening, the number of considered working fluids is larger, and it is more likely to identify fluids with desirable properties considering multiple criteria such as thermodynamic performance, environmental friendliness, safety and cost. For example, the high flammability of hydrocarbons could be reduced by adding a non-flammable fluid [48,49]. Fluids which result in high process pressures could benefit from being mixed with a low pressure fluid. This could result in a reduction in piping and heat exchanger costs [25]. Additionally, for the same condenser bubble point (condensing fluid outlet temperature), it is possible for zeotropic mixtures to have a higher increase in the coolant temperature due to the temperature glide. For the same amount of heat transfer, the mass flow rate of cooling water can thereby be smaller for mixtures. This can result in lower size and cost for cooling water circulating pumps, and cooling towers [5].

#### *3.5. Method Selection for Other Thermodynamic Processes*

Temperature profile matching is not only utilized for zeotropic mixtures, but also for pure fluids where temperature profile matching in the preheater has been used for optimizing the ORC system performance [50,51]. In addition, the use of a recuperator can result in almost perfect alignment of the temperature profiles of the heated liquid and the cooled vapor [51]. In such situations, it is important to check that the mean temperature differences and the *UA*¯ values do not get excessively low and high, respectively. In power cycle units where the pressure is supercritical, for example transcritical ORC units or supercritical CO2 units, temperature profile matching is possible in the heat transfer process between the hot fluid and the supercritical working fluid. When comparing such units with power cycle units using subcritical pressures it is also important to account for differences in mean temperature differences and *UA*¯ values in order not to overestimate the performance of the units employing supercritical pressures (see also Section 3.2). Due to the curved temperature profile of the supercritical heating process it is necessary to discretize the heat exchanger for identifying the pinch point location. Thus, it is possible to define constraints on the mean temperature difference or *UA*¯ values of the heat exchangers with limited additional effort compared to applying minimum pinch point temperature difference constraints.

The implementation of constraints on either mean temperature differences or *UA*¯ values rather than minimum pinch point temperature differences, should also be considered for other power cycles utilizing zeotropic mixtures as working fluids. Examples of such cycles are the Kalina cycle using ammonia/water mixtures, and physical absorption cycles using lithium-bromide/water mixtures.

The alternative methods discussed in this paper are also useful in combination with computer aided molecular design (CAMD) [52–54], and continuous molecular targeting (CoMT) [55,56] methods, which consider the molecular optimization of the working fluid. In such optimization problems, the ORC process model is typically based on thermodynamics, since a full thermoeconomic model including heat exchanger sizing would be too extensive to implement at this stage. Although the CAMD and CoMT methods are able to identify thermodynamic optima, it is possible that the fluids designed are not thermoeconomically optimal. By using minimum pinch point temperature difference based models, there is a risk that benefits due to temperature profile matching is overestimated. It is therefore important to check whether there is a correlation between *UA*¯ values or mean temperatures, with the performance ranking of the designed fluids. If this is the case, it is worthwhile considering implementation of constraints on mean temperature differences or *UA*¯ values. Cignitti et al. [57] carried out a CAMD based optimization integrating ORC process and working fluid design, and found different optimum working fluids depending on whether the selected heat exchanger constraints were based on minimum pinch point temperature differences or *UA*¯ values.

#### **4. Conclusions**

In this paper, four different methods for performance comparison of pure fluids and zeotropic mixtures in ORC systems were assessed. The methods were characterized by which modeling approach was used for representing the performance of the heat exchangers in the systems. The methods compared the net power output of the fluids based on either the same minimum pinch point temperature differences, the same mean temperature differences, the same *UA*¯ values, or the same heat transfer areas for all fluids.

The comparison of propane, i-butane, propane/i-butane (0.2/0.8) and propane/i-butane (0.8/0.2) based on the same values of condenser pinch point temperature differences suggests that the highest net power outputs are achieved by the mixtures for all values of condenser pinch temperature difference. When compared based on the same values of condenser mean temperature differences or *UA*¯ values, the results suggest that propane/i-butane (0.8/0.2) achieves the highest net power output. However, the mixture propane/i-butane (0.2/0.8) is outperformed by propane at condenser mean temperature differences above 3 ◦C and *UA*¯ values below 4000 kW/◦C. When comparing the net power outputs of the fluids based on the same condenser heat transfer areas, the highest performance is achieved by propane at heat transfer areas below 2000 m2, while propane/i-butane (0.8/0.2) achieves the highest performance at heat transfer areas above 2000 m2. In the heat transfer area based comparison, propane achieves higher net power outputs than propane/i-butane (0.2/0.8) for all considered values of the condenser heat transfer area. The results suggest that the fluid i-butane achieves the lowest net power outputs of the four fluids in all the considered cases.

A fluid performance ranking of 30 working fluids assuming the same minimum pinch point temperature differences for all fluids, indicates that the net power outputs of zeotropic mixtures are up to 13.6% higher compared to the best pure fluids in the mixtures. On the other hand, by assuming that the sum of the condenser and primary heat exchanger *UA*¯ value is the same for all fluids, the results indicate that the net power outputs of zeotropic mixtures are only up to 2.56% higher compared to the best pure fluids in the mixtures. Similarly, the estimated performance benefit of using transcritical ORC units decreases from 18.8% in the minimum pinch point temperature difference based comparison to 1.1% in the *UA*¯ value based comparison.

The method assuming equal minimum pinch point temperature differences for all fluids was deemed to result in optimistic estimations of the benefits of using zeotropic mixtures, while the methods assuming equal mean temperature differences or *UA*¯ values were deemed to result in conservative estimations. The method assuming equal heat transfer areas for all fluids was deemed too comprehensive for thermodynamic optimization considering modeling complexity and computational time. This indicates that it is beneficial to use the method assuming equal minimum pinch point temperature differences and the method assuming equal *UA*¯ values (or mean temperature differences) concurrently in preliminary fluid selection, since they result in different conclusions regarding the thermodynamic performance of working fluids.

Relevant future work within this research topic could comprise an economic optimization of an ORC system considering a group of selected working fluids. By carrying out the working fluid selection for the economic analysis based on two or more of the thermodynamic methods assessed in the present paper, it is possible to judge which of the methods identifies the more economically beneficial working fluids.

**Author Contributions:** Conceptualization, J.G.A., M.R.K. and F.H.; Formal analysis, J.G.A.; Funding acquisition, F.H.; Investigation, J.G.A.; Methodology, J.G.A., M.R.K. and F.H.; Project administration, F.H.; Supervision, M.R.K. and F.H.; Validation, J.G.A. and M.R.K.; Writing—original draft, J.G.A.; and Writing—review and editing, M.R.K. and F.H.

**Funding:** This research was funded by Innovationsfonden, The Danish Council for Strategic Research in Sustainable Energy and Environment project ID: 1305-00036B.

**Acknowledgments:** The work presented in this paper was conducted within the frame of the THERMCYC project ("Advanced thermodynamic cycles utilising low-temperature heat sources", project ID: 1305-00036B; see www.thermcyc.mek.dtu.dk) funded by Innovationsfonden, The Danish Council for Strategic Research in Sustainable Energy and Environment. The financial support is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**


#### **Appendix A**

Table A1 displays the variation in net power output, condenser mean temperature difference, condenser *UA*¯ values, and condenser areas as functions of the condenser pinch point temperature difference for the working fluids propane, i-butane, propane/i-butane (0.2/0.8) and propane/i-butane (0.8/0.2). The data are plotted in Figures 3, 5, 6, 9, and 10.

**Table A1.** Variation of net power output (*W*˙ *net*), condenser mean temperature difference (Δ*Tm*,*cond*), condenser *UA*¯ values (*UA*¯ *cond*), and condenser areas (*Acond*) as functions of the condenser pinch point temperature difference (Δ*Tpp*,*cond*) for propane, i-butane and the mixtures propane/i-butane (0.2/0.8) and propane/i-butane (0.8/0.2).


#### **References**


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