**1. Introduction**

The organic Rankine cycle (ORC) power plant is a viable technology for conversion of heat to electricity. The heat-to-electricity conversion is enabled by circulation of an organic working fluid in a closed thermodynamic cycle. When the temperature of the heat input is low or the electrical power output of the plant is low, the ORC system features advantages compared to the steam Rankine cycle, since the working fluid properties of organic fluids are favorable over the properties of steam in these applications [1–4].

A way to improve the system efficiency when utilizing low-temperature heat is to use a zeotropic mixture as the working fluid [5–7]. Zeotropic mixtures change the temperature during the phase change, which is opposed to the isothermal phase change process of pure fluids. The temperature difference between the saturated vapor and liquid temperatures is typically denoted as the temperature glide. By employing zeotropic mixtures as working fluids in ORC units, it is possible to utilize the temperature glide to reduce the temperature difference during heat transfer in the primary (heat input) heat exchanger and condenser. On the other hand, the use of zeotropic mixtures is often related to larger heat exchangers due to degradation of heat transfer performance [8], and lower mean temperatures of the condenser and primary heat exchanger.

The performance of pure fluids and zeotropic mixtures have previously been compared based on a wide range of performance indicators employing various modeling methods. The methods employed are typically thermodynamic optimization or economic (thermoeconomic or technoeconomic) optimization. In thermodynamic optimization, the objective function can, for example, be the thermal efficiency, exergy efficiency, or the net power output. The modeling detail is typically restricted to flow sheet level including energy and mass balances. This approach has been used extensively for preliminary fluid selection. When used for selection and comparison of pure fluids and mixtures, a value for the minimum pinch point temperature difference in the heat exchangers is typically fixed and assumed equal for all fluids. When evaluated based on this approach, there is a general consensus in the scientific literature that the zeotropic mixtures provide significant thermodynamic benefits compared to pure fluids [6,9–14]. For a 120 ◦C geothermal heat source, Heberle et al. [9] found that i-butane/i-pentane (0.8/0.2)mole achieves 8% higher second law efficiency compared to pure i-butane. Andreasen et al. [10] identified 30 high performing fluids based on net power output for two heat sources and found that 19 fluids were zeotropic mixtures for a 120 ◦C heat source while 24 were zeotropic mixtures for a 90 ◦C heat source. Lecompte et al. [11] reported a 7.1–14.2% increase in the second law efficiency for zeotropic mixtures compared to the corresponding pure fluids for a 150 ◦C heat source. For heat source temperatures ranging from 150 ◦C to 300 ◦C, Braimakis et al. [12] compared the performance of five hydrocarbons and their mixtures, and found that zeotropic mixtures achieved the highest performance for all the investigated temperatures. The performance gains are generally attributed to improved temperature profile matching in the condenser [6,10] resulting in reduced exergy destruction (or irreversibilities) [9,11,13]. Another general conclusion from such studies is that the ORC units using mixtures require heat transfer equipment with larger capacities (*UA*¯ values) [9–12] and heat transfer areas *A* [13] when compared to pure fluids. Thereby, it remains unclear whether the increased performance compensates for the larger investment required for the heat exchangers when zeotropic mixtures are used as working fluids.

Baik et al. [15] fixed the total cycle *UA* value and optimized a transcritical ORC unit using R125 and three subcritical ORC units using R134a, R152a and R245fa. The results suggest a 5% larger net power output of the transcritical cycle compared to the highest performing subcritical cycle (R134a). In a comparison of pure and mixed working fluids for ORC units, Baik et al. [16] fixed the total cycle heat transfer area assuming tube-in-tube configurations for heat exchangers. Based on this comparison, they concluded that the use of zeotropic mixtures did not have a significant impact on the performance of the condensation process for transcritical ORC units. Bombarda et al. [17] compared the performance of an ORC unit and a Kalina cycle unit for diesel engine waste heat recovery based on equal logarithmic mean temperature differences in the heat exchangers, and found that the two cycles obtained similar performance. The works by Baik et al. [15,16] and Bombarda et al. [17] focus on specific case studies, and do not include an assessment of the employed methods or the implications of selecting those methods.

The trade-off between increased investment in heat transfer equipment versus improved thermodynamic performance can be accounted for in economic optimizations of ORC units. The models employed in economic analyses are typically based on a flow sheet level model for determining the thermodynamic states in the process, which is combined with economic models for estimating economic performance criteria, for example the net present value or levelized cost of electricity. In the economic models, the cost of the ORC unit is typically determined from equipment cost correlations usually involving sizing of heat transfer equipment. Previous studies employing thermoeconomic or technoeconomic optimization methods for fluid comparisons do not clearly

indicate whether mixtures or pure fluids are more feasible to use [18–25]. Le et al. [18] minimized the levelized cost of electricity for n-pentane/R245fa mixtures, and found that pure n-pentane yielded the lowest values. A similar conclusion was reached by Feng et al. [19] in a comparison based on a multi-objective optimization of levelized cost of electricity and exergy efficiency. In an other study, Feng et al. [20] found that a mixture of R245fa and R227ea was unable to reach lower levelized cost of electricity than R245fa. For a case study based on waste heat recovery, Heberle and Brüggemann [21] minimized the system cost per unit exergy for R245fa, i-butane, i-pentane, and i-butane/i-pentane, and found the lowest values for pure i-butane. Oyewunmi and Markides [22] investigated the thermoeconomic trade-offs for binary mixtures of n-butane, n-pentane, n-hexane, R245fa, R227ea, R134a, R236fa, and R245ca, and also found that pure fluids were the most cost-effective. On the other hand, Heberle and Brüggemann [23] demonstrated a 4% reduction in the electricity generation cost for propane/i-butane compared to i-butane for utilization of a geothermal heat source at 160 ◦C. Based on multi-objective optimizations of exergy efficiency and specific ORC unit investment cost, Imran et al. [24] found improved economic and thermodynamic performance for R245fa/i-butane (0.4/0.6)mass compared to pure R245fa and i-butane. Andreasen et al. [25] found that the outcome of the performance comparison between R32, and R32/R134a (0.65/0.35) depends on the amount of investment made. At high investment costs, the mixture R32/R134a (0.65/0.35) obtained higher performance than R32, while the two fluids reached similar performance at low investment costs. A major drawback of using the economic optimization methodology is the high model complexity and computational time required compared to thermodynamic methods. For this reason, thermodynamic methods are preferred for fluid screenings where many fluid candidates are considered.

As indicated above, contradicting conclusions are resulting from thermodynamic and economic optimization regarding the feasibility of using zeotropic mixtures. This is especially the case when the minimum pinch point temperature differences are assumed to be equal for all fluids. Thus, there is a risk that fluid screenings based on thermodynamic optimization and fixed minimum pinch point temperature difference assumptions might identify economically infeasible fluids. This indicates a need for improved methods for fluid screening, enabling effective identification of economically feasible zeotropic mixtures.

Alternative thermodynamic methods have been proposed and discussed in relation to vapor compression cycles [26,27]. McLinden and Radermacher [26] proposed a method for specifying the total heat exchanger area per unit capacity, and claimed that this method provides a fair basis for comparing the performance of pure fluids and mixtures. Högberg et al. [27] assessed three methods for comparing the performance of pure fluids and mixtures in heat pump applications. The first method was based on equal minimum approach temperatures (equivalent to equal minimum pinch point temperature differences), the second was based on equal mean temperatures in the heat exchangers and the third on equal heat exchanger areas. They concluded that the first method should be avoided, while the third method is the preferred method. The second method was evaluated good enough for rough performance estimations.

In the framework of preliminary performance evaluation of zeotropic mixtures and pure fluids for ORC systems, an assessment of available methods for modeling the heat exchangers is relevant, since the same values of the minimum pinch point temperature differences result in higher performance and larger heat transfer equipment for zeotropic mixtures [9–13]. Therefore, it should be considered whether the use of zeotropic mixtures results in higher performance when the same size of heat transfer equipment is used for the zeotropic mixtures and the pure fluids. Since the assumption of the same minimum pinch point temperature differences does not result in the same size of heat transfer equipment, it is relevant to consider alternative methods for modeling the performance of the heat exchangers in ORC systems. The relevance of an assessment of methods for thermodynamic performance evaluation of working fluids, is supported by the strong preference towards fixing the minimum pinch point temperature difference presented in the scientific literature. Generally, there is a lack of a quantitative assessment of the implications of selecting this approach in comparison to

alternative options. Such an assessment is particularly relevant in the case of performance comparison of pure fluids and zeotropic mixtures for ORC systems, since significant thermodynamic performance benefits have been estimated for zeotropic mixtures compared to pure fluids for the same values of minimum pinch point temperature differences [6,9–14], while economic optimizations have resulted in contradicting conclusions regarding the feasibility of using pure fluids and zeotropic mixtures [18–25].

The objective of the present study was to quantify the influence of different modeling methods on the results of the thermodynamic performance comparison of working fluids for ORC systems. The analysis considered methods which are relevant at an early stage in the ORC unit design procedure when many working fluid candidates are considered as possible alternatives. The conventional method of assuming the same minimum pinch point temperature differences in the heat exchangers for pure fluids and zeotropic mixtures was compared to three alternative methods for specifying heat exchanger performance in thermodynamic modeling of ORC systems. The four methods considered in this study are: (1) assuming the same minimum pinch point temperature differences for all working fluids; (2) assuming the same mean temperature differences for all working fluids; (3) assuming the same thermal capacity values (*UA*¯ values, the product of the overall heat transfer coefficient, *U*¯ , and the heat transfer area, *A*) for all working fluids; and (4) assuming the same heat transfer areas for all working fluids. First, it was considered how the net power outputs of ORC units using the working fluids propane, i-butane, and two mixtures of propane/i-butane (mole compositions of 0.2/0.8 and 0.8/0.2) vary as a function of the condenser size, represented by the minimum pinch point temperature difference, the mean temperature difference, the thermal capacity (*UA*¯ ) value, and the heat transfer area, respectively. Subsequently, a fluid ranking considering 30 working fluids (pure fluids and mixtures in subcritical and transcritical configurations) was made using the following methods: (1) assuming that all fluids have the same minimum pinch point temperature differences in the condenser and primary heat exchanger respectively; and (2) assuming that the sum of the primary heat exchanger and condenser thermal capacity (*UA*¯ ) is the same for all fluids. Based on the results of the analyses, the methods were assessed and the feasibility of using zeotropic mixtures in ORC power systems was discussed.

The major novelty of the paper is that it provides a quantitative assessment of using different methods for specifying heat exchanger performance in the thermodynamic comparison of zeotropic mixtures and pure fluids for ORC power systems. Such an assessment has not previously been carried out in relation to ORC power systems. In comparison to the method assessments for vapor compression cycles presented by McLinden and Radermacher [26] considering subcritical mixtures of R22/R114 and R22/R11, and Högberg et al. [27] considering subcritical mixtures of R22/R114 and R22/R142b, we extended the analysis by including a fluid ranking considering 30 different pure fluids and zeotropic mixtures comprising both subcritical and transcritical configurations. The conclusions obtained are not only relevant for ORC power systems, but also apply for other thermodynamic processes, as discussed in the paper.

Section 2 describes the implementation of the different models and methods. Section 3 presents and discusses the results of the analyses and includes the method assessment. The paper is ended by Section 4 where the conclusions of the study are presented.

#### **2. Methods**

The ORC unit analyzed in this study consisted of an expander, a condenser (cond), a pump and a primary heat exchanger (PrHE) (see Figure 1). The heat input to the unit was provided by a hot water stream, while the heat released from condensation of the working fluid was transferred to a cooling water stream. The case of liquid heat source and sink fluids justified the use of counter-flow heat exchangers, which enabled the utilization of temperature profile matching in the primary heat exchanger and condenser. The mechanical power generated by the expansion of the working fluid was transferred to a generator, enabling the ORC unit to deliver a net power output (*W*˙ *net*) defined by the difference between the power consumption of the pump and the expander (neglecting electrical and mechanical losses):

$$
\dot{W}\_{net} = \dot{m}\_{wf} \left[ h\_3 - h\_4 - (h\_2 - h\_1) \right] \tag{1}
$$

The numerical simulation models were developed in Matlab-<sup>R</sup> 2018b [28] using the commercial software REFPROP-<sup>R</sup> version 9 [29] for working fluid property data, and the open source software CoolProp version 4.2 [30] for properties of water. The assessment and comparison of the methods was demonstrated based on a case assuming a hot fluid inlet temperature of 120 ◦C. A detailed comparison of the net power output variation as a function of the minimum pinch point temperature difference, the mean temperature difference, the *UA*¯ value, and the heat transfer area of the condenser, respectively, was carried out. The working fluids selected for the detailed comparison were, propane, i-butane, and two mixtures of these fluids, which have previously showed promising performance in subcritical ORC systems [10,21]. The mole compositions of the two mixtures were selected to be 0.2/0.8 and 0.8/0.2, since these compositions result in a temperature glide around 5 ◦C, corresponding to the selected temperature rise of the cooling water. Subsequently, the performance of propane/i-butane was compared with the 29 other fluids (pure fluids and mixtures in subcritical and transcritical configurations) identified by Andreasen et al. [10].

**Figure 1.** A sketch of the organic Rankine cycle system.

#### *2.1. Thermodynamic ORC Process Model*

The thermodynamic models described here provide the basis for the four different methods compared in this study. The only difference between the three methods employing constraints on the minimum pinch point temperature differences (Δ*Tpp*), the mean temperature differences (Δ*Tm*), or the *UA*¯ values of the heat exchangers, was the calculation of the heat exchanger performance variable (i.e., Δ*Tpp*, Δ*Tm*, or *UA*¯ was calculated and constrained). The fourth method, which based the performance comparison on heat exchanger surface areas, needed to be supplemented by models for dimensioning of heat exchangers (see Section 2.2).

The modeling conditions used for simulating the ORC unit were based on Andreasen et al. [10] and are shown in Table 1. Additional assumptions were as follows: no pressure loss in piping or heat exchangers, no heat loss from the system, and steady state condition and homogeneous flow. The decision variables were optimized to maximize the net power output of the ORC system, while respecting the constraints on primary heat exchanger and condenser performance, and the minimum expander outlet vapor quality. The optimization was carried out in two steps, where the first optimization step was carried out by running the particle swarm optimizer available in Matlab with a population of 30,000 for 50 iterations. The best solution found in the first step was used as the starting point for Matlab's pattern search optimizer. In Table 1, the primary heat exchanger

and condenser constraints are denoted as minimum pinch point temperature difference constraints, however these constraints were substituted by constraints on maximum values of *UA*¯ depending on which method was applied. Note that the heat exchanger parameters were implemented as constraints and not as fixed parameters. However, by optimizing the primary heat exchanger pressure, degree of superheating, working fluid mass flow rate, and the condensation temperature, the optimum values of minimum pinch point temperature differences or *UA*¯ values converged to the limiting values.



\* Results presented in Section 3.2 employ heat exchanger constraints based on the *UA*¯ value rather than minimum pinch point temperature differences. \*\* The condenser minimum pinch point temperature difference was varied in steps of 1 ◦C.

For the primary heat exchanger and condenser, a counter-current flow heat exchanger configuration was assumed. The location of the minimum pinch point temperature difference in the primary heat exchanger was assumed to be at the inlet, outlet, or the saturated liquid point. The temperature difference in the condenser was checked at the working fluid outlet (bubble point) and at the dew point. Calculations of *UA*¯ values and mean temperature differences were done by discretizing the primary heat exchanger and the condenser in *n* = 10 control volumes. In the discretization, it was ensured that the bubble and dew points were always located on control volume boundaries. The total *UA*¯ values of the heat exchangers were calculated by summing the contribution from each control volume (*UA*¯ )*j*:

$$\text{dDA} = \sum\_{j=1}^{n} (\text{D}\mathbf{I}A)\_{j} = \sum\_{j=1}^{n} \frac{\dot{Q}\_{j}}{(\Delta T\_{lm})\_{j}} = \sum\_{j=1}^{n} \left[ \frac{\dot{m}\_{\text{c}}(h\_{\text{c},o} - h\_{\text{c},i})}{(T\_{h,o} - T\_{\text{c},i}) - (T\_{h,i} - T\_{\text{c},o})} \cdot \ln\left(\frac{T\_{h,o} - T\_{\text{c},i}}{T\_{h,i} - T\_{\text{c},o}}\right) \right]\_{j} \tag{2}$$

where *Q*˙ is the heat transfer rate, Δ*Tlm* is the log mean temperature difference, *T* is temperature, subscript *j* refers to control volume *j*, subscripts *c* and *h* refer to the cold and hot side of the heat exchanger, and subscripts *i* and *o* refer to inlet and outlet of control volume *j*. The log mean temperature correction factor was not included in the expression, since the heat exchangers were assumed to enable counter-current flow. Counter-current flow is required in order to utilize the temperature glide of zeotropic mixtures for temperature profile matching with the hot fluid and the cooling water, and can be achieved with plate, tube-in-tube, and single-pass shell-and-tube heat exchangers.

The mean temperature difference was calculated based on the following equation:

$$
\Delta T\_m = \frac{\dot{Q}}{\overline{U}A} \tag{3}
$$

#### *2.2. Shell-and-Tube Heat Exchanger Model*

A shell-and-tube heat exchanger model was used for estimating the heat transfer area of the condenser. The model was used for estimation of the heat transfer areas presented in Section 3.1.4. The heat exchanger was assumed to have one tube pass and one shell pass (see Figure 2).

The heat transfer surface area was calculated based on the following equation:

$$A = \pi d\_{\rm ou} L N\_{\rm t} \tag{4}$$

where *dou* is the outer tube diameter, *L* is the tube length, and *Nt* is the number of tubes.

The tube length required for transferring the required heat was calculated by discretization of the heat exchanger:

$$L = \sum\_{j=1}^{n} L\_j = \sum\_{j=1}^{n} \frac{(\bar{\mathcal{U}}A)\_j}{(\bar{\mathcal{U}}A)'\_j} \tag{5}$$

where (*UA*¯ ) *<sup>j</sup>* is the *UA*¯ per length of tube, which was calculated as:

$$\frac{1}{(\overline{\Omega}A)'\_{j}} = \frac{1}{a\_{in,j}\pi d\_{in}N\_{t}} + \frac{\ln\left(d\_{out}/d\_{in}\right)}{2\pi\lambda\_{t}N\_{t}} + \frac{1}{a\_{out,j}\pi d\_{out}N\_{t}}\tag{6}$$

where *din* is the inner tube diameter, *λ<sup>t</sup>* is the thermal conductivity of the tube material, *αin*,*<sup>j</sup>* is the inner tube heat transfer coefficient (hot side), and *αou*,*<sup>j</sup>* is the outer tube heat transfer coefficient (cold side).

**Figure 2.** A sketch of the shell-and-tube condenser.

In the heat exchanger model, the number of control volumes was equal to 30. In case the working fluid was superheated vapor at the inlet to the condenser, the condenser was sized to perform both the desuperheating and the condensation of the working fluid. An overview of the implemented heat transfer and pressure drop correlations is provided in Table 2. The modeling conditions assumed for the condenser are listed in Table 3. The tube diameter, tube pitch ratio and baffle cut ratio were selected to represent commonly used values according to the guidelines provided by Shah and Sekuli´c [31]. A low value of the shell bundle clearance corresponding to a fixed tube sheet design [31] was selected. This enabled a design without sealing strips, since there was no need to restrict the bypass flow between the shell inner wall and the tube bundle. The tube-to-baffle hole diametral clearance and the

shell-to-baffle diametral clearance values were selected based on the values used in Example 8.3 in Shah and Sekuli´c [31]. The thermal conductivity of the tube material was selected to represent stainless steel [31]. The pressure drops were fixed to ensure comparable pumping power for all considered ORC systems. The values of pressure drop were selected to ensure that the flow velocities of the liquid in the shell and the vapor in the tubes were within the limits specified by Coulson and Richardson [32]. The tubes were arranged in a 30◦ triangular configuration to enhance heat transfer performance [31,33] and no tubes were placed in the window section in order to minimize tube vibration problems [31]. Shell side heat transfer and pressure drop correction factors accounting for larger baffle spacing at the inlet and outlet ducts compared to the central baffle spacing were neglected.

The model of the shell-and-tube heat exchanger was previously presented and verified by Andreasen et al. [25] and Kærn et al. [34]. The implementation of the Bell–Delaware method [35–37] was verified by comparison with the outline presented by Shah and Sekuli´c [31]. The cross-flow, leakage flow, and by-pass flow areas were predicted within 0.11% (discrepancies were due to rounding errors) of the values reported in Example 8.3 in Shah and Sekuli´c [31]. The shell side heat transfer coefficient and pressure drop for single phase flow of a lubricating oil were predicted within 0.15% (discrepancies were due to rounding errors) of the values reported in Example 9.4 in Shah and Sekuli´c [31]. The implementation of the condensation heat transfer correlation was verified to be within 0.8% of the predicted heat transfer coefficients for i-butane presented in Figure 5 in Shah [38]. Discrepancies can be attributed to inaccuracies in obtaining data points from the figure.


**Table 2.** Shell-and-tube heat exchanger model overview.

**Table 3.** Condenser modeling conditions.


(†) The number of tubes and baffle spacing were selected to obtain the specified pressure drops through a numerical solving procedure.

#### **3. Results and Discussion**

#### *3.1. Influence of Heat Exchanger Parameters*

In the following, it is demonstrated how the results of a net power output comparison among pure fluids and zeotropic mixtures is affected by which heat exchanger performance parameter is used as basis for the comparison. First, the condenser size is represented using the minimum pinch point temperature difference and subsequently the condenser size is represented by mean temperature differences, *UA*¯ values and heat transfer areas. The analysis presented in Section 3.1 is based on the simulation data listed in Table A1 in Appendix A.

#### 3.1.1. Minimum Pinch Point Temperature Difference Based Comparison

Figure 3 shows the maximized net power output as a function of the condenser minimum pinch point temperature difference for i-butane, propane/i-butane (0.2/0.8), propane/i-butane (0.8/0.2) and propane. For all fluids, an approximately linear trend was observed, and the absolute difference in terms of net power output among the fluids was independent of value selected for the condenser minimum pinch point temperature difference. Sketches of the ORC unit *T*,*s*-diagrams for the four fluids are displayed in Figure 4.

**Figure 3.** Net power output versus pinch point temperature difference for the condenser.

**Figure 4.** *Cont.*

**Figure 4.** *T*,*s*-diagrams for the four ORC units using propane, i-butane, propane/i-butane (0.2/0.8), and propane/i-butane (0.8/0.2) with Δ*Tpp*,*cond* = 5 ◦C.

The variation of *UA*¯ and Δ*Tm* for the condensers are depicted in Figure 5. When the minimum pinch point temperature difference was the same for the pure fluids and the mixtures, the heat transfer equipment used for mixture condensation was associated with larger values of *UA*¯ and smaller values of mean temperature difference. The performance comparison was therefore affected by whether the fluids were compared based on the same values of the minimum pinch point temperature difference, mean temperature difference or *UA*¯ .

**Figure 5.** Condenser *UA*¯ and mean temperature difference versus pinch point temperature difference.

3.1.2. Mean Temperature Difference Based Comparison

The plot depicted in Figure 6 is generated by exchanging the minimum condenser pinch point temperature difference represented on the horizontal axis in Figure 3 with the mean temperature difference. Note that the optimized solutions displayed in Figures 3 and 6 are the same. For each fluid, the left most points in Figure 6 correspond to the solutions with a minimum pinch point temperature difference in the condenser of 10 ◦C, while the right most points correspond to the optimized solutions with minimum pinch point temperature difference values of 1 ◦C. The filled marker represent the solutions with a minimum pinch point temperature difference of 5 ◦C.

For all fluids plotted in Figure 6, the relationship between the mean temperature difference and the net power output were approximately linear. This was also the case when the fluids were compared based on the same values of condenser pinch points. However, when compared based on the mean temperature differences, the curves for the pure fluids and the mixtures were displaced relative to each other. Generally, the mixtures achieved mean temperature differences that were similar to the pinch point temperature differences, while the pure fluids had mean temperature differences that were 1.5–3 ◦C higher than the pinch points. This means that the performance improvement obtained by mixtures was rated less when the comparison was based on the same values of mean temperature differences than on the same values of minimum pinch point temperature differences. The results shown in Figure 6 suggest that the performance of propane was higher than that of propane/i-butane (0.2/0.8) for mean temperature differences higher than 3 ◦C, whereas propane/i-butane (0.2/0.8) reached higher net power outputs than those of propane for all values of the condenser pinch point temperature difference in the pinch point based comparison (see Figure 3).

A comparison of the condensation processes for propane and propane/i-butane (0.2/0.8) is illustrated in the *QT*˙ -diagrams (heat transfer rate versus temperature diagrams) depicted in Figures 7 and 8. Figure 7 displays the comparison based on equal values of minimum pinch point temperature differences (Δ*Tpp* = 5 ◦C). The condensation process of propane is displayed as a horizontal line, since the optimum solution resulted in condensation from saturated vapor to saturated liquid. The optimum solution for propane/i-butane (0.2/0.8) involved 10 ◦C of desuperheating. Disregarding the desuperheating process, the condensation process for propane/i-butane (0.2/0.8) was carried out at a lower temperature than the condensation of propane, resulting in a lower mean temperature for the mixture. Due to the match between the temperature glide of the mixture and the temperature increase of the coolant, the minimum pinch point temperature difference value could be achieved throughout most of the condensation process. This resulted in dissimilar mean temperatures for the pure fluid and the mixture. The mean temperature was Δ*Tm* = 7.2 ◦C for propane, while it ess Δ*Tm* = 5.2 ◦C for the mixture. When the pinch point temperature difference of propane/i-butane (0.2/0.8) was increased by 2 ◦C, the mean temperatures of the two fluids were equal. This situation is displayed in Figure 8. When Δ*Tm* = 7.2 ◦C for both fluids, the temperature difference between the coolant and the condensing working fluid was lowest for the mixture in the left half of the *QT*˙ -diagram (from 0% to 50% heat transfer rate), while it was lowest for propane in the remaining part of the diagram (from 50% to 100% heat transfer rate).

**Figure 6.** Net power output as a function of condenser mean temperature difference.

**Figure 7.** *QT*˙ -diagram of condensation when Δ*Tpp* = 5 ◦C for propane and propane/i-butane (0.2/0.8).

**Figure 8.** *QT*˙ -diagram of condensation when Δ*Tm* = 7.2 ◦C for propane and propane/i-butane (0.2/0.8).
