#
Thermo-Economic Analysis of Zeotropic Mixtures and Pure Working Fluids in Organic Rankine Cycles for Waste Heat Recovery^{ †}

^{*}

^{†}

## Abstract

**:**

_{PP,C}at the pinch-point of the condenser and a low minimal temperature difference ΔT

_{PP,E}at the pinch-point of the evaporator. Choosing isobutane as the working fluid leads to the lowest costs per unit exergy with 52.0 €/GJ (ΔT

_{PP,E}= 1.2 K; ΔT

_{PP,C}= 14 K). Considering the major components of the ORC, specific costs range between 1150 €/kW and 2250 €/kW. For the zeotropic mixture, a mole fraction of 90% isobutane leads to the lowest specific costs per unit exergy. A further analysis of the ORC system using isobutane shows high sensitivity of the costs per unit exergy for the selected cost estimation methods and for the isentropic efficiency of the turbine.

## 1. Introduction

## 2. Methods

#### 2.1. Exergy Analysis

_{HS}= 6 bar). The mass flow and the outlet temperature of the heat source are chosen according to a thermal heat input of 3 MW. For the analysis, an air-cooled system is considered. R245fa, isobutane and isopentane, as well as the zeotropic mixture of isobutane/isopentane, are examined as ORC working fluids. Previous analysis show that isobutane and isobutane/isopentane lead to high second law efficiencies for the considered heat source temperature [25]. In order to evaluate the pure components of the fluid mixture, also isopentane is included to the analysis. In addition, R245fa is examined as benchmark, since this working fluid is commonly used in existing ORC power systems at the considered temperature level [30,31]. For the considered mixture, the composition is varied in discrete steps of 10 mol%. The temperature difference in the evaporator and condenser are chosen as independent design variables in order to identify the most cost-efficient process parameters. The analysis is conducted neglecting pressure and heat losses in the pipes and components. In Table 1 the boundary conditions for the cycle simulations are shown.

_{II}of the ORC is calculated by:

_{G}and P

_{Pump}correspond to the power of the generator and the pump. P

_{Fans}is related to the power of the air cooler fans. The exergy flow of the heat source $\dot{E}$

_{HS}is obtained by multiplying the specific exergy e

_{HS}with the mass flow rate ṁ

_{HS}. The specific exergy could be calculated by:

_{0}= 15 °C and p

_{0}= 1 bar). Corresponding to Bejan et al. [32], the exergy analysis is extended by an exergy balance for each system component k:

_{F}and $\dot{E}$

_{P}describe the exergy flow rate of the fuel and the product. The exergy flow rate $\dot{E}$

_{L}includes heat losses to the surrounding or exergy that leaves the system in a physical way, like exhaust gases. Here, $\dot{E}$

_{L}= 0, due to neglected heat losses. The exergy flow rate $\dot{E}$

_{D}represents the exergy destruction rate associated to irreversibilities. Exemplarily, the exergy destruction rate of the preheater can be calculated as:

_{m,PH}is the thermodynamic mean temperature of the heat source in the preheater.

#### 2.2. Component Design and Economic Analysis

_{0}in US $ depending on the parameter Y:

_{1}, K

_{2}, and K

_{3}are listed in Table 2. Alternatively, bare module costs are estimated by data of Ulrich and Vasudevan [34]. A conversion ratio of 0.815 is considered to convert the PEC in Euro. Due to maximal ORC pressures below 35 bar, additional cost factors are only considered in Section 3.3.

_{2001}) of 397 into relation to the value of 2014 with 575, the inflation and the development of raw material prices are taken into account [33]. For the costs of the major components of the ORC power plant C

_{ORC,MC}the PEC are summarized. In this study, the total investment costs of the power plant module C

_{TM}are calculated by multiplying C

_{ORC,MC}by the factor F

_{costs}= 6.32. According to Bejan et al. [32] this parameter represents additional costs like installation, piping, controls, basic engineering, and others in the case of the construction of a new facility. In addition, the authors specify the factor F

_{costs}= 4.16 for the expansion of existing facilities. Alternatively, the total module costs are estimated according to Turton et al. [33]. Therefore, bare module equipment costs for a component at real operating conditions C

_{BM}is calculated by multiplying the obtained purchased equipment costs C

_{0}by corrections factors depending on material F

_{m}and pressure F

_{p}.

_{TM,Turton}are defined by:

_{tot}of each heat exchanger is calculated by:

_{o}represents the heat transfer coefficient at the outside of the tube, respectively, the shell side and α

_{i}corresponds to the heat transfer coefficient at the inside of the tube. The inner and outer radius of the tube are represented by r

_{i}and r

_{o}. The thermal conductivity of the tube corresponds to λ

_{t}. The outer diameter of the tubes is 20 mm and the wall thickness of the tube is 2 mm. In order to calculate the required diameter of the shell and the number of tubes, the maximal flow velocities of 1.5 m/s for liquid flows and 20 m/s for gaseous flows are assumed according to chapter O1 of the VDI Heat Atlas [35]. In general, the ORC working fluid is led inside the tubes. Regarding the tube layout, a squared pitch and a pitch-to-diameter ratio of 1.22 are assumed. The considered heat transfer correlations for the calculation of α

_{i}, depending on phase state and flow configuration are listed in Table 3. A detailed overview of the correlations is provided in appendix B. In case of the preheater and the evaporator, the method of Kern [36] is applied for the shell side (α

_{o}). For the air-cooled condenser a tube bank staggered arrangement is applied. In this context, a cross-flow heat exchanger with finned tubes is considered and the following design parameters are assumed: fin height of 3 mm, a fin thickness of 0.3 mm, a fin spacing of 2 mm, and a transversal tube pitch of 60 mm. The air-side heat transfer coefficient is determined by the method of Shah and Sekulic [37]. For all considered heat exchangers, the heat transfer surface is finally calculated by:

_{log}is the logarithmic mean temperature difference:

_{LMTD}is equal 1 for condensation and boiling heat transfer. In this study, the simplifying assumption of F

_{LMTD}= 1 is also met for single phase heat transfer.

#### 2.3. Exergy Costing

_{k}describe the costs of the k-th component depending on operation and maintenance $\dot{Z}$

_{OM}and capital investment $\dot{Z}$

_{CI}. In order to calculate the described cost streams the economic boundary conditions listed in Table 4 are assumed.

_{P,tot}. In this study, the generated electricity is considered as the product of the system and the $\dot{E}$

_{P,tot}correspond to the power output of the generator. In this context, the auxiliary power requirements are covered by electricity from the grid. Alternatively, the net power output of the system can be considered in the denominator of Equation (13). The exergy rate of the fuel $\dot{E}$

_{F,tot}represents the exergy rate of the waste heat source transferred to the ORC system.

_{MC}:

_{TM}:

_{CI}are the yearly financial linked costs and E

_{annual}is the annual amount of generated electricity.

## 3. Results and Discussion

#### 3.1. Identification of Cost-Efficient Design Parameters

_{p,tot}are identified depending on the minimal temperature difference ΔT

_{PP}in the evaporator and condenser. In order to vary the minimal temperature difference, the corresponding upper and lower ORC pressure is adapted. In Figure 2, the specific costs of the product are shown exemplarily for R245fa. The most cost-efficient design parameters for this ORC working fluid are ΔT

_{PP,E}= 1 K and ΔT

_{PP,C}= 13 K. For these parameters, costs per unit exergy of 56.8 €/GJ are obtained. Considering a minimal temperature difference between 0.5 K and 6 K for the evaporator and 8 K and 14 K for the condenser, the maximum costs per unit exergy of 60.0 €/GJ are calculated (ΔT

_{PP,E}= 6 K; ΔT

_{PP,C}= 8 K). In general, the cost minimum is a compromise between rising power output and increasing costs with decreasing minimal temperature difference in the heat exchangers. The results show that the condenser is crucial for the total PEC. Due to the highest amount of transferred thermal energy combined with the lowest logarithmic mean temperature difference, the highest heat transfer areas and component costs are obtained for the condenser. In case of the most cost-efficient solution for R245fa, the PEC of the condenser are 47.6%, the PEC of the turbine are 36.8%, PEC of the preheater and the evaporator are 14.1% and PEC of the pump are 1.5% in relation to the total PEC of the major ORC components. To summarize: the most cost-effective parameters show a low ΔT

_{PP}for the evaporator and a high value in case of the condenser. This general result is also suitable for water-cooled systems. A previous thermo-economic study of geothermal, water-cooled ORC systems showed similar results [24].

#### 3.2. Comparison of ORC Working Fluids

_{PP,E}, always the most cost-effective parameter is chosen. In Figure 3b specific costs of the product are shown for selected mole fractions of the zeotropic mixture isobutane/isopentane.

_{PP,E}= 1.2 K and ΔT

_{PP,C}= 14 K. At these operational parameters the maximum ORC pressure is reached in case of isobutane. R245fa and isopentane lead to 9.2% and 15.0% higher costs per unit exergy (see Table 5). Although, these alternative pure working fluids show optimal design parameters with a lower minimum temperature difference, the gross power output is 10.8% and 14.6% lower. Due to the high power requirements of the ORC pump in case of isobutane, the net second law efficiency is only between 1.0% and 3.0% higher compared to R245fa and isopentane. The total heat exchange area differs only slightly for the considered working fluids. Compared to isobutane, the total heat exchange area is 0.3% lower for R245fa and 2.1% higher for isopentane.

_{ORC,MC}(449,917 €), isobutane leads to the lowest SIC due the high power output. In comparison, R245fa leads to the lowest C

_{ORC,MC}(439,336 €). Nevertheless the SIC are 9.3% higher compared to isobutane. The LCOE listed in Table 4 confirm the so-far described economic results for pure working fluids. In this context, the working fluid isobutane show the lowest LCOE with 106.5 €/MWh. R245fa and isopentane show 1.3% and 3.6% higher values.

_{PP,E}= 2 K and ΔT

_{PP,C}= 15 K specific costs of 53.8 €/GJ are obtained. The costs per unit exergy are 3.5% higher compared to the most efficient component isobutane. The total heat exchange area is 3.6% lower for 90/10 compared to isobutane, which leads to 2.0% lower C

_{ORC,MC}. At the same time the power output is 5.5% lower. It should be noted that, based on the LCOE, the zeotropic mixture leads to most cost-efficient solution. For the listed operational parameter in Table 4 the ORC with the working fluid isobutane shows a 0.5% higher LCOE. The differences between the discussed economic parameters result from a different cost balancing. For the calculation of LCOE, costs for capital investment and costs for operation and maintenance are considered. In contrast, the exergo-economic method also includes costs for unused exergy which is released to the environment (see Equation (12)). In the case of the zeotropic mixture, this portion of costs leads to higher specific costs per unit exergy compared to isobutane. The contrary results of the parameters LCOE and c

_{p,tot}suggest a nearly economic equivalence of the identified ORC system based on isobutane and the zeotropic mixture isobutane/isopentane as working fluid.

#### 3.3. Sensitivity Analysis for Selected Boundary Conditions

_{PP,E}= 2 K and ΔT

_{PP,C}= 12 K.

_{costs}. This general behavior can be adopted to other working fluids and operational parameters. The sensitivity analysis for the working fluids isobutane, isobutane/isopentane (90/10), and R245fa at the most cost-effective parameters show qualitatively equal results. Regarding the considered economic parameters, costs for process integration and the cost factor F are the most important input data. For systems with higher module costs the sensitivity is even more pronounced. In case of R245fa as working fluid, the specific costs increase by 0.19 €/GJ per % deviation from the standard costs for process integration. Compared to isobutane (according to Figure 4: 0.17 €/GJ per % deviation), this is an increase in sensitivity of 9.2%.

_{p,tot}. In this context, the costs per unit exergy for the working fluid isopentane is decreased from 59.8 €/GJ to 59.1 €/GJ. Isobutane still leads to the most cost-effective ORC system. The specific costs are increased by 0.4% compared to the initial efficiency assumption. In case of R245fa or isopentane as workings fluid, the turbine design calculations show high values for the size parameter SP and the mean diameter D

_{m}. Hence, high isentropic efficiencies are obtained in conjunction with a large turbine size. For further investigations, the design parameters could be used as input for more precise cost estimations. In this context, exemplarily the turbine cost correlation of Astolfi et al. [17] could be mentioned.

_{PP,E}= 1.2 K and ΔT

_{PP,C}= 14 K the results are listed in Table 7.

_{P,tot}is 28.4 %, for LCOE 81.4% and for SIC 287.0%. The calculation of bare module costs in conjunction with cost correlation of Turton et al. [33] lead to the lowest economic parameters. For the alternative cost database of Ulrich and Vasudevan [34], which also provides bare module costs, the costs per unit exergy are 7.9% higher. A comparison of SIC for waste heat recovery units with literature data [22,23,26] or guide prices from manufactures indicate the generalization of the approach of Bejan et al. [32] by multiplying the total PEC by a certain factor F

_{cost}. As a consequence, the resulting absolute costs should be interpreted with caution. Nevertheless, an evaluation of different technical solutions, working fluids, or operational parameters for constant boundary conditions seems justifiable.

## 4. Conclusions

_{PP,E}= 1.2 K; ΔT

_{PP,C}= 14 K). Regarding the considered mixture isobutane/isopentane, a mole fraction of 90% isobutane leads to the lowest costs per unit exergy. The economic parameters show a high sensitivity regarding the isentropic efficiency of the turbine and the selected cost estimation methods. First results are presented for an implementation of more detailed models concerning these impact factors. Based on this analysis, the presented thermo-economic model will be extended in further work.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ORC | Organic Rankine Cycle |

## Nomenclature

A | heat transfer area | (m^{2}) |

c | costs per unit exergy | (€/GJ) |

C | costs | (€) |

$\dot{C}$ | cost rate | (€/h) |

D | diameter | (mm) |

e | specific exergy | (kJ/kg) |

$\dot{E}$ | exergy flow | (kW) |

F | correction factor | (-) |

h | specific enthalpy | (kJ/kg) |

K | constant | (-) |

ṁ | mass flow | (kg/s) |

Ns | specific speed | (-) |

p | pressure | (bar) |

P | power | (kW) |

r | radius | (m) |

rd | relative deviation | (%) |

s | specific entropy | (kJ/(kgK)) |

SIC | specific investment costs | (€/kW) |

SP | size parameter | (-) |

T | temperature | (°C) |

U | overall heat transfer coefficient | (W/(m^{2}K)) |

Y | capacity/size parameter | (kW) or (m^{2}) |

$\dot{Z}$ | cost rate | (€/h) |

α | heat transfer coefficient | (W/(m^{2}K)) |

ΔT | temperature difference | (K) |

η | efficiency | (%) |

## Subscript

C | condenser |

CI | capital investment |

CM | cooling medium |

D | destruction |

E | evaporator |

F | fuel |

G | generator |

HS | heat source |

i | inner |

in | inlet |

is | isentropic |

II | second law |

k | k-th component |

L | loss |

LMTD | logarithmic mean temperature difference |

log | logarithmic |

m | mean |

net | net |

o | outer |

out | outlet |

O&M | operation and maintenance |

P | product |

PH | preheater |

PP | pinch point |

Pump | pump |

s | specific |

t | tube |

tot | total |

0 | reference state |

## Appendix A

#### R245fa

**2006**, 51, 785–850. [Google Scholar] [CrossRef]

**2003**, 42, 3163–3178. [Google Scholar] [CrossRef]

**2002**, 47, 932–940. [Google Scholar] [CrossRef]

**2013**, 41, 043105. [Google Scholar] [CrossRef]

#### Isobutane

**2006**, 35, 929–1019. [Google Scholar] [CrossRef]

**2000**, 21, 343–356. [Google Scholar] [CrossRef]

**2002**, 47, 1272–1279. [Google Scholar] [CrossRef]

**2013**, 41, 043105. [Google Scholar] [CrossRef]

#### Isopentane

**2006**, 51, 785–850. [Google Scholar] [CrossRef]

**2013**, 41, 043105. [Google Scholar] [CrossRef]

#### Isobutane/Isopentane

## Appendix B

_{l}and α

_{g}are calculated by Equation (B1). In Equation (B3) ρ correspond to density and x to vapor quality.

_{0}represent experimental fitted constants. The following assumptions are made: β = 2 × 10

^{−4}m/s and B

_{0}= 1. The mole fraction of liquid and gaseous phase of the component i corresponds to x

_{i}and y

_{i}. The temperatures T

_{si}describe the saturation temperature of the mixture component.

_{eff}represents the heat transfer coefficient for the zeotropic mixture, while α(x) is calculated according to Equation (B5) using fluid properties of the fluid mixture. For the heat transfer coefficient in the gaseous phase α

_{g}Equation (B7) is applied:

_{g}is the ratio between the sensible part of the condensation of the zeotropic mixture and the latent part. Here, c

_{p,g}represents the heat capacity of the gaseous phase, T

_{G,Cond}the temperature glide at condensation, and Δh the corresponding enthalpy difference.

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**Figure 2.**Costs per unit exergy for R245fa as ORC working fluid depending on the minimum temperature difference in the evaporator and condenser.

**Figure 3.**Specific costs per unit exergy (

**a**) for selected pure ORC working fluids and (

**b**) for the zeotropic mixture isobutane/isopentane depending on the minimum temperature difference in the condenser.

**Figure 4.**Cost per unit exergy as a function of selected parameters for the working fluid isobutane (ΔT

_{PP,E}= 2 K; ΔT

_{PP,C}= 12 K).

Parameter | Value |
---|---|

mass flow rate of heat source ṁ_{HS} | 10 kg/s |

outlet temperature of heat source T_{HS,in} | 80 °C |

inlet temperature of cooling medium T_{CM,in} | 15 °C |

temperature difference of cooling medium ΔT_{CM} | 15 °C |

maximal ORC process pressure p_{2} | 0.8∙p_{crit} |

isentropic efficiency of feed pump η_{i,P} | 75% |

isentropic efficiency of turbine η_{is}_{,T} | 80% |

efficiency of generator η_{G} | 98% |

**Table 2.**Equipment cost data used for Equation (5) according to [33].

Component | Y; Unit | K_{1} | K_{2} | K_{3} |
---|---|---|---|---|

pump (centrifugal) | kW | 3.3892 | 0.0536 | 0.1538 |

heat exchanger (floating head) | m^{2} | 4.8306 | −0.8509 | 0.3187 |

heat exchanger (air cooler) | m^{2} | 4.0336 | 0.2341 | 0.0497 |

turbine (axial) | kW | 2.7051 | 1.4398 | −0.1776 |

**Table 3.**References for the considered heat transfer correlations (for details see Appendix B).

Heat Exchanger | Tube Side |
---|---|

preheater | Sieder and Tate [38] |

evaporator (pure working fluid) | Steiner [39] |

evaporator (zeotropic mixture) | Schlünder [40] |

condenser (pure working fluid) | Shah [41] |

condenser (zeotropic mixture) | Silver, Bell, and Ghaly [42,43] |

Parameter | Value |
---|---|

Lifetime n | 20 years |

Interest rate ir | 4.0% |

Annual operation hours | 7500 h/year |

Cost rate for operation and maintenance C_{O&M} | 0.02∙$\dot{Z}$_{CI} |

Costs for process integration C_{PI} | 0.2∙C_{ORC,MC} |

Power requirements of the air-cooling system | 5 kW_{e}/MW_{th} |

Electricity price €/kWh | 0.08 €/kWh |

Parameter | Isobutane | R245fa | Isopentane | Isobutane/Isopentane |
---|---|---|---|---|

A_{PH} (m^{2}) | 173.2 | 100.0 | 90.8 | 108.1 |

A_{E} (m^{2}) | 123.1 | 118.1 | 118.6 | 112.8 |

A_{C} (m^{2}) | 747.1 | 821.7 | 856.0 | 785.0 |

P_{G} (kW) | 387.8 | 345.9 | 331.0 | 366.4 |

P_{Pump} (kW) | 60.1 | 21.6 | 12.1 | 41.4 |

ΔT_{PP,E} (K) | 1.2 | 1.0 | 1.0 | 2.0 |

ΔT_{PP,C} (K) | 14.0 | 13.0 | 13.0 | 15.0 |

η_{II} (%) | 30.3 | 30.0 | 29.4 | 30.0 |

SIC_{MC} (€/kW) | 1161.9 | 1270.1 | 1336.2 | 1203.0 |

SIC_{TM} (€/kW) | 7343.2 | 8027.3 | 8445.0 | 7602.7 |

LCOE (€/MWh) | 106.5 | 107.9 | 110.3 | 106.0 |

c_{p,tot} (€/GJ) | 52.0 | 56.8 | 59.8 | 53.8 |

Parameter | Isobutane | R245fa | Isopentane | Isobutane/Isopentane |
---|---|---|---|---|

η_{i,T} (%) | 78.5 | 80.2 | 80.6 | 78.8 |

rd_{ηi,T} (%) | 1.9 | 0.3 | 0.8 | 1.5 |

SP (-) | 0.0486 | 0.0729 | 0.0820 | 0.0508 |

D_{m}
(mm) | 130.5 | 195.7 | 220.1 | 136.7 |

c_{p,tot} (€/GJ) | 52.2 | 56.7 | 59.1 | 54.0 |

rd_{cp,tot} (%) | 0.4 | 0.2 | 1.3 | 0.4 |

**Table 7.**Economic parameters for selected cost estimation methods and cost databases in case of isobutane at the operational parameters ΔT

_{PP,E}= 1.2 K and ΔT

_{PP,C}= 14 K.

Cost Estimation Method | c_{p,tot} (€/GJ) | LCOE (€/MWh) | SIC_{TM} (€/kW) |
---|---|---|---|

F_{costs} = 6.32 | 52.0 | 106.5 | 7332.5 |

F_{costs} = 4.31 | 46.4 | 83.2 | 5000.5 |

C_{TM,Turton} | 40.5 | 58.7 | 2554.7 |

C_{TM,Ulrich} | 43.7 | 71.9 | 3875.1 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Heberle, F.; Brüggemann, D.
Thermo-Economic Analysis of Zeotropic Mixtures and Pure Working Fluids in Organic Rankine Cycles for Waste Heat Recovery. *Energies* **2016**, *9*, 226.
https://doi.org/10.3390/en9040226

**AMA Style**

Heberle F, Brüggemann D.
Thermo-Economic Analysis of Zeotropic Mixtures and Pure Working Fluids in Organic Rankine Cycles for Waste Heat Recovery. *Energies*. 2016; 9(4):226.
https://doi.org/10.3390/en9040226

**Chicago/Turabian Style**

Heberle, Florian, and Dieter Brüggemann.
2016. "Thermo-Economic Analysis of Zeotropic Mixtures and Pure Working Fluids in Organic Rankine Cycles for Waste Heat Recovery" *Energies* 9, no. 4: 226.
https://doi.org/10.3390/en9040226