# Thermo-Economic Evaluation of Organic Rankine Cycles for Geothermal Power Generation Using Zeotropic Mixtures

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Reliability of Fluid Properties

#### 2.2. Process Simulation and Second Law Analysis

**Figure 1.**(

**a**) Scheme of the geothermal ORC power plant; (

**b**) Corresponding T,s-diagram for the ORC using the working fluid isopentane.

_{PP}in the heat exchangers is assumed to be constant. In this context, the process pressures of the ORC are adapted by user subroutines. The reinjection temperature of the geothermal fluid is chosen as an independent design variable to obtain the maximum power output of the system. Therefore, the Cycle Tempo internal optimization routine is used. A relative accuracy for convergence of 1.0·10

^{−4}is considered. The plant performance is evaluated neglecting pressure and heat losses in the pipes and components. Fluid properties of water are considered for the geothermal fluid. For the sensitivity analysis, the mixture composition is varied in discrete steps of 10 mol%. Additional boundary conditions are listed in Table 1. The mass flow rate of the brine of 65.5 kg/s is selected according to typical conditions for the Upper Rhine Rift Valley, one of the most suitable regions for geothermal power generation in Germany.

_{II}is calculated according to:

_{G}corresponds to the generated power of the system and P

_{P}represents the power applied by the pump. The maximum power output of geothermal source, the exergy flow Ė

_{GF}, is obtained by multiplying the specific exergy e of the geothermal fluid with its mass flow ṁ

_{GF}. The specific exergy e is calculated according to:

_{0}is set to 15 °C and p

_{0}= 1.5 MPa.

_{log}:

_{in}and ΔT

_{out}correspond to the temperature difference between ORC working fluid and heat source or sink at the inlet and outlet of the heat exchanger. The UA parameter is only suitable for qualitative comparisons and serves as a rough impression of the required heat exchanger dimensions. For a comprehensive thermo-economic evaluation the heat exchange surfaces have to be determined. This includes the application of suitable heat transfer correlations and geometries. In the following, the selected design criteria are described.

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

Mass flow rate of geothermal fluid ṁ_{gf} (kg/s) | 65.5 |

Inlet temperature of geothermal fluid T_{GF,in} (°C) | 80–180 |

Pressure of geothermal fluid p_{gf} (bar) | 15 |

Minimal reinjection temperature T_{GF,rein} (°C) | 25 |

Minimal temperature difference internal heat exchanger ΔT_{PP,IHE} (K) | 5 |

Minimal temperature difference preheater ΔT_{PP,PHE} (K) | 5 |

Minimal temperature difference condenser ΔT_{PP,COND} (K) | 5 |

Temperature difference of the cooling medium ΔT_{CM} (K) | 5 |

Inlet temperature of cooling medium T_{CM,in} (°C) | 15 |

Maximal ORC process pressure p_{2} (bar) | 0.8∙p_{crit} |

Isentropic efficiency of feed pump η_{i,P} (%) | 75 |

Isentropic efficiency of turbine η
_{i,T} (%) | 80 |

Efficiency of generator η_{i,G} (%) | 98 |

#### 2.3. Heat Exchanger Design

_{S}, density ρ, viscosity ν and thermal diffusivity a.

_{id}, which represents the linear interpolation between the values for pure components. Heberle et al. [50] show that for potential binary mixtures used as ORC working fluids the model of Schlünder [51] is applicable:

_{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 correspond to x

_{i}and y

_{i}. The temperatures T

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

_{ORC}/p

_{crit}). In analogy to the evaporation process, a reduction of heat transfer due to additional mass transfer has to be considered for zeotropic mixtures. Therefore, we apply the method of Sliver, Bell and Ghaly [53,54]. In Equation (10) α

_{eff}represents the heat transfer coefficient for the zeotropic mixture, while α(x) is calculated according to Equation (9) using fluid properties of the fluid mixture. For heat transfer coefficient in the gaseous phase α

_{g}Equation (11) 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.

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

_{o}represents the heat transfer coefficient at the outside of the tube, respectively, 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}. Finally, the required heat transfer surface is determined according to Equation (3), including a safety factor of 1.2.

#### 2.4. Cost Estimations

_{0}at ambient operating conditions and using carbon steel construction:

_{10}C

_{0}= K

_{1}+ K

_{2}∙log

_{10}(Y) + K

_{3}(log

_{10}(Y))

^{2}

_{1}, K

_{2}and K

_{3}are listed for the considered main components in Table 2. In addition, minimal and maximal values for Y are included. If a component exceeds the maximal value several parallel arranged components are considered. The listed cost data are from the year 2001. By setting the corresponding Chemical Engineering Cost Plant Index (CEPCI) of 397 into relation to the value of May 2014 with 574, inflation and the development of raw material prices are taken into account. To convert the PEC in Euro a conversion ratio of 0.8 (as at 10 December 2014) is considered. The total investment costs of the ORC power plant C

_{tot,ORC}are calculated by multiplying the sum of the PEC by the factor 6.32. According to Bejan et al. [56] this parameter represents additional costs like installation, piping, controls, basic engineering and others in relation to the purchased equipment costs of the major components.

Component | Y; unit | K_{1} | K_{2} | K_{3} | Y_{min} | Y_{max} |
---|---|---|---|---|---|---|

Pump (centrifugal) | kW | 3.3892 | 0.0536 | 0.1538 | 1 | 300 |

Heat exchanger (floating head) | m^{2} | 4.8306 | −0.8509 | 0.3187 | 10 | 1000 |

Turbine (axial) | kW | 2.7051 | 1.4398 | −0.1776 | 100 | 4000 |

#### 2.5. Economic Parameters

_{F}have to be calculated. Therefore, exploration costs with 16.5 million € and costs for land and an insurance with 2 million € are assumed [38]. Other costs are set as 3% of the total investment costs. Costs for operation and maintenance C

_{O&M}, including personnel costs, are set to 2% of the total investment costs. The credit period is 20 years and the interest rate is 6.5%. Annual operation hours of 8,000 h/a are assumed to calculate the annual amount of generated electricity E

_{annual}:

## 3. Results and Discussion

#### 3.1. Selection of Zeotropic Fluid Mixtures

_{1}= 25 °C) is a major selection criteria for potential mixtures. In this context a ratio between temperature difference of the cooling medium and temperature glide of the zeotropic mixture at condensation equal 1 is favourable. Therefore, zeotropic mixtures showing a maximum temperature glide T

_{G,max}below 3 K at condensation are excluded in this study. Mixture components of different class of substances are not taken into account for this study with respect to reliability of fluid properties. Components with high differences of saturation temperature, like water and ammonia, are disregarded. These mixtures are more suitable for separation processes like the Kalina Cycle. In addition, uncertainties for heat transfer correlations and significant concentration shifts have to be expected. Predefined ternary or multi-component mixtures, like R404a or R417a, well-known from air-conditioning or refrigeration, are not considered because of chlorinated components, azeotropic characteristics or low temperature glides. The investigated fluid mixtures are listed in Table 3. Furthermore, the maximum temperature glide at condensation and evaporation conditions, wet (–) or dry (+) characteristics and considered references to predict the fluid properties are presented. For some mixtures, a change of the characteristics occur depending on mixture composition (–/+).

**Table 3.**Maximum temperature glides at condensation and evaporation conditions, slope of the dew line and references for fluid property prediction of the investigated fluid mixtures

Fluid Mixture | T_{G,max} (°C)@ T_{1} = 25 °C | T_{G,max} (°C)@ T_{4} = 80 °C | dT/ds | Reference |
---|---|---|---|---|

R134a/R236fa | 6.05 | 4.00 | –/+ | [58] |

R134a/R245fa | 15.14 | 11.13 | –/+ | [58] |

R134a/RC318 | 5.17 | 3.52 | + | [58] |

R152a/R245fa | 12.70 | 8.99 | –/+ | [58] |

R227ea/R245fa | 9.51 | 6.33 | + | [58] |

R236fa/R365mfc | 15.63 | 12.22 | + | [58] |

R245fa/R365mfc | 6.50 | 5.92 | + | [58] |

propane/isobutane | 7.21 | 5.14 | –/+ | [59] |

n-butane/n-pentane | 10.45 | 8.60 | + | [59] |

isobutane/isopentane | 12.21 | 9.90 | + | [59] |

n-pentane/n-hexane | 8.55 | 7.27 | + | [59] |

isohexane/n-pentane | 4.32 | 3.67 | + | [58] |

#### 3.2. Reliability of Fluid Properties

**Figure 2.**Vapour pressure calculated by REFPROP compared to experimental data for selected ORC working fluids.

_{crit}= 196.6 °C). Vapour pressure measurements of R245fa by Feng et al. [67] show a mean relative deviation of 0.4% compared to REFPROP. The maximum relative deviation of −2.1% is related to low temperatures.

**Figure 3.**VLE data calculated by REFPROP compared to experimental data for fluid mixtures considering natural hydrocarbons as mixture components.

**Figure 4.**VLE data calculated by REFPROP compared to experimental data for fluid mixtures regarding fluorinated hydrocarbons as mixture components.

**Figure 5.**(

**a**) Predicted liquid and gaseous density depending on temperature compared to experimental data for n-pentane; (

**b**) liquid density as a function of mixture composition and pressure calculated by REFPROP compared to experimental data for propane/isobutane.

#### 3.3. Second Law Analysis

**Figure 6.**Second law efficiency as a function of heat source temperature for ORC systems using pure working fluids (

**a**) natural hydrocarbons (

**b**) fluorinated hydrocarbons.

_{4}of 15.8 bar is below the maximum value of 0.8·p

_{crit}. In case of an inlet temperature of the geothermal fluid of 130 °C (Figure 7b), the maximum pressure of 23.4 bar is reached. The pinch-point is still at state point 4. For a temperature of 140 °C, the pinch point shifts to the inlet of the preheater, while p

_{4}and T

_{4}stay constant. This allows a reduction of the reinjection temperature to 37.9 °C and an efficiency maximum can be observed (see Figure 6b). For R245fa, at same conditions, a reinjection temperature of 65.2 °C is determined. Thus, 7.4 MW more thermal power is transferred to the ORC using R227ea as a working fluid. The gross power output is 0.9 MW higher compared to R245fa.

**Figure 7.**Temperature-enthalpy flow-diagram for the ORC with R227 at different inlet temperature of the geothermal fluid of (

**a**) 110 °C; (

**b**) 130 °C; and (

**c**) 150 °C.

**Figure 8.**Second law efficiency as a function of heat source temperature for ORC systems using zeotropic mixtures as working fluids (

**a**) natural hydrocarbons (

**b**) fluorinated hydrocarbons.

**Table 4.**Most efficient mixture compositions (mole fractions) corresponding to Figure 8a.

T_{GF,in} (°C) | Isobutane/Isopentane | n-Butane/n-Pentane | n-Pentane/n-Hexane | n-Pentane/Isohexane | Propane/Isobutane |
---|---|---|---|---|---|

80 | 90/10 | 80/20 | 80/20 | 50/50 | 80/20 |

90 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

100 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

110 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

120 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

130 | 90/10 | 90/10 | 80/20 | 50/50 | 90/10 |

140 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

150 | 90/10 | 90/10 | 80/20 | 50/50 | 80/20 |

160 | 90/10 | 90/10 | 80/20 | 50/50 | 50/50 |

170 | 90/10 | 90/10 | 80/20 | 50/50 | 20/80 |

180 | 90/10 | 90/10 | 80/20 | 50/50 | 10/90 |

**Table 5.**Most efficient mixture compositions (mole fractions) corresponding to Figure 8b.

T_{GF,in} (°C) | R134a/R236fa | R134a/R245fa | R152a/R245fa | R227ea/R236fa | R227ea/R245fa | R236fa/R245fa | R236fa/R365mfc | R245fa/R365mfc |
---|---|---|---|---|---|---|---|---|

80 | 60/40 | 80/20 | 80/20 | 30/70 | 70/30 | 40/60 | 90/10 | 60/40 |

90 | 60/40 | 90/10 | 80/20 | 30/70 | 70/30 | 40/60 | 90/10 | 60/40 |

100 | 60/40 | 90/10 | 80/20 | 40/60 | 70/30 | 40/60 | 90/10 | 60/40 |

110 | 60/40 | 90/10 | 80/20 | 50/50 | 70/30 | 40/60 | 90/10 | 60/40 |

120 | 60/40 | 90/10 | 80/20 | 90/10 | 80/20 | 40/60 | 90/10 | 60/40 |

130 | 60/40 | 90/10 | 80/20 | 90/10 | 90/10 | 90/10 | 90/10 | 60/40 |

140 | 60/40 | 90/10 | 80/20 | 60/40 | 80/20 | 90/10 | 90/10 | 60/40 |

150 | 20/80 | 90/10 | 90/10 | 20/80 | 70/30 | 90/10 | 90/10 | 60/40 |

160 | 20/80 | 70/30 | 90/10 | 10/90 | 50/50 | 90/10 | 90/10 | 60/40 |

170 | 10/90 | 60/40 | 80/20 | 10/90 | 40/60 | 70/30 | 90/10 | 60/40 |

180 | 10/90 | 30/70 | 50/50 | 10/90 | 20/80 | 40/60 | 80/20 | 60/40 |

**Figure 9.**Second law efficiency and UA parameter depending on mixture composition for the most efficient zeotropic mixtures and a geothermal fluid temperature of 120 °C.

_{G,Cond}/ΔT

_{CM}equal 1.

**Figure 10.**UA parameter for the considered heat exchanger depending on mixture composition of isobutane/isopentane at a geothermal fluid temperature of 120 °C.

**Figure 11.**Second law efficiency and UA parameter depending on mixture composition for selected zeotropic mixtures and a geothermal fluid temperature of 160 °C.

#### 3.4. Heat Exchanger Design

_{id}is shown for the selected zeotropic mixtures isobutane/isopentane, propane/isobutane and R227ea/R245fa at a heat source temperature of 120 °C. In general, the results show a slight reduction of the heat transfer characteristics in case of condensation. For isobutane/isopentane the most distinctive reduction with up to 18% is obtained. This is due to a low mass flux density and high enthalpy difference at condensation. In case of high mass flux densities, like for propane/isobutane and R227ea/R245fa, the reduction is less pronounced with maximal 8%. The general behavior agrees with literature for experimental investigations of flow condensation of zeotropic mixtures [76,77]. In contrast, the reduction of pool boiling heat transfer coefficient is more significant. For isobutane/isopentane and propane/isobutane a minimum for α/α

_{id}is obtained in case of an equimolar fraction. The reduction is 45% and 48%. In case of R227ea /R245fa, the reduction is 37% at 40 mol% R245fa. In principle, high heat transfer coefficients are obtained for more volatile working fluids with higher process pressures and thus higher gaseous density.

^{2}is relatively high. In case of an equimolar concentration, a logarithmic mean temperature difference of 8.1 K and a total heat transfer surface of 3,021.4 m

^{2}are determined. The most efficient pure component isobutane leads to a logarithmic mean temperature difference of 7.2 K and a total heat transfer surface of 2,996.0 m

^{2}.

**Figure 12.**(

**a**) Reduction of the heat transfer coefficient at condensation and evaporation (pool boiling) for zeotropic mixture depending on mixture composition (

**b**) total heat transfer surface of the ORC power plant for a geothermal fluid temperature of 120 °C.

**Table 6.**Heat exchange surface, mean logarithmic temperature difference and transferred amount of thermal energy for each heat exchanger depending on mixture composition (isobutane/isopentane).

Parameter | 0/100 | 10/90 | 20/80 | 30/70 | 40/60 | 50/50 | 60/40 | 70/30 | 80/20 | 90/10 | 100/0 |
---|---|---|---|---|---|---|---|---|---|---|---|

A_{PHE} (m^{2}) | 280.6 | 272.2 | 301.4 | 294.5 | 302.1 | 312.4 | 329.4 | 342.4 | 366.1 | 390.4 | 411.3 |

ΔT_{log,PHE} (K) | 13.5 | 13.9 | 13.4 | 13.2 | 13.3 | 13.4 | 13.2 | 13.5 | 13.4 | 13.6 | 13.9 |

Q̇_{PHE} (MW) | 3.44 | 3.42 | 3.38 | 3.48 | 3.56 | 3.68 | 3.81 | 4.01 | 4.22 | 4.53 | 4.85 |

A_{EVP} (m^{2}) | 495.8 | 518.3 | 600.2 | 622.5 | 614.8 | 587.7 | 537.0 | 473.1 | 404.5 | 330.4 | 274.3 |

ΔT_{log,EVP} (K) | 19.2 | 17.6 | 18.7 | 17.2 | 16.9 | 16.8 | 17.2 | 17.2 | 17.8 | 18.3 | 18.5 |

Q̇_{EVP} (MW) | 12.02 | 11.55 | 13.53 | 12.56 | 12.54 | 12.50 | 12.72 | 12.39 | 12.48 | 12.14 | 11.39 |

A_{COND} (m^{2}) | 2638.5 | 3541.1 | 3160.9 | 2455.2 | 2234.6 | 2121.8 | 2128.3 | 2156.8 | 2396.0 | 2915.9 | 1911.0 |

ΔT_{log,COND} (K) | 7.2 | 5.1 | 6.4 | 7.5 | 8.0 | 8.1 | 8.0 | 7.4 | 6.5 | 5.1 | 7.2 |

Q̇_{COND} (MW) | 13.94 | 13.34 | 15.32 | 14.46 | 14.53 | 14.60 | 14.92 | 14.76 | 15.02 | 14.96 | 14.66 |

A_{IR} (m^{2}) | 719.5 | 917.8 | 568.3 | 448.5 | 388.0 | 359.7 | 353.2 | 374.7 | 442.4 | 581.4 | 349.43 |

ΔT_{log,IR} (K) | 6.5 | 7.2 | 10.3 | 12.6 | 13.7 | 13.9 | 13.3 | 11.9 | 9.5 | 6.6 | 5.9 |

Q̇_{IR} (MW) | 0.94 | 1.36 | 1.29 | 1.29 | 1.25 | 1.22 | 1.17 | 1.14 | 1.11 | 1040.3 | 0.60 |

A_{total} (m^{2}) | 4134.3 | 4331.6 | 4062.5 | 3372.2 | 3151.5 | 3021.9 | 2994.7 | 2972.3 | 3166.7 | 4218.1 | 2946.0 |

P_{T} (kW) | 1520.7 | 1623.0 | 1587.7 | 1581.3 | 1583.5 | 1598.3 | 1623.1 | 1659.0 | 1704.0 | 1755.3 | 1631.5 |

P_{P} (kW) | 27.8 | 34.2 | 35.6 | 42.3 | 47.6 | 53.4 | 59.1 | 66.9 | 74.5 | 84.7 | 94.6 |

_{g}, differ only slightly. This is due to the assumption of a constant flow velocity in the pipes. In addition, Pr

_{l}or Pr

_{g}show only a low dependence on the increased process pressure. As a result, the reduction of condensation heat transfer coefficients is almost identical compared to the geothermal inlet temperature of 120 °C. Regarding the evaporation heat transfer, a more pronounced reduction for fluid mixtures can be observed. In case of an equimolar concentration for propane/isobutane, a reduction of 54% is calculated. Considering the mixture R227ea/R245fa the maximal reduction is 43%. Again, not mole fractions with the most evident reduction of heat transfer characteristics lead to the highest heat transfer surface (see Figure 13b). High total heat transfer surfaces for propane/isobutane and R227ea/R245fa occur for the most efficient mixture compositions. For these concentrations the ORC leads to a minimal reinjection temperature for the geothermal fluid and, therefore, a maximum for heat input to the ORC is obtained. Exemplarily, for the equimolar mixture R227ea/R245fa a higher amount of 29.0% thermal energy is transferred to the ORC compared to pure R245fa. As a consequence and taken into account the reduction of heat transfer characteristics, a 66.5% higher total heat transfer surface results. Local maxima for the total heat transfer surface can be observed for mole fractions, which lead to a good match of the temperature profiles in the condenser. In this context, 90 mol% R227ea could be mentioned exemplarily.

**Figure 13.**(

**a**) Reduction of the heat transfer coefficient at condensation and evaporation (pool boiling) for zeotropic mixtures depending on composition; (

**b**) total heat transfer surface of the ORC power plant for a geothermal fluid temperature of 160 °C.

#### 3.5. Economic Parameters

**Figure 14.**(

**a**) Specific investment costs for the ORC power plant depending on mixture composition for a geothermal fluid temperature of 120 °C; (

**b**) electricity generation costs.

**Table 7.**PEC for the major components depending on mixture composition (isobutane/isopentane) at a geothermal fluid temperature of 120 °C.

Parameter | 0/100 | 10/90 | 20/80 | 30/70 | 40/60 | 50/50 | 60/40 | 70/30 | 80/20 | 90/10 | 100/0 |
---|---|---|---|---|---|---|---|---|---|---|---|

C_{IR} (k€) | 115.9 | 148.0 | 92.9 | 75.6 | 67.1 | 63.2 | 62.3 | 65.3 | 74.7 | 94.9 | 61.8 |

C_{PHE} (k€) | 52.6 | 51.5 | 55.3 | 54.4 | 55.4 | 56.8 | 59.1 | 60.9 | 64.1 | 67.5 | 70.4 |

C_{EVP} (k€) | 82.3 | 85.6 | 97.7 | 101.0 | 99.9 | 95.8 | 88.3 | 79.1 | 69.4 | 59.3 | 51.7 |

C_{K} (k€) | 427.3 | 573.5 | 511.9 | 397.7 | 361.9 | 343.6 | 344.7 | 349.3 | 388.1 | 472.3 | 309.5 |

C_{T} (k€) | 354.0 | 360.9 | 358.3 | 357.4 | 357.2 | 357.8 | 359.2 | 361.1 | 363.6 | 366.3 | 357.2 |

C_{Pump} (k€) | 7.1 | 7.9 | 8.0 | 8.8 | 9.4 | 10.1 | 10.7 | 11.6 | 12.4 | 13.4 | 14.4 |

C_{total,ORC} (k€) | 6568.4 | 7756.9 | 7105.4 | 6288.0 | 6010.2 | 5861.3 | 5841.9 | 5860.3 | 6145.1 | 6785.2 | 5467.5 |

**Figure 15.**(

**a**) Specific investment costs for the ORC power plant depending on mixture composition (

**b**) electricity generation costs for a geothermal fluid temperature of 160 °C.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Heberle, F.; Brüggemann, D.
Thermo-Economic Evaluation of Organic Rankine Cycles for Geothermal Power Generation Using Zeotropic Mixtures. *Energies* **2015**, *8*, 2097-2124.
https://doi.org/10.3390/en8032097

**AMA Style**

Heberle F, Brüggemann D.
Thermo-Economic Evaluation of Organic Rankine Cycles for Geothermal Power Generation Using Zeotropic Mixtures. *Energies*. 2015; 8(3):2097-2124.
https://doi.org/10.3390/en8032097

**Chicago/Turabian Style**

Heberle, Florian, and Dieter Brüggemann.
2015. "Thermo-Economic Evaluation of Organic Rankine Cycles for Geothermal Power Generation Using Zeotropic Mixtures" *Energies* 8, no. 3: 2097-2124.
https://doi.org/10.3390/en8032097