#
Thermo-Economic and Heat Transfer Optimization of Working-Fluid Mixtures in a Low-Temperature Organic Rankine Cycle System^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Models and Methodology

#### 2.1. ORC Thermodynamic Model

#### 2.2. Heat Exchanger Sizing

^{-1}·K

^{-1}), and are discretized (for modelling purposes) into 100 (variable-sized) segments, i (=1–100), each segment having an equal heat transfer/duty, i.e., ${\dot{Q}}_{\mathrm{in}}/100$ or ${\dot{Q}}_{\mathrm{out}}/100$. A typical segment is illustrated in Figure 1. In all heat exchangers, the working fluid flows through the tube-side (tb), while the heat source and sink streams are the shell-side (sh) fluids. Thus, the total rates at which heat is transferred to/from the working fluid in relation to Equations (3) and (5), respectively, are given by:

#### 2.3. Component Cost Estimation

#### 2.4. Application and Problem Definition

_{e}Birdsville geothermal ORC power-plant in Birdsville, Australia [41], with an inlet temperature (${T}_{\mathrm{hs,in}}$) of 98 ${}^{\circ}$C and a flow-rate of 27 kg·s

^{−1}. This is typical of what is obtainable from (low-pressure) geothermal reservoirs and also (low-grade) waste-heat streams in industrial processes [42]. The heat sink is a water stream at ambient conditions (in at 20 ${}^{\circ}$C, out at 30 ${}^{\circ}$C).

## 3. Results and Discussion

#### 3.1. Optimal Cycles with Working-Fluid Mixtures

#### 3.2. Sizing and Costing of Optimal ORC Systems

#### 3.2.1. Heat Exchanger Sizing for Optimal ORC Systems

^{2}and 15 m

^{2}for the preheaters and desuperheaters, respectively) are much smaller than those associated with the two-phase heat exchangers (maximum range of 32 m

^{2}and 95 m

^{2}for the evaporators and condensers respectively). This is important, in that it suggests that working-fluid mixtures have a more profound effect on the Evaporator and Condenser sizes than they do on the single-phase heat-exchangers, at least in the present study.

^{2}(${x}_{\mathrm{R-227ea}}$ = 0) to 204 m

^{2}(${x}_{\mathrm{R-227ea}}$ = 0.5). This implies an increase in HTA of 85% when a working-fluid mixture is substituted for a pure working fluid (or, conversely, a decrease in HTA of 45% when a working-fluid mixture is substituted with a pure working fluid). Such large differences in HTAs between working-fluid mixtures and pure fluids can lead to considerable differences in plant size and cost, in favour of the pure working fluids.

#### 3.2.2. Cost Estimation of Optimal ORC Systems

#### 3.3. Heat Input Limitations and Other Working-Fluid Mixtures

- ${\dot{Q}}_{\mathrm{in,lim}}$ is allowed to attain a maximum possible value; this is the case in Section 3.1 where the optimal cycle heat input (${\dot{Q}}_{\mathrm{in}}$) for different working fluids is seen to vary between 3.2 MW and 4.0 MW.
- ${\dot{Q}}_{\mathrm{in,lim}}=2.5$ MW.
- ${\dot{Q}}_{\mathrm{in,lim}}=1.0$ MW.

#### 3.4. Multi-Objective Cost-Power Optimization

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

A | Heat transfer area [${\mathrm{m}}^{2}$] | Ev | Evaporator |

${C}_{\mathrm{B}}$ | Component-base cost [£] | HTA | Heat-transfer area |

${c}_{P}$ | Isobaric specific heat-capacity [kJ·kg${}^{-1}$·K${}^{-1}$] | HTC | Heat-transfer coefficient |

${d}_{\mathrm{SH}}$ | Degree of superheat [-] | HX | Heat exchanger |

$dx$ | Tube thickness [m] | LHS | Left-hand side |

h | Specific enthalpy [kJ·kg${}^{-1}$] | ORC | Organic Rankine cycle |

h | Heat-transfer coefficient [kW·m${}^{-2}$·K${}^{-1}$] | PH | Preheater |

H | Pump head [m] | RHS | Right-hand side |

k | Thermal conductivity [kW·m${}^{-1}$·K${}^{-1}$] | SH | Superheater |

$\dot{m}$ | Mass flow-rate [kg·s${}^{-1}$] | ||

P | Pressure [bar] | Subscripts | |

$PR$ | Expander pressure ratio [-] | ‘1’, ‘2’, ‘3’, ‘4’ | Working-fluid state points |

q | Vapour quality on mass basis [-] | ‘cond’ | Condensation |

$\dot{Q}$ | Heat flow-rate [kW] | ‘crit’ | Critical |

s | Specific entropy [kJ·kg${}^{-1}$·K${}^{-1}$] | ‘cs’ | Heat sink |

T | Temperature [°C] | ‘evap’ | Evaporation |

U | Overall HTC [kW·m${}^{-2}$·K${}^{-1}$] | ‘exp’ | Expander |

$\dot{V}$ | Volumetric flow-rate [m${}^{3}$·s${}^{-1}$] | ‘hs’ | Heat source |

$VR$ | Expander volume ratio [-] | ‘i’ | Segment number |

w | Specific work-output [kJ·kg${}^{-1}$] | ‘in’ | Input |

$\dot{W}$ | Power [kW] | ‘is’ | Isentropic |

x | Mass fraction [-] | ‘lim’ | Limit |

‘lm’ | Logarithm mean | ||

Greek symbols | ‘max’ | Maximum | |

η | Efficiency [%] | ‘min’ | Minimum |

μ | Dynamic viscosity [Pa·s] | ‘n’ | Normalized |

ρ | Density [kg·m${}^{-3}$] | ‘out’ | Output/Outlet |

‘s’ | Isentropic | ||

Abbreviations | ‘sh’ | Shell-side | |

CAMD | Computer-aided molecular design | ‘tb’ | Tube-side |

CHP | Combined heat and power | ‘th’ | Thermal |

Cn | Condenser | ‘v’ | Vapour volume |

DSh | Desuperheater | ‘wf’ | Working fluid |

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**Figure 1.**

**Left**: ORC T–s diagram for the case of a pure (single-component) working fluid.

**Right**: Heat-exchanger segment showing flow directions on the shell (sh) and tube (tb) sides.

**Figure 2.**Optimal net power-output (maximum ${\dot{W}}_{\mathrm{net}}$) with corresponding operating phase-change pressure, and evaporation and condensation temperature glides at optimal operating conditions. (

**a**) n-pentane + n-hexane; (

**b**) temperature glides; (

**c**) R-245fa + R-227ea.

**Figure 3.**Expander volumetric flow-rate, volume and pressure ratio at optimal power output. (

**a**) n-pentane + n-hexane; (

**b**) R-245fa + R-227ea.

**Figure 5.**Heat-transfer areas along the phase-change heat exchangers (Evaporator and Condenser) for R-245fa + R-227ea system. (

**a**) evaporator; (

**b**) condenser.

**Figure 6.**Normalized total heat-transfer areas for heat exchangers with the different working-fluid mixtures. Normalization parameters are given in Table 3. (

**a**) n-pentane + n-hexane; (

**b**) R-245fa + R-227ea.

**Figure 7.**Optimal ORC systems’ component costs (bars; LHS axes) and total component costs (line; RHS axes). Component-base costs, ${C}_{\mathrm{B}}$ are indexed in year 2006, with the following currency conversions: £1 ≡ €1.47, $1.84. The legend in Figure 7a applies to both figures. (

**a**) n-pentane + n-hexane; (

**b**) R-245fa + R-227ea.

**Figure 8.**Maximum net power output and related rated costs (in pounds per kW) for ORC systems with working fluid mixtures. Cycle heat input is not restricted, i.e., ${Q}_{\mathrm{in,lim}}$ is allowed to attain a maximum possible value; ‘x’ represents the mass fraction of the first component fluid in each working-fluid mixture pairing. Component-base costs, ${C}_{\mathrm{B}}$, are indexed in the year 2006, with the following currency conversions: £1 ≡ €1.47, $1.84.

**Figure 9.**Maximum net power output and related rated costs (in pounds per kW) for ORC systems when employing working fluid mixtures. Cycle heat input is restricted to 2.5 MW, i.e., ${Q}_{\mathrm{in,lim}}=2.5$ MW; ‘x’ represents the mass fraction of the first component fluid in each working-fluid mixture pairing. Component-base costs, ${C}_{\mathrm{B}}$, are indexed in the year 2006, with the following currency conversions: £1 ≡ €1.47, $1.84.

**Figure 10.**Maximum net power output and related rated costs (in pounds per kW) for ORC systems that employ working fluid mixtures. Cycle heat input is restricted to 1.0 MW, i.e., ${Q}_{\mathrm{in,lim}}=1.0$ MW; ‘x’ represents the mass fraction of the first component fluid in each working-fluid mixture pairing. Component-base costs, ${C}_{\mathrm{B}}$, are indexed in the year 2006, with the following currency conversions: £1 ≡ €1.47, $1.84.

**Figure 11.**The pareto optimal curves for the multi-objective optimization (maximum net power and minimum rated costs in pounds per kW) of ORCs with two sets of working-fluid mixtures. Component-base costs, ${C}_{\mathrm{B}}$, are indexed in the year 2006, with the following currency conversions: £1 ≡ €1.47, $1.84. (

**a**) n-pentane + n-hexane; (

**b**) R-245fa + R-227ea.

Component | S | F | ${\mathit{C}}_{\mathbf{0}}$ | ${\mathit{C}}_{\mathbf{1}}$ | ${\mathit{C}}_{\mathbf{2}}$ |
---|---|---|---|---|---|

Pump | $\dot{V}\sqrt{H}$ (m^{3}·s^{−1}·m^{1/2}) | 2.7 | 9.0073 | 0.4636 | 0.0519 |

Expander | ${\dot{W}}_{\mathrm{exp}}$ (kW) | 1.0 | 6.5106 | 0.8100 | 0.0000 |

Expander * | ${\dot{W}}_{\mathrm{exp}}$ (kW) | 1.0 | 7.3194 | 0.8100 | 0.0000 |

Heaters/Coolers | HTA (m^{2}) | 1.0 | 10.106 | −0.4429 | 0.0901 |

Evaporator/Condenser | HTA (m^{2}) | 1.0 | 9.5638 | 0.5320 | −0.0002 |

**Table 2.**Cycle parameters for ORC systems optimized for maximum net power output using n-pentane + n-hexane and R-245fa + R-227ea working-fluid mixtures.

${\mathit{x}}_{{\mathbf{\text{C}}}_{\mathbf{6}}{\mathbf{\text{H}}}_{\mathbf{14}}}$ | ${\dot{\mathit{W}}}_{\mathbf{\text{net}}}$ | ${\mathbf{\eta}}_{\mathbf{\text{th}}}$ | ${\mathit{w}}_{\mathbf{\text{exp}}}$ | ${\dot{\mathit{W}}}_{\mathbf{\text{pump}}}$ | ${\dot{\mathit{m}}}_{\mathbf{\text{wf}}}$ | ${\mathit{d}}_{\mathbf{\text{SH}}}$ | ${\dot{\mathit{m}}}_{\mathbf{\text{cs}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{PH}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{Ev}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{DSh}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{Cn}}}$ | ${\mathit{x}}_{\mathbf{\text{227ea}}}$ | ${\dot{\mathit{W}}}_{\mathbf{\text{net}}}$ | ${\mathbf{\eta}}_{\mathbf{\text{th}}}$ | ${\mathit{w}}_{\mathbf{\text{exp}}}$ | ${\dot{\mathit{W}}}_{\mathbf{\text{pump}}}$ | ${\dot{\mathit{m}}}_{\mathbf{\text{wf}}}$ | ${\mathit{d}}_{\mathbf{\text{SH}}}$ | ${\dot{\mathit{m}}}_{\mathbf{\text{cs}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{PH}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{Ev}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{DSh}}}$ | ${\dot{\mathit{Q}}}_{\mathbf{\text{Cn}}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

kW | % | $\mathbf{\text{kJ}}\mathbf{\xb7}{\mathbf{\text{kg}}}^{\mathbf{-}\mathbf{1}}$ | kW | $\mathbf{\text{kg}}\mathbf{\xb7}{\mathrm{s}}^{\mathbf{-}\mathbf{1}}$ | - | $\mathbf{\text{kg}}\mathbf{\xb7}{\mathrm{s}}^{\mathbf{-}\mathbf{1}}$ | MW | MW | MW | MW | kW | % | $\mathbf{\text{kJ}}\mathbf{\xb7}{\mathbf{\text{kg}}}^{\mathbf{-}\mathbf{1}}$ | kW | $\mathbf{\text{kg}}\mathbf{\xb7}{\mathrm{s}}^{\mathbf{-}\mathbf{1}}$ | - | $\mathbf{\text{kg}}\mathbf{\xb7}{\mathrm{s}}^{\mathbf{-}\mathbf{1}}$ | MW | MW | MW | MW | ||

0.0 | 161 | 5.00 | 21.1 | 2.17 | 7.74 | 0.45 | 73.1 | 0.47 | 2.75 | 0.30 | 2.75 | 0.0 | 163 | 4.97 | 11.5 | 4.05 | 14.5 | 1.00 | 74.7 | 0.50 | 2.78 | 0.48 | 2.64 |

0.1 | 179 | 5.25 | 21.8 | 2.20 | 8.29 | 0.18 | 77.2 | 0.53 | 2.88 | 0.23 | 3.00 | 0.1 | 187 | 5.17 | 11.8 | 5.18 | 16.2 | 1.00 | 82.1 | 0.60 | 3.01 | 0.52 | 2.92 |

0.2 | 193 | 5.43 | 22.5 | 2.16 | 8.68 | 0.00 | 80.5 | 0.57 | 2.99 | 0.18 | 3.19 | 0.2 | 204 | 5.30 | 11.7 | 6.44 | 18.0 | 0.84 | 87.1 | 0.70 | 3.15 | 0.49 | 3.15 |

0.3 | 204 | 5.55 | 23.3 | 2.05 | 8.86 | 0.00 | 83.2 | 0.59 | 3.09 | 0.19 | 3.29 | 0.3 | 214 | 5.39 | 11.1 | 7.88 | 19.9 | 0.54 | 90.1 | 0.78 | 3.20 | 0.41 | 3.36 |

0.4 | 211 | 5.61 | 23.7 | 1.92 | 8.98 | 0.00 | 84.9 | 0.61 | 3.15 | 0.20 | 3.35 | 0.4 | 219 | 5.42 | 10.3 | 9.66 | 22.3 | 0.11 | 91.6 | 0.87 | 3.17 | 0.25 | 3.58 |

0.5 | 214 | 5.64 | 23.9 | 1.78 | 9.03 | 0.00 | 85.8 | 0.62 | 3.18 | 0.20 | 3.38 | 0.5 | 219 | 5.40 | 9.79 | 11.0 | 23.5 | 0.12 | 91.7 | 0.91 | 3.14 | 0.26 | 3.57 |

0.6 | 213 | 5.61 | 23.8 | 1.62 | 9.02 | 0.00 | 85.8 | 0.62 | 3.18 | 0.21 | 3.38 | 0.6 | 213 | 5.33 | 9.02 | 12.7 | 25.1 | 0.00 | 90.6 | 0.95 | 3.05 | 0.21 | 3.57 |

0.7 | 208 | 5.55 | 23.4 | 1.44 | 8.94 | 0.00 | 84.7 | 0.60 | 3.15 | 0.20 | 3.34 | 0.7 | 204 | 5.21 | 8.29 | 14.3 | 26.3 | 0.00 | 88.6 | 0.97 | 2.94 | 0.22 | 3.48 |

0.8 | 198 | 5.44 | 22.7 | 1.26 | 8.77 | 0.00 | 82.4 | 0.58 | 3.06 | 0.20 | 3.24 | 0.8 | 191 | 5.06 | 7.52 | 15.9 | 27.5 | 0.00 | 85.9 | 0.98 | 2.81 | 0.22 | 3.37 |

0.9 | 183 | 5.28 | 21.7 | 1.06 | 8.48 | 0.00 | 78.4 | 0.53 | 2.93 | 0.19 | 3.09 | 0.9 | 179 | 4.89 | 6.80 | 17.9 | 29.0 | 0.00 | 83.3 | 0.99 | 2.67 | 0.23 | 3.25 |

1.0 | 161 | 5.05 | 20.2 | 0.85 | 8.02 | 0.00 | 72.3 | 0.47 | 2.71 | 0.17 | 2.85 | 1.0 | 170 | 4.76 | 6.19 | 20.2 | 30.7 | 0.00 | 81.4 | 1.02 | 2.55 | 0.24 | 3.17 |

Pentane + Hexane | PH | Ev | DSh | Cn | R-245fa + R227ea | PH | Ev | DSh | Cn |
---|---|---|---|---|---|---|---|---|---|

${A}_{\mathrm{min}}$ (m${}^{2}$) | 21.8 | 48.5 | 15.8 | 80.8 | ${A}_{\mathrm{min}}$ (m${}^{2}$) | 24.5 | 51.1 | 15.2 | 109 |

${A}_{\mathrm{max}}$ (m${}^{2}$) | 25.8 | 65.3 | 23.4 | 150 | ${A}_{\mathrm{max}}$ (m${}^{2}$) | 37.2 | 82.6 | 29.9 | 204 |

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**MDPI and ACS Style**

Oyewunmi, O.A.; Markides, C.N. Thermo-Economic and Heat Transfer Optimization of Working-Fluid Mixtures in a Low-Temperature Organic Rankine Cycle System. *Energies* **2016**, *9*, 448.
https://doi.org/10.3390/en9060448

**AMA Style**

Oyewunmi OA, Markides CN. Thermo-Economic and Heat Transfer Optimization of Working-Fluid Mixtures in a Low-Temperature Organic Rankine Cycle System. *Energies*. 2016; 9(6):448.
https://doi.org/10.3390/en9060448

**Chicago/Turabian Style**

Oyewunmi, Oyeniyi A., and Christos N. Markides. 2016. "Thermo-Economic and Heat Transfer Optimization of Working-Fluid Mixtures in a Low-Temperature Organic Rankine Cycle System" *Energies* 9, no. 6: 448.
https://doi.org/10.3390/en9060448