# Thermoeconomic Evaluation of Modular Organic Rankine Cycles for Waste Heat Recovery over a Broad Range of Heat Source Temperatures and Capacities

^{*}

## Abstract

**:**

_{2}emissions from industries. Before market penetration, high efficiency modular concepts have to be developed to achieve appropriate economic value for industrial decision makers. This paper aims to investigate modularly designed ORC systems from a thermoeconomic point of view. The main goal is a recommendation for a suitable chemical class of working fluids, preferable ORC design and a range of heat source temperatures and thermal capacities in which modular ORCs can be economically feasible. For this purpose, a thermoeconomic model has been developed which is based on size and complexity parameters of the ORC components. Special emphasis has been laid on the turbine model. The paper reveals that alkylbenzenes lead to higher exergetic efficiencies compared to alkanes and siloxanes. However, based on the thermoeconomic model, the payback periods of the chemical classes are almost identical. With the ORC design, the developed model and the boundary conditions of this study, hexamethyldisiloxane is a suitable working fluid and leads to a payback period of less than 5 years for a heat source temperature of 400 to 600 °C and a mass flow rate of the gaseous waste heat stream of more than 4 kg/s.

## 1. Introduction

- Which chemical class of ORC working fluids can be applied in a wide range of heat source temperatures?
- Which ORC design is favorable to cover also a broad range of heat source thermal capacities?
- Which aspects must be included in a thermoeconomic model to allow for a robust and holistic evaluation of modular ORC units?
- For which range of heat source temperatures and thermal capacities are ORC units economically feasible?

## 2. Theory

#### 2.1. Industrial Waste Heat

- The values for the electric power potential from waste heat recovery differ significantly, however, it is a common fact that a huge potential is available.
- The thermal capacity of industrial waste heat flows strongly depends on application ranging from a few kW up to several MW.
- Industrial waste heat covers a broad range of heat source temperature, however, 300 °C and 600 °C seems to be a promising range for electricity generation from waste heat [25].

#### 2.2. Organic Raninke Cycle

## 3. Methodology

#### 3.1. Approach for Modular Design of ORC Units

#### 3.2. Selection of Working Fluids

#### 3.3. Boundary Conditions

#### 3.4. Thermodynamic and Constructional Evaluation Parameters

_{0}= 15 °C:

_{1}and ΔT

_{2}are the temperature differences at inlet and outlet of the heat exchanger. Assuming a constant heat exchange coefficient as a first estimation for all working fluids, the heat exchange capacity is proportional to the heat exchanger area and to its cost.

_{is,t}:

_{ratio}between outlet and inlet is a measure for the complexity of the turbine:

#### 3.5. Overall Flow Chart

## 4. Thermodynamic and Constructional Evaluation

#### 4.1. Thermodynamic Results

_{crit}, the system is most efficient if the preheating just shifts from evaporation to preheating (see Figure 6, middle). Therefore, the higher the heat source temperature, the higher the critical temperature of the working fluid must be for an efficient system. However, an optimal value which is valid for all chemical classes and, therefore, a rule like “the critical temperature always has to be X K below the heat source temperature” cannot be established as next to the critical temperature, the slope of the boiling point line also influences the location of the pinch point.

#### 4.2. Analysis of Constructional Parameters

- Alkylbenzenes are favorable working fluids concerning exergetic efficiency, dimension of the turbine (SP) and heat exchanger (kA).
- Linear siloxanes have significant advantages concerning the complexity of the turbine due to low rotational speed.
- n-Alkanes combine the disadvantages of both formerly mentioned chemical classes.
- None of the chemical classes outperforms in all relevant parameters.

## 5. Thermoeconomic Evaluation

#### 5.1. Thermoeconomic Modeling

#### 5.1.1. Heat Exchanger

_{x}is related to the vapor fraction [83]:

_{g}

_{0}is the heat transfer coefficient of the gas phase and α

_{l}

_{0}of the liquid phase according to Equation (7).

_{r}being the reduced pressure p/p

_{crit}:

#### 5.1.2. Pump

#### 5.1.3. Turbine

#### 5.1.4. Piping

#### 5.2. Thermoeconomic Results

## 6. Modularly-Designed ORC

## 7. Conclusions

- Taking into account thermodynamic, construction and economic parameters, linear siloxanes and within this group, the working fluid hexamethyldisiloxane is a promising candidate for waste heat recovery in a broad range of heat source temperatures and capacities.
- A concept with direct contact evaporator, internal recuperator, and expansion by a turbine is a favorable design for modularly-based ORC units.
- A holistic thermoeconomic approach has to be based on scaling and complexity parameters. Especially for the turbine, the typically used exponential cost estimation method is not appropriate as technology leaps can occur depending on the working pressure.
- For the boundary conditions and turbine model within this study, a modular concept based on hexamethyldisiloxane, a temperature range of 400 to 600 °C and a mass flow rate exceeding 4 kg/s can be recommended.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

Abbreviations | ||

a | year | |

CF | Cash flow | |

D_{3} | hexamethylcyclotrisiloxane | |

D_{4} | octamethylcyclotetrasiloxane | |

D_{5} | decamethylcyclopentasiloxane | |

MD_{2}M | decamethyltetrasiloxane | |

MDM | octamethyltrisiloxane | |

MM | hexamethyldisiloxane | |

O | oxygen | |

ORC | Organic Rankine Cycle | |

P | plant | |

PBP | payback period | |

PR-BM | Peng-Robinson Boston-Mathias | |

Ref | reference plant | |

Si | silicium | |

STHE | shell-and-tube heat exchanger | |

sub | subcritical | |

super | supercritical | |

Subscripts | ||

0 | dead state | |

c | countercurrent | |

crit | critical | |

ex | exergetic | |

g | gaseous | |

HS | heat source | |

i | component i | |

is | isentropic | |

l | liquid | |

max | maximum | |

p | pump | |

r | reduced | |

s | specific | |

s | saturation | |

t | turbine | |

TGU | turbine-generator-unit | |

Symbols | Unit | |

T | temperature | °C, K |

A | heat exchanger area | m² |

C | capacity | W, m² |

D | diameter | m |

F | correction factor | - |

h | specific enthalpy | kJ/kg |

I | investment costs | € |

kA | heat exchanger capacity | W/m² |

L | length | m |

LMTD | logarithmic mean temperature difference | K |

M | exponential factor | - |

M | molar mass | g/mol |

$\dot{m}$ | mass flow rate | kg/s |

n | rotational speed | 1/s |

NTU | number of transfer units | - |

Nu | Nusselt number | - |

Pr | Prandl number | - |

$\dot{Q}$ | heat flux | W |

R | density ratio | - |

Re | Reynolds number | - |

s | specific entropy | kJ/kgK |

SP | size parameter | M |

$\dot{V}$ | volume flow rate | m³/s |

x | vapor fraction | - |

Greek symbols | ||

η | efficiency | |

ζ | pipe friction factor |

## Appendix A. Physico-Chemical Properties of Evaluated Working Fluids

**Table A1.**Molar mass M, saturation temperature T

_{s}at 1 bar, saturation pressure p

_{s}at 85 °C, critical temperature T

_{crit}and pressure p

_{crit}for evaluated working fluids.

Name | Abbreviation | M | T_{s} (1 bar) | p_{s} (85 °C) | T_{crit} | p_{crit} |
---|---|---|---|---|---|---|

g/mol | K | bar | K | bar | ||

n-pentane | 72.15 | 309.22 | 4.16 | 469.70 | 33.70 | |

n-hexane | 86.18 | 341.88 | 1.63 | 507.60 | 30.25 | |

n-heptane | 100.20 | 371.58 | 0.67 | 540.20 | 27.40 | |

n-octane | 114.23 | 398.83 | 0.28 | 568.70 | 24.90 | |

n-nonane | 128.26 | 423.97 | 0.12 | 594.60 | 22.90 | |

n-decane | 142.28 | 447.30 | 0.05 | 617.70 | 21.10 | |

n-undecane | 156.31 | 469.08 | 0.02 | 639.00 | 19.50 | |

n-dodecane | 170.34 | 489.48 | 0.01 | 658.00 | 18.20 | |

methylbenzene | toluene | 92.14 | 383.78 | 0.46 | 591.75 | 41.08 |

ethylbenzene | 106.17 | 409.35 | 0.20 | 617.15 | 36.09 | |

n-propylbenzene | 120.19 | 432.39 | 0.10 | 638.35 | 32.00 | |

hexamethyldisiloxane | MM | 162.38 | 373.67 | 0.63 | 518.70 | 19.14 |

octamethyltrisiloxane | MDM | 236.53 | 425.70 | 0.12 | 564.40 | 14.40 |

decamethyltetrasiloxane | MD_{2}M | 310.69 | 467.50 | 0.02 | 599.40 | 12.27 |

hexamethylcyclotrisiloxane | D_{3} | 222.46 | 408.26 | 0.21 | 554.20 | 16.63 |

octamethylcyclotetrasiloxane | D_{4} | 296.62 | 448.15 | 0.05 | 586.50 | 13.32 |

decamethylcyclopentasiloxane | D_{5} | 307.77 | 484.10 | 0.01 | 619.15 | 11.60 |

## Appendix B. Boundary Conditions for Economic Evaluation

Parameter | Value | Unit | Reference |
---|---|---|---|

operational life time | 20 | a | |

full load hours | 8000 | h/a | |

price of electricity | 12.88 | €-Cent/kWh | [98] |

ancillary costs | 35 | % of invest | [28] |

specific cost of cooling | 0.1288 | €-Cent/kWh_{th} | [28,99,100] |

specific cost of maintenance | 2.0 | % of invest per year | [99] |

specific cost of insurance | 2.0 | % of invest per year | [101] |

specific cost of process integration | 20 | % of invest | [101] |

specific cost of personnel | 40 | €/h | |

working hours of personnel | 260 | h/year | [75] |

inflation electricity | 4.0 | % | |

inflation general | 2.0 | % | |

tax rate | 28.8 | % | |

interest rate | 4.0 | % | |

share of loan capital | 100 | % | |

redemption time | 20 | a | |

redemption rate | 5.0 | % |

## Appendix C. Temperature-Entropy-Diagrams of the Investigated Working Fluids

**Figure A1.**T,s-diagrams of investigated working fluids (

**A**) n-alkanes; (

**B**) alkylbenzenes; (

**C**) linear siloxanes; and (

**D**) cyclic siloxanes.

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**Figure 1.**Potential of electric power generated from industrial waste heat in different regions (operating hours: 8760 h/a).

**Figure 2.**Scheme of Organic Rankine Cycle plant (

**left**: basic ORC with heat source and heat sink;

**right**: ORC including internal recuperator (heat source and sink aren’t shown for clarity reasons)).

**Figure 3.**Approach of modular design: derive different plants P1 to P4 for various heat source temperatures and mass flow rates from one reference plant (Ref.).

**Figure 4.**Overview of datasets (defined in Section 3.5) used in each chapter and results of related parameters (defined in Section 3.4 and Section 5.2).

**Figure 5.**Exergetic efficiency for supercritical and subcritical mode of operation for varied heat source temperature ((

**A**) n-alkanes; (

**B**) alkylbenzenes; (

**C**) linear siloxanes; and (

**D**) cyclic siloxanes).

**Figure 6.**Temperature-heat flow-diagram (

**A**) pinch point at beginning of evaporation; (

**B**) pinch point during preheating; (

**C**) pinch point beginning of preheating).

**Figure 7.**Heat exchange capacity (

**A**), volume flow ratio (

**B**), size parameter (

**C**) and rotational speed (

**D**) depending on the heat source temperature.

**Figure 8.**Payback period (

**A**) in years and cash flow (

**B**) in million € for all four chemical classes depending on heat source temperature.

**Figure 9.**Net power output of hexamethyldisiloxane depending on heat source temperature and mass flow rate.

**Figure 10.**Heat exchanger area of hexamethyldisiloxane depending on heat source temperature and mass flow rate.

**Figure 11.**Turbine rotational speed of hexamethyldisiloxane depending on heat source temperature and mass flow rate.

**Figure 12.**Size parameter of hexamethyldisiloxane depending on heat source temperature and mass flow rate.

**Figure 13.**Volume flow ratio of hexamethyldisiloxane depending on heat source temperature and mass flow rate.

**Figure 14.**Payback period (

**A**) in years and cash flow (

**B**) in million € after operating time for hexamethyldisiloxane at different mass flow rates (red and hollow triangles: assumption of reduced investment costs).

Efficiencies | Value |
---|---|

isentropic, turbine | 75% |

mechanical, generator | 95% |

isentropic, pump | 80% |

electromechanical, pump | 85% |

Minimum Temperature Approach of Heat Exchangers | |

heater | 35 K |

internal recuperator | 10 K |

condenser | 10 K |

Pressure and Temperature | |

maximum pressure subcritical | p(s_{max}) |

minimum pressure supercritical | 1.02·p_{crit} |

maximum pressure supercritical | 1.30·p_{crit} |

minimum temperature after heater | T(s_{max}) |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Preißinger, M.; Brüggemann, D. Thermoeconomic Evaluation of Modular Organic Rankine Cycles for Waste Heat Recovery over a Broad Range of Heat Source Temperatures and Capacities. *Energies* **2017**, *10*, 269.
https://doi.org/10.3390/en10030269

**AMA Style**

Preißinger M, Brüggemann D. Thermoeconomic Evaluation of Modular Organic Rankine Cycles for Waste Heat Recovery over a Broad Range of Heat Source Temperatures and Capacities. *Energies*. 2017; 10(3):269.
https://doi.org/10.3390/en10030269

**Chicago/Turabian Style**

Preißinger, Markus, and Dieter Brüggemann. 2017. "Thermoeconomic Evaluation of Modular Organic Rankine Cycles for Waste Heat Recovery over a Broad Range of Heat Source Temperatures and Capacities" *Energies* 10, no. 3: 269.
https://doi.org/10.3390/en10030269