# Power Generation Targets from Hot Composite Curves

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

_{H}, isentropic expansion, isothermal heat removal into a heat sink at temperature T

_{L}, and isentropic compression. In order for power to be generated in the cycle, T

_{H}needs to be greater than T

_{L}. The Carnot cycle assumes that there is no energy lost due to friction, no exchange of heat between various parts of the engine, and no transfer of heat from the cycle to the surrounding environment. The efficiency of the Carnot cycle can be calculated as

_{i}to T

_{i}

_{+1}, the heat available from the source profile segment is given by

_{j}is the heat capacity flowrate (kW/K) of the profile segment, T

_{i}is the inlet temperature (K) and T

_{i}

_{+1}is the exit temperature (K) of the heat source composite after heat has been removed. The heat capacity flow rate is the product of the heat capacity and the flow rate of the stream. Equation (3) is applied for isothermal intervals where H

_{v,j}is the latent heat (kW). For maximum power generation, the low temperature reservoir is assumed to be an isothermal utility at ambient temperature (T

_{L}) with an infinite heat capacity flow rate.

_{H}= T

_{i}

_{+1}. This will forfeit power generation potential and therefore present a lost opportunity for power generation. To increase power generation from the heat source profile, multiple Carnot cycles can be deployed, as illustrated in Figure 3. As the number of cycles approaches infinity, the hot temperature reservoirs of the Carnot cycles will approach the heat source profile and power generation will be maximized.

_{i}

_{+1}to T

_{i}

_{i}

_{+1}= T

_{i}, the maximum work becomes:

- (a)
- The heat transferred from the hot streams (or composite) present in the interval into the cycle is determined using Equation (2) in the case of a non-isothermal interval, or using Equation (3) in the case of an isothermal interval.
- (b)
- The interval power generation efficiency is determined using Equation (8) in the case of a non-isothermal interval, or using Equation (9) in the case of an isothermal interval.
- (c)
- The maximum amount of power that can be generated from the heat available in the interval is determined as the product of available heat from (a) and interval power generation efficiency from (b).

## 3. Results and Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

CP_{j} | Heat capacity flow rate of hot composite in non-isothermal interval j |

H_{v,j} | Latent heat of hot composite in isothermal interval j |

H_{i} | Enthalpy of hot composite at interval inlet temperature |

H_{i}_{+1} | Enthalpy of hot composite at interval exit temperature |

Q_{j} | Heat ejected from hot composite in interval j |

${S}_{j}^{\mathrm{gen}}$ | Entropy generation in interval j |

S_{i} | Entropy of hot composite at interval inlet temperature |

S_{i}_{+1} | Entropy of hot composite at interval exit temperature |

T_{i} | Initial temperature of hot composite in interval j |

T_{i}_{+1} | Final temperature of hot composite in interval j |

T_{H} | Temperature of the high temperature reservoir |

T_{L} | Temperature of the low temperature reservoir |

T_{0} | Dead state temperature |

${W}_{j}^{\mathrm{max}}$ | Maximum theoretical power generation in interval j |

${\eta}_{j}^{\mathrm{max}}$ | Maximum power generation efficiency in interval j |

${\eta}_{\mathrm{sys}}^{\mathrm{max}}$ | Maximum power generation efficiency across all temperature intervals |

Ψ | Availability |

## Appendix A

## References

- Oluleye, G.; Jobson, M.; Smith, R. A hierarchical approach for evaluating and selecting waste heat utilization opportunities. Energy
**2015**, 90, 5–23. [Google Scholar] [CrossRef] - Öhman, H.; Lundqvist, P. Comparison and analysis of performance using Low Temperature Power Cycles. Appl. Therm. Eng.
**2013**, 52, 160–169. [Google Scholar] [CrossRef] - Minea, V. Power generation with ORC machines using low-grade waste heat or renewable energy. Appl. Therm. Eng.
**2014**, 69, 143–154. [Google Scholar] [CrossRef] - Tchanche, B.F.; Lambrinos, G.; Frangoudakis, A.; Papadakis, G. Low-grade heat conversion into power using organic Rankine cycles—A review of various applications. Renew. Sustain. Energy Rev.
**2011**, 15, 3963–3979. [Google Scholar] [CrossRef] - Linnhoff, B. Thermodynamic Analysis in the Design of Process Networks. Comput. Chem. Eng.
**1979**, 3, 283–291. [Google Scholar] [CrossRef] - Dhole, V.R.; Linnhoff, B. Total site targets for fuel co-generation, emissions, and cooling. Comput. Chem. Eng.
**1993**, 17, 101–109. [Google Scholar] [CrossRef] - El-Halwagi, M.M. Sustainable Design through Process Integration; Elsevier: Amsterdam, The Netherlands, 2012; pp. 1–14. [Google Scholar] [CrossRef]
- Hackl, R.; Andersson, E.; Harvey, S. Targeting for energy efficiency and improved energy collaboration between different companies using total site analysis (TSA). Energy
**2011**, 36, 4609–4615. [Google Scholar] [CrossRef] - Bungener, S.; Hackl, R.; Van Eetvelde, G.; Harvey, S.; Marechal, F. Multi-period analysis of heat integration measures in industrial clusters. Energy
**2015**, 93, 220–234. [Google Scholar] [CrossRef] - Marechal, F.; Kalitventzeff, B. Targeting the integration of multi-period utility systems for site scale process integration. Appl. Therm. Eng.
**2003**, 23, 1763–1784. [Google Scholar] [CrossRef] - Stijepovic, V.Z.; Linke, P.; Stijepovic, M.Z.; Kijevčanin, M.L.J.; Šerbanović, S. Targeting and design of industrial zone waste heat reuse for combined heat and power generation. Energy
**2012**, 47, 302–313. [Google Scholar] [CrossRef] - Linnhoff, B.; Dhole, V.R. Shaftwork targets for low-temperature process design. Chem. Eng. Sci.
**1992**, 47, 2081–2091. [Google Scholar] [CrossRef] - Mavromatis, S.P.; Kokossis, A.C. Conceptual optimisation of utility networks for operational variations—I. Targets and level optimisation. Chem. Eng. Sci.
**1998**, 53, 1585–1608. [Google Scholar] [CrossRef] - El-Halwagi, M.; Harell, D.; Dennis Spriggs, H. Targeting cogeneration and waste utilization through process integration. Appl. Energy
**2009**, 86, 880–887. [Google Scholar] [CrossRef] - Curzon, F.L. Efficiency of a Carnot engine at maximum power output. Am. J. Phys.
**1975**, 43, 22. [Google Scholar] [CrossRef] - Ondrechen, M.J.; Andresen, B.; Mozurkewich, M.; Berry, R.S. Maximum work from a finite reservoir by sequential Carnot cycles. Am. J. Phys.
**1981**, 49, 681–685. [Google Scholar] [CrossRef] - Ibrahim, O.M.; Klein, S.A.; Mitchell, J.W. Optimum Heat Power Cycles for Specified Boundary Conditions. J. Eng. Gas Turbines Power
**1991**, 113, 514–521. [Google Scholar] [CrossRef] - Park, H.; Kim, M.S. Thermodynamic performance analysis of sequential Carnot cycles using heat sources with finite heat capacity. Energy
**2014**, 68, 592–598. [Google Scholar] [CrossRef] - Marmolejo-Correa, D.; Gundersen, T. New graphical representation of exergy applied to low temperature process design. Ind. Eng. Chem. Res.
**2013**, 52, 7145–7156. [Google Scholar] [CrossRef] - Sandler, S.I. Chemical, Biochemical, and Engineering Thermodynamics; John Wiley & Sons: New York, NY, USA, 2006; Volume A5. [Google Scholar]

Example | Stream | CP (kW/K) | T_{in} (K) | T_{out} (K) | Q (kW) |
---|---|---|---|---|---|

Case 1 | Stream 1-1 | 7 | 560 | 350 | 1470 |

Stream 1-2 | 9 | 560 | 490 | 630 | |

Stream 1-3 | 290 | 600 | 560 | 11,600 | |

Case 2 | Stream 2-1 | ∞ | 500 | 500 | 6700 |

Stream 2-2 | 10 | 500 | 350 | 1500 | |

Stream 2-3 | 15 | 560 | 500 | 900 | |

Stream 2-4 | 10 | 600 | 500 | 1000 | |

Stream 2-5 | 90 | 600 | 560 | 3600 | |

Case 3 | Stream 3-1 | ∞ | 450 | 450 | 6300 |

Stream 3-2 | 20 | 450 | 350 | 2000 | |

Stream 3-3 | 30 | 400 | 350 | 1500 | |

Stream 3-4 | 26 | 600 | 450 | 3900 |

Stream | CP (MW/K) | T_{in} (K) | T_{out} (K) | Q (MW) |
---|---|---|---|---|

Stream 1 | 0.15 | 523 | 313 | 31.5 |

Stream 2 | 0.25 | 473 | 353 | 30.0 |

© 2018 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/).

## Share and Cite

**MDPI and ACS Style**

Al-Ani, O.; Linke, P. Power Generation Targets from Hot Composite Curves. *Energies* **2018**, *11*, 403.
https://doi.org/10.3390/en11020403

**AMA Style**

Al-Ani O, Linke P. Power Generation Targets from Hot Composite Curves. *Energies*. 2018; 11(2):403.
https://doi.org/10.3390/en11020403

**Chicago/Turabian Style**

Al-Ani, Omar, and Patrick Linke. 2018. "Power Generation Targets from Hot Composite Curves" *Energies* 11, no. 2: 403.
https://doi.org/10.3390/en11020403