Carnot method

The Carnot method is a process for dividing the fuel input (primary energy), but also other input factors such as CO ₂ emissions or variable costs, among the by-products in the case of energetic by- products . It uses the workability of the energetic co-products according to Carnot's efficiency as a distribution key . It thus corresponds to an exergetic equivalence number method, since the same exergy content is assessed equally. The primary area of ​​application is cogeneration , but other energetic co-products are also conceivable, such as B. the generation of cold using the waste heat for heating purposes or the generation of compressed air and heat. It has the advantage that no external reference values ​​are required for dividing the input stream into the output streams, but that only endogenous process parameters are required for this.

Allocation factor for the fuel

The proportion of fuel that is required for the generation of the by-products electricity A and heat H can be calculated as follows , taking into account the first and second law of thermodynamics :

a _el = (1 η _el ) / (η _el + η _c η _th )
a _th = (η _c η _th ) / (η _el + η _c η _th )
Note: a _el + a _th = 1

with
a _el : allocation factor for electrical energy, d. H. the proportion of fuel required for electricity generation
a _th : allocation factor for thermal energy, d. H. the proportion of the fuel that is required for heat generation

η _el = A / Q _BS
η _th = H / Q _BS
A: electrical work
H: released useful heat
Q _BS : supplied fuel heat

and
η _c : Carnot factor 1-T _i / T _s (Carnot factor for electrical energy is 1 )
T _i : lower temperature, inferior (environment)
T _s : upper temperature, superior (useful heat)

In heating systems with different flow and return temperatures, the upper temperature is approximately the mean temperature of the heating energy.
T _s = (T _VL + T _RL ) / 2
For higher thermodynamic accuracy requirements, the logarithmic mean is used.
T _s = (T _VL -T _RL ) / ln (T _VL / T _RL )

Fuel factor

The fuel intensity or factor for electrical energy f _{BS, el} or thermal energy f _{BS, th} is the ratio of specific input to output.

f _{BS, el} = a _el / η _el = 1 / (η _el + η _c η _th )

f _{BS, th} = a _th / η _th = η _c / (η _el + η _c η _th )

Primary energy factor

To determine the primary energy factors, the upstream chain of the fuel used must also be included.

f _{PE, el} = f _{BS, el} · f _{PE, BS}
f _{PE, th} = f _{BS, th} · f _{PE, BS}

with
f _{PE, BS} : primary energy factor of the fuel

Effective efficiency

The reciprocal of the fuel factor (BS intensity) describes the efficiency of the assumed sub-process, which is responsible for generating only electrical or only thermal energy. This equivalent efficiency thus corresponds to the effective efficiency of the "virtual boiler" or the "virtual power plant" within a CHP plant.

η _{el, eff} = η _el / a _el = 1 / f _{BS, el}
η _{th, eff} = η _th / a _th = 1 / f _{BS, th}

with
η _{el, eff} : effective efficiency of electricity generation in the CHP process
η _{th , eff} : effective efficiency of heat generation in the CHP process

Quality of the energy conversion

In addition to the efficiency, which describes the quantity of usable final energies, the quality of the energy conversion according to the second law of thermodynamics is of particular importance. The exergy decreases with increasing entropy . With exergy, the quality of the energy and not just the quantity is considered. That is why an energy conversion should also be judged according to its exergetic quality. In the case of the product "thermal energy", the temperature level at which it is present plays an important role. The exergetic efficiency η _x thus describes how much of the working capacity of the energy input remains in the energetic by-products after the conversion process. Using the example of CHP, the following relationship emerges:

η _{x, total} = η _el + η _c η _th

The allocation according to the Carnot method always results in:
η _{x, total} = η _{x, el} = η _{x, th}

with
η _{x, total} = exergetic efficiency of the coupling process
η _{x, el} = exergetic efficiency of the virtual boiler
η _{x, th} = exergetic efficiency of the virtual generator

Derivation

The derivation is based on the example of a two-dimensional joint production with input I and the first product O ₁ and the second product O ₂ . f are the respective factors to be divided (primary energy, CO ₂ emissions, variable costs, etc.).

${\displaystyle {\text{Bewertung des Inputs}}={\text{Bewertung des Outputs}}}$

${\displaystyle f_{i}\cdot I=f_{1}\cdot O_{1}+f_{2}\cdot O_{2}}$

f _i , I, O ₁ , O ₂ are known. An equation is obtained with two unknowns f ₁ and f ₂ , which can be solved with a large number of tuples ( f ₁ , f ₂ ). The second equation used is the transformability of product O ₁ into O ₂ and vice versa.

${\displaystyle O_{1}=\eta _{21}\cdot O_{2}}$

η ₂₁ is the conversion factor from O ₂ to O ₁ , the reciprocal value 1 / η ₂₁ = η ₁₂ describes the inverse transformation. A reversible conversion is assumed in order not to favor either of the two directions. The evaluation of both sides by the factors f ₁ and f ₂ is therefore also equivalent due to the interchangeability. Output O ₂ evaluated with f ₂ must result in the same as the convertible output O ₁ evaluated with f ₁ .

${\displaystyle f_{1}\cdot (\eta _{21}\cdot O_{2})=f_{2}\cdot O_{2}}$

This can be plugged into the first equation above and further transformed:

${\displaystyle f_{i}\cdot I=f_{1}\cdot O_{1}+f_{1}\cdot (\eta _{21}\cdot O_{2})}$

${\displaystyle f_{i}\cdot I=f_{1}\cdot (O_{1}+\eta _{21}\cdot O_{2})}$

${\displaystyle f_{i}=f_{1}\cdot (O_{1}/I+\eta _{21}\cdot O_{2}/I)}$

${\displaystyle f_{i}=f_{1}\cdot (\eta _{1}+\eta _{21}\cdot \eta _{2})}$

${\displaystyle f_{1}=f_{i}/(\eta _{1}+\eta _{21}\cdot \eta _{2})}$

with η ₁ = O ₁ / I and η ₂ = O ₂ / I

See also

• Residual value method
• Finnish method
• Equivalence digit method
• Nicolas Léonard Sadi Carnot
• Second law of thermodynamics

literature

• AGFW: Worksheet FW 309 Part 6 , Energetic evaluation of district heating - Determination of specific CO ₂ emission factors, June 2016.
• Hans Hertle: The use of exergy flows in communal electricity-heating systems , 5th Congress 100% Renewable Energy Regions, Kassel, September 2013.
• Hans Hertle et al .: The use of exergy flows in municipal electricity-heat systems to achieve CO ₂ neutrality in municipalities by 2050 , UBA-FB-00, ifeu - Institute for Energy and Environmental Research, Heidelberg, October 2014 .
• Andrej Jentsch: A novel exergy-based concept of thermodynamic quality and its application to energy system evaluation and process analysis , dissertation, TU Berlin, 2010.
• Marc Rosen: Allocating carbon dioxide emissions from cogeneration systems: descriptions of selected output-based methods , Journal of Cleaner Production, Volume 16, Issue 2, January 2008, Pages 171–177.
• Association of German Engineers: VDI Guideline 4608 Part 2 , Energy Systems - Combined Heat and Power - Allocation and Evaluation, July 2008.
• DIN EN 15316-4-5: 2017 Energetic assessment of buildings - Method for calculating the energy requirements and degree of utilization of the systems - Part 4–5: District heating and district cooling
• DIRECTIVE (EU) 2018/2001 on the promotion of the use of energy from renewable sources , 2018-12-11. Annex V, C. Method, b) and Annex VI, B. Method, d)

Individual evidence

1. ↑ NN: Compressed air heat power plant HWV 20. (PDF) energiewerkstatt, 2015, accessed on May 1, 2018 . 
2. ↑ Susanne Krichel, Steffen Hülsmann, Simon Hirzel, Rainer Elsland, Oliver Sawodny: More clarity in compressed air - exergy flow diagrams as a new basis for efficiency considerations in compressed air systems. (PDF) In: Journal for Oil Hydraulics and Pneumatics 56 (2012). 2012, accessed May 1, 2018 . 
3. ↑ Tymofii Tereshchenko, Natasa North: Uncertainty of the allocation factors of heat and electricity production of combined cycle power plant . In: Applied Thermal Engineering . tape 76 , February 5, 2015, ISSN  1359-4311 , p. 410-422 , doi : 10.1016 / j.applthermaleng.2014.11.019 .