1. The duality between exergy efficiencies and exergy costs
The duality between exergy efficiencies and exergy costs. A general theory and the Relative Free Energy function.
Antonio Valero,
CIRCE – Instituto de Investigación en Recursos y Consumos Energéticos.
University of Zaragoza (Spain)

2. Motivation
Costing is one of the most important applications of exergy. Exergy allows more precise allocations than energy or even money when two or more stream bifurcations appear in energy systems.
Exergy cost analysis has become a complementary analysis of energy systems. However, such analyses strongly depend on the practitioner expertise.
A number of “reasonable” decisions need to be taken to get fair results.
“This paper focus on developing a mathematical theory that support such decisions but also to analyze the pitfalls or weaknesses of conventional exergy costing”
A general theory and the Relative Free Energy function.

3. Motivation
Costing is one of the most important applications of exergy. Exergy allows more precise allocations than energy or even money when two or more stream bifurcations appear in energy systems.
Exergy cost analysis has become a complementary analysis of energy systems. However, such analyses strongly depend on the practitioner expertise.
A number of “reasonable” decisions need to be taken to get fair results.
“This paper focus on developing a mathematical theory that support such decisions but also to analyze the pitfalls or weaknesses of conventional exergy costing”
Applying Thermoeconomics to the Analysis of North American Food Chain

4. Applying Thermoeconomics to the Analysis of North American Food Chain
Motivation
The Global 2000 Report (Barney, 1980) presented a flow diagram of energy form American food production.
For some 3.6 GJ (per capita/year) of human food energy, 35.5 GJ of fossil fuel energy have been expended, not counting the “solar gift” of 80 GJ that is absorbed by the plants used in the process.
It seems more than plausible that the energy “demand” from agriculture and food processing can be reduced dramatically with essentially no sacrifice of wellbeing.
Applying Thermoeconomics to the Analysis of North American Food Chain

5. Applying Thermoeconomics to the Analysis of North American Food Chain
Objectives
How much fossil fuels can be saved if we recycling crop residues?
How much fossil fuels and harvest area could be saved if we improve the efficiency of vegetal and animal production processes?
How much fossil fuels and harvest area could be saved if we change our diet and consume more vegetables and less meat?
How food demand could be increasing according to increasing population?
How this kind of questions could be answered using Thermoeconomics?
Applying Thermoeconomics to the Analysis of North American Food Chain

6. The Fuel Product Diagram1 2
Vegetal Biomass Production
Harvest Production
Animal Food Production
Vegetal Food Production
Human Food Demand 3 4 5 2 3 4 5 80 60 7
51.5
3.5 15
13.5
1.9
3.1
3.6 1
Applying Thermoeconomics to the Analysis of North American Food Chain

7. The Fuel-Product TableF0 F1 F2 F3 F4 F5
TOTAL P0 80 7 15
13.5
115.5 P1 60 P2 5
51.5
3.5 P3
1.9 P4
3.1 P5
3.6
8.6 67
66.5 17
Applying Thermoeconomics to the Analysis of North American Food Chain

8. The Fuel-Product Table
The fuel product table is the matrix representation of the productive process in terms of useful energy.
Each element Eij represents the production of the process –i– that becomes resources of the process –j–, measure in terms of useful energy.
(Fuel) F0 F1 … Fj Fn P0
E01
E0j
E0n P1
E10
E11
E1j
E1n Pi
Ei0
Ei1
Eij
Ein Pn
En0
En1
Enj
Enn
(Product)
(System Resources)
(System Demand)
Applying Thermoeconomics to the Analysis of North American Food Chain

9. The Demand Driven Model
The demand driven model allow to determine the system resources cost as a function of:
The production demand:
The efficiency of each process:
The junction ratios:
The resources required in each process could be obtained as:
The cost per production unit could be obtained as:
Applying Thermoeconomics to the Analysis of North American Food Chain

10. The Resources Driven Model
The resources driven model allow to determine the system production and their costs as a function of:
The system resources:
The efficiency of each process:
The distribution ratios:
The resources required in each process could be obtained as:
The production cost could be obtained as:
Applying Thermoeconomics to the Analysis of North American Food Chain

11. The Exergy Cost Input-Output Table
The Exergy Cost Input-Ouput table is the matrix representation of a production process in terms of exergy cost, i.e. the system resources, measured in term of exergy Cij, required to obtain a internal or final product of the process.
CF,0
CF,1 …
CF,j
CF,n
CP,0
C01
C0j
C0n
CP,1
C10
C11
C1j
C1n
CP,i
Ci0
Ci1
Cij
Cin
CP,n
Cn0
Cn1
Cnj
Cnn
Properties
Applying Thermoeconomics to the Analysis of North American Food Chain

12. Applying Thermoeconomics to the Analysis of North American Food Chain
Food Chain Base Case
The graph shows the biomass and fossil fuels required to obtain one unit of product for each process on the USA Food Chain.
To produce 1 Kcal of meat we need more than 10 Kcal of fossil fuels, meanwhile to produce a kcal of vegetable food we need only 5 Kcal of fossil fuels.
The exergy cost analysis lets to identify the most inefficient processes in order to improve them.
Applying Thermoeconomics to the Analysis of North American Food Chain

13. Exergy Cost Input-Output Table
CF,0
CF,1
CF,2
CF,3
CF,4
CF,5
TOTAL
CP,0 80 7 15
13.5
115.5
CP,1
CP,2
7.25
74.675
5.075 87
CP,3
89.675
CP,4
18.575
CP,5
108.25
Applying Thermoeconomics to the Analysis of North American Food Chain

14. Question 1: Recycling Biomass
What happen if we recycling 10% of crop residues (2 GJ), keeping the imports and human consumption constant?
The graph show the results to apply the “Resources Driven Model” to simulate a reduction of 2 GJ of the fossil fuel consumption of the harvest production (E02= 5) and an increase of the efficiency of the vegetal biomass production
It shows than the unit cost of human food production in terms of fossil fuels is reduced in a 5,6%.
Applying Thermoeconomics to the Analysis of North American Food Chain

15. Question 2: Process Efficiency Analysis
What happen if the efficiency of each individual process is improving a 10%?
The graph shows the result to apply the “Demand driven Model” to this simulation, by increasing the efficiency of each individual process
It show that improving the efficiency and reducing the losses on the last stages of the human food production process, the most important fossil fuels savings are obtained.
Applying Thermoeconomics to the Analysis of North American Food Chain

16. Question 3: Changes in Food Diet
What happen if the consumption of meat is reduced in 10% percent, maintaining the final demand of energy per person?
The graph shows the result to apply the “Demand driven Model” to this simulation, by modifying the junction ratios of the last process.
It shows that a change of diet implies a saving of 13.42% of biomass resources and 5.73% of fossil fuels
Applying Thermoeconomics to the Analysis of North American Food Chain

17. Question 4: Increasing Population
The USA population has been increased 10% in the last 10 years.
What happen if population increase a 1% every year? Of course the energy consumption of energy both biomass and fossil fuels increase 1%. And what happen if the biomass energy free supplied by the sun, that is equivalent to the harvest area, could not increase?
A simulation using the fuel-product model is shown, where the energy food demand is increase 1%, by keeping constant the biomass supply, and modifying the imports.
A reduction of 8.9% in the imports is required with a increase of 0.25% in the fossil fuel consumption.
Applying Thermoeconomics to the Analysis of North American Food Chain

18. Question 4: Increasing PopulationF0 F1 F2 F3 F4 F5
TOTAL P0 80 7 15
13.5
115.5
15,15
13,635
0,000
115,785 P1 60 P2 5
51.5
3.5
4.45
52,015
3.535 P3
1.9
1.919 P4
3.1
3.131 P5
3,6
3.6
3,636
3.636
8.6 67
66.5 17
8,086
67,165
17,17
5,05
Fuel-Product table comparison for increasing food demand in 1% keeping constant the biomass supply.
Applying Thermoeconomics to the Analysis of North American Food Chain

19. Applying Thermoeconomics to the Analysis of North American Food Chain
Conclusions
We are shown the capabilities of Thermoeconomics as a tool for the analysis of macroeconomics energy and environmental systems, by applying this methodology to the analysis of the food chain.
It has been shown that an animal-based diet requires more energy, land and another natural resources than plant-based diet. Reducing the meat consumption in 10% but supplying the same calories, reducing the fossil fuel consumption in 6% and land requirements in 13.5%.
Recycling biomass appears as an important fossil fuel saving. If we recycling 10% of the crop waste, we reduced the total fossil fuel consumption in 5.6%.
We should take care about the efficiency of last food production stages. An increasing of 10% provides 7% of fossil fuel saving.
Applying Thermoeconomics to the Analysis of North American Food Chain

20. Applying Thermoeconomics to the Analysis of North American Food Chain
Conclusions
Thermoeconomics is a general theory of energy saving based on Second Law analysis that has been commonly used in the analysis of power a chemical plant since the 70’s.
We have demonstrated that Thermoeconomics and in particular Symbolic Exergoeconomics could be applied to a wider variety of energy and environmental systems in order to simulate and evaluate energy saving policies.
The methodology presented here could be considered as an extension of the economic input-output analysis called “Exergy Input-Output Analysis”.
Applying Thermoeconomics to the Analysis of North American Food Chain

21. Applying Thermoeconomics to the Analysis of North American Food Chain
Thank you very much for your attention!
Applying Thermoeconomics to the Analysis of North American Food Chain