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)

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.

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

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

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

The Fuel Product Diagram 1 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

The Fuel-Product Table   F0 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

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

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

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

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

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

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

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

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

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

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

Question 4: Increasing Population   F0 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

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

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

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