APPLYING THERMOECONOMICS TO THE ANALYSIS OF ... - circe

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Every human activity has an environmental impact, with the food system being an important (and mandatory) human activity. There is a wide variation in environmental impact according to the type of food, and the method of producing the food. An important feedback principle links the environment and food systems. The environment influences the quality and capacity of food production, which in turn influences the environment. A degraded environment may be less healthy for humans and other organisms, and also less able to produce the range and amount of food that an environment in better condition could achieve (Riley, M., 2005). Each basic process that comprises the food chain has an efficiency and a resources cost that could be evaluated by means of the thermoeconomic analysis, allowing the identification of improving options. 2. THE FUEL –PRODUCT MODEL Symbolic Exergoeconomics (Torres, 2004) provides general relationships between the production demand and the resources cost with the efficiency and irreversibilities of the individual process of an energy system. It is based on the productive structure of the system and is represented by the fuel – product table, (fig. 1) which describes how the production processes are related. F0 F1 … Fn P0 E01 … E0n P1 E10 E11 … E1n … … … Eij … Pn En0 E1n … Enn Figure 1. Generic Fuel-Product Table In this table, the useful energy carried from the i-th process to the j-th process is represented as E ij . The sum of each row of the table is the production of each process, and the sum of each column is the resources or fuel required for each process. Symbolic exergoeconomic provides two different representations of the productive model: The FP representation allows relating the production and the cost of each process of the system as a function of: F ≡ E , … E • The external resources ( ) e 10 n0 • The efficiency of each process, represented by K D , a diagonal matrix whose elements are the unit • consumption of each process: κi ≡ Fi / Pi . The distribution ratios, represented by FP , a matrix whose elements are defined as yij ≡ EjiPj. The production of each process is obtained as: ( ) 1 P =〈 P| Fe The total production demand is calculated as: where 〈 P| = KD− − FP (1) t P T = y0P F e (2) y ( , , ) is a vector that contains the distribution ratios related to the environment. t where 0 ≡ y01 … y0n The production cost of each process is given by: * CP=〈 P | C0where * 〈 P | = ( UD− −1 FP ) (3) the vector C0 ≡ ( c01E01, …, c0nE0n) contains the cost of the external resources and c 0i represents its unitary cost. The magnitude used to measure the external resources determines the type of cost obtained. The other representation, called PF representation, allows expressing the resources and their costs as a function of: • The production demand P s ≡ ( E10, …, En0) • The efficiency of each process i i / i F P ≡ ε • The junction ratios, represented by PF , a matriz which elements are defined as qij ≡ Eij/ Fi The resources used in each process are obtained as: ( ) 1 F = F Pswhere 〈 F | = HD− − PF (4) −1 and HD ≡ K D is a diagonal matrix (n× n), containing the efficiency ε i of each process. The cost per production unit can be obtained as: 888
Proceedings of ECOS 2009 22 nd International Conference on Efficiency, Cost, Optimization Copyright © 2009 by ABCM Simulation and Environmental Impact of Energy Systems August 31 – September 3, 2009, Foz do Iguaçu, Paraná, Brazil t P where cˆ0i ≡ c0iq0, i. The total cost of the external resources 0 c = F c ˆ (5) 0 0 C can be expressed as a function of the system demand as: t C = cˆ F P (6) Using these relationships is it also possible to determine the variation of the total resources as a function of the variation of the parameters of the PF representation: n ⎛ ⎞ Δ C0 = ∑⎜c0iΔ q0 iFi + ∑ cP, jΔ qjiFi + cF, iΔ κiPi + cP, iΔEi0⎟ (7) i= 1 ⎝ j ⎠ The above expression is known as the Fuel Impact Formulae (Torres et al., 2002), the first two terms correspond to the variation of the junction (structural) ratios, the third term to the variation of the processes efficiency and the last term to the system demand variation. Through the example presented in the next section, we will show how thermoeconomics can be applied to a macroeconomic system such as the American food chain, giving insights on improving options. 3. APPLYING THERMOECONOMICS TO THE ANALYSIS OF THE FOOD CHAIN The Global 2000 Report (Barney, 1980) presented a flow diagram of energy for American food production (see figure 2). For around 3.6 GJ (per capita) of human food energy, 35.5 GJ of technical energy are expended, without accounting for 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 could be substantially reduced with essentially no sacrifice of wellbeing (Weizsacker, 1997). And thermoeconomics could help to identify and quantify these reductions. According to the diagram of figure 2, the food chain system could be decomposed into five basic processes, represented in the productive diagram of figure 3. 80 60 1 2 (1) Vegetal biomass production (2) Harvest production (3) Animal food production (4) Vegetal food production (5) Human food demand 7 0 51.5 5 3.5 s 15 3 4 13.5 Figure 3. Productive diagram of the food chain in the USA 3.1. The base food chain The thermoeconomic model of the base food chain of Fig. 3 is represented by the following Fuel-Product table. From this table it is possible to obtain the production cost of each process. In this example we are interested to separate the cost associated to fossil fuels and the cost associated to biomass energy, because the saving of these resources has a different interpretation. Fossil fuels are required in all processes of food production: draining, irrigation, chemical products, mechanical manufacturing, cattle raising, food preparation, shipping and distribution…, whereas biomass energy is provided by the plants, taking energy from the sun. 889 1.9 3.1 5 3.6
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