Thermodynamics and Thermoeconomics

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Thermodynamics and Thermoeconomics Int.J. Applied Thermodynamics, ISSN 1301-9724 Vol.2 (No.1), pp.5-18, March-1999 Thermodynamics and Thermoeconomics Yehia M. El-Sayed Advanced Energy System Analysis 41658 Higgins Way, Fremont, CA 94539 - USA Tel/Fax: 510 656 2783 E-Mail: [email protected] Abstract Raising the efficiency of an energy system is within the domain of thermodynamics. Raising the efficiency cost-effectively (Thermoeconomics) is a multi-disciplinary problem in which thermodynamics interfaces other disciplines of knowledge which in this particular case are design, manufacture and economics. This paper deals with a communication/optimization strategy, via the concept of costing equations, whereby the system can be analyzed and optimized for minimum cost within the domain of thermodynamics. The communication/optimization strategy is explained. The generation of costing equations is demonstrated. A gas turbine power system and seawater distillation process system are used as examples for improved design point and improved configuration. The results of their optimized design points for configurations in order of increasing complexity are displayed on cost-efficiency coordinates. Key words: second law analysis, costing, thermoeconomics, optimization. thermoeconomics has been impressive in few 1. Introduction directions. Valero et al (1994, 1996), El-Sayed One of the cornerstones of sustainable (1996) and Lazzaretto and Tsatsaronis (1997) may development is the cost-effective fuel saving of represent the different directions of development. systems that use or produce useful energy. This, in The directions are not yet free from inconsistencies turn, calls for more intensive and extensive system (Cerqueira and Nebra 1998). analysis while the system is still in its design phase. This paper follows the second direction by the Such analysis has to be multi-disciplinary. author. Costing equations are introduced as Accessing the analysis from the discipline of rational carriers of the essential information needed thermodynamics is the advantage of Thermo- for optimal system design given a cost objective economics. function. The results of two previous applications Thermoeconomics was first developed during (El-Sayed 1996, 1997b) of the concept and its the sixties. The name was coined by professor M. optimization algorithm are presented. Recently in Tribus (1962). Seawater desalination processes other publications, the concept has been extended were of prime concern to gain insight in the with almost no added information (El-Sayed interaction between the surface of separation and 1997a, 1998) to the prediction of the system’s part- the energy requirement. Even though at that time load performance equation and to the optimal oil prices were 0.1 to 0.2 today’s prices, the impact operation of a group of systems of known part-load on the price of water was significant compared to performance equations conventional water prices. The publication by El- In this paper, the need for a communication/ Sayed and Evans (1970) was perhaps one of optimization strategy to handle the complexity of earliest on the subject matter. Later the interest in multi-disciplinary system optimization is first further development of Thermoeconomics to considered. The extraction of relevant information handle energy-intensive systems in general was for optimal system design from design models initiated by professor R. Gaggioli (1980, 1983). representing current or innovative design practices Many researchers responded positively to the of the system devices is then explained using a initiation. In the last 25 years, the development of Int.J. Applied Thermodynamics, Vol.2 (No.1) 5 design model for a heat exchanger as an example. system decision variables to be thermodynamic The extracted information is presented as a costing variables follows naturally. These decisions will be equation for each considered device. This mostly efficiency coefficients of the system devices procedure is the added burden to purely (adiabatic efficiency, effectiveness, pressure loss thermodynamic analysis. An application to a ratios, heat loss ratios, temperature differences, power system (gas turbine) and another to process extent of reaction....) beside few decisions that system (seawater distillation) are then considered belong to the system as a whole such as pressure for improved design point and improved and temperature levels. configuration. 2.1. Decomposition at the Discipline Level 2. The Communication/Optimization Strategy Expressing {c} and {A} in terms of Any attempt claiming system improvement thermodynamic variables allows treating the should be explicitly characterized by an objective optimization process within the thermodynamic function, decision variables that are the degrees of domain and hence the system is decomposed at the improvement freedom, and an approach to system discipline level. In many situations {c} can be decomposition. These three features are not treated as constants depending on time and independent from each other. They have to be location. The costing equations described in the considered simultaneously to establish a next section give {A} in terms of thermodynamic communication/optimization strategy. variables. In this paper {c} are treated as constants. A cost objective function suitable for the Figures 1, 2 illustrate the concept of costing design phase of an energy-intensive system is the equations. Figure 1 shows a theoretical scenario in production cost for a given capacity: which the disciplines of thermodynamics, design and manufacture communicate directly while being J = ∑cF*F+ ∑cz*Z +C R (1) embedded in a given economic environment. Each or the net cost function discipline assumes a suitable computation model of inputs (decisions variables {Y}), constraining J = ∑cF*F+ ∑cz*Z-∑cP*P+C R (1a) relations, and outputs (dependent variables {X}). where J is a cost, c F and c P are unit prices of feeds The decision variables {Y} depend on the flow of F and products P as occurring in the market place information from the discipline of thermody- and c z is a capital discount rate. C R is a constant namics. The objective of thermodynamics is to remainder cost as far as the design phase is minimize fuel and/or maximize products by concerned. Equation (1a) suits more multi-product targeting the highest possible system efficiency. systems, such as cogeneration, since it responds to The objective of design is to minimize materials the relative values of the products as perceived in given the efficiency levels of the respective the market place. The negative of its J is a devices. The objective of manufacture is to profitability that is maximized. It also reduces to minimize the labor and the energy of shaping these the production cost of Equation (1) for single materials. Each discipline has its own optimizer. A product systems of given product rate since ∑cP*P master optimizer iterates all minimization reduces to a constant. Equation (1) can be applied processes and records all rounds of optimization to a multi-product case, but assumptions equal to until the cost objective function is minimized. The the number of products less one are needed to minimized cost c amin *A min of each device is then allocate the production cost to each product. listed against its corresponding input thermody- namic variables to its design model {V }. The Z is a capital cost of a device that is further T,D resulting correlation establishes the concept of expressed as c *A or ∑ c *A where c is a unit cost a a a costing equations. The quality of the correlation of a characterizing surface or volume of the device. determines the quality of the costing equation. The cost minimization of an energy system of Figure 2 assumes thermodynamics as the active interconnected devices interfaces at least four discipline and shows an indirect communication disciplines of knowledge: Thermodynamics {F,P}, with the disciplines of design, manufacture and Design {A}, Manufacture {c a} and Economics {c F, economics through costing equations and a set of cP, c z}. economic prices {c f,c p,c z}. Of course if the costs of To enhance optimization, decomposition is devices are available as function of loading and needed at the discipline level as well as the device efficiency, there would be no need for costing level. Since the creation of a system occurs in the equations. At the moment this is not the case and discipline of thermodynamics, the selection of the probably will not be the case. Prices of devices in 6 Int.J. Applied Thermodynamics, Vol.2 (No.1) Economic Manufacture Models Design Models Thermodynamic Model Envirnmt Initial Capital New Costs {Y M}1 {Y D}1 {Y T} Z {V } V } {V } 1 min M 1 {X =F (X ,Y ,V )} D, M 1 {X =F (X ,Y ,V )} T, D 1 Mi M M M D, M Di D D D T,D ------------ ------------ c A A {V } a1 min ------------ 1 1 min ------------ TC1 --------------- {X Ti =F T (X T,Y T)} optimizer optimizer {V T } ---------------- ---------------- ---------------- Zn min {V M}n {Y M}n {Y D}n ---------------- c an min n A n min n optimizer optimizer Fuels {c a min } {A min } {V T, D }1,2,...n Products Master Recorder of all optimizers’ results optimizer Unit Costs {c f,c z,c p} J(YT) {c a min } Costing Equations’ Generator n1 n2 {A min } {Z=c a*A{V T}} 1,2,..n = {c a* k * V T1 * V T2 *.....} 1,2,......n {V T, D }1,2,...n Yes No J Min ? V Variable, decision or dependent Subcripts Y Decision Variable T Thermodynamic X Dependent Variable D Design, T,D Thermodynamic input to design F Function, Fuel M Manufacture, D,M Design input to manufacture Z Minimized Capital Cost of a Device B Boundary A Minimized Characterizing Surface a Surface area C Unit Costs f Fuel J Cost Objective Function p Product = ∑ c f * F + ∑ c z * Z -∑cp * P z Capital Figure 1. Direct interdisciplinary exchange of information.
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