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Exergy Accounting - the Energy That Matters V THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 1 Exergy Accounting - The Energy that Matters V. Fachina, PETROBRAS 1 Exergy means the maximum work which can be Abstract-- The exergy concept is introduced by utilizing a extracted from a control volume. Also it is the maximum general framework on which are based the model equations. An energy quantity which can be made useful after discounting exergy analysis is performed on a case study: a control volume the irreversible losses. Finally, exergy means a physical, for a power module is created by comprising gas turbine, chemical contrast level between a control volume and its reduction gearbox, AC generator, exhaustion ducts and heat nearby surroundings. regenerator. The implementation of the equations is carried out Now considering the economical realm, Fig. 1 can be by collecting test data of the equipment data sheets from the respective vendors. By utilizing an exergy map, one proposes translated as follows: the reversible losses as either business both mitigating and contingent countermeasures for maximizing productivity losses or refundable taxes; the irreversible ones the exergy efficiency. An exergy accounting is introduced by as either nonrefundable taxes or inflation; the right arrows as showing how the exergy concept might eventually be brought up product and service values; the left ones as product and to the traditional money accounting. At last, one devises a unified service investments. approach for efficiency metrics in order to bridge the gaps A word of advice: a control volume means either a between the physical and the economical realms. physical or logical reality subset bounded by our observation. For instance, it may encompass either a production asset or an Index Terms—energy management, energy measurement, entire organization or an economical sector or the whole entropy planet. Depending on how one sets the observation boundaries, the reversible losses from a control volume can be I. INTRODUCTION useful for another neighbor control volume. As to the irreversible losses, they go out to the surrounding environment to which they can be either harmful or not depending on the nergy is a loophole, it is something which brings about E observer. movement in the space-time fabric of the universe, it is omnipresent, it manifests itself in infinite forms within a control volume through works, enthalpy flows, heat, and it is W ∑W never destroyed. A more technical definition follows reference IN OUT [4]: “Energy is a scalar quantity that cannot be observed CONTROL VOLUME directly but can be recorded and evaluated by indirect E E OUT measurements. The absolute value of the energy of a system is IN difficult to measure, whereas the energy change is relatively LOSSES easy to evaluate”. On the other hand, exergy means the quality of a determined energy quantity for being useful depending on the processes occurring either within a control volume or in its IRREVERSIBLE REVERSIBLE nearby surroundings. In actual processes exergy never remains the same because it is partially consumed by the inherent irreversibility of the control volume. When one carries out an Fig 1. Generalized control volume exergy balance, the result is never zero and thus one creates a quantity termed “exergy destruction” in order for the exergy quantities before and after the control volume to get even. For II. THE PHYSICAL REALM instance, regarding a heat flow, that one cannot be all useful due to the Second Law of Thermodynamics. When one does EXERGY an exergy balance, one finds out an exergy loss; nevertheless, there is no energy loss due to the First Law of Equation. (1) is a general one for exergy which comprises Thermodynamics. the gravity and the electromagnetic forces (thermodynamics, Firstly considering the physical realm, Fig. 1 draws on chemical, electric-magnetic), of which the thermodynamic and the conceptual framework of the reference [3]: enthalpy flows chemical ones are modeled as to reference [2]. The variables ΣEIN and works ΣWIN are inserted into a control volume, are: m, mass; μ, specific internal energy; P, pressure; ν, which then transforms those ones into other works ΣWOUT and specific volume; T, temperature; s, specific entropy; c, other enthalpy flows ΣEOUT and process losses. Those losses chemical concentration; g, gravity acceleration; z, position. are split into two parts, the reversible ones, which can still be harnessed, and the irreversible ones or exergy destruction. 1 Vicente Fachina is with Petrobras, Brazil [email protected] THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 2 E = E THERMO + E CHEM + E ELEMAG + E GRAVITY (1) CASE STUDY ∴ E THERMO = m[]()()()μ − μ + P ν −ν − T s − s Figure 2, which is drawn from Fig. 3, shows a control 0 0 0 0 0 volume for the Petrobras FPU – Float Production Unit P53 ⎡ ⎤ ∴ E CHEM = m ()μ c − μ c power modules. There are three inlets: fuel (gas or liquid), ⎢∑ i i 0 0 ⎥ atmospheric air and process water; and four outlets: works ⎣ i ⎦ (electric energy from the AC generators), process hot water, ∴ E GRAVITY = mg z − z ()0 exhaust gases and heat exchanged in the cooling systems as well as by natural air convection and radiation from the pieces EXERGY FLOW of equipment. Equation (2) stems from (1) for the exergy flows in thermodynamics, chemistry and gravity; the electric-magnetic exergy is not covered in this work. The new variable here is: h, specific enthalpy. ⎡ ⎤ (2) E& = m& ()()(h−h0 −T0 s−s0 + μici −μ0c0 )()+ g z −z0 ⎢ ∑ ⎥ ⎣ i ⎦ EXERGY FLOW BALANCE Equation (3) stems from Fig. 1 for the exergy balance in a general control volume. The following convention is used: incoming variables have positive sign and those ones going out of the control volume have negative one. The initial parenthesis refers to the exergy balance due to the enthalpy flows in the realm of Thermodynamics and Chemistry; the bracket refers to the thermal exergy flows associated with the thermal flows represented by Q and the exergy destruction or irreversibility, ED; the last part refers to the net work. Fig 2. Control volume for the Petrobras FPU P53 power modules; WHRU In an isolated control volume with no enthalpy flow or stands for Waste Heat Recovery Unit.. heat or work, the total exergy variation equals to minus the exergy destruction or irreversibility, that is, exergy always MODEL ASSUMPTIONS decreases (or entropy increases) in an isolated control volume. For determining the exergy distribution in the Petrobras That is another statement for the Second Law of FPU P53 power modules, one has assumed the following Thermodynamics, which applies to isolated control volumes simplifying hypothesis: only. Also the exergy variation is negative in a control volume in which ΣEIN equals to ΣEOUT and WIN is zero. By simplifying and rearranging (3) for a steady-state 1. Steady state operation; control volume in which ΣE is zero, one can bring up (4) in a 2. Exhaust gases as ideal ones; dimensionless format. 3. Enthalpy flows at chemical balance as to the environment. ⎡ ⎛ T ⎞ ⎤ 0 RESULTS E= ()EIN −EOUT −⎢ ⎜1− ⎟Qi +ED⎥− ()WOUT−WIN (3) ∑∑ ∑⎜ T ⎟ ∑ ⎣ i ⎝ i ⎠ ⎦ The heat values are determined by applying the energy conservation balance (The First Law of Thermodynamics) to ⎛ T ⎞ control volumes comprising each piece of equipment in Fig. 2. ⎜1 − 0 ⎟Q + E ∑ ()E + W i ∑ ⎜ ⎟ i D (4) Then (4) is utilized to calculate the exergy losses. OUT i ⎝ T i ⎠ + = 1 As to the exergy of the exhaust gases after the heat E + W E + W ∑ ()i ∑ ()i regenerator, (4) is utilized locally over a control volume IN IN enveloping it and by making all the works equal to zero. All such values are based on the data sheets from Rolls-Royce, http://www.rolls-royce.com, for aero-derivative gas turbine systems. The results are displayed in Fig. 3. One should notice the differences among the values of energy, exergy as well as their decreasing values with the increasing of the environment temperature. THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 3 steady-state: a) the heat carried away by the exhaust gases after the heat regenerator and by the natural air convection and radiation through the walls of both the exhaust piping and the heat regenerator itself amounts 4.5% out of the incoming Energy x Exergy Distribution for the FPU-P53 Generation Module exergy, which mean about 10MW; b) the heat carried away by (Considering 03 turbines on line) the equipment cooling systems as well as by natural air convection and radiation amounts 7.5% out of the incoming 400 exergy, which mean about 17MW. In order to reduce the 12% reversible losses only one may 350 Process water exergy Exhaust gas exergy have: a) regenerating systems for amine and glycol for the 300 Electrical exergy sweetening and dehydrating of the natural gas; b) fuel gas 250 Thermal exergy preheating for keeping a safe distance from the dew point of 200 Exergy destruction heavy fractions; c) adsorbing cooling system in the inlet MW 150 Exergy input combustion air for aiding on more mass flow entering the Energy input 100 combustion chamber; d) room warming through heat 50 exchange between hot water from the cooling systems and ambient air. 0 287 298 309 In order to reduce the 41% irreversible losses only one may Environment temperature [K] have either more efficient combustion chambers or better materials or better fuels able to withstand higher combustion temperatures and pressures. Fig. 3. Energy, exergy distributions for the Petrobras FPU P53 power However, all these depend on both technical, economical modules. Process water exergy: hot water for heating oil; Exhaust gas exergy: studies for new concept designs and on technological gas from combustion processes; Electrical exergy: from the AC generators; advances in the related pieces of equipment as well as on Thermal exergy: heat removed by the cooling systems and by natural convection; Exergy destruction: exergy consumed by the irreversible better quality levels in construction and fuels.
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