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THE 8th LATIN-AMERICAN CONGRESS ON GENERATION AND TRANSMISSION - CLAGTEE 2009 1

Exergy Accounting - The that Matters V. Fachina, PETROBRAS 1

Exergy means the maximum which can be Abstract-- The exergy concept is introduced by utilizing a extracted from a control . 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 . 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 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 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, 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 . 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 ; P, ; ν, which then transforms those ones into other works ΣWOUT and specific volume; T, ; 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: (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.

⎡ ⎤ E& = m ()()(h−h −T s−s + μ c −μ c )()+ g z −z (2) &⎢ 0 0 0 ∑ i i 0 0 0 ⎥ ⎣ 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 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 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 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 exergy have: a) regenerating systems for amine and glycol for the 300 Electrical exergy sweetening and dehydrating of the ; 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 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 able to withstand higher combustion and . 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. The 47% exergy processes. Exergy input: fuel exergy; Energy input: fuel energy efficiency represents the current state-of-the-art for such systems. It is worthwhile by now doing an analogy between the thermodynamical flows and the economical ones as to Fig. 2: IV. THE ECONOMICAL REALM on both the thermodynamical and the economical realms, energy and monetary flows are conserved, the latter ones due EXERGY ACCOUNTING to accounting rules. Generally stated, all flows going into the Exergy accounting means applying both the first and the control volume must equal those ones which either remain second to a selected control volume inside it or go out of it. in order to pinpoint those quantities of energy which are given Now doing an analogy between the economical realm and economical values because they do matter to the end user. the 2nd Law of Thermodynamics, one may think of the same Figure 4 exemplifies a typical project economical money quantity being less worthy due to either inflation or feasibility study and Fig. 5 exemplifies the exergy destruction taxes or market variables, and that depends on the surrounding of an asset over its lifecycle, from its installation up to its environment roughly about the same way as entropy values decommissioning. Equation 5 is the sum of both the depend on the environmental temperature. destructed and lost exergy and it stems from (3). For Therefore, there happens to be an analogy between combining both the economical and the exergy analysis, one Thermodynamics and Economy by comparing the physical can define the ratio between the NPV values and the value and monetary flows. from (5), thus yielding Fig. 6. Therefore, the issue is to minimize the value of (5), hence maximizing the Fig. 6 ratio III. DATA ANALYSIS and thus minimizing the environmental impact. Reference [3] In Fig. 2 one can carry out two calculations: depicts types of flow in several economical sectors. 1) By the traditional energy (not exergy) efficiency metric, the losses happen to be 12% from the heat and exhaust gases carried away to the environment, thus yielding 88% energy efficiency; 2) On the other hand, besides the 12% thermal losses, there happen to be 41% irreversible ones as well, which imply 47% exergy efficiency. By the energy method, those 41% irreversible losses are embedded into the output values, thus yielding that 88% energy efficiency. Considering three turbines operating on-line at THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 4

EXERGY METRICS Aiming at either benchmarking surveys or project managing for energy efficiency, one utilizes efficiency metrics

which can vary wildly as to each asset type. One way to enable comparisons among either production assets of the same kind or distinct ones is to utilize the exergy concept, through which one can determine their irreversibility in a

common language, in energy units, and also take into consideration the nearby environment into which they are inserted. To determine the exergy efficiency of a production

asset, one takes the first part of (4), thus deriving (6). It is Fig. 4. The NPV-Net Present Value over the lifecycle of a production asset. worth noting that the two laws of Thermodynamics are EPC stands for Engineering-Procurement-Construction; O&M stands for followed, the one for energy conservation and the other for the Operation and Maintenance; illustration only. irreversibility of real processes. Such an efficiency metric is also called the Second Law Energy Efficiency, ψ, that which accounts for entropy variations as well.

()E +W ∑ i (6) OUT ψ = ∑ ()E +W i IN

As the environmental issue has become a serious concern for the of both the businesses and the planet in the 21st century, a proper metric should be devised in order to

account for that. Usually one takes the ratio between the mean value of the equivalent mass of carbon dioxide emitted to the environment, the “carbon footprint”, and the mean value of Fig. 5. The irreversibility values over the lifecycle of a production asset; illustration only. the energy consumed by the production asset, such a rate having usually the dimension MTe(CO2)/TWh. One can

transform that ratio into a dimensionless one, αCO2, by multiplying the numerator by the formation exergy of the

carbon dioxide, about 20 kJ/mol as to reference [2], thus

creating a dimensionless metric, TJe(CO2)/TJ as to (7).

E CO2 α = D (7) CO2 E +W ∑ () IN

By making α as other exergy destructions beyond that one

due to the greenhouse gas emissions and β as thermal losses, one can reshape (4) as to (8).

Fig. 6. The ratio between the NPV and the wasted and lost exergy; illustration ψ + (α + α + β )= 1 (8) only. CO2

Δt

E = ∫[]∑()()E& − E& + ∑ W& −W& dt (5) The variables in (8) are not linearly independent on one 1−ψ IN OUT IN OUT 0 another: reducing the emission of equivalent carbon dioxide shall imply on reducing the exergy efficiency as well if either heat regenerators or combined cycles or less irreversible exergy conversion systems are not added. Figure 7 is a conceptual plot for showing the of a control volume towards less CO2, zero-CO2 exergy sources, from 2% to 0% for instance as to (7); note the sum of all THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 5 values equals the unity for having to follow (8). Such an The same concept can be applied to the CCC by replacing

“exergy disclosure” or an equivalent friendlier format may be the saved energy by the captured CO2 mass. added to the conventional accounting balance of an Equation (10) shows a simpler CSE calculation from organization in response to the much needed stringent making constant the cost, the saved energy and the interest environmental constraints for the planet. rate. For a zero interest ratio, CSE equals to the C/S ratio. T1 may represent a typical asset with relatively high exergy efficiency; T2 may be well the case of an oil-supply chain ⎛ C ⎞ asset with CCS-Carbon Capture and Storage technology; T3 CSE = a n / i ⎜ ⎟ (10) may represent a “green asset”, that with no CO emissions. T4 ⎝ S ⎠ 2 illustrates the evolution of an already green asset; T5 may 1− ()1+ i −n resemble an “artifical tree” for energy generation. Note that ∴an / i = even in a 100% “green” system, one shall never get rid of the i irreversibility issue. The T3 scenario is the one to use non-carbon energy chain i: interest rate supplies for which the value of (7) is zero. Nevertheless, a T3 an/i: present value factor at i and n control volume has also irreversibility, as formerly stated, as well as thermal losses and so it must be worked out in order to For instance, a 5-year energy efficiency project to spend minimize the alpha and beta terms from (8), thus maximizing $1million/yr on either a new build product or product upgrade the value of the exergy efficiency. An example of T3 scenario and to save 40GWh/yr would have about $0.10/kWh CSE for may be a hydrogen economy: hydrogen is to be produced in a 5% yearly interest rate. If one compares that value to a $0.20/kWh price, one concludes it is cheaper saving energy decentralized ways, close to users, by either hydro power or than buying additional one. That project would be paid back or solar power or geothermal power, thus making roughly within 8 months after its completion. the whole energy chain carbon-free as to reference [1]. Actually both CSE and CCC metrics should be used to Nevertheless, a mix of the three sceneries is to last for some rank green projects. decades, a complete phasing out from oil and phasing into hydrogen by mid 21st century. Also (7) can be utilized for valuating environmental impacts in terms of monetary values. For instance, if one considers 1% tax deduction over business revenue for each

1% reduction in CO2 emission, then $10million/yr shall result as a cost avoidance figure for a one billion/yr business. Symmetrically, a 1% fee over business revenue should hold for each 1% increase in CO2 emission. The coupling of (7) to economic figures has to be properly designed, implemented and audited. Therefore, energy can and must be saved by reducing both the irreversible losses and the reversible ones, thus increasing the value of (6).

Energy efficiency projects can be ranked by both the CSE- Cost of Saved Energy and the CCC-Cost of Carbon Capture Fig. 7. Exergy efficiencies, reversible and irreversible losses along time in a metrics as to (9). See reference [1] for further reading. control volume; conceptual plot

n − j ∑C j ()1+ i j j (9) CSE = n ∑ S j j

n: number of time periods j: time period index th ij: interest rate at the j time period th Cj: EPC costs at the j time period th Sj: saved energy at the j time period

THE 8th LATIN-AMERICAN CONGRESS ON ELECTRICITY GENERATION AND TRANSMISSION - CLAGTEE 2009 6

V. CONCLUSION This paper has shown an alternative metric for energy efficiency by utilizing the exergy concept which brings all the irreversibility up within a control volume. Using the energy concept, one gets 88% efficiency for a power module with heat regenerator. On the other hand, using the exergy concept, one gets 47% efficiency, which is more representative because that value does not hide the irreversibility of the processes within that control volume. One has derived a metric for environmental efficiency which relates the exergy lost by the carbon dioxide emission to the environment and the exergy in terms of works and enthalpy flows consumed by the control volume. That metric is dimensionless and the lesser such a value the better for the environment and that indicates as well how much it is withdrawn from all the exergy consumed by the control volume. Also one has shown it is possible and desirable to unite the CO2 emission metric with economic figures so to bridge a gap between the physical and the economical realms. By devising either a green tax or a green incentive, one can foster energy efficiency projects which in turn may be ranked by both the CSE and CCC metrics.

VI. REFERENCES Technical Reports: [1] Lovins, Amory B., 2004, “Energy Efficiency, Taxonomy Overview”, http://www.rmi.org

Dissertations: [2] WALL, G., 1986, “Exergy – A Useful Concept”, Mölndal, Sweden, http://exergy.se, Ph.D. dissertation, Physical Resource Theory Group, Chalmers University ofTechnology, Göteborg, Sweden

Standards: [3] ISO 13601, 1998, “Technical Energy Systems – Structure for Analysis – Energyware Supply and Demand Sectors”, Figure 3

Books: [4] I. Dincer, M. Rosen, Exergy-Energy, Environment and . Elsevier, 2007, p. 2.

VII. BIOGRAPHY

Vicente Fachina was born in Resende/RJ, Brazil, on Aug 15, 1962. He graduated in Mechanical Engineering at IME (Instituto Militar de Engenharia), pos-gratuated in Mechatronics Engineering at UERJ (Universidade Estadual do Rio de Janeiro) and got a master degree in Energy at UNITAU (Universidade de Taubaté). His professional experience encompasses 25 years as product development engineer and project manager in multinational companies in Brazil, USA, Canada, and currently at Petrobras in Brazil.