Exergy efficiency graphs for thermal power plants

Energy xxx (2015) 1e10

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Exergy efficiency graphs for thermal power plants J. Taillon a, *, R.E. Blanchard b a b

ANDRITZ, Helsinki, Finland Loughborough University, Loughborough, UK

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 October 2014 Received in revised form 23 January 2015 Accepted 19 March 2015 Available online xxx

Despite the strong support for exergy in thermodynamics, the industry still relies on energy based power plant efficiencies. The paper exposes errors with energy based efficiencies and improves the graphical representation of plants efficiencies. Among others, energy efficiencies cannot recognised that Combined Heat and Power (CHP) plant may be less efficient than condensing plants or that fossil fuel based plants should always be more efficient than any biomass plants because irreversibilities from biomass spontaneous thermo-chemical reactions are much higher than with coal or natural gas. Profitability equations fail to distinguish the true technical efficiency so exergy must be used, if only to enhance power plants understanding. Two novel graphs are introduced. Graph #1 combines all in a single graph; total, electrical and thermal exergy efficiencies. Graph #2 splits thermal exergy efficiency into two components related to; plant thermal losses and useful heat output quality. Data from 24 existing and design plants is used to support the graphs. Graph #1 shows different rankings of efficiencies than what is typically understood by the industry. Graph #2 shows that achieving further higher thermal energy efficiency barely increases the total exergy efficiency. If possible, it is better to increase the useful heat output quality. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Exergy Energy Efficiency Graphs Cogeneration Biomass

1. Introduction For thermal power plant efficiency analysis, the typical approach by the industry (i.e. companies, institutions and governments) relies almost exclusively on energy conservation principles as stated by the 1st law of thermodynamics. This approach is flawed mainly for two reasons; (a) heat and fuel input energy terms cannot be added to power and (b) irreversibilities are ignored. The correct approach must involve an exergy analysis based on the 1st and 2nd law of thermodynamics. Even with the explicit support for exergy in the thermodynamic literature [1e4], it is “not generally and widely accepted by the industry” [5]. Specifically to evaluate plant efficiencies, the authors propose two areas where exergy literature could be improved to popularize its usage. First, any new arguments which can demonstrate the weakness of the current approach should be published. While it is certainly advantageous to highlights benefits of exergy analysis e.g. “normally meaningful and useful” [5], “appears to be a more powerful tool than energy analysis for power cycles” [3] with case studies to

* Corresponding author. E-mail addresses: [email protected] (J. Taillon), [email protected] (R.E. Blanchard).

demonstrate its applicability. It is also important to highlights weaknesses associated with the industrial current approach, something seldom seen in the literature. This paper will present weaknesses and potential sources of errors using data from existing and conceptual power plants. The second area wants to improve the graphical representation of exergy efficiencies to facilitate its adoption within the industry. Graphs as opposed to listings are useful. They “reveal data” [6]. The exergy literature often use exergy-only Grassman diagrams [7] or combined with energy [3] or alike [8] and histograms [9] to illustrate exergy destructions of internal sub-processes. As this paper is concerned with multiple overall plant performances, these tools are not suitable for such comparisons. The authors introduce two graphs novel to the industry and exergy practitioners alike which will facilitates exergy efficiencies comparisons between various plants. Graph #1 plots in a single graph electrical, thermal and total exergy efficiencies. Graph #2 splits the thermal exergy efficiency in two components related to; plant thermal losses and useful heat output quality based on the 1st and 2nd law respectively. Data from power plants will be used to support these graphs. As a reminder, exergy represents the maximum useful work a system can achieve within a reference environment (25 C, 1 atm). The concept utilizes the 1st and 2nd laws and is particularly suitable for the study of thermo-chemical systems [10]. The 2nd law uses the

http://dx.doi.org/10.1016/j.energy.2015.03.055 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Taillon J, Blanchard RE, Exergy efficiency graphs for thermal power plants, Energy (2015), http://dx.doi.org/ 10.1016/j.energy.2015.03.055

2

J. Taillon, R.E. Blanchard / Energy xxx (2015) 1e10

entropy concept to quantify energy that is not available to a system or “taxed by nature prior to use” [11], referred as irreversibilities. 2. Methodology The objectives of this paper are to introduce two novel exergy efficiency graphs and expose weaknesses of the typical industrial approach. Section 3 describes a potential barrier against exergy but yet provides a fundamental reason why exergy should be used. Section 4 describes weaknesses of energy efficiencies and is mainly written for the industry to understand the shortcomings of their approach using data from 18 power plants. Section 5 focuses on a power plant model and derives balance equations to develop the graphs. Using these graphs, section 6 plots and interprets the efficiencies of 24 power plants. The plant's technologies are listed in Table 2 and the necessary input data to reproduce these graphs are listed in the appendix with their numerical results. 3. Barrier against exergy A potential barrier to exergy could be its seemingly futility when energy parameters (heat, power and fuel input) are multiplied by their costs rates. As shown in the operating profitability equations (1) and (2), the costs rates neutralize these energy parameters into pure monetary values.

V V þ Q_ p AðMWhÞ*Phe pop ¼ WAðMWhÞ*Pel MWh MWh V E_ in AðMWhÞ* Pf MWh

(2)

The above profitability equations exist in various styles and form the basis of many industrial feasibility studies. As an example, for district heating evaluation, the joint costs function [15] given by (3) takes its origin from (2).

Fuel Costs ðHeat ValueÞ þ aðElectricity ValueÞ ¼ 1þa htot

4. Weakness of current approach The energy based efficiency equation typically used in the industry is given by (4) and equally applies to power only plants ðQ_ p ¼ 0Þ and cogeneration plants;

htot ¼

Useful energy W þ Qp W þ Q_ p ¼ Fuel input energy E_ in

(4)

As explained by Kanoglu et al. [3], “work and heat have the same units but are fundamentally difficult to add because they are different, with work being more valuable than heat”. Numerous publications [16e20] used this ratio wrongly as a mean to compare power plant efficiencies. In fact, this equation should not be associated with the word “efficiency” because it does not represent the true ratio of useful outputs to input energy in similar quality terms. An alternate term could be “utilization factor” as proposed by Ref. [11]. References [16e20] are from well-known institutions (e.g. International Energy Agency, European Commission, COGEN), a consultant and a scientific journal which indicate that this situation affects the entire industry. To propose any changes to such a widespread practice, might very well be a daunting task. 4.1. Heat and fuel energy converted to work equivalent components

(1) h i pop ¼ WA Pel ðVÞ þ Q_ p A Phe ðVÞ E_ in APf ðVÞ

paper will demonstrate, can only be done using the exergy concept. Moreover, for public institutions to identify efficient technologies, costs must be excluded. Therefore this ability to calculate the true technical efficiency is a benefit and an important property of exergy.

(3)

Often the economics of a project determines its faith. For example, if a project is selected among other technologies, is it because its costs were advantageous or its technology was better. Using exergy, inputs and outputs are all evaluated on an equivalent basis, namely work. Therefore, their exergy amount provides a reference point to whatever monetary value they have in real life. For example, compared to steam, the specific exergy content of hot water is less but in monetary terms, hot water revenues may be worth more than steam. In this case, the value of hot water is more advantageous than the technology to produce it. Since costs are volatiles over time and vary among countries with different energy policies, one might want to (or should) evaluate the technology on its own, if only to enhance our understanding of the project. To do so, technical efficiency must be disconnected from costs and, as this

To correctly account for plants efficiencies, a) useful output heat and b) fuel energy input must be converted into work equivalent components and c) irreversibilities must be accounted for. 4.1.1. Useful output heat As the fuel input is, in itself, a heat component, it is converted into work by going through a real heat engine (e.g. turbines, engines) as shown in Fig 1. The useful output products are; work and some useful heat. In all fairness, this useful heat must also be treated like work and go through an engine; namely a perfect heat engine. Such engine satisfies four conditions; frictionless, adiabatic, cyclic and heat source and sink are reservoirs. In doing so, the only irreversibilities arise from the temperature difference between the reservoirs. This concept takes its origin from the well-known Carnot engine. 4.1.2. Fuel energy input The fuel energy input is converted into a work equivalent component by its chemical exergy value. Such values are either found in the exergy literature or calculated through formulae. A formula often used in exergy papers is the one developed by Szargut and Styrylska in 1964 [21]. This paper used a different equation (5) introduced recently for biomass fuels [22] and was chosen because it seemed easy to use and its authors claim a good correlation with the traditional Szargut model. It is not the purpose of this paper to put any other judgement on this peer-reviewed equation. For non-biomass fuels, the exergy content are found in the literature.

Table 1 Needed input data. Fuel input data Power Useful heat output (district heating) Useful heat output (steam) Exhaust flue gas

Ultimate analysis (CHONS þ ash %-w), moisture (%-w), flow rate (kg/s), Net (kJ/s) Cold and hot water temperature (K), flow rate (kg/s) Flow rate (kg/s), temperature (K), pressure (bar) Temperature (K)



3

Table 2 Technologies of the 24 power plants. Abbreviation

Description

BGGE

Biomass Gasification based on Gas Engines: These plants may include a dryer (fuel is wood chips, C) or not (fuel is pellets, P). The product gas from the bubbling fluidized bed (BFB) gasifier feeds gas engines with recovered heat used for district heating. Combustion steam cycle plant: These plants use the conventional Rankine cycle built with the latest technologies in boilers and steam turbines. Integrated Gasification Combined Cycle: These plants may include a dryer (if fuel is wood chips). The biomass is fed to a pressurized BFB gasifier. The product gas from the gasifier is fed to a combined cycle equipped with a gas turbine, heat recovery steam generator and steam turbine. The plant works in condensed mode (CO) with no useful heat or in back pressure mode (BP) where the useful heat is either hot water district heating and/or low pressure steam. Internal combustion engine: Description of this plant is found in Ref. [12]. Super-critical pressure boiler with a steam turbine is found in Ref. [13]. Combined cycle plant based on gas and steam turbines is found in Refs. [13,14].

COMB IGCC

ICE SC ST CC

0

Fig. 1. Conversion of useful heat ðQ_ p Þ into an equivalent work component ðQ_ p Þ.

ech db ¼ 1812:5 þ 295:606C þ 587:354H þ 17:506O þ 17:735N þ 95:615S 31:8Ash (5) 0 _ ch E_ in ¼ m_ f ech AF ¼ mf edb ð1 wÞ

(6)

With respect to fuel input values, a weakness of the current approach concerns the LHV (lower heating values) and HHV (higher heating values). Using LHV assumes that all water formed by combustion is vapour and the latent heat of vaporization in the fuel is not recovered when the water condenses back. Since exergy uses 25 C as reference where water is a liquid, the latent heat is considered as available energy. This explains partly why biomass specific chemical exergy ðech Þ is higher than its LHVdb. If the latent db heat is not recovered, the exergic value and HHV will be higher than the true energy content of the fuel. Recovered or not, the exergy destruction and HHV will correctly account for the latent heat as heat loss to the environment (typical) or useful heat (e.g. by using flue gas condensers) but unlike the usage of heating values, only exergy converts this heat, loss and useful, into work equivalent components. 4.1.3. Include irreversibilities Once fuel energy input and heat outputs are correctly evaluated, a final portion remains to make the available energy balance. This portion is known as irreversibilities and is completely ignored by the sole use of energy conservation principles. As irreversibilities and heat losses to the environment accumulate, available energy or exergy is destroyed. Spontaneous thermo-chemical reactions [10,23], mechanical friction and thermal transfer between finite

temperatures are among others, important sources of irreversibilities in power plants. Irreversibilities from spontaneous thermo-chemical reactions are significant. Biomass oxidation reactions destroy 50% of exergy input in either gasification [24] or combustion [24,25]. Natural gas and coal are reported to destroy 33% [13,26] and 25% [13] respectively. Mechanical friction is unavoidable and takes the form of heat losses to the environment. Irreversibilities from thermal transfer through finite temperature occur because heat sources and sinks are not reservoirs and when exposed to colder environment, hot bodies cools down naturally. To keep constant thermal transfer, extra energy must be added to compensate for the unavoidable cooling. As a result, the above irreversibilities reduce available energy and importantly, are quantified with the use of exergy. 4.2. Weaknesses related to total and electrical efficiencies 4.2.1. Total efficiencies Fig. 2 shows potential sources of errors using energy based efficiencies as expressed by (4) from a sample of 18 plants. Three examples are highlighted; (A) In terms of total energy efficiency (horizontal axis), the most efficient plant is COMB 1 at 88.9% but in exergy terms, this plant drops to 18th position with an efficiency of 30.2%, as shown by the dashed lines. This is explained by the plant relative large heat output (45 MJ/s) and as it is not converted, it falsely overestimates its energy efficiency. (B) On an exergy basis, the most efficient plant is the ICE NG power plant based on natural gas (39.7%). This makes sense because chemical exergy destructions are significantly lower with fossil fuels than biomass. Yet, this plant ranked only 9th on an energy based efficiency (80.1%). (C) In exergy terms condensing power plants (IGCC 3, 5CO, 6CO and 7CO) can be more efficient than


4


Fig. 2. Electrical efficiency versus total efficiency based on energy and exergy (exclude cases 16, 19, 20, 22, 23 and 24 from appendix).

Table 3 Electrical efficiencies comparison between IGCC 3 and IGCC 7 CO.

! Jel ¼

W 0 E_in

! ¼

W E_in

E_in 0 E_ in

! ¼ ðhel Þ

E_in 0 E_ in

!

IGCC 3 wood chips, 45%-w

IGCC 7 CO bagasse, 10%-w

¼(0.397)(0.794)

¼(0.385)(0.838)

¼0.315

¼0.323

! ¼ ðhel Þ

LHVAR ech AR

Jel¼

cogeneration power plants (COMB 1) regardless of plant capacity (fuel energy input) as COMB 1 (76 MJ/s) is a larger plant than IGCC 3 (45 MJ/s) or 7CO (48 MJ/s). A fact undetected by the current practice because of the large gap in energy and exergy efficiencies between CHP and condensing plants.

4.2.2. Electrical efficiencies For power only plants, a typical error is to assume that with electrical energy efficiency around 40% (38.5%40.9%) the rest of energy is lost as heat, as reported by the IEA (page 18) [27]. As explained earlier, this is wrong because most of the unavailable energy arises from irreversibilities and not heat losses to the environment. For CHP plants, sometimes the industry omit the heat component and use the electrical energy efficiency to gauge cogeneration power plants efficiencies. This approach is wrong as useful heat is an energy which cannot be ignored. For CHP plants, total exergy efficiencies are significantly lower than energy based efficiency values. That is not to say that no effort should be spent to capture and make use of this heat. On the contrary cogeneration improves significantly the efficiency because if this recovered heat was in fact produced on its own, it would entail additional energy conversion losses from spontaneous chemical reactions, thermal transfer and heat losses. Electrical energy efficiencies (Fig 2, vertical axis) are higher than on an exergy basis mainly because those were based on LHV. Also rankings are similar aside from the following two condensing plants; IGCC 7CO and IGCC 3. While IGCC 3 electrical energy efficiency (hel ¼ 39.7%) is superior to IGCC 7CO (hel ¼ 38.5%), they have a reverse ranking on an exergy basis as shown in Table 3.

The reason for this is due to the high moisture of IGCC 3 and its 0 effect on the fuel input energy to exergy ratio ðE_ in =E_ in Þ. The plant IGCC 3 feeds on 45% moisture wood chips as opposed to 10% bagasse for IGCC 7CO. Equation (7) shows that as moisture content (w) increases, LHVAR decreases more rapidly than ech AR thus reducing the input energy to exergy ratio as shown in table 3 leading to a reversed ranking.

E_ in 0 E_ in

!

LHVAR LHVdb ð1 wÞ w hfg ¼ ch ¼ eAR ech ð1 wÞ

(7)

db

In short, electrical, thermal and total efficiencies must be evaluated on an exergy basis and applied to all power plants, condensing and cogeneration alike. From these examples, one can generalized and state that with different technologies (e.g. combustion, gasification, torrefaction, pyrolysis, co-firing, combined cycles, internal engines, fuel cells) and chemically different fuels with different moistures (e.g. cellulosic biomass, bio-oil, waste, natural gas, oil, coal), different efficiency values emerge and affect the reliability of the conventional approach. 5. Exergy based power plant model The idea of producing graph #1 was inspired by a paper from Rosen [28] where after some algebra a thermal exergy component 0 Þ was expressed in terms of the electrical exergy efficiency ðW=Ein but then Rosen deviated to other issues. The present authors realized that this characteristic could be used to produce thermal efficiency parametric lines linked to the electrical and total efficiencies, all in a single graph.



Similarly, for graph #2, the inspiration came from Moran and Shapiro [10] in their discussion about exergy efficiency and matching end use to source where they defined an “exergetic efficiency” (ε) composed of two components and given by;

1 T0 Tp ε¼ h 1 T0 =Ts

5

0 0 0 Q_ s ¼ W þ Q_ p þ Q_ L

box 2 exergy balance

(18)

Q_ s ¼ W þ Q_ p þ Q_ L

box 2 energy balance

(19)

(8)

However, their model applies only to a closed system receiving heat only. Using a similar analogy but for a power plant producing work with or without useful heat the following closed system steady state power plant exergy model is drawn in Fig. 3. The plant is supplied by fuel input ðE_ in Þ and useful outputs are _ and heat ðQ_ p Þ. The plant is divided by an imaginary net power ðWÞ line where supplied heat ðQ_ s Þ is transferred from box 1 to box 2. Each box loses heat to the environmentðQ_ L1 ; Q_ L2 Þ. Exergy is destroyed in the sub-processes of box 1 and 2 ðE_ d1 ; E_ d2 Þ.

5.2. Graph #1: exergy efficiency equations and parametric lines

5.1. Energy and exergy balance equations

For graph #1, the thermal exergy efficiency parametric lines are created using the following equation;

This paper defines the total exergy efficiency by;

Jtot ¼ ¼

0 Useful exergy outputs W þ Q_ p Fuel input exergy 0 _ Q

W p 0 þ 0 _ _ Ein Ein

Energy and exergy balance equations for box 1 and 2 are;

Jtot ¼ Jel þ

0 0 0 E_ in ¼ Q_ s þ Q_ L1 þ E_ d1


(9)

E_ in ¼ Q_ s þ Q_ L1


(10)

0 0 0 Q_ s ¼ W þ Q_ p þ Q_ L2 þ E_ d2


(11)

Q_ s ¼ W þ Q_ p þ Q_ L2


(12)

From exergy theory [10], the total exergy destruction ðE_ d Þ is a 0 0 combination of heat losses ðQ_ L Þ and irreversibilities ðE_ d Þ given by;

0 0 0 0 E_ d ¼ E_ in W þ Q_ p ¼ Q_ L þ E_ d

E_ d2 ¼ 0

/

0 E_ d1 ¼ E_ d

(14)

As for heat losses to the environment, the vast portion comes out as flue gas through the stack. As such, it would be fair to express total heat losses as such;

Q_ L1 ¼ 0

/

Q_ L2 ¼ Q_ L

(15)

Combining the above equations gives; 0 Q_ s

0 0 ¼ E_ in E_ d

Q_ s ¼ E_ in


(16)


(17)

(20)

Jth Jel Jel

(21)

where Jtot and Jel represents the x and y axis respectively. The parametric lines are formed by setting a specific Jth constant for corresponding values for Jtot and Jel. (e.g. Jtot 20%e52%, Jel 10%e 50% and Jth 0%e15%). 5.3. Graph #2: exergy efficiency equations and parametric lines The objective for graph #2 is to split the thermal exergy efficiency (Jth) in two components. Using equations (13), (16) and (17), a new thermal exergy efficiency equation is given by;

(13)

Assuming the process flows from left to right then all subprocesses can be accounted for by moving the imaginary line to the far right. With this assumption, all exergy destructions are accounted for by box 1 and expressed by;

¼ Jel þ Jth

Jth ¼

0 Q_ p 0 E_ in

¼

0! Q_ p 0 Q_ s

0

0! Q_ s 0 E_ in

1 TT0p Qp ¼ 1 TT0s Qs

0 0 E_ in E_ d 0 E_

1 0 0 1 1 TT0p E_ d Q_ L C B @ A Qp C ¼B 0 A 1 @ Ein E_ in 1 TT0s

!

in

(22)

For the far right portion of equation (22), the 1st term represents the quality of the product heat. As exergy theory dictates, a smaller gap between source and product temperatures improves quality and efficiency. The 2nd term represents the portion of available energy deducted by only exergy destruction caused by irreversibilities, excluding plant's heat losses to the environment. The product of the 1st and 2nd terms is defined as an exergetic factor ðt0ex Þ based on the 2nd law only. The 3rd term represents the conventional thermal energy efficiency (Qp/Ein) used by the industry and defined by the 1st law. Thus (22) can be defined as two components;

Jth ¼ t0ex ðhth Þ

(23)

The parametric lines are built from equation (23) and formed by setting Jth constant for a whole set of values for hth (x-axis) and t0ex (y-axis). 5.4. Calculation of the variables

Fig. 3. Closed system steady state power plant exergy model.

This section calculates the efficiency equations variables 0 0 0 0 ðE_ in ; Q_ L ; Q_ p ; E_ d ; Ts ; Tp Þ in terms of the input data from Table 1.E_ in


6


can be calculated from equations (5) and (6) and E_ d from equation (13). Combining equations (17) and (19) gives;

Q_ L ¼ E_ in W Q_ p

(24)

Assuming that the average heat loss boundary temperature (TL) is closest to the exhaust flue gas temperature, the following heat loss exergy equation becomes; 0 Q_ L ¼

1

T0 _ T Q L ¼ 1 0 Ein W Q_ p TL TL

(25)

Ts >1 TL

(33)

Alternatively, in terms of input data, these two equations can be derived with the following corresponding equations;

TL

Tp

W þ 1 > Tp QL ! W þ 1 > TL Qp

(34)

(35)

Similarly, the equation for the supplied heat exergy equation is given by; 0 Q_ s ¼

1

T0 T Qs ¼ 1 0 W þ Q_ p þ Q_ L Ts Ts

(26)

Combining equation (18) with (26), the average heat supplied temperature gives;

1 W þ Q_ p þ Q_ L A Ts ¼ T0 @ 0 0 Q_ p Q_ p þ Q_ L Q_ L 0

(27)

Useful heat output exergy values for steam and hot water district heating are given by;

0 Q_ p

st

0

Q_ p

¼ m_ st ðhðTst Þ hðT0 ÞÞ T0 ðsðTst ; pst Þ sðT0 ; p0 ÞÞ ¼ m_ st Dhp T0 Dsp ST

DH

(28)

¼ m_ DH ðhðTh ; pÞ hðTc ; pÞÞ T0 ðsðTh ; pÞ sðTc ; pÞÞ ¼ m_ DH Dhp T0 Dsp DH (29)

The product temperature (Tp) is derived from (30) and after simplification gives (31) where the subscript “x” represents steam or district heating (DH) given by (28) and (29) respectively;

0 T Q_ p ¼ m_ p Dhp T0 Dsp ¼ m_ p 1 0 Qp Tp

(30)

Dhp x Tp ¼ Dsp x

(31)

5.5. Model validation To develop graph #2 the conventional power plant model of a simple rectangle with its corresponding inputs ðE_ in Þ and outputs _ Q_ p ; Q_ L Þ is not adequate because the model does not explicitly ðW; account for the high temperature heat source ðQ_ s Þ. This is corrected with the insertion of an imaginary vertical line in the model. This simplistic model gives a lower source temperature (Ts) than the flue gas temperature (TP). From the 2nd law of thermodynamics, if work and/or heat are extracted from a system then the supplied temperature must be higher than its exit temperatures as expressed by the following inequalities (32) and (33). These inequalities were numerically confirmed for all plants and values of Ts, Tp and TL are shown in the appendix.

Ts >1 Tp

(32)

6. Exergy efficiency graphs To further emphasize the benefit of graphical representation with numerous data points, readers can refer to the appendix and try to discern the various power plants efficiency rankings. It is likely to be a challenging task. 6.1. Graph #1; electrical, thermal and total exergy efficiencies Graph #1 shown in Fig. 4 is developed from equations (20) and (21). Condensing power plants are shown on the 0% thermal exergy efficiency line and for the cogeneration plants, their thermal exergy efficiency range between 2% and 15%. For biomass power plants, IGCC plants exhibit the largest electrical efficiencies because they are based on a combined cycle. The graph shows that most biomass IGCC plants running in condensed mode are more efficient than single cycle cogeneration plants (BGGE, COMB). With IGCC 5 and 6, the shift from condensed (CO) to BP (back pressure) increases both thermal and total exergy efficiencies but reduces electrical exergy efficiency (A). The BP (back pressure) cases obtain the highest thermal exergy efficiencies because their heat output is low pressure steam (higher heat quality) as opposed to district heating hot water (lower heat quality). The graph shows also that all fossil fuels (natural gas, oil and coal) display higher efficiencies mainly because they experience much less exergy destructions from their spontaneous thermo-chemical reactions as explained in section 4.1.3. 6.2. Graph #2: split of the thermal exergy efficiency The 2nd graph makes use of equations (22) and (23) and splits the thermal exergy efficiency value into two fundamental components; an exergetic thermal factor ðt0ex Þ and a thermal energy efficiency (hth). Fig. 5 plots these two terms and the parametric curves represent the same thermal exergy efficiency (Jth) of Fig. 4. The heat output for all plants is hot water district heating except for three plants; IGCC 2, IGCC 5BP and IGCC 6BP which deliver low pressure steam. Usually, steam displays a high exergetic factor because it has a lower gap between its product and source temperature and is referred as high quality heat. (B) Because the district heating product temperature of IGCC 7bBP (371K) is higher than IGCC 7aBP (347K), its exergetic factor (vertical axis) is higher. This increase in temperature implies a thermal exergy efficiency improvement from 5.7% to 7.9% as indicated by the thermal parametric lines in Fig 5. (C) IGCC 1 shows low thermal energy efficiency because the plant could not sell all of its useful heat to the DH network. (D) BGGE 1P is more efficient than BGGE 1C because it uses pellets which does not require fuel drying. Energy to remove water from the pellets is excluded from the plant balance. This increases the energy



7

Fig. 4. Electrical, thermal (parametric lines) and total exergy efficiencies.

Fig. 5. Exergetic factor versus thermal energy and exergy (parametric lines) efficiencies.

efficiency (hth) by 8.1%. The thermal exergetic factor ðt0ex Þ also increases by 1.2% because irreversibilities (thermal transfer between finite temperatures) from drying fuel are not introduced. From the parametric curves, the thermal exergy efficiency (Jth) increases by 1.5% as can be seen in both graphs. From graph #1, the switch from chips to pellets (from BGGE 1C to BGGE 1P) allow the plant to increase its electrical and total exergy efficiency by 2.1% and 3.8% respectively. The 2nd graph also shows that at high energy efficiency levels, reducing heat losses further barely increases the thermal exergy efficiency and by the same token, the total exergy efficiency of the plant. If at all possible, increasing useful output heat quality will be more beneficial. These few examples (A), (B), (C) and (D) serve only as examples on how these graphs can be used and the numerical values were taken from the appendix. 7. Conclusions This paper showed the weaknesses of the traditional approach for power plant efficiency analysis which relies solely on the principle of conservation of energy.

Three examples were highlighted; a) a combustion plant, which ranked 1st on an energy efficiency basis due to its high unconverted thermal energy component, slipped to 18th position on an exergy basis b) in exergy terms, the most efficient power plant is fuelled by natural gas mainly because fossil fuels have much lower chemical exergy destruction but yet, ranked 9th on an energy efficiency basis c) power plants running in condensing mode could be more efficient than cogeneration plants contrary to conventional belief. With the conventional approach, these weaknesses cannot be detected and may become more prominent as different technologies (e.g. combustion, gasification, torrefaction, pyrolysis, co-firing, combined cycles, internal engines, fuel cells) and chemically different fuels with different moistures (e.g. cellulosic biomass, biooil, waste, natural gas, oil, coal) are introduced. A different ranking of efficiencies emerges which affects the reliability of the conventional approach and ultimately, could influence public support policies. Exergy analysis may seem obsolete when plant performance is based on a profitability basis as all terms are on a pure monetary basis. But with volatile costs and fluctuating energy policies among countries there is a need to evaluate power plants efficiencies


8


can be qualified as true and complete because they are based on exergy and combine these three efficiencies and can easily be used by the industry.

purely on a technical basis, independent of costs, which leads to exergy. This ability to calculate the true technical efficiency is a benefit and an important property of exergy. This paper introduced two graphs, novel to the industry and exergy practitioners alike. Graph #1 (Fig.4) combines electrical, thermal (parametric lines) and total exergy efficiencies, all in a single graph. Graph #2 (Fig 5) splits thermal exergy efficiency into a thermal exergetic factor and the thermal energy efficiency. The 1st term relates to the quality of heat as governed by the 2nd law while the 2nd term relates to the 1st law. The product of these two terms is the thermal exergy efficiency similarly displayed as parametric lines in both graphs. Graphical representation often brings a richer perspective and facilitates comprehension as opposed to listings of data. The graphs

Cases Technology Plant for design and operational plants Technology Useful heat Fuel type Parameters Symb Ultimate analysis C H O N S Ash Moisture w : Fuel input (energy) E: in Fuel input (exergy) Ein Fuel input rate m_ f Power output (net) W Heat output (energy) Q_ Heat output (exergy) Q_ 0 District heating Hot water Cold water Flow rate Steam Pressure Temperature Flow rate Efficiencies Energy Total Electrical Thermal Exergy Total Electrical Thermal Thermal exergetic Supplied temperature Product temperature Exit loss temperature

Acknowledgement The authors would like to thank Mr. Paterson McKeough and Mr Kari Salo for their support. The authors did not receive any funding for this paper.

Appendix

1 IGCC 1 Design IGCC DH Wood chips

2 IGCC 2 Design IGCC Steam Wood chips

3 IGCC 3 Design IGCC n/a Wood chips

4 IGCC 5 CO Design IGCC n/a Bagasse pellets


6 IGCC 5 BP Design IGCC Steam Bagasse pellets

7 IGCC 6 BP Design IGCC Steam Bagasse pellets

%-w %-w %-w %-w %-w %-w %-w kJ/s kJ/s kg/s kW kJ/s kJ/s

49.50 5.60 42.11 0.20 0.08 2.50 45 43,546 54,859 4.89 15,628 7828 1529

49.50 5.60 42.11 0.20 0.08 2.50 50 102,061 132,198 12.96 29,900 47,793 10,767

49.50 5.60 42.11 0.20 0.08 2.50 45 45,300 57,068 5.09 17,969 0 0

48.15 5.67 41.45 0.36 0.02 4.35 10 158,900 189,705 10.55 65,000 0 0

48.15 5.67 41.45 0.36 0.02 4.35 10 167,400 199,853 11.12 67,500 0 0

48.15 5.67 41.45 0.36 0.02 4.35 10 158,900 189,705 10.55 51,600 85,204 22,299

48.15 5.67 41.45 0.36 0.02 4.35 10 167,400 199,853 11.12 53,200 90,701 23,738

TH Tc m_ dh

110 85 74.3

pst Tst m_ st

bar(a) C kg/s

5 152 31

5 152 33

htot hel hth

% % %

53.9% 35.9% 18.0%

76.1% 29.3% 46.8%

39.7% 39.7% 0.0%

40.9% 40.9% 0.0%

40.3% 40.3% 0.0%

86.1% 32.5% 53.6%

86.0% 31.8% 54.2%

Jtot Jel Jth tex

% % % % K K K

31.3% 28.5% 2.8% 15.5% 609 371 399

30.8% 22.6% 8.1% 17.4% 551 385 399

31.5% 31.5% 0.0%

34.3% 34.3% 0.0%

33.8% 33.8% 0.0%

662 0 399

574 0 339

568 0 339

39.0% 27.2% 11.8% 22.8% 575 410 339

38.5% 26.6% 11.9% 22.8% 570 410 339

Ts Tp TL

[29]

Units

C C kg/s

Cases Technology Plant for design and operational plants [29] Technology Useful heat Fuel type Parameters Ultimate analysis C %-w H %-w O %-w N %-w S %-w Ash %-w

2 121.00 18.36


9 IGCC 7a BP Design IGCC DH Bagasse pellets

10 IGCC 7b BP Design IGCC DH Bagasse pellets

11 BGGE 1 P Design BGGE DH Wood pellets

12 BGGE 2 P Design BGGE DH Wood pellets

13 BGGE 1 C Design BGGE DH Wood chips

14 BGGE 2 C Design BGGE DH Wood chips

15 BGGE 3 P Operational BGGE DH Wood pellets

48.15 5.67 41.45 0.36 0.02 4.35

48.15 5.67 41.45 0.36 0.02 4.35

48.15 5.67 41.45 0.36 0.02 4.35

50.20 5.80 42.72 0.10 0.03 1.12

50.20 5.80 42.72 0.10 0.03 1.12

50.20 5.80 42.72 0.10 0.03 1.12

50.20 5.80 42.72 0.10 0.03 1.12

50.20 5.80 42.72 0.10 0.03 1.12



9

(continued ) Moisture Fuel input (energy) Fuel input (exergy) Fuel input rate Power output (net) Heat output (energy) Heat output (exergy) District heating Hot water Cold water Flow rate Steam Pressure Temperature Flow rate Efficiencies Energy Total Electrical Thermal Exergy Total Electrical Thermal Thermal exergetic Supplied temperature Product temperature Exit loss temperature

w : E: in Ein m_ f W Q_ Q_ 0

%-w kJ/s kJ/s kg/s kW kJ/s kJ/s

TH Tc m_ dh

pst Tst m_ st

bar(a) C kg/s

htot hel hth

% % %

Jtot Jel Jth tex

% % % % K K K

Ts Tp TL

10 48,300 57,664 3.21 18,600 0 0

10 48,300 57,664 3.21 15,600 23350 3295

10 48,300 57,664 3.21 15,600 23350 4561

10 20,790 23,056 1.23 5313 11,965 1614

10 19,848 22,011 1.17 5379 11,255 1516

45 19,486 23,824 2.09 4974 9637 1693

45 18,267 22,334 1.95 5057 9029 1586

10 19,489 21,613 1.15 5375 11,268 1519

83 65 310.0

110 85 221.7

94 50 64.8

94 50 60.9

94 50 68.0

94 50 63.7

94 50 61.0

38.5% 38.5% 0.0%

80.6% 32.3% 48.3%

80.6% 32.3% 48.3%

83.1% 25.6% 57.6%

83.8% 27.1% 56.7%

75.0% 25.5% 49.5%

77.1% 27.7% 49.4%

85.4% 27.6% 57.8%

32.3% 32.3% 0.0%

32.8% 27.1% 5.7% 11.8% 533 347 399

35.0% 27.1% 7.9% 16.4% 512 371 399

30.1% 23.0% 7.0% 12.2% 468 345 363

31.3% 24.4% 6.9% 12.3% 478 345 363

26.3% 20.9% 5.5% 11.0% 471 345 363

28.1% 22.6% 5.5% 11.0% 484 345 363

31.9% 24.9% 7.0% 12.2% 481 345 363

C C kg/s

Cases Technology Plant for design and operational plants [29] Technology Useful heat Fuel type Parameters Ultimate analysis C %-w H %-w O %-w N %-w S %-w Ash %-w Moisture w %-w : Fuel input (energy) E: in kJ/s Fuel input (exergy) Ein kJ/s Fuel input rate m_ f kg/s Power output (net) W kW Heat output (energy) Q_ kJ/s _ 0 Heat output (exergy) Q kJ/s District heating Hot water TH C Cold water Tc C Flow rate m_ dh kg/s Steam Pressure pst bar(a) Temperature Tst C Flow rate m_ st kg/s Efficiencies Energy Total htot % Electrical hel % Thermal hth % Exergy Total Jtot % Electrical Jel % Thermal Jth % Thermal exergetic tex % Supplied temperature Ts K Product temperature Tp K Exit loss temperature TL K

649 0 399 16 BGGE 4 P Design BGGE DH Wood chips

17 COMB 1 Opera-tionnal COMB DH Wood biomass

18 COMB 2 Design COMB DH Wood biomass

19 COMB 3 Design COMB DH Wood biomass

20 COMB coal Ref [14] COMB n/a Coal

50.20 5.80 42.72 0.10 0.03 1.12 45 32,477 39,707 3.48 8290 16,062 2827

49.80 6.50 42.50 0.20 0.00 1.00 51 76,000 98,377 9.45 22,536 45,000 7200

50.20 5.80 42.72 0.10 0.03 1.12 45 18,267 22,334 1.95 3105 11,508 1841

50.20 5.80 42.72 0.10 0.03 1.12 45 32,477 39,707 3.48 5521 20,460 3274

94 50 113.5

94 50 289.1

94 50 73.9

94 50 131.5

90 70 2.3

75.0% 25.5% 49.5%

88.9% 29.7% 59.2%

80.0% 17.0% 63.0%

80.0% 17.0% 63.0%

80.1% 35.1% 45.0%

28.0% 20.9% 7.1% 11.0% 486 345 363

29.1% 22.9% 6.2% 10.4% 505 345 423

22.1% 13.9% 8.2% 11.0% 445 345 423

20.9% 13.9% 8.2% 11.0% 435 345 423

145,370 4.85 60,000

41.3% 41.3% 0.0%

21 ICE NG Ref [12] ICE DH Natural gas

427 453 0.0087 150 192 30

39.7% 33.1% 6.6% 14.7% 515 353

22 SC ST coal Ref [13] SC ST n/a Coal

23 CC LNG Ref [13] CC n/a LNG

24 GT NG Ref [14] CC DH Me-thane

1.7 MJ/s 67 666,100

361,030 85,110 7.06 1.64 166,000 30,000 12,760 212 25 14.0

0%

0%

39.9% 39.9% 0.0%

46.0% 46.0% 0.0%

50.2% 35.2% 15.0%


10


Nomenclature

References

A Ash C e E_

[1] Prins MJ, Ptasinski KJ, Janssen FJJG. Thermodynamics of gas-char reactions: first and second law analysis. Chem Eng Sci 2003;58(3):1003e11. [2] Saidur R, BoroumandJazi G, Mekhilef S, Mohammed HA. A review on exergy analysis of biomass based fuels. Renew Sustain Energy Rev 2012;16(2): 1217e22. [3] Kanoglu Mehmet, Dincer Ibrahim, Rosen MA. Understanding energy and exergy efficiencies for improved energy management in power plants. Energy Policy 2007;35(7):3967e78. [4] Khaliq A, Kumar R, Dincer I. Exergy analysis of an industrial waste heat recovery based cogeneration cycle for combined production of power and refrigeration. J Energy Resour Technol 2009;131(2):022402-1e022402-9. [5] Ibrahim D, Rosen MA. Exergy. 2nd ed. GB: Elsevier Science; 2012. [6] Tufte E. The visual display of quantitative information. Graphic Press; 1983. [7] Hepbasli A. A key review on exergetic analysis and assessment of renewable energy resources for a sustainable future. Renew Sustain Energy Rev 2008 4;12(3):593e661. [8] Abusoglu A, Kanoglu M. First and second law analysis of diesel engine powered cogeneration systems. Energy Convers Manag 2008 8;49(8):2026e31. [9] Hongbin Z, Yuman C. Exergy analysis of a steam power plant with direct aircooling system in China. In: Power and Energy Engineering Conference, 2009. Asia-Pacific: APPEEC 2009; 2009. [10] Moran Michael J, Howard NS. Fundamentals of engineering thermodynamics. Chichester: John Wiley & Sons, Ltd; 2006. € Boettner DD, Norberg SA, Tamm G, Whipple JR. On the teaching of [11] Arnas AO, performance evaluation and assessment of a combined cycle cogeneration system. J Energy Resour Technol 2009;131(2). 025501-1. [12] Badami M, Mura M. Exergetic analysis of an innovative small scale combined cycle cogeneration system. Energy 2010;35(6):2535e43. [13] Jin H, Kobayashi M, Nunokawa M, Ishida M. Exergy evaluation of two current advanced power plants: supercritical steam turbine and combined cycle. J Energy Resour Technol 1997;119(4):250e6. [14] Muneoz JR, Michaelides EE. The impact of the model of the environment in exergy analyses. J Energy Resour Technol 1999;121(4):268e76. € din J, Henning D. Calculating the marginal costs of a district-heating utility. [15] Sjo Elsevier Appl Energy 2004;78:1e18. [16] Bauen A, Berndes G, Junginger M, Londo M, Vuille F. Bioenergy e a sustainable and reliable energy source. A review of status and prospects. IEA Bioenergy, IEA Bioenergy: ExCo; 2009. p. 06. [17] Public Law 2011/0172 (COD) Proposal for a Directive of the European Parliament and the Council on Energy Efficiency and Repealing Directives 2004/8/EC and 2006/32/EC. 2011. [18] COGEN Europe. What is cogeneration?. April 2013. [19] Davies Gareth, Wood P. The potential and costs of district heating networks. €yry Energy (Oxford) Ltd and Faber Maunsell; 2009. Po [20] Cullen Barry, McGovern Jim. The quest for more efficient industrial engines: a review of current industrial engine development and applications. J Energy Resour Technol 2009;131(2). 021601-1. [21] Stepanov VS. Chemical energies and exergies of fuels. Energy; 20(3):235e42. [22] Song GH, Shen LH, Xiao J. Estimating specific chemical exergy of biomass from basic analysis data. Ind Eng Chem Res 2011;50(16):9758e66. [23] Khan Academy, Khan S. Gibbs free energy and spontaneity. Available at: https://www.khanacademy.org/science/physics/thermodynamics/v/gibbsfree-energy-and-spontaneity [accessed 27.12.2013]. [24] Taillon J. Comparative exergy analysis of biomass cogeneration systems based on gasification and combustion. School of Electronic, Electrical and Systems Engineering, CREST, Loughborough University; 2012. [25] Dadkhah-Nikoo A, Bushnell DJ. Analysis of wood combustion based on the first and second laws of thermodynamics. J Energy Resour Technol 1987;109(3):129e41. [26] Dunbar William R, Noam L. Understanding combustion irreversibility. ASME industrial and environmental applications. 1991. p. 81e90 (AES-Vol. 25/HTDVol. 191). [27] IEA International Energy Agency. Tracking clean energy progress 2013. IEA Input to the Clean Energy Ministerial. [28] Rosen MA. Comparison based on energy and exergy analyses of the potential cogeneration efficiencies for fuel cells and other electricity generation devices. Int J Hydrogen Energy;15(4):267e74. [29] Reference design and operational power plants from Carbona Inc. and ANDRITZ.

0 E_ 0 E_

d

0 E_ d H h HHV LHV m_ N O p P Q_ 0 Q_ S s T W w

availability (hours) ash content (%-w) carbon (%-w) exergy (kJ/kg) fuel energy rate (kJ/s) fuel exergy rate (kJ/s) exergy destruction rate (kJ/s) exergy destruction (total) rate (kJ/s) hydrogen (%-w) enthalpy (kJ/kg) higher heating value (kJ(kg) lower heating value (kJ/kg) mass flow rate (kg/s) nitrogen (%-w) oxygen (%-w) pressure (bar) price (currency) heat (energy) rate (kJ/s) heat (exergy) rate (kJ/s) sulphur (%-w) entropy (kJ/kg) temperature (K) work (MW) humidity ratio (%-w)

Greek symbols h energy efficiency a power to heat ratio ðW=Q_ p Þ p profit (V) j exergy efficiency t0ex exergetic thermal factor ε exergetic efficiency Subscripts and superscripts AF as fed AR as received c cold ch chemical db dry basis el electrical dh district heating water f fuel fg saturation h hot he heat in input L loss op operating p product s supplied th thermal st steam tot total


Exergy efficiency graphs for thermal power plants

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