Energy Convers. Mgmt Vol. 28, No. 2, pp. 117-121, 1988 0196-8904/88 $3.00+0.00 Printed in Great Britain Pergamon Press plc

SECOND LAW (EXERGY) ANALYSIS OF VARIOUS TYPES OF COAL

A L O K S R I V A S T A V A EER Technologies Corporation, 1801 Alexander Bell Drive, Reston, VA 22091, U.S.A.

(Received 16 August 1986; received for publication 29 July 1987)

Abstract--This communication presents a second law, or exergy, analysis of various types of coal from major mines of the world. The customary first law analysis gives only the quantity of energy, while the second law defines the quality of energy also. The projected increase in coal utilization in power plants makes it desirable to evaluate the energy content of coal both quantitatively and qualitatively, which will result in proper design, matching and installation of equipment.

Coal combustion Second law analysis Exergy

NOMENCLATURE

E = Internal energy HOp = Enthalpy of reaction at constant pressure HV = Heating value

HHV = Higher heating value (h°f)R = Enthalpy of formation of reactants (h°f)p = Enthalpy of formation of products

LHV = Lower heating value Ma2 o = Mass of water

fl = Quality of coal (E/HV) flss = Quality of coal using Szargut and Styrylska

relation AG = Change in Gibbs's free energy

= Exergy or thermodynamic availability Ech., = Standard chemical exergy of elements

r/c.n.N.o.s = Number of moles; subscript C, H, N, O and S refers to carbon, hydrogen, nitrogen, oxygen and sulfur, respectively

r/i = Number of moles of elements qo.~ = Number of moles of oxygen ~/p = Number of moles of product r/g = Number of moles of reactants P = Products P0 = Pressure of standard state

PP.0 = Partial pressure of combustion products at ambient atmosphere

Po2 = Partial pressure of oxygen at ambient atmos- phere

Q = Thermal energy R = Gas constant S = Entropy T O = Temperature of initial state V = Volume

Wma x = Maximum work

matched with one another. The second law, or exergy, analysis enables one to determine the max imum work that can be expected from the energy device or process. For example, electrical energy is of higher quali ty than thermal energy because it can be conver ted a lmost entirely into mechanical work.

Exergy analysis of energy devices and processes is no t new and goes back to the last century. However, its implicat ions were not fully appreciated until more recently. Extensive research and deve lopment work in the Soviet Un ion and o ther eastern block countr ies is going on, mainly concent ra ted in the field of power plants [1]. Surprisingly, the U.S.A. and other western countr ies are just now realizing the impor tance of exergy analysis for energy processes. Accordingly, there does not even exist a clear a rgument on many aspects of the field [2], and a s tandard nomencla ture also does not exist. A descript ion of the concept of t he rmodynamic availability, or exergy, has been recently presented by Kest in [3].

The objective of this paper is to present the exergy of various types of coal f rom the major mines of the world. The methodology presented here was originally developed by G h a m a r i a n and Cambel [4] and was used for Illinois No. 6 coal. The au thor feels it is impor t an t to extend the analysis for o ther types of coal so tha t utilities and industries relying heavily on a par t icular coal can determine its potent ia l directly.

INTRODUCTION

The deplet ion of non-renewable energy sources and the high cost associated with them have led engineers to reassess how energy may be utilized more efficiently.

The t radi t ional first law analysis, a l though neces- sary, does not give a complete picture of the limita- t ions and potential i t ies of the var ious componen t s of an energy system. This may result in the instal la t ion of equipment tha t is not properly designed and

EC.M. 2 8 / ~ A

GEOLOGY OF COAL

The widespread occurrence of coal t h roughou t the world reflects the mechan ism by which coal is formed ----essentially the accumula t ion of decaying plant debris in low-lying areas with subsequent a l ternat ion and solidification of tha t debris into various grades of coal.

The op t imum condi t ions for coal fo rmat ion have been in temperate and subtropical regions where high

117

118 SRIVASTAVA: EXERGY ANALYSIS OF COAL

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120 SRIVASTAVA: EXERGY ANALYSIS OF COAL

rainfall provided an environment for prolific growth of forests. At the same time, such growth occurred in swampy areas where the debris decayed in an aqueous environment which prevented oxidation in air. Coastal swamps and basin lowlands, historically, provided such conditions in almost every geologic age.

The conversion of plant debris to coal involves loss of oxygen, nitrogen and hydrogen through bacterial action, with an attendant increase in the carbon content. Substances resistant to bacterial action, such as waxes and resins, remain in the coal. Various levels of coal formation are represented by peat, lignite, bituminous, and anthracite coals.

Bituminous coal represents the final stage of coal formation in undisturbed fiat land. In regions where there has been extensive folding of the earth's crust, the Appalachian Mountains, for example, additional heat and pressure have caused further devolatiliz- ation of the coal, producing a product especially high in carbon content, anthracite coal.

HEATING VALUE OF COAL

The second law analysis of coal requires a knowl- edge of its heating value. Although this is a well known concept, as developed by Ghamarian and Cambel [4], the author will review it here very briefly.

The standard enthalpy of combustion H°p is commonly defined as

--HOp = HV = Q = ~ qR(h°f)R -- ~ qp(h°f)p, (1) R P

where the subscript 0 refers to the standard state: T0=298.16K and P0=0.1 MPa.

Two heating values are commonly defined depend- ing on whether or not the water in the products is in the liquid state. These are the higher (HHV) and the lower (LHV) heating values, which are related as follows:

HHV = LHV + MH~o'htg. (2)

Based on the calculated values of the LHV of numerous solid homogeneous organic compounds presented by Szargut and Styrylska [6], the empirical equations expressing the heating value of compounds of carbon, hydrogen, oxygen and sulfur can be expressed as

LHVc/n/o..r~:s = 427.03482qc + 90.881 lr/n

- 207.4643qo

+ 297.0116qs MJ/kg (3a)

for qo/qc <~ 0.5, and

LHVc;H/o/N/s = 425.73849qc + 91.51107qH

-- 199.15224qo

+ 297.0l 16qs MJ/kg (3b)

for qo/qc <~ 1.0.

Here, it is important to note that sulfur is treated as a free species, ignoring its bond energy, because, for oxidation of sulfur,

H ° = - 297.0116 MJ/kmole. (4)

Therefore,

HHV = LHV + 21.978qu. (5)

EXERGY ANALYSIS OF COAL

The chemical energy of the fuel that can be converted into work also depends upon the system as well as its surroundings. Kestin [3] and Ghamarian [4] defined availability, or exergy, e as

E = - Wmax = E + Po V - ToS - ~#RqR. (6)

Therefore, the exergy can also be defined as the maximum work that can be obtained when the reactants are at the dead state.

Considering the zero exergy reference and dead state temperature 25°C, pressure 0.1 MPa and a stable configuration of the various elements, the exergy of the fuel can be written as

where A G ° = H R p - T o A S ° = - H V - T o S ° is the standard free enthalpy of formation of the com- pound, and Ech,i is the standard chemical exergy of the elements. Using these, one can calculate the standard chemical exergy per mole of any compound as

pP0

where Po2.0 and Pc,0 represents the partial pressures of oxygen and that of combustion products in the ambient atmosphere, respectively.

Tables representing the standard chemical exergy of pure substances have been published by Sussman [2] and for numerous solid organic compounds by Szargut and Styrylska [6].

Using the third law, or Nernst's law of thermo- dynamics, Ghamarian and Cambel[4] found the empirical equations for the exergy of carbon, hydro- gen, oxygen, nitrogen and sulfur compounds to be

Exergycoal = 443.35208r/c + 105.30292,1 n

- 184.17053qo + 32.65797qn

+ 513.159qs (9a)

for qo/rlc <~ 0.5, and

Exergyco,i = 441.41299t/c + 106.98818q~

-- 171.1451qo + 20.59097qN

+ 513.159qS (9b)

for r/o/r/c ~ 1.0.

SRIVASTAVA: EXERGY ANALYSIS OF COAL 121

Here, it is assumed that the effect of pressure is not changing the thermodynamic properties of the coal.

NUMERICAL RESULTS AND DISCUSSION

Mathematically, the estimation of the heating value of coal requires an accurate analysis of the coal composition which is reported in two different ways: the "ultimate analysis", which is the determination of the masses of the important elements--carbon, hydrogen, nitrogen, oxygen (by difference), and sulfur--and the "proximate analysis", which is the determination of the masses of moisture, volatile matter, fixed carbon (by difference) and ash.

The ultimate analysis of various types of coal from the major mines of the world is taken from Gorbaty et al. [7] and presented in Table 1. Illinois No. 6 is the most common coal in the U.S.A. and is used as a reference coal in designing utility plants. Table 1 is quite explicit, and designers can choose appropriate heating and exergy values of design coal, rather than depending on Illinois No. 6 coal data.

The quality of fuel, as the ratio of exergy to energy of its unit quantity, can be defined as

E

/~ - H V ' ( 1 0 )

These values are also calculated and presented in column 12 of Table 1. The range offl is from 1.04 to 1.11. Ghamarian and Cambel[4] reported that the quality of fuel (fl) may be greater or tess than unity. But, as a matter of fact, the author observed that fl is always greater than 1, which means that the maximum obtainable work is always greater than the heating value or energy liberated by the chemical reaction. Considering the equation E = - - A g ° = - ( A H - T o A S ) , Gibb's free energy concept, the difference should be made up by heat supplied from the environment, which may result in higher entropy of the final state than the initial state.

From the equation developed by Szargut and Styrylska [6], based on molar ratios, one has

H flss - - 1.0438 + 0.0158 --

HV C

These flss values are also calculated and presented in the last column of Table 1. Both fl ratios, calcu- lated by (10) and (1 l), are the same with a reasonable degree of accuracy.

It is also observed that the maximum value of the exergy from coal is nearly 38 MJ/kg with a carbon percentage of 90; afterward, it decreases even when the C% is increasing. Therefore, for design purposes, the coal with 90% carbon can be considered as the maximum heating and exergy value coal. It is also observed that, for higher values of the carbon percentage, fl ~ flss.

Using the actual data of various coals, in con- clusion, it is observed that E is always greater than HV. Therefore, in designing coal fired utility plants, designers should consider the second law, or exergy, value of coal, which gives the quality of the fuel, in addition to the first law value or quantity of fuel required. Arrangements should be made to enhance the entropy of the final state by providing more energy from the atmosphere, so that the maximum work can be obtained from the processes.

Acknowledgements--The author wishes to thank Dr H. S. Dhillon for facilitating the conduct of this research. Thanks are also due to Professor A. B. Cambel for suggesting the problem. Typing support of Central Word Processing Department is also appreciated.

REFERENCES

I. J. E. Ahern, The Exergy Method of Energy Systems Analysis. Wiley, New York (1980).

2. M. V. Sussman, Availability (Exergy) Analysis. A Self- Instruction Manual. Tufts University (1980).

3. J. Kestin, Energy 4, 679 (1980). 4. A. Ghamarian and A. B. Cambel, Energy 7, 483 (1982). 5. American Society of Testing & Materials Classification,

"Specification for classification of coals by rank". Report No. ASTMD-388-66 (1972).

6. J. Szargut and T. Styrylska, Brennstoff-Warme-Kraft 16, 589 (1964).

7. Gorbaty M. L. et al. (editors) Coal Science, Vol. l, p. 52. Academic Press, New York (1982).

O N + 0.0813 + 0.0471 ~-. ( l l )