and Environmental Protection
http://ago.helion.pl ISSN 1733-4381, Vol. 12 nr 3 (2010), p-1-8
Calculation of Enthalpy of Formation for Combustible Substances Nadziakiewicz J.
Silesian Technical University Gliwice, Poland
e-mail: jan.nadziakiewicz@polsl.pl
Abstract
The energy balance equation for chemical reactions need expressing all energy streams as total enthalpies – physical and chemical. There are several ways of expressing chemical enthalpies of substances, in most cases for combustible substances they are calorific values. But when the combustion process takes place simultaneously with other reaction the enthalpy of formation of substances should be applied. This enthalpy is easy to find for substances of known chemical composition but for non-uniform substances of complicated composition it is difficult to apply such parameter. In the paper the method of determining the enthalpy of formation basing on the fuel properties and ash composition is presented. Some examples for solid fuels (coal, wood) and for liquid and gas fuels are also presented.
Obliczanie entalpii tworzenia substancji palnych
Streszczenie
Składniki bilansu energii procesów termicznych ujmują entalpie całkowite substancji – fizyczną i chemiczną. Spośród kilku sposobów wyrażania entalpii chemicznej najczęściej używana jest wartość opałowa. Jednak w procesach, w których oprócz procesu spalania zachodzą inne procesy chemiczne wielkość ta nie może być zastosowana – wówczs stosowana jest entalpia tworzenia. Entalpia tworzenia dla substancji o znanym składzie chemicznym może być znaleziona w tablicach, jednak dla substancji o złożonym lub nieznanym składzie stosowane entalpii tworzenia jest utrudnione. Poniżej przedstawiono sposób wyznaczania wartości entalpii tworzenia dla paliw o nieznanym składzie opierający się na wartości opałowej oraz na składzie popiołu uzyskanego z jego spalania. Przedstawiono kilka przykładów obliczeniowych dla paliw stałych (węgiel, drewno), ciekłych i dla gazu ziemnego.
1. Chemical enthalpy of substances
The energy balance equations for various processes can be set up only if one can define all the elements in equations in units of energy: enthalpy or internal energy. Special attention is
needed when chemical processes are analysed because chemical enthalpies of all substances should be defined.
The most popular way of describing the energy introduced to the system with the combustible substances is using their calorific value: Higher CV or Lower CV.
This method of calculating the components of energy balance is convenient when combustible substances and chemically neutral substances are taking part in the process. More complicated situation is when several simultaneous chemical processes with various substances and various energy effects take place. In these cases other methods of expressing the enthalpies of substances are used: that are enthalpy of formation or enthalpy of devaluation [1]. Of course all these parameters are interrelated with each other and all methods are compatible and give the same results of calculation of final energy effect.
2. Enthalpy of formation
For the energy balance of reaction involving oxidation (combustion) of fuel and simultaneously other chemical reactions (like reduction, absorption) the enthalpy of formation of the fuel of an unknown chemical composition is needed. This makes the difficulty in determining all elements of the energy balance. The only parameter possible to measure for the fuel is Higher Heating Value, which can be done in the calorimeter called calorimetric bomb, then the Lower Heating Value is calculated according to the hydrogen and water contents in the fuel:
r
h
w
Q
r
f
Q
W
d=
s−
⋅
=
s−
(
+
9
)
⋅
(3)
Where: w [kg H2O/kg f.] - humidity of fuel
It is possible to determine the enthalpy of formation Hs of the fuel on the basis of its Lower Heating Value Wd and other measured parameters. To explain this procedure the scheme of the energy balance of fuel combustion can be of some help.
Complete
combustion
T = T
n, p = p
nFuel m
f= 1kg
Air n’
aFlue gas n”
fgAsh m
ashHeat of reaction
Q
Substrates
Products
Archives of Waste Management and Environmental Protection, vol. 12 issue 3 (2010) 3 This scheme presents the substances involved in the combustion process undergoing without the change of thermodynamic parameters (all temperatures are equal to Tn and pressures to pn), that means only changes in chemical enthalpies are taken into balance. It is assumed, that the combustion is complete and combustion products (flue gas, ash) do not contain any combustible substances.
The energy balance of process presented in Fig.2. using Lower Calorific Values has a form:
( )
Mi
n
( )
Mi
m
i
Q
n
W
m
f⋅
d f+
a'⋅
a=
"fg⋅
fg+
ash⋅
ash+
,
(4)
mf = 1kg is the mass of fuel, n’a [kmole air/kg f.] is the amount of air supplied to the process, n”fg [kmole flue gas/kg f.] – amount of flue gas, mash [kg ash/kg f.] – amount of ash, i [kJ/kg] and (Mi)[kJ/kmole] are enthalpies and molal enthalpies of substrates and products of combustion.
Since the temperatures of fuel, air and ash are the same and equal to Tn their physical enthalpies are equal zero and in this equation only the chemical enthalpy of fuel and heat remains:
Q
W
m
f⋅
d=
(5)
The same energy balance can be made basing on the enthalpies of formation H of solid substances and molal enthalpies of formation (MH) of gaseous substances taking part in the process:
Q
H
m
MH
n
MH
n
H
m
f⋅
f+
'
a⋅
(
)
a=
"
fg⋅
(
)
fg+
ash⋅
ash+
(6)
The important question is the enthalpy of formation of ash, which is the composition of several mineral components:
∑
⋅
=
⋅
i i i ash ashH
m
H
m
(7)
Where mi and Hi are masses and respective enthalpies of formation of all mineral components of ash.
Assuming enthalpy of formation of air equal zero: (MH)a = 0 and combining equations (5) and (6) by eliminating the value of Q one can obtain the relation between the enthalpy of formation of fuel Hf and its LHV Wd. Dividing obtained equation by mass of fuel mf one can determine the enthalpy of formation of the fuel Hf [kJ/kg fuel].
(
)
fg ash ash fg f d fW
n
MH
m
H
H
=
+
"⋅
+
"⋅
,(8)
or:(
)
CO H O(
)
H O SO(
)
SO ash ash CO f d fW
n
MH
n
MH
n
MH
m
H
H
=
+
⋅
+
⋅
+
⋅
+
"⋅
2 " 2 2 " 2 2 " 2 ,(8a)
In this relation all elements should be calculated according to their amounts in flue gas n” [kmole/kg f.] and molal enthalpies of formations (MH)i, m”ash [kg ash/kg.f] is the amount of ash produced from 1 kg of fuel.
If one knows the composition of ash represented by concentrations si of all components then the relation in eq.(8) can have the form:
∑
⋅
⋅
=
⋅
=
⋅
i i i ash ash ash ash f ashH
s
A
H
m
H
m
m
"(7a)
Where Aash is the contents of ash in original dry fuel.
3. Practical examples
As numerical examples values of enthalpy of formation for some types of fuels were calculated – that were two types of hard coal (from Poland and from Germany), biomass (wood), sewage sludge, oil and biogas. The elementary compositions of these fuels and the compositions of ashes were taken from literature. The LHV were also taken from literature or were calculated according Dulong formula. For oil and gas the ash amount was assumed as zero (mash = 0).
The flue gas compositions (n”CO2, n”H2O, n”SO2) were calculated according the stoichiometry formulas with the assumptions that the oxidation was complete and air excess ratio was equal to 1. The calculations were made for dry fuels since the elementary composition of such fuels are determined in laboratories. The data for calculations and results are presented in tables. Table 1. presents the composition of fuels taken for considerations.
Table 1. Composition of fuels – dry basis. KWK Śląsk [2] German coal [3] Wood [4] Sewage sludge [5] Heating oil [1] Biogas [6] Ad 0,139 0,114 0,008 0,423 0,000 CH4 0,60 Cd 0,737 0,743 0,500 0,282 0,859 CO2 0,33 Hd 0,051 0,044 0,063 0,046 0,111 N2 0,01 Nd 0,012 0,015 0,001 0,029 0,004 O2 0,00 Sd 0,005 0,007 0,000 0,006 0,020 H2O,g 0,06 Od 0,056 0,077 0,428 0,206 0,006 Cld 0,000 0,000 0,000 0,009 0,000 Total 1,000 1,000 1,000 1,000 1,000 1,00
The other values needed for the calculations in eq. 7a are the compositions of ashes obtained after the combustion of these fuels. The values of ashes components concentrations are given in Table 2. Beside the ash composition in that table the values of enthalpies of formation (molal and mass) for these components are given. This makes possible calculation of elements of eq.7a.
Archives of Waste Management and Environmental Protection, vol. 12 issue 3 (2010) 5 Table 2. Ash components of analyzed fuels and their enthalpies of formation.
KWK Śląsk German coal Wood Sludge (MH)i Hi
Ash % % % % kJ/kmol kJ/kg SiO2 0,5471 0,4451 0,5872 0,1583 -852036,5 -14180,5 Al2O3 0,1765 0,1883 0,1355 0,0658 -1277112 -12525,6 Fe2O3 0,0798 0,1128 0,0610 0,1471 -831715 -5208,31 CaO 0,0672 0,0846 0,0898 0,5098 -635623 -11334,2 MgO 0,0406 0,0514 0,0344 0,0375 -602941 -14957,6 Na2O 0,0093 0,0070 0,0142 0,0007 -416695,5 -6723,17 K2O 0,0176 0,0211 0,0507 0,0031 -361178 -3834,04 TiO2 0,0083 0,0091 0,0119 0,0043 -942750 -11799,1 BaO 0,0009 0,0000 0,0000 0,0000 -558527 -3642,41 Mn3O4 0,0014 0,0000 0,0000 0,0000 -1389404 -6072,3 SrO 0,0007 0,0000 0,0000 0,0000 -589952 -5693,42 P2O5 0,0059 0,0020 0,0148 0,0589 -1532702 -5851,24 SO3,s 0,0447 0,0785 0,0005 0,0133 -440159,5 -5497,73 Taking all the values for calculations as well as Lower Heating Values of fuels one can calculate all terms of equation (8) and determine enthalpies of formation of analyzed fuels. The values of Wd, enthalpies of formation of flue gas Hfg and enthalpy of formation of ash Hash and final values of enthalpies of formation of fuels (all calculated for 1 kg of fuel) and of biogas (data given for 1m3 of gas) are given in Table 3.
Table 3. Lower Heating Values and Enthalpies of formation of terms of equation (8) for 1 kg of fuel. KWK Śląsk kJ/kg German coal kJ/kg Wood kJ/kg Sludge kJ/kg Heating oil kJ/kg Biogas kJ/m3 Wd 25843,75 30208,35 18705,26 12600,00 39300,00 21471,01 nfg(MHfg) -30378,95 -29835,63 -24050,52 -14822,42 -41553,71 -29956,79 mashHash -1702,46 -1482,58 -96,58 -4419,56 0,00 0,00 Hf -6237,66 -1109,85 -5441,85 -6641,98 -2253,71 -8485,78 The values given in Table 3. Are also presented in Fig.3. in the form of columns: positive value columns represent Lower Heating Values Wd of fuels while negative value columns represent enthalpies of formations of fuels Hf.
If the enthalpy of formation of moist fuel is needed it can be calculated from the relation:
(
)
f d H Olw
f
w
H
w
H
H
,=
1
−
⋅
,+
⋅
2 ,(9)
In this formula HH2O,l = -15902,7 kJ/kg.
Similar calculations can be made on the basis of Higher Heating Values Qs of substances taking into account the relation (3).
4. Discussion and summary
All the values of enthalpies of formation are negative what is in agreement with theory of this parameter. As can be seen from Table 3 and Fig.3 the enthalpy of ash has minor influence on the final value of Hf with the exception of the sludge (high content of ash). This is a positive feature because the accuracy of determination of composition of ash is not very high.
The knowledge of values of enthalpies of formation of various substances is important for preparing energy balances of chemical reactions. It takes place especially when the parallel reactions of combustion and other chemical reaction take place.
The enthalpy of formation is easy to find in tables for chemically defined substances, but not for substances of unknown chemical composition and of non uniform structure. This specially take place when waste materials are incinerated or utilized by thermal methods. In these cases it is possible to determine the enthalpy of formation on the basis of heating value and composition of ash obtained during combustion.
Some examples for fuels are presented above and similar procedure can be applied for other combustible substances – fuels or waste.
References
Archives of Waste Management and Environmental Protection, vol. 12 issue 3 (2010) 7 [2] Data of Łaziska mine (Poland).
[3] Żelkowski J.: Kohlecharakterisierung und Kohleverbrennung. VGB Powertech. 2004. [4] Wandrasz J., Paliwa formowane. Gliwice. Poland. 2007.
[5] M. Bele´n Folgueras at al.: Influence of Sewage Sludge Addition on Coal Ash Fusion. Energy & Fuels 2005, 19, 2562-2570.
