3.2.2.1 The higher heating value per unit mass of fuel
The gross or higher heating values HHV for coals can also be empirically obtained by using the Dulong equation (Annamalai and Puri, 2007), namely:
HHV[kJ/kg] = 33800 YC + 144153 YH — 18019 YO + 9412 YS (3.2)
where YC, YH, YN, YO and YS are mass fractions of C, H, N, O and S.
Another relation due to Mott and Spooner is (Mason and Gandhi, 1980):
if O < 15%
HHV [kJ/dry kg] = 103.5C%+ 1418.3 x H% + 94.2S% — 145.1 x O (organic)% (3.3) if O > 15%
HHV [kJ/dry kg] = 103.5 x C% + 1418.3 x H% + 94.2 x S%
— {153.2 — 72 x O%/(100 — A%)} x O% (3.4)
Here A = ash content.
Channiwala (1992) considered over 200 species of biomass and fitted the following equation to the data:
HHV [kJ/dry kg] = 34910 YC + 117830 YC — 10340 YO — 21110 YA + 10050 YS — 1510 YN
(3.5)
The experimental data have an error of about 1.5%.
Boie empirical equation for HHV of any fuel CcHhNnOoSs (Annamalai and Puri, 2007):
HHV[kJ/kmole] = 422272 x C + 117387 x H — 155371 x O + 100480 xN + 335508 x S (3.6)
where C, H, O, N and S are the number of carbon, hydrogen, oxygen, nitrogen and sulfur atoms respectively in the fuel. The same equation can be used to determine the stoichiometric oxygen in kg per empirical kg of fuel:
Vo2 = 32 {C + H/4 — (1/2)O + S} = 32C{1 + (H/C)/4 — (1/2)(O/C) + (S/C)} (3.7)
HHV [kJ/kg] = C{422272 + 117387 x (H/C) — 155371 x (O/C)
+ 100480(N/C) + 335508 x (S/C)} (3.8)
Based on the Boie equation, the enthalpy of formation can be derived as:
h0FJ = 28752 x{C — 0.888 x H — 6.168 x O + 6.199N + 1.337 S} [kJ/kmole] (3.9)
|
Table 3.3. Fuel Properties (adopted from Sweeten et al., 2006 and TAMU, 2006).
|
Fuel
|
Type
|
Source
|
Ash
|
Dry loss
|
FC
|
VM
|
C
|
|
Coal
|
ar
|
T1: Fuel Properties
|
5.3300
|
15.1200
|
42.3800
|
37.1700
|
60.3000
|
|
Litter biomass
|
ar
|
T1: Fuel Properties
|
26.8100
|
11.6200
|
10.9100
|
50.6500
|
28.4400
|
|
Sewage sludges in Thailand (C1)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
38.4000
|
6.1000
|
8.6000
|
53.0000
|
31.1000
|
|
Sewage sludges in Thailand (C2)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
42.0000
|
5.1000
|
6.7000
|
51.2000
|
27.5000
|
|
Sewage sludges in Thailand (C3)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
43.0000
|
5.4000
|
7.0000
|
50.0000
|
26.4000
|
|
Sewage sludges in Thailand (C4)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
48.4000
|
6.4000
|
4.0000
|
47.6000
|
23.9000
|
|
Sewage sludges in Thailand (C5)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
51.8000
|
3.7000
|
6.0000
|
42.2000
|
20.9000
|
|
Sewage sludges in Thailand (C6)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
61.8000
|
4.1000
|
3.7000
|
34.5000
|
18.0000
|
|
Sewage sludges in Thailand (C7)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
56.0000
|
3.4000
|
5.0000
|
39.0000
|
19.5000
|
|
Sewage sludges in Thailand (C8)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
63.5000
|
3.9000
|
3.2000
|
33.3000
|
14.5000
|
|
Sewage sludges in Thailand (C9)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
64.0000
|
3.7000
|
3.1000
|
32.9000
|
15.3000
|
|
Sewage sludges in Thailand (C10)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
67.6000
|
3.2000
|
1.8000
|
30.6000
|
12.7000
|
|
Sewage sludges in Thailand (C11)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
72.9000
|
4.4000
|
2.2000
|
24.8000
|
10.6000
|
|
Sewage sludges in Thailand (H1)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
39.4000
|
6.6000
|
5.1000
|
55.5000
|
26.7000
|
|
Sewage sludges in Thailand (H2)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
40.6000
|
5.6000
|
6.8000
|
52.6000
|
29.6000
|
|
Sewage sludges in Thailand (H3)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
45.9000
|
4.6000
|
6.5000
|
47.7000
|
25.5000
|
|
Sewage sludges in Thailand (H4)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
45.7000
|
6.9000
|
3.9000
|
50.4000
|
25.0000
|
|
Sewage sludges in Thailand (H5)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
60.2000
|
4.6000
|
3.2000
|
36.6000
|
19.0000
|
|
Sewage sludges in Thailand (I1)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
42.3000
|
5.2000
|
3.2000
|
54.5000
|
25.1000
|
|
Sewage sludges in Thailand (I2)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
51.6000
|
5.0000
|
2.8000
|
45.6000
|
22.6000
|
ar: as received
|
|
HHV-DAF
|
H
|
N
|
O
|
S
|
HHV,
kJ/kg
|
Boie,
kJ/kg
|
HHV-DAF,
kJ/kg
|
Chemical formula
|
|
3.6200
|
0.9600
|
14.5000
|
0.2300
|
23710
|
30025
|
29805
|
CH0.7139N0.0136O0.1805S0.0014
|
|
3.7100
|
3.0350
|
22.7900
|
0.6600
|
12060
|
19564
|
19587
|
ch1.5512n0.0915°0.6015s0.0087
|
|
4.2000
|
3.3000
|
24.3000
|
1.1000
|
13900
|
21824
|
22565
|
CH1.6059N0.0910O0.5865S0.0132
|
|
4.1000
|
4.0000
|
23.3000
|
1.1000
|
13200
|
21099
|
22759
|
ch1.7729n0.1247o0.6360s0.0150
|
|
4.1000
|
4.3000
|
23.7000
|
0.9000
|
12600
|
20673
|
22105
|
ch1.8467n0.1396o0.6739s0.0128
|
|
3.9000
|
3.8000
|
21.8000
|
1.3000
|
11000
|
21111
|
21318
|
CH1.9404N0.1363O0.6847S0.0204
|
|
3.4000
|
3.3000
|
21.7000
|
0.9000
|
10100
|
19077
|
20954
|
ch1.9344n0.1354o0.7794s0.0161
|
|
2.9000
|
2.3000
|
16.7000
|
0.8000
|
9400
|
21140
|
24607
|
ch1.9158n0.1095o0.6964s0.0166
|
|
3.2000
|
3.1000
|
19.4000
|
0.8000
|
8700
|
19778
|
19773
|
CH1.9514N0.1363O0.7468S0.0154
|
|
2.6000
|
2.6000
|
18.1000
|
1.2000
|
6900
|
17539
|
18904
|
CH2.1322N0.1537O0.9370S0.0310
|
|
2.5000
|
2.3000
|
17.7000
|
0.5000
|
6500
|
18108
|
18056
|
ch1.9430n0.1289o0.8684s0.0122
|
|
2.0000
|
1.8000
|
17.5000
|
0.6000
|
5700
|
15509
|
17593
|
CH1.9430N0.1289O0.8684S0.0122
|
|
2.0000
|
1.6000
|
15.7000
|
0.4000
|
4300
|
16491
|
15867
|
CH2.2436N0.1294O1.1118 S0.0141
|
|
4.0000
|
4.3000
|
27.5000
|
0.7000
|
13300
|
18697
|
21947
|
CH1.7814N0.1381O0.7731 s0.0098
|
|
4.6000
|
5.0000
|
21.5000
|
1.0000
|
12800
|
23212
|
21549
|
ch1.8479n0.1448o0.5452s0.0127
|
|
3.9000
|
4.2000
|
21.7000
|
1.0000
|
12400
|
21145
|
22921
|
CH1.8186N0.1412O0.6388S0.0147
|
|
3.8000
|
3.7000
|
24.3000
|
0.8000
|
11100
|
19941
|
20442
|
ch1.8074n0.1269o0.7296s0.0120
|
|
3.0000
|
2.7000
|
16.8000
|
1.2000
|
8200
|
21606
|
20603
|
ch1.8775n0.1218o0.6637s0.0237
|
|
4.0000
|
3.8000
|
26.1000
|
0.9000
|
10900
|
18912
|
18891
|
CH1.8950N0.1298O0.7805S0.0134
|
|
3.2000
|
2.9000
|
20.3000
|
2.0000
|
9900
|
20259
|
20455
|
ch1.6837n0.1100o0.6742s0.0332
|
|
|
Table 3.3. Continued.
|
Fuel
|
Type
|
Source
|
Ash
|
Dry loss
|
FC
|
VM
|
C
|
|
Sewage sludges in Thailand (I3)
|
dry
|
Predicting the heating values of sewage sludges in Thailand
|
58.8000
|
4.7000
|
3.0000
|
38.2000
|
18.3000
|
|
Misc. manure
|
ar
|
n/a
|
36.3825
|
50.5000
|
2.3760
|
10.7910
|
9.7020
|
|
Sheep manure
|
ar
|
n/a
|
10.9098
|
47.8000
|
7.3080
|
34.0344
|
21.1932
|
|
Mortality Biomass source:
|
ar
|
Properties ofthe fuels (MB)
|
34.2000
|
0.9600
|
10.4700
|
54.3700
|
38.4500
|
|
Brent
Auvermann
(before
treatment)
|
|
Cofired coal
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
14.7000
|
5.0000
|
61.1400
|
24.1600
|
72.7500
|
|
Pine shavings
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
0.1000
|
45.0000
|
15.2000
|
84.7000
|
49.1000
|
|
Reed Canary Grass
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
4.1000
|
65.2000
|
19.8000
|
76.1000
|
45.8000
|
|
Sheep manure
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
20.9000
|
47.8000
|
14.0000
|
65.2000
|
40.6000
|
|
Dairy free-stall
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
62.3000
|
70.3000
|
7.1000
|
30.6000
|
22.1000
|
|
Misc. manure
|
dry
|
T3: Proximate, ultimate and ash analyses of coal, pine shavings, and animal waste
|
73.5000
|
50.5000
|
4.8000
|
21.8000
|
19.6000
|
|
DB soil surface
|
ar
|
n/a
|
59.9100
|
12.2100
|
3.9200
|
23.9900
|
18.0200
|
|
DB seperated
|
ar
|
n/a
|
14.9300
|
25.2600
|
13.0000
|
46.8800
|
35.2000
|
|
solids
|
|
Texas lignite
|
ar
|
n/a
|
11.5000
|
38.3000
|
25.4000
|
24.8000
|
37.2000
|
|
Wyoming
|
ar
|
n/a
|
5.6000
|
32.9000
|
33.0000
|
28.5000
|
46.5000
|
|
sub-bituminous
|
|
Thus an approximate method based on the Boie heat value exists to compute hf of any empirical fuel. If only mass fractions of C, H, N, O and S are known as YC, YH, YN, YO and YS, then the higher heating value of the fuel becomes:
HHVF [kJ/kgfuel] = 35160 YC + 116225 YH — 11090 YO + 6280 YN + 10465 YS (3.10)
One can deduce the lower or net heat value (LHV) when hydrogen in water is excluded giving: LHVf [kJ/kgfuel] = 35160 YC + 94438 YH — 11090 YO + 6280 YN + 10465 YS (3.11)
|
HHV-DAF
|
H
|
N
|
O
|
S
|
HHV,
kJ/kg
|
Boie,
kJ/kg
|
HHV-DAF,
kJ/kg
|
Chemical formula
|
|
3.4000
|
1.8000
|
18.7000
|
1.8000
|
9000
|
20907
|
21845
|
CH2.2093 N0.0843 O0.7670 S0.0368
|
|
1.2375
|
0.4950
|
1.6335
|
0.0495
|
3585
|
35730
|
27330
|
CH1.5167N0.0437°0.1264 S0.0019
|
|
2.6622
|
1.0962
|
16.0254
|
0.3132
|
8372
|
21455
|
20275
|
CH1.4937N0.0443 O0.5676 S0.0055
|
|
3.9700
|
0.2900
|
22.7100
|
0.0500
|
12774
|
24118
|
19701
|
CH1.2278N0.0065O0.4433 S0.0005
|
|
3.9100
|
1.5000
|
4.8700
|
2.2700
|
30512
|
35070
|
35770
|
ch0.6391n0.0177o0.0502s0.0117
|
|
6.4000
|
0.2000
|
44.0000
|
0.2000
|
19475
|
19876
|
19494
|
CH1.5500N0.0035 O0.6727 S0.0015
|
|
45.8000
|
1.0000
|
42.9000
|
0.1000
|
16838
|
19300
|
17558
|
CH1.5837N0.0187O0.7031 s0.0008
|
|
5.1000
|
2.1000
|
30.7000
|
0.6000
|
16037
|
21455
|
20274
|
ch1.4937n0.0443 O0.5676 S0.0055
|
|
2.9000
|
1.1000
|
11.5000
|
0.1000
|
8836
|
26380
|
23438
|
CH1.5604N0.0427O0.3906 S0.0017
|
|
2.5000
|
1.0000
|
3.3000
|
0.1000
|
7243
|
35730
|
27332
|
CH1.5167N0.0437O0.1264 S0.0019
|
|
1.4500
|
1.1500
|
7.0700
|
0.1900
|
4303
|
26260
|
15434
|
CH0.9568N0.0547O0.2945 s0.0039
|
|
3.1200
|
1.9300
|
19.1500
|
0.4300
|
12817
|
23455
|
21430
|
CH1.0540N0.0470O0.4084 S0.0046
|
|
2.1000
|
0.7000
|
9.6000
|
0.6000
|
14290
|
29009
|
28466
|
CH0.6713N0.0161 O0.1937 S0.0060
|
|
2.7000
|
0.7000
|
11.3000
|
0.3000
|
18194
|
29772
|
29584
|
CH0.6905 N0.0129O0.1824 S0.0024
|
|
Correlation for adiabatic flame temperature with ash and moisture content is shown and plotted in Figure 3.8.
Figure 3.9 shows the higher heat or gross heat value of C-H-O fuel in kJ per kg of fuel.
3.2.2.2
The higher heat value per unit stoichiometric oxygen The heat value per unit stoichiometric oxygen (vO2) defined as:
|
Figure 3.6. Synergistic NOX reduction from co-firing biomass (adopted from Tillman, 2000).
|
|
Figure 3.7. Higher heating valuesHHV for cattle ration, raw FB, partially composted FB, finished composted FB, coal, and respective FB + 5% crop residue blends (adopted from Sweeten et al., 2003).
|
It is well known that the HHVO2 is almost constant for most fuels. For Boie equation, the HHVO2 is given as:
HHVO2 [kJ/kg of O2] = {422272 + 117387 x (H/C) — 155371 x (O/C) + 100480(N/C)
+ 335508 x (S/C)}/(32{1 + (H/C)/4 — (1/2)(O/C) + (S/C)})
(3.13)
|
Figure 3.8. Correlation of adiabatic flame temperature with moisture and ash contents; Tadiabatic [K] = 2285 — 1.8864 x H2O + 5.0571 x Ash — 0.3089 x H2O x Ash — 0.1802 x H2O2 — 0.1076 x Ash2, H2O and Ash in fractions; multiply T adiabatic in K by 1.8 to obtain T (Annamalai et al., 2007b; Sami et al., 2001).
|
|
Figure 3.9. Variation ofHHV with H/C and O/C in C-H-O fuels.
|
Ignoring S and N, trace elements in fuel, Figure 3.10 plots HHVo2, in kJ per kg of oxygen as HHV/vO2 constant. It is apparent that the HHV per unit mass of O2 burned is approximately the same of about 14250 kJ/kg of oxygen (18.6kJ/SATP liter of oxygen, where SATP means at standard atmospheric temperature and pressure ) or 3280kJ/kg stoich air (3.9kJ/SATP liter of air) for most fuels. For methane, the literature states that HV per unit O2 is 13550 kJ per kg of O2 (17.7kJ/SATP liter of O2) while Boie based equation yields 13934 kJ/kg of O2. For n-octane,
the value is 13640 kJ per kg of O2 or 17.82 kJ/liter of O2 (SATP) for CH4 while Boie yields 13730 kJ/kg O2 for Octane.
Figure 3.11 plots the respiratory quotient (RQ), a term used in biological literature (Annamalai and Silva, 2011) and defined as CO2 per kmole of stoichiometric oxygen, an indication of global
warming potential) for various biomass fuels. Typically RQ is about 1 (which is same as that of glucose, C6Hi2O6) for biomass fuels.
3.2.2.3 Heat value of volatile matter
In Figure 3.11 we see how H/C relates in fat, protein, biomass and coal. If the heat of pyrolysis is neglected, the heat of combustion of the coal can be represented as a combination of the contribution from the volatile matter (HVVVM) and the contribution from the fixed carbon (HVCFC) in relation to their mass percentages:
HV Coal = HVv VM + HVc FC
If FC = 1 — VM as in the case of dry ash-free (DAF) coals, one can correlate the heating values of volatiles HVv to VM (Annamalai and Puri, 2007). The Volatile Matter Higher heating value (HHVVM) was calculated using:
where HHV is the as received heating value, FC% is the amount of fixed carbon present in the fuel, HHVFC is the higher heating value of the fixed carbon (enthalpy of formation/molecular weight), and VM% is the amount of volatile matter present in the fuel.
