Combustion Calculations

Knowing the fuel analysis, excess air, and ambient conditions, one may perform combustion calculations as shown in the following text.

Example 1.1

Natural gas having CH 4 = 83.4%, C 2 H 6 = 15.8%, and N 2 = 0.8 by volume is fired in a

boiler using 15% excess air. Ambient temperature is 20°C and relative humidity is 80%. Perform combustion calculations and determine the flue gas analysis.

Solution

From steam tables, the saturated vapor pressure at 20°C (68°F) is 0.34 psia = 0.0239 kg/cm 2 a.

At 80% relative humidity, P w = 0.8 × 0.0239 = 0.0191 kg/cm 2 a

Combustion Calculations

M = .622 × 0.0191/(1.033 – 0.0191) = 0.012 (same information may be obtained from

Figure 1.1). Combustion of methane may be expressed as CH 4 +2O 2 = CO 2 + 2H 2 O or 1 mol of CH 4 requires 2 mol (volumes) of O 2 or 2 × 100/21 = 9.53 mol of air for combustion (air contains 21% volume of oxygen and rest nitrogen). Similarly,

2C 2 H 6 + 7O 2 = 4CO 2 + 6H 2 O or 1 mol of ethane requires 3.5 mol of O 2 or 3.5 × 100/21 = 16.68 mol of dry air for combustion.

Tables 1.1 and 1.2, which give the air required for theoretical combustion of various fuel constituents, may also be used to arrive at these values.

Hence, 100 mol of fuel requires 83.4 × 9.53 + 15.8 × 16.68 = 1058.3 mol of theoretical dry air. Considering 15% excess air factor, actual dry air required = 1.15 × 1058.3 = 1217 mol.

Excess air = 0.15 × 1058.3 = 158.7 mol; excess O 2 = 158.7 × 0.21 = 33.3 moles and N 2 formed = 0.79 × 1217 = 961 mol; air moisture = 1217 × 28.84 × 0.012/18 = 23.5 mol. (We multiplied moles by molecular weight [MW] to get the weight and then converted the moisture in air to volume basis by dividing by the MW of water vapor; here 28.84 is the MW of air and 18 that of water vapor.)

Tables 1.1 and 1.2 may also be used to get the amount of CO 2 ,H 2 O, and N 2 formed. For example, 1 mol of methane forms one mole of CO 2 . One mole of ethane forms two moles of CO 2 . Similarly, 1 mol of CH 4 forms 2 mol of H 2 O, and 1 mol of ethane forms 3 mol of H 2 O. Hence, total amount of CO 2 and H 2 O formed is

CO 2 = 83.4 × 1 + 2 × 15.8 = 115 mol; H 2 O = 2 × 83.4 + 3 × 15.8 + 23.5 = 237.7 mol (23.5 mol is the air moisture);

N 2 = 961+0.8 (fuel nitrogen) = 961.8 mol; O 2 (excess) = 33.3 mol

Total moles of flue gas formed = 115 + 237.7 + 961.8 + 33.3 = 1347.8 mol Flue Gas Analysis and Air–Flue Gas Quantities

% volume CO 2 in flue gases = (115/1347.8) × 100 = 8.5% % volume H 2 O = (237.7/1347.8) × 100 = 17.7% N 2 = (961.8/1347.8) × 100 = 71.36% %O 2 = (33.3/1347.8) × 100 = 2.47%.

This analysis is on wet basis. To convert to dry basis, one has to subtract the water content and recalculate the analysis. (Dry analysis is required as some instruments measure the oxygen content on dry basis from which excess air is computed.)

On dry basis, CO 2 = 8.5 × 100/(100 – 17.7) = 10.3%, O 2 = 2.47 × 100/(100 – 17.7) = 3%, and N 2 = 71.36 × 100/(100 – 17.7) = 86.7%. For efficiency calculations, one has to know the dry and wet air quantities and dry and wet flue gas formed per kg of fuel. See Table 1.3. For nonluminous heat transfer calculations, one requires the partial pressures of CO 2 and H 2 O.

p w = 237.7/1347.8 = 0.176 atm and p c = 115/1347.8 = 0.085 atm. MW of flue gas = 8.5 × 44 + 17.7 × 18 + 71.36 × 28 + 2.47 × 32 = 27.70. CO 2 on mass basis in flue gas is required for emission calculations as it is considered a

pollutant. % weight of CO 2 in flue gas = 8.5 × 44/27.7 = 13.5. One may also compute the emissions of CO 2 /million J of heat input.

Amount of fuel fired per million J of energy input on higher heating value (HHV) basis = 106/ (53.940 × 106) = 0.01854 kg fuel. (HHV of the fuel is 53,940 kJ/kg [or 53.94 × 106 J/kg] as shown later.)

Hence, CO 2 formed = 20.4 × 0.01854 × 0.135 = 0.051 kg/MM J. Per MM Btu (1054 MM J), the CO 2 emissions = 1054 × 0.051 = 53.75 kg (118.5 lb). (20.4 is the quan- tity of wet flue gas produced, kg/kg fuel, see Table 1.3.)

TABLE 1.1

Combustion Constants (Part 1) S team G

Heat of Combustion c

Btu/lb No. Substance

Btu/cu ft

Net d en er

Formula

Mol. Wt a Lb per cu ft b Cu ft per lb b Sp. gr. Air = 1000 b Gross

Net d Gross

4 Nitrogen (atm.)

N 2 28.016

0.07439 c 13.443 c 0.9718 e —

5 Carbon monoxide

6 Carbon dioxide

Paraffin series C n H 2n+2

C 2 H 6 30.067

0.08029 c 12.455 c 1.04882 e 1792

C 3 H 8 44.092

0.1196 c 8.365 c 1.5617 c 2590

C 4 H 10 58.118

0.1582 c 6.321 c 2.06654 e 3370

C 4 H 10 58.118

0.1582 e 6.321 e 2.06654 e 3363

C 5 H 12 72.144

0.1904 e 5.252 e 2.4872 c 4016

C 5 H 12 72.144

0.1904 e 5.252 e 2.4872 e

C 5 H 12 72.144

0.1904 e 5.252 e 2.4872 e 3993

C 6 H 14 86.169

0.2274 e 4.398 e 2.9704 c 4762

Olefin series C n H 2n

16 Ethylene

C 2 H 4 28.051

21,041 19,691 18 n-Butene (butylene)

C 3 H 6 42.077

0.1110 e 9.007 e 1.4504 e

C 4 H 8 56.102

0.1480 e 6.756 e 1.9336 e

C 4 H 8 56.102

0.1480 e 6.756 e 1.9336 e 3068

C 5 H 10 70.128

rs rs

Aromatic series C n H 2n–6

21 Benzene

C 6 H 6 76.107

0.2060 c 4.852 c 2.6920 e 3751

C 7 H 8 92.132

0.2431 c 4.113 e 3.1760 e 4484

C 8 H 10 106.158

0.2803 e 3.567 e 3.6618 e 5230

Miscellaneous gases

24 Acetylene

C 2 H 2 26.036

0.3384 e 2.955 e 4.4208 e 5854 f 5654 f 17,298 f 16,708 f la

25 Naphthalene

C 10 H 8 128.162

tion

26 Methyl alcohol

CH 3 OH

0.0846 e 11.820 e

27 Ethyl alcohol

C 2 H 5 OH

0.1216 e 8.221 e 1.5890 e 1600.3

0.0456 e 21.914 e 0.5961 e 441.1

3,983 3,983 30 Hydrogen sulfide

7,100 6,545 31 Sulfur dioxide

0.09109 e 10.979 e 1.1898 e 647

— — 32 Water vapor

0.04758 e 21.017 e 0.6215 e —

— — Source: Ganapathy, V., Industrial Boilers and HRSGs, CRC Press, Boca Raton, FL, 2003, p238.

All gas volumes corrected to 60°F and 30 in. Hg dry. For gases saturated with water at 60°F, 1.73% of the Btu value must be deducted. a Calculated from atomic weights given in the Journal of the American Chemical Society, February 1937.

b Densities calculated from values given in gL at 0°C and 760 mmHg in the International Critical Tables allowing for the known deviations from the gas laws. Where the coefficient of expansion was not available, the assumed value was taken as 0.0037 per 0°C. Compare this with 0.003662, which is the coefficient for

a perfect gas. Where no densities were available, the volume of the mole was taken as 22.4115 L. c Converted to mean Btu per lb (1/180 of the heat per lb of water from 32°F to 2120°F) from data by Frederick D. Rossini, National Bureau of Standards, letter

of April 10, 1937, except as noted. d Deduction from gross to net heating value determined by deducting 18,919 Btu/lb mol water in the products of combustion. Osborne, Stimson, and Ginnings,

Mechanical Engineering , p. 163, March 1935, and Osborne, Stimson, and Flock, National Bureau of Standards Research Paper 209. e Denotes that either the density or the coefficient of expansion has been assumed. Some of the materials cannot exist as gases at 60°F and 30 in. Hg pressure,

in which case the values are theoretical ones given for ease of calculation of gas problems. Under the actual concentrations in which these materials are present, their partial pressure is low enough to keep them as gases. f From third edition of Combustion.

TABLE 1.2

Combustion Constants (Part 2) S

team G

Cu ft per cu ft of Combustible

Lb per lb of Combustible

Required for Combustion

Flue Products

Required for Combustion

Flue Products

Experimental Error No. Substance

N 2 in Heat of (±%)

4 Nitrogen (atm.) —

5 Carbon monoxide

6 Carbon dioxide —

ste H

Paraffin series C n H 2n+2

0.11 ss a

0.05 n dP

Olefin series C n H 2n 16 Ethylene

18 n-Butene (butylene)

19 Isobutene

20 n-Pentene

Aromatic series C n H 2n–6

0.12 u b

0.21 st ion

Miscellaneous gases 24 Acetylene

0.16 al cu

26 Methyl alcohol

27 Ethyl alcohol

— 30 Hydrogen sulfide

SO 2 —

0.30 31 Sulfur dioxide

— 32 Water vapor

— 33 Air

— Source: Ganapathy, V., Industrial Boilers and HRSGs, CRC Press, Boca Raton, FL, 2003, p238.

Where no densities were available, the volume of the mole was taken as 22.4115 L. c Converted to mean Btu per lb (1/180 of the heat per lb of water from 32°F to 2120°F) from data by Frederick D. Rossini, National Bureau of Standards, letter of

April 10, 1937, except as noted. d Deduction from gross to net heating value determined by deducting 18,919 Btu/lb mol water in the products of combustion. Osborne, Stimson, and Ginnings,

case the values are theoretical ones given for ease of calculation of gas problems. Under the actual concentrations in which these materials are present, their partial pressure is low enough to keep them as gases. f From third edition of Combustion.

8 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

TABLE 1.3

Dry and Wet Flue Gas Analysis

% volume CO 2 8.5 10.3 H 2 O

17.64 0 N 2 71.36 86.7 O 2 2.47 3.0

Molecular weight of the fuel = (83.4 × 16 + 15.8 × 30 + 0.8 × 28)/100 = 18.3.

w da = kg dry air/kg fuel = 1217 × 28.84/1830 = 19.18. w wa = kg wet air/kg fuel = 19.18 + 23.5 × 18/1830 = 19.41. w dg = kg dry flue gas/kg fuel = (115 × 44+33.3 × 32 + 961 × 28)/1830 = 18. w wg = kg wet flue gas/kg fuel = (115 × 44+33.3 × 32 + 961.8 × 28 + 237.7

× 18)/1830 = 20.4. Water Formed per kg of Fuel

This is an important piece of information as it gives an idea of how much water can be condensed in a condensing economizer if used. In the earlier example, the MW of flue

gas = 27.7. The % weight of H 2 O in the flue gas = 17.64 × 18/27.7 = 11.46. It was shown ear-

lier that w wg = amount of wet flue gas formed per kg of fuel = 20.4. Hence, the amount of water vapor formed per kg fuel fired = 0.1146 × 20.4 = 2.34 kg. Typically, for natural gas, it varies from 2.15 to 2.4. Similar calculations may be carried out for fuel oil. For no. 2 fuel

oil at 15% excess air, it can be shown that % volume CO 2 = 11.57, H 2 O = 12.29, N 2 = 73.63,

O 2 = 2.51. MW of flue gas = 11.57 × 44 + 12.29 × 18 + 73.63 × 28 + 2.51 × 32 = 28.72.% weight

of H 2 O in flue gas = 12.29 × 18/28.72 = 7.7%. The amount of flue gas produced per kg fuel is about 18. Hence, 0.077 × 18 = 1.39 kg of water vapor is produced per kg of fuel fired at 15% excess air. On an average, it varies from 1.3 to 1.5 kg/kg fuel, much smaller than that for natural gas. Hence, more energy can be recovered in latent heat form with flue gas from combustion of natural gas than with fuel oils.

Combustion Calculations