Question 12.2: A natural gas is burned in a gas turbine combustor under the......
A natural gas is burned in a gas turbine combustor under the following conditions:
• Natural gas composition (in molar fractions r_{i}): CH_{4} = 0.88, C_{2}H_{6} = 0.07, CO = 0.02, CO_{2} = 0.03
• Isobaric specific heat of the flue gas c_{pg} = 1.34 kJ/m³K
i. Oxyfuel stoichiometric combustion of natural gas in pure oxygen
ii. Conventional stoichiometric combustion of natural gas in air
• LHV_{i}: 35.93 MJ/m³ for CH_{4}, 64.5 MJ/m³ for C_{2}H_{6}, and 12.64 MJ/m³ for CO
Calculate (a) the lower heating value of the natural gas, (b) the volume V_{O_{2}} of combustion oxygen or air V_{air}, (c) the volume of flue gas V_{g}, (d) the volume V_{i} of flue gas components and their molar fractions r_{i}, and (e) the adiabatic combustion temperature t_{ad}.
Lower heating value of natural gas
\mathrm{LHV}=\Sigma r_{i}\,\mathrm{ }\mathrm{LH}\mathrm{V}_{\mathrm{i}}=0.88\times35.93+0.07\times64.5+0.02 \times 12.64=36.386\,\mathrm{MJ}/\mathrm{}\mathrm{}\mathrm{m}^{3}Oxyfuel Stoichiometric Combustion of Natural Gas in Pure Oxygen
1. Volume of oxygen required for stoichiometric combustion of 1 m³ of natural gas
V_{\mathrm{O_{2}}}\,=\,2{\mathrm{CH}}_{4}\,+\,(2\,+\,6/4)\;{\mathrm{C}}_{2}{\mathrm{H}}_{6}\,+\,0.5{\mathrm{CO}}=\;2\times0.88+3.5\times0.07+0.5\times0.02=2.015\;{\mathbf{m}}^{3}/{\mathrm{m}}^{3}
2. Volumes of the flue gas constituents, in m³ per m³ of natural gas
• Carbon dioxide volume
= 1.07 m3/m3
• Water vapor volume
V_{\mathrm{H_{2}O}}\,=\,2{\mathrm{CH}}_{4}\,+\,3{\mathrm{C}}_{2}\mathrm{H}_{6}\,=\,2\times0.88\,+\,3\times0.07\,=\,1.97\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3}3. Volume of wet flue gas, in m³ per m³ of natural gas
V_{\mathrm{g}}\,=\,V_{\mathrm{CO_{2}}}+V_{\mathrm{H_{2}O}}\,=\,1.07+1.97\,=\,3.04\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3}4. Composition of flue gas, in molar (volumetric) fractions
{\mathrm{r_{CO_{2}}}}=V_{\mathrm{CO}_{2}}/V_{\mathrm{g}}=1.07/3.04=0.352{\mathrm{r_{H_{2}O}}}=V_{\mathrm{H_{2}O}}/V_{\mathrm{g}}=1.97/3.04=0.648
5. Ignoring sensible heat of oxygen and fuel, adiabatic combustion temperature
t_{\mathrm{ad}}=\mathrm{{LHV}}/(V_{\mathrm{g}}\,\mathrm{{c}}_{\mathrm{pg}})=36,386\,\mathrm{{kJ}}/{\mathrm{m}}^{3}/(3.04\,\mathrm{{m}}^{3}/{\mathrm{m}}^{3}\times1.34\,\mathrm{{kJ/m^{3}K}})=8932^{\circ}\mathrm{{C}}Conventional Stoichiometric Combustion of Natural Gas in Air
1. Stoichiometric volume of air requirement per unit mass of fuel
V_{\mathrm{air}}\,=\,V_{\mathrm{O_{2}}}/0.2 1=\,2.01 5/0.2 1=9.6\,\mathrm{m^{3}/m^{3}}2. Flue gas volume and composition
V_{C O_{2}}\,=\,1.07\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3},\;V_{\mathrm{{H_{2}O}} }\,=\,1.97\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3},\;V_{N_{2}}\,=\,0.79,V_{\mathrm{air}}=0.79\times9.6\,{\mathrm{m}}^{3}/{\mathbf{m}}^{3}\,=7.58\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3}
V_{\mathrm{g}}=V_{\mathrm{CO_{2}}}+V_{\mathrm{H_{2}O} }+V_{\mathrm{N_{2}}}=1.07+1.97+7.58=10.62\,{\mathrm{m}}^{3}/{\mathrm{m}}^{3}
3. Molar fractions of flue gas components
\mathrm{r}_{N_{2}}\,=\,7.58/10.\mathbf{6}2\,=\,0.7 14
4. Ignoring sensible heat of air and fuel, adiabatic combustion temperature
t_{\mathrm{ad}}=\mathrm{{LHV}}/(V_{\mathrm{g}}\,\mathrm{{c}}_{\mathrm{pg}})=36,386\,/(10.62\times1.34)=2557^{\circ}\mathrm{C}Calculation results for combustion of natural gas in pure oxygen and air are summarized in Table 12.2.
Calculations of oxyfuel and conventional combustion of a fuel oil are presented in Example 12.3.
| TABLE 12.2 Flue Gas Volume and Composition and Adiabatic Combustion Temperature for Stoichiometric Oxyfuel and Conventional Combustion of Natural Gas (Example 12.2) |
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| V_{\mathrm{g}}\left(\mathrm{m}^{3}/\mathrm{m}^{3}\right) | r_{\mathrm{CO_{2}}}\left(\mathrm{m}^{3}/\mathrm{m}^{3}\right) | r_{\mathrm{H_{2}O}}\left(\mathrm{m}^{3}/\mathrm{m}^{3}\right) | r_{\mathrm{N_{2}}}\left(\mathrm{m}^{3}/\mathrm{m}^{3}\right) | t_{\mathrm{ad}}\left(^{\circ}\mathrm{C} \right) | |
| Oxyfuel combustion | 3.04 | 0.352 | 0.648 | 0 | 8932 |
| Conventional combustion | 10.62 | 0.101 | 0.185 | 0.714 | 2557 |