When burnt the flue gas issuing out of the furnace

Question

Combustion problem NO- 13
An imported British coal as fired in a furnace analyses-
C = 67.9%
H = 4.4%
S= 0.8%
N=1.6%
O=7.9%
Ash = 4.5%
Moisture = 12.9%

When burnt , the flue gas issuing out of the furnace at 545 oc analyses on dry basis as CO₂ =14.5 % , O₂ = 4.7%, N₂ = 80.8 % , Other relevant data are- Gross C.V. of coal =28000 kj /kg , ambient temperature = 15^oc
Specific heat of dry flue gas , Cp = 1.341 kj/Nm³ . ^oc
Specific heat of steam = 1.92 kj /kg .^oc

Heat of codensatio of water vapour at 15^oc =2454 kj/kg

Calculate the -
A . volume (Nm³ ) of actual air used for combustion per kg of as fired coal.
B - sensible heat in the dry flue gas expressed as % of net C.V. of coal.
c- heat loss in the combustion of hydrogen and in the moisture in the coal as kj/kg of coal.

SOLUTION - PART A ---

Basis - 1 kg coal-
Constituents quantity per kg of coal kg atom o kg mole theoretical oxygen
Kgmole
C 0.679 0.679/12 =0.0565 0.565
H 0.044 0.044/2 =0.022 0.011
S 0.008 0.008/32 =0.00025 0.00025
N 0.016 0.016 /28 = 0.00057 --
O 0.079 0.079/32 = 0.00246 -0.00246
TOTAL 0.0653

THEORETICAL FLUE GAS VOLUME PRODUCED , Nm3
CO₂ = 0.0565*22.4 = 1.265 Nm³
H₂O = 0.011 *22.4 = 0.2464 Nm³
SO₂= 0.00025 *22.4 = 0.0056 Nm³
N₂= 0.00057822.4 = 0.0127 Nm³

Total theoretical oxygen requirement = 0.0653 kg mole = 0.0653 *22.4 = 1.46272 Nm³
Theoretical air requirement = 1.46272*100/21 = 6.965 Nm³
Now, flue dry gas from combustion of 1 kg of coal will contain
N₂ , from theoretical air = 6.965*0.79 = 5.50 Nm³

Let , excess air = x Nm³
Total flue gas volume = 1.265 + 0.0065 +0.0127 +5.50 +x = ( 6.783 + x) Nm³
Total flue gas volume of (CO₂ +SO₂) in flue gas = 1.265 + 0.0056 = 1.27 Nm³
(since SO₂ is reported as CO₂ in orsat - analysis)-

By carbon dioxide balance-
% CO₂ in dry flue gas = Volume of CO₂ / Total volume of flue gas *100
14.5 = (1.27 /6.783 +x )*100
14.5 (6.783 +x ) = 1.27*100 =127
6.783 + x = 127/14.5= 8.758
X = x = 8.758 - 6.783 = 1.975 Nm³

Part A - SO , Actual air used /kg of as fired coal = theoretical air + excess air
= 6.965 + 1.975 = 8.94 Nm³

Part -B- Sensible heat loss per kg of coal

= volume of dry flue gas *specific heat * temp.diff erence

= ( 6.783 +1.975 )*1.341 *(545-15) = 8.758 *1.341*530 = 6224.5 kj
Now, net C.V. of coal = gross C.V. - ( 2454 * total weight of moisture)
Weight of water as moisture in 1 kg of coal = 12.9 /100 = 0.129 kg
Water produced by combustion of H2 present in coal =2.2*18 /100 = 0.2958 kg
Total weight of water = 0.129 +0.2958 =0.525 kg/kg of as fired coal
Net C.V.= =28000 - ( 2454*0.525) = 26712 KJ/KG
SO ,Sensible heat loss as % of net C.V. of coal = 6240/26712 *100 = 23.3%

Part -C -
Heat loss due to combustion of hydrogen and moisture in coal will be summation of that due to the cooling of steam to 100 ^oc and the latent of condensation and cooling of water to 15 ^oc.
Heat lost per kg of coal = 0.525 * ( 545- 100 ) *1.92 + 0.525*2454 = 347.7 +1288.3 = 1636 kj