1. Energy Balance Analysis of A Furnace/Combustion SystemBY
Dr. P M V Subbarao
Mechanical Engineering Department
I I T Delhi
A Criteria for performance Rating .

2. Enthalpy of Formation
General combustion occurs at temperatures above 250C and above 100kPa.
A most valid reference state for combustion is 250C & 100kPa.
Let us define a new enthalpy with reference to 250C & 100kPa.
This is called Enthalpy of Formation.
Why?
All substances in elemental form will have an enthalpy of formation of zero at 250C & 100kPa
Enthalpy of other forms can be defined using first law analysis.

3. Enthalpy of Formation of A Substance
The enthalpy of formation of a compound,           is the enthalpy change when one mole of compound is formed under standard conditions from one mole of its constituent elements in their standard state.
e.g.   
                                                         
                                                            
=>                                      
                                                        

4. Enthalpy of Combustion of A Fuel
The enthalpy         of combustion (or the heat of combustion) is the enthalpy change when one mole of compound reacts completely with excess oxygen under standard conditions.
e.g.   
                                       

5. Enthalpy of Formation of A Fuel
The enthalpy of formation of a fuel,           is the enthalpy change when one mole of fuel is formed under standard conditions from one mole of its constituent elements in their standard state.
                                                         
                                                            
                                    
                                                        

6. First Law Analysis of Photosynthesis:SSSF
Starch (or amylum) - a polymeric carbohydrate made of a mixture of varying amounts of two glucose polymers amylose and amylopectin.
(An approximate formula for starch is often given as (C6H10O5)x where x is around 100.)
It is found in many green plants as an energy storage medium, in tubers such as potatoes, in the roots of vegetables like carrots, and in the seeds of grains like rice, wheat and barley.
Because it has no precise molecular formula, its molar enthalpies of combustion and formation are not defined, but its standard enthalpy of combustion for 1 kilogram of material is kJ.
From a knowledge of the enthalpy of formation of carbon dioxide and water and the enthalpy of combustion of starch, a figure for the kilogram enthalpy of formation of starch may be obtained using first Law.

7. Calorific Value of A Fuel
Heat to be removed from a combustion chamber when one kg or kmol of fuel is completely burnt and both reactants and products are at 250C & 0.1MPa
First Law Analysis:
- QCV +nO n fuel hfuel = S n fluegas hf,0fluegas
Q = -CV
n kmoles of flue gas
1 kmol fuel
At 250 C & 0.1MPa
n kmols O2
At 250 C & 0.1MPa

8. Enthalpy of formation
Enthalpy of formation of a substance at any temperature and pressure:
h f,TP = hf0 + Dhf
Standard tables were developed for standard substances for wide range of temperatures.
Dhf = hf – hf0

9. First Law Analysis of Combustion at Site
CXHYSZOK +e 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash + Moisture in fuel→ P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

10. Thermal Structure of A Boiler Furnace
DPNL SH
Platen SHTR R H T
LTSH
Economiser
APH ESP ID Fan
drum
Furnace
BCW
pump
Bottom ash
stack
screen
tubes

12. Direct Method of Furnace Performance Analysis
Energy balance:
Fuel Energy = Steam Enthalpy + Losses.
Measurements:
Steam Flow Rate
Steam properties
Fuel flow rate.
Difficulties:
Measurement of steam flow rate.
Measurement of fuel flow rate.
Errors in measurements.

13. Performance Testing of Furnace
Air Flow Rate
Dry Flue gas Analysis
Ex. Gas Flow Rate

14. Indirect Method of Furnace Performance Analysis
CXHYSZOK +e 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel → P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash
Dry Exhaust gases: P CO2 +R SO2 + T N2 + U O2 + V CO kmols.
Volume of gases is directly proportional to number of moles.
Volume fraction = mole fraction.
Volume fraction of CO2 : x1 = P * 100 /(P +R + T + U + V)
Volume fraction of CO : x2= VCO * 100 /(P +R + T + U + V)
Volume fraction of SO2 : x3= R * 100 /(P +R + T + U + V)
Volume fraction of O2 : x4= U * 100 /(P +R + T + U + V)
Volume fraction of N2 : x5= T * 100 /(P +R + T + U + V)
These are dry gas volume fractions.
Emission measurement devices indicate only Dry gas volume fractions.

15. Measurements:
Volume flow rate of air.
Volume flow rate of exhaust.
Dry exhaust gas analysis.
x1 +x2 +x3 + x4 + x5 = 100 or 1
Ultimate analysis of coal.
nCXHYSZOK +en 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1 CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7 C + Ash

16. → P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash
nCXHYSZOK +en 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1 CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7 C + Ash
x1, x2,x3, x4 &x5 : These are dry volume fractions or percentages.
Conservation species:
Conservation of Carbon: nX = x1+x2+x7
Conservation of Hydrogen: nY = 2 x6
Conservation of Oxygen : nK + 2 ne (X+Y/4+Z-K/2) = 2x1 +x2 +2x3 +2x4+x6
Conservation of Nitrogen: e n 3.76 (X+Y/4+Z-K/2) = x5
Conservation of Sulfur: nZ = x3
Re arranging the terms:
CXHYSZOK +e 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash Moisture in fuel
→ P CO2 +Q H2O +R SO2 + T N2 + U O2 + V CO + W C + Ash

17. Specific Flue Gas Analysis
For each kilogram of fuel:
Air : e 4.76 (X+Y/2+Z-K/2) * 29.9 /100kg.
CO2 : P * 44/100 kg.
CO : V * 28/100 kg.
Oxygen in exhaust : 32 * U/100 kg.
Unburned carbon: 12*12/100 kg.

18. Thermal Structure of A Boiler Furnace
DPNL SH
Platen SHTR R H T
LTSH
Economiser
APH ESP ID Fan
drum
Furnace
BCW
pump
Bottom ash
stack
screen
tubes

19. Heat gained by boiling water
Loss due to moisture in air.
Loss due to moisture in fuel.
Loss due to combustion generated moisture.
Dry Exhaust Gas Losses
Fuel Energy
Hot gas
Flue gas
Heat loss from furnace surface.
Unburned carbon losses.
Incomplete combustion losses.
Loss due to hot ash.
Heat gained by superheater & reheater
Heat gained by economizer & air preheater

20. Various Losses in A SG Heat loss from furnace surface.
Unburned carbon losses.
Incomplete combustion losses.
Loss due to hot ash.
Loss due to moisture in air.
Loss due to moisture in fuel.
Loss due to combustion generated moisture.
Dry Exhaust Gas Losses.

21. Enthalpy of Formation of A Substance
First Laws for SG in SSSF Mode (in molar form):
S Q +n air hair + n fuel hfuel = S n fluegas hfluegas + S W
n fuel
n air
n fluegas Q
Wfans

22. Dry Exhaust Gas Losses For 100 kg of fuel.
QDEGL = S n fluegas Dhfluegas
QDEGL = n CO2 DhCO2 + n CO DhCO + n O2 DhO2 + n N2 DhN2 + n SO2 DhSO2 kJ.
QDEGL = P DhCO2 + R DhSO2 + T DhN2 + U DhO2 + V DhCO kJ.
Alternate method:
Total number of moles of dry exhaust gas nex.gas = P+R+T+U+V
QDEGL = nex. Gas Cp,exgas (Tex.gas - Tatm)
Cp.exgas = 30.6 kJ/kmol. K

23. Accurate Calculation of Gas Enthalpy
For any gas

24. Properties of Gases Air 1.05 -0.365 0.85 -0.39 Methane 1.2 3.25 0.75C0 C1 C2 C3
Air
1.05
-0.365
0.85
-0.39
Methane
1.2
3.25
0.75
-0.71
CO2
0.45
1.67
-1.27
0.39
Steam
1.79
0.107
0.586
-0.20 O2
0.88
0.54
-0.33 N2
1.11
-0.48
0.96
-0.42

25. Unburned carbon losses.
For 100 kg of fuel
QUCL = W * MC * Calorific Value of Carbon : kJ
QUCL = W * 12 * kJ.

26. Optimization of Furnace Parameters.

27. Incomplete combustion losses
For 100 kg of fuel:
QICL = V * MCO * CV of CO. kJ.
QICL = V * 28 * kJ.

28. Loss due to moisture in Combustion air
For 100 kg of fuel:
QMCAL = e 4.76 (X+Y/2+Z-K/2) * 29.9 * w * Csteam * (Tg – 25) kJ
Where w is absolute or specific humidity : kg of moisture per kg of dry air.
Csteam is the specific heat of steam at constant pressure : 1.88 kJ/kg C.
Tg is the temperature of exhaust gas.

29. Losses due to moisture in fuel & combustion generated moisture.
For 100 kg of fuel:
QML = ( M +9* Y) { Csteam * (Tg – 25) } kJ.
M is the moisture content in the fuel, %.
Y is the combustible hydrogen atoms in the fuel.

30. Loss due to hot ash or Slag
For 100 kg of fuel
QASL = A * Cpas * Tash
Where Cash, is the specific heat of ash, 0.5 – 0.6 kJ/kg K.
Tash is the temperature of the ash or slag.
Tash = Varies from 300 to 800 oC

31. Heat loss from furnace surface
Loss due to Surface Radiation and Convection.
QRCL = As ( hs) (Tsurface - Tamb) kW
As = Total surface area, m2
hs = Surface heat transfer coefficient.
For 100 kg of fuel:
Rate of heat loss/fuel flow rate * 100

33. Optimization of Furnace Parameters.

36. Off Design Performance

37. Gas Turbine for Power Generation