Energy Balance Analysis of A Steam Generator

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# Energy Balance Analysis of A Steam Generator - PowerPoint PPT Presentation

Energy Balance Analysis of A Steam Generator. BY P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi. A Criteria for performance Rating ……. First Law for SG:Steady State Steady Flow. Q. W fans. Q steam. m fuel. m air. Q loss.

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### Energy Balance Analysis of A Steam Generator

BY

P M V Subbarao

Associate Professor

Mechanical Engineering Department

I I T Delhi

A Criteria for performance Rating ……..

Some Valid Assumptions
• The role of a furnace is to promote combustion and generate high enthalpy (Temperature) gas products.
• Not for accelerating or decelerating the fluid. ⇒ Vi = Ve
• Not for lifting or dropping the fluid. ⇒ Zi = Ze
• There is some amount of heat transferred to boiling water.
• The loss to the ambient should be minimum.
Direct Method of SG 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.

Performance Testing of SG

Air Flow Rate

Dry Flue gas Analysis

Ex. Gas Flow Rate

Indirect Method of SG Performance Analysis
• For every 100 kg of Coal.

But A gas analyzer measures dry volume percentages of individual gases.

Output of A Gas Analyzer
• Total Dry Exhaust gases: P +R + T + U + V kmols.
• Volume of gases is directly proportional to number of moles.
• Volume fraction = mole fraction.
• Volume fraction of CO2 : x1
Output of A Gas Analyzer
• Volume fraction of CO2 : x1 = P * 100 /(P +R + T + U + V)
• Volume fraction of CO : x2= V * 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.
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.
• Combustible solid refuse.

nCXHYSZOK +en 4.76 (X+Y/4+Z-K/2) AIR +

Moisture in Air + Ash

x1 CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7 C + Ash

Stoichiometry for 100 kmols of Exhaust Gas
• nCXHYSZOK +en 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7C + 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
nCXHYSZOK +en 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → x1CO2 +x6 H2O +x3 SO2 + x5 N2 + x4 O2 + x2 CO + x7C + Ash
• Re arranging the terms (Divide throughout by n):

CXHYSZOK +e 4.76 (X+Y/4+Z-K/2) AIR + Moisture in Air + Ash & Moisture in fuel → (x1/n)CO2 +(x6/n) H2O +(x3/n) SO2 + (x5/n) N2 + (x4/n) O2 + (x2/n) CO + (x7/n) C + Ash

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

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.
Various Energy 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.

Loss due to moisture in air.

• Loss due to moisture in fuel.
• Loss due to combustion generated moisture.
• Dry Exhaust Gas Losses
• ~ 4.5%

Heat gained by boiling water

40%

Fuel Energy

100%

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

40%

Heat gained by economizer & air preheater

12%

Energy Credits
• Chemical Energy in the fuel.
• Energy credit supplied by sensible heat in entering air (recycling of energy).
• Energy credit supplied by sensible heat in the fuel(Recycling of energy).
• Energy credit supplied by auxiliary drives.

Wfans

Qsteam

n fuel

n fluegas

n air

Qfans

Furnace Energy Balance

• First Law for Furnace in SSSF Mode (in molar form):
Dry Exhaust Gas Losses
• As gasses are leaving at temperature higher than ambient temperature.
• For 100 kg of fuel.
• QDEGL =S n fluegasDhfluegas
• QDEGL = n CO2DhCO2 + n CODhCO +n O2DhO2 +n N2DhN2 + n SO2DhSO2 kJ.
• QDEGL =PDhCO2 + RDhSO2+ TDhN2 + U DhO2+ V DhCOkJ.
• 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
• Typical value of DEGL ~ 4.5%
Unburned carbon losses.
• For 100 kg of fuel
• QUCL = W * MC * Calorific Value of Carbon : kJ
• QUCL = W * 12 * 33820 kJ.
Incomplete combustion losses
• For 100 kg of fuel:
• QICL = V * MCO * CV of CO. kJ.
• QICL = V * 28 * 23717 kJ.
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.
• Tg is the temperature of exhaust gas.
• For 100 kg of fuel:
• QML = ( M +9* Y) {2442 + Csteam * (Tg – 25) } kJ.
• M is the moisture content in the fuel, %.
• Y is the combustible hydrogen atoms in the fuel.
Loss due to hot ash or Slag
• For 100 kg of fuel
• QASL = A * Cp,ash * Tash
• Where Cp.ash, 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
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