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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 ……. 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

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
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
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.
slide7

Performance Testing of SG

Air Flow Rate

Dry Flue gas Analysis

Ex. Gas Flow Rate

indirect method of sg performance analysis
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
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 analyzer10
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.
slide11
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
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
slide13
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
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
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.
slide16

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
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.
slide18

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
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
Unburned carbon losses.
  • For 100 kg of fuel
  • QUCL = W * MC * Calorific Value of Carbon : kJ
  • QUCL = W * 12 * 33820 kJ.
incomplete combustion losses
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
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.
losses due to moisture in fuel combustion generated moisture
Losses due to moisture in fuel & combustion generated moisture.
  • 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
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
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