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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 ……. 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

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  1. 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 ……..

  2. First Law for SG:Steady State Steady Flow Q

  3. Wfans Qsteam m fuel m air Qloss First Law Analysis of Furnace:SSSF

  4. 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.

  5. Wfans Qsteam m fuel m air Qloss First Law Analysis of Furnace:SSSF

  6. 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.

  7. Performance Testing of SG Air Flow Rate Dry Flue gas Analysis Ex. Gas Flow Rate

  8. Indirect Method of SG Performance Analysis • For every 100 kg of Coal. But A gas analyzer measures dry volume percentages of individual gases.

  9. 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

  10. 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.

  11. 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

  12. 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

  13. 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

  14. 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.

  15. 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.

  16. 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%

  17. 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.

  18. Wfans Qsteam n fuel n fluegas n air Qfans Furnace Energy Balance • First Law for Furnace in SSSF Mode (in molar form):

  19. 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%

  20. Accurate Calculation of Gas Enthalpy • For any gas

  21. Properties of Gases

  22. Unburned carbon losses. • For 100 kg of fuel • QUCL = W * MC * Calorific Value of Carbon : kJ • QUCL = W * 12 * 33820 kJ.

  23. Incomplete combustion losses • For 100 kg of fuel: • QICL = V * MCO * CV of CO. kJ. • QICL = V * 28 * 23717 kJ.

  24. 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.

  25. 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.

  26. 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

  27. 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

  28. Off Design Performance

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