Combustion and Heat production equipment

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					Combustion and Heat production equipment

              Jean-Marie SEYNHAEVE

  • PART 1 : Theoretical background

         1.1 Combustion = Chemical reaction
         1.2 Heating values of fuels

  • PART 2 : Heat production : equipment

         2.1 Energy balance and equipment efficiency
         2.2 Combustion control
         2.3 Illustration of burners
         2.4 Practical problems


                 Production de la chaleur - Chaudière   1
    Part 1 : Theoretical background - Table of contents

I - COMBUSTION : CHEMICAL REACTION
       1.1 Examples of Chemical Reaction of Combustion, Fundamental Laws
       1.2 Air Required for Combustion - Flue Gases contents
                 1.2.1 Solid or Liquid Fuel
                 1.2.2 Gas Fuel
                 1.2.3 Practical Problems
II - HEATING VALUES OF FUELS
       2.1 Heat of Reaction - Some Examples
       2.2 Definition of the Heating Value of a Fuel
       2.3 How to evaluate the Heating Value of Fuels
                 2.3.1 Solid or Liquid Fuel
                 2.3.2 Gas Fuel
       2.4 Practical Examples of Evaluation




                          Production de la chaleur - Chaudière             2
 I. Combustion – Chemical reaction : Fundamental laws

Combustible Elements in Fuels :

      C S H2 CO CH4 C2H4 C2H6 C3H8 ......
      Alcans : CnH2n+2
      Alcens : CnH2n
      Aromatics ...
Combustion :     Chemical Reaction of Oxidation + HEAT
        C + O2                                CO2
        S + O2                                SO2
        H2 + ½ O2                             H2O
        CO + ½ O2                             CO2
        CH4 + 2 O2                            CO2 + 2 H2O
        C2 H4 + 3 O2                          2 CO2 + 2 H2O
        ........
        CnH2n+2 + ½ ( 3n + 1 ) O2             n CO2 + ( n + 1 ) H2O

                      Production de la chaleur - Chaudière             3
Chemical BALANCED reactions in terms of number of MOLES

     CnH2n+2 + ½ ( 3n + 1 ) O2  n CO2 + ( n + 1 ) H2O


           nC                                nC           +       n      O2
        ( n + 1 ) H2                     ( n + 1 ) H2 + ½ ( n + 1 ) O2

       ½ ( 3n + 1) O2                                         ½ ( 3n + 1 ) O2
Molecular weight of molecules :
         TYPE OF MOLECULE                   MOLECULAR WEIGHT
              Carbon C                           12 kg/kmole
               Suffer S                          32 kg/kmole
             Hydrogen H2                          2 kg/kmole
              Oxygen O2                          32 kg/kmole
              Nitrogen N2                        28 kg/kmole

    Example : C2H6 : 2x12 kg/kmole + 3x2 kg/kmole = 30 kg/kmole

                       Production de la chaleur - Chaudière                     4
Some important laws :

AVOGADRO
At same pressure and temperature, 1 kmole of every gas occupies the same volume.

For Normal Conditions ( t= 0 °C, p = 760 mm Hg) :         Vkmole  22.414 m3

LAVOISIER             The total MASS in reaction remains constant

Application to air composition (combustive) : O2 N2 ( Ar Ne Xe … )
  - Molar Fractions = Volume Fractions for air ( Avogadro Law ) : [i]
         [O2] = 0.210 (kmole of O2 / kmole of Air or m3 of O2 / m3 of Air)
         [N2] = 0.790    "      N2         "         "     N2      "
  - For Air : 1 kmole of O2 + 0.79/0.21 ( 3.76 ) kmole of N2
  - Mass fraction for air : (i)
   0.210 kmole of O2 = 6.72 kg of O2                     O2   6.72 28.84  0.233
   0.790 kmole of N2 = 22.12 kg of N2             
   1 kmole of Air    = 28.84 kg of Air                   N 2   22.12 28.84  0.767
                           Production de la chaleur - Chaudière                         5
        Air required for Combustion – Production of flue gases
               Pouvoir comburivore – Pouvoir fumigène

Fuel composition
    • For solid and liquid fuel : elementary mass composition
          • Combustible Elements : C (H) (S) ...
          • Oxygen in Fuel : (O)                                n

          • Humidity : (H2O)                                    i   1
                                                               i 1
          • Inert Elements : (N) (Ash)
    • For gas fuel : molar (volume) composition
          • Combustible components : [H2 ] [CO ] [CH4 ] [C2H4 ] [C2H6] ...
          • (Oxygen in Fuel : [O2 ])                   n
          • Humidity : [H2O ]
          • Inert Elements : [N2 ] [CO2 ] …          i 1
                                                               
                                                          [i ]  1

Definition : Excess of air

          Practical Air Requirement
                                                   1  Stoechiometry
           Theoretical need of Air

                        Production de la chaleur - Chaudière                 6
              SOLID and LIQUID FUEL - Combustion accounting

     Elements before combustion                      Elements after combustion - Flue gases
 1 kg of fuel  kmole of fuel kmole of O 2 kmole CO 2 kmole SO 2 kmole H 2 O       kmole N 2     kmole O 2
      (C)        (C)/12 of C    (C)/12      (C)/12        -           -                -             -
     (H)         (H)/2 of H2     (H)/4         -          -         (H)/2              -             -
     (S)         (S)/32 of S   (S)/32          -       (S)/32         -                -             -
     (O)        (O)/32 of O2   -(O)/32         -          -           -                -             -
     (N)        (N)/28 of N2       -           -          -           -             (N)/28           -
    (H2O)     (H2O)/18 of H2O      -           -          -       (H2O)/18             -             -
    (Ash)             -            -           -          -           -                -             -
     ….               …            …          …          …            …               …              …
Stoechiometry                     O2       (C)/12     (S)/32  (H)/2+(H2O)/18 (N)/28+3.76 O2        -
Excess of Air                 (-1) O2                                         3.76( -1) O2 ( -1) O2
   TOTAL                        O2       (C)/12     (S)/32  (H)/2+(H2O)/18 (N)/28+3.76 O2 ( -1) O2


                                                                     3
                 Air requirement for combustion in m                     N /kg   of fuel
                                      22.414/0.21O2

                                                                          3
             Flue gases produced by combustion in m                           N /kg   of fuel
      22.414 [(C)/12+(S)/32+(H)/2+(H2O)/18+(N)/28+3.76O2+(-1) O2]


                                     Production de la chaleur - Chaudière                              7
  SOLID and LIQUID FUEL – Flue gases composition

The flue gases composition is usually given for a DRY SAMPLE

                  C 
    [CO2 ]'        12
                Den '
               S 
    [ SO2 ]'       32
                Den '
                                                      Possible measurements …
                 3.76  O2 
                                    N2 
    [ N 2 ]'                               28
                           Den '
                    1  O2
    [O2 ]' 
                     Den '

                           C    S    N  
Dry sample         Den '                               4.76  1  O2
                             12      32          28

                         Production de la chaleur - Chaudière                   8
                     GAS FUEL - Combustion accounting
Elements before combustion                        Elements after combustion - Flue gases
1 m 3 N of fuel      m 3 N of O 2     m 3 N of CO 2   m 3 N of H 2 O            m 3 N of N 2               m 3 N of O 2
      [H2]              1/2 [H2]           -               [H2]                    -                           -
     [CO]              1/2 [CO]        1/2 [CO]              -                     -                           -
     [CH4]             2 [CH4]           [CH4]          2 [CH4]                    -                           -
    [C2H4]             3 [C2H4]        2 [C2H4]         2 [C2H4]                   -                           -
    [C2H6]            3.5 [C2H6]       2 [C2H6]         3 [C2H6]                   -                           -
       …                   …               …                …                     …                            …
     [H2O]                 -               -              [H2O]                    -                           -
    [CO2]                  -             [CO2]               -                     -                           -
       [N2]                -               -                                     [N2]
       …                   …               …              …                       …                             …
Stoechiometry             O2          CO2,fg           2Ofg             [N2]+3.76 O2                       -
Excess of Air         ( -1) O2                                            3.76( -1) O2                 ( -1) O2
   TOTAL                O2           CO2,fg          2Ofg             [N2]+3.76 O2                ( -1) O2

                                                                       3             3
                  Air requirement for combustion in m                      N/   m        N   of fuel
                                             /0.21O2

                                                                            3                3
           Flue gases produced by combustion in m                               N/   m           N   of fuel
                        CO2,fg+H2Ofg+[N2]+3.76O2+(-1) O2

                                    Production de la chaleur - Chaudière                                                  9
       GAS FUEL – Flue gases composition

The flue gases composition is usually given for a DRY SAMPLE




     [CO ]' 
               CO         2, fg
          2
                        Den '
                  [ N 2 ]  3.76  O2           Possible measurements …
     [ N 2 ]' 
                           Den '
                     1  O2
     [O2 ]'                       ...
                      Den '




!
    Dry sample          Den '  CO2, fg  [ N2 ]   4.76 1 O2  ...


                        Production de la chaleur - Chaudière                10
          Objectives of those accounting tables



 Practical point of view                   Theoretical point of view

Stack

        Volume fraction on             • Excess of air evaluation
         Dry Flue Gases          • Combustion control
                                       • Heat production equipment efficiency




                       Flue Gases
                     Analysis Device

          Purging



                      Production de la chaleur - Chaudière                11
      II. Heating values of fuels (Pouvoir calorifique)
Combustible Elements in Fuels :
      C S H2 CO CH4 C2H4 C2H6 C3H8 ......
      Alcans : CnH2n+2
      Alcens : CnH2n
      Aromatics ...
Combustion :                                                    /      / 22.414
 N°            Chemical Reaction                  Heat          Heat      Heat
           Ref. : Standard Conditions           kJ/kmole        kJ/kg    kJ/m3N
  1   C + O2  CO2                               404400        33700        -
  2   C + ½ O2  CO                              121400        10117        -
  3   S + O2  SO2                               296930         9279        -
  4   CO + ½ O2  CO2                            283000        10107     12626
  5   C + 2 H2  CH4                             85800          7140
  6   H2 + ½ O2  H2O VAP                        241800        120900    10790
  7   H2 + ½ O2  H2O LIQ                        285800        142900    12750
  8   CH4 + 2 O2  CO2 + 2 H2OVAP                802200        50040     35790
                  
  9   CH4 + 2 O2      CO2 + 2 H2OLIQ             890200        55637     39710
                        Production de la chaleur - Chaudière                       12
Principle of Energy balance :
                Reaction 1 = Reaction 2 + Reaction 4
                  404400 = 121400 + 283000

                Reaction 8 = Reaction 1 + 2 x Reaction 6 - Reaction 5
                  802200 = 404400 + 2 x 241800 - 85800
Heating (calorific) value – Pouvoir calorifique : Definition
  Calorimeter of MALHER Experiment at constant VOLUME
    Fuel + Air                                   Cooling
    Patm , t = 25 °C


                        Hot flue gas                          Cold flue gas
                                                                  At t = 25°C
                                               
Adiabatic combustion
                             Heat which is extracted = Heating value

 Calorimeter of YOUNGER          Experiment at constant PRESSURE

                         Production de la chaleur - Chaudière                    13
Type of Heating value          4 types


    • 1st distinction : Constant Volume or Constant Pressure ?
                          In practice CVv never used …

    • 2nd distinction :
                                    H2O Vapour  Lower (Net, inférieur) CV
      Flue gas at 25 °C
                                    H2O Liquid  Higher (Gross, supérieur) CV

      In practice:          HCV  USA, UK, Natural Gas …
                            LCV  G,F,I,H,B, …



       Conclusion :         HCVv LCVv HCVp LCVp




                          Production de la chaleur - Chaudière               14
             Evaluation of Heating Values of fuels

Heating Values of Solid or Liquid Fuels

   • Fuel composition : reference 1 kg of fuel
        Elementary composition : (C) (H) (S) … (O) (H2O) (N) …


   • Heating for solid or liquid fuel :


                      HCV            i HCV
                               i  combustible
                                                       i   in kJ / kg

                      LCV           i LCV
                              i  combustible
                                                   i       in kJ / kg




                         Production de la chaleur - Chaudière           15
                 Heating Values of Gas Fuels

• Composition of gas fuel : reference 1 m3N
       Combustible components             H2  CO CH4  C2 H4 ...
          Inert components               O2   N2  CO2  ...  H2O...
• Heating for gas fuel :

                HCV             i HCV
                           i  combustible
                                                     i
                                                                  3
                                                         in kJ / mN

                LCV             i LCV
                           i  combustible
                                                 i
                                                                  3
                                                         in kJ / mN

          HCV  12750  H 2   12620 CO   39710 CH 4 
                    58950 C2 H 4   69210 C2 H 6 ... in kJ / mN
                                                                   3


          LCV  10790  H 2   12620 CO   35790 CH 4 
                    56920 C2 H 4   63200 C2 H 6  ... in kJ / mN
                                                                    3




                       Production de la chaleur - Chaudière                  16
Combustibles solides
      PCIBRUT = [1 - (cen) - (H2O)] PCIPUR & SEC - 2501 (H2O)

    CHARBON            PCIPUR & SEC = 35000 … 35500 kJ/kg

    BOIS               PCIPUR & SEC  18500 kJ/kg
                       si (H2O) = 0.20
                       PCIBRUT  14300 kJ/kg


Combustibles liquides
                 PCI     = 44000 … 42000 kJ/kg
                                              
               fractions  légères         lourdes


                       Production de la chaleur - Chaudière     17
Combustibles gazeux
    CH4
            PCI = 802 400 kJ/kmole = 50 150 kJ/kg

          1 kmole CH4  22.414 m3N

            PCI = 35 800 kJ/m3N

          1 kmole CH4  2 kmole H2O = 36 kg H2O

            PCS - PCI = 36 x 2501 = 90 036 kJ/kg

            PCS = 892 436 kJ/kmole = 39 816 kJ/m3N

            PCS  1.11
            PCI



                  Production de la chaleur - Chaudière   18
                              Examples of Evaluation

       1. Liquid fuel (fuel-oil, gas-oil, gasoline, kerosene …) :

                        nH
                a          1.5 ... 1.9
                        nC

               Where a is the number of atoms of hydrogen per atom of carbon

               Calculate the HCV and the LCV

                                                                             Calorific Values of Liquid Fuels
 a      (H)     (C)       HCV    LCV


                                           Calorific value (kJ/kg)
                                                                     50000
1.50   0.111    0.889    45833   43378
1.55   0.114    0.886    46192   43663                               48000
1.60   0.118    0.882    46547   43947
1.65   0.121    0.879    46900   44229                               46000
1.70   0.124    0.876    47250   44508                                                                                 HCV
                                                                     44000
1.75   0.127    0.873    47598   44785                                                                                 LCV
1.80   0.130    0.870    47943   45061                               42000
1.85   0.134    0.866    48286   45334
1.90   0.137    0.863    48627   45606                                   1.50     1.60      1.70      1.80      1.90         2.00
                                                                                   a (number of hydrogen per carbon)


                                 Production de la chaleur - Chaudière                                                          19
2. Natural gas :

      CH 4   0.820
      Cn H m   0.030 ( with n  ...3... and m  ...8...)
       N 2   0.140
                                Calculate the HCV and the LCV
      CO2   0.010



  HCV  39710*0.820  69210*0.030  34639 kJ / mN
                                                3


  LCV  35790*0.820  63200*0.030  31244 kJ / mN
                                                3




                   Production de la chaleur - Chaudière         20
              Part 2 : Heat Production Equipment

I - ENERGY BALANCE AND EQUIPMENT EFFICIENCY
       1.1 Scheme of heat production equipment
       1.2 Input and output of energy
       1.3 Efficiency and Description of Losses
II - COMBUSTION CONTROL
III - ILLUSTRATION
       3.1 Gas Burners, Oil Burners, Coal-Fired Stokers
       3.2 Pulverised Fuel System
       3.3 Multiple Fuel Burners
       2.4 Boilers (fire tubes, water tubes)

IV - PRACTICAL PROBLEM



                          Production de la chaleur - Chaudière   21
                I. Energy balance and efficiency

1. Scheme of heat production equipment


                        Heat exchanger
       Burner                                                Flue Gas
Fuel




 Air


                           Load to be heated

                      Production de la chaleur - Chaudière              22
 Fuel
         - Mass Flow Rate : qC ( kg/s )
         - Calorific Value : HCV or LCV ( kJ/kg )

Air
         - Air required for combustion : V
                                          A,           ( kg of air/kg of fuel )
         - Specific : hA ( kJ/kg )

Flue Gas
         - Flue gas produced : VF, ( kg of flue gas/kg of fuel )
         - Specific enthalpy of flue gas : hF=cF.tF ( kJ/kg )
Load to be heated

        - Useful Thermal Power transferred to load : QUSE ( kW )

                     Production de la chaleur - Chaudière                    23
2. Input and Output of Energy


      - INPUT OF ENERGY

                  QC ( LCV      +    VA,    hA )               ( kJ/s or kW )
                                         
                  kg/s kJ/kg        kg/kg kJ/kg



      - OUTPUT OF ENERGY (in kW)

        . Useful Thermal Power ( Energy transferred to load ) : QUSE

        . Energy Loss in Flue Gases : qC VF, hF

        . Energy Loss from Walls (convection, radiation): QWALL = r qC LCV

        . Energy Loss from Unburn Fuel (proportion i) : i qC LCW



                         Production de la chaleur - Chaudière                    24
3. Efficiency of heat production equipment


         Input of Energy                         Output of Energy


       QC  LCV  VA, hA            QUSE  QCVF , hF  iQC LCV  rQC LCV


         Definition                 QUSE       QUSE
              of                            
         Efficiency                QAvailable QC LCV

         After calculation

     1   Losses  1  (e  i  r )            - i : unburn fuel loss
              VF , hF  VA, hA                 - e : loss in flue gases ( loss in stack )
    with e                                       - r : radiation ( convection ) heat loss
                      LCV

                           Production de la chaleur - Chaudière                         25
                       II. Combustion control
1. Optimisation of combustion - Criteria
     1st point :
                   The e loss is a function of

            . VF, and VA, : both depending on 
            . hF or temperature of flue gases tF : role of economiser !!!

                   Conclusion : e  if   or tF 

     2nd point :

                   Unburn loss i : i  if   with a limit ( See diagram )

      Criteria of combustion optimisation

                   1 -  minimum , but no unburn fuel in flue gases
                   2 - Temperature of flue gases tF minimum ( Attention !!! )


                          Production de la chaleur - Chaudière                  26
Combustion control -Diagram




    Production de la chaleur - Chaudière   27
Combustion control -Diagram




    Production de la chaleur - Chaudière   28
2. Parameters controlling the combustion
          . Volume fractions of CO2 , O2 on dry flue gas :

                [CO2]' or / and [O2]' in flue gas   ( excess of air )  e loss
                             Dry Sample of Flue Gas !
          . Control of unburn fuel :

                - [CO]' in flue gases : some rules

                       100 ppm for combustion of gas or fuel
                       400 ppm for combustion of coal

                - Unburn solid fuel :

                      . Carbon particles in flue gases :
                            Checking particles by "smoke pump" device
                      . Unburn fuel in ash :
                            Checking by chemical analysis
          . Flue gas temperature :

                e loss evaluation ( comparison between burners ... )
          . Vacuum in fire place :

                control of dirtiness of flue gas circuits
                            Production de la chaleur - Chaudière                   29
                 Corrosion acide
                           SO3  H2O  H2SO4
                           SO2  1 O2  H2O  H2SO4
                t fs             2

                                 Gasoil ; gaz naturel
                                 Fraction molaire dans gaz brûlés
              (t fs + ta0 )                                        à =1
       tp =                          [H2O] = 0.12       ; 0.19
                       2
                                     [H2O] = 0.114 ; 0.181         à  = 1.05
                                     psat      0.114 ; 0.181
                                     tsat       49°C       58°C
t a0
              Seuil de condensation : tp = tsat  tfs = 2 tsat - ta0

                               si ta0 = 0°C           tfs = 98°C ; 116°C

                            Production de la chaleur - Chaudière                30
                         Charge partielle
        P0


                                                                            Pu
                                               • Charge / Régime :
        P0*
                                                                       R=
                                                                            Pu*

                                               • Pertes fixes (parois) : @ kP0 *


                                               • Pertes proportionnelles : @ πRP0 *

                                               • Puissance utile :
                                                        Pu = P0 - kP0 - πRP *
                                                                           0
k P0*
                                Pu*    Pu

                                   R           • Rendement nominal :
                   0.5         1


                   Pu * P0 * - kP0 * - πRP0 *
              η* =      =                     = 1- k - π
                   P0 *          P0 *

                          Production de la chaleur - Chaudière                     31
                   Charge partielle
• Rendement à charge partielle :

                                Pu
                  η=
                       Pu + kP0 * + πRP0 *

             or   Pu = RPu * = Rη* P0 *

    On obtient finalement

                                               Rη*                η*
                                        η=                =
       FORMULE DE DITTRICH                 R + k (1 - R )          æ1     ö
                                                              1+ k ç -
                                                                   ç     1÷
                                                                          ÷
                                                                          ÷
                                                                   çR
                                                                   è      ø




                       Production de la chaleur - Chaudière               32
                                     Charge partielle
                             Rendement d'une chaudière à charge partielle
                                                     = 0.12
             0.9
                                                                                               0.86

            0.85


             0.8
                                                                                               0.84
                                                                                                      0.82
Rendement




            0.75                                                        k = 0.02
                                                                        k = 0.04
             0.7
                                                                        k = 0.06
            0.65


             0.6


            0.55


             0.5
                   0   0.1     0.2    0.3     0.4        0.5    0.6      0.7       0.8   0.9                 1

                                            Coefficient de charge (R)




                                      Production de la chaleur - Chaudière                                       33
III. Illustrations




        GAZ - AIR                       CONNECTION
        MIXTURE                          TO BURNER




     Gas burners

 Production de la chaleur - Chaudière                34
Liquid fuel burners




Production de la chaleur - Chaudière   35
                 Cas d’étude : Économiseur d’une chaudière
                                 Vapeur
                              3 bars, 135 °C

               Brûleur
   Gaz                                                      Cheminée
                                     Chaudière
  naturel                                                  [O2] = 0.03
                                                           Tf = 180 °C
          Air de
        combustion
            T = 20 °C                Eau
                                d’alimentation                  Economiseur



                                                 • Caractéristiques économiseur
• Caractéristiques chaudière
                                                 (AU) : 0.7 kW/K
  Puissance thermique : 10 MW                    Courant croisé « fluides non mélangés »
  Utilisation : 4000 h/an                        Durée de vie : 10 ans
  Prix du combustible : 0.25 €/m3N               Coût de l’installation : 30000 €
                                                 Entretien : 2000 €

                         Production de la chaleur - Chaudière                         36
PCI 



        Évaluation des conditions de fonctionnement de la chaudière

                                            Combustible

            • Composition : [CH4] = 0.81 [C2H6] = 0.05 [N2] = 0.11 [CO2] = 0.03 ...

            • Pouvoir calorifique :       PCS  12750  H 2   12620 CO   39710 CH 4 
                                          58950 C2 H 4   69210 C2 H 6   ...

                                                       PCS = 35626 kJ/m3N

                                             Pth
            • Débit nominal :     Qcomb               Qcomb = 0.287 m3N /s
                                            PCS

            • Consommation annuelle :              C = 0.287 x 3600 x 4000 = 4132800 m3N /an


            • Coût annuel combustible :      Fcombustible   f C        Fcombustible= 1033202 €/an




                                 Production de la chaleur - Chaudière                                 37
PCI 


                                        Combustion

                    Avant combustion                               Après combustion
              Combustible     1 Nm3       Nm3 O2       Nm3 CO2     Nm3 H2O Nm3 N2       Nm3 O2
                  [CH4]        0.81        1.620        0.810       1.620       -           -
                 [C2H6]        0.05        0.175        0.100       0.150       -           -
                   [N2]        0.11          -            -           -       0.110         -
                  [CO2]        0.03          -          0.030         -         -           -
                    Air          -           -            -           -       6.749         -
             Stoechiométrie      1         1.795        0.940       1.770     6.859         -
                Pratique                  1.795        0.940       1.770  6.75 +0.11 1.795(


                                        1.795    1
                              O2                     0.03           = 1.147
                                  '
        • Excès d ’air :
                                        6.75  1.05

        • Pouvoir comburivore:                    1.795
                                        Va ,                  Va, = 9.804 m3N d ’air / m3N de gaz
                                                    0.21
        • Pouvoir fumigène :      Vf ,  0.940 1.770   6.75  0.11 1.795   1

                                          Vf, = 10.826 m3N d ’air / m3N de gaz
        • Débit d’air :       Qair  QcombVa ,             Qair = 2.814 m3N /s = 3.638 kg/s
        • Débit de fumée : Q fumée  QcombV f ,            Qfumée = 3.107 m3N /s = 4.017 kg/s

                               Production de la chaleur - Chaudière                                    38

				
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posted:12/10/2012
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