Methane is fed to a furnace at
25°C
and a molar flow rate of
100gmol/hr
. This fuel is subject to a combustion reaction in the furnace:​​
fuel+
ν
oxygen
O
2
→
ν
carbondioxide
CO
2
+
ν
water
H
2
O(v)
, ​where
ν
species
is the stoichiometric coefficient of the chemical species. ​An excess of oxygen entering at
150°C
is used for the combustion reaction, so that the conversion of the fuel is total. The value of the inlet molar flow rate of oxygen and nitrogen are taken equal to 1000 gmol/hr. We apply the energy balance for reacting systems using the heat of reaction method [1].
Here, we determine:
◼
  • 1. the heat duty in
    kJ/hr
    (labeled
    ▪
    Q
    in the process flowchart) for user-set values of exit temperature of the exhaust gases
    • or
    ◼
  • 2. the adiabatic flame temperature (i.e., for
    ▪
    Q
    =0
    ) labeled
    T
    ad
    in the process flowchart.
    • By specifying the exit temperature of the furnace (equal to 900 °C), the enthalpy balance at steady operation requires that excess heat (denoted by
    ▪
    Q
    ) from the exothermic reaction has to be removed. ​By specifying adiabatic operations, the heat released by the reaction raises the temperature of the exhaust gases (
    T
    ad
    =1238°C). ​You can change the inlet molar flow rate of nitrogen and observe its effect on both on
    ▪
    Q
    and
    T
    ad
    .​Results are benchmarked against their counterparts obtained using Aspen-Hysys.
    The adiabatic flame temperature (i.e., for
    ▪
    Q
    =0
    ) labeled
    T
    ad
    in the process flowchart.
    Heat of combustion in kJ/mol
    DH=-890.36;​​​​Qdot=stH20100H5+stCO2100H4+(ndot1-100stO2)H3+ndot0H2-ndot1H1-ndot0H0+100(DH);(*energybalanceforreactingsystemsusingtheheatofreactionmethod*)
    Reference state is gas 25°C and 1 bar
    H0=NIntegrate[29.010^-3+0.219910^-5x+0.572310^-8x^2-2.87110^-12x^3,{x,25,150}];H1=NIntegrate[29.1010^-3+1.15810^-5x-0.607610^-8x^2+1.31110^-12x^3,{x,25,150}];​​​​H2=Integrate[29.010^-3+0.219910^-5x+0.572310^-8x^2-2.87110^-12x^3,{x,25,Tad}];H3=Integrate[29.1010^-3+1.15810^-5x-0.607610^-8x^2+1.31110^-12x^3,{x,25,Tad}];​​H4=Integrate[36.1110^-3+4.23310^-5x-2.88710^-8x^2+7.46410^-12x^3,{x,25,Tad}];​​H5=Integrate[33.4610^-3+0.68810^-5x+0.760410^-8x^2-3.59310^-12x^3,{x,25,Tad}]+44.01;(*waterheatofvaporisationis44.01kJ/mol*)
    Stochiometric coefficients
    stH20=2;stCO2=1;stO2=2;
    Inlet flow rates for O2 and N2
    ndot1=1000;​​ndot0=1000;
    sol=FindRoot[stH20100H5+stCO2100H4+(ndot1-100stO2)H3+ndot0H2-ndot1H1-ndot0H0+100(DH)0,{Tad,3000,4000}]
    Out[]=
    {Tad1238.36}
    In[]:=
    GraphicsGreen,Opacity[0.4],EdgeForm[{Black,Thick}],Rectangle[{0,0},{2,2}],Opacity[1],Style[Text["Furnace",{1,1},{0,0}],Bold,28,Black],Opacity[1],Thickness[0.01],Arrowheads[Large],Black,Arrow[{{-1.5,1.75},{0,1.75}}],Style[Text["Methane",{-1.0,1.65},{0,0}],14,Black],Style[Text["100 moles/hr 25°C",{-1.0,1.45},{0,0}],14,Black],Red,Arrow[{{-1.5,0.65},{0,0.65}}],Style[Text[Row[{"pure oxygen: ",NumberForm[ndot1,{4,1}]," moles/hr"}],{-1.5,0.45},{0,0}],14,Red],Style[Text[Row[{"pure nitrogen: ",NumberForm[ndot0,{4,1}]," moles/hr"}],{-1.5,0.25},{0,0}],14,Red],Style[Text["150°C",{-1.0,0.05},{0,0}],14,Red],Blue,Arrow[{{2,1.35},{3,1.35}}],​​Style[Text["exhaust gases",{2.05,1.25},{-1,0}],14,Blue],Style[Text[Row[{"oxygen: ",NumberForm[(ndot1-100stO2),{4,1}]," moles/hr"}],{2.05,1.05},{-1,0}],14,Blue],Style[Text[Row[{"nitrogen: ",NumberForm[(ndot0),{4,1}]," moles/hr"}],{2.05,0.85},{-1,0}],14,Blue],Style[Text[Row[{"water: ",NumberForm[100stH20,{4,1}]," moles/hr"}],{2.05,0.65},{-1,0}],14,Blue],Style[Text[Row[{"carbon dioxide: ",NumberForm[100stCO2,{4,1}]," moles/hr"}],{2.05,0.45},{-1,0}],14,Blue],​​Style[Text[Row[{
    Style["T",Italic]
    "ad"
    ," = ",NumberForm[Tad/.sol,{5,1}],"°C"}],{2.05,0.25},{-1,0}],14,Blue],Gray,Dashed,Arrowheads[Large],Thickness[0.015],Arrow[{{1.6,1.5},{2.3,1.5},{1.6,1.8},{2.6,1.8}}],StyleTextRow
    •
    Style["Q",Italic]
    ," = ",NumberForm[0,{2,1}]," kJ/hr",{2.7,1.804},{-1,0},18,Black,Bold,BackgroundLightGray,AspectRatio1.2,ImageSize{500,380}
    Out[]=
    hysys output : see the temperature of the exit vapor stream V
    ​​
    The heat duty in
    kJ/hr
    (labeled
    ▪
    Q
    in the process flowchart) for user-set values of exit temperature of the exhaust gases
    In[]:=
    Clear[Qdot];
    In[]:=
    Te=900;H0=NIntegrate[29.010^-3+0.219910^-5x+0.572310^-8x^2-2.87110^-12x^3,{x,25,150}];H1=NIntegrate[29.1010^-3+1.15810^-5x-0.607610^-8x^2+1.31110^-12x^3,{x,25,150}];​​H2=Integrate[29.010^-3+0.219910^-5x+0.572310^-8x^2-2.87110^-12x^3,{x,25,Te}];​​H3=NIntegrate[29.1010^-3+1.15810^-5x-0.607610^-8x^2+1.31110^-12x^3,{x,25,Te}];​​H4=NIntegrate[36.1110^-3+4.23310^-5x-2.88710^-8x^2+7.46410^-12x^3,{x,25,Te}];​​H5=NIntegrate[33.4610^-3+0.68810^-5x+0.760410^-8x^2-3.59310^-12x^3,{x,25,Te}]+44.01;​​​​Qdot=stH20100H5+stCO2100H4+(ndot1-100stO2)H3+ndot0H2-ndot1H1-ndot0H0+100(DH)(*inkJ/hr*)
    Out[]=
    -26394.5
    In[]:=
    GraphicsOrange,Opacity[0.4],EdgeForm[{Black,Thick}],Rectangle[{0,0},{2,2}],Opacity[1],Style[Text["Furnace",{1,1},{0,0}],Bold,16,Black],Opacity[1],Thickness[0.01],Arrowheads[Large],Black,Arrow[{{-1.5,1.75},{0,1.75}}],Style[Text["Methane",{-1.0,1.65},{0,0}],14,Black],Style[Text["100 moles/hr 25°C",{-1.0,1.45},{0,0}],14,Black],Red,Arrow[{{-1.5,0.65},{0,0.65}}],Style[Text[Row[{"pure oxygen: ",NumberForm[ndot1,{4,1}]," moles/hr"}],{-1.5,0.45},{0,0}],14,Red],Style[Text[Row[{"pure nitrogen: ",NumberForm[ndot0,{4,1}]," moles/hr"}],{-1.5,0.25},{0,0}],14,Red],Style[Text["150°C",{-1.0,0.05},{0,0}],14,Red],Blue,Arrow[{{2,1.35},{3,1.35}}],​​Style[Text["exhaust gases",{2.05,1.25},{-1,0}],14,Blue],Style[Text[Row[{"oxygen: ",NumberForm[(ndot1-100stO2),{4,1}]," moles/hr"}],{2.05,1.05},{-1,0}],14,Blue],Style[Text[Row[{"nitrogen: ",NumberForm[(ndot0),{4,1}]," moles/hr"}],{2.05,0.85},{-1,0}],14,Blue],​​Style[Text[Row[{"water: ",NumberForm[100stH20,{4,1}]," moles/hr"}],{2.05,0.65},{-1,0}],14,Blue],Style[Text[Row[{"carbon dioxide: ",NumberForm[100stCO2,{4,1}]," moles/hr"}],{2.05,0.45},{-1,0}],14,Blue],​​Style[Text[Row[{
    Style["T",Italic]
    "exit"
    ," = ",NumberForm[Te,{5,1}],"°C"}],{2.05,0.25},{-1,0}],14,Blue],Gray,Dashed,Arrowheads[Large],Thickness[0.015],Arrow[{{1.6,1.5},{2.3,1.5},{1.6,1.8},{2.6,1.8}}],StyleTextRow
    •
    Style["Q",Italic]
    ," = ",NumberForm[-Qdot,{8,1}]," kJ/hr",{2.7,1.804},{-1,0},18,Black,Bold,BackgroundLightGray,AspectRatio1.2,ImageSize{500,380}
    Out[]=
    hysys output : see the Heat Flow result

    References

    [1] R. M. Felder and R. W. Rousseau, Elementary Principles of Chemical Processes, 3rd ed., New York: John Wiley & Sons, 2004.

    CITE THIS NOTEBOOK

    Combustion of Methane in a furnace using Wolfram & Aspen-Hysys​
    by Housam Binous and Ahmed Bellagi
    Wolfram Community, STAFF PICKS, December 4, 2025
    ​https://community.wolfram.com/groups/-/m/t/3585342