Calculate coal consumption of coal-fired boiler from air flow

It is not always easy to determine the coal consumption of a coal-fired boiler which is generally used at power plants; therefore, different methods are used which are compared to determine the most likely consumption.

One method to determine the coal consumption is to use the air flow and the oxygen content in the flue gas. If the coal composition is known, the flue gas composition can be determined and from the oxygen in the flue gas the coal flow can be calculated.

This method will be useful to:

  • Confirm the measured coal consumption
  • Calculate the carbon dioxide (CO2) and sulphur dioxide (SO2) emissions.

Coal combustion

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Coal-fired boiler combustion

Coal consists of C, H2, O2, N2, S, H2O and air consists of O2, N2 and Ar.

The following combustion reactions take place in the boiler:

 
 
 
 

Symbols and constants

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The following is a list of symbols which will be used:

  •  ,  ,  ,  ,   = mass fractions of C, H2, O2, N2 and S in the coal according to the ultimate analysis based on air dry (ad) coal.
  •   = mass fraction of total coal moisture based on air dry (ad) coal. Total moisture is the sum of superficial moisture and inherent moisture. However, normally the mass fraction of superficial moisture ( ) is based on received (ar) coal and the inherent moisture mass fraction ( ) is based on an air dry (ad) coal basis. The total moisture can be written in terms of   and   as follows:
        (This formula is derived later in the article.)
  •  ,  ,  ,  ,  ,   = number of moles of components in coal ending up in the boiler (kmol/h). Note that both inherent moisture and superficial moisture ends up in the boiler.
  •   = mass flow of air dry coal flow which is completely combusted (kg/h)
  •   = air flow (kmol/h). Take note that this is the total air flow to the boiler. It includes both the measured air flow and the air leaking into the fire box.
  •   = mol fraction of water vapour in air (due to air humidity)
  •   = conversion of component i during combustion. For example, about 90% of S will convert to SO2. Thus,  . Very little N2 will convert to NO2. Thus,   will be very small.

Air composition

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The following air composition is assumed:

Component Dry air
(mol frac)
Humid air
(mol frac)
N2 0.781 (1-wa) × 0.781
O2 0.21 (1-wa) × 0.21
Ar 0.009 (1-wa) × 0.009
H2O 0 wa
Total 1.000 1.000

If another composition needs to be used, only change the 0.781, 0.21 and 0.009 constants throughout the document.

Number of moles before combustion

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The following table shows the number of moles of each component before combustion:

Component Name MW (kg/kmol) Moles of component before combustion
Air Air (humid)  
Airdry Air dry  
C Carbon 12  
H2 Hydrogen 2  
O2 Oxygen 32  
N2 Nitrogen 28  
S Sulphur 32  
Ar Argon 40  
H2O Water 18  

Component balance before and after combustion

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The following table shows the number of moles before and after combusion of the coal with air:

Short Component MW
kg/kmol
Reaction Moles before Change Moles after combustion
C carbon 12        
H2 hydrogen 2        
O2 oxygen 32 All combustion reactions      
N2 nitrogen 28        
S sulphur 32        
CO2 carbon dioxide 44        
H2O water 18        
NO2 nitrogen dioxide 46        
SO2 sulphur dioxide 64        
Ar argon 40 n/a      

Develop formula

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Total flue gas

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The total flue gas is the sum of all the products and all unreacted components, except sulphur (S) which will not leave with the flue gas but will leave with the ash.

 

 
 

Substitute the mol fractions ni with equations in table above:

 

 
 
 
 
 

Where   and   is in kmol/h,   in kg/h,   in mass fraction,   in mol fraction,   in fraction

Oxygen in flue gas

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The oxygen in the flue gas can be written as follows:

 

 

Substitute the mol fractions ni with equations in table above:


 


 
 

Where   and   is in kmol/h,   in kg/h,   in mass fraction,   in mol fraction,   in fraction

% oxygen in flue gas

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The percentage oxygen in flue gas is given by the following formula:

 


If substituting above formulas into this, then:

   


Get "Coal" on the left and "Air" on the right:


   


 

 


 

 


Taking the right hand side separately:


 


 


 


Combining the two equations again:

Coal consumption (total combustion)

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Thus, the total air dry coal which underwent total combustion is:

 

Where:

  •   is air-dry coal in kg/h. This is the coal which fully combusted and excludes the portion of the coal which leaves with the ash. If the CO2 and SO2 emissions are calculated, this value can use used as is. However, if one wants to compare this calculated value with the actual coal received, on should take into consideration the uncombusted coal in the ash.
  •   is the humid air flow in kmol/h with a dry air composition of 21 mol% oxygen, 78.1 mol% nitrogen and 0.9% argon.
  •  

Individual components in flue gas

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The individual components in the flue gas is then the following (kmol/h):

 
 
 
 
 
 
 
 
 
 
 
 
 
 

Emissions

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The CO2, SO2 and NO2 emissions can be calculated as follows:

 
 
 

Calculating water vapour in air from humidity

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If:

  •   = Ambient temperature in °C
  •   = Relative humidity as a fraction between 0 and 1
  •   = Atmospheric pressure in kPa
  •   = Vapour pressure (at ambient temperature) in kPa
  •   = Mol (volume) fraction of water in air

The maximum amount of water vapour in air is:

 

The actual mol fraction of water in air is:

 

The following Buck equation is a very good approximation of the vapour pressure of water below 100°C:

 

Thus, the mol fraction of water in air is:

 

Total coal moisture in terms of superficial and inherent moisture

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The superficial moisture fraction (ms) is based on as received (AR) coal and the inherent moisture fraction (mi) is based on air dry (AD) coal. However, the total moisture (m), can be expressed in terms of ms and mi on an air dry basis as follows.

 

If:

 

Then:

 
 

Also see

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  • Mass flow rate of coal consumption and theoretical air mass
  • Application of mass and energy balances to determine coal, air required and flue gas flow rates in a power plant], Katende, Landry Mbangu, 2019
  • Calculation of combustion air required for burning solid fuels (coal / biomass / solid waste) and analysis of flue gas composition], Lizica Simona Paraschiv, Alexandru Serban, Spiru Paraschiv, 6 September 2019