Mean specific heat of flue gas 2

[GarethJones]

Calculation of dry flue gas loss to the procedures of ASME PTC 4.1 requires the calculation of the mean specific heat of the flue gas between the reference temperature and the final gas temperature. Values of the instantaneous specific heat at these two temperatures are obtained from a nomograph.

The question is, how does one calculate the mean specific heat using this data? I think I am correct in assuming that it is not the average of the instantaneous values.

 

[25362]

The enthalpy of the gas is the product of the mass, the mean Cp and the temperature difference. Thus, if you have the Cp's for the two temperatures under consideration, the values for 1 kg flue gas could be obtained from:

Enthalpy=Cp_mean(T₂-T₁)=Cp₂T₂-Cp₁T₁​

==>

Cp_mean=[Cp₂T₂-Cp₁T₁]/(T₂-T₁)​

I believe I understood your question and hopefully answered correctly.

 

[athomas236]

I assume you are asking for the correlations with numbers so you can make these calcs, will check my notes and get back to you
athomas236

 

[bhupesh241]

I need to calculate the mean specific heat capacity of a flue gas.Problem is, the flue gas is a product of oxy-fuel combustion with CO2 as a major component and rest being H20.
The temperature of the combustion system varies from 1000 to 1400°c and pressure from atmospheric to 16 bar.
Can you suggest me how I can calculate it.
Also, i need to calculate the adiabatic flame temperature for the same system when concentration of oxygen is varied from 21 to 40% . vol.

 

[davefitz]

bhupesh241:
As far as computing the sensible heat or mean specifc heat of the flue gas for high gas temperatures, such as adiabatic flame temperature- at high temps over 2200F there is s significant departure from linearity due to dissassociation, ionization and generation of new species- the best method is to obtain a chart of sensible heat as a function of temperature for typical gas mixtures ( usually as a function of % H20) froma chemical engineering handbook.

 

[25362]

If your combustion is done with air the major contributor by volume to your product gases is nitrogen, not CO2.

The specific heat values (cal/g.K) aren't much affected by a pressure rise from 1 bar to 16 bar. For CO2 the drop would be less than 0.5 %, and less than 1% for nitrogen and H2O. Thus using the Cp values for 1 bar wouldn't introduce appreciable errors. Perry VI might serve as a good source of information.

As for the estimation of the adiabatic temperature you may visit thread610-50077 as a reference.

The effect of using oxygen-enriched air would be a reduction in the volume of combustion gases by having less nitrogen, thus increasing the adiabatic theoretical temperature that would otherwise be obtained with air.

A quick approximation for this temperature could be obtained from

t=[P+Q1+Q2+140(CO2)+200(H2O)+70(N2)]/[0.649(CO2)+0.561(H2O)+0.389(N2)

where,

P is the lower calorific value of the fuel, kcal/m³ at normal conditions
Q1,Q2, the enthalpy of the air and fuel entering the combustion process
CO2, H2O, N2 are the volumes of product gases of combustion in m³ at normal conditions, as obtained from a stoichiometric equation when burning 1 normal cubic meter of gas.

For example, when burning 1 normal cubic meter of a refinery gas with a composition C_1.6H_4.8 (P=12420 kcal/normal m³) with air (21% oxygen), the resulting volume of product gases at normal conditions: 1.6 CO2; 2.4 H2O; 10.5 N2.

Thus, the estimated adiabatic temperature of combustion, assuming Q1=Q2=0, would be:

t=(12420+0+0+140x1.6+200x2.4+70x10.5)/(0.649x1.6)+0.561x2.4+0389x10.5)= 2135^oC

I leave to you the temperature estimation for a 40% oxygen-rich air.

A Rosin-Fehling H-T graph with 0% xs air would tell us that the corrected "maximum" for 12420/14.5=857 kcal/Nm³ of combustion gases would be 1980^oC.

This means that the cooling effect resulting from the endothermic dissociation of CO2 and H2O brings about a drop of ~7.3% in the initially estimated temperature value.

As an aside, please note that the "corrected" maximum for burning hydrocarbon fuels moves somewhat to lower-than-theoretical air.

Besides, the same adiabatic temperature, +/- 10^oC, is obtained when burning refinery gas or fuel oil, provided one uses equal xs air percentages!

 

[davefitz]

for dry air, CO, CO2, O2, N2 the heat capacity is around 0.22-0.24, but for H2O vapor the Cp is about 0.48, so the percent H2o by weight has the largest impact on fluegas sensible heat or heat capacity . Most simplified curves of sensible are vs temp and vs % H2O content.

Formation of NO is significant at 1640 K. Disassociation of O2 to O is also significant at 1640K. N2 dissassociates to N at about 3500 K.

 

[25362]

Please note that in industrial heaters adiabatic temperatures cannot be attained because of heat radiated in statu nascendi to the cooler surfaces therein. A factor that cools the combustion products. Heat losses through the walls of the combustion chamber as well as excess air are additional factors that contribute to bring down the flame temperature below the adiabatic estimated maximum.

The degree of molecular dissociation of gases due to temperature is also a function of their partial pressure. As an example, at 2000^oC and 0.1 ata. partial pressures, water decomposes 4.3% by volume, and CO2 12.5% by volume. At 0.2 ata. partial pressures the figures are 3.4 and 10%, respectively. To add to what Davefitz has said about decomposition: at 3000^oC and 0.04 ata. partial pressure, these gases decompose 70.6 and 94.9% by volume, respectively.

As for the published Cp (kcal/kg) values at 1000^oC, and 1500^oC of some relevant gases:

O2: 0.268/0.278
N2: 0.29/0.303
CO2: 0.309/0.322
H2O: 0.59/0.65
H2: 3.71/3.96
CO: 0.294/0.306
SO2: 0.207/0.212
air: 0.283/0.295

For a theoretical complete combustion of a fuel oil without excess air, an estimated flue gas composition would roughly be: 74N2+14CO2+12H2O. The published Cp of such a flue gas at 500^oC: 0.297, and at 1000^oC: 0.328.

 

[TD2K]

Back to the original question, I have an old second year (or so) textbook with 'mean' specific heats of various components of flue gas. Essentially, you looked up the flue gas temperature and read off the 'mean' Cp for that temperature and then multiplied the mass flow and by the flue gas temperature less your base case temperature to get the enthalphy loss of that component.

The heat capacities for the various components were a quadratic eqn of the form Cp = A + BT + BT^2 where T was the temperature and A, B and C were constants. That gives you the Cp at a given temperature but doesn't cover the heat balance case where your base temperature is say 60F but your stack temperature is 450F. I 'assumed' (don't recall if I ever did any checks of this) that the 'mean' Cp had been calculated to simply avoided the need to integrate the Cp equation over range of temperatures to get the total heat loss. I'll have to dig that book out.