Dulong formula

The Dulong'sche Association formula is a method for determining the calorific value (now calorific value ) on the basis of the elemental analysis of a fuel and an empirically determined formula.

Action

In fuels , in particular in the various coals , the following elements and components are contained, the mass fractions (about kg of fuel per kg) are added according to one:

${\displaystyle {\text{Kohlenstoff}}\,(c)+{\text{Wasserstoff}}\,(h)+{\text{Sauerstoff}}\,(o)+{\text{Schwefel}}\,(s)+{\text{Stickstoff}}\,(n)+{\text{Wasser}}\,(w)+{\text{Asche}}\,(a)=1}$

Based on the calorific values ​​of the individual components, Pierre Louis Dulong derived the association formula for the approximate determination of the calorific value in MJ / kg (also called the lower calorific value): ${\displaystyle H_{\mathrm {u} }}$

${\displaystyle H_{\mathrm {u} }=33{,}9\cdot c+121{,}4\cdot (h-o/8)+10{,}5\cdot s-2{,}44\cdot w}$

Werner Boie modified this formula using experimentally determined calorific values :

${\displaystyle H_{\mathrm {u} }=34{,}8\cdot c+93{,}9\cdot h-10{,}8\cdot o+10{,}5\cdot s+6{,}3\cdot n-2{,}44\cdot w}$

The determination of the lower calorific value is based on standard chemical conditions (25 ° C, 101.325 kPa) for fuel and air as well as the reaction products after they have cooled down, without taking into account the heat gain due to water vapor condensation . Considering the enthalpy of condensation of water vapor, the calculated calorific value or upper heat value to

${\displaystyle H_{\mathrm {o} }=H_{\mathrm {u} }+m_{\mathrm {w} }\cdot r_{\mathrm {o} }(\vartheta _{\mathrm {o} })}$

where represents the mass fraction of the water in the exhaust gas in relation to the fuel mass used. It results from the water content in the fuel and the water vapor produced by the combustion of the hydrogen content . ${\displaystyle m_{\mathrm {w} }}$ ${\displaystyle h}$

${\displaystyle m_{\mathrm {w} }=9\cdot h+w}$

The enthalpy of evaporation is also to be included. ${\displaystyle r_{\mathrm {o} }=2442\,\mathrm {kJ/kg} }$

The lower the water and hydrogen content of the fuel, the smaller the differences between calorific value and lower calorific value.

literature

• Beiz, W., Grote, K.-H: Pocket book for mechanical engineering , Springer-Verlag, Berlin, 1986.

Web links

• Characterization of substitute fuels with regard to their fuel properties (accessed on May 22, 2020)
• Determination of the energy efficiency in plants for thermal waste treatment (accessed on May 22, 2020)
• X-ray fluorescence analysis for the process-related analysis of reducing agents for the blast furnace process (accessed on May 22, 2020)
• Characterization of the energy potential of sewage sludge via the calorific value (accessed on May 22, 2020)