Calculation of a waste-gas calorific value
The typical vent-gas analysis from the recycle stream in an oxyhydrochlorination process for the production of dichloroethane (DCE) (British patent BP 1,524,449) is given below, percentages on volume basis.
O _{2} 7.96, \quad CO _{2}+ N _{2} 87.6, \quad CO 1.79, \quad C _{2} H _{4} \quad 1.99, \quad C _{2} H _{6} \quad 0.1, \quad \text { DCE } 0.54Estimate the vent gas calorific value.
Component calorific values, from Perry and Chilton (1973)
CO 67.6 kcal/mol = 283 kJ/mol
C _{2} H _{4} 372.8 = 1560.9
C _{2} H _{6} 337.2 = 1411.9
The value for DCE can be estimated from the heats of formation. Combustion reaction:
C _{2} H _{4} Cl _{2}( g )+2 \frac{1}{2} O _{2}( g ) \rightarrow 2 CO _{2}( g )+ H _{2} O ( g )+2 HCl ( g )
\Delta H_{f}^{\circ} from Appendix D
CO _{2}=-393.8 kJ / molH _{2} O =-242.0
HCl = -92.4
DCE = -130.0
\begin{aligned}\Delta H_{c}^{\circ} &=\sum \Delta H_{f}^{\circ} \text { products }-\sum \Delta H_{f}^{\circ} \text { reactants } \\&=[2(-393.8)-242.0+2(-92.4)]-[-130.0] \\&=-1084.4 kJ\end{aligned}
Estimation of vent gas c.v., basis 100 mols.
| Component | mols/100 mols | Calorific value (kJ/mol) | Heating value | ||
| CO | 1.79 | x | 283.0 | = | 506.6 |
| C _{2} H _{4} | 1.99 | 1560.9 | 3106.2 | ||
| C _{2} H _{6} | 0.1 | 1411.9 | 141.2 | ||
| DCE | 0.54 | 1084.4 | 585.7 | ||
| Total | 4339.7 | ||||
\begin{aligned}\text { Calorific value of vent gas } &=\frac{4339.7}{100}=43.4 kJ / mol \\&=\frac{43.4}{22.4} \times 10^{3}=1938 kJ / m ^{3}\left(52 Btu / ft ^{3}\right) \text { at } 1 bar , 0^{\circ} C\end{aligned}
Barely worth recovery, but if the gas has to be burnt to avoid pollution it could be used in an incinerator such as that shown in Figure 3.16, giving a useful steam production to offset the cost of disposal.
