Calorific value and air from ultimate analysis

Formulas

Dulong's formula (mass fractions):

$$HCV = 33\,800\,C + 144\,000\left(H - \frac{O}{8}\right) + 9\,270\,S\ \ \text{kJ/kg}$$

Here $C = 0.82$, $H = 0.12$, $O = 0.04$, $S = 0.01$.

(a) Higher calorific value

$$\begin{aligned} H - \frac{O}{8} &= 0.12 - 0.005 = 0.115 \\ HCV &= 33\,800(0.82) + 144\,000(0.115) + 9\,270(0.01) \\ &= 27\,716 + 16\,560 + 92.7 \\ &= 44\,369\ \text{kJ/kg} \end{aligned}$$

(b) Lower calorific value

Each kg of hydrogen forms 9 kg of steam, whose latent heat is not recovered.

$$\begin{aligned} LCV &= HCV - 9H\,(2442) \\ &= 44\,369 - 9(0.12)(2442) \\ &= 44\,369 - 2\,637 \\ &= 41\,731\ \text{kJ/kg} \end{aligned}$$

(c) Minimum air

The oxygen needed per kg of fuel is $\frac{8}{3}C + 8\left(H - \frac{O}{8}\right) + S$. Air contains 23 % O₂ by mass, so:

$$\begin{aligned} A_{min} &= \frac{100}{23}\left[\frac{8}{3}C + 8\left(H-\frac{O}{8}\right) + S\right] \\ &= 4.348\,[2.187 + 0.920 + 0.010] \\ &= 4.348 \times 3.117 = 13.55\ \text{kg air/kg fuel} \end{aligned}$$

Here $\tfrac{8}{3}(0.82) = 2.187$ kg of O₂ is for carbon (C + O₂ → CO₂ needs 32/12 kg O₂ per kg C), $8(0.115) = 0.920$ kg is for hydrogen, and $1 \times 0.01$ kg is for sulphur.

Answer: HCV = 44 370 kJ/kg (about 44.4 MJ/kg); LCV = 41 730 kJ/kg (about 41.7 MJ/kg); minimum air = 13.55 kg per kg of fuel.