E3.16 Adiabatic Saturation

Example 3.16: Combustion gases containing 30% water vapor, 8% CO₂, 5% O₂, and 57% N₂ are quenched from 2000 °F to the adiabatic saturation temperature. Water at 70 °F is used to quench stream. Determine the exit temperature of the quenched gases; amount of water theoretically required. The following data apply:

Solution: 1 hour of operation

Guess final temperature of quenched gases, T = 640 °R

Heat lost during cooling of combustion gases, q₁

q₁ = nC_p(T_a - T) = 1.578´10⁶ Btu

Read vapor pressure of water, p_s = 7.511 psi

Mole fraction of water = x_s = 7.511/14.696 = 0.511

Mole ratio of water, X_s= x_s/(1 - x_s) = 1.045

Mole of water in outgoing gas, n_w = X_s(1 - x_wi)n = 73.176 lbmol

Mass of water added, m_w = (n_w - x_win)´18 = 777.17 lb

Find enthalpy of water, h_g = 1138.2 Btu/lb

Heat gained by water, q₂ = m_w(h - h_f) = 8.55´10⁵ Btu

We can see that heat lost during cooling of combustion of gases is not equal to heat gained by water, we will guess again for final temperature of quenched gases.

Final temperature = 188 °F

Mass of water added = 1421 lb