Desuperheater Water Injection Rate

A desuperheating station is a mass balance and an energy balance solved together, and nothing more exotic. Steam comes in at $\dot{m}_1$ and $h_1$, spray water joins it at $\dot{m}_w$ and $h_w$, and what leaves is the sum of the two masses carrying the sum of the two energies. Set the mixed enthalpy to the target $h_2$, rearrange, and the water you need is $\dot{m}_w = \dot{m}_1 (h_1 - h_2)/(h_2 - h_w)$. The numerator is the heat you have to take out per kilogram of steam and the denominator is how much heat each kilogram of water can absorb before it too reaches the target, so the answer is one divided by the other. A worked case: 10 kg/s of steam at 3,300 kJ/kg to be brought to 2,900 kJ/kg with feedwater at 700 kJ/kg needs 10 × 400/2,200 = 1.82 kg/s of spray, which is 18% more mass leaving the station than entered it.

Enthalpies do the work here, not temperatures, and that is deliberate. Specific heat is not constant across a desuperheating range, and the outlet may end up anywhere from heavily superheated to saturated, so a $mc\Delta T$ balance quietly drifts while an enthalpy balance stays exact. Three practical notes. Everything at the outlet is at the DOWNSTREAM pressure, so if the station also drops pressure, read $h_2$ at the pressure the steam leaves at rather than the pressure it arrived at. Do not aim at saturation: spray control needs superheat left over to prove the water has all evaporated, and 10 to 15 degrees is the usual minimum, because a target on the saturation line means any overshoot puts liquid water into a hot pipe. And the extra mass is real, so the downstream line, the safety valve capacity and the process user all see more steam than the upstream meter reads, which is a good thing when the water is treated feedwater and a very bad thing when it is not, since every dissolved solid in that spray goes straight into the header.