It is a common question to wonder what is the minimum temperaure can be expected when blowing N2 across a hydrocarbon liquid, such as purging and drying lines during shutdown. This is especially of concern with propane, propylene, etc. The question first came to me with respect to specifying MDMT for rail cars, but I have seen other posts with respect to purging plant equipment and piping.
Although I think the theory is pretty easy to understand, I have noticed that some engineers under-estimate the power of evaporative cooling
=========THEORY=============
The theory is from energy balance as follows: Incoming N2 at 20degC blows through (mixing with) the liquid. The N2 will evaporate hydrocarbons which will remove heat causing the system to cool. The amount of hydrocarbons being evaporated decreases as the system temperature drops (lower vapor pressure) until eventually the enthalpy of the incoming N2 is balanced with the heat being removed by the evaporated hydrocarbons. No further temperature decrease occures. This is the minimum expected temperature.
By energy balance
FN2*Cp*(TN2-T) = FHC*HVap(T)
Also, the flow of N2 and hydrocarbon are related by DaltonÆs law of partial pressures
FHC/(FHC+FN2) = PHC(T)/P --> FHC=FN2*PHC(T)/(P-PHC(T))
On substitution for FHC, the flow term FN2 can also be eliminated giving
Cp*(TN2-T) = PHC(T)*HVap(T)/((P-PHC(T))
The resulting temperature, T, is found using the solver in Excel
Where:
T= final mixture temperature, degC, NOTE: this is the temperature of interest
FN2= mole flow N2, kmol/h
FHC= mole flow hydrocarbon, kmol/h
Cp= heat capacity of N2, assumed constant (29.1 KJ/KMOL-K) over the range of interest
TN2= incoming nitrogen temperature, degC
HVap(T)= heat of vaporization of the hydrocarbon, this is a function of temperature per DIPPR Heat of Vaporization equation over a wide range but a constant local value can be used as a simplification near the solution, KJ/KMOL
P= system pressure, kPaa
PHC(T)= partial pressure (vapor pressure) of hydrocarbon, a function of temperature per AntoineÆs equation, kPaa
========RESULTS============
Table 1. Expected lowest purging temperature with 20C N2 at 85KPaa (my local ambient pressure)
[tt]
T TB TC Hvap Vapor Press
Component (degC) (degC) (degC) (KJ/KMOL) (KPaa)