Dear All,
I am working on a NGL storage proj which is a part of frac train debottlenecking proj where it was suggested that the 140 m^3/hr NGL feed (Dethanized liq) should bypass frac train and be stored in the existing spherical storage (Dia =16.69m, 690 kPag design pressure) during shutdown/commissioning time of frac train.
The vapor pressure of NGL that enters the storage is 517 kPaA @ 14 deg C, whereas the design pressure and PSV set P =690 kPag (780 kPaA). Tank is uninsulated and during the time of bypass the ambient air temp may go up to 31.7 deg C on a certain day.
I simulated the stored NGL temperature as 26 deg C when its vapor pressure will reach 90% of set pressure and PSV may start to lift at that point. After reaching here, I took the unsteady state heat transfer calculation route to solve this.
M*Cp*dT/dt = U*A*(Tair -T) ..(neglecting flow out of the sphere for being conservative, i.e. 200 m^3/hr)
M= stored mass at 90% full vessel, density =540 kg/m^3.
Cp = average mass cp, based on 14 deg C and 26 deg C.
T = storage temperature at time "t" , deg C
t = time, hr=?
U = 26.7 W/m^2-Deg C (4.7 BTU/hr-ft^2-deg F), based on the Aerstin and Street article at wind velocity of 10 mph. for uninsulated tank. I think I can rigorously resolve U from Kothari article as well to double check value.
Volume of liquid at 90% vessel height is 2364 m^3.
The equation above is conservative as I didn't include NGL entering and leaving the storage. In my opinion, this vessel should have an insulation cuz if the mass M is small, then it will reach PCV set pressure before it lifts PSV in less than an hour. The liquid is pumped out at 200 m^3/hr.
Question1: MCp dT/dt = U*A*(Tair-T) - M(in)*Cp*(T-Tngl)-M(out)*H, where H is enthalpy of liquid pumped out at different T, but it doesn't change a lot, can I take it as constant?
if the above equation in question 1 is set up right to include all heat sources and could you guide me how to solve them or a simpler alternate solution.
All criticism, help and advise are welcome. Thanks in advance.