Pumping down coil in SAGD

[Rostamina]

[highlight #729FCF][/highlight]

Hey I'm looking to solve a pumping problem: A downhole tool needs to be cooled by pumping water from surface through 73mm coil tubing in 7 inch casing. The tool operates with 180oC max (downhole condition), we want to cool it to 70oC, pump through coil tubing where the tool is attached at the end, with water coming in at 10oC. We want to know what pump rate will be required. Flow will be turbulent. Material is carbon steel, with coil thickness of 3.96mm.

I just need someone to point me in the right direction for this heat transfer problem. So far I've used q= UA dT = mC dT, but someone told me i need to use the log mean temperature change, I'm a bit confused so if anyone can help point me in the right direction I would appreciate it.

 

[Rostamina]

I would like to reiterate:

The wellbore temperature is 180oC at the bottom, the water pumped is at 10oC and we want to cool the tool to 70oC. Heat transfer will be between water and coil tubing (convection) then from the coil to the water on the annulus (outside) of the coil (also convection). We can assume a well length of 1000m.