Heat Transfer with the sea

[Igor D]

Greetings from Brazil,

I am trying to build a spreadsheet to estimate how cold a fluid would be at the end of a pipe.

This non-insulated steel pipe (let`s say ~3000ft long), would be vertical in the sea, from surface to sea bed. At surface a pump would pump down, with a certain constant flow rate.

This is out of my expertise, so I`d like to have some guidance from the community.

Initial doubts, on how to work it (but please advise):

1. I am thinking about dividing this 3000ft long pipe into ten 300ft sections. So I`d solve them separately in a sequence, from top to bottom. Each 300ft section would have a constant sea temperature along it, for simplification.
2. Sea water gradient goes from ~80degF at surface to ~40degF at ~600ft, where it would remain, at least for simplification, at a constant temperature of 40degF until the sea bed.
3. I don`t know how to treat the sea here. I`d like to assume it never heats up (even very close to the pipe) for simplification. I think I could say it is a constant heat (cold) source. Please advice.
4. Because of friction, fluid would generate heat as it flows down (I`d be pumping sea water, for simplification, if any).

Doubts on how to iterate it:

T=to
static conditions before start pumping down

T=t1
1. solve the first 300ft section
- assume fluid enters this section at 80degF and after moving the entire 300ft, the final temperature is the heat generated by friction plus initial temperature minus heat lost to the pipe which is at sea temperature

2. do the same for all other 9 sections, using for each section the average sea temperature at depth as the initial temperature
- after all 9 sections have been calculated, this is the end of iteration 1 (end of T=t1)

T=t2
1. again, solve first 300ft section
- here I am lost, as fluid enters the top of the first section with the same temperature from surface (80degF), but how do I take into consideration the exit temperature already calculated on the previous iteration? If i don`t, this temperature will never change and I think the iteration converges and freezes.

2. solve the second 300ft section (and repeat for the other sections)
- initial temperature for each section is the exit temperature of first section at T=t1

Please advise the formulas to be used. I was reading INCROPERA chapter 8 about internal flow and think that maybe the constant surface temperature approach could work.

Thanks,

Igor

 

[Snickster]

I have checked the calculations and have following comments.

You calculation of overall U-value looks correct if the "h" values for inside and outside coefficients are correct. You used a h-value of 2000 W/m2-K for both inside and outside convection film coefficients. Data I have indicate values for turbulent flow is more like 700 btu/hr-ft2-F which is close to 4000 W/m2-K. However on the inside of the pipe the velocity is low at 1.76 ft/sec so possibly you are in or close to laminar flow so you may be correct using 2000 W/m2-K and on outside flowrate over pipe is unknown so again you may be right in your assumption of 2000 there also. For the "k-value of steel I see some references state as about 50 W/m-K so it is close to what you show.

The equation for delta T of the fluid in each segment should be based on the flowrate (10.2 kg/sec) not the total mass in each segment. The basic heat transfer equation is:

Q=m(Cp)(delta T)

If Q is in total heat transfer (say in BTU) of a given differential slice of mass m (say in pounds) involved in the heat transfer as it travels from the beginning of any given segment to the end of that segment, it can be proven that this is the same results as

*Q=*m(Cp)(delta T)

Where *Q is heat transfer rate (say in BTU/sec) of the entire segment and *m is mass flowrate (say in pounds/sec). In other words:

*Q/*m = Q/m = (Cp)(delta T)

Therefore

(delta T) = *Q/*m(Cp)

Sorry but I think in US imperial units.

I performed a calculation on your spreadsheet attached using mass flowrate instead of total mass of segment highlighted in red. It is basically same as you obtained in your Column "M" hidden cells except I started heat transfer in 0 to 20 meter segment using 30 C constant temperature of fluid, averaged sea water temperature outside of that segment, then determined heat transfer in that segment. Then dividing heat transfer in segment by Cp(*m) and subtracting from initial temperature of segment I determine resulting temperature at end of segment - then repeated calculation so on and so on.