Heat transfer to/from burried oil pipleline 1

[friedmanroy]

Hello
Please, your help:

I have real problem of heat tranfer of oil line, I have to solve:
Gasoline flows through a steel pipe line that is burried in the ground. I need to know the exit temp of gasoline in the exit from the pipe.
I know:
Properties of Gasoline
Cp = 2.22 Kj/Kg K
Density = 740 kg/m[sup]3[/sup]
k : 0.15 W/mK
Viscosity= 0.88 cSt (0.88X 10[sup]-6[/sup] m[sup]2[/sup]/sec)
µ = 6.512·10[sup]-4[/sup] kg/m s
Flowrate = 500 m[sup]3[/sup]/hour=100 kg/sec
V (velocity)=0.76 m/Sec
T inlet of the Gasoline to the pipe = 13 deg C
T of ground= 16 deg C

Pipe properties:
Material : Carbon Steel
Outside Diameter: 20 inch= 0.508 m
Inside Diameter: 19 inch=0.4826 m
k=54 W/mK
Density=7833 kg/m[sup]3[/sup] (of the carbon steel)
Length of pipeline=2730 meter

How do I solve this?
1) Find Pr number for gasoline:
Pr=µ Cp/k
Pr=(6.512·10[sup]-4[/sup]·2220/0.15)=9.63
Re= (0.76 ·0.4826/0.88·10[sup]-6[/sup])=416,790
Nu=0.029 Re[sup]0.8[/sup] Pr [sup]0.43[/sup]=2406
Nu=h·D/k
h=Nu k/D = 2400 ·0.15 /0.4826 = 750 W/m[sup]2[/sup]K ( is that for the Gasoline only?)

Now, I think I have to use the follwing, but I am not sure how:
U=(1/h[sub]i[/sub]+ r[sub]i[/sub]/k ln(r[sub]o[/sub]/r[sub]i[/sub])+(r[sub]i[/sub]/r[sub]o[/sub]·1/h[sub]o[/sub])[sup]-1[/sup]

How do I calculate the the conduction of the ground/soil ? (lets assume that k= 0.5 W/mK for the soil)
Is the method diffrent if the soil(ground) is hotter or colder than the inlet temp of Gasoline?
Please help me find the outlet temp of Gasoline...

Thanks alot
Roy

 

[BigInch]

Sorry, but this appears to be an exercise in BS math. Don't kid yourself. Your inlet temperature is 13C. Ground temp is 16. From that data you can pretty much be sure that the maximum temperature you will reach is 16C. I suggest to you that first, you don't need to know the inlet temperature to within an accuracy of 3C. If you can calculate this, you won't be able to do so within an accuracy of 3C (too many unknowns), so useless, unless you just like to look at decimal places in Excel.

If the gasoline is warmer than the soil, then the gasoline will probably cool down in the pipe, right. If colder than the soil, it will warm up. That's pretty elementary physics logic. Pr / Re / Nu / h calculates the heat transfer from the gasoline in the film next to the pipe wall. You will add that to the heat transfer coefficient of any other materials involved in the transfer; the pipe wall, insulation if any and soil.

In any case you are using the customary method. EXCEPT you don't calculate the ground's thermal coefficient of conduction. You must measure that in the field. Thermal conductivity of soil can vary from 0.15W/m-K, for an extremely dry sand, to nearly 1.8 for a water saturated soil. As you might guess, some digging is in order. The effective conductivity of the soil will also vary with burial depth of the pipeline; see "shape factor".

Keep on studying, but for now pick a number (13 OR 16C) according to whatever temperature you need to use to make your next and ultimate answer conservative. I doubt you need or can calculate anything better, especially until you know the thermal conductivity of the soil.

 

[BigInch]

We usually try to only answer questions, rather than actually do somebody else's work for free, so
Here's what you need to look at,
TM 5-852-5/AFR 88-19 Volume 5
Chapter 12

http://armypubs.army.mil/eng/DR_pubs/dr_a/pdf/tm5_852_5.pdf

Any questions?

 

[zdas04]

I would simplify BigInch's post by saying "would you have to do anything differently if the outlet was 13C, 16C or some intermediate value?" The answer is almost certainly "No", so the exercise really is pointless.

If the inlet temp was 160C, then the answer could easily be "Yes". In that case I always start by calculating the thermal entry length (i.e., the distance required to reduce the dT by 80%). If the thermal entry length is less than the length of the pipe, then I use the ground temp for the outlet. If it is greater than the length of the pipe and it is in a region that matters, then your only choice is a thermodynamic simulator and some very detailed soil samples. The sand/soil numbers that BigInch quoted are for dry materials, a bit of moisture changes them dramatically.

This is absolutely a case where you need to determine if the answer will drive you to a different design. If not, don't worry about it. If so, then apply the appropriate level of engineering.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

First rule of engineering: Do only the calculations necessary to arrive at the answer to your question.

 

[Duwe6]

". . . are for dry materials, a bit of moisture changes them dramatically." Orders of Magnitude differences. Renders any calculation silly and irresponsible, unless you only calculate the boundary conditions; dry soil, saturated soil - warm rain. saturated soil -= cold, freezing rain. And when you calculate the absolute outside limits, there is a pretty good chance that your item will never actually reach any of those limits during its lifetime.