Heat generated due to friction in a pipe. 2

[Jbizzlefosho]

Long time lurker, first time poster. I've searched here and Google in general without finding a reasonable solution.

I'm trying to find an equation that I could use in Excel that would tell me the temperature gain from friction flow in a pipe.

Thank you ahead of time for any information that you have and feel free to ask for any clarificaiton I might add.

 

[zekeman]

You need to define the fluid flow system and the thermal environment, the pipe cross section and state whether the heat flow is adiabatic.
You must know that it is an unusual question since friction is relatively small and in real world terms it is usually neglected

 

[Jbizzlefosho]

Thanks for the reply.

I’m looking at a system for the transportation of Propane and Butane through a 14"/16" pipe at 8600 BPH. This wouldn't be considered adiabatic as heat would be lost to the surrounding area.

I'm trying to approach this by breaking down the temperature gain/loss into three components. Heat loss from the Joules-Thompson effect, heat loss to the surrounding ground, and heat gained from friction. I have the first two parts, just not the last.

I understand that generally the heat generated from friction is ignored, but when trying to model match, I am finding that I require much lower heat transfer coefficients than seems reasonable in order to match my data. This makes me believe that another factor, such as heat from friction, is occurring.

I hope this helps.

 

[Compositepro]

That would be very close to the power being consumed by your pump. Please realize that just because your pump has a 5 hp motor does not mean it uses 5 hp. Power used by the pump will be Q x delta P. Q is volumetric flow rate and delta P is the pressure change across the pump. Almost all this energy will end-up as heat in your fluid except for energy used to change the elevation of the fluid.

 

[zekeman]

Would you please explain the system you are dealing with.And BTW, what is BPH?
Are you saying
" I have a gas flowing thru a pipe embedded in earth initial state T1,p, T=, distance along pipe, meters , flow rate."
If this is the system, then you have to write the dynamic flow equations using the standard mechanical and thermal equations that are involved.
The Joule- Thomson effect, I believe is not a heat loss term, but a temperature change due to the reduction of pressure caused by friction in the pipe.
So this complex problem involves fluid flow and thermal equilibrium.
I believe you should be working with internal energy and flow work.
It would help if you drew us a picture of the system.

 

[racookpe1978]

BPH may be "barrels per hour" . For a propane pipeline 16 inches in dia? Seems a bit small of a flow rate to be worried about heat gain from friction.

 

[dcasto]

You will have a temperature DROP in the line not a gain

 

[katmar]

See thread378-301968 The temperature rise will be the same whether the pressure drop is through a valve or because of friction in the pipe. Normally it is so small that it is not considered.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[chicopee]

Initially, I would look at this OP as an isothermal process based on a temperature of the soil if it is a buried pipe or ambient temperature if above ground; and then make a decision.

 

[Jbizzlefosho]

Thank you all for the replies. Let me see if I can answer everybody’s questions.

This is a Google Earth screen shot of the system. The blue line on the west side has a 14" diameter and the rest is 16". This is all buried pipe and is about 65 miles long.

When I say BPH, I mean barrels(oil) per hour or just over 100 gpm. The Propane/Butane enters the pipe at 100F and ~865psi. I know the density, specific heat, viscosity, JT coeff, overall heat transfer coeff, etc. For this specific case, I'm using 90F ground temp. I can already calculate my head/pressure loss, I just need to refine my temperature calculations.

In my spreadsheet, I have set it up to where the pipe is broken into ~170ft segments, and for each segment, I'm trying to calculate the deltaT from the JT effect, friction, and the temp loss to the surrounding ground independently of each other. I am summing each respective deltaT to get the end temperature at each segment. Am I wrong in my analysis method?

I understand that generally the DeltaT from friction is negligible, but in this case with the viscosity and velocity that it might have a greater role than most would think.

Does anybody have an equation describes what I'm looking for?

I hope this helps.

 

[trashcanman]

Excuse me but, I believe this is not quite in agreement with Thermodynamics, " Heat loss from the Joules-Thompson effect,"

This process does not include heat loss, as the enthalpy of the fluid does not change.

 

[zekeman]

Here is the fundamental energy equation for fluid flow from any textbook on the subject.Assuming no change of elevation,
p1v1 +u1 + V1^2/2g+q=P2v2 +u2 +V2^2/2g

p pressure
u= internal energy
v specific volume
V= velocity
q= heat added from ground= U*(Tg-T)*Area pipe segment.

At the entrance of each pipe segment, you have u1(T1) and if, as you say you know the pressure drop, p1-p2, then with some minor assumptions on V, you should easily get T2 as a function of the p2 and u2.(per Joule Thomson) You could use iteration, if your assumptions are inaccurate, but a solution for each segment is pretty fast if the segment lengths are small enough.

BTW, 8600BPH doesn't translate to 100gpm.

 

[25362]

Assuming that all the friction, as pressure loss, is converted to heat, with no change of phase, consider that:

[•] Δp[sub]f[/sub] is the pressure drop due to friction, expressed in N/m[sup]2[/sup]
[•] ρ is the fluid density, expressed in kg/m[sup]3[/sup]

Then,

[•] Δp[sub]f[/sub]/ρ has the dimensions of energy per unit mass:

N/m[sup]2[/sup] ÷ kg/m[sup]3[/sup] = N•m/kg = J/kg​

Thus, knowing the specific heat of the fluid one can estimate the "resulting" temperature climb.

 

[zekeman]

Ah, looking at the problem again I am puzzled about where Joule-Thomson effect occurs.I thought it is a gas phenomenon.
At 100F the vapor pressure of propane is 187 psi and the start pressure is
865 psi. How does J-T happen in this environment?

 

[25362]

The J-T effect happens on real fluids (liquids and gases) but in this particular case there is an insignificant heat up effect on the order of -0.003[sup]o[/sup]F/psi for butane and about -0.0004 [sup]o[/sup]F/psi for propane. See thread124-132825.

 

[zekeman]

So, if you accept the fact that in this case, J-T is negligible then you can get a good answer analytically, viz
W'cdT/dx=-vdp/dx +U*Pi*D*(Tg-T)
W' flow rate lb/hr
D pipe OD
c specific heat of liquid
pi 3.14
Tg ground temperature
T temperature of liquid along pipe

The first term on the RHS is fairly constant c(due to constant pressure gradient from friction) over a constant diameter pipe
after division of eq(1) by w'c and simplifying substitutions
(2) d(T-Tg)/dx=K+B*(Tg-T)
where
K=-vdp/dx/w'c
B= U*Pi*D/w'c
The solution to (2) is
T-Tg=K/B+(Ti-Tg-K/B)exp(-Bx)
T=Tg+K/B+(Ti-Tg-K/B)exp(-Bx)
Ti= entering temperature of fluid
No need for spreadsheet.

 

[Jbizzlefosho]

@ 25362 and Zekeman,

Thank you so much! You equations make sense and have helped me greatly!