Pressure drop in annulus of two different materials 2

[chestilow]

We are in the process of performing the hydraulic calculations for a series of annuli that consist of an inner pipe of HDPE and outer pipe of carbon steel. Does anybody have any experience in taking into consideration the two different friction factors present on the outside flow?

Thanks,

Colin

 

[MikeHalloran]

Check the Reynolds number; if the flow is laminar the material doesn't matter.

If the flow is turbulent, that implies a large pressure drop. If that's true, or if there's any restriction downstream, you may have other problems.

Check the buckling pressure on the inner pipe.



Mike Halloran
Pembroke Pines, FL, USA

 

[chestilow]

Mike,

The Reynolds number is app. 4400, so it is considered turbulent flow. The annuli are part of a ciculation loop. The fluid is pumped through the center (HDPE) pipe and then it comes back up on the outside, so the inner pipe will actually have a greater pressure on the ID than the OD. We are trying to size the pumps for the loop. I was hoping to see if there was a way to take into consideration the different materials. It is not a necessity, but it would help in not overdesigning the pumps.

 

[BRIS]

The friction factors for HDPE and steel are not substantially different. I cannot see that taking the average of the too will not give you a good enough answer.

I would be more concerned over the method of calculation of friction losses in the annuli?

 

[katmar]

Colin,

From what I have seen, zdas04 is the guy with the most experience of this application. See his comments in the following threads

thread378-111534
thread378-100815
thread378-99074

Depending on the temperature of your fluids, it may be necessary to check the differential expansion of HDPE and steel.

Katmar

 

[zdas04]

Katmar,
Thanks for the vote of confidence.

Chestilow,
As I said in the threads referenced above, the tricky part is defining the effective diameter of the annulus. The technique that I've found matches measured data very well is:

d = ((ID_outer+OD_inner)²(ID_outer-OD_inner)³)^(1/5)

Then you just use the result in your flow equations. I've gotten good results with this technique in vertical flow with steel casing and spoolable composite inner pipe (I've never had much luck hanging HDPE in wellbores, it tends to creep under a tensile load). I used the friction factors for steel.

For horizontal pipe I've used steel inside of steel and gotten good results when the pipe had centralizers. Without centralizers the AGA equation with an epsilon for new steel significantly understated the pressure drop.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[zdas04]

While I had all of the information spread out on my desk, I went ahead and wrote faq378-1142 which has some additional information. Let me know if it is helpful.

David

 

[chestilow]

David,

Thanks for the help. Could you please let me know what the origin of the "Petroleum" method is? I've looked in several references and haven't been able to locate it elsewhere. I know that if I present it to the Project Engineer, he will want to know where it came from.

Thanks,

Colin

 

[zdas04]

It is in a lot of places. The best reference is Handbook of Natural Gas Engineering edited by Donald Katz, published by McGraw Hill. My version was published in 1959 and I'll give you my kids before I'd turn lose of it. Page 310 he has the equation.

For a more mainstream source, try Petroleum Engineering Handbook Edited by Howard Bradely and published by the Society of Petroleum Engineers. In the Feb, 1992 printing it is on page 34-27 (equation 49).

Neither book does a great job of deriving it, but it isn't the only empirical eqation in Petroleum Engineering. I've tried to derive it myself, but I always get sidetracked before I make much progress (it is so easy to get sidetracked in Katz, there is so much good information that every time I open it I find myself wandering around).

In both references, they show D⁵ because that is the diameter they need for the flow equation they are describing. I've had really good luck taking the fifth root and using the result.

David

 

[SNORGY]

I have worked on a problem like this before (flow of hot oil through the annular space in jacketed pipe). I have made some efforts to derive some practical salient equations that will address roughness, friction factors, hydraulic diameters, effective diameters, etc. Through this endeavour, I have been able to produce equations that suggest that the "Petroleum Engineering" method to determine effective diameter is very similar to the approach that I have taken; in a sense, I have almost derived the expression as given by zdas04. The only modification I would make is to state the following:

* Darcy - Weisbach, inner pipe (after some algebra):

h=[(8fLQ^2)/(g*(pi)^2*d^5)]

* Darcy - Weisbach, outer pipe, hydraulic diameter:

h=[(fL/(do-Di))*(u^2)/(2*g)]
u=[(4Q)/(pi*(do^2-Di^2))]
hence h=[(8fLQ^2)/(g*(pi)^2*{(do+Di)^2*(do-Di)^3})]

I hope I haven't messed up on the brackets and parentheses, but I think anyone reading this can easily figure out what I meant in the event that I have.

In the above, the theory that I follow uses the uncorrected hydraulic diameter dh=(do-Di) in the Darcy - Weisbach equation, and then applies corrections to compute an effective diameter de=dh/y and an effective Reynolds Number Re=R/y, where a curve fitting algorithm for y produces an equation of the form:

y=[-0.763 + 1.593*(Di/do)^0.5 + 1.844*exp(-Di/do)].

When you compare the two expressions for dynamic head loss h as given above, you can see the similarity to the expression for effective diameter used in the "Petroleum Engineering" method. The difference is, I am inclined to not exactly equate the effective diameter as the fifth root of the expression and treat it as the equivalent diameter of a circular pipe. Rather, I am inclined to take the head loss directly from the above.

The reference I have used is a textbook:

FLUID MECHANICS - Frank M. White
Second Edition, 1986, McGraw-Hill Inc.
(see Example 6.14, page 329)

If anyone would like to see my derivations (or check them in the event I am out to lunch), including the iteration scheme applied to the Colebrook equation to determine the friction factor, let me know.

SNORGY