Calculation of collapse pressure of steel pipe

[salmon2]

I already posted this in another forum and was directed by a helper to here. Hopefully, can see more discussion.

My question is about how to calculate collapse pressure of steel casing or tubing including imperfection effects, such as tolerance, residual stress, etc.

I am using the paper "A new empirical formula for collapse resistance of commercial casing" by T. Tamano, T. Mimaki and S. Yanaimoto. This empirical model included the effect of tolerances, residual stress and seems pretty good. The formula are:

1) Elastic collapse pressure
Pea=2*E/(1-v^2)/(D/t)/(D/t-1)^2
where E is elastic modulus, v possion ration, D Outer diameter and t wall thickness

2) yield collapse pressure
Pyie=2*YS*(D/t-1)/(D/t)^2*(1+1.47/(D/t-1))
where YS is anxial yield strength

3) imperfection factor
H=0.0808*u(%) + 0.00114*e(%) - 0.1412RS/YS
where u is ovality in % and e eccentricity in % and RS is circumferential residual stress at the insider surface of tubing

4) The empirical collapse pressure will be
P=0.5*(Pea+Pyie)-(0.25(Pea-Pyie)^2+Pea*Pyie*H)^0.5

The applicable range of D/t will be between 10 ~ 26.

The tubing I work with is either API 5CT or 5L, seamless or ERwelded. The tolerance I order is either OD/wall controlled or ID/wall depending the tubing manufacturing process. The problems I have are how to calculate the u, e and RS.

1) on the ovality u, people already discussed somewhere before, the prevailing one will be u = (Dmax-Dmin)/Davg. Say the OD tol is +/-1%, then u = 2%. This single imperfection will decrease the pressure calculation as above by 30%! my question is this seems overconservative and underestimate the collapse pressure a lot compared with testing? I am thinking either tube manufacturing did not use up the full range of OD tolerance or the calculation of u should be restricted at one cross section and then used the max u only because where is mostly the spot to collapse and the max u from each cross section should be much smaller than theoretical limit, 2% in this case. I would like to hear your expertise explanation on this.

2) on eccentricity, e, people use e = (t_max-t_min)/t_avg. Say the wall thickness tolerace is +/-10%, then e equals to 20%. Again is this overconservative or should be restricted to one cross section only…?

3) how to measure the residual stress on the internal surface only? Is there any way I can calculate it? I know I can cut a ring longitudinally and compare the OD before and after cutting, but that is the effective residual stress throughout the wall thickness and it varied a lot between different heats, roughly same chemistry and heat treatment.

4) finally, is there other better models available including the imperfection effect people know of?

 

[BigInch]

Yes it decreases the collapse pressure by 30%, but the collapse pressure is relatively high for most typical cases, so no harm done for the typical case.

If your case is not typical, very deep water, etc. no choice but to use a heavier wall thickness. The dimensional tolerances are what they are, there is a probability that they will be reached and I don't believe its practical (very costly) to specify less, nor reject those that fall above a lesser tolerance either.

And it only takes one collapse in one joint to trigger all the rest of the joints to flatten as well. Pretty significant risk. IMO you need to discuss reducing the ovality and dimensional tolerance with your boss before continuing along this line.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[rconner]

With regard to the statement, "I know I can cut a ring longitudinally and compare the OD before and after cutting, but that is the effective residual stress throughout the wall thickness" was just curious, how exactly do you figure "compare the OD before and after cutting" (longitudinally) is the "effective residual stress throughout the wall thickness"? [I guess I agree of course that what movement/deformation you is likely some effects of residual stress.]
In any case as I suspect virtually all steel pipes ever made or tested (to confirm theoretical, or develop empirical formulae etc.) by researchers from Mr. Timoshenko and Roark on down, and by designers in establishing safety factors etc., have had "variations" (including residual stress and many others), I was just curious (I guess like BigInch) what is driving the desire now to look at the specific parameters you talk about above in this depth?

 

[salmon2]

I will respond to your comments in one post.

BigInch - I understand that specifying less tolerance is going to be pretty costly and that is exactly what we trying to avoid if possible. For instance, ERW is wide known having better dimensional tolerance than seamless even though both of them can easily conform to API tubing standards because API is pretty loose. So for this case, we can easily specify a less tolerance without paying mills any premium since the ERW capability will naturally produce much less variance.

rconner - the paper I quoted specified the residual stress on ID will affect collapse pressure, but the way cutting a ring is a measure of average or effective residual stress throughout the wall, not the stress on ID only. So I am not certain if I am using the correct residual stress when using the formula in the paper.

The reason I brought this up is because we are in oil and gas industry and we are using steel pipe as downhole casing which is suggest very high pressue - pushing the collapse pressure really. So if we can get higher pressue rating, it will be very good for advertising our products and indeed we need higher rating if we can, not just an attention attractor.

So I am checking the theoretical model to see which parameter we can mess around to improve pressure rating and then investigate the practicability.

 

[salmon2]

So IF we only have two options - either increase wall thickness or reduce tolerance, we will investigate which way is better or cheaper. It is totally possbile that bearing with an extra with smaller tolerance is cheaper than increasing wall thickness to gain the same benefit, right?

I personally feel the paper I quoted is very good and just wondered if any better work out there. Then we can minimize testing.

 

[BigInch]

As long as you think you can really believe that pipe installed in an oil/gas well stays round... you're OK. I see pleanty of opportunity for it to go out of round well before it ever arrives at the well site, never mind down-hole. And to be totally (and somewhat brutally) honest, if somebody told me that, I'd have to look for another supplier... quickly. Maybe you should do a market survey before you jump on that one.

"If everything seems under control, you're just not moving fast enough."
- Mario Andretti- When asked about transient hydraulics

http://virtualpipeline.spaces.msn.com

 

[salmon2]

BigInch,

Sorry for the confusion, we are using special casing as perforating which goes into casing and punches holes on casing. But because of there is no industry standard for perforating, so we reference casing standards most of time adding some of our own requirements.

Our tubes usually have pretty heavy wall. So far I only seen straightness of long tubes being screwed during shipping, not ovality.

Salmon2