collapse pressure of casing/tubing 1

[salmon2]

I meant to post here, but accidently posted it first in the ASTM forum. Anyway.

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?

 

[JoeTank]

I am not someone with a lot of experience with collapse pressure for tubing, but I may be able to offer a few comments. My expereience is mostly with plate structures like tank, vessel and large diameter piping (ie; penstocks). Imperfections of only a few percent on diameter can significantly affect buckling pressures. The 30% reduction cited does not seem out of line. Residual stresses due to weld shrinkage are often at or very close to the yield strength of the base metal.

Joe Tank

 

[salmon2]

JoeTank, appreciate your comment.

But I was hoping to see more discussion. Anybody could enlighten me on the ovality and residual stress difference of hot finished seamless, cold drawn seamless and ERW pipes? I understand that ERW and hot finished seamless are OD/wall controlled and cold drawn seamless is ID/wall controlled.

 

[ladracu]

The effect of eccentricity seems independent from D/t ratio
and symmetric in ec. This can be established in the model by
taking Hy
ec = He
ec proportional to ec2 and Ht
ec = 0.
The effect of residual stress may be considered symmetric
in rs and is more pronounced in the transition region than in
the elastic region. Collapse pressures for tubulars with very
low D/t ratio are largely unaffected by residual stress. Taking
different functions Hy
rs, Ht
rs and He
rs that are quadratic, or
even quartic, in rs may approximate this.
Finally, the effect of stress-strain curve shape can be very
significant. If the proportional limit of the material is much
lower than the yield strength (the stress reached at 0.5% total
strain) the stiffness above the proportional stress reduces
below the Young’s modulus and this in turn decreases the
collapse strength. Pipes that have undergone cold working, for
instance due to cold straightening or due to diametrical
expansion, will generally show this effect, quite possibly
reducing the collapse strength by up to tenths of percent

 

[ladracu]

an spe paper

 

[salmon2]

Ladracu, I apreciate your comment and especially the paper. I just printed out the paper you shared and have not read it yet. But I will very soon.

It is interesting that your paper and the paper I quoted in my original post are having one common author. I am sure this is going to be a very best paper.

 

[MJCronin]

salmon..

Suggest that you repost in the "Piping & Fluid Mechanics Forum" or, as an alternate, perhaps the people who specify and design shell-and-tube HXs can give you some help.

You will get more structural mechanics types there....

Just a comment.... Why are you doing this ?

The external collapse pressure of tubing must be very high for most common wall thicknesses

 

[salmon2]

MJCronin,

Thanks for the direction. I will do so.

I am in oil and gas industry, we use a lot of steel pipe for casing which require very high collapse pressure rating, can be as high as 30ksi.

Salmon

 

[ladracu]

Salmon, don't mention it. I hope the paper helped. I am just curious what do you try to do? I mean either you have a critical application to go in such details or you simply have nothing better to do. I beg your pardon if I seem to be impolite, it's not my intention, but I think as long as that model doesn't become an industry standard, your boss will not allow you to use it, unless this is the only way.
From time to time I get also interested in such advanced theories and I even write some software but it doesn’t keep me too much, I’m a lazy guy.
By the way, I did not see if the ovality is somehow related to the wellbore dogleg. I am sure the cross section shape changes if the casing is in a crooked hole.
Please contact me on kingmobutu@hotmail.com for further discussions – if you like.

 

[salmon2]

Pressure rating is one very important parameter to our customer. Our tubing are usually specially made tubing, so I think, I think, we can use whatever model to publish our pressure rating as long as it meets experiments or we are willing to take the risk of failure in the field.

But I have to agree that the main reason behind this is that I am bored sometime. I am very technical so I tend to know things in details. My boss buy it or not does not really bother me any more.

Sorry for the confusion, our product is actually not wellbore casing, it is perforating which goes into casing and punches holes in casing. But there is no industry standard for perforating, so we borrow casing standard with some additional requirements for perforating. Downhole can be under very high pressure, so our perforating should not collapse which can damage the components inside the tube.