The Dry Salvages

One thing you must get very clear in your head is that when we design casing (or any other type of structure) we are not attempting to predict failure. Predicting actual failure is near impossible even when you have the most complete data you can imagine, and in the case of oilfield tubes and borehole conditions predicting failure is impossible. So our goal is to calculate some design limits and select our casing such that the anticipated loads do not exceed those limits.

Calculating design limits and predicting failure are separate and distinct processes. Engineers have no idea how to predict failure accurately.

A design limit should naturally be linked to some strength property of the structural member which is a tube in our case. Since we have already stated that we cannot predict actual failure of the tube there must be some other strength property of the tube that we can reliably predict. And in fact there is and it is the yield stress of the metal from which the tube is made.

The yield stress (sometimes referred to as the yield strength) of a metal such as steel is well defined and relatively easy to determine experimentally. A piece of the metal is cut into the shape of a test sample and it is placed in a device that pulls tension on it (or applies compression). In a simplified version of this test we can mark off a distance on the sample before the test is begun and call it L. As tension is applied to the sample it begins to stretch slightly and the original length we delineated as L gets longer. It increases by some amount we will call ∆L. We can then define the uniaxial strain in the direction of the load as ε = ∆L L so that it is simply the change in length divided by the original length. We can also measure the cross-sectional area of the sample and call it A. If the tensile load of the machine at any time is P then we can define the uniaxial stress in the sample as σ =P A.

Figure 6 - 1. Test specimen for uniaxial stress test.

Then if we record the uniaxial stress and strain as the test is being conducted it would give us a plot similar to this one.

Figure 6 - 2. Simple stress-strain relationship for uniaxial test of carbon steel.

This simple uniaxial test is quite easy to do and gives us some very useful results. The point where the slope goes from linear to nonlinear is called the elastic limit or yield point. Up to that point the material behaves elastically. At any point below the elastic limit the load can be removed (returned to zero) and the strain will also return to zero.

That is what we call elastic behavior. But once the sample is deformed beyond that point the material enters a plastic region and when the load is removed and reduced to zero the strain will not go back to zero. It has undergone some permanent deformation or plastic deformation.

In many cases the behavior of the metal at the yield point is somewhat more complicated than that in the above illustration. Sometimes the behavior becomes nonlinear before the yield stress is reached and that point is called the proportional limit. Ductile steels often exhibit this behavior and materials like cast iron seldom exhibit a distinctive yield point. There are other cases where the stress actually decreases slightly after the yield stress is reached and hence there is an upper yield stress and a lower yield stress. This is typical of some steel alloys. In many cases the yield point is indistinct and the yield point is defined as some arbitrary point offset from the proportional limit by a specified amount of strain (API does this). We are not going to concern ourselves with those details, but rather assume that as long as we do not exceed the published yield stress for the casing material that its behavior is linear and elastic.

The behavior of the metal in the elastic range is easy to measure and predict. And as long as the load on the metal does not exceed the yield point the metal will behave exactly the same every day with every load. Once the metal goes into the plastic region, however, things get considerably more complicated. The stress-strain relationship becomes nonlinear and the yield point is no longer a constant; it changes and becomes a history dependent property of the metal. It is no longer possible to predict the behavior of the metal without new tests or a record of its load history plus some additional properties not revealed by the simple uniaxial tensile test.

The design limit we will use is the yield stress of the material.

The yield stress or some fraction of it is the design limit of almost every structure designed and built in the world. There are very few exceptions. The only equipment in the oilfield that is designed to operate in the plastic region is coiled tubing when it is cyclically bent over the reel, guide arch, and injector. Typically it may experience strains an order of magnitude greater than at the yield stress of the tube.

Now that we have established what will constitute our design limit, the yield stress, we must look at the various ways in which loads affect the casing. Several distinct types of loading are possible, either singly or in combination.

• Tensile

• Burst

• Collapse

These are the items we used in our preliminary design and the allowable values based on the yield stress of the materials are published in API Bulletin 5C2 for API standard

tubes as well as many other places. In the previous chapters we explored various ways to determine the loads that we would encounter in various wells. In the last chapter we looked up the allowable values of the tubes in the tables and selected the casing whose strength would exceed our predicted loads in collapse and burst, and then made certain that it was strong enough in tension so that it would support its own weight. It is a simple and straight forward procedure. Though that is the method often used for many years and still used in some areas, it does not account for one critical fact. If a tube is subjected to a combination of tension or compression plus an internal or external pressure then the values in those tables are meaningless.

In our simple uniaxial test we loaded the sample in only one direction, but most casing is not loaded in only one direction. The next step of the process is to determine how to apply the results of the uniaxial test in a three dimensional loading situation. That brings us to combined loading and how we account for the ways in which it affects our design.