rfitts,
There is not much information here but maybe that doesn't matter. It is likely that all you will get from B31.3 is some general philosophy and a general mandate for what you must do (you won't find applicable equations there). You have to ask yourself:
When you ask for "minimum analysis", according to whom?
(Jurisdiction?, owner?, Code?)
What do you need the calculations to determine?
What loadings are on this thing (static and transient)?
What are the actual pressure boundary design T and P?
How long do you need it to last (seriously)?
What does the design specification say about the above?
Upon reflection, you might find that temperature gradients and thermal fatigue are the most limiting failure mechanism. B31.3 will not help you there but it does tell you that they must be considered. It smells a lot like a finite element analysis will be needed to answer the obvious questions.
There is a sort of analogy, an attemporator (desuperheater) installed inside a large diameter steam pipe. The steam pipe has its design requirements and they are quite different from the condensate piping that feeds the attemporator. Where they all come together, it is a very grey area from a Code point of view.
Sorry for the "non-answer
Regards, John.