I'll paraphrase (ie not word for word) two sections from a good reference, Piping Handbook 7th Edition by Mohinder L. Nayyar. The section of the book is an attempt to provide an overview of B31.3 and serve as a basic guide to the design of process piping. Its a thick read, but worth owning as you will digest it section by section over the years.
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From Section C.320 Process Piping Systems: Pressure Design of Piping Componnents: Bends and Elbows:
With regards to pressure design of piping components (in process piping systems)... the minimum required wall thickness at a pipe bend after bending should be determined as for straight pipe. The bend radius is typically a minimum of 3 x nominal diameter, but bends as tight as 1.5 times the diameter are possible with appropriate heat treatment methods.
Elbows that are manufactured in accordance with any of the standards in Table 326.1 of B31.3 are suitable at their rated temperature and pressure. Any elbows made to nominal pipe thickness (like ASME B16.9) are allowed for use with pipe of the same nominal wall thickness.
From Section C.350: Fabrication, Assembly, and Erection of Process Plant Piping: Bending and Forming:
It is allowable to bend a pipe to any radius that will result in bend arc surfaces free of cracks and buckles, but recommended to have bend radii equal to at least 3 times the pipe diameter AND fabricated in accordance with ES-24, Pipe Bending Methods, Tolerances, Process and Material Requirements of the Pipe Fabrication Institute. Tighter bends approaching 1.5 x dia are possible but will probably need heat treatment (induction bending methods).
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In summary, you are permitted to bend the pipe to 1.5 x dia. If you don't have the means, you could buy elbows that require welding or bolting. The tighter radius comes with a price in the overall pipe design (stresses/flexibility/constructability). Check out the sections on design and fabrication for your fluid service in B31.3.