Please see ASME B31.3-1996 328.4.4 Alignment section.
It says alignment should be within the dimensional limits in the WPS and engineering design.

I think two factors are considered here.
1) Can you weld withoug welding defects with some misalignment?
If you have very skilled GTA welder, you can demonstrate through PQ test to achieve "maximum possible misalignment".
1.6mm is generally accepted misalignment.
The welder should avoid any lack of fusion due to high-low(misalignment).
If you have automatic welding system, it is difficult to have some misalingment.
2) Engineering design factor
If you have small diameter pipe and big misalignment, material flow inside pipe may be influnced by the misalignment. However, this does not happen in real welding field. We have very little misalign problem for smaller pipe.

For your case, I would like to recommend followings;

1) Develop welding procedure to handle some misalignment.
Please post your exact situation, I will recommend some welding process.
2) If you fail, machine inside to get perfect alignment.
(If you machine a lot, please check design strength)

Dong Won Oh
South Korea

There are three kinds of flange misalignment:
1. Angular misalignment. The flanges' faces are not parallel, there's a certain angle between them.
2. Parallel misalignment. The flanges' longitudinal center lines don't concide, they're parallel and there's a certain distance, or offset, between them.
3. Circumferential misalignment. The flanges are rotated in a certain degree from each other. Bolt holes don't coincide exactly.
For these situations, most Engineering & Construction Companies' standards and piping books specify the following tolerances:
For case 1. 1/2 (one half) degree or 1/16 inch (roughly 1,5 mm) measured at the flange tip, whichever is less.
For case 2. 1/16 inch (1,5 mm) as the maximum distance between the center lines.
For case 3. 1/16 inch (1,5 mm) difference measured at any bolt hole.
If your case has fallen slightly beyond these tolerances, don't get in panic, there may be a solution, with your client (or the Engineering Dept. of your Company) approval.
For case 1. Put a thicker gasket, it will take up the angular misalignment.
For case 2. This misalignment usually shows up when the piping is erected, before bolting the flanges together. Play with the piping supports (raise a little bit, lower a little bit etc) until the flanges are aligned.
For case 3. With a round file, enlarge the bolt holes a little bit so that the bolts can be inserted and taken off freely. What you can not do, of course, is to put less diameter bolts.
These clues don't sound as "good engineering practice"? May be not, but sometimes they're the only thing you can do to complete a job on schedule. That's why your client (or Engrg. Dept. of your Co.) approval is needed.
Giovanni S. Crisi
Sao Paulo - Brazil