API 579 - MAT and temperature reduction

[Water_Guy]

API 579 section 3.4.3 b) has me confused. Especially step 4 and equation 3.5 and how that relates to Figure 3.7 for the ‘Temperature Reductions’.

I’ve been determining the MAT on sections of a relief valve’s discharges in cases of auto-refrigeration and temperatures below -20 deg F, either the ‘Stress basis’ for sections of piping, or “Pressure Basis’ for flanges. Stresses are from the pipe stress analysis.
API 579 Level 2 – paragraph 3.4.3 b):
Step 4:

Subparagraph “i)” is pretty self-explanatory, less than the ratio threshold: MAT = -155 deg F.

The next paragraph “ii)” and specifically equation (3.5) the ‘max[ (MAT – Tr), (-55 deg F)] has me confused.

If the stress ratio is slightly above the ratio threshold, where say the Tr would be 100 deg. That would mean equation 3.5 would look like:
Case 1. MAT = max[(-20 – 100), (-55 deg F)] or MAT = max [-120, -55], MAT = -55 deg F ???

Or what if the stress ratio is really low, indicating high stress, say a Tr around 15 deg. That would mean equation 3.5 would look like:
Case 2. MAT = max[(-20 – 15), (-55 deg F)] or MAT = max [-35, -55], MAT = -35 deg F ????

Case 2 makes sense, Higher stress lower MAT.

But what about Case 1? With a high stress ratio and corresponding higher Tr, does equation 3.5 set the MAT for a low stress at -55 deg F. But at -155 deg for a being at or below the ‘Threshold’?

I know that I’m looking at it wrong, but can’t get it straight in my head. So, I’m looking for some clarifying ‘words of wisdom’.

 

[akpipelineengr]

With a high stress ratio and corresponding higher Tr

You've got this backwards. A high stress ratio gives a lower Tr. Look at Figure 3.7. Case 2 has a higher stress and lower Tr, so it has a higher MAT than Case 1.

I don't fully understand your question, but below the Rts threshold from Figure 3.7, we are confident in the behavior of the steel down to -155°F. Then for materials whose MAT_STEP1 is established only from material grade and thickness, Eq 3.5 is limited to -55°F because of uncertainty in the behavior of untested steel at higher stresses. Low temperature impact testing would provide a more solid technical basis for MAT_STEP1 and permit the full use of the temperature reduction metholodogy as in Eq 3.6.

 

[Water_Guy]

Thank you 'akpipelineengr'
You're right, I had it backwards.

I guess my basic question is looking at the results in the two example Cases that were described above, specifically Case 1
Case 1: Lower stress ratio, a higher Tr. Putting that higher value in equation 3.5 and then taking the 'Max' between that two values, -120 and -55. Shouldn't a lower stress (higher Tr) result in a lower (colder) MAT? Meaning setting the MAT at -120?