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Keep in mind that the MDMT and MAWP are related to each other. As you decrease the MAWP, you decrease the coincident ratio, thus decreasing the MDMT.
Let's assume that the vessel MAWP is limited by the shell with the following conditions:
design pressure = 200 psi
design temp. = 375°F
design MDMT = -49°F
joint efficiency = 0.85
corrosion allowance = 0.125"
shell material = SA-106-B (14" STD pipe)
MAWP = S x E x t / (Ro - 0.4t) = 17100 x 0.85 x 0.203 / (7 - 0.4 x 0.203) = 426.46 psi
Now let's calculate for the rated MDMT for three different cases of MAWP.
Case 1: MAWP = 426.46 psi
tn = 0.375" x 0.875 = 0.328"
Unadjusted MDMT = -20°F (Curve B)
tr = MAWP x Ro / (S x E + 0.4 x MAWP) = 426.46 x 7 / (17100 x 0.85 + 0.4 x 426.46) = 0.203"
Coincident ratio = tr x E* / (tn - c) = 0.203 x 0.85 / (0.328 - 0.125) = 0.85
From Fig. UCS-66.1, temperature reduction = 15°F
Adjusted MDMT = -20 - 15 = -35°F
Since the adjusted MDMT of -35°F is warmer than the design MDMT of -49°F, you need to impact test or change material.
Case 2: MAWP = 350 psi
tn = 0.375" x 0.875 = 0.328"
Unadjusted MDMT = -20°F (Curve B)
tr = MAWP x Ro / (S x E + 0.4 x MAWP) = 350 x 7 / (17100 x 0.85 + 0.4 x 350) = 0.167"
Coincident ratio = tr x E* / (tn - c) = 0.167 x 0.85 / (0.328 - 0.125) = 0.699
From Fig. UCS-66.1, temperature reduction = 30°F
Adjusted MDMT = -20 - 30 = -50°F
Rated MDMT = -50°F (no impact test required)
Case 3: MAWP = design pressure = 200 psi
tn = 0.375" x 0.875 = 0.328"
Unadjusted MDMT = -20°F (Curve B)
tr = MAWP x Ro / (S x E + 0.4 x MAWP) = 200 x 7 / (17100 x 0.85 + 0.4 x 200) = 0.096"
Coincident ratio = tr x E* / (tn - c) = 0.096 x 0.85 / (0.328 - 0.125) = 0.402
From Fig. UCS-66.1, temperature reduction = 92°F
Adjusted MDMT = -20 - 92 = -112°F
Rated MDMT = -55°F (per UCS-66(b)(2))(no impact test required)
As you can see, MDMT decreases as MAWP decreases. If you still want to use SA-106-B without impact test, you need to rate your vessel with an MAWP that will satisfy the design MDMT of -49°F. This is assuming that your vessel MAWP and MDMT is governed by the SA-106-B shell.