Dynamic Emergency Depressuring (Blowdown) & Fire Relief Inventory Analyzer

API Standard 521 dictates that emergency depressuring systems must be capable of reducing vessel internal pressure to **$100\text{ psig}$ ($6.895\text{ barg}$) or $50\%$ of the vessel design pressure (MAWP) within 15 minutes**, whichever pressure is lower. For high-pressure gas vessels subjected to pool or jet fire radiation, metal shell yield strength diminishes rapidly above $400^\circ\text{C}$; depressuring reduces hoop stress below the failing strength of hot steel.

Under external pool fire impingement, heat absorbed by the wetted vessel surface is formulated per API 521: $$Q_{\text{fire}} = 43{,}200 \cdot F \cdot A_w^{0.82} \quad (\text{Btu/h})$$ where $F$ is the insulation environment factor ($1.0$ for bare uninsulated steel, $0.15\text{--}0.30$ for fireproof insulation), and $A_w$ is the wetted surface area. The blowdown restriction orifice bore ($d_o$) is sized to exhaust both the initial gas mass and fire-generated boil-off vapor through choked sonic flow.

As gas rapidly expands across the restriction orifice, severe isenthalpic Joule-Thomson refrigeration drops fluid temperature deep into sub-zero territory (often $-30^\circ\text{C}\text{ to }-60^\circ\text{C}$). The steel vessel shell cools due to internal convective heat transfer: $$\frac{d T_{\text{wall}}}{dt} = \frac{h \cdot A_{\text{wall}}}{M_{\text{steel}} \cdot C_{p,\text{steel}}} (T_{\text{fluid}} - T_{\text{wall}})$$ If the minimum metal wall temperature drops below the vessel Minimum Design Metal Temperature (MDMT, typically $-29^\circ\text{C}$ for standard ASTM A516 carbon steel), catastrophic brittle fracture occurs, requiring low-temperature carbon steel (LTCS) or impact-tested metallurgy.