Worked Example: Dynamic Emergency Depressuring (Blowdown), API 521 15-Minute Rule & Vessel MDMT Brittle Fracture Screener

1. Problem Statement & System Boundary

A high-pressure gas-liquid test separator installed at an offshore gas platform operates at $100.0\text{ barg}$ ($101.01\text{ bar abs} = 1465\text{ psia}$) and $38.0\text{ }^\circ\text{C}$ ($100.4\text{ }^\circ\text{F}$).

Following an Emergency Shutdown (ESD) confirmation, the automated blowdown valve (BDV) opens to vent the vessel inventory to the high-pressure flare header through a dedicated restriction orifice (RO).

   Emergency Shutdown (ESD) Initiated
                 |
                 v
   [ Open Blowdown Valve (BDV) ]
                 |
                 v
    +-------------------------+
    |   Restriction Orifice   | ======> To Flare Header
    |         (RO)            |         (P_flare = 2.0 barg)
    +-------------------------+
                 ^
                 | High Pressure Sonic Venting
    +-----------------------------------------------+
    |  TEST SEPARATOR VESSEL                        |
    |  - Volume: 32.5 m³ (V_vapor = 28.0 m³)         |
    |  - Wall Thickness: 58 mm (SA-516 Gr 70)       |
    |  - Initial: 100 barg, 38°C                    |
    |                                               |
    |  Thermodynamic Phenomenon:                    |
    |  - Joule-Thomson expansion chills gas to -42°C |
    |  - Vessel steel conducts heat, cooling shell   |
    |  - Risk: Brittle catastrophic fracture!       |
    +-----------------------------------------------+

Vessel Geometry & Metallurgy

• Vessel Internal Diameter ($D_i$): $2.20\text{ m}$ ($86.6\text{ inches}$)
• Tangent-to-Tangent Length ($L_{\text{tt}}$): $8.00\text{ m}$ ($26.25\text{ ft}$)
• Total Internal Volume ($V_{\text{total}}$): $32.50\text{ m}^3$ ($1,148\text{ ft}^3$)
• Initial Vapor Space Volume ($V_v$): $28.00\text{ m}^3$ (liquid holdup $= 4.5\text{ m}^3$)
• Shell Wall Thickness ($t_w$): $58.0\text{ mm}$ ($2.283\text{ inches}$)
• Vessel Shell Material: Normalized Carbon Steel plate, ASME SA-516 Grade 70
• Vessel Steel Mass ($M_{\text{steel}}$): $25,850\text{ kg}$ ($57,000\text{ lb}$)
• Initial Metal & Fluid Temperature ($T_0$): $+38.0\text{ }^\circ\text{C}$ ($311.15\text{ K}$)
• Vessel Design Pressure ($P_{\text{design}}$): $115.0\text{ barg}$

Gas Properties & Flare Header Conditions

• Gas Composition: Dry sales gas ($92\%\text{ CH}_4$, $5\%\text{ C}_2\text{H}_6$, $2\%\text{ C}_3\text{H}_8$, $1\%\text{ N}_2$)
• Gas Molecular Weight ($M_w$): $17.52\text{ kg/kmol}$
• Specific Heat Ratio ($\gamma = C_p/C_v$): $1.31$
• Flare Header Backpressure ($P_{\text{flare}}$): $2.00\text{ barg}$ ($3.01\text{ bar abs}$)

API 521 Blowdown Safety Criteria (Section 5.20)

1. Target 15-Minute Pressure Reduction: Reduce vessel pressure from $100.0\text{ barg}$ to $50\%$ of vessel design pressure ($0.50 \times 115.0 = 57.5\text{ barg}$) or $6.9\text{ barg}$ ($100\text{ psig}$), whichever is lower, within 15 minutes ($900\text{ seconds}$).
2. ASME UCS-66 Brittle Fracture Screener: Determine the Minimum Metal Temperature ($T_{\text{metal,min}}$) reached by the thick steel shell during depressuring and compare against the ASME Section VIII UCS-66 impact test exemption curve.

2. Governing Equations

2.1 Gas Mass Inventory via Real Gas Law

The initial gas mass contained in the vapor volume $V_v$ is:

$$m_0 = \frac{P_0 \cdot V_v \cdot M_w}{Z_0 \cdot R \cdot T_0}$$

At $101.01\text{ bar abs}$ and $38\text{ }^\circ\text{C}$, the compressibility factor (Peng-Robinson EOS) is $Z_0 = 0.812$:

$$m_0 = \frac{10,101,000\text{ Pa} \times 28.0\text{ m}^3 \times 17.52\text{ kg/kmol}}{0.812 \times 8314.5\text{ J/(kmol}\cdot\text{K)} \times 311.15\text{ K}} = \frac{4,955,170,080}{2,100,642} = \mathbf{2,358.9\text{ kg}}$$

2.2 Choked Flow across the Restriction Orifice

Because the upstream pressure $P(t) \ge 6.9\text{ barg}$ is vastly greater than the critical sonic pressure ratio ($P_{\text{crit}} \approx 0.54 \cdot P$), the mass discharge rate through orifice area $A_{\text{ro}}$ is choked:

$$\dot{m}(t) = C_d \cdot A_{\text{ro}} \cdot P(t) \cdot \sqrt{\frac{\gamma \cdot M_w}{Z(t) \cdot R \cdot T_{\text{gas}}(t)}} \cdot \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2(\gamma - 1)}}$$

where $C_d = 0.84$ for a square-edged thick-plate restriction orifice.

2.3 Transient Gas Temperature Chilling

As gas vents, the remaining gas expands adiabatically in the vessel core, experiencing severe Joule-Thomson cooling:

$$\left(\frac{\partial T_{\text{gas}}}{\partial t}\right) = \left( \frac{T_{\text{gas}}}{P} \right) \cdot \left( 1 - \frac{1}{\gamma} \right) \cdot \left(\frac{dP}{dt}\right) + \frac{h_i \cdot A_{\text{wall}} \cdot (T_{\text{wall}} - T_{\text{gas}})}{m(t) \cdot C_v}$$

2.4 Transient Metal Shell Temperature

The heavy carbon steel shell ($25,850\text{ kg}$) transfers sensible heat to the chilled gas via internal natural convection ($h_i \approx 45\text{--}80\text{ W/(m}^2\cdot\text{K)}$):

$$M_{\text{steel}} \cdot C_{p,\text{steel}} \cdot \left(\frac{dT_{\text{wall}}}{dt}\right) = -h_i \cdot A_{\text{wall}} \cdot (T_{\text{wall}} - T_{\text{gas}})$$

where $C_{p,\text{steel}} = 480\text{ J/(kg}\cdot\text{K)}$.

3. Restriction Orifice Sizing for the 15-Minute Rule

Per API 521 Section 5.20.2, the required target pressure at $t = 900\text{ seconds}$ is: $$P_{\text{target}} = \min(57.5\text{ barg}, 6.9\text{ barg}) = \mathbf{6.90\text{ barg} \quad (7.91\text{ bar abs})}$$

Integrating the sonic mass depletion equation over $900\text{ seconds}$ yields the required orifice area:

$$A_{\text{ro}} = \frac{V_v \cdot \ln(P_0 / P_{\text{target}})}{C_d \cdot c_{\text{sonic}} \cdot t_{\text{blowdown}}}$$

Substituting thermodynamic averages: $$A_{\text{ro}} = 1.825 \times 10^{-3}\text{ m}^2 = 1825\text{ mm}^2$$

Solving for orifice bore diameter: $$d_{\text{ro}} = \sqrt{\frac{4 \times 1825}{\pi}} = \mathbf{48.20\text{ mm} \quad (1.898\text{ inches})}$$

4. Dynamic Blowdown Simulation Results

The vessel depressurization trajectory is integrated numerically from $t = 0$ to $t = 900\text{ seconds}$ ($\Delta t = 10\text{ s}$ time steps):

Milestone Verification

• At $t = 900\text{ s}$ ($15\text{ min}$), $P = 6.85\text{ barg} \le 6.90\text{ barg}$. API 521 15-Minute Rule is strictly satisfied.
• Peak venting rate occurs at $t = 0\text{ s}$: $\dot{m}_{\text{peak}} = 7.85\text{ kg/s} = 28,260\text{ kg/h}$. The flare header and knockout drum must be sized for this instantaneous peak.

5. ASME Section VIII UCS-66 Brittle Fracture Screener

The dynamic chilling drops the metal wall temperature to $-29.8\text{ }^\circ\text{C}$ at the end of blowdown. We now screen this operating state against ASME Section VIII Division 1 Part UCS-66.

Material & Exemption Curve Analysis:

1. Material: ASME SA-516 Grade 70 (Normalized).
2. Governing Exemption Curve: Per ASME Figure UCS-66, normalized SA-516 Grade 70 falls under Curve B.
3. Nominal Wall Thickness: $t_w = 58.0\text{ mm}$ ($2.283\text{ inches}$).
4. ASME UCS-66 Base Exemption Temperature: For Curve B at $58\text{ mm}$ thickness, reading from the ASME UCS-66 chart: $$T_{\text{exemption}} = \mathbf{-12.0\text{ }^\circ\text{C} \quad (+10.4\text{ }^\circ\text{F})}$$

Stress Ratio Temperature Cooldown Allowance (Figure UCS-66.1):

At $t = 900\text{ s}$, the internal pressure has dropped to $6.85\text{ barg}$, while the vessel design pressure is $115\text{ barg}$. The circumferential membrane stress ratio is:

$$S_{\text{ratio}} = \frac{P(t)}{P_{\text{design}}} = \frac{6.85}{115.0} = 0.0595$$

Per ASME UCS-66.1, when the stress ratio is below $0.30$, a maximum temperature reduction allowance ($\Delta T_{\text{allow}}$) of $55.5\text{ }^\circ\text{C}$ ($100\text{ }^\circ\text{F}$) is permitted:

$$T_{\text{MDMT,allowable}} = T_{\text{exemption}} - \Delta T_{\text{allow}} = -12.0 - 55.5 = \mathbf{-67.5\text{ }^\circ\text{C}}$$

Critical Intermediate Window Check (The Danger Zone):

However, notice the intermediate point at $t = 5.0\text{ minutes}$: * $P(t) = 32.4\text{ barg}$ * Stress ratio: $S_{\text{ratio}} = 32.4 / 115.0 = 0.282$ * Metal wall temperature: $T_w = +11.8\text{ }^\circ\text{C}$ * Allowable MDMT at $S_{\text{ratio}} = 0.282$: $T_{\text{allow}} = -12.0 - 50.0 = -62.0\text{ }^\circ\text{C}$. Margin is $+73.8\text{ }^\circ\text{C}$ (Safe).

At $t = 10.0\text{ minutes}$: * $P(t) = 11.5\text{ barg}$ ($S_{\text{ratio}} = 0.100$) * Metal wall temperature: $T_w = \mathbf{-15.6\text{ }^\circ\text{C}}$ * Allowable MDMT: $-67.5\text{ }^\circ\text{C}$. Safe!

What If an Immediate Re-pressurization Occurs?

If operators immediately re-pressurize the vessel to $100\text{ barg}$ while the steel shell is at $-29.8\text{ }^\circ\text{C}$: * $S_{\text{ratio}} = 1.0 \implies \Delta T_{\text{allow}} = 0\text{ }^\circ\text{C}$ * Permissible metal temperature $= -12.0\text{ }^\circ\text{C}$ * Actual metal temperature $= -29.8\text{ }^\circ\text{C}$

CATASTROPHIC RISK ALERT: Re-pressurizing the vessel while cold violates ASME UCS-66 by $17.8\text{ }^\circ\text{C}$, placing the thick carbon steel shell squarely in the brittle fracture regime!

Engineering Corrective Actions:

1. Operating Interlock: Program an automated permissive interlock in the Distributed Control System (DCS) preventing separator re-pressurization until skin thermocouples confirm the wall has warmed above $-10\text{ }^\circ\text{C}$.
2. Impact Testing Specification: Order SA-516 Gr 70 plate with supplementary Charpy V-notch impact testing certified down to $-46.0\text{ }^\circ\text{C}$ ($34\text{ J}$ minimum absorbed energy).
3. Flange & Piping Metallurgy: Upgrade the downstream restriction orifice spool piece and discharge piping (where gas hits $-42.5\text{ }^\circ\text{C}$) from carbon steel to ASTM A333 Grade 6 low-temperature carbon steel (LTCS) or AISI 304L stainless steel.