7.2 Release Scenarios, Hole Sizes, Inventory Isolation, and Fluid Phase Behavior

Release Scenario Architecture under API RP 580 and API RP 581

Consequence analysis under API RP 580 (4th Edition) relies on constructing physical Release Scenarios that simulate the flow rate, state transition, atmospheric dispersion, and ignition or toxic impact of process fluids escaping a pressure boundary. When a component breaches, the magnitude of the resulting consequence depends heavily on four physical factors: Release Hole Size ($d_n$), Fluid Physical Phase, System Operating Energy (Temperature & Pressure), and Isolable Inventory Mass ($m_{inv}$).

API RP 581 (Part 3) standardizes quantitative release modeling by establishing discrete hole size distributions and rigorous hydrodynamic discharge equations to calculate initial fluid mass release rates ($W_n$, expressed in $lbm/s$ or $kg/s$).

---

Standardized Release Hole Sizes ($d_n$)

Rather than evaluating an infinite continuum of potential breach dimensions, API RP 581 standardizes release scenario calculations across four discrete hole sizes for each component item:

1. Small Release Hole ($d_1 = 0.25\text{ in} / 6.4\text{ mm}$): Simulates localized pinhole leaks, packing failures, small fitting cracks, instrument tubing shear, or pitting penetrations. Small releases occur at high statistical frequencies but generate lower immediate mass release rates.
2. Medium Release Hole ($d_2 = 1.0\text{ in} / 25.4\text{ mm}$): Simulates failure of small-bore branch connections (e.g., sample points, thermowell couplings, vent/drain nipples) or localized wall thinning splits.
3. Large Release Hole ($d_3 = 4.0\text{ in} / 101.6\text{ mm}$): Simulates major nozzle separations, large piping cracks, or severe structural breaches in vessels.
4. Rupture ($d_4 = d_{rupture}$): Simulates catastrophic full-bore pipe guillotine rupture ($d_4 = D_{pipe}$) or complete vessel shell burst ($d_4 > 4.0\text{ in}$). Rupture releases result in rapid inventory depressurization and maximum mass release rates.

---

Fluid Mass Discharge Rate Calculations ($W_n$)

Upon loss of containment, initial fluid mass discharge rate ($W_n$) is governed by fluid physical phase and operating pressure.

1. Incompressible Subcooled Liquid Discharge Equation

For liquids operating below their normal boiling point ($T_s < T_{bp}$), fluid flow through a release orifice is governed by Bernoulli's hydrodynamic equation:

$$W_n = C_d \cdot A_n \cdot \sqrt{2 \cdot \rho_l \cdot (P_s - P_{atm}) \cdot g_c}$$

Where:

• $W_n$: Initial liquid mass discharge rate ($lbm/s$ or $kg/s$).
• $C_d$: Discharge coefficient (standardized as $C_d = 0.62$ for sharp-edged orifices).
• $A_n$: Cross-sectional area of release hole size $n$ ($A_n = \frac{\pi \cdot d_n^2}{4}$, in $in^2$ or $m^2$).
• $\rho_l$: Liquid density at storage temperature ($lbm/ft^3$ or $kg/m^3$).
• $P_s - P_{atm}$: Pressure differential across the vessel wall ($psi$ or $Pa$).

2. Compressible Gas/Vapor Choked Flow Equation

For gases and vapors, when the operating storage pressure ($P_s$) exceeds the critical pressure ratio threshold ($P_s / P_{atm} > \left[ \frac{\gamma+1}{2} \right]^{\frac{\gamma}{\gamma-1}}$), gas velocity through the orifice reaches sonic speed (mach 1.0). Under sonic choked flow conditions, mass release rate is independent of downstream atmospheric pressure:

$$W_n = C_d \cdot A_n \cdot P_s \cdot \sqrt{ \frac{\gamma \cdot M}{R \cdot T_s} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{\gamma - 1}} }$$

Where:

• $\gamma$: Ideal gas heat capacity ratio ($C_p / C_v$, typically $1.3$ to $1.4$ for hydrocarbons).
• $M$: Fluid molecular weight ($g/mol$ or $lbm/lb\text{-}mol$).
• $R$: Universal gas constant.
• $T_s$: Operating storage temperature ($K$ or $^\circ R$).

---

Inventory Grouping and Isolation Valve Classification

The total mass of fluid released into the atmosphere ($m_{release}$) depends not only on initial flow rate ($W_n$) but also on total available Isolable Inventory Mass ($m_{inv}$) and the speed of emergency isolation.

Concept of Inventory Groups

An Inventory Group consists of a collection of interconnected vessels, heat exchangers, and piping circuits that cannot be isolated from one another during an emergency. The total isolable mass ($m_{inv}$) equals the combined fluid contents of all components within the inventory boundary.

Emergency Isolation Valve Classes (API RP 581 Table 4.1)

API RP 581 categorizes facility isolation capabilities into four discrete classes based on valve automation and detection speed:

Leak Duration Capping Rule ($t_{max} = 3600\text{ s}$)

API RP 581 mandates that continuous leak duration ($t_{ld}$) is capped at a maximum limit of $1\text{ hour} (3600\text{ seconds})$ for risk modeling. The total release mass for hole size $n$ is calculated as:

$$m_{release, n} = \min\left[ W_n \times t_{ld}, m_{inv} \right]$$

Where $t_{ld} = \min\left[ t_{iso}, 3600\text{ s} \right]$. If total isolable inventory ($m_{inv}$) is smaller than calculated continuous flow ($W_n \times t_{ld}$), the inventory empties completely, limiting release mass to $m_{inv}$.

---

Fluid Phase Behavior and Flashing Liquid Thermodynamics

When pressurized process fluids escape to atmospheric conditions, thermodynamics dictates phase transition and atmospheric dispersion behavior:

1. Subcooled Non-Volatile Liquid Release

Fluids stored well below boiling point (e.g., diesel, heavy gas oil, water) remain liquid upon release. Liquid spills to the ground, forming a spreading pool. Consequence is dominated by pool fire thermal radiation or ground/water spill contamination.

2. Superheated Flashing Liquid Release

Liquefied gases stored under pressure above their atmospheric boiling point (e.g., propane, butane, anhydrous ammonia, hydrofluoric acid) undergo instantaneous flashing upon depressurization.

Flashing Liquid Mechanics:

1. Vapor Fraction Flash ($f_v$): A portion of the liquid flashes violently into vapor, calculated by enthalpy balance:

$$f_v = \frac{C_{p,l} \cdot (T_s - T_{bp})}{\Delta H_{vap}}$$

1. Aerosol Droplet Entrainment ($f_{entrain}$): The violent expansion of flashing vapor shatters the remaining un-flashed liquid into microscopic aerosol droplets (droplet diameter $<50\,\mu m$). Rather than falling to the ground, aerosol droplets remain suspended in the expanding vapor cloud, dramatically increasing effective cloud mass ($W_{cloud}$):

$$W_{cloud} = W_n \cdot \left[ f_v + (1 - f_v) \cdot f_{entrain} \right]$$

Suspended aerosol clouds travel downwind as heavy, dense vapor clouds, posing extreme toxic dispersion or catastrophic Vapor Cloud Explosion (VCE) hazards.

---

Technical Worked Example: Deethanizer Overhead Accumulator Vessel

Component Parameters:

• Fluid: Pressurized Propane ($100\% \text{ C}_3\text{H}_8$), storage temperature $T_s = 110^\circ\text{F} (316.5\text{ K})$, operating pressure $P_s = 220\text{ psig} (1.617\text{ MPa})$.
• Inventory Mass: $m_{inv} = 45,000\text{ lbm} (20,412\text{ kg})$.
• Isolation Capability: Class A ROIV system ($t_{iso} = 180\text{ s}$). Flashing liquid vapor fraction $f_v = 0.35$, entrainment $f_{entrain} = 0.50$.

Release Scenario Discharge and Inventory Summary Table:

Analytical Conclusions:

For small and medium hole sizes, Class A emergency isolation limits release duration to $180\text{ seconds}$, leaving the majority of inventory inside the vessel. However, for large hole and rupture scenarios, fluid mass discharge rate ($W_n$) is so immense that the entire $45,000\text{ lbm}$ inventory exhausts into the atmosphere in $95\text{ seconds}$ and $23.8\text{ seconds}$ respectively, blowing past Class A valve closure times and releasing the maximum cloud mass of $30,375\text{ lbm}$.