PSV Inlet Pressure Loss

1. The 3% Rule

API 520 Part II Section 6.2 establishes the fundamental requirement for PSV inlet piping: the non-recoverable pressure loss between the protected equipment and the pressure safety valve inlet flange must not exceed 3% of the valve set pressure at the rated flow capacity.

Why 3%?

The 3% limit is derived from the typical blowdown (re-seat pressure differential) of spring-loaded pressure relief valves. Most conventional PSVs have a blowdown of 7-10% of set pressure. If inlet pressure loss exceeds 3%, the effective pressure at the valve inlet drops far enough below set pressure that the valve attempts to re-seat while the vessel pressure is still above set. This creates the rapid open-close cycling known as chatter.

When Is the 3% Rule Checked?

2. Chatter & Flutter

Chatter is the rapid, full-stroke opening and closing of a PSV at frequencies of 10 to 100 Hz. It is the most common and most destructive consequence of excessive inlet pressure loss. A chattering PSV can destroy its seat in a matter of seconds and lose the ability to seal, resulting in a continuous leak or complete failure to relieve.

The Chatter Cycle

Understanding the chatter mechanism is essential for diagnosing and preventing the problem. The sequence of events is as follows:

Chatter vs. Flutter vs. Cycling

Consequences of Chatter

3. Darcy-Weisbach Method

The Darcy-Weisbach equation is the standard method for calculating frictional pressure loss in pipe. For PSV inlet loss verification, it is applied to determine the total non-recoverable pressure drop from the vessel nozzle to the PSV inlet flange.

Friction Factor: Colebrook-White Equation

The Darcy friction factor depends on the Reynolds number and the relative roughness of the pipe. For turbulent flow (Re > 4000), the Colebrook-White implicit equation is used:

Since the Colebrook-White equation is implicit in f, it must be solved iteratively. Common approaches include:

• Swamee-Jain approximation: Explicit formula accurate to within 1% for 5000 < Re < 10^8 and 10^-6 < ε/D < 10^-2
• Newton-Raphson iteration: Starting from Swamee-Jain, typically converges in 3-5 iterations
• Moody chart: Graphical lookup, useful for manual verification

Reynolds Number

Gas Density at Conditions

For gas and vapor service, the fluid density must be calculated at the relieving conditions (relieving pressure and temperature). Using the ideal gas law:

Velocity and Mach Number

Example: Gas Service Inlet Loss

4. Equivalent Length Method

The equivalent length method converts fittings, valves, and other flow obstructions into an equivalent length of straight pipe that would produce the same pressure drop. This method, documented in Crane Technical Paper 410, is the standard approach for PSV inlet loss calculations.

L/D Ratios for Common Fittings

Each fitting type is assigned an L/D ratio (equivalent length in pipe diameters). The actual equivalent length in feet is obtained by multiplying L/D by the pipe internal diameter in feet.

K-Factor Method (Alternative)

An alternative to the equivalent length method is the resistance coefficient (K-factor) method, which is sometimes more accurate for specific fittings:

5. Inlet Pipe Sizing

Proper inlet pipe sizing is the primary means of controlling PSV inlet pressure loss. The relationship between pipe diameter and pressure drop is strongly non-linear: pressure drop varies approximately with the fifth power of diameter for a given flow rate (since both velocity and friction factor change with diameter).

General Sizing Rules

API 526 Orifice Sizes and Typical Inlet Connections

Effect of Pipe Size on Pressure Drop

The sensitivity of pressure drop to pipe diameter is dramatic. For the same flow rate, doubling the pipe diameter reduces the velocity by a factor of 4 (area doubles squared) and reduces the pressure drop by approximately a factor of 32 (fifth power relationship). This is why increasing one pipe size is often sufficient to move from a failing to a passing 3% check.

6. Best Practices

Following established best practices for PSV inlet piping design eliminates the vast majority of inlet loss problems. These recommendations are drawn from API 520 Part II, API 521, and decades of industry operating experience.

Inlet Piping Design Rules

Common Design Mistakes

Pilot-Operated PSVs

Pilot-operated pressure relief valves (POPRVs) are an alternative when conventional spring-loaded valves cannot meet the 3% rule. POPRVs sense pressure through a small pilot line connected upstream of any inlet piping losses, making them largely immune to inlet pressure drop effects.

Multiple PSVs on Common Inlet Header

When multiple PSVs share a common inlet header, the 3% rule applies to the total flow through the header. Special considerations include:

• Simultaneous relief: If multiple valves can open simultaneously, the header must be sized for the combined flow.
• Staggered set pressures: If PSVs have different set pressures, check each combination of open valves against the 3% rule.
• Header sizing: The common header is typically two pipe sizes larger than the largest individual PSV inlet to accommodate multiple flows.
• Individual laterals: Each lateral from the header to a PSV must also satisfy the 3% rule independently.

References

• API 520 Part II (6th Ed., 2015) — Sizing, Selection, and Installation of Pressure-Relieving Devices: Part II — Installation
• API 521 (6th Ed., 2014) — Pressure-Relieving and Depressuring Systems
• API 526 (7th Ed., 2017) — Flanged Steel Pressure-Relief Valves
• ASME BPVC Section VIII, Division 1 — UG-125 through UG-137: Pressure Relief Devices
• Crane Technical Paper 410 (26th printing) — Flow of Fluids Through Valves, Fittings, and Pipe
• GPSA Engineering Data Book, Chapter 18 — Safety, Relief, and Environmental
• NFPA 30 — Flammable and Combustible Liquids Code