Slug Forces in Piping Engineering

                                

Understanding Slug Forces in Piping Engineering as per ASME B31.3

In industrial piping systems, fluid movement isn't always smooth. Sudden changes in flow conditions can generate powerful forces that, if not properly accounted for, can cause vibrations, misalignment, or even structural failure. Among these forces, slug force, rupture disc force, and relief valve (PSV) force are critical considerations for safe and efficient piping design.

ASME B31.3, the Process Piping Code, provides guidelines for handling these forces, ensuring that pipelines are designed to withstand them effectively. This article explores each of these forces, how they are calculated, and how to design proper support systems to mitigate their impact.

What is a Slug in Piping?

A slug is a large mass of liquid moving as a unit through a gas-filled pipeline. This phenomenon is common in multiphase flow systems, where gas and liquid phases separate due to differences in density and velocity.

When a slug reaches a bend, valve, or obstruction, it generates a sudden force due to momentum change. If not properly accounted for, this force can cause pipe movements, leading to mechanical failures.

Calculating Slug Force

Slug forces depend on the velocity, density, and cross-sectional area of the liquid phase in the pipeline. Two key formulas are used for different scenarios:

1. Slug Force at a Pipe End or Sudden Stop

This equation estimates the impact force when a slug comes to an abrupt halt, such as hitting a closed valve:

$$F = \rho A V^2$$

Where:

• $F$ = Force due to slug impact (N)
• $\rho$ = Fluid density (kg/m³)
• $A$ = Internal cross-sectional area of the pipe (m²)
• $V$ = Velocity of the slug (m/s)

This formula is widely used for calculating the force exerted when a slug reaches an obstruction in the pipe.

2. Slug Force at an Elbow or Bend

When a slug changes direction at an elbow, the force is distributed based on the angle of the bend. The force is given by:

$$F = \rho A V^2 \sqrt{2(1 - \cos \theta)}$$

Where:

• $\theta$ = Angle of the elbow (degrees)

• If $\theta = 0^\circ$ (straight pipe), force is zero.

• If $\theta = 90^\circ$ (right-angle bend), force is at its maximum.

This formula is crucial for stress analysis in pipelines with multiple bends, especially in gas-liquid systems where slugging is frequent.

Rupture Disc Force

A rupture disc is a pressure relief device designed to burst at a predetermined pressure to protect piping and equipment from overpressure conditions.

When a rupture disc bursts, it releases high-pressure fluid, generating a reaction force on the pipe. This force is calculated as:

$$F = P A$$

Where:

• $P$ = Pressure before rupture (Pa)
• $A$ = Rupture area (m²)

The force from a ruptured disc must be considered in support design, especially in high-pressure applications where sudden energy release can cause severe vibrations.

Relief Valve (PSV) Reaction Force

A Pressure Safety Valve (PSV) is designed to open when the system pressure exceeds safe operational limits, allowing gas or liquid to escape and preventing catastrophic failure. However, the sudden discharge of fluid creates a reaction force on the piping system, which must be properly accounted for in design considerations.

Reaction Force Equations

General Formula:

The reaction force due to the sudden release of fluid is given by:

$F=2\times P\times A$

Where:

• $F$ = Reaction force (N)
• $P$ = Set pressure (Pa)
• $A$ = Selected orifice area (m²)

Momentum and Pressure Thrust Components

ASME B31.1-1992, Appendix II provides a more detailed equation for calculating reaction force, considering both momentum thrust and pressure thrust:

$F=\frac{W\cdot V}{g_c}+(P-P_a)A$

Where:

• $F$ = Total reaction force (N)
• $W$ = Mass flow rate (kg/s)
• $V$ = Exit velocity (m/s)
• $g_c$ = Gravitational conversion factor
• $P$ = Static pressure at the discharge point (Pa)
• $P_a$ = Atmospheric pressure (Pa)
• $A$ = Discharge area (m²)

Considerations for Gas and Liquid Flow

For Gas Flow:

• The force calculation primarily depends on mass flow rate and velocity.
• Choked flow conditions can influence the effective pressure and velocity at discharge.

For Liquid Flow:

• Additional factors such as the discharge coefficient and pipe resistance should be taken into account.
• The reaction force may vary depending on the density and compressibility of the fluid.

Supporting for These Forces

To ensure the structural integrity of a piping system, engineers must design proper support mechanisms:

1. Pipe Supports & Restraints

• Anchors: Fixed supports to prevent pipe movement.
• Guides & Stoppers: Prevent excessive lateral movement.
• Expansion Loops: Absorb energy from transient forces.

2. Dynamic Analysis

• Transient Fluid Analysis: Tools like AFT Impulse and Pipenet model slug force impacts.
• Pipe Stress Analysis: Software like CAESAR II evaluates the effect of slugging and relief valve forces.

3. Snubbers & Dampers

These devices absorb and dissipate energy from transient forces, reducing the risk of vibrations and structural damage.

4. Reinforced Pipe Supports

Strong pipe shoes, trunnions, and clamps help secure piping in areas experiencing high slug, rupture, or PSV forces.