Acoustic Induced Vibration (AIV) is a flow induced vibration phenomena that can result in fatigue failures in piping systems leading to major safety and economic consequences such as damage to assets, environmental impact and loss of life.

This article discusses guidelines that are available in the industry to identify piping systems that are prone to Acoustic Induced Vibration (AIV) failures and the suggested mitigation measures to avoid potential AIV  failures.

## What is Acoustic Induced Vibration (AIV)

AIV is a common phenomena in gas service applications in refinery, oil, gas and petrochemical industry when high frequency acoustic energy is generated by a pressure reducing device such as a safety relief valve, choke valve, control valve or orifice plate. The phenomena is common to large capacity relief valves, flare and blow-down systems. The pressure reducing device produces an area of turbulent mixing and shock waves immediately downstream of the device that generates high frequency circumferential vibration in the piping wall. The frequency typically varies between 500Hz to 2000Hz and its amplitude or power level is dependant on the mass flow rate and pressure drop across the device.

Video below will provide an indication on the various mode shapes for pipe wall subject to circumferential vibration.

The circumferential vibration of the pipe wall due to high acoustic energy has the potential to generate high dynamic stress levels at asymmetric connections in downstream piping such as:

• Tees and Branch connections.
• Small bore connections such as vents, drains, instrument and sample connections.
• Welded pipe supports such as pipe shoes and anchors.

The above mentioned asymmetric discontinuities are potential fatigue failure points. It may be noted that the time to AIV faiures is short due to high frequency response.

## Predicting the Acoustic Energy Level

The internal sound power level at the pressure reducing device can be calculated from the following equation:

Lw = 10 log$$\left[M^2*\left(\frac{P_1-P_2}{P_1}\right)^{3.6}*\left(\frac{T}{W}\right)^{1.2}\right]$$ + 126.1 + K

where:

Lw = sound power level in dB

M = mass flow rate in kg/s

P1 = upstream pressure in kPa absolute

P2 = downstream pressure in kPa absolute

T = temperature in Kelvin

W = molecular weight

K = Correction factor to account for sonic flow. Its value is 0 for nonsonic flow and 6 for sonic flow conditions

## Predicting the susceptibility of piping system to risk of AIV failure

The Energy Institute (EI) guidelines recommends Likelihood of Failure (LOF) as a form of assessment for screening lines that are prone to AIV. As per EI guidelines, the LOF is not an absolute probability of failure and is based on simplified models to ensure ease of application. Higher LOF scores suggests greater susceptibilty of piping system to risk of AIV failure. Based on LOF score, the following actions are recommended:

### LOF greater than equal to 1 (LOF ≥ 1)

• The main line shall be redesigned.
• Small bore connections on the main line shall be assessed.
• A visual survey shall be undertaken to check construction, support and potential vibration transmission to adjacent pipework.

### LOF greater than equal to 0.5 and less than 1 (1.0 > LOF ≥ 0.5)

• The main line should be redesigned.
• Small bore connections on the main line shall be assessed.
• A visual survey shall be undertaken to check construction, support and potential vibration transmission to adjacent pipework.

### LOF greater than equal to 0.3 and less than 0.5 (0.5 > LOF ≥ 0.3)

• Small bore connections on the main line shall be assessed.
• A visual survey shall be undertaken to check construction, support and potential vibration transmission to adjacent pipework.

### LOF less than 0.3 (LOF < 0.3)

• A visual survey shall be undertaken to check construction, support and potential vibration transmission to adjacent pipework.

A paper published by Carucci and Mueller in 1982 to investigate failures in thin walled piping identified a relationship between level of acoustic energy in the piping system and AIV failures. Figure below shows the design limit curve which is a plot of Carucci and Mueller (C-M) data representing internal sound power level Lw on the vertical axis vs nominal pipe diameter on the horizontal axis. If the predicted sound power level based on the formula in section above falls below the design limit curve, the piping system is deemed safe for AIV. If the predicted sound power level falls above the design limit curve, then the piping system needs to be evaluated to introduce control measures to mitigate the detrimental effects of AIV. Larger deviations from the design limit curve may call for more intensive measures to mitigate AIV failures. The safe design criteria curve is valid for non-continuous service not exceeding twelve hours.

The C-M curve shows 36 points of which 9 points represented by alphabets (A,B1,B2,C,D,E,F,G & H) represent AIV failures whereas the 27 points denoted by numbers 1-27 represent non-failures. It may be noted that point F which is substantially below the design limit curve was due to a weld undercut and had no abnormal behaviour after the weld was repaired. Hence it does not represent AIV failure. Referring to the above C-M curve it is noted that there are no AIV failure cases below the power level of 155 dB. Accordingly, EI guidelines require LOF assessment only for valves that generate sound power level greater than 155 dB. As per the flowchart in section T2.7 of EI guidelines, if the power level is less than or equal to 155 dB, the main line is assigned a LOF value of 0.29 and requires only a visual survey to be carried out for the line. If the sound power level exceeds 155 dB, the next weld discontinuity is assessed taking into consideration the attenuation in the line as well as additional power level due to other sources. The LOF for the weld discontinuity is calculated based on flowchart  T2.6 of EI guidelines.

## Reducing Power Level of the source for avoidance of AIV failure

Reduction in sound power level generated by pressure reducing device may be considered to reduce the risk of AIV failure. The following options may be considered:

• Pressure reduction in stages by using more than one valve.
• Using low-noise trim in valves.
• Using multi-stage restriction orifices.

Since the weld downstream of the reducing valve is prone to AIV failure, the overall design objective is to improve the structural integrity of the piping system by eliminating asymmetric discontinuities at branch weld connections and pipe support weld attachments.

## Increasing Pipe Wall Thickness for avoidance of AIV failure

The design limit curve developed by Carucci and Mueller does not take into consideration changes in pipe wall thickness. In 1997, Eisinger F.L developed the relationship between pipe diameter to thickness ratio (D/t) and sound power level at which failure could occur. The data are plotted as two lines, one line representing the fatigue limit and the other line which is 3dB lower than the fatigue limit, representing the allowable design limit. Eisinger's plot of D/t vs Sound power level suggests that a D/t ratio less than 64 is desirable in piping systems to avoid the potential of fatigue failure.

EI guidelines suggest increase in pipe wall thickness to reduce LOF. Any decisions to increase pipe wall thickness should be made at an early stage of the project as changes at later stages can have significant cost impact and delays in project execution.

## Recommended measures on Axisymmetric discontinuities for avoidance of AIV failure

A component is said to be axisymmetric if any two of its three principal moments of inertia are equal. Thus a flange welded on a piping system is axisymmetric. Axisymmetric discontinuities in the pipe wall, such as at flanges and stiffener rings have been found not to be potential fatigue failure points. This is because the pipe wall vibration amplitudes gradually damp out due to cylindrical shell stiffening effect. Hence, the only recommended precautions to be taken for axisymmetric discontinuities are to ensure good quality full penetration welds with no undercuts.

## Recommended measures on Asymmetric discontinuities for avoidance of AIV failure

A component is said to be asymmetric if none of its three principal moments of inertia are equal. Thus a branch connection on a piping system is asymmetric. Axisymmetric discontinuities in the pipe wall have been found to be potential fatigue failure points. Assessment based on EI guidelines generates a LOF value at each weld discontinuity on the main line and recommends corrective actions where the LOF is equal to 1. Weldolet and set-on branch connections are not recommended for AIV service as the discontinuity at the weld joint results in high stress intensification and renders the connection susceptible to fatigue failure.  Following types of branch connections are recommended:

• Forged or Wrought Tees
• Contoured outlet fittings such as sweepolets
• Full Wrap Reinforcement connections

The use of sweepolet ensures that the high stress levels at branch connections are remote from the welds. Similarly, for full-encirclement reinforcement, besides change in type of connection from asymmetric to axisymmetric, the wall thickness is increased locally resulting in lower stress levels.

Welded pipe support shoes also represent asymmetric discontinuity. It is recommended to replace welded shoe supports by clamped shoes for avoidance of AIV failure. Second option is to weld the shoe to a full encirclement saddle. Figure below shows the recommended shoe support arrangement for avoidance of AIV fatigue failure.

### Recommendations for small bore branch connections

The corrective actions prescribed in EI guidelines recommends improving the improving the response of the small bore connection (SBC) rather than reducing the excitation from the main line. For small bore branches two inches and below it is recommended to brace them back to the header by bracing them in two planes. The header should have sufficient straight lengths between adjacent small bore branches to accomodate the bracing supports. Bracing of SBC from the main line ensures that the small bore connection is not restricted from any movement with respect to the main line.

## Other Standards which address AIV failures

Annex-A of NORSOK Standard L-002, 2009 edition addresses Acoustic Fatigue in piping systems.

API Standard 521 requires that the potential for acoustic fatigue be evaluated through methods prescribed in EI Guidelines.