Clarification of Sound Power Level Evaluation for Acoustically Induced Vibration Fatigue
There are multiple sources of vibration in piping that can lead to failures, usually occurring at welds, penetrations, or other ‘discontinuities’. The EI Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework1 indicates the following common causes of piping vibration:
- Flow induced turbulence
- Mechanical excitation
- Surge/momentum changes due to valve operation
- High frequency acoustic excitation
Pressure-relieving and related systems often operate at choked-flow conditions, which generate the high frequency acoustic energy associated with high dynamic stress levels that can cause “circumferential discontinuities on the pipe wall, such as small bore connections, fabricated tees or welded pipe supports” to fail quickly.1, §2.3.4, p. 13 Given the applicability of this potential failure mode to pressure-relieving systems, API Standard 521 §184.108.40.206 also discusses this acoustical fatigue.
The EI Guidelines (Flowchart T2-5, High frequency acoustic fatigue assessment) and API Standard 521 (Equation 43) provide a calculation for the estimation of the acoustical energy that can be generated based on the work of Carucci and Mueller3; however, there are some confusing aspects that are worthy of clarification.
Acoustic excitation occurs at locations of sonic flow. The generation of the high frequency acoustical energy is associated specifically with compressible fluid flow achieving sonic conditions. The ‘choking’ that occurs at these conditions results in a significant amount of useful mechanical energy being ‘lost’, some of which is converted to internal thermal energy and some of which is converted into the high frequency acoustical energy of interest here.
Sustained flow rates at very high (but not sonic) velocities can cause flow induced turbulence, which can generate a wide spectrum of frequencies; however, “the majority of the excitation is concentrate at low frequency (typically below 100 Hz); the lower the frequency, the higher the level of excitation from turbulence.”1, §2.3.1, p. 7
As a result, we will only calculate an estimate for the generation of high frequency acoustical energy as cited above for locations where sonic flow is predicted (‘sources’ of the high frequency acoustic energy). Specifically, we would look at any place where sudden expansion of compressible fluid flow takes place: pressure relief valves, depressuring or control valves, restriction orifices, pipe expanders, and expanding tees. The evaluation for a given piping segment starts at the first instance of choking.
Attenuation occurs downstream of the source. As the sound energy travels down the pipe wall, some reduction in the power (attenuation) occurs. The guidelines are pretty clear about the attenuation due to lengths of constant area piping (6dB for every 100 pipe diameters of length). Attenuation also occurs at expansions that have subsonic flow in accordance with AExp=2(D2 ⁄ D1 -1), where D2 is the downstream inner diameter and D1 is the upstream inner diameter4. Attenuation is also expected to occur at tees that have subsonic flow, although we are not aware of any publicly available information on the magnitude of this attenuation.
With the interest in circumferential discontinuities in the pipe, we specifically look at locations of small bore branch connections (for example, bleeder valves) and tees (for example, where a bypass branch ties into the discharge line, and where the discharge line ties into the flare header). The attenuation of the sound power level from the source to the location of interest is calculated, and then compared to the screening criterion (155 dB).
Choking in series uses logarithmic addition of sound power levels. The relatively straightforward calculation process just described gets complicated whenever sonic flow is encountered en route to the location of interest. In this case, the acoustical energy generated by the sonic flow conditions needs to be added to the acoustical energy coming from the upstream source(s). Both the EI Guidelines and API Standard 521 provide the logarithmic addition needed to combine the acoustic energies at a point. To give an order of magnitude of the effect of this logarithmic addition, if two equal sound power levels are added together, the outgoing sound power level is 3 dB (10·log10 (2)=3.01) greater than the incoming sound power levels.
It is useful to note that this logarithmic addition is also employed when the location of interest is a tee having a sound generating source upstream of both legs of the tee.
Sonic flow factor is specifically for branched tees with choked flow. Based on a number of instances of acoustically induced failures reported, one common location of failure is at a branch connection into a tee, and specifically for cases where the branch connection is smaller in diameter than the tee body and choked flow occurs at this point. There is likely additional vibration caused by the turbulent flow and impingement on the tee opposite of where the branch ties in, as well as the oft-cited “intensified dynamic strain response” at the tee.
If one were to use the process outlined above for the simple, common setup of a single sound-generating source (pressure relief valve) that discharges into a larger flare header with sonic flow predicted at the tee, one would perform the following:
- Estimate the sound power level at the pressure relief valve
- Attenuate the sound power level through the discharge piping to the tee branch
- Estimate the sound power level at the tee due to sonic flow
- Logarithmically add the sound power levels (2) and (3) and compare to the screening criterion, perhaps with an additional safety factor given industry experience with failures at this location
Given that the logarithmic addition is inconvenient, it would be nice to have a simple rule of thumb to work with, especially for this common configuration. Also, since we seem to have more failures for this specific configuration (branch tee with sonic flow), an additional safety factor on the screening criterion would be justified. Rather than adjust the screening criterion, we can ‘kill two birds with one stone’ by specifying a factor to add for this specific configuration that encompasses both elements. This is the basis for the “Sonic Flow Factor” of 6dB, which is ill-defined in the EI Guidelines and perhaps a bit ambiguous in API Standard 521.
A complicated example for clarification. To illustrate each of these clarifications, we provide an example below derived from an actual installation we have evaluated.
AIV example illustrating points above
 Energy Institute. “Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework”. 2nd Edition, 2008 Jan.
 American Petroleum Institute. “API Standard 521: Pressure-relieving and Depressuring Systems”. 6th Edition, 2014 Jan.
 Carucci VA, Mueller RT. “Acoustically induced piping vibration in high capacity pressure reducing systems”. In 92-/WAPVP-8, pp. 1-13. American Society of Mechanical Engineers. 1982.
 Melhem GA. “Estimate Vibration Risk for Relief and Process Piping”. In American Institute of Chemical Engineers 2013 Spring Meeting, 9th Global Congress on Process Safety. April 2013.