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Evaluate pressure relief system forces in existing installations

01.01.2013  |  Smith, D.,  Smith & Burgess LLC, Houston, TexasWhite, J.,  Smith & Burgess LLC, Houston, TexasFrenk, B. ,  Frenk Water Technologies LLC, Byron, Illinois

The purpose of this study is to limit the number of relief valves that require rigorous engineering calculations to determine the adequacy of the installation.

Keywords: [relief valves] [pressure relief valves] [modeling] [valves]

Pressure relief devices control the amount and disposition of material during a process upset while simultaneously protecting process equipment from damage due to overpressure caused by the upset. The devices most commonly used for these purposes are pressure relief valves (PRVs) and pressure safety valves (PSVs).

Quite a bit of engineering research, testing and analysis has been performed to improve assessment of relief valve suitability and the ability of associated installations to protect equipment from overpressure. One area that has less prescriptive requirements is analysis of the structural integrity of the relief device installation during the emergency event.

These installations are not designed for continuous flow, but rather sporadic flow, often at choked or sonic conditions. This article takes a brief look at the existing evaluation of reaction forces for PRVs. It also performs a detailed baseline analysis of typical installations to develop a screening tool for evaluating an existing facility, and identifies the results when tested against an existing petrochemical facility.

The purpose of this study is to limit the number of relief valves that require rigorous engineering calculations to determine the adequacy of the installation. Often, it is assumed that PRV installations are simple and easy to design. However, practical experience has shown that PRVs, particularly devices that discharge to the atmosphere, are the most easily manipulated during the actual construction phase and often are not installed as they were intended.

See Fig. 1 for two examples of installations that were likely not installed as designed. Clearly, not all existing relief valve installations meet the specifications recommended by industry practice.


  Fig. 1. Examples of PRV installations where
  little or no engineering piping design was
  performed or design was not followed. 

Reaction force analysis methodology

During an overpressure event, the discharge of a PRV imposes a load, referred to as a reaction force, on the collective installation. This force creates a bending moment that is both a function of the quantity and state of the release and the physical layout of the piping installation (i.e., the lever arm created by the installation). The stress caused by the reaction force is propagated into and through the PRV and then into the inlet piping and vessel nozzle, unless the system is properly supported.

API reaction force analysis. The American Petroleum Institute (API) provides guidance for determining pressure relief requirements for pressure relief device installations. API 520, Part 2, states that PRV outlet piping should be independently supported and properly aligned. Stresses due to forced directional alignment of PRV piping are also mentioned; however, that topic will not be discussed in this article. The authors’ collective practical experience has demonstrated that a significant portion of atmospheric relief devices do not have piping supports in place, as described in Fig. 2.


  Fig. 2. Recreation of figure from API 520 for
  a typical relief valve installation. Note: The
  support should be as close as possible to
  the centerline of the vent pipe. F = the
  reaction force, and A = the cross-sectional
  area of discharge pipe. 

API 520, Part 2, provides a basis calculation for the reaction forces in the event of vapor or two-phase releases directly to the atmosphere. There is no discussion in this section of the reaction forces developed during a liquid release. Furthermore, no guidance is presented with respect to applying these results or determining if an installation is acceptable; instead, the burden is placed on the designer to ensure that the installation is appropriate. While this may be reasonable for the design of new facilities, evaluating the adequacy of existing facilities becomes much more complicated.

The formulas from API 520, Part 2, are listed below for relief devices discharging to the atmosphere:

API 520, Part 2, Customary units for vapor relief reaction forces:


API 520, Part 2, US customary units for two-phase relief reaction forces:


F = Reaction force at the point of discharge to the atmosphere, pound force (lbf)
k = Ratio of specific heats (CP/CV) at the outlet conditions
W = Flow of any gas or vapor, pound mass (lbm)/hr
CP = Specific heat at constant pressure
CV = Specific heat at constant volume
T = Temperature at the outlet, °R
M = Molecular weight of the process fluid
A = Area of the outlet at the point of discharge, in.2
P = Static pressure within the outlet at the point of discharge, psig
x = Weight fraction vapor at exit conditions
ρg = Vapor density at exit conditions, lbm/ft3
ρl = Liquid density at exit conditions, lbm/ft3
Pe = Absolute pressure at pipe exit, psia
Pa = Absolute ambient pressure, psig.

DIERS reaction force analysis. The Design Institute for Emergency Relief Systems (DIERS) provides similar guidance for the consideration of reaction forces and the determination of the acceptability of a relief device installation. Additional recommendations are provided for a suggested piping layout to avoid excessive lever arms, as recreated in Fig. 3. In this illustration, the system on the left has significantly more stress due to the increased lever arm and direction of discharge when compared to the system on the right.


  Fig. 3. Even the smallest modification in piping
  design can have a significant effect on the
  resulting reaction forces. 

Additionally, emphasis is placed on the importance of evaluating the reaction forces for all credible overpressure contingencies, not simply the controlling contingency. This is important because the physical properties are not always the same, and, in some cases, the controlling contingency for sizing may be a vapor stream, while the controlling case for the reaction forces may be a two-phase stream.

Reaction force case study analysis

A piping system may respond far differently to a dynamic load than to a static load of the same magnitude. Static loads are those applied slowly enough so that the piping system has time to react and internally distribute the loads, thereby remaining in equilibrium.

With dynamic loads—those that change quickly—the piping system may not have time to internally distribute the loads, so forces and movements are not always resolved, resulting in unbalanced and potentially concentrated loads and pipe movement.

The typical action of relief valve venting is an impulse load, where the flowrate and associated forces ramp up from nominally zero to some value, remain relatively constant for the duration of the release, and then ramp down to zero again. When the relief valve opens, the discharge fluid creates a jet force that acts on the piping system. This force increases from zero to its full value over a time frame similar to the opening time of the valve. The relief valve remains open until sufficient fluid is vented to relieve the overpressure situation. When the valve closes, the reduction in flow corresponds to the loss of the jet force over the closing time of the valve.

Multiple relief valve piping configurations were examined for both static and dynamic conditions, using analysis software. The stresses calculated during the analysis were checked against the allowable stresses per American Society of Mechanical Engineers (ASME) standards. Additionally, the analysis was used to determine if a flange leak was likely. In all cases, the dynamic condition was determined to be the governing condition for the structural integrity of the piping system.

The leakage check examined the tendency of the flanges to separate under the applied piping loads. ASME B31.3 does not directly address flange leakage. The purpose of this analysis was to determine piping failure and not flange leaks.

From extensive tests, “It has been determined that, even under unusually severe bending stresses, flange assemblies did not fail in the flange proper, by fracture of the bolts or by leakage across the joint face. Structural failure occurred almost invariably in the pipe adjacent to the flange, and, in rare instances, across an unusually weak attachment weld. Leakage well in advance of failure was observed only in the case of threaded flanges.”1

These findings, which suggest that the structural integrity of the piping is the major area of concern for any stress analysis and should be considered over flange leakage, serve as the basis for these evaluations.

Many different process connections have been observed in field installations: Welding-reducing tees, weld/thread o-lets, and unreinforced “stub-in” connections. Unreinforced stub-in connections result in the highest ratio of calculated to code-allowed stresses, followed by o-lets and then welding-reducing tees for the same relief system-applied piping loads. The model used in the current evaluations has been confined to welding-reducing tees.

The allowable code stresses are below the yield and well below the tensile, as indicated in Table 1, for commonly used carbon steel materials. The net result is that there is a 19% to 24% safety factor between the code allowable for occasional loading and the yield point where the material begins to fail. The relief valve models were evaluated to establish relief pressures at which the calculated stresses were within 5% of each of the allowable occasional, yield and tensile stresses.


Modeling details. The relief valves were modeled as an “open discharge,” with a vertical pipe discharging directly to the atmosphere. As shown in Fig. 4, the process connection is mounted on a pipe header with a welding-reducing tee. This arrangement was chosen to provide a more realistic representation of “typical” installations together with the inherent flexibility of the tee/header connection. The vent pipe is the same diameter as the outlet connection on the valve and is unsupported at the elbow, with a 6-foot-long vertical vent pipe.


  Fig. 4. Sample of the model basis. 

Another software program was used to determine the physical properties along the vent pipe required to calculate the thrust and momentum forces (Fig. 5):

  • Average velocity along the vent pipe
  • Average temperature across the outlet of the vent pipe
  • Average velocity at the elbow.

  Fig. 5. Sample of the velocity profile output. 

The relief valve was modeled as an orifice at the end of a converging nozzle. The orifice was set to produce the capacity calculated by a relief valve analysis for the given inlet conditions using the certified orifice size. The following assumptions were made regarding the analysis:

  • The process fluid was vapor
  • The manufacturer’s certified orifice diameters (from the National Board of Boiler and Pressure Vessel Inspectors’ Relief Device Certification NB-18) were used in place of standard API orifice diameters to provide more realistic discharge flow
  • Valve opening and closing time was 8.0 milliseconds, and venting would last for one second; these numbers are specific to the valve manufacturer, and they appear to be typical throughout the relief valve industry
  • Wind loadings were not considered
  • All piping was considered to be schedule 40 carbon steel
  • Relief valve inlet flanges were specified as required for process considerations
  • Relief valve outlet flanges were specified to American National Standards Institute (ANSI) RF 150.

Screening study and results

The objective of developing the screening tool was to provide a fairly quick method to identify relief valves that were likely to need either support or more detailed analysis to verify the adequacy of the existing installation. For the purpose of simplification, several assumptions were made, as described below:

  • All relief valves discharging to a closed disposal system are adequately supported for an individual release
    • Relief valve installations that discharge to a closed system are, by definition, supported by at least the point of discharge, and the purpose of this screening is to identify relief valves that require support—not to evaluate the adequacy of existing supports
    • Due to the complexity of a supported common disposal system, these systems are excluded from the scope of this study
  • All liquid and two-phase relief contingencies require detailed analysis
    • Water hammer is a much bigger concern for liquid and two-phase releases than for reaction forces, and is therefore an item to be evaluated outside of reaction forces
    • Additionally, the dynamic effects of flashing flow create far too many variables to include in a simplistic screening
  • All nonstandard PRV sizes require detailed analysis
    • While this statement may not be true for every installation, for the purposes of developing an automated tool to identify relief valves that may need detailed engineering, the obvious decision is to flag any installation that falls out of the normal range
    • For the purposes of this study, the standard was defined by the flanged relief valve sizes listed in API 526 and shown in Fig. 6.


  Fig. 6. Relief valve size configurations
  evaluated as per API 526. 

PRV installations can be characterized as either typical or complex. Since the generic screening methodology was performed using a typical PRV configuration (as seen in Fig. 4), some method of identifying configurations with more complex piping had to be identified. For the purposes of this study, any piping configuration containing more than “change of direction” fitting (elbow, 45° bend, branch tee, etc.) was considered to be complex. Fig. 3 was used as the basis for this assumption.

PRVs installed and sized for only the external fire contingency will not require a reaction force evaluation. While this may seem counterintuitive, as external fire is the prevailing overpressure contingency in pressure relief system design, it is proposed that a PRV installation cannot be deemed adequate by a reaction force analysis in the event of an external fire.

The heating effect on the relief device from a fire is unknown, and it can be more significant for the relief device installation (particularly the outlet piping and the valve body itself) than the stresses caused by the flowrate. It is proposed that the failure of a relief valve installation due to reaction forces is more likely to be controlled by the reduction in tensile strength of the installation due to the heat input, than to be controlled by the system design.

PRVs installed and sized for only the liquid hydraulic expansion contingency will not require a reaction force evaluation. Liquid hydraulic expansion cases are often nominal rates for which a small thermal PRV is installed. In many cases, the PRV possesses a capacity far greater than the required relief load. Additionally, the non-steady-state nature of a thermal expansion event tends to result in the unsustained releases that do not develop typical fluid flow characteristics. Taking these factors into account, it was determined that hydraulic expansion scenarios do not require pipe stress screening.

Qualitative screening. The screening study was divided into two phases, one being qualitative screening against assumptions, as set forth above, and the other being against the criteria set forth in the base-case study for each relief valve size. The qualitative step was performed stepwise, as a discussion tree, as represented in Table 2.


The qualitative screening step identified 32 installations that are acceptable “as is,” 45 that require more detailed analysis (including the potential review of why two-phase/liquid releases are being sent to the atmosphere), and 112 installations that are not covered by this screening.

The second stage of the screening was developed based on “generic” pressure relief device installations. The intention was to draw a line separating PRV installations into three categories:

  • Installations predicted to be acceptable as installed
  • Installations that will require detailed engineering analysis to determine the adequacy of the installation
  • Installations that are expected to require proper piping support if a detailed engineering analysis is performed; the results of this screening are shown in Table 3.

This screening was performed against all 189 relief device installations rather than the remaining 112 from the qualitative screening, due to the fact that three possible results exist rather than the two previously used. A relief valve installation that was flagged as needing a detailed analysis in the qualitative step may be identified as a device that is predicted to require support irrespective of a detailed analysis. Additionally, a relief device sized only for fire may be identified as an installation requiring support, even before the effects of temperature change can be examined.

To perform this screening, the existing PRV installations were divided into typical and complex groups, as described previously. For typical installations, a threshold value of 90% was used when comparing the installation to screening tool-generated stresses for each relief valve size. This means that relief valves having a relief pressure within 90% of the threshold for occasional loading were flagged as requiring detailed engineering analysis. Similarly, relief pressures exceeding 90% of the threshold for yield stress were flagged as likely requiring support, regardless of the detailed analysis. For complex PRV installations, the threshold value was lowered to 70% of the occasional loading and yield stress limits, respectively.

The results of the quantitative screening, shown in Table 3, indicate that most of the valves predicted to require support (28 of the 37 identified) fall into the category of those predicted to exceed the yield stress. Therefore, these valves were identified as installations that do not require detailed analysis to determine if support is required.

Overall results. The results of both screening studies were combined to create an actionable list of items for ensuring the physical integrity of the PRV installations, as shown in Table 4. For the facility studied, the aggregate of the two screenings predicted that 28 pressure relief installations would require support (even if a detailed engineering study was performed), and an additional 34 PRV installations would require a more detailed engineering study to determine the adequacy of the installations. Overall, more than 30% of the relief valves studied were found to require action.


A sample was taken from each of the three categories, and detailed analyses were performed to verify these results. Of those samples, all relief device installations predicted to require support did indeed require support to avoid exceeding the yield stress. Likewise, all sampled installations predicted to be adequate were found to be adequate. Of the sampled devices predicted to require detailed engineering analysis, all but one exceeded the yield stress, and that installation did exceed the allowable stress.

The purpose of this study was to provide a solid screening tool to prevent the cost of performing a detailed engineering evaluation on every relief device installation, and the end result met this objective. In some cases, it may be more cost-effective to simply support PRV installations for which a detailed study is suggested, rather than to perform the detailed study.


Overpressure protection analysis has evolved significantly since the inception of the process safety management (PSM) standard, but the mechanical stress applied to the piping during overpressure events appears to have been, for the most part, overlooked. Criteria for identifying pressure relief device installations that may exceed allowable stress levels were developed from these systems. These criteria were then evaluated against a petrochemical facility’s pressure relief systems and benchmarked for validity as a first-pass tool to identify installations potentially requiring physical supports. For the facility studied, approximately two-thirds of the PRV installations were predicted to be adequate with respect to reaction forces, with the remaining installations being broken into two categories: those requiring support and those requiring further analysis.

This proves that, in practice, a significant percentage of PRV installations do not meet the desired structural integrity with regard to reaction forces. This study demonstrates a screening tool that allows plants to focus resources on the relief valve installations most likely to fail due to reaction forces. HP


1 Peng, L.-C. and T.-L. Peng, Pipe Stress Engineering, ASME, New York, 2009.

The authors
  Jason White, PE, is a senior process engineer with Smith & Burgess LLC, a process safety consulting firm based in Houston, Texas. Mr. White has seven years of experience in PSM compliance, specializing in relief systems design and analysis for the refining, natural gas and petrochemical industries. He received BS and MS degrees in chemical engineering from the University of Missouri, and is a licensed professional engineer in the state of Texas. 

  Dustin Smith, PE, is the co-founder and principal consultant of Smith & Burgess LLC, a process safety consulting firm based in Houston, Texas. As a consultant, Mr. Smith has extensive experience with helping refineries and petrochemical facilities maintain compliance with the PSM standard. He has more than a decade of experience in relief systems design and PSM compliance. His experience includes both domestic and international projects. Mr. Smith is a chemical engineering graduate of Texas A&M University and a licensed professional engineer in Texas. 

  Bill Frenk is a mechanical engineer and the owner of Frenk Water Technologies LLC, a mechanical engineering consulting firm based in Byron, Illinois. He is also a consultant for Smith & Burgess LLC. Mr. Frenk has extensive experience utilizing Caesar II software in both onshore and offshore applications. He received a BS degree in mechanical engineering from Southern Illinois University. 

Have your say
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DSB 123

It is not noted that the equations given in the article are only applicable where the flow through the RV is "critical" or "choked". If the flow is sub-critical then these equations are not strictly applicable.

Randal Caffery

Very good that this problem is addressed. A couple of thoughts on fire PRVs and hydraulic expansion.
Fire case - Agree that a failure of piping might actually be OK in a fire; at least the vessel/equipment will relieve. That a PRV may not function properly in a fire seems to be a trouble area. Considering weakened vessel strength with heat and a PRV set at MAWP which may be away from the heat source is also a troubling thought. I've heard of de-pressurization (blowdown) for some cases; maybe that's on option.
Liquid Expansion - I've witnessed allegedly liquid packed vessels being blowndown after a hydrotest and was amazed at how long the water is shooting out of a small bleed valve; sometimes appearing to be getting vaporized/sheared into small droplets (maybe high velocity lowering pressure and flashing occurring?). While the some air left in the system may be the culprit, I wondered if the stretching of the steel under hydrotest resulted in the prolonged blowdown. With the fact that most relief devices have a blowdown pressure below set pressure, I can see a liquid relief device may relieve for a time long enough to establish steady state flow.
Just some thoughts to consider when applying engineering judgment in some cases.


please,in case of design metering station we need to put a pressure safety valve to realize the crude oil to the relief tank( in my case i have crude oil ) so i in this case please give me the solution for the following :
1- how we can calculate the back pressure for pressure safety valve(psv)?
2- how we can design a vessel under the pressure ( closed tank) for to save crude oil after the crude oil exit from pressure safety valve(psv) ?

Joe Bucci

I work in the HVAC industrie, how often do boiler PRV's need to be recertified? And do refrigerant PRV's need to be recertified?

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