# Modeling a Pressure Safety Valve

Pressure Safety Valves (PSV), Pressure Relief Valves (PRV), and other pressure relieving devices offer protection against overpressure in many types of hydraulic systems. Piping systems protected by pressure relieving devices are found in oil refineries, chemical plants, power plants and many other facilities with liquid, steam or gas process applications. Modeling a fully open relieving device in PIPE-FLO Professional, Flow of Fluids or PIPE-FLO Compressible offers benefits such as determining the flow rate through the device, the pipe inlet head loss, and the amount of back pressure at the outlet of the device. Oil & Gas industry pays particular attention to the inlet pipe head loss and back pressure using the API Standard 520 to size and select pressure relieving devices (henceforth referred to as a PSV).

Once a PSV is selected, PIPE-FLO can be used to model the performance of a fully open PSV in the overall piping system.

This article reviews a four step process of modeling a PSV with PIPE-FLO:

- Convert the PSV discharge coefficient (Cd) to a control valve flow coefficient (Cv)
- Add the Cv value at fully open into the control valve device in PIPE-FLO
- Add the PSV set pressure, plus 10%, to the set pressure of the inlet tank.
- Check the fluid zone in each pipeline when a gas is being modeled.

Additionally, this article covers how to confirm the Cd to Cv conversion with PIPE-FLO Professional and discusses the limitations of the method when choked flow conditions are encountered. Further discussion of the conversion of Cd to Cv can be seen in the Knowledge Base article, "Relationship Between Flow Coefficient and Discharge Coefficient" This article is attached below.

Note 1: We recommend sizing and selecting a PSV by following your local city, state, and country codes and standards.

Note 2: If PIPE-FLO calculates a choked flow condition, then calculated results should be closely evaluated as some of the results will be invalid.

**Step 1, Determining the flow coefficient Cv from the discharge coefficient Cd **

PIPE-FLO does not have a native PSV device so the control valve device has to be used to model a PSV. The discharge coefficient (Cd) will have to be converted to a flow coefficient (Cv) because a control valve is characterized by a flow coefficient (Cv or Kv) and a PSV is characterized by a discharge coefficient (Cd or Kd) and orifice area.

For the Cd to Cv conversion, the API 520 standard (Sizing, Selection, and Installation of Pressure Relieving Devices in Refineries) can be compared to the ANSI/ISA-75.01 (IEC 60534-2-1 equivalent) (Flow Equations for Sizing Control Valves) to derive the relationship between Cd and Cv. Engineered Software has done an analysis to verify the accuracy of the conversion using the Water and Air Capacity tables from several PSV manufacturers and calculated results using PIPE-FLO.

For Liquids, the conversion equation is:

Cv = 38 x A x Cd

Where A = actual orifice area

Cd = certified liquid discharge coefficient

38 lumps together all the unit conversions into one constant

For a gas, the conversion equation is:

Cv = 27.66 x A x Cd

Where A = actual orifice area

Cd = certified gas discharge coefficient

27.66 lumps together all the unit conversions into one constant

The constants are different because the Cd of a relief valve is different depending on whether the fluid is a liquid or a gas.

The Cd and actual orifice area (A) are needed from the PSV manufacturer, which can be obtained from their catalog or valve data sheet. An example from the manufacturer of a PSV with a Type F Orifice is shown below.

**Finding the Discharge Coefficient:**

This chart show for the United States, ASME Sec. VIII, Approval Number M37224, Orifice type E-T, the Coefficient of discharge, K is 0.801 for steam/gas and 0.579 for liquid.

**Finding the Actual Orfice Area for a Type F: **

This chart shows the Type F actual orifice area is 0.394 in^2.

Using the conversion equations for a gas and liquid, the Cv can be calculated from the above information:**Cv = 27.66 x (0.394) x (0.801) = 8.729Cv = 38 x (0.394) x (0.579) = 8.669**

Note 3: The actual orifice area and certified liquid discharge coefficient must be used in the liquid conversion equation, the steam/gas certified discharge coefficient must be used with the gas conversion equation. The values of the flow coefficient are within reasonable engineering accuracy no matter which equation is used.

This calculated Cv value can be entered as the fully open Cv of a control valve in PIPE-FLO.

__Step 2: Adding the Cv value at fully open into the control valve device inside PIPE-FLO__

A PSV is added to a PIPE-FLO model by using a control valve device . The control valve is set fully open and the Cv value entered. An example PIPE-FLO model example is shown below.

This model shows a tank with a 220 psi set pressure (this represents a 200 psi PSV set pressure), inlet pipe, a PSV set fully open, and a discharge pipe open to atmosphere.

*Note 4: It is recommended to verify your PIPE-FLO flow rate units match your design flow rate units.*

Once the control valve has been added to the model, open the control valve dialog box, select the flow control valve button and set the control valve to fully open. The control valve dialog box is shown below.

Next, select the data tab and enter the valve size and seat size. The control valve data dialog box is shown below.

This example shows a 1.5 in valve size and a 1.5 seat size was used.

The control valve calculator can be used to generate the Cv, Fl, and Xt profiles for the data table. The control valve calculator dialog box is shown below.

This example shows a linear motion, angle body style, contoured plug type, open flow direction, quick opening characteristic curve, 100 % open and Cv of 8.72 was entered. The Cv of 8.72 was determined by step 1. The body style, trim type, and flow direction has no impact on the calculated Cv profile, so you can select any of the available options for these characteristics.

The calculated Cv results are shown below:

The Fl and Xt value at 100% open needs to be changed to 1 because these are not used in the pressure relief device sizing equations.

Note 5: PIPE-FLO uses the entered Cv of 8.72 in the pressure drop and flow rate calculations for the PSV when it is fully open.

__Step 3: Adding the PSV set pressure, plus 10%, to the set pressure of the inlet tank__

The tank pressure must be set to represent the set pressure of the PSV, plus 10%. The capacity charts for water, steam and air from the manufacturer are listed at 10% overpressure. This 10% overpressure represents the valve at the fully open disk design and correlates to the PIPE-FLO control valve being fully open. This overpressure condition is modeled by increasing the tank set pressure by 10% of the PSV set pressure. An example tank dialog box is shown below.

This example shows 220 psi being entered for the tank pressure. The PSV set pressure was 200 psi.

__Step 4: Checking the fluid zone in each pipeline when a gas is being modeled__

Different fluid zones may need to be created when modeling gases based the density of the gas changing as it travels down a pipeline. The density changes due to the pressure loss of the pipe and there are boundary limits to the Darcy-Weisbach equations based on different percentage of pressure drops. Different percentages of pressure drop for the Darcy-Weisbach equation is discussed in the Knowledge Base # 427, "Check your Compressible system conditions within PIPE-FLO Professional". This article is attached below.

An example fluid zone dialog box is shown below.

This example shows two different fluid zones. One fluid zone is Air 60F at 220 psi and the second is Air 60F at 0 psi. PIPE-FLO does not have a limit on the number of fluid zones per model.__Confirming the Cd to Cv conversion:__

The calculated results for the previous example PIPE-FLO Professional model is shown below.

From this model, the following can be seen.

- The tank pressure is set to 220 psi, which represent a 200 psi PSV set point, plus 10%.
- The inlet pipe has length of .001 ft, so any head loss is negligible. The fluid zone in the inlet pipe has a fluid pressure of 220 psi, matching the pressure in the tank and inlet pipe.
- The flow through the PSV is 1363 scfm.
*(Note: the units are Standard Cubic Feet per Minute.)* - The choked flow rate, Qmax, is 1367 scfm, so the valve is very near the choked flow condition.
- The outlet pipe has length of .001 ft, so any head loss is negligible. A new fluid zone was created in the outlet pipe because outlet pipe's air pressure is not the same as the inlet pipe's air pressure. The outlet pipe's pressure is zero and a new fluid zone was created for this pipe with Air at 0 psi.

PIPE-FLO Professional calculated flow rate of 1363 can be compared to the manufactures Type F PSV Air Capacity Chart. The Air Capacity Chart is shown.

This chart shows at 200 psi of Air at 60F, for a Type F PSV, the capacity is 1359 scfm. PIPE-FLO calculated a flow rate of 1363 scfm and the difference is only 4/1359 = 0.29 %.

Note 6: the Cd and actual orifice area were used to determine Cv for the control valve in the PIPE-FLO model. Manufacturers have different Cd and actual orifice sizes for their PSV design. Please refer to the PSV manual that corresponds to PSV brand and type being modeled.

__Choked Flow Limitations__

What may not be apparent in hand calculations is the condition of choked flow in a control valve. During the iteration process, PIPE-FLO checks for choked flow conditions, however, PIPE-FLO has limitations when choked flow is detected.

Choked flow in a control valve in a gas application occurs when the velocity of the gas at the vena contracta approaches the speed of sound. In liquid applications, choked flow occurs when the fluid pressure at the vena contracta drops significantly below the fluid vapor pressure and the valve's Liquid Pressure Recovery Factor (FL) is low enough that the fluid pressure does not rise back above the vapor pressure. No further drop in downstream pressure will result in an increase in flow rate, so the flow is at a maximum.

Some of the PIPE-FLO calculated results are invalid because the flow rate (and therefore the head loss and dP) of the inlet and outlet pipelines of the control valve is based on the set flow rate of the control valve and not the maximum flow rate that is attainable with the valve. Under these conditions, the calculated head loss and pressure drop of the pipes are higher than what would be obtained in the field.

The following PIPE-FLO model shows a choked flow condition with the PSV. The PSV is turned red and the calculated results should be closely evaluated for engineering accuracy.

This example shows a system where the calculated flow rate (4215 scfm) exceeds the QMax (4122 scfm) of the PSV. PIPE-FLO generates a warning message and the calculated results should be closely evaluated. For example, the two outlet pipe pressure drops would slightly lower, causing the PSV outlet pressure to be slightly lower. The engineer may want to perform some hand calculations to verify the overall accuracy of the model.

In summary, a PSV can be modeled in PIPE-FLO as a control valve. The PSV discharge coefficient and actual orifice area can be used to calculate a flow coefficient for the control valve data. With the tank having a set pressure 10% greater than the PSV set pressure, PIPE-FLO Professional calculates pipe head losses, pipe velocities, back pressure and the flow rate throughout the system. If choked flow occurs, PIPE-FLO will turn the device red and generate an error message. Under choked flow condition, the calculated results must be closely evaluated to ensure they are within reasonable engineering accuracy.

Note 7: All above models are for demonstration purposes only. ESI claims no accuracy of these models and your company agrees to hold ESI harmless and to fully indemnify ESI for any and all liabilities, claims, suits, or other legal actions arising out of the use of the Piping System Models.

Note 8: Leser API 526 Safety Relief Valve Catalog was used in this article. Leser GmbH & Co. KG is not affiliated with PIPE-FLO or Engineered Software and this article does not imply an endorsement for ESI products.