PRV Sizing (API 520) Back
FLUID

Pressure Relief Valve Sizing (API 520)

Calculate required orifice area per API 520 and select the API letter designation. Handles gas, vapor, and liquid service with back-pressure correction (Kb) and discharge coefficient (Kd).

Parameters
Phase Gas/Vapor
Set Pressure P_set
kPa
Back Pressure P_back
kPa
Molecular Weight MW
g/mol
Temperature T
K
Required Flow Q
kg/h
Results
Required Area A (mm²)
API Orifice Selection
Back-pressure Factor Kb
Relieving Pressure P₁ (kPa)
Flow Rate vs Required Orifice Area
API Standard Orifice Sizes (selected highlighted)
LetterArea (mm²)Area (in²)Status
Visualization
Theory & Key Formulas

$A = \dfrac{W}{C \cdot K_D \cdot P_1 \cdot K_b}\sqrt{\dfrac{TZ}{M}}$

$C = 0.03948\sqrt{k\left(\dfrac{2}{k+1}\right)^{\frac{k+1}{k-1}}}$

■ Liquid (API 520 Part I)
$A = \dfrac{Q}{38 K_D K_w K_v K_c}\sqrt{\dfrac{G}{P_1 - P_2}}$

P₁ = P_set × 1.1 + 101.325 [kPa abs]
K_D = 0.65 (liquid), 0.975 (gas/vapor)

What is API 520 PRV Sizing?

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What exactly is a Pressure Relief Valve (PRV) and why do we need a special standard like API 520 to size it?
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Basically, a PRV is a safety device on equipment like tanks or reactors. If pressure gets dangerously high, it opens to vent fluid and prevent an explosion. API 520 is the industry bible for calculating the exact size of the valve's opening (the orifice) so it can release just enough flow to bring the pressure down safely. If you undersize it, the equipment could still rupture. Try moving the "Required Flow Rate (W)" slider in the simulator above to see how the required area changes instantly.
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Wait, really? The formula looks different for gas and liquid. Why is that, and what's that "C" constant in the gas equation?
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Great observation! Gases are compressible and their flow depends heavily on properties like specific heat ratio (k). The constant "C" encapsulates that physics. For liquids, which are nearly incompressible, the sizing is more about density and flow rate. In the simulator, when you switch the service type selector from "Gas/Vapor" to "Liquid", you'll see the underlying equation change. A common case is sizing a valve for a propane vapor line versus one for a water pump discharge.
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I see the "Kb" and "Kd" factors in the simulator. What are those for, and what happens if I set them wrong?
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Those are crucial correction factors. Kd is the "discharge coefficient," which accounts for real-world flow losses through the valve (it's always less than 1). Kb is the "backpressure correction factor." If there's pressure in the discharge pipe, it can hinder the valve's flow! For instance, in a flare header system, high backpressure can choke the valve. If you ignore Kb (set it to 1), you might undersize the valve. Try adjusting the Kb slider from 1.0 down to 0.8 and watch the required area jump.

Physical Model & Key Equations

The governing equation for gas or vapor service calculates the minimum required orifice area (A) based on the mass flow rate of the relieving fluid and its thermodynamic properties.

$$A = \dfrac{W}{C \cdot K_D \cdot P_1 \cdot K_b}\sqrt{\dfrac{T \cdot Z}{M}}$$

Where:
A = Required orifice area (mm² or in²).
W = Required mass flow rate (kg/h or lb/h).
C = Gas flow constant, derived from the specific heat ratio (k).
K_D = Rated discharge coefficient (typically 0.975 for vapor).
P_1 = Upstream relieving pressure (barg or psig).
K_b = Backpressure correction factor.
T = Relieving temperature (K or °R).
Z = Compressibility factor.
M = Molecular mass of the gas.

The gas constant C is not arbitrary; it comes from isentropic nozzle flow theory, linking the valve's critical flow to the fluid's energy capacity.

$$C = 0.03948 \sqrt{k \left( \dfrac{2}{k+1}\right)^{\frac{k+1}{k-1}}}$$

Where:
k = Specific heat ratio (Cp/Cv). This value determines how the gas expands and accelerates through the orifice. A higher k (like for air = 1.4) results in a different C than a lower k (like for steam ≈ 1.3). This is why you must input the correct fluid property in the simulator.

Real-World Applications

Refinery & Chemical Plant Protection: Every distillation column, reactor, and pressure vessel in a refinery has multiple PRVs. Engineers use API 520 to size valves for scenarios like a cooling water failure causing a column to overheat and overpressure. The simulator's parameters mirror the real data they work with.

LNG (Liquefied Natural Gas) Terminals: Sizing valves for cold methane vapor (-160°C) requires careful input of temperature (T), molecular weight (M), and compressibility (Z). An undersized valve could lead to a catastrophic release of flammable gas.

Pharmaceutical Batch Reactors: During an exothermic (heat-releasing) reaction, a runaway reaction can generate gas faster than the system can handle. API 520 sizing determines the valve area needed to vent this sudden gas generation and keep operators safe.

Oil & Gas Pipeline Stations: Pumps and compressors are protected by PRVs. High backpressure in a discharge header (modeled by the Kb factor) is a common issue here. The standard ensures the selected valve letter designation (like 'P' or 'Q') has enough area even under backpressure conditions.

Common Misconceptions and Points to Note

When you start using this tool, there are a few pitfalls that engineers, especially those with less field experience, often stumble into. First and foremost, do not confuse "set pressure" with "operating pressure". The "Absolute Set Pressure P1" you input into the tool is the absolute pressure, which is the pressure at which the valve starts to open (the set pressure) plus atmospheric pressure. For example, if the set pressure is 10 barg (gauge), P1 becomes approximately 11 bara. Getting this wrong will throw off all your calculations, so be careful.

Next, do not assume that "back pressure is always atmospheric pressure". If the valve outlet is connected to a closed system or a flare header, the back pressure is constantly fluctuating. Especially for conventional safety valves (not balanced bellows type), rising back pressure significantly weakens the valve opening force due to the "backpressure effect". You should consider keeping Kb at 1.0 in the tool as representing an almost ideal condition only.

Finally, remember that a valve with the exact "Required Orifice Area" from your calculation results does not exist. You select a standard size valve (e.g., D0.5 inch, D1 inch, etc.) from the catalog that has the closest, and greater, flow capacity to the calculated area. Choosing a valve that is "just enough" is ill-advised. It's practical wisdom to include a reasonable margin, anticipating process variations or future production increases.

How to Use

  1. Enter the set pressure (PSET) in psig using the slider or numeric field—typical range 50–3000 psig for industrial applications
  2. Input the back pressure (PBACK) in psig, accounting for static head in liquid service or atmospheric pressure in gas service
  3. For gas/vapor service, enter molecular weight (MW) in lb/lbmol; for liquids, use MW=1.0 or the actual value if known
  4. Click Calculate to determine the required orifice area (in²) and the corresponding API 520 letter designation (A through T)
  5. Cross-reference the letter size against manufacturer datasheets to select the actual PRV model with that flow capacity coefficient

Worked Example

A refinery fuel gas system operates at PSET=125 psig with PBACK=15 psig (flare header pressure). The gas mixture has MW=22 lb/lbmol. Using API 520 equations: the relieving pressure is 125+15=140 psia; the capacity factor K=21.9 for superheated gas; required orifice area ≈0.32 in². This corresponds to API letter D (0.307 in²) or E (0.503 in²). Selecting E provides a safety margin. A typical PRV for this duty might be a 1-inch angle-body valve with Cv=8.5, certified to 145 psig.

Practical Notes

  1. Back pressure must include all static elevation head and downstream system resistance; underestimating PBACK causes valve chatter and inadequate discharge
  2. For compressible service (gas/vapor), use actual Z-factor and Cp/Cv ratio from thermodynamic data; default K=21.9 assumes ideal gas behavior only
  3. API letter designation jumps are nonlinear (D=0.307, E=0.503, F=0.785 in²); select the next size up if calculated area falls between standard sizes to avoid undersizing
  4. Liquid service requires API 520 Part I friction loss coefficients; this calculator assumes gas/vapor equations unless MW indicates incompressible fluid
  5. Always verify manufacturer test data and compliance certificates—letterization alone does not guarantee performance; actual valve Cv must match process flow requirements