A PSV sizing calculation in Excel combines a documented relief load with an appropriate pressure-relief sizing equation. API 521 helps establish credible overpressure scenarios and relief-system requirements; API 520 Part I addresses device sizing and selection. API 520 Part II addresses installation. These tasks must be completed together before a valve can be accepted for service.
This guide provides a reproducible, single-phase nitrogen example using a critical-flow gas equation. It calculates a required effective area of 107.26 mm² and identifies an API E effective orifice as a preliminary candidate. It does not certify a valve or replace the installation, disposal system, and process-safety reviews.
Quick answer: how do you size a PSV in Excel?
Define the credible relief scenario and required mass flow. Enter relieving temperature, absolute inlet and outlet pressures, gas properties, and justified correction factors. Check whether flow is critical, calculate the required area, and compare it with standard effective orifices. Confirm the selected valve’s certified capacity and installation limits separately.
| Worked-example output | Result |
|---|---|
| Required nitrogen relief rate | 1,000 kg/h |
| Relieving inlet pressure | 1,201.325 kPa absolute |
| Relieving temperature | 323.15 K |
| Outlet-to-inlet pressure ratio | 0.08434 |
| Ideal-gas critical pressure ratio | 0.52828 |
| Calculated effective area | 107.26 mm² |
| Preliminary API effective orifice | E: 126.45 mm² |
API 520 versus API 521: which calculation belongs where?
| Reference | Role in the workflow |
|---|---|
| API 521 | Identify and assess applicable overpressure causes, relief loads, and disposal/depressuring-system requirements |
| API 520 Part I | Size and select a suitable pressure-relieving device for the applicable fluid and relieving conditions. |
| API 520 Part II | Evaluate installation, including inlet and outlet piping considerations. |
| API 526 | Standardized flanged steel pressure-relief valve details, including effective orifice designations |
| Applicable construction code | Establish equipment protection requirements, allowable pressure limits, and relevant certification rules. |
The API digital catalogue lists API 520 Part I, 10th edition; Part II, 7th edition; and API 521, 7th edition. Confirm the edition, addenda, errata, and project requirements actually governing your installation. A calculation labelled “API” is not proof that every applicable requirement has been checked.
API’s overview of Standard 521 explains its pressure-relieving and depressurizing-system scope. For related terminology, see GrowMechanical’s pressure relief valve sizing guide; use the governing standards and manufacturer data for acceptance criteria.
Step 1: Establish the relief scenario and mass flow
Do not begin by copying the normal operating flow into the sizing equation. The required relief rate depends on what can enter, be generated, or expand during the specific overpressure event at relieving conditions.
| Potential scenario | Information needed to determine the load |
|---|---|
| Blocked outlet | Maximum credible inlet flow at the relieving pressure and credible remaining outlets |
| Control valve or regulator failure | Upstream conditions, failed-open flow path, restriction capacity, and downstream relieving conditions |
| Loss of cooling | Heat input, phase behavior, inventory, and vapor generation |
| External fire | Applicable fire model, exposed equipment, wetted area where relevant, heat input, and fluid response |
| Tube rupture | Pressure difference, connecting geometry, source limitations, and receiving-system response |
| Liquid thermal expansion | Trapped liquid volume, heat input, expansion properties, and suitable liquid-relief method |
Document each applicable case separately. The governing case is the one requiring the controlling device capacity or area after considering its properties and conditions; it is not necessarily the case with the largest mass flow.
Example basis: assume a reviewed blocked-outlet study has established a nitrogen inflow of 1,000 kg/h at the relevant relieving condition, with no credited normal outlet. This tutorial takes that value as an illustrative input. It does not calculate regulator failure capacity or establish that a blocked outlet governs a real vessel.
Step 2: Define the pressure and property assumptions.
The example assumes a single-phase, ideal-gas-like nitrogen stream, a preliminary effective-area gas sizing basis, and no upstream rupture disk. It uses negligible inlet loss and an outlet pressure equal to local atmospheric pressure solely for the arithmetic example.
Set pressure is assumed to be 10 barg, with the protected equipment’s applicable MAWP also assumed to be 10 barg. The example uses 10% overpressure as a stated case assumption. Whether that allowance is permitted depends on the construction code, relief case, and arrangement; it is not a universal API allowance.
Keep the terms distinct:
- Set pressure: the specified valve opening pressure under its stated service conditions.
- Overpressure: pressure rise above valve set pressure.
- Accumulation: pressure rise above the protected equipment’s MAWP.
- Backpressure: pressure at the valve outlet, including superimposed and built-up contributions as applicable.
Overpressure and accumulation only coincide numerically under particular conditions, such as the simplified equal set-pressure/MAWP basis used here.
Step 3: Enter the Excel inputs
Create a worksheet named PSV_Gas. Enter labels in column A, values in column B, and units in column C. The formulas below depend on these exact cell assignments.
| Cell | Input | Value | Unit or basis |
|---|---|---|---|
| B2 | Required relief mass flow W | 1000 | kg/h |
| B3 | Set pressure | 10 | bar gauge |
| B4 | Assumed overpressure fraction | 0.10 | decimal |
| B5 | Local atmospheric pressure | 101.325 | kPa absolute |
| B6 | Relieving temperature | 50 | °C |
| B7 | Molecular weight M | 28.0134 | kg/kmol |
| B8 | Ideal-gas heat-capacity ratio k | 1.40 | dimensionless |
| B9 | Compressibility factor Z | 1.00 | assumed |
| B10 | Effective discharge coefficient Kd | 0.975 | preliminary gas sizing assumption |
| B11 | Backpressure correction Kb | 1.00 | assumed for this case |
| B12 | Combination correction Kc | 1.00 | no upstream rupture disk |
| B13 | Valve outlet pressure P₂ | 101.325 | kPa absolute at relief |
Use gas properties at the relieving condition. Z = 1 and k = 1.4 are explicit simplifications here, not defaults for every gas. Hydrocarbon mixtures, near-critical fluids, and strongly nonideal gases may require more rigorous property and flow models.
The coefficient Kd = 0.975 belongs to the stated preliminary effective-area basis. Do not treat it as a universal certified coefficient for every valve. Manufacturer-certified coefficients and areas must be used as a compatible pair during final selection.
Step 4: Convert relieving pressure and temperature
For the simplified pressure basis with negligible inlet loss:
P₁ = Pset,g(1 + overpressure fraction) + Patm
Convert the set-pressure term from bar to kPa before adding atmospheric pressure:
P₁ = 10 × 100 × 1.10 + 101.325 = 1201.325 kPa absolute
Enter in B16:
=B3*100*(1+B4)+B5Convert Celsius to kelvin in B17:
=B6+273.15The result is 323.15 K. The 10% allowance is applied to the gauge set pressure in this example, not to the absolute pressure including atmosphere.
In a real installation, distinguish the protected-equipment pressure from the valve-inlet flowing pressure. Evaluate inlet losses using the applicable installation method and valve requirements; do not hide an inlet-loss problem by raising the allowable pressure in the spreadsheet.
Step 5: Check critical versus subcritical flow
For the ideal-gas check used here, the critical downstream-to-upstream absolute pressure ratio is:
rcritical = [2/(k + 1)]k/(k − 1)
Calculate it in B18:
=IF(B8<=1,NA(),(2/(B8+1))^(B8/(B8-1)))Calculate the actual ratio in B19:
=IF(OR(B16<=0,B13<=0),NA(),B13/B16)For this case:
- Critical ratio = 0.52828.
- Actual P₂/P₁ = 101.325/1201.325 = 0.08434.
Because the actual ratio is below the critical ratio, the example uses the critical-flow gas equation. Put a status message in B20:
=IF(OR(B16<=0,B13<=0,B13>=B16,B8<=1),"CHECK INPUTS",IF(B19<=B18,"CRITICAL","SUBCRITICAL - USE OTHER METHOD"))Spirax Sarco’s safety-valve sizing guidance explains critical and subcritical flow. A choked-flow check does not mean backpressure has no effect on valve operation, lift, stability, or the applicable correction factor.
Step 6: Calculate the gas coefficient C
For the unit convention used in this article:
C = 0.03948 × √{k[2/(k + 1)](k + 1)/(k − 1)}
Enter in B21:
=IF(B8<=1,NA(),0.03948*SQRT(B8*(2/(B8+1))^((B8+1)/(B8-1))))At k = 1.40:
C = 0.0270332
The numerical constant embeds the chosen unit convention. It is not interchangeable with the coefficient used in a US customary equation. LESER’s Safety Valve Engineering handbook distinguishes the SI and US customary coefficient forms.
This worksheet deliberately flags k ≤ 1 for review rather than silently extending the expression through its singular form at k = 1.
Step 7: Calculate the required effective area
The critical-flow gas equation in the stated unit convention is:
A = [W/(C × Kd × P₁ × Kb × Kc)] × √(T × Z/M)
| Symbol | Meaning | Required unit |
|---|---|---|
| A | Required effective area | mm² |
| W | Required mass flow | kg/h |
| P₁ | Absolute valve-inlet relieving pressure | kPa absolute |
| T | Absolute relieving temperature | K |
| M | Molecular weight | kg/kmol |
| Z, k | Gas property inputs | dimensionless |
| Kd, Kb, Kc | Applicable sizing/correction factors | dimensionless |
Enter the guarded sizing formula in B22:
=IF(OR(B20<>"CRITICAL",B2<=0,B7<=0,B9<=0,B10<=0,B10>1,B11<=0,B11>1,B12<=0,B12>1,B17<=0),NA(),B2/(B21*B10*B16*B11*B12)*SQRT(B17*B9/B7))Substituting the example values:
A = [1000/(0.0270332 × 0.975 × 1201.325 × 1 × 1)] × √(323.15 × 1/28.0134)
A = 107.26465 mm² ≈ 107.26 mm²
The open-source Fluids safety-valve documentation provides a separately inspectable implementation of the API 520 gas equation. Its software interface uses kg/s, Pa, and m² with internal conversions; do not copy this article’s kg/h and kPa values directly into that interface.
Step 8: Compare with API effective orifices
For this small example, create the following lookup table in D2:E5:
| Cell in column D | Orifice letter | Cell in column E | Effective area, mm² |
|---|---|---|---|
| D2 | D | E2 | 70.96760 |
| D3 | E | E3 | 126.45136 |
| D4 | F | E4 | 198.06412 |
| D5 | G | E5 | 324.51548 |
These are conversions of 0.110, 0.196, 0.307, and 0.503 in² using exactly 645.16 mm²/in². The effective areas are listed in the Baker Hughes Consolidated sizing reference, which also distinguishes them from actual manufacturer areas.
In an Excel version supporting XLOOKUP, use B23 for the preliminary letter:
=XLOOKUP(B22,$E$2:$E$5,$D$2:$D$5,"OUTSIDE TABLE",1)Use B24 for the selected effective area:
=XLOOKUP(B22,$E$2:$E$5,$E$2:$E$5,NA(),1)Match mode 1 means exact match or the next larger value. The result is E, 126.45136 mm². D is too small. This deliberately limited table stops at G; a result above its range must not silently select G.
The orifice letter is not the inlet flange size, outlet flange size, or a manufacturing instruction. Final selection requires the specific valve model, certified capacity, pressure/temperature rating, materials, spring or pilot arrangement, and backpressure suitability.
Step 9: Run a calculation consistency check
Calculate capacity using the selected effective area and exactly the same preliminary factors:
Wcheck = AselectedC × Kd × P₁ × Kb × Kc × √[M/(T × Z)]
Enter in B25:
=B24*B21*B10*B16*B11*B12*SQRT(B7/(B17*B9))The result is approximately 1,178.87 kg/h. This demonstrates arithmetic consistency and the next-size selection. It is not a manufacturer-certified capacity and should not be presented as one on a procurement datasheet.
A larger orifice is not automatically a better choice. Excess capacity can contribute to unstable operation in some installations, while installation losses and valve dynamics still require assessment.
How sensitive is the required area?
Change one input at a time while holding the others fixed. These cases show mathematical sensitivity; they do not establish permissible valve conditions.
| Illustrative change | Required area | Implication |
|---|---|---|
| Base case | 107.26 mm² | E is the preliminary candidate |
| Required flow increases to 1,250 kg/h | 134.08 mm² | E is insufficient; the limited table selects F |
| Relieving temperature rises to 100°C | 115.26 mm² | Higher absolute temperature increases required area |
| Applicable Kb changes to 0.90 | 119.18 mm² | A capacity-reduction factor increases required area |
| Applicable Kc changes to 0.90 | 119.18 mm² | Combination-device derating must be included when applicable |
The Kb = 0.90 case is not a rule for 10% backpressure. Obtain Kb from the applicable method and valve data. Likewise, do not assign Kc = 0.90 to every rupture-disk installation without checking the permitted basis and any certified combination factor.
What must be checked beyond the spreadsheet?
Evaluate the total relief path, not only the valve. The outlet pressure assumed here is atmospheric with negligible discharge-line loss; actual piping will generally create built-up backpressure.
- Inlet system: nonrecoverable pressure loss, piping arrangement, isolation controls, and valve stability.
- Outlet system: superimposed and built-up backpressure at the applicable relief flows, including credible simultaneous loads.
- Disposal: appropriate vent, recovery, treatment, or flare destination; dispersion, noise, reaction forces, and personnel exposure.
- Valve selection: certified capacity, fluid compatibility, temperature limits, operating-pressure margin, and manufacturer restrictions.
- Documentation: relief-case register, calculation revision, equipment limits, assumptions, P&ID references, and independent review.
Nitrogen is nonflammable, but a release can create an oxygen-deficiency hazard. The example’s atmospheric pressure assumption is not authorization to discharge into an occupied area.
For an overview of device categories, see GrowMechanical’s pressure safety device guide. Device type does not remove the need to verify the complete relief system.
Common Excel errors and limitations
| Error | Correction |
|---|---|
| Using barg in the gas equation | Convert inlet and outlet pressures to the specified absolute units |
| Using Celsius under the square root | Convert to kelvin |
| Entering kg/s into the kg/h equation | Convert the mass-flow units consistently |
| Mixing actual area and effective Kd | Use a compatible area/coefficient basis |
| Using the critical-flow equation when P₂/P₁ is too high | Use the applicable subcritical method |
| Sizing only the largest mass-flow case | Compare required areas using each case’s conditions |
| Applying the gas equation to flashing liquid | Use an appropriate flashing or two-phase method |
Keep formula cells protected and expose input units. Add a visible scope statement: single-phase gas, critical flow, preliminary effective-area sizing. Retain unrounded results internally and record the source of every property and correction factor.
This sheet does not cover steam-specific corrections, liquid viscosity corrections, two-phase relief, reactive runaway, fire-load derivation, or time-dependent depressurization. Those services need their own validated methods. A numerically plausible result does not establish that the selected model is applicable.
Frequently asked questions
Does API 521 calculate the PSV orifice area?
API 521 addresses overpressure scenarios, relief requirements, and associated system considerations. API 520 Part I supplies sizing and selection methods for the applicable service. Both are needed in a complete relief-system workflow.
Can I use the normal process flow as the relief rate?
Only if a documented scenario assessment establishes that it represents the required relieving load. Failed-open controls, upstream pressure, blocked outlets, and heat input can produce loads different from normal operation.
Why must PSV gas sizing use absolute pressure?
Gas-flow relationships depend on absolute thermodynamic pressure. A gauge reading excludes local atmospheric pressure, so it cannot be used unchanged in the stated equation or critical-pressure-ratio check.
Is 10% overpressure always allowed?
No. The permitted pressure rise depends on the governing construction code, protected equipment, relief case, and device arrangement. The 10% value in this article is an explicit illustrative assumption.
Does critical flow mean backpressure is irrelevant?
No. Critical flow describes a flow regime. Backpressure may still affect valve opening, lift, capacity corrections, and stability; the discharge system and manufacturer limits must be checked.
Can I use an API E orifice for the example immediately?
E is only a preliminary effective-area candidate. Confirm the specific valve’s certified capacity and compatible sizing basis, then verify installation, backpressure, materials, pressure rating, and the complete set of applicable relief cases.
Is a downloadable PSV Excel file included?
This article supplies cell-by-cell formulas for reproducing the example. It does not claim that a downloadable or certified PSV workbook has been supplied. Any project workbook should include validation, scenario records, unit controls, and independent engineering review.
Use the calculation to support a documented selection
For the stated nitrogen case, the required effective area is 107.26 mm², and the preliminary API E area is 126.45 mm². The calculation is useful because its inputs, unit conversions, flow-regime check, and selection logic can be reviewed.
Complete the relief-case assessment, certified valve selection, and piping/disposal review before applying the result to an installation. Explore further process and equipment calculation resources at GrowMechanical.
