Sizing a pressure relief valve (PRV) for liquids per API 520
A pressure relief valve (PRV/PSV) protects vessels and piping against overpressure by discharging excess liquid when the pressure reaches the set point. API 520 sizing computes the required orifice area and selects the next-larger standard API 526 orifice.
When to use
Use it whenever the pressure in a vessel, heat exchanger, blocked pump, or pipe segment could exceed the MAWP (maximum allowable working pressure) due to thermal expansion of trapped liquid, control failure, external fire, or a blocked discharge. For liquids, the relief valve is the standard overpressure protection device (and often code-mandated, as in ASME Section VIII). The calculation belongs to the plant safety design phase: it sets the relieving rate of the governing scenario, determines the orifice area per API 520, and anchors the purchase specification to the standardized API 526 orifice (letters D through T). The key concern is choosing the correct relieving scenario and the correction factors (viscosity, backpressure, rupture disk) consistent with the actual installation.
What a relief valve does and why you size it
The pressure relief valve (RV — or PSV in the generic sense) is the last line of defense against overpressure in a liquid system. When the pressure in a vessel, heat exchanger, blocked pump, or pipe segment exceeds the MAWP (maximum allowable working pressure), the valve opens and discharges the excess fluid, preventing rupture. Unlike a gas/vapor safety valve — which opens with a pop — a liquid valve opens proportionally to the excess pressure, reaching full capacity at the design overpressure.
Sizing answers one concrete question: what flow area is enough to pass the relieving flow of the worst-case scenario without letting the pressure rise above the allowable limit? The answer comes from API Standard 520 Part 1, and the final specification is tied to the standardized orifices of API 526.
Foundation: the API 520 area equation
For liquids, API 520 §5.8 gives the required effective discharge area (SI form):
A = (11.78 · Q) / (Kd · Kw · Kc · Kv) · √(G / ΔP)
Each term has a clear physical role:
- Q is the relieving flow rate (in L/min) of the governing scenario — not the operating flow rate.
- ΔP = P₁ − P₂ is the driving force: the relieving pressure P₁ (set plus the accumulated overpressure) minus the backpressure P₂.
- G is the liquid’s specific gravity — denser fluids need more area for the same flow rate.
- Kd is the model’s certified discharge coefficient (typically 0.62–0.75 for liquids).
- Kw, Kc, and Kv are the correction factors for backpressure, rupture disk, and viscosity.
The constant 11.78 already embeds the unit conversion; that is why it is critical to respect the unit system (Q in L/min, ΔP in kPa, A in mm²). Swapping units without adjusting the constant is a recurring gross error.
The viscosity iteration loop (Kv)
The Kv factor corrects the effect of viscous friction at the orifice and depends on the Reynolds number, which in turn depends on the orifice area — a circular dependency the standard resolves by iteration:
- Estimate A with Kv = 1 (assuming a low-viscosity fluid).
- Select the next-larger API 526 orifice above that area.
- Compute Re with the velocity and diameter of the chosen orifice (not of the theoretical area — an explicit requirement of §5.8.2).
- Recompute Kv from Kv = 1 / (0.9935 + 2.878/√Re + 342.75/Re¹·⁵).
- Repeat until the area converges.
For water and light products, Re is usually above 10⁵ and Kv ≈ 1 — the correction is negligible and the iteration converges on the first pass. For heavy oils, glycols, and resins, however, Re falls into the 10³–10⁴ range, Kv drops below 1, and the area grows, possibly pushing the selection to the next orifice. Below Re ≈ 100 you leave the correction’s validity range and should evaluate a special valve.
Backpressure, rupture disk, and the relief scenario
- Backpressure (Kw). The discharge pressure reduces ΔP. When the built-up component is high (a header shared by several valves), a conventional valve may fail to reseat; in that case you use a balanced bellows or a pilot-operated valve, applying Kw < 1 as the backpressure ratio rises above ~15% of set.
- Rupture disk (Kc). An upstream rupture disk without a combined-capacity certification penalizes the flow: Kc = 0.90; without a disk, Kc = 1.00.
- Relief scenario (API 521). The flow rate Q comes from the worst credible case: thermal expansion of trapped liquid, blocked outlet with an active pressure source, control failure, or external fire. Each has its own flow rate and allowable overpressure (10% non-fire, 21% fire, 25% thermal expansion). Size for the most demanding combination.
From theoretical area to a purchasable orifice (API 526)
The API 520 area is continuous, but commercial valves exist only in the 14 API 526 orifices (letters D through T, from 71 to 16,774 mm²). The rule is straightforward: pick the smallest orifice whose area is ≥ the required area. An important practical consequence — the installed valve always has capacity equal to or greater than the calculated value, and that surplus is the over-capacity margin. A very small margin (a few percent) deserves attention, because flow variations within the scenario can consume it.
Tie-in with the standards
The method is that of API 520 Part 1 (sizing), supported by API 526 (orifices) and API 521 (definition of relief scenarios and loads). The allowable overpressure limit derives from ASME Section VIII Division 1, and the equivalent ISO reference is NBR ISO 4126. Following the standard is what makes the number defensible in an audit: it defines the conditions under which the certified Kd is valid, the Reynolds range over which the Kv correction applies, and the backpressure limits that dictate the choice among conventional, balanced, and pilot-operated valves. Stepping outside those ranges — Re below 100, backpressure without a Kw factor, a poorly chosen relief scenario — means abandoning the basis that guarantees protection, and the sizing is no longer trustworthy.
Formulas and fundamentals
ΔP = P₁ − P₂ = Pset·(1 + overpressure) − P₂ ΔP [bar or kPa] is the driving force across the valve. P₁ = relieving pressure (set + accumulated overpressure); P₂ = total backpressure at the discharge (superimposed + built-up). Pset = set pressure [barg]; typical overpressure 10% (non-fire), 21% (fire), or 25% (thermal relief).
A = (11.78 · Q) / (Kd · Kw · Kc · Kv) · sqrt(G / ΔP) Liquid sizing equation. A [mm²] = effective discharge area; Q [L/min] = relieving flow rate; Kd = certified discharge coefficient [-]; Kw = backpressure correction factor [-]; Kc = rupture-disk combination factor [-]; Kv = viscosity correction factor [-]; G = liquid specific gravity (water = 1) [-]; ΔP [kPa] = relieving differential pressure.
Kv = 1 / (0.9935 + 2.878/sqrt(Re) + 342.75/Re^1.5) Corrects the area for viscous liquids as a function of the Reynolds number Re at the orifice. Re ≥ 10⁵ → Kv ≈ 1 (negligible); Re in the 10³–10⁴ range → Kv < 1 and the area grows. The calculation is iterative: estimate A with Kv = 1, evaluate Re at the chosen API 526 orifice area, and recompute Kv until it converges.
Re = (ρ · v · d) / μ, with v = Q / A_orif and d = sqrt(4·A_orif/π) Re sets the viscosity regime. ρ [kg/m³] = density; v [m/s] = orifice velocity; d [m] = equivalent diameter of the selected API 526 orifice; μ [Pa·s] = dynamic viscosity. The standard requires evaluating Re at the AREA OF THE CHOSEN ORIFICE, not at the preliminary area.
A_orif (API 526) ≥ A_required → pick the SMALLEST letter that satisfies it The computed area is theoretical; a real valve exists only in the 14 standardized API 526 orifices (D=71 mm², E=126, F=198, G=325, H=506, J=830, K=1186, L=1841, M=2323, N=2800, P=4116, Q=7129, R=10323, T=16774 mm²). Select the first orifice with area ≥ A_required; the surplus is the capacity margin.
Standards & methods
- API Standard 520 Part 1 (sizing and selection)
- API Standard 526 (standardized orifices, letters D through T)
- API Standard 521 (relief scenarios and loads)
- ASME Boiler & Pressure Vessel Code, Section VIII Div. 1 (allowable overpressure)
- ABNT NBR ISO 4126 (safety devices for protection against overpressure)
Typical reference values
| Quantity | Typical range | Note |
|---|---|---|
| Discharge coefficient Kd (liquid) | 0.62 to 0.75 | Manufacturer-certified: Consolidated ≈ 0.65; Crosby JOS ≈ 0.744; Mercer ≈ 0.75. |
| Overpressure | 10% / 21% / 25% | 10% non-fire (ASME VIII); 21% fire case; 25% thermal-expansion relief / pilot-operated. |
| Rupture-disk combination factor (Kc) | 0.90 or 1.00 | 0.90 with an upstream rupture disk lacking a combined-capacity certification; 1.00 without a disk. |
| Backpressure factor (Kw) | 0.59 to 1.00 | = 1 for a balanced-bellows valve with backpressure ≤ 15% of set; drops as the backpressure ratio rises. |
| Blowdown differential / set tolerance | set ± ASME tolerance | Set pressure = cracking pressure; ASME tolerance ±2 psi (set ≤ 70 psi) or ±3% (set > 70 psi). |
| Validity range of the Kv correction (Re) | Re ≥ 100 | Re < 100 (highly viscous) falls outside the range of API 520 §5.8.2; evaluate a special valve. |
Worked example
Balanced-bellows PRV on a product vessel (G=0.85)
Inputs
- Relieving flow rate (Q)
- 90 m³/h
- Set pressure (Pset)
- 10 barg
- Overpressure
- 10 %
- Total backpressure (P₂)
- 1.0 barg
- Specific gravity (G)
- 0.85 -
- Discharge coefficient (Kd)
- 0.65 -
Results
- Relieving pressure (P₁)
- 11.0 barg
- Relieving differential (ΔP)
- 10.0 (1000) bar (kPa)
- Required area (A_req)
- ≈792 mm²
- Reynolds at the orifice
- ≈2.8×10⁵ -
- Selected API 526 orifice
- J (830 mm²) -
With 10% overpressure, the relieving pressure rises to 11 barg; after subtracting the 1 barg backpressure, the differential is 10 bar (1000 kPa). The required area works out to ~792 mm². Because the backpressure (1/11 ≈ 9%) is below 15%, the factor Kw = 1 for the balanced bellows, and the high Reynolds number (≈2.8×10⁵) leaves Kv ≈ 1 — the viscosity correction is negligible for this light product. The theoretical 792 mm² is not purchasable: you select the next-larger standard API 526 orifice, the J orifice at 830 mm², giving a capacity margin of ~5%. If the fluid were a heavy oil (Re in the 10³ range), Kv would drop below 1, the area would rise, and the next orifice (K) might be required.
Common mistakes
- Using the operating pressure as ΔP. The driving force is P₁ − P₂, where P₁ = set × (1 + overpressure); ignoring overpressure undersizes or oversizes the area.
- Forgetting the backpressure (P₂). In shared relief headers, built-up backpressure reduces ΔP and, in a conventional valve, can even prevent reseating — requiring a balanced bellows or pilot-operated design.
- Applying Kv = 1 to a viscous fluid. For heavy oils and glycols (low Re), Kv can fall well below 1 and the required area grows; the correction is iterative, not a single guess.
- Stopping at the theoretical area. The computed area is not purchasable: you must select the next-larger standard API 526 orifice (D through T) — the real valve will have more capacity than required.
- Choosing the wrong relief scenario. Thermal expansion of trapped liquid, external fire, control failure, and blocked outlet yield very different flow rates; size for the scenario with the highest required flow (API 521).
- Confusing a relief valve (liquid, proportional lift) with a safety valve (gas/vapor, pop-action lift). The Kd, the lift curve, and the sizing equation are different.
Frequently asked questions
What is the cracking pressure of a relief valve?
It is the pressure at which the valve begins to open — it coincides with the set pressure. From that point on, the lift is proportional to the excess pressure (typical liquid behavior), reaching full capacity at the design overpressure (usually 10%). The set tolerance follows ASME: ±2 psi up to 70 psi of set, ±3% above that.
What is the difference between a relief valve and a safety valve?
A relief valve (RV) is for liquids and opens proportionally to the overpressure. A safety valve is for gases and vapors and opens with a fast pop action. The sizing equations, the discharge coefficient Kd, and the lift curve are different; the generic pressure safety valve (PSV) covers both when specified for the service.
Why is the computed area not the area of the valve I buy?
Because the API 520 theoretical area is continuous, but commercial valves exist only in the 14 standardized API 526 orifices (letters D through T). You select the smallest orifice with area ≥ the required area; that is why the real valve always has capacity equal to or greater than the calculated value, and the surplus is the over-capacity margin.
When does the viscosity factor Kv matter?
When the liquid is viscous and the Reynolds number at the orifice drops (heavy oils, glycols, resins). For Re ≥ 10⁵, Kv ≈ 1 and can be ignored. Below that, Kv < 1 and the required area increases. The calculation is iterative: size with Kv = 1, evaluate Re at the chosen orifice, and recompute Kv until it converges. Below Re ≈ 100 you leave the standard's range.
How does backpressure affect the sizing?
Backpressure P₂ reduces the differential ΔP = P₁ − P₂, requiring more area. In addition, in a conventional valve, high backpressure hampers reseating and shifts the set point. So, with variable (built-up) backpressure above ~10% of set, you use a balanced bellows or a pilot-operated valve and apply the factor Kw < 1 according to the backpressure ratio.
Which relief scenario should I use for sizing?
The one that produces the highest required relieving flow rate, per API 521. For liquids, the common scenarios are thermal expansion of trapped liquid, blocked outlet with an active pressure source, control failure (valve wide open), and external fire. Each scenario has its own flow rate and allowable overpressure; size for the most critical combination.
Glossary
- Relief valve (RV / PSV)
- A protection device that opens automatically to discharge excess fluid when the pressure reaches the set point, protecting the equipment against overpressure. For liquids, it opens proportionally.
- Set pressure (cracking pressure)
- The pressure at which the valve begins to open, normally equal to the MAWP of the protected equipment. It is the point where discharge starts.
- Overpressure
- The percentage increase above set allowed while the valve discharges full flow. Typical: 10% (non-fire), 21% (fire), 25% (thermal expansion / pilot-operated).
- Backpressure
- The pressure at the valve discharge, the sum of the superimposed (static, before opening) and the built-up (generated by the flow itself in the header). It reduces the differential and may require a balanced bellows.
- API 526 orifice
- A set of 14 standardized discharge areas (letters D through T, from 71 to 16,774 mm²) that define the commercial sizes of relief/safety valves.
- Discharge coefficient (Kd)
- The fraction of the ideal flow actually discharged, certified by test for each valve model. For liquids it is typically between 0.62 and 0.75.