valve-sizing

name	valve-sizing
description	Control valve sizing — Cv/Kv calculation for liquid (ISA/IEC 60534), gas (compressible, critical flow), steam (superheat/saturated), inherent flow characteristics (equal percentage, linear, quick opening), installed characteristics, rangeability, valve authority N, pressure drop allocation, actuator sizing (pneumatic, electric), fail-safe position, and ISA 75.01/IEC 60534-2 methodology.
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Control Valve Sizing — Complete Skill

Cv and Kv Definitions

Cv (US): flow of water at 60°F [15.6°C] in GPM through valve at ΔP = 1 psi pressure drop Kv (metric): flow of water at 15°C in m³/h through valve at ΔP = 1 bar Relationship: Cv = 1.156 × Kv; Kv = 0.865 × Cv

Physical interpretation: Cv = 1.0: 1 GPM water flow at 1 psi ΔP; small valve Cv = 100: 100 GPM water at 1 psi; medium control valve (e.g., DN 50 globe) Cv = 10,000: large pipeline valve (e.g., DN 300 butterfly)

Liquid Sizing (ISA 75.01 / IEC 60534-2-1)

Non-Choked Liquid

Basic liquid Cv: Cv = Q / (N₁ × F_p × √(ΔP / G_f))

Where: Q = volumetric flow [gpm or m³/h] N₁ = numerical constant: 1.0 (Q in gpm, ΔP in psi); 0.865 (Q in m³/h, ΔP in bar) F_p = piping geometry factor (for reducers/expanders; F_p = 1.0 if no fittings) ΔP = p₁ − p₂ [psi or bar] G_f = specific gravity at flowing temperature (water = 1.0)

Check for choked flow: ΔP_choked = F_L² × (p₁ − F_f × p_v) If ΔP > ΔP_choked: choked; use ΔP_choked in Cv equation

F_L: liquid pressure recovery factor (valve type dependent; see valve-cavitation skill) F_f = 0.96 − 0.28 × √(p_v / p_c) [p_v = vapor pressure; p_c = critical pressure of fluid]

Example: Water at 20°C; Q = 50 m³/h; p₁ = 8 bar; p₂ = 5 bar; ΔP = 3 bar; G_f = 1.0; F_p = 1.0 p_v = 0.023 bar (water at 20°C); F_f = 0.96 (negligible for water at low T) F_L for globe valve = 0.90; ΔP_choked = 0.90² × (8 − 0.96 × 0.023) = 0.81 × 7.978 = 6.46 bar Since ΔP = 3 bar < 6.46 bar: not choked Cv = 50 / (0.865 × 1.0 × √(3/1.0)) = 50 / (0.865 × 1.732) = 50 / 1.498 = 33.4

Select: next available Cv ≥ Cv_required × SF SF = 1.0 at rated flow; typically select standard Cv = 40 or 50; at design flow valve open ~70–80%

With Viscosity Correction (High-Viscosity Liquids)

Viscosity correction factor F_v: F_v = (ν / 100)^(1/3) for ν > 100 cSt [approximately; detailed from ISA charts] Or: Reynolds number valve factor F_R from ISA 75.01 Appendix A R_v = N₂ × F_p × Q / (ν × Cv)^(1/2) [N₂ = 76,000 for gpm/psi; or 23,800 for m³/h/bar] F_R from table vs. R_v; adjusted Cv = Cv_non-visc / F_R

Applicable when: ν > 100 cSt (heavy oil, glycol, polymer solutions)

Gas and Steam Sizing

Compressible Flow (ISA 75.01)

Gas/vapor Cv formula: Cv = Q_scfh / (N₇ × F_p × p₁ × Y × √(x × M × T₁ × Z₁)) [Q in SCFH; p₁ in psia; T₁ in °R; M = molecular weight; Z₁ = compressibility] Or: Cv = W / (N₆ × F_p × Y × √(x × p₁ × ρ₁)) [W in lb/h; ρ₁ in lb/ft³]

Where: x = ΔP / p₁ [pressure ratio] x_T = pressure drop ratio at choked (critical) flow for valve type (from manufacturer; typically 0.6–0.75 for globe) Y = 1 − x/(3 × F_γ × x_T) [expansion factor; accounts for gas density change; Y = 1.0 for liquid; Y ≥ 0.667 for gas] F_γ = γ/1.40 [specific heat ratio factor; F_γ = 1.0 for air/diatomic gases] If x > F_γ × x_T: choked flow; use x = F_γ × x_T; Y = 0.667

Metric form (IEC 60534-2-1): Cv = ṁ × √(M × T₁ × Z₁) / (N₉ × F_p × p₁ × Y × √(x)) N₉ = 94.8 (ṁ in kg/h; p₁ in bar; T₁ in K; Cv gives m³/h water equivalent)

Natural gas example (SG = 0.6 vs. air; M = 17.4 g/mol; γ = 1.27): ṁ = 5,000 kg/h; p₁ = 60 bar; p₂ = 55 bar; T₁ = 288 K; Z₁ = 0.88 x = 5/60 = 0.0833; x_T (globe) = 0.65; F_γ = 1.27/1.40 = 0.907 F_γ × x_T = 0.907 × 0.65 = 0.590; x < 0.590 → not choked Y = 1 − 0.0833/(3 × 0.907 × 0.65) = 1 − 0.0833/1.769 = 1 − 0.047 = 0.953 Cv = 5,000 × √(17.4 × 288 × 0.88) / (94.8 × 1.0 × 60 × 0.953 × √0.0833) = 5,000 × √(4,415) / (94.8 × 60 × 0.953 × 0.2887) = 5,000 × 66.5 / (1,572) = 332,500 / 1,572 = 211.5 Select Cv = 250 (DN 100 globe valve; ~85% open at design)

Steam Sizing

Saturated steam (simplified): Cv = W / (2.1 × p₁ × Y_steam) [W in lb/h; p₁ in psia; Y_steam = expansion factor] For critical flow: Cv = W / (1.4 × p₁) [choked; p₂/p₁ < 0.55]

Superheated steam: Substitute ρ₁ = p₁ / (0.0051 × (T_super + 273)) × (1 + superheat correction) [approximate] Use IEC 60534 full procedure with steam properties from steam tables

Inherent Flow Characteristics

Cv vs. Stem Position

Equal percentage: Cv(l) = Cv_max × R^(l−1) [l = fraction stem travel 0–1; R = rangeability ratio; R = 50 typical] At l = 0: Cv = Cv_max/R (not zero; minimum flow); at l = 1: Cv = Cv_max log(Cv) is linear with stem travel → equal % change in Cv per unit stem travel Preferred for: most process control; provides self-linearizing when ΔP varies with flow

Linear: Cv(l) = Cv_max × l [linear Cv vs. stem position] Preferred for: liquid level control at constant ΔP; blend control; applications where ΔP constant

Quick opening: Cv increases rapidly near closed position; poor control; primarily on-off service; emergency valves

Installed Characteristics

Valve pressure drop fraction: At = ΔP_valve / ΔP_total_system [valve authority or pressure drop ratio] At = 1.0: entire system ΔP across valve → installed = inherent characteristic At < 0.3: installed characteristic greatly distorted from inherent; equal-% degrades to quasi-linear or worse

Installed equal-% becomes nearly linear when At = 0.3–0.5 → often desired result System design: allocate 30–50% of total system ΔP to control valve

Rangeability: R = Cv_max / Cv_min [usable turndown range] Equal percentage: R ≈ 50 (150:1 effective with inherent; installed reduces to ~20:1) Required: maximum flow / minimum controllable flow; must be ≤ R of selected valve

Actuator Sizing

Pneumatic Actuator

Diaphragm actuator force: F = A_diaphragm × p_supply [N; A = diaphragm effective area; p_supply = instrument air pressure] Typical: p_supply = 0.2–1.0 bar (3–15 psi) or 0.4–2.0 bar (6–30 psi) A_diaphragm = π × D_d² / 4 [D_d = diaphragm diameter; 150–400 mm common]

Required actuator force: F_required = F_seat_load + F_packing + F_stem_weight + F_unbalance Seat load: F_seat = π × d_seat × w_seat × contact_stress [w_seat = seat width; typical contact 15–35 MPa] Packing friction: F_packing = 0.10–0.20 × packing gland bolt load

Fail-safe: Air-to-open (AO): spring returns closed on loss of air → fail-closed; required for emergency block valves on flammable/toxic Air-to-close (AC): spring returns open → fail-open; required for cooling/quench services Selection: HAZOP determines fail-safe position for each valve

Electric Actuator

Torque requirement: T = valve break torque × SF (SF = 1.5–2.0); or from valve manufacturer Power: P = T × ω / η_gearbox [ω = valve shaft angular velocity; η ≈ 0.5–0.7] Sizing: select motor with rated torque ≥ T_required

Valve Selection Summary

Valve type selection by application:

Application	Recommended Type	C_v range	F_L	Notes
General liquid	Globe (single seat)	0.1–3,000	0.8–0.95	Best control; bidirectional
High-capacity liquid	Ball (characterized)	10–20,000	0.55–0.70	Higher Cv; less accurate
Slurry/viscous	Pinch/diaphragm	Varies	—	No internal trim contact
High-ΔP gas	Globe with anti-noise	0.1–1,000	0.8–0.95	Noise-critical
Isolation gas	Ball/butterfly	High	—	On/off service
Steam throttling	Globe (heavy body)	0.1–2,000	0.85–0.92	Thermal expansion provision
Cryogenic	Globe (extended bonnet)	—	—	Cold box; LNG service

Standards and References

Standard	Scope
IEC 60534-1	Control valve terminology
IEC 60534-2-1	Sizing equations for incompressible flow
IEC 60534-2-3	Sizing equations for compressible flow
ISA 75.01.01	Flow equations (US equivalent to IEC 60534-2)
ISA 75.11.01	Inherent flow characteristics
ANSI/FCI 70-2	Control valve seat leakage classification

Output

Provide: service conditions (fluid: liquid/gas/steam; composition; T₁ [°C]; p₁ [bar]; p₂ [bar]; ΔP [bar]; flow Q [m³/h] or W [kg/h] at design and turndown; G_f or M; viscosity if > 100 cSt), sizing calculation (applicable standard: IEC 60534-2-1/2-3; formula selected; Y if gas; x and x_T; F_L if liquid; F_p if reducers; Cv_required = [value] at design flow; Cv_turndown = [value]; rangeability ratio required), choked flow check (ΔP_choked [bar] for liquid; x_choked for gas; result: choked or not; if choked: limiting Cv calculation), valve selection (type: globe/ball/butterfly/other; inherent characteristic: equal %/linear; DN [mm]; Cv_rated; % open at design; valve body material; trim material), actuator (pneumatic ATO/ATC; diaphragm area [cm²]; supply pressure range [bar]; spring range; fail-safe position; or electric torque [N·m]; motor size [W]), rangeability (Cv_max/Cv_min = R; required turndown; installed characteristic at At = ΔP_v/ΔP_system; control quality: good/marginal/poor), cavitation/noise check (σ_v for liquid; Lp_A for gas — reference sister skills), and applicable standard (IEC 60534-2-1 for liquid; IEC 60534-2-3 for gas; ISA 75.01.01; FCI 70-2 for leakage class).