Gas Control Valve Sizing
Calculation for Compressible Flow Coefficients ($C_v/K_v$) per ISA-75.01-2012 / IEC 60534-2-1 Standards.
1. Project Data
2. Process Data
| Case Description | Flow () | Inlet P₁ () | Outlet P₂ () | Req. \(C_v\) / \(K_v\) |
|---|---|---|---|---|
| Maximum Case | 0.00 / 0.00 | |||
| Normal Case | 0.00 / 0.00 | |||
| Minimum Case | 0.00 / 0.00 |
3. Gas Properties
4. Valve Details
5. Specification Datasheet
| Point | Flow () | P₁ () | ΔP () | Req $C_v$ | Opening % | Regime | Inlet Mach | Outlet Mach | Exp. $Y$ |
|---|
Engineering Reference & Technical Basis
1. Mass Flow Physics, Expansion Factor & $N_6$
Gas sizing differs from liquid sizing because gases are compressible. As gas passes through the valve restriction, its density decreases due to the drop in pressure. The Expansion Factor ($Y$) accounts for this density change and the change in the jet area. The sizing standards use a numerical constant $N_6$ to allow for standard units: 63.3 for US Customary ($lb/h, psia, lb/ft³$) or 27.3 for Metric ($kg/h, bar, kg/m³$).
- $W$: Mass flow rate ($lb/h$ or $kg/h$).
- $x$: Pressure drop ratio ($\Delta P / P_1$).
- $\rho_1$: Inlet density, calculated as $\rho_1 = \frac{P_1 \cdot MW}{Z \cdot R \cdot T_1}$.
2. Compressibility Factor ($Z$) Correlation
This tool estimates $Z$ using the Pitzer Virial Correlation for library gases. It calculates Reduced Temperature ($T_r = T / T_c$) and Reduced Pressure ($P_r = P / P_c$) and estimates $Z$ as:
Where $B^0 = 0.083 - 0.422 / T_r^{1.6}$ and $B^1 = 0.139 - 0.172 / T_r^{4.2}$. This correlation is reliable for moderate pressures and temperatures above the critical point.
3. Critical (Choked) Flow
When the velocity at the valve "vena contracta" reaches the speed of sound, the flow becomes choked. Increasing the pressure drop further will not increase the flow rate.
The flow regime is defined by the pressure drop ratio $x$:
- Sub-critical ($x < x_{choked}$): Velocity is subsonic. Flow increases with pressure drop. $Y$ is calculated normally.
- Choked ($x \ge x_{choked}$): Velocity is sonic (Mach 1). Flow is limited. Sizing uses $x_{choked}$ and $Y = 0.667$. Also known as Critical Flow.
4. Vena Contracta & Pressure Recovery
The Vena Contracta is the point in the fluid stream where the cross-sectional area is at its minimum and velocity is at its maximum. This is the point of lowest pressure ($P_{vc}$).
In gas service, if the pressure at the vena contracta drops below the critical pressure ratio, sonic velocity (Mach 1.0) is achieved. High-recovery valves (like Ball or Butterfly) have a smaller vena contracta area relative to the trim opening, leading to lower $x_T$ values and earlier choking compared to low-recovery Globe valves.
5. Recommended Gas Velocity Limits
Excessive velocity leads to aerodynamic noise, vibration, and erosion. Limits are typically expressed as a fraction of the speed of sound (**Mach Number**). The values below reflect Mechanical Integrity limits (vibration/fatigue) rather than strict noise limits.
| Location | Service Type | Max Mach Number |
|---|---|---|
| Valve Inlet | Continuous | ≤ 0.40 Mach |
| Valve Outlet | Continuous (Standard Trim) | ≤ 0.80 Mach |
| Valve Outlet | Intermittent / Relief | ≤ 0.90 Mach |
| Valve Outlet | Low Noise Trim | ≤ 0.30 Mach |
6. Flow Characteristic Selection (Gas Service)
Used primarily for:
- Pressure Reducing Stations where the inlet pressure is constant and downstream demand varies.
- Systems where the valve pressure drop ($\Delta P$) is a constant and dominant part of the total system pressure loss ($\Delta P_{valve} > 50\%$).
- Compressor Bypass (Anti-surge) valves requiring fast, proportional opening.
Used primarily for:
- Gas Flow Control Loops where the available pressure drop decreases significantly as the flow rate increases ($\Delta P_{valve} < 25\%$ of system $\Delta P$).
- Temperature Control applications involving heat exchangers.
- Systems with high rangeability requirements (e.g., 50:1) to provide fine control at low flow rates.