Quick Summary:
- Two-phase and multiphase flow through control valves — mixtures of liquid and vapour, or oil, water, and gas — creates sizing challenges that standard single-phase Cv equations cannot address: using liquid-only or gas-only sizing methods for two-phase service results in severely undersized or oversized valves, causing loss of process control and valve damage.
- The Chisholm, homogeneous, and separated-phase models provide different levels of engineering rigour for two-phase flow sizing, each with defined applicability ranges and accuracy limitations that must be matched to the specific flow conditions and required sizing precision.
- Beyond sizing accuracy, two-phase flow creates practical valve problems including erosion from impinging liquid droplets, slug flow that generates mechanical shock loads, and cavitation when dissolved gas comes out of solution through the valve — all requiring specific design provisions to achieve acceptable service life.
Why Two-Phase Flow Is Different
Standard valve sizing equations — the IEC 60534 liquid sizing equation and the gas/vapour sizing equations — assume a single, homogeneous phase flowing through the valve. In single-phase liquid flow, the fluid is incompressible and the mass flow rate and volume flow rate maintain a fixed relationship. In single-phase gas flow, the fluid is compressible but can be characterised by defined thermodynamic relationships. Two-phase flow violates both assumptions simultaneously: the mixture is partially compressible, the two phases may travel at different velocities (slip between phases), and the phase ratio changes as pressure drops through the valve.
Two-phase flow occurs in many industrial applications: condensate return lines where steam flashes to two-phase as pressure drops; production wellheads where reservoir fluid contains dissolved gas that comes out of solution; heat exchangers where partial condensation or vaporisation occurs along the flow path; distillation column reboilers and reflux lines; refrigeration systems; and any liquid pipeline where temperature rises close to the bubble point.
The Homogeneous Flow Model
The simplest two-phase flow model is the homogeneous model, which treats the gas-liquid mixture as a single pseudo-fluid with properties calculated as mass-weighted averages of the individual phase properties. The key parameter is the mixture density, calculated as:
ρ_mix = 1 / (x/ρ_gas + (1-x)/ρ_liquid)
where x is the mass quality (mass fraction of vapour) and ρ_gas, ρ_liquid are the individual phase densities at the upstream conditions. The mixture viscosity and other properties are similarly averaged. The homogeneous Cv calculation then uses the mixture density in a modified single-phase liquid sizing equation.
The homogeneous model is most accurate when the phases are well-mixed and travel at the same velocity — conditions that occur at high flow velocities (above 3 m/s) and with fine bubble or droplet dispersion. It overestimates flow capacity (and therefore underestimates Cv) in stratified or slug flow regimes where the phases separate and the gas phase can “shortcut” through the valve at lower resistance. For engineering sizing purposes, the homogeneous model provides a conservative (larger Cv) estimate that is appropriate for preliminary design.
The Chisholm Method
The Chisholm correlation introduces a correction to the homogeneous model that accounts for the velocity difference (slip) between phases. The Chisholm parameter Γ (gamma) is a function of the ratio of gas-to-liquid density and an empirical constant C that depends on the flow regime:
Γ = (ρ_liquid/ρ_gas)^0.5
The two-phase pressure drop multiplier φ²_L (phi squared) is then calculated as:
φ²_L = 1 + C/X + 1/X²
where X is the Lockhart-Martinelli parameter (ratio of liquid-phase to gas-phase pressure drop components) and C is the Chisholm constant (C = 20 for turbulent-turbulent flow, the most common case in industrial two-phase valve applications).
The Chisholm method gives a more accurate prediction of two-phase pressure drop across the valve than the homogeneous model for a wider range of flow qualities and regimes. It is the recommended method for preliminary control valve sizing when two-phase inlet conditions are known but detailed flow regime analysis is not available. However, it was developed from pipe flow data and its application to the complex internal geometry of control valve trim is an approximation — accuracy of ±30–50% in Cv prediction is typical, which is acceptable for most engineering sizing purposes.
ISA/IEC Approach to Two-Phase Sizing
IEC 60534-2-1 does not provide a dedicated two-phase flow sizing method but notes that for mixtures of vapour and liquid, the sizing should account for the mixture properties. In practice, the standard engineering approach recommended by control valve manufacturers for two-phase inlet conditions is to separate the total mass flow into its liquid and vapour components, calculate the Cv contribution from each phase independently using the appropriate single-phase equation, and then combine the results using a root-sum-of-squares method:
Cv_total = √(Cv_liquid² + Cv_vapour²)
This method treats each phase as if it independently flows through the valve and adds their Cv contributions quadratically. It is a simplification but gives results that are within engineering accuracy for moderate quality ranges (x = 0.1 to 0.9) and is widely used in industry as a practical first estimate. Below 10% quality (mostly liquid) or above 90% quality (mostly vapour), the single-phase equation for the dominant phase with a correction factor for the minor phase is more appropriate.
Flash Across the Valve
When a liquid enters a valve above its bubble point pressure and the downstream pressure is below the bubble point, the liquid partially vaporises (flashes) across the valve. This is distinct from two-phase inlet flow — here the inlet is a single-phase liquid, but vaporisation occurs as the pressure drops through the valve body. The result is a two-phase mixture at the outlet that occupies a far larger volume than the inlet liquid.
Flash across the valve occurs in hot water/condensate control valves (condensate at high pressure flashing to a low-pressure steam-water mixture), pressure let-down stations on liquid hydrocarbon pipelines (liquid crude or condensate at high wellhead pressure flashing as it is throttled to separation pressure), and liquid carbon dioxide service.
The sizing approach for flashing liquids must account for the density change through the valve. The inlet is sized as a liquid using the inlet density; the outlet piping is sized for the two-phase mixture using the outlet density — which may be 10–100 times lower than the inlet liquid density. If the valve outlet and immediately downstream pipe are not enlarged to accommodate the volume increase, extremely high two-phase velocities will cause erosion and noise problems.
The valve body itself must also be considered: the flash point — the location within the valve where vaporisation begins — should ideally occur at or downstream of the vena contracta, not in the upstream body cavity. Valve manufacturers provide flash calculation software and recommendations on trim configuration (cage or plug design) to move the flash point downstream and away from the primary seating surfaces where impinging two-phase flow would cause accelerated erosion.
Slug Flow and Mechanical Impact
Slug flow — a two-phase regime where large liquid plugs (slugs) alternate with gas pockets in horizontal or inclined piping — creates significant mechanical challenges for valves. When a liquid slug arrives at a partially open control valve, it suddenly increases the mass flow through the valve by a factor of 5–20 (the ratio of liquid to gas density), creating a step change in differential pressure and a hydraulic shock as the slug decelerates against the valve restriction.
Valves in slug flow service experience rapid, unpredictable changes in the forces on the closure element — the plug or disc is cyclically loaded by liquid slug impacts and then unloaded during gas pocket passage. These loading cycles cause fatigue of valve trim components, particularly the plug-to-cage guide surfaces, and can cause instability of the control valve if the slug frequency is close to the natural frequency of the valve trim assembly.
Slug flow valves must be specified with robust trim designs: heavy-walled cages, plug guides with ample wall thickness, and hard-faced seating surfaces to resist the combined erosion and impact damage. Control valve performance during slug flow is necessarily poor — the slug-by-slug variation in flow is too fast for the control loop to track. The engineering approach is usually to accept poor control during slug events and specify the valve to survive the mechanical loading without damage, rather than attempting to provide close process control through the slug.
Erosion in Two-Phase Service
Two-phase flow is inherently erosive to valve internals when the liquid droplets or entrained solid particles carried in the gas phase impact valve surfaces at high velocity. The erosion rate depends on impact velocity, particle or droplet size, hardness of the impacting material, and hardness of the target surface. For liquid droplet erosion in wet gas service, the erosion rate is approximately proportional to the cube of the impact velocity — small increases in velocity cause large increases in erosion rate.
The most vulnerable locations in a valve subject to droplet erosion are the downstream side of the plug and seat, the cage walls immediately downstream of the pressure reduction ports, and the pipe wall immediately downstream of the valve outlet flange. Hard-face coatings (tungsten carbide, chrome carbide) on these surfaces extend service life significantly. A minimum hardness of 60 HRC at the impacted surfaces is typically recommended for severe droplet erosion service.
Erosion monitoring using ultrasonic thickness measurement (UT) of the valve body wall and cage at the erosion-prone locations should be incorporated into the inspection programme for two-phase service valves. A baseline UT survey at installation provides the reference thickness; annual UT surveys track the erosion rate and allow remaining life to be calculated and maintenance planned before wall thickness falls below the minimum allowable.
Selecting Valve Type for Two-Phase Service
Not all valve types are equally suitable for two-phase and multiphase flow service. The preferred types share a common characteristic: a flow path that minimises abrupt changes in direction and velocity, reducing the impingement erosion that is the primary damage mechanism in two-phase service.
Globe control valves with low-recovery, high-Fl trim (cage-guided with restricted ports) are the standard choice for two-phase control service — the cage structure prevents direct impingement of the two-phase jet on the body walls, and the hard-faced cage and plug resist erosion. Angle-body globe valves (where the outlet is at 90 degrees to the inlet) are preferred for flashing service because the body geometry accommodates the change in flow velocity and direction inherent in the phase change without the pressure recovery losses that occur in a straight-body globe valve.
Ball valves are used for two-phase isolation service but are generally unsuitable for throttling two-phase flow — the sharp-edged orifice of a partially open ball valve creates intense jets that cause rapid erosion of both the ball seat and the downstream pipe. Butterfly valves are similarly unsuitable for two-phase throttling service. Gate valves are acceptable for full-bore isolation in two-phase service, provided they are operated fully open or fully closed and are not throttled.
Conclusion
Two-phase and multiphase flow valve sizing and design is one of the most technically challenging areas in industrial valve engineering. The engineer who relies on standard single-phase sizing equations for two-phase service will consistently produce wrong answers — sometimes producing valves that are too small to control the process, sometimes producing valves so large that they are unstable. Applying the appropriate two-phase model for the specific flow conditions, accounting for flashing across the valve, designing for slug flow mechanical loading, and specifying erosion-resistant materials are the engineering tasks that separate a reliable two-phase valve installation from one that fails within months of startup.