It is a well-established fact that shear forces in valves cause droplet break-up and emulsification in multiphase flows. The shearing of droplets in high intensity turbulent areas within the valve causes oil droplets to deform and break. The results of emulsification and droplet break-up of the dispersed phase is reduced efficiency in downstream separation equipment.
This series of articles will look at how droplet shearing in valves affects the downstream droplet size and separation efficiency. Effect of valve trim and other solutions to reduce the harm of valve shearing on downstream separation equipment will be presented, backed up with field and test data.
The two phenomena governing the droplet size in a multiphase flow are droplet breakup and droplet-droplet coalescence. To what extent one of these phenomena is dominating, is affected by both fluid characteristics and the hydrodynamics. Fluid characteristics involve factors such as the oil concentration, droplet size distribution, oil and water density, oil and water viscosity, water temperature and salinity, and surfactants. Hydrodynamics are related to the flow regimes the droplets encounter and the forces exerted by these. For oil and gas production, the flow is turbulent and the droplet size is therefore a function of the intensity of the turbulence.
Droplet Break-up Theory
The mechanism of droplet breakup is typically expressed as a balance between the external stresses from the continuous phase and the surface stress of the droplet, plus the viscous stress of the fluid inside the droplet. The external stresses may destroy the droplet, while the surface stress and viscous stress restore the droplet's form. The balance of these stresses leads to a maximum stable droplet diameter, dmax
. For droplets larger than dmax
, the external stress overcome the restorative stresses, and the droplet breaks.
This balance of forces has been expressed mathematically by for example Hinze  where maximum droplet size that can survive a certain turbulent flow regime is given as:
Critical Weber number [-]
σ Interfacial tension [N/m]
ρc Density continuous phase [kg/m³]
ε Mean energy dissipation rate per unit mass [W/kg]
The critical Weber number, the density, and the interfacial tension are all solely dependent on the fluid properties and composition. The mean energy dissipation rate per unit mass is therefore often regarded as the single measure of the turbulence intensity, allowing this factor to be used to evaluate the magnitude of droplet break-up or emulsification in a multiphase mixture.
For fluid flow through a valve or orifice, the mean energy dissipation rate per unit mass can be expressed as [2,3]:
The permanent pressure drop [Pa]
Q Flow rate [m³/s]
Volume used for energy dissipation [m³]
According to this equation, ε is directly proportional to 1/Vdis
for constant process conditions and fluid compositions. Increasing the volume engaged in energy dissipation will, therefore, result in a decrease in ε, increasing the maximum droplet size that can tolerate the flow regime in the valve.
Effect of Inlet Droplet Size
As discussed, the maximum droplet that can survive the turbulent flow regime in a valve is directly related to the energy dissipation rate. For constant fluid properties and process conditions, the maximum droplet size that can be sustained by the turbulent flow regime, dmax
is only dependent on the orifice or valve design. As a result, inlet droplets larger than dmax
, will be reduced to dmax
, which is clearly shown in Figure 1. This figure shows measurements of the Dv50 droplet size upstream and downstream of a valve, where the fluid composition and process conditions are kept constant and the only varying parameter is the inlet droplet size distribution.
Figure 1: Online measurements of Dv50 upstream and downstream a valve. (Click to enlarge figure)
In the figure, the red lines show the Dv50 at the inlet of the valve and the blue lines show Dv50 at the outlet of the valve. As expected from the theory, it is clearly seen that the outlet droplet size is not affected by the inlet droplet size distribution; at least as long as the inlet droplets are larger than dmax
. Another way to show this is by looking at the droplet size distributions from the same test, as shown in Figure 2. Here it is seen that the outlet distributions are the same, regardless of the inlet distribution. The one exception is the purple distribution, which is already smaller than dmax
and therefore not significantly affected by the turbulence in the valve.
Figure 2: Online measurements of droplet size distribution upstream and downstream a valve. (Click to enlarge figure)
Development of Bimodal Distributions
The energy dissipation rate is not homogeneously distributed in a valve. There will always be pockets of high intensity turbulence and high energy dissipation rates, and pockets with lower intensity turbulence. Not all droplets will pass through the same areas, and will therefore not experience the same shearing effect. This can cause what is known as bimodal droplet size distributions. Bimodal distributions show two or more tops in the droplet size distribution, and generally has a higher concentration of small droplets, i.e., the tail end of the distribution. This phenomenon becomes more prominent at increasing differential pressure, as shown in Figure 3. This graph shows the outlet droplet size distributions for a conventional valve for different pressure drops, with constant inlet droplet size and fluid properties. The results show a distinct increase in the tail end of the droplet size distribution, containing the smallest droplets.
Figure 3: Outlet droplet size distributions from a conventional valve at different pressure drops