The effect of shear on oil-water mixture

Introduction

 

Oil-water mixtures easily form dispersions when subjected to high turbulence. As discussed in the article turbulence and multiphase flow, there are two governing mechanisms that control the process of fluids mixing: droplet coalescence and droplet break-up. The presence of shear forces in turbulent flow is a result of velocity fluctuations of eddies of various sizes. In the scale of large eddies, turbulence is anisotropic. By decreasing eddy scale, turbulence becomes more isotropic. At very small eddy sizes, viscous forces dominate the turbulence. Consequently, little energy is contained by the smallest eddies because most of kinetic energy is dissipated into heat.

 

Kolmogorov (1941) proposed in his theory that the scale at which energy is dissipated is a function of the parameters that are relevant for the smallest eddies. He stated that these parameters are the rate at which the energy is cascaded from bigger to smaller scale eddies, \varepsilon, and the kinematic viscosity, \upsilon, which determines the conversion of the kinetic energy into heat.

 

The size range where the energy cascade takes place is called the inertial subrange. Here energy is cascaded downwards to smaller eddies without dissipating energy. In this inertial subrange the eddy properties depend only on , which is called energy dissipation rate per unit mass. This parameter describes conversion of kinetic energy into the heat due to large velocity gradients created by eddies of different scales.

 

While high turbulence causes shearing and droplet break-up of bigger droplet into smaller ones, it also promotes the coalescence of small droplets at the same time. These two processes balance each other in terms of intensity of turbulence (energy dissipation rate) and the maximum stable droplet size of the dispersed phase. The general correlation is that the higher the dissipation rate, the lower maximum droplet size.

 

 

Droplet coalescence and break-up mechanisms

 

The coalescing process in turbulent flow consists of two sub-processes: droplet collision, and drainage of the fluid film between collided droplets. Eq. 1 shows the collision frequency for equally sized droplets in the inertial subrange of turbulence.  This equation determines how often two droplets collide.

 

\omega_{{col}}=\left ( \frac{32\pi}{3} \right )\cdot(\varepsilon\cdot d) ^{1/3}\cdot d ^{2}\cdot n        (1)

 

Where

 

\varepsilon = energy dissipation rate per unit mass, m2/s3 or W/kg

d = droplet diameter, m

n = number of droplets of diameter d per unit volume, m-3

 

The collision frequency increases if the number of droplets, the size of droplets or the turbulence intensity increases. In order to coalesce, the fluid film between droplets need to be drained. The coalescence probability is governed by the time it takes to drain the fluid film and the droplet interaction time. The drainage mechanism describes the process of continuous phase film drainage between two droplets. This process mainly depends on the fluid properties and not on the flow regime.

 

Figure 1. – Schematic process of droplet collision and coalescence.

Figure 1. – Schematic process of droplet collision and coalescence.

 

Droplets interact differently with eddies of different size in the turbulent flow. Eddies that have larger size than the droplets, transport these droplets through the flow field. Eddies, which are smaller or equal to the size of the droplets cause droplet deformation and break-up. Eddies colliding with the droplets break them, if they have sufficient energy to overcome the droplet’s internal forces. This means that the shear forces acting on the droplets deform and break them into smaller droplets. Eventually, internal forces will counteract the deformation. This is because the smaller droplets have higher internal restoring stresses, which oppose the external deformation. If the droplets remain long enough in the turbulent zone or if the turbulent flow maintains its intensity over a long distance, the droplet break-up process will stabilize and result in a maximum stable dispersed droplet size.

 

The maximum stable droplet size that can exist at a given flow and fluid conditions has been described by Hinze (1955) as:

 

d_{{max}}=We_{{crit}}^{3/5}\cdot\left ( \frac{\sigma}{\rho} \right ) ^{3/5}\cdot\varepsilon\frac ^{-2/5}                (2)

 

Where:

 

d_{{max}} = maximum droplet diameter, m

We_{{crit}} = Critical Weber number, -

\sigma = interfacial tension between the oil and water phases, N/m

\rho_{{c}} = density of continuous phase, kg/m3

 

Shear forces affect both coalescence and droplet break-up. Medium level of shear is actually beneficial for promoting droplet coalescence and increasing the average droplet size if the fluid mixture contains small droplets. Conversely, the intense turbulence stimulates high level of shear and results in a highly dispersed mixture with small average size of the droplets. Smaller droplets take longer time to separate and in presence of emulsifying agents they can form stable emulsions.

 

Hinze did not include the viscosity of the dispersed phase in its formulation of the maximum droplet diameter. Many therefore regard this equation only to be valid for lighter, low viscous oil and water mixtures where the viscosity of the dispersed phase is close to that of the continuous phase. Others, for example Davies (1985), have included the viscosity of the dispersed phase, making that equation also valid for heavy viscous oil and water mixtures.

 

 

Stability of oil-water emulsions

 

From a theoretical point of view, all emulsions are unstable systems because there is a natural tendency for immiscible liquids to separate. However, many emulsions can remain stable over a long period. Emulsions can be classified as loose, medium and tight emulsions depending on how long it takes them to separate.

 

The stability of emulsions is an important factor that needs to be considered during the separation process. The droplet size distribution and the chemical composition are parameters that mainly affect the stability. The stability increases when the average droplet size of the dispersed phase decreases. For the chemical composition, emulsifying agents play a major role in enhancing the stability of dispersion. Asphaltenes and wax, naturally present in crude oil, often act as emulsifiers. They form an interfacial film around the droplets and thereby obstruct the coalescing process. With increasing asphaltene and wax concentrations, the level of stability increases.

 

There are also other factors affecting the stability of emulsions. Presence of solids or fines can increase the stability of the emulsion. This is caused by the particles stabilizing the droplets of the dispersed phase.  In order to act as stabilizers, the particles must therefore be much smaller than the size of the emulsion droplets. Another important parameter is temperature as it can affect emulsion stability significantly. Higher temperature decreases viscosity of the emulsion and accelerates the interfacial film drainage during the droplet collision. The thermal energy of droplets increases with higher temperature, leading to more frequent droplet collision. pH of the emulsion is another factor that influences the emulsion stability. pH of the continuous phase affects the rigidity of the interfacial films of the dispersed droplets.

 

 

Additional reading

 

Kolmogorov, A.N. 1941. Dissipation of energy in locally isotropic turbulence. Compt. Rend. Acad. Sci. USSSR, Vol. 32, No. 1

Zande, M.J, van der. 2000. Droplet Break-up in Turbulent Oil-in-Water Flow Through a Restriction. PhD dissertation, Delft University of Technology, Delft, the Netherlands (June 2000)

Davies, J.T. 1985. Drop Size of Emulsions Related to Turbulent Energy Dissipation Rates. Chem. Eng. Sci., Vol. 40, No. 5, pp. 839-842.

Kokal, S. L., 2002. Crude Oil Emulsions: A State-Of-The-Art Review. Paper SPE 77497 presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 29 September – 2 October. http://dx.doi.org/10.2118/77497-MS

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