Application of Computational Fluid Dynamic (CFD) for Modeling and Simulation of Oil Movement in Water

The role of simulation becomes more important recently as a counterpart of experimental works in the field of engineering. This is because of that it can depict and forecast behavior and results with saving time and experimental works with involving some governing equations.
Modelling and simulation of oil movement in water can be used for several engineering applications, such as:

• Wastewater treatment such as in API separator, plate oil/water separator.
• Investigate the process of injection well and production well in crude petroleum oil drilling process.
• Manufacturing process, such as food processing, petroleum refinery, wet oil extraction, etc.

Mixture consisted of water and oil has some characteristics, among other things they cannot blend well since the two substances are immiscible fluid. Since oil is less dense than water, it always resides on water surface. When oil is dispersed in water, its droplets will go up to the water surface due to buoyancy effect. The buoyancy effect results from difference of water and oil density. Then, oil is naturally separated from water by gravity-aided separation.

Neglecting frictional force, two forces act to a single oil droplet: Gravitational force (Fg) attracts the oil to move downward, While buoyant force (Fb) pushes the droplet upward.

Fb = m_w.g, since m = ρ.V,

      Fb = ρ_w.V_oil.g
      Fg = ρ_oil.V_oil.g,

Where:

m = mass of water (g),
g = gravitational constant = 9.8 m/s²,
ρ_w = density of water (g/cm³)
V = volume of oil droplet (cm³)

Fg = ρ_oil.V_oil.g,

Where:
m = mass of water (g),
g = gravitational constant = 9.8 m/s²,
ρ_oil = density of water (g/cm³)
V = volume of oil droplet (cm³)

Buoyant force on Oil Droplet

Resultant force: ΣF = F_b - F_g

Downward force = (-) sign, upward force = (+) sign,

The equation above is further rearranged to:

ΣF = ρ_w g.V - ρ_oil g.V = (ρ_{w –} ρ_oil) x gV

Since water density (ρ_w) is greater than that of Oil (ρ_oil), then,

(ρ_{w –} ρ_oil) has (+) value, the oil is directed upward.