Let Stokes’ Law Solve Oily Water Problems
Written by: Leonard Ardizzone
Oil in water continues to be a major problem for the general industry. The general industry uses city water
for manufacturing processes or for clean-up purposes. Oil (crude) is a complex hydrocarbon substance
composed of thousands of different kinds of molecules. However, to simplify our discussion, I will term
“Oil” to mean petroleum-based hydrocarbons. Once oil begins to contaminate the water stream, other
problems occur, such as:
• Efficiency loss in the manufacturing process
• Down time due to water change-out and clean up
• Bacterial growth and odors
• Unhealthy working conditions
• Disposal cost/treatment
Applications that generate oily water are:
• Indoor maintenance area wash down
• Machine or Mobile vehicle equipment wash down
• Parts washers
• Quench oil/Degreasing systems
• Fuel storage facilities
• Offshore/Onshore production facilities
• Rainwater Runoff from tank bottoms
• Rainwater Runoff from parking lots and outdoor maintenance areas
• Machine tool coolant clean-up of tramp oils
• Marine applications
Before discussing the oil water solutions using Stokes’ Law, one needs to understand there are two (2)
categories of oil water conditions;
• Oil in Water Emulsions
• “Free” Oil in Water
An oil in water emulsion can be mechanical, i.e. generated by a pump, or chemical emulsion caused
by surfactants or other chemicals. A definition offered by Forrest E. Love is “An emulsion is an apparently
homogenous mixture in which one liquid is dispersed as droplets throughout a second immiscible liquid”.
How does one address oily water problems? Stokes’ Law can provide the solution for separating “free oil”
from water since it describes the mathematical separation relationship.
Vr = g (dw - do) Do2
-Vr = rise velocity of the oil droplet in cm/sec
-g = gravitation constant (980 cm/sec )
-h = viscosity of water in poise
-dw = specific gravity of the water in gm/cm3
-do = specific gravity of the oil in gm/cm3
-Do = diameter of the oil droplet in cm
For Stokes’ Law to be valid, the following conditions must occur:
• Laminar Flow
• Particles (Oil droplets) must be spherical
The two major components in Stokes’ Law that have the biggest impact are; the oil droplet size and the
density (specific gravity) difference between the oil and the water. In most cases, the physical mixture of oil
and water will separate by gravity since oil has a lower specific gravity and will float on the water. Figure 1
demonstrates the rise distance versus time for various oil droplets sizes.
Stokes’s Law can be used to size an empty separator vessel having an inlet/outlet and an oil dam near
the outlet. See figure 2.
The two major components in Stokes’ Law that have the
biggest impact are; the oil droplet size and the density
(specific gravity) difference between the oil and the water. In
most cases, the physical mixture of oil and water will separate
by gravity since oil has a lower specific gravity and will float on
the water. Figure 1 demonstrates the rise distance versus time
for various oil droplets sizes.
Stokes’s Law can be used to size an empty separator vessel
having an inlet/outlet and an oil dam near the outlet. See figure 2.
As the oily water flows horizontally through the separator vessel,
the oil droplets rise vertically, at a velocity depending on the oil
droplet size and density. If the oil droplets should rise the “x” distance, below the dam, before its
horizontal movement carries it out, then the oil droplets are captured by the dam and cannot flow to the outlet chamber. This is known as the “residence time” and can be expresed as: Rt = v/q, where v = volume (gallons) and q = flow rate (gpm), i.e. if the tank in figure 2 is 50 gallons and the flow rate is 5 gpm, then the Rt = 10 minutes from inlet to outlet. Using Stokes’ Law, if an oil droplet is 20 microns, water temperature 68F, oil s.g. of 0.85, then using a short form of Stokes’ Law: V = 0.001286 (d s.g.) Dsq. = 0.001286 (1 – 0.85) 20sq. = 0.077 in/min. or ~ 13 min. /in... If the “x” distance height = 6” then much of the oil droplets will pass under the dam, hence the need for coalescer plate media. Another important consideration is how the oily water is being delivered to the separator vessel. Gravity flow will have the least effect on shearing oil droplets. However, inlet piping with many elbows will shear oil droplets. Shearing will create smaller oil droplets and begin an emulsion process. Pumps have the greatest effect on shearing oil droplets. Therefore, if a pump is used, the type of pump is very important. Diaphragm pumps or screw pumps are considered to be low shearing pumps and are recommended for oil water separation. Filtration engineers will know the efficiency of each pump type and be able to calculate the mean diameter oil droplet size that is generated from
different pump designs and gravity flow.
The next concept is the Standard Deviation (SD). The standard deviation has to do with the oil droplet distribution by volume. Once one knows the mean oil droplet size, due to the delivery method, one can determine the standard deviation. The SD determines how great the populations of oil droplets by volume are from the mean droplet size. This can be demonstrated using a bell shape curve, see figure 3 and 4.
As we can see from figures 3 and 4, the closer the bell curve is to the mean the standard deviation approaches 1. If the standard deviation is 1, then all the oil droplets will be the same size as the mean, which is not logical.
The recommended method is to use an “Enhanced Gravity Separator” (EGS) and Stokes’ Law calculations for sizing. This is a scientific approach to solving oily water separation problems. An EGS consists of non consumable coalescing plate media with surface area containing at least 100 sq.ft./cu.ft. This engineering method will produce an accurate effluent forecast. The information required for this calculation is:
• Type of application
• Water flow rate
• Temperature range
• Type of oil and specific gravity
• Influent oil levels – in ppm
• Effluent requirements
• Type of water (fresh or salt)
• Presence and identity of surfactants
• Nature of solids, type and specific gravity
• Gravity or Pump flow
The more accurate the influent data used, the more accurate the effluent water quality prediction. Even if the oily water is emulsified, an EGS should be used as a pre-filter upstream of the final chemical treatment system. If one is hauling waste water, an EGS can remove much of the oil, reducing the hauling cost.
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