# Fluid Mechanics – Oil Spill Calculation for Chem Engineers

OIL SPILL PROJECT NO. 6 Statement of Problem: In this project, the goal is to apply the knowledge of fluid dynamics in order to determine the effect of two parameters (oil density and volume fraction) on how long will it take for an oil drop to rise a distance of 1m in an oil/water distribution. Data: The following information was provided; | |Water | |  | | | | | | | | | |Oil Droplets | | |? |1030 |kg/m3 | |? d |850 – 950 |kg/m3 | |µr |0. 0008 |kg/(m-s) | |Dp |0. 1 – 1. 0 |mm | |g |9. 8 |m/s2 | |? |0 – 0. 5 |  | | | |Distance |1 |m | | | Calculations: Part 1:

In this part, the goal was to determine the effect of volume fraction on separation time. In order to determine the effect of volume fraction on settle-time, the density of oil was assumed to be constant with an average value of 900 kg/m3. Volume fraction was varied from a value of 0 to 0. 5 and by using the Zigrang-Sylvester relationships provided by the instructor, the coefficients a,b and c were calculated. The settling velocity U? was then determined by using the following relationship; U? = c – (c2 – a2)1/2

Finally, the time was determined for the oil drops to rise by a distance of 1m by using the following relationship; Timesettle = Distance / U? Part 2: In the 2nd part of the problem, the density of the oil drops was varied between 850 kg/m3 to 950 kg/m3 in order to determine the effect of varying oil density on settling time. The following equations were used; Ar = Dp3g? (? p – ? ) / µ2 Rep = Ar/18(1+0. 0579Ar0. 412) -1. 214 ut = µRep / ? Dp The Archimedes numbers were negatives because oil drops were rising instead of settling down due to gravity.

Finally, the settling time was determined by, timesettle = distance / ut Summary and Discussion of Results: In order to determine the exact flow rate, it is necessary to determine the effect of these two parameters. Our goal in this project was to learn the effect of these two parameters on settling time. The plots for part 1 show that by increasing the volume fraction of oil drops while holding the density of oil to be constant at an average value of 900 kg/m3, the settling time increases as well.

The higher the volume fraction of oil drops, the greater time it will require for the oil drops to rise to a distance of 1m. Similarly for part 2, if the density of oil increases, the separation time increases but not as much as the change due to volume fraction. The density change does not effect the settling time as much as the volume fraction, but both parameters do effect the separation time linearly. The plots for the final results including the Excel calculation sheets are attached herewith.