## 2 June 2015 Extracting oil, cleaning soil.

In the last blog I got excited about the Eötvös number and how it applied to detergency. A colleague looked at the blog and said "Of course this is the same as applying the Bond number to soil remediation and to extended oil recovery (EOR)". When people say "of course" that often means that almost no one knows this. In hindsight it's rather obvious that cleaning soil from clothes and removing oil from a well must follow similar rules, but it wasn't obvious at the time. So I had to sit down and write another app.

The app combines a number of themes into a single calculation. The Bond number, B, is just 2x Eötvös and is the balance of gravity and surface forces. If you are pumping water up through some soil or rock in order to remove contaminants or oil, a large Bond number will cause the drops to rise. In addition there is the Capillary Number, Ca, which is the ratio of inertial effects (velocity x viscosity) to surface energy effects. Again a large capillary number helps. In fact the two are combined into a single "Trapping Number", though because I find the term unhelpful I've just called it the CB number. CB2 = (Ca+B)2. For flows which are horizontal the Bond effect is zero so CB=Ca.

Because you are removing oils from pores in soil/rock there is a resistance that can be calculated from pore diameters and fluid flows. The net result of this calculation is that there is a critical value of CB, CBcrit, below which the oil or contamination just sits there, however much water you might pump. That is why it is so hard to extract oil or remove contamination from soil. It's not that you don't extract much of the oil, it's that you extract none of it.

When you put these formulae into the Removal app it is clear that the best way to get CB to be greater than CBcrit is to reduce the interfacial tension (IFT) via the right choice of surfactant. If the interfacial tension is, say, 20mN/m then any old surfactant will get it down to, say, 4mN/m. But the optimal surfactant will reduce it to 0.04mN/m, i.e. by a factor of 100. This means that the difference between a good and bad surfactant gives a B is 100x larger and Ca is also 100x larger, something that could only be achieved by pumping 100x faster or increasing the viscosity 100x.

This is exactly the same logic as found for detergency. To get a low IFT requires knowledge of the oil (or pollutant), salinity and temperature which can all be combined via HLD theory to indicate the best place in surfactant space. Use the theory to get it right and lots of extra oil comes out of the well or lots of pollutant is cleared from the soil. Get it wrong and you've just pumped a lot of unhelpful surfactant into the ground.