## Oil and Contamination Removal

### Quick Start

In the IFT app we saw that interfacial tension gets dramatically smaller when HLD=0. It turns out that to effectively sweep out oil from a well with water, you need a high Capillary Number which is proportional to 1/IFT. Going from a typical IFT of 1 to an IFT of 0.001 automatically gives a 1000x boost the Capillary Number. If you needed a 1000x boost by other means you would have to increase the flow velocity or viscosity by that amount - a much harder task than adding the right surfactant package.

### Oil and contamination removal

_{0}

_{hi}

When you want to remove more oil from an oil well (EOR Extended Oil Recovery) or you want to remove a contaminant from soil, you have three choices:

- Pump a lot of water at high velocity
- Pump less water but at a higher viscosity with a polymer additive
- Pump less water but with a very low interfacial tension (IFT) between oil (or contaminant) and water.

There is no right answer - it depends on circumstances. But generally it gets so hard to remove via the first two methods that eventually a surfactant-based method is required. As we will see, for the surfactant route just throwing in any old surfactant will not work. Only at super-low IFT do interesting things start to happen. And to get super-low IFT requires HLD~0, i.e. you need to choose the surfactant Cc in terms of the temperature and salinity of the soil plus the EACN of the contaminant.

The key, much-noted fact, is that extraction efficiency follows a characteristic curve with very little extraction for whateve effort is put in, then a steep increase in extraction, followed by a plateau. Although these characteristic curves can be described in many ways, for simplicity a standard Van Genuchten equation is used which has 4 parameters:

`φ = φ_"hi" + (φ_0-φ_"hi")/[1+((CB)/(CB_"crit"))^n]^"1-(1/n)"`

φ_{0} is the original level of oil/contaminant and φ_{hi} is the plateau level at high flows - remaining oil is there for other reasons. CB is the Capillary-Bond Number (sometimes called the Trapping Number), CB_{crit} is the critical value where stuff starts to happen. n is an exponent that controls the shape of the curve.

The things we can control are the Capillary Number, Ca, which is the ratio of inertial to IFT effects, i.e. velocity U times viscosity η over IFT γ:

`Ca=(Uη)/γ`

and the Bond Number, B, which is the ratio of gravitational to IFT effects which depend on gravity, g, density difference Δρ and a typical radius of a drop, r:

`B=(gΔρr^2)/γ`

Given the assumption that the oil is being pumped upwards so that gravitational effects work in the same direction as capillary effects, the driver for removal is `CB =sqrt(Ca²+B²)`. If the Horizontal option is checked then the Bond number is set to zero so CB is identical to Ca.

In the app you get to enter U, r, γ, Δρ, η as the physical parameters. Then you enter the two values for φ along with a critical value for CB. Because this can vary by orders of magnitude, you enter a log value. So if CB_{crit}=0.001, i.e. 10^{-3} you enter -3.

It comes as no surprise to find that a typical 2-order of magnitude reduction in IFT (from 4 to 0.04mN/m) that can be achieved by choosing the right surfactant to give HLD~0 is a very effective way for sweeping out oil or contaminants.

This notion of critical capillary or Bond numbers permeates surfactant science. The use of the Eötvös number (=B/2) for detergency is shown in the Eötvös Roll-up app. Other approaches via critical Weber numbers have also been shown to be important for contaminant removal.