# Purification of Produced Water by Solvents to Enhance Oil Recovery and Reuse Separated Droplets
## 4 Discussion
### Hansen Solubility Parameters and Produced Water  
A basic rule of chemistry is that \"like dissolves like\". However, it is intriguing that substances with markedly different functional groups, such as xylene, cyclohexanone, methanol, or tetrahydrofuran, are capable of effectively dissolving the residual oil in produced water. Conversely, substances with the same functional group, such as cyclohexanone, acetone, and butanone--all ketones--exhibit markedly different capacities for dissolving the residual oil in produced water. An approach that can explain these seemingly inexplicable behaviours is the Hansen solubility parameters (HSPs) [38]. According to [PERSON], two substances interact with each other and dissolve in one another if their cohesion energies are similar. It is proposed that the cohesion energy of a substance, \(E\), comprises three components: energy due to London dispersion forces, \(E_{D}\); energy due to the polarity of molecules, \(E_{P}\); and energy due to hydrogen bonding, \(E_{H}\):  
\[E=E_{D}+E_{P}+E_{H}. \tag{3}\]  
If the total solubility parameter, \(\delta\), is defined as the square root of the cohesion energy density as follows,  
\[\delta=\sqrt{\frac{E}{v}}, \tag{4}\]  
and if the cohesion energy, \(E\), is expressed in J/mol and the molar volume, \(v\), in cm\({}^{3}\)/mol, then the units of the total solubility parameter are MPa\({}^{1/2}\). The parameters of dispersion, \(d_{D}\); polarity, \(d_{P}\); and hydrogen bonding, \(d_{H}\); respectively, are as follows:  
\[\delta_{D}=\sqrt{\frac{E_{D}}{v}}\quad\delta_{P}=\sqrt{\frac{E_{P}}{v}}\quad \delta_{H}=\sqrt{\frac{E_{H}}{v}}, \tag{5}\]  
where the units of the parameters thus defined are also MPa\({}^{1/2}\). Therefore:  
\[\delta^{2}=\delta_{D}^{2}+\delta_{P}^{2}+\delta_{H}^{2}. \tag{6}\]  
Figure 8: Percentage of residual oil removed from produced water versus various volumes of solvents. In the three-dimensional Hansen space, the distance between two substances, 1 and 2, \(Ra\), is defined as  
\[R_{a}=\sqrt{4(\delta_{D2}-\delta_{D1})^{2}+(\delta_{P2}-\delta_{P1})^{2}+(\delta _{H2}-\delta_{H1})^{2}}, \tag{7}\]  
where the units are MPa\({}^{1/2}\). This definition is like the definition of distance in Euclidean spaces, with the exception that the term related to the dispersion solubility parameters \(d_{D1}\) and \(d_{D2}\) is multiplied by 4. The Hansen solubility parameters of any substance form the centre of a \"_solubility sphere_\" with a radius \(Ro\), where \"_good solvents_\" for the considered substance have a distance to the centre, \(Ra\), equal to or less than the solubility radius, and \"_poor solvents_\" have a greater distance. The parameter Radius of Energy Difference, \(RED\), is defined as follows:  
\[RED=\frac{R_{a}}{R_{0}} \tag{8}\]  
Therefore, \(RED\leq 1\) for good solvents of the considered substance and \(RED>1\) for poor solvents. These conditions can be extended to any energetic interaction between substances, not only for solubilisation processes but also for adsorption, absorption, coating resistance, suspension stability, free surface energy [39], or for the specific case addressed in this article: the destabilization of oil emulsions in produced water by solvents. From the perspective of Hansen solubility parameters, the present study considers the criterion that a solvent is an \"effective destabilizer\" of oil emulsions when, upon treating 100 mL of produced water with 25 mL of the solvent, the residual oil concentration, R, is reduced to less than 20 ppm. Table 4 presents the Hansen solubility parameters of the tested solvents. Solvents that are effective destabilisers are marked with a \"1\", while ineffective ones are marked with a \"0\".