Analytical Solution of Slug Low Salinity Waterflooding

Results of laboratory experiments show that injection of low-salinity water (LSW) can increase oil recovery up to 40% when compared to waterflooding. Although the mechanisms that act during LSW are still not well understood, one of the most accepted phenomena is the multi-component ion exchange (MIE) theory. In this work we derive the analytical solution for a one-dimensional two-phase multi-component flow, considering the ion exchange theory. In order to obtain the mass balance equations, ions such as \(Na^{+}, Ca^{2+}\) , \(Cl^{-}\) were considered in water solution, flowing and adsorbing in the porous media according to Langmuir isotherm. The mathematical model is composed by 3 hyperbolic partial differential equations obtained from the conservation laws for oil, water and for the ions dissolved in water. For the continuous injection problem, the solution is self similar and, for slug injection, wave interactions appear.