Flow of Brine Solution with Dissolved Ions in an 1-Directional Porous Media

Abstract

In this work we consider the injection of water with dissolved ions into a linear horizontal porous rock cylinder with constant porosity and absolute permeability initially containing oil and water in several proportions. The water is assumed to have low salinity concentration, where some ions are dissolved, we also assume that there is in the rocks some possible minerals that can dissolve or precipitate in water phase. There are two chemical fluid components as well as two immiscible phases: water and oil, (w, o). The dissolved ions are: positive divalent ions: calcium ions, Ca2 and magnesium ions, Mg2; negative divalent ions: sulphate ions, SO24 ; positive monovalent ions: sodium ions, Na ; negative monovalent ions: cloride ions, Cl. The cations are modeled to be involved in fast ion exchange process with a surface negative S which can absorb the positive ions, Ca2, Mg2 and Na; the quantities of cations absorbed for the surface S are denoted by βCa, βMg and βNa, for calcium, magnesium and sodium. We use simple mixing rules. We disregard any heat of precipitation/dissolution of substance reactions or ion desorption. Moreover we disregard any volume contraction effects resulting from mixing and reactions in any phase. Here we solve the Riemann problem and we give several numerical examples.