Abstract Among different Enhanced Oil Recovery (EOR) methods, the injection of chemical solutions plays an important role in mature fields additional recovery. Analytical models for 1-D displacement of oil by water with chemical compounds have been developed since the 1960´s. The interfacial activity and mobility control of a chemical flooding process are affected by the concentrations of the ionic species that are present in the water. This problem involves complex physical-chemical processes of interphase mass transfer, phase transition and transport properties changes. The one-phase displacement solution has been already developed and it is a well-known problem. However, its application is limited to already water flooded reservoirs. In this paper the solution of the two-phase problem is presented. A flow potential associated with the conservation of water phase is introduced and used as a new independent variable instead of time. This technique permits splitting the system of equations into a thermodynamic system and one transport equation. It is possible to show from analytical modelling of multi-component polymer/surfactant flood that the concentration "part" of the solution is completely defined by adsorption isotherms (thermodynamic part, called auxiliary system) and does not depend on relative permeabilities and phase viscosities. The number of auxiliary equations is less than the number of equations in the compositional model by one. Once the multi-component adsorption problem is solved, the 2-phase flow behavior can be predicted. This work shows analytical solutions of 1-D oil displacement by water containing two adsorbing cations and one anion for different salt concentrations in injected and formation waters. Electroneutrality and Gapon equilibrium equation are considered. One of the most important applications of these solutions is design of chemical flooding regardless of the water saturation.
Introduction Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: chemical methods, solvents methods and thermal methods. The chemical fluids most commonly injected are polymers, surfactants and micellar solutions.
One-dimensional displacement of oil by an aqueous solution containing several chemicals species considering adsorption is described by an (n+1)´(n+1) hyperbolic system of conservation laws, where n is the number of components in the displacing phase. Continuous polymer injection results in a Riemann problem for this hyperbolic system. The displacement of oil by a polymer slug with water drive is described by an initial and boundary value problem with piecewise constant initial data and results in wave interactions.
The Riemann problem for the displacement of oil by hot water is mathematically equivalent to one-component polymer flooding (n=1) for a convex sorption isotherm. Several Riemann solutions for the case n=2have already been found and a graphical procedure for the solution of this problem was developed.
The Riemann solution for n-component polymer flooding was found for the case where the i-th adsorbed concentration depends only on the concentration of thei-th component in the aqueous phase. Exact solutions for non-self-similar slug problems were also published.
The Riemann solution for the (n+1)´(n+1) system for two-phase n-component displacement was studied in several papers for any arbitrary shape of sorption isotherms. The particular case of one-phase n-component flow leads to an (n)´(n) hyperbolic system, which was used for solving the Riemann problem. The projection and lifting procedures developed allow the calculation of any Riemann solution for the two-phase system once the associated one-phase solution is known. The theory developed is based on the fact that the Riemann problem solutions depend on a single parameter,x/t. Thus, the theory cannot be extended to non-self-similar Cauchy/initial-boundary value problems.