Cation Exchange in Chemical Flooding: Part 1--Basic Theory Without Dispersion
Authors: Pope G.A. , Lake L.W. , Helfferich F.G. 
Published: December 2007

Abstract
The interfacial activity and mobility control of a chemical flooding process are affected by the concentrations of the cationic and anionic species that travel with the surfactant and polymer. In this paper we use equations from the literature to paper we use equations from the literature to describe the environmental composition changes resulting from cation exchange that occurs as a chemical flood traverses a reservoir.
This paper presents examples of two or three exchanging cations (calcium, sodium, and magnesium) with and without mobilized oil present and with up to four fluids in a typical chemical flooding sequence (connate water, preflood, slug, and polymer drive). The results indicate how cation polymer drive). The results indicate how cation exchange and adsorption may be incorporated into a chemical flood design.
The general theory from which the results are developed is based on the concept of "coherence." This theory allows any number of exchanging cations to be present and allows adsorption of surfactant, polymer, or other species and their interaction with cation exchange to be included.

Introduction
A key requirement for a successful chemical flood is to provide an adequate ionic environment for the surfactant, to ensure that the desired interfacial activity, phase behavior, and mobility control are maintained. Aside from the inplace and injected ionic compositions and mixing through dispersion, crossflow, etc., this environment may be affected deeply by cation exchange with clays, solubility of minerals, and adsorption on rock. The importance of cation exchange effects in chemical flooding recently has been stressed and need not be reiterated here.
We describe a fundamental theoretical analysis of cation exchange and adsorption phenomena in reservoir flooding. The treatment is applicable to multicomponent systems with any kind of equilibrium relations, specifically including interactions between components, but presumes idealized behavior with respect to fluid dynamics, absence of dispersion, immiscibility of aqueous and oleic phases, and conservation of local equilibrium. The treatment is an adaptation of multicomponent chromatographic theory to practical problems of chemical and related floods.
The bask problem is that the components involved in a chemical flood--water, cations, surfactant, polymer, and oil--are coupled with respect to their transport properties, and only a theory of coupled, multicomponent systems can adequately describe their dynamic behavior. At first glance, one may be inclined to assume that a mixture injected as a slug might traverse the reservoir as such, changing its composition a little by mixing with fluids ahead and behind or by loss to, or gain from, the rock over which it travels, but otherwise conserving its integrity. Multicomponent theory shows this idea is too naive. Rather, an injection sets off a set of "waves" (composition variations) that advance at different speeds and between which new compositions arise that bear little resemblance to the injected and previously present compositions, or any that could be formed from these by mixing. Moreover, the wave patterns generated by successive injections of different fluids may overlap and interfere and, thereby, modify injected compositions. Injected components thus generate their own environment through dynamic interactions. To be sure, it is not impossible, in principle, to operate under conditions ensuring that an injected active surfactant slug retains its favorable environment and thus its activity through most or all of the reservoir, but this often may prove impracticable. The task then is to design the flood so that a favorable environment is generated in-situ. This paper tries to present a theoretical basis that will paper tries to present a theoretical basis that will facilitate such design.
SPEJ
P. 418