Mass Transfer Between Phases in a Porous Medium: A Study of Equilibrium
Authors: Raimondi P. , Torcaso M.A. 
Published: December 2007

Abstract
To study mass transport in systems simulating oil recovery processes, different porous media were saturated with a mobile (carrier phase) and a stationary phase. Slugs of carrier phase containing a small amount of solute were displaced with pure carrier phase. By analogy to the chromatographic processes, the velocity of the solute can be predicted from a knowledge of the partition coefficient and the saturation provided that equilibrium between the two phases exists. Equilibrium was found to exist for different porous media, solutes and rates. The conditions were varied over the range normally encountered in the laboratory and in the field. The longitudinal dispersion of a solute undergoing interphase mass transfer was also investigated.
Introduction
The production of hydrocarbons by gas cycling, enriched gas drive and CO2 or alcohol displacement involves, among other factors, relative motion between two phases and compounds, hereafter called solute, which are soluble in both phases. The solute is carried forward by the faster flowing phase at a lower velocity than the average velocity of that phase. Retardation of the solute is caused by chromatographic absorption and desorption in the slower flowing phase and by the degree of departure from equilibrium. At equilibrium the concentration of solute in the two phases can be related by the equation*
(1)
where Csw and Cso are the concentration of solute in the aqueous and oleic phases respectively and K is the equilibrium ratio, or partition coefficient.
Displacement theories must contain an explicit assumption with regard to equilibrium, i.e., whether the compositions can be related by Eq. 1. The existance of equilibrium depends, in general on the relative velocity between the phases. Unfortunately, other factors such as gravity segregation and viscous fingering, also depend on velocity. For this reason, whenever effects of rate on displacement were observed, it was practically impossible to discern what caused them - lack of equilibrium or the factors mentioned above.
Equilibrium between phases has been the subject of extensive studies in fields such as extraction or chromatography. It has received only small attention in flow through the type of porous media encountered in oil production. For this reason a method was developed which makes it possible to study the movement of a solute as it is affected by rate, type of porous media, partition coefficient and carrier phase, but in the absence of segregation or fingering. The information obtained enables one to determine when the assumption of equilibrium can be made.
Briefly, the method consists of (1) saturating the core with a mobile and an immobile phase, (2) injecting a slug made up of the same fluid as the mobile phase and a small concentration of mutually soluble solute, (3) measuring the lag and the peak height of the slug at arrival and (4) correlating these variables with fluid properties such as partition coefficient and mixing constants of the medium.
PROPOSED MECHANISM
The principles of chromatography are combined with the equation of longitudinal mixing to predict the velocity of a solute slug compared to the bulk velocity and the peak height of a slug. The equation so obtained is valid under equilibrium conditions only. Therefore, a comparison between experimental and predicted results will give a measure of departure from equilibrium. This work was done with either the oleic or the aqueous phase being immobile. For simplicity, the following development is based on the case where the oleic phase is immobile. However, the treatment is the same in either case.
SPEC
P. 51ˆ