Propagation of Tracers through Cores with Mass Transfer into an Immobile Fluid Phase
Authors: Mennella Aniello , Bryant Steven L. , Lockhart Thomas P. 
Published: December 2007

Abstract
The analysis of a tracer experiment requires care when one of the fluid phases within the porous medium is immobile but miscible with the tracer carrier fluid. High levels of dispersion (Pe &lt; 10) are commonly encountered in this situation. Applying the classical analytical expression for the tracer concentration in an infinite core is straightforward and convenient but introduces significant mass balance errors at low Peclet numbers. Theoretical effluent concentration histories from a finite core in the absence of interphase mass transfer span a well-defined and relatively limited area on a plot of concentration versus time. Comparison of experimental effluent histories with this family of curves provides a rapid test of whether mass transfer into the immobile phase is important. At high mass transfer rates the effluent history becomes insensitive to the volume fractions of the fluid phases. Thus it can be difficult to determine a unique set of fitting parameters. To avoid this difficulty, experiments should be conducted at high flow rates (low residence times) or with slowly diffusing tracers.

Introduction
Tracer tests are widely used in the laboratory and in the field to characterise the degree of dispersion associated with flow through a porous medium. Another important application is the determination of volume fractions of fluids occupying the pore space. This application depends upon tracer molecules transferring from the carrier phase into the fluid phase of interest. Examples include evaluating residual oil saturations; determining volumes of organic contaminants in soil or aquifers; estimating excluded pore volume for flow of polymer solutions; and quantifying the volume of "dead-end" pores. Another example arises in studies of water-shutoff treatments using polymer gels, where it is often of interest to determine the volume fraction of the pore space occupied by polymer gel, or the volume fraction open to flow.
Various methods have been developed to extract volume fractions or dispersion coefficients from tracer data. The simple analytical form of the tracer behaviour in an infinite core without mass transfer admits graphical methods and easy computations for determining dispersion. Analytical solutions for finite cores are also available, though their form is somewhat less convenient for graphical application. Increased computer power has overcome this disadvantage and more recently has opened the way to routine application of complicated mathematical models that do not admit analytical solutions. Indeed, the parameter-fitting process itself can now be readily automated. Moments of the effluent concentration history provide a means of determining volume fractions without reference to any particular mathematical description of the system.
When applied and analysed properly, tracer tests are simple, reliable and inexpensive methods for probing porous media. Indeed, for some field applications they represent the only method of assessing large soil or rock volumes. This paper focuses on the laboratory determination of the volume fractions of pore space occupied by various fluid phases, with particular reference to the case when one phase is a water-based polymer gel. Because the resistance of a gel-treated rock to water flow is a property of particular interest, tracer test are sometimes conducted flowing brine through a core containing gel. As the tracer is carried by the brine, it will inevitably diffuse into the gel at a rate that is not known a priori.
This paper continues with a summary of the physical problem to be treated and the assumptions made in the mathematical analysis. As our objective is apply well-known results to a less familiar problem, rather than to develop new analysis, the mathematical exposition is deliberately concise. A series of simple examples of the application of these equations follows.
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