An approximate semianalytical solution for tracer injection tests in a confined aquifer with a radially converging flow field and finite volume of tracer and chase fluid

Abstract

An approximate analytical solution describing the movement of a conservative tracer of finite volume in a radially converging flow field is proposed. The solution is divided into two phases: injection and transport. During the injection phase, an injection of chase fluid immediately following the tracer is allowed. Hydrodynamic dispersion effects are assumed to be negligible during this phase. The geometry of the tracer plume is determined by a particle‐tracking technique. During the plume transport phase, the tracer plume is approximated by a series of contiguous pulses. An approximate analytical solution for each pulse has been derived through linearization of the transport equation. The approximate solution has been verified by comparison with numerical solutions. The distribution of tracer in space and time is obtained by summing the contributions from all the pulses. Four geometrical parameters governing the geometry of the tracer plume immediately after injection are presented and discussed. The solution shows that the geometry of the initial tracer plume has an effect on the breakthrough curves. The volume of tracer and chase fluid has to be taken into account in tracer test design and data analysis. Limitations of the proposed solution are also discussed.

Interpretations of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant Site

“…In general, this assumption remains valid if (1) the ratio of the volume of fluid injected to the volume of fluid contained within a single pore volume within the area defined by the two wells is small and (2) the ratio of fluid velocity caused by injection to fluid velocity due to pumping is large at the location of the injection well. These two constraints can be expressed, respectively, as (after Guvanasen and Guvanasen, 1987):…”

“…If these assumptions are violated, the plume of the injected fluid will not form a perfect ring, but will be oblong. These two constraints are expressed in the following equations, respectively (after Guvanasen and Guvanasen, 1987 . These equations are used to verify that the assumptions of the conceptual model regarding tracer and chaser injection into the aquifer in the presence of a convergent-flow field are valid.…”

A Laplace transform power series solution for solute transport in a convergent flow field with scale‐dependent dispersion

“…To date, no analytical solutions of any special functions are available for scale‐dependent dispersion equations in cylindrical coordinates; therefore the solution obtained must be compared with a numerical solution. This method of verification was used by Gelhar and Collins [1971] and Guvanasen and Guvanasen [1987]. The Laplace transform finite difference (LTFD) technique was employed to generate numerical solution in this study.…”

Influence of injection conditions on field tracer experiments

“…Guvanasen and Guvanasen (1987) studied the influence of an injection performed with a finite volume of tracer followed by an intense water flush. They represent the tracer injection as a radially diverging piston flow (no dispersion) around the injection well, without considering wellbore mixing.…”