Boundary Conditions for Convergent Radial Tracer Tests and Effect of Well Bore Mixing Volume

Convergent radial flow tracer tests have a complex spatial nonaxial transport structure caused by the flow in the vicinity of the injection well and its finite mixing volume. The formulation of the boundary value problem, and especially the treatment of the boundary conditions at the injection well, is nontrivial. Hodgkinson and Lever [1983], Moench [1989, 1991], and Welty and Gelhar [1994] have developed different models and methods for the analysis of breakthrough curves in the extraction well. To extend interpretation techniques to breakthrough curves in the zone between injection and extraction wells, an analysis of conventional transport models is given, and improved boundary conditions are formulated for a convergent radial tracer test problem. The formulation of the boundary conditions is based upon a more detailed analysis of the kinematic flow structure and tracer mass balance in the neighborhood of the injection well. Two practical applications of revised boundary conditions for field data analysis are given. First, the note explains anomalous high well bore mixing volumes of injection wells found by Cady et al. [1993] and allows one to establish the role of mixing versus other processes (retardation, matrix diffusion, etc.). Second, it is shown that the improper use of Moench's [1989] model can produce bias in the characteristics of breakthrough curves in the extraction well under conditions that involve a significant mixing factor in the injection well. A numerical example indicates an error in peak concentrations on a breakthrough curve by as much as 70% and in peak arrival time by 10% for Peclet numbers Pe = 10 2. The effect becomes slightly less significant for Pe = 1.