Can Peclet Numbers Depend on Tracer Species? Going Beyond SW Test Insensitivity to Advection or Equilibrium-Exchange

Abstract

Readers familiar with the notion of a Peclet number (as used within the context of tracer transport modeling, and tracer test interpretation) must have felt somewhat shocked by this strange assertion: “The first experiments ... have been conducted to quantify the solid-liquid phase interface using tracers with different Peclet numbers and matrix diffusion coefficients”, to be read in a paper published (2012) by a well-known Journal. Moreover, the reference (2007) cited therein, pretended to be the origin for this assertion, was found to contain lots of disappointing, confusing, poorly formulated stuff, but not even the slightest hint as to how [tracers with] different Peclet numbers could be used to quantify something like fluid-rock interface areas. Since the Journal does not publish comments or discussions on already published papers, we would like to take advantage of the generous communication platform offered by the Stanford Geothermal Workshop, and re-examine some basic representations on how tracers with different transport-reaction properties, in conjunction with various tracer test designs (inter-well, single-well), can be used to determine specific parameters of either (I) the system or medium through which the tracers are transported, or (II) of those tracers themselves, or (III) of some transport-reaction processes whose relevance is not restricted to the tracer species used in that particular test, or of (IV) other substances or entities of which the tracers are supposed to act as representatives. For each of these categories, wonderful examples can be found in the great treasury of geothermal and tracer test studies conducted over decades by researchers with different interest focus (Bear, Becker, Brown, Carrera, Chrysikopoulos, Doughty, Grant, Gringarten, Haggerty, Horne, Kocabas, Kohl, Kolditz, Maloszewski, Murphy, Neretnieks, Palmer, Plummer, Pruess, Robinson, Rose, Rybach, Sanjuan, Schroth, Shapiro, Shook, Tomich, Tsang, Tsang, Zemel, Zuber, and many more). While revisiting some of those paradigms, we try to identify and understand some of the motives that might have nourished the incriminated phrase (“tracers with different Peclet numbers”), and finally reveal it to be less unreasonable than it appeared at first glance.