Gaining insights into reactive fluid-fractured rock systems using the temporal moments of a tracer breakthrough curve

In this paper, we show that the tracer breakthrough curves (BTCs), when the tracer chemically interacts with the solid matrix of a fractured rock, are considerably different than when it does not. Of particular interest, is the presence of a long pseudo steady state zone in the BTCs, where the tracer concentration is more or less constant over a long period of time. However, such a zone of constant concentration is not visible when either the tracer does not interact with the solid, or does so at an extremely fast rate. We show that these characteristics of the BTCs could be correlated to the parameters of the system. We develop expressions for the mean residence time and its variance for a chemically active and inactive tracer. We show that chemical interaction between the tracer and the solid increases the mean residence time and the increase depends on the distribution coefficient. We also show that the variance of residence time for a chemically active tracer is much larger than that for an inactive tracer, and it depends on both the distribution coefficient and the rate of chemical reaction. We verify these calculations against synthetic tracer BTCs, where the temporal moments are calculated by numerically integrating the tracer evolution curves. Even though we developed the mathematical expressions assuming an idealized fracture-matrix system, we believe that the mathematical expressions developed in this paper can be useful in gaining insights into reactive transport in a real fractured rock system.