A Study of the Effect of Fracture Walls on Tracer Transport

Abstract

Summary Subsurface permeable systems are heterogeneous at multiple scales and are often fractured. Flow and transport in the subsurface formations are impacted by the presence of fractures, both natural and induced. The effects of permeability heterogeneity and fractures on tracer tests are not well-understood. Echo-tracer (i.e., single-well-injection withdrawal) and transmission-tracer (i.e., dipole) tests can provide information on the flow and transport-system heterogeneity in layered formations. The reversal of flow paths in the echo tests tends to cancel out the non-Gaussian, high-permeability flow behavior in the tracer histories, as observed in laboratory experiments. A question arises whether similar Echo-tracer behavior may be observed in tracer responses for an extreme case of heterogeneity, such as a multiporosity fractured permeable system. A fractured rock consists of high-permeability contrast with high fracture permeability and low matrix permeability, often differing by orders of magnitude. The tracer response from an echo test as well as a transmission test in fractured systems, with high level of heterogeneity, is known to be controlled by the extent of molecular diffusion into the matrix. Dispersion may be dominant in the fracture volume, whereas the molecular diffusion is expected to occur across the fracture/wall interface. We discuss the 1D propagator of diffusion, with convection, and its behavior in the presence of a reflecting and absorbing fracture wall. A wave model is presented to understand the tracer transport in a fracture with differential-diffusion properties. The model predicts that diffusion and adsorption of tracer can produce a retardation of the tracer propagation in the fracture in a transmission-tracer test. The retardation leads to a difference in the arrival times of the tracer, which can then be used to calculate the length of a fracture. The model prediction is compared with published transmission-tracer test experimental data in a fractured till rock. Comparison of the model prediction of tracer-front-arrival times shows good agreement. The arrival time depends on the diffusion coefficient, average time of exposure of the solution to the fractured system, the length of the fracture, and the fracture spacing. Prediction of the echo-tracer test shows that for a fractured system, the retardation of the tracer produces a delayed arrival of the diffusing tracer as opposed to the nondiffusing tracer. The study adapts existing techniques for simple-wave description of tracer transport to a fractured system with absorbing walls. The model for prediction of front movement in the fractured system is novel.