CONVERGENT RADIAL DISPERSION IN A DOUBLE-POROSITY AQUIFER WITH FRACTURE SKIN - ANALYTICAL SOLUTION AND APPLICATION TO A FIELD EXPERIMENT IN FRACTURED CHALK

An exact Laplace transform solution to the problem of dispersion, advection, and adsorption of a tracer due to its injection in a steady, horizontal, radially convergent flow field in a densely fractured, porous formation (double-porosity aquifer) is presented. The porous blocks were assumed to be covered with a layer of material (fracture skin) of negligible volume and storage capacity that provides a resistance to diffusion in the rock matrix. Longitudinal dispersion, advection, and adsorption dominate transport of the tracer in the fractures, and diffusion and adsorption dominate movement of the tracer in the blocks. Dimensionless breakthrough curves are used to illustrate the influence of various aquifer and tracer properties. In support of the model a detailed analysis is performed of a published multitracer field test, conducted in a layer of densely fractured chalk in Bethune, France. Of the three tracers analyzed, two are nonsorptive but have widely different free water diffusion coefficients, and one is slightly sorptive. Analysis of measured breakthrough curves, matched by trial and error to theoretical responses, reveals that by allowing for fracture skin on block surfaces, one can obtain (1) pure-advection arrival times that are independent of the tracer used, (2) values of mass recovery consistent with measured values, and (3) relative values of effective diffusion coefficients that are consistent with known free water diffusion coefficients for the separate tracers. Reasonable estimates of longitudinal dispersivity and fracture porosity are also obtained.