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

An exact Laplace transform solution to the problem of dispersion, adve ction, and adsorption of a tracer due to its injection in a steady, ho rizontal, radially convergent flow field in a densely fractured, porou s 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 diff usion and adsorption dominate movement of the tracer in the blocks. Di mensionless breakthrough curves are used to illustrate the influence o f various aquifer and tracer properties. In support of the model a det ailed analysis is performed of a published multitracer field test, con ducted in a layer of densely fractured chalk in Bethune, France. Of th e three tracers analyzed, two are nonsorptive but have widely differen t free water diffusion coefficients, and one is slightly sorptive. Ana lysis of measured breakthrough curves, matched by trial and error to t heoretical responses, reveals that by allowing for fracture skin on bl ock surfaces, one can obtain (1) pure-advection arrival times that are independent of the tracer used, (2) values of mass recovery consisten t with measured values, and (3) relative values of effective diffusion coefficients that are consistent with known free water diffusion coef ficients for the separate tracers. Reasonable estimates of longitudina l dispersivity and fracture porosity are also obtained.