Asymptotic solutions for solute transport: A formalism for tracer tomography

An asymptotic approach to the solution of the transport equation, in the limit of rapid spatial and temporal variation, produces an extremely efficient formalism for the inversion of tracer data. The technique provides tracer concentration sensitivities to porosity, permeability, and pressure gradient variations in just a single simulation run. The calculated sensitivities compare well with those derived using a numerical perturbation method, at a fraction of the computational requirements. An application to a conservative tracer test at Hill Air Force Base in Utah indicates the efficiency and utility of the approach for characterizing three-dimensional variations in flow properties. On the basis of tracer concentration histories at 12 multilevel samplers and three extraction wells, some 44 tracer curves in all, significant small-scale variability in permeability is inferred. In general, the permeability is found to decrease as the lower boundary of the aquifer is approached. The permeability trends we find are consistent with tracer swept volume calculations based upon a moment analysis.