Issues and Options in the Delineation of Well Capture Zones under Uncertainty

The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT-MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach. An alternative for all types of media is the capture probability (CP) approach, which is based on the solution of the standard advection-dispersion equation in a backward mode, making use of the analogy between forward and backward transport processes. Within this context, we review the current controversy about the correct form of the conceptual model for transport, finding that the advection-diffusion model, which represents the diffusive interchange between streamtubes with differing velocities, is more physically realistic than the conventional advection-dispersion model. For mildly to moderately heterogeneous materials, stochastic theories and simulation experiments show that this process converges at the field scale to an effective advection-dispersion process that can be simulated with conventional transport models using appropriate macrodispersivity values. For highly heterogeneous materials, stochastic theories do not yet exist but there is no reason why the process should not converge naturally as well. Macrodispersivities appear to be formation-specific. The advection-dispersion model can be used for capture zone delineation in heterogeneous granular media. For fractured porous systems, hybrid equivalent porous medium and discrete fracture network or CP-based approaches may have potential. In general, capture zones delineated by PT without MC will always be too small and should not be used as a basis for land-use decisions.