LAGRANGIAN SIMULATION OF HEAVY-TAILED NONLOCAL TRANSPORT IN LAB- AND FIELD-SCALE TESTS: IS THERE SUCH A THING AS A LOCAL SCALE?

It has long been hoped that predictions of the movement of pollutants dissolved in groundwater could, in theory, be made with any level of accuracy. The only impediment to a perfect, deterministic prediction was gathering enough data about the aquifer and the pollutant. For a conservative solute, the transport problem is reduced to identifying the hydraulic conductivity (K) and porosity at enough points. This view assumes that 1) either the aquifer as a whole or its statistical properties can be adequately described by “enough” points, and that 2) the physics of transport are well known on some smallest scale (say, the hand-specimen or lab column sample). The first assumption is often violated by the presence of either long-range dependence, nonstationary aquifer properties, or heavy-tailed data. The second assumption requires that the local advection-dispersion equation (ADE) is a valid model of the concentration at the small scale. Recent re-examinations of laboratory experiments indicate that this may not be valid even in relatively homogeneous material at very small scales. The core and lab-scale data indicate that the governing equation is non-local in space and/or time. This simple observation changes the way that solute transport must be simulated or predicted. A random K field, no matter how well characterized or finely discretized, cannot capture the nonlocality. Nor can a nonlocal model of ensemble transport (CTRW, fractional-order ADEs, etc.) be applied without local conditioning. We provide the link between the two approaches by defining a nonlocal transport model that allows conditioning of by measured data at any and all points. We also develop a novel fractal model of random fields that allows different scaling in different directions and completely user-defined correlation structures (including none) in any direction. The two approaches may be combined to discern the interplay between nonlocality and discretization.