Nonlinear Dynamic Processes as a Source of Uncertainty for Flow Simulations through Partially Saturated Fractured-Porous Media

The concept of nonlinear dynamics and chaos can be used to provide an alternative explanation for the irreducible uncertainty of seemingly erratic temporal and spatial oscillations of variables characterizing unsaturated flow and transport within fractured-porous media. The goals of this presentation are to discuss the physical processes and to quantify the uncertainty of flow characteristics caused by deterministic-chaotic, nonlinear dynamic processes. The presentation will be based on the results of a series of several infiltration tests, including the time-domain and phase-space interpretation of infiltration and outflow rates, capillary pressure, and dripping-water frequency. It will be shown that the apparent "randomness" of the flow field is caused by the interplay of intrafracture film flow and water dripping, coalescence, divergence, and mixing of multiple flow paths along fracture surfaces. These processes result in chaotic advection, diffusion, mixing, and feedback phenomena. Because direct measurements of variables characterizing a variety of flow and transport processes under field conditions are not technically feasible, only the cumulative effect of these processes can be characterized. The lack of specific measurements leads to a limited knowledge about initial conditions needed for solving deterministic differential or difference-differential equations. This limitation, in turn, leads to the uncertainty in predictions of flow processes. Moreover, it would be difficult, if not impossible, to distinguish between the two components of the total uncertainty--epistemic and aleatoric uncertainties. Quantification of the uncertainty of nonlinear dynamic oscillations caused by both deterministic and random components of time- series data is performed using the cluster analysis, moments analysis and the concept of information entropy. This work was supported by the U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231.