Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by processes of nonlinear dynamics, liquid-gas exchange, dilation, fracturing, etc., which cannot be described by classical models of fluid dynamics. The objective of this paper is to show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80 bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2-D and 3-D pseudo-phase space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas inflow in the bentonite core, before the breakthrough, the development of dilatant pathways is characterized by the process of chaotic diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is characterized by a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model, can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

Uncertainty is typically defined as a potential deficiency in the modeling of a physical process, owing to a lack of knowledge. Uncertainty can be categorized as aleatoric (inherent uncertainty caused by the intrinsic randomness of the system) or epistemic (uncertainty caused by using various model simplifications and their parameters). One of the main reasons for model simplifications is a limited amount of meteorological data. This paper is devoted to the epistemic uncertainty quantification involved in two components of the hydrologic balance-evapotranspiration and net infiltration for interglacial (present day), and future monsoon, glacial transition, and glacial climates at Yucca Mountain, using the data from analogue meteorological stations. In particular, the author analyzes semi-empirical models used for evaluating (1) reference-surface potential evapotranspiration, including temperature-based models (Hargreaves-Samani, Thornthwaite, Hamon, Jensen-Haise, and Turc) and radiation-based models (Priestly-Taylor and Penman), and (2) surface-dependent potential evapotranspiration (Penman-Monteith and Shuttleworth-Wallace models). Evapotranspiration predictions are then used as inputs for the evaluation of net infiltration using the semi-empirical models of Budyko, Fu, Milly, Turc-Pike, and Zhang. Results show that net infiltration ranges are expected to generally increase from the present-day climate to monsoon climate, to glacial transition climate, and then to the glacial climate. The propagation of uncertainties through model predictions for different climates is characterized using statistical measures. Predicted evapotranspiration ranges are reasonably corroborated against the data from Class A pan evaporometers (taking into account evaporation-pan adjustment coefficients), and ranges of net infiltration predictions are corroborated against the geochemical and temperature-based estimates of groundwater recharge and percolation rates through the unsaturated zone obtained at Yucca Mountain.