Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Abstract

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 nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here 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-D 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 2D and 3D 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 influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas 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 resumed back to 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.

Stress field disruption allows gas-driven microdeformation in bentonite to be quantified

“…This includes: (i) the provision of internal state data that can be used to facilitate damage mechanics modelling, (ii) an initial understanding of the frequency-magnitude distribution of gas pathways, (iii) a metric quantifying the degree of fracture opening/closure during the gas pathway propagation and therefore self-sealing efficiency and (iv) insight into the spatial evolution of gas-driven stress field disruption under pressurised conditions. Frequency-magnitude data indicate the presence of a population of 100’s or 1000’s of gas pathways and is consistent with previous findings inferring chaotic behaviour in such systems 53 . In such cases, deterministic prediction may be less achievable.…”

Low hydrogen solubility in clay interlayers limits gas loss in hydrogen geological storage

“…H 2 uptake and transport across a clay-based engineered barrier system is an important process that needs to be considered for nuclear waste disposal. 15–17…”

“…H 2 uptake and transport across a claybased engineered barrier system is an important process that needs to be considered for nuclear waste disposal. [15][16][17] Signicant effort has been made to understand CO 2 intercalation into expansive clay interlayers. .…”