Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model

Abstract

Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution-versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

“…As mentioned by Delay et al [32], Lagrangian schemes (particle tracking methods) are more accurate and less computationally intensive than Eulerian schemes. The main Lagrangian schemes include random-walk particle tracking (RWPT) method [33,34], convolution-based particle tracking (CBPT) method [35,36], and continuous-time random-walk (CTRW) method [37,38]. For very heterogeneous media such as fractured rock mass, flow velocities may span several orders of magnitude.…”

Mechanisms of anomalous dispersion in flow through heterogeneous porous media

“…The observation plain is the right boundary of the domain at x = 512. The first passage times are determined according to (4) through an average over the 10 5 particles in single realizations and between 10 3 realization for each random field under consideration.…”

“…Anomalous dispersion has been widely observed in transport through heterogeneous porous media [1][2][3][4][5]. It manifests itself in heavy tails in solute arrival time distributions, or breakthrough and the non-linear evolution of the second centered moments of solute distributions.…”

“…Anomalous dispersion can be caused by different physical processes, chemical heterogeneity [6,7], the interplay of physical heterogeneity and diffusion [8,9], and physical heterogeneity alone. Here, we concentrate on the impact of physical heterogeneity in the distribution of hydraulic conductivity [4,5,10,11]. In highly heterogeneous fields fast flow concentrates along highly permeable preferential paths consisting of connected structures of large hydraulic conductivity [12][13][14].…”

Migração de solutos em basalto fraturado: quantificação experimental em laboratório e validação matemática

“…A hipótese de que a fratura pode ser considerada um canal de placas planas paralelas, separadas por uma abertura constante (Snow, 1965) Keller et al, 1995;Ishibashi et al, 2015) e de campo (Novakowski et al, 1995;Kang et al, 2015) indicaram que essa descrição da fratura muitas vezes não é adequada para a caracterização do transporte de poluentes. A falha do modelo de placas planas paralelas em explicar muitos resultados está amplamente documentada por Neuman (1987 ≤0,20).…”