Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

Abstract

[1] The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short-and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.

Dynamic effects on capillary pressure–Saturation relationships for two‐phase porous flow: Implications of temperature

“…In such systems, capillary pressure plays a crucial role in determining the motion of fluids within the porous media. [1][2][3][4][5][6][7][8] In addition, temperature variation may affect such flows where the hydraulic properties of the porous media such as hydraulic conductivity and water retention are temperature dependent. [9][10][11][12] Conventional approaches for modeling of immiscible two-phase flow in porous media involve the use of an extended version of Darcy's law 3,13,14 for multiphase flows in conjunction with the use of constitutive relationships between capillary pressure, saturation, and relative permeability (P c -S-K r ) based on quasi-static conditions.…”

Ensemble phase averaged equations for multiphase flows in porous media. Part 1: The bundle-of-tubes model

“…In these systems, capillary action plays a crucial role in driving the motion of fluids within the porous media (Washburn, 1921;Richards, 1931;Scheidegger, 1974;Ianson and Hoff, 1986;Hall et al, 1984;Gray and Hassanizadeh, 1991;Liu, 1991;Hassanizadeh and Gray, 1993;Alava et al, 2004;Faybishenko, 2004). Extensive theoretical investigations and advanced experimental techniques, such as neutron radiography, have been applied to study the motion of the fluids (Gummerson et al, 1979;Hassanizadeh and Gray, 1993;Moseley and Dhir, 1996;Beliaev and Hassanizadeh, 2001;Gray et al, 2002;Lockington and Parlange, 2003;Tsakiroglou et al, 2003;Culligan et al, 2004;Shiozawa and Fujimaki, 2004;El Abd et al, 2005;Manthey et al, 2005;Le Guen and Kovscek, 2006;Hilfer, 2006;Czachor, 2007;Hall, 2007).…”

Dimensionality of heavy metal distribution in waste disposal sites using nonlinear dynamics

“…A number of recent studies [25][26][27][28] examine the application of nonlinear deterministic dynamics that improves the accuracy of geostatistics by taking into account the synergistic action of factors such as disposal of different types of wastes in the same area, varying soil horizons, groundwater flow and transport phenomena.…”