Elements of Fractal Generalization of Dual‐Porosity Model for Solute Transport in Unsaturated Fractured Rocks

Abstract

In this study, new elements were developed to generalize the dual-porosity model for moisture infiltration on and solute transport in unsaturated rocks, taking into account fractal aspects of the percolation process. Random advection was considered as a basic mechanism of solute transport in self-similar fracture systems. In addition to spatial variations in the infiltration velocity field, temporal fluctuations were also taken into account. The rock matrix, a low-permeability component of the heterogeneous geologic medium, acts as a trap for solute particles and moisture. Scaling relations were derived for the moisture infiltration flux, the velocity correlation length, the average velocity of infiltration, and the velocity correlation function. The effect of temporal variations in precipitation intensity on the infiltration processes was analyzed. It showed that the mode of solute transport is determined by the power exponent in the advection velocity correlation function and the dimensionality of the trapping system, both of which may change with time.

Fractal Characterization of Multiscale Fracture Network Distribution in Dolomites: Outcrop Analogue of Subsurface Reservoirs

“…Many researchers have investigated the fractal behaviors of different natural phenomena but also from fractures from outcrop observations and experiments [8,12,14,21,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. In fault/fracture characterization, fractal geometry is used to describe fault/fracture patterns [11,13,21,43,57,[63][64][65][66][67][68][69][70][71][72][73][74], fluid flow through fracture or double porosity media [12,52,56,56,[75][76][77][78] and discrete fracture networks (DFNs)…”

Geometric and Fractal Characterization of Pore Systems in the Upper Triassic Dolomites Based on Image Processing Techniques (Example from Žumberak Mts, NW Croatia)

“…Knowledge of pore size distribution is critical for understanding both the mechanisms and storage [18]. The fractured rocks, aquifers, or reservoirs consist of two overlapping subsystems: one represents fractures, and the other represents the porous matrix [21][22][23]. The general flow through the rock is established by a more permeable system (fractures), while a less permeable system (matrix blocks), which have a large storage capacity, feeds fluid into the fractures [23,24].…”

Nonclassical Transport Processes in Geologic Media: Review of Field and Laboratory Observations and Basic Physical Concepts

“…This review was the first step in developing mathematical modeling approaches for flow and transport processes in variably saturated heterogeneous and fractured media (Dykhne et al, 2008; Bolshov et al, 2008; Goloviznin et al, 2008). Our aim was to review field and laboratory observations that illustrate the fundamental mechanisms of flow and transport, and to provide an introduction to our development of the main physical and mathematical concepts that, in our view, provide a basis for describing transport processes in geologic media.…”

“…The references cited reflect our interest and experience. Our goal was to provide an experimental background for the physical and mathematical approaches developed here and in Dykhne et al (2008), Bolshov et al (2008), and Goloviznin et al (2008) For a more detailed discussion of recent approaches to modeling transport in highly heterogeneous media, we refer to Sahimi (1995), National Research Council (1996, 2001), and Faybishenko et al (2000b)…”