Characterizing flow and transport in fractured geological media: A review

Several mechanisms can extend the equilibrium domain of a liquid phase into the solid region of the normal phase diagram. The causes of premelting, which include surface melting, interface curvature and substrate disorder, occur in all types of substances, including H2O. In the case of H2O, premelting can have important environmental consequences, among which are the heaving of frozen ground, breakdown of rock and concrete, sintering of snow, flow of glaciers, scavenging of atmospheric trace gases by snow and ice, and the electrification of thunderclouds. The article reviews the basic mechanisms of premelting and discusses their roles in the environmental phenomena. The principal results of numerous studies are reviewed, and trends in current research are outlined.

http://iopscience.iop.org/article/10.1088/0034-4885/58/1/003/pdf

The premelting of ice and its environmental consequences

We investigate the validity of applying the “local cubic law” (LCL) to flow in a fracture bounded by impermeable rock surfaces. A two-dimensional order-of-magnitude analysis of the Navier-Stokes equations yields three conditions for the applicability of LCL flow, as a leading-order approximation in a local fracture segment with parallel or nonparallel walls. These conditions demonstrate that the “cubic law” aperture should not be measured on a point-by-point basis but rather as an average over a certain length. Extending to the third dimension, in addition to defining apertures over segment lengths, we find that the geometry of the contact regions influences flow paths more significantly than might be expected from consideration of only the nominal area fraction of these contacts. Moreover, this latter effect is enhanced by the presence of non-LCL regions around these contacts. While contact ratios of 0.1–0.2 are usually assumed to have a negligible effect, our calculations suggest that contact ratios as low as 0.03–0.05 can be significant. Analysis of computer-generated fractures with self-affine walls demonstrates a nonlinear increase in contact area and a faster-than-cubic decrease in the overall hydraulic conductivity, with decreasing fracture aperture; these results are in accordance with existing experimental data on flow in fractures. Finally, our analysis of fractures with self-affine walls indicates that the aperture distribution is not lognormal or gamma as is frequently assumed but rather truncated-normal initially and increasingly skewed with fracture closure.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98WR02285

Flow in rock fractures : the local cubic law assumption reexamined

The morphology of fractured rock surfaces is studied in terms of their scaling invariance. Fresh brittle fractures of granite and gneiss were sampled with a mechanical laboratory profilometer, and (1 + 1)-dimensional parallel profiles were added to build actual maps of the surfaces. A first step in the scaling invariance description is a self-affine analysis using three independent methods. The root-mean-square and the maximum-minimum difference of the height are shown to follow a power law with the sample length. The return probability and the Fourier spectrum are also computed. All these approaches converge to a unique self-affine exponent: ζ = 0.80. Analysis over a broad statistical set provides a reproducibility error of ±0.05. No significant differences between the isotropic granite and the markedly anisotropic gneiss appear for the scaling exponents. An analysis of the profilometer shows that the two main drawbacks of the setup are not significant in these analyses. The systematic errors of the scaling analysis are estimated for the different methods. Isotropy of the scaling invariance within the mean fracture plane is shown either with the result obtained from different fracture orientations or with the two-dimensional Fourier spectrum of the surface topography itself. The analysis is brought further into the multifractal framework. The structure functions are shown to have power law behavior, and their scaling exponent varies nonlinearly with the moment order. Finally, the corresponding conserved process belongs to a universal multifractal class with α = 1.5 for the Levy index and C1 = 0.3 for the fractal codimension of the mean singularities. The three indices (ζ, α and C1) completely characterize the scale invariance. The multifractal behavior is significant for physical properties which depend on high-order moments like contact. According to this study and that of other groups, the self-affine exponent ζ is constant over a large range of scales and for different fracture modes and various materials. This opens the possibility that there exists a form of universality in the cracking process. It appears that only the prefactor of the roughness is dependent on material and mode.

Scaling invariance of crack surfaces

We recorded the height of a granitic fault surface as a function of position along one-dimensional profiles. We show that the profiles exhibit an "anisotropic" scaling invariance: self-affinity. The difference between the maximum and the minimum height, and the standard deviation of the height, over a length L are propor- tional to L½, where (  0.84. Other properties such as the Return Probability distribution or the Power Spectrum of the profile com- fort this result. This self-affne property is in good agreement with recent works on artificial fractured surfaces. Previous studies at field scale are consistent with this concept.

https://eost.unistra.fr/fileadmin/upload/EOST/Jean_Schmittbuhl/Publications/Articles/1993_GRL_Schmittbuhl_etal.pdf

Field measurements of the roughness of fault surfaces

The topography of natural fracture surfaces has a strong influence on the flow and transport properties of fractures. In this paper we investigate the role of anisotropic surface roughness on fluid flow, solute transport, and electrical current flow in fractures. Our results show that the directional characteristics of the surfaces are more important in determining fracture transport properties than is the degree of roughness. Roughness oriented parallel to the primary flow direction substantially enhances fluid and solute transport rates through fractures, with the effect becoming more apparent as the amount of contact area between the surface increases. Roughness oriented transverse to the flow direction inhibits flow rates and delays the movement of solute through the fracture.

The effect of anisotropic surface roughness on flow and transport in fractures

Parallel plate models are inadequate to describe the hydraulic and transport properties of natural fractures with rough surfaces. A two-dimensional numerical simulation of flow and solute migration in a fracture with fractal surfaces is presented. The macroscopic transport properties of the fractures are derived by comparison of the numerical simulations to predictions of a one-dimensional advection dispersion model. This makes it possible to determine effective dispersivities and solute velocities for the mathematically generated surfaces. The effects of adsorption, travel distance and channeling phenomena on the transport properties are examined. The modeling indicates that the effective velocity of the solute differs from that of the average fluid particle due to transverse and longitudinal dispersion and diffusion. These conclusions agree with field measurements of flow and transport in fractures.

Mollie E. Thompson

Papers

The effect of anisotropic surface roughness on flow and transport in fractures

Numerical simulation of solute transport in rough fractures