Session IV- Fracture Flow

Fluid Transport in Rough Fractures

Shemin Ge, Miles Waite, and Hartmut Spetzler [Department of Geological Sciences, University of Colorado]

Study of fluid and chemical transport processes in the upper part of the earth's crust greatly depends on our understanding on the hydrologic parameters such as hydraulic permeability. Fractures ranging from microcracks to large-scale faults are common features in rock formations. The objective of this research is to investigate the dependency of fracture permeability on fracture geometry. The research consists of three intertwined components: 1) analytical study, 2) laboratory experiment, and 3) numerical modeling. The analytical study provides theoretical guidance for understanding fracture permeability. The laboratory experiments provide first-hand data on flow characteristics in fractures and for model verification. The numerical modeling, verified by the analytical study and the laboratory experiments, serves as a predictive tool for situations that are beyond the capability of analytical tools and laboratory experiments.

We have conducted a theoretical study on the characteristics of flow in a rough fracture, which resulted in generalized definitions of fracture aperture and tortuosisty. A new governing equation for incompressible laminar flow in rough fractures was derived, incorporating two vectorial variables of fracture geometry: true aperture and tortuosity. The new equation is more general than the well-known Reynolds equation and can be reduced to the latter when the variations in tortuosity and aperture are small. Explicit analytical solutions of fracture permeability were derived for two non- smooth fractures using this new governing equation. The results show that the error in permeability estimation by using the Reynolds equation can be significant. In a sinusoidal surface fracture, the new equation shows a significant improvement over the solution of the Reynolds equation in both fracture permeability and pressure calculations. This theoretical work not only advanced the fracture permeability calculation, but also laid the foundation for further numerical and experimental studies.

Parallel to the theoretical work, we also conducted laboratory experiments and numerical simulations. We designed and built a simple apparatus for measuring fracture permeabilities of controlled geometries. Experiments using smooth and parallel glass fractures were conducted first to calibrate the apparatus. After good agreement between the experimental results and the theoretical values of fracture permeability was achieved on the parallel glass model, we extended the experiments to a sinusoidal surface fracture between two blocks made of aluminum. The numerical modeling involved developing a lattice gas automata (LGA) model, an emerging numerical method in studying fluid flow dynamics. The lab experiments and LGA modeling have produced important and interesting results. We conducted a comparative analysis on the predicted permeability using the conventional parallel plate model, improved theoretical model, experimental data, and LGA simulation. Such analysis led to a new averaged normal aperture scheme which yields the best estimation of permeability for a variety of fracture geometries.

Fast Flow in Unsaturated Rock Fractures

Tetsu K. Tokunaga and Jiamin Wan [Lawrence Berkeley National Laboratory]

Although fractures in rock are well-recognized as pathways for fast flow, the mechanistic basis for unsaturated fast flow remains incompletely understood. Most conceptual models for fast flow require high saturations in fractures, despite the fact that this condition is not often observed in the vadose zone. Flow fingering and transient fracture flow during episodic infiltration events are recognized as gravity-driven fast flow mechanisms which occur along locally essentially saturated pathways. However, the possibility that fast flow could occur along unsaturated fracture (macropore) pathways has received much less consideration. The goal of this study is to develop and experimentally test conceptual models for fast flow in unsaturated rock fractures. Two previously unrecognized mechanisms which permit fast flow in unsaturated fractures are film flow and surface zone flow. This paper provides further results concerning film flow, and introduces the importance of surface zone fast flow along unsaturated fractures of low permeability rock.

A conceptual model for film flow in unsaturated fractures was recently presented, along with laboratory experiments illustrative of its general characteristics (Water Resour. Res. 33, 1287-1295, 1997). In this model, water film thickness can build up along fracture surfaces when matric potentials are high enough to sustain effectively saturated conditions in the underlying matrix. As matric potentials increase (approach zero) within this range, water films expand along fracture surfaces by first filling finer scale roughness features, and progressively filling coarser roughness features. The hydraulic properties necessary for characterizing steady-state film flow in unsaturated fractures of porous rock were identified as surface analogs to porous medium properties. These are the matric potential-dependent film transmissivity, the (non-hysteretic) film moisture characteristic function, and the average film velocity. The transmissivity of films increases with film thickness, and supports fast gravity-driven flow. More recently, tests of the importance of surface roughness on film flow were conducted on ceramic blocks with simple, corrugated roughness features. Controlling influences of fracture surface channels and ridges were quantitatively demonstrated in these experiments. Another part of this study on film flow concerns transient processes in unsaturated fractures. The film hydraulic diffusivity has been identified and measured through steady-state and transient experiments.

In addition to film flow, the hydraulic characteristics of some vadose zone rocks exhibit fast flow along "fracture surface zone" pathways. Surface zone fast flow can occur when the surfacial regions of rock blocks (along fracture flow pathways) are more permeable than the bulk matrix. This condition can arise from permeability-enhancing alterations of physical (microfracturing) or chemical (precipitation-dissolution fracture coatings) origin, and will tend to be more significant when the bulk rock is low in permeability. Surface zone fast flow was tested qualitatively and quantitatively through two types of sorptivity (imbibition) experiments. Qualitative evidence for surface zone fast flow was obtained through experiments in which water flows parallel to the fracture, into both the surface zone and bulk rock simultaneously. More quantitative measurements of surface zone fast flow were obtained through imbibition normal to the fracture surface, with water first entering the surface zone, then the bulk rock. Experiments on a welded tuff revealed fracture surface zone pore water velocities about 900 times faster than that of the bulk rock. Experiments on a rhyolite showed about 30 times faster flow in the surface zone than in the bulk rock.

This study has introduced two mechanisms capable of explaining fast flow in unsaturated fractured rock, film flow, and surface zone flow. The validity of the proposed mechanisms was supported through multiple experimental tests. Future research will include aperture influences in order to obtain a more complete understanding of flow in partially saturated fractures.

Film-Straining of Colloids in Unsaturated Media: Theory and Experiments

Jiamin Wan, Tetsu K. Tokunaga, and Srinivas Veerapaneni [Earth Sciences Division, Lawrence Berkeley National Laboratory]

A physically based model for transport of colloids in unsaturated porous media has not previously been available, despite the importance of colloid-facilitated chemical transport. A film-straining theory is introduced in this study, which proposes that transport of suspended colloids can be retarded due to physical restrictions imposed by thin water films in partially saturated porous media. A quantitative, mechanistic model is provided to predict the film-straining efficiency. In this model, the concepts of "critical matric potential" and "critical saturation" are introduced, at which thick film interconnections between pendular rings are broken and film straining begins to become effective. The modeled magnitude of colloid transport through water films depends on the ratio of colloid size to film thickness, and on flow velocity. Effective penetration of hydrophilic colloids through unsaturated porous media is predicted when a system is above the critical saturation value. For colloids smaller than the thickness of adsorbed thin water films, the model predicts that colloids can still be efficiently transported, even when the system matric potential and saturation are lower than their critical values. The model was tested through experiments on transport of hydrophilic latex particles (4 sizes from 0.01 to 1.0 µm), in sand columns of three different grain-sizes, at flow rates spanning four orders of magnitude. The conceptual basis of this model is supported by good agreement between the wide range of experiments and model predictions using only two adjustable parameters. These results have been published in Environmental Science and Technology (August, 1997, 31, 2413-2420).

The nature of water film influences on retardation of colloid transport in unsaturated media is a critical aspect of the film straining theory. We have begun a series of experiments on spherical particle motion in flowing films in order to understand mechanisms underlying the film-straining phenomenon. Our initial work in this area utilizes larger scale systems, due to experimental simplicity. Spherical particles in the range of 20 to 800 µm diameter, in films ranging in thickness from 250 to 700 µm have been studied on an inclined glass plate, under steady-state flow. Experimentally observed velocities of particles smaller than film thickness are in agreement with theoretically predicted values. Experimental results show that the velocity of the particle increases with its diameter until the particle size is about 70% of the film thickness. At this depth, the particles are essentially in linear shear flow and the presence of the free surface is not felt by the particle. The velocity of the particle peaks when its diameter is about 70% of the film thickness, at which the particle experiences higher drag. The particle velocity is observed to decrease with size when its diameter is greater than 70 to 80% of the film thickness. Unlike expectations from the earlier film-straining model, particle movement is observed to cease when its diameter is slightly greater than that of film thickness. Upcoming research will be extended to smaller scales, rough fracture surfaces, and nonspherical particles.

Observations of Dissolution During Fracture Flow in Marble

W. B Durham and W. L. Bourcier [Lawrence Livermore National Laboratory]

We have carried out a series of reactive flow experiments in Carrara marble to determine the feasibility of using surface profilometry to determine the relationship between local fracture aperture and rate of reaction. Preliminary results have been very encouraging.

The experiments are simple in concept, but rather tedious to carry out because of the fine scale of observation necessary on a sample of macroscopic proportions. The idea is to begin with a well-characterized fracture in a mineralogically simple rock, flow a reactive fluid through the fracture, performing simultaneous numerical simulation of that fluid flow, and then examine the fracture aperture for topographic changes that will help identify systematic relationships between fluid flow and reaction rates.

The initial investigation uses Carrara marble because of its simple mineralogy and high reactivity with water at room temperature. If feasibility is demonstrated, later experiments will be carried out on different mineralogies. Samples begin as right circular cylinders approximately 50 mm in diameter and 75 mm in length. We introduce a single rough axial fracture by Brazil splitting.

Using our surface profilometer, we then digitize the surface topography of both faces of the fracture. Given the high precision of the profilometer and precision reference points on the rock itself, we are able to reconstruct the fracture aperture digitally with a positional uncertainty (in the plane of the fracture) of better than 0.05 mm and an elevation resolution of about 0.01 mm. Given the digital image of the fracture, we can numerically simulate fluid flow patterns. Although a Lattice Boltzmann or full Navier-Stokes simulation would give a more accurate picture of fluid flow, we have been using a much less time-consuming Reynolds equation simulator to give an image of flow that is at least qualitatively correct.

Once the fracture is digitized, we reassemble the rock and jacket it in an assembly that allows fully saturated fluid flow through the fracture from one end of the sample to the other. We apply a light confining pressure to the assembly mainly to prevent short-circuiting of fluid around the outside of the rock. In our first experiments we have used an undersaturated fluid in a recirculating mode to cause dissolution of material from the fracture faces. We performed two reaction sequences, the first dissolving a total of 0.5 g from the rock faces, the second dissolving another 1.0 g. The total material removed is the equivalent of a uniform layer from both sides of the rock of thickness about 0.08 mm. If material was in fact removed nonuniformly, it should be easily resolvable by profiling.

The digitized images from the surfaces following the second dissolution step gave a very clear indication of nonuniform dissolution. Dissolution patterns do not show obvious relationships to surface topography of individual surfaces, but they do show a relationship to fracture aperture (i.e. the difference between the two surfaces). While there are many trends to investigate, one of the most obvious correlations is also one of the most intriguing: dissolution seems to be most rapid along the sides of high volume flow channels. As far as we know, these measurements represent the first time that patterns of dissolution have been compared to patterns of flow in two-dimensional flow. Analysis is of the images is ongoing.

A second sample is presently undergoing a series of dissolution steps under conditions of constant (as opposed to steadily increasing) saturation. If, as the first sample suggests, dissolution is associated with higher volume flow channels, then we expect to see somewhat higher dissolution in those channels with respect to the first sample.

Solute Dispersion in Partially Saturated Variable Aperture Fractures

Russell L. Detwiler, Harihar Rajaram [Department of Civil, Environmental and Architectural Engineering, University of Colorado]
Robert J. Glass [Flow Visualization and Processes Laboratory, Sandia National Laboratories]

In a saturated fracture, solute dispersion is influenced by both mean solute velocity and aperture variability. In a partially saturated fracture, where a portion of the fracture is occupied by an immobile phase, the structure of the entrapped phase (which is influenced by the aperture field), also significantly influences solute dispersion. The entrapped structures increase flow tortuosity, thus enhancing solute dispersion. Through a combination of physical and numerical experiments we investigate the relationship between aperture variability, entrapped phase geometry, solute velocity and solute dispersion.

Physical experiments were carried out in smooth-walled (constant aperture) and rough-walled (variable aperture) analog glass fractures. Fracture aperture, solute concentration, and phase distribution within the fractures were measured at high spatial resolution (0.16 x 0.16 mm) using a light transmission technique. Using this technique we obtained accurate concentration measurements over the entire flow field many times during each experiment. These concentration fields highlight transport phenomena that must be incorporated into any comprehensive conceptual model, most notably, boundary layers along the edges of entrapped structures. These boundary layers enhance solute channeling at the leading edge of a solute plume and hinder the removal of solute that has diffused into the low flow regions (created by the boundary layers) at the tail end of the solute plume. In addition to enhancing solute dispersion, this will have a significant influence on the dissolution rate of an entrapped phase.

These experiments are directly compared to numerical simulations of flow and transport in the partially saturated fracture. Additionally, by varying gravitational forces during invasion of the non-wetting phase, different phase distributions within the measured aperture field are simulated using modified percolation theory (Glass et.al., in review). The effect of phase structure on solute transport is then investigated based on numerical simulations.

Finger Velocity and Flux Scales for Double-Diffusive Convection in a Hele-Shaw Cell: Experimental Determination

Clay A. Cooper [Desert Research Institute and Hydrologic Sciences Program, University of Nevada, Reno]
Robert J. Glass [Subsurface Flow and Transport Processes Laboratory, Sandia National Laboratories]
Scott W. Tyler [Desert Research Institute and Department of Environmental and Resource Sciences, University of Nevada, Reno]

We have conducted experiments to investigate the evolution and development of double-diffusive finger convection in a Hele-Shaw cell. A gravitationally stable, two-component fluid can become double-diffusively unstable to fingers if the diffusivities of the two components are different, and if the faster-diffusing component is stabilizing while the slower-diffusing component is de-stabilizing to the vertical density gradient. A set of experiments were conducted such that a sodium chloride solution was overlain by a solution of sucrose within the gap (of order 0.5 mm) of the cell. All controlling parameters were held constant between experiments except for the initial sucrose solution.

Using a light transmission technique, we were able to measure the concentration field of a passive dye tracer dissolved in the NaCl solution. The instability evolves at the interface (actually a ÔzoneÕ) and develops into finite amplitude structures (fingers) with time. We see qualitative behavior that is much different than systems in which viscous forces do not play a significant role. In most of our experiments, the fingers grew to the top and bottom of the cell, and did not form layers as is common in experiments with fluid (non viscous) systems of similar vertical dimension. One experiment close to the stability boundary (buoyancy ratio of 2.80; a buoyancy ratio of 2.85 is stable), showed fingers that grew to a finite length and essentially stopped. Diffusion from the fingertips was the dominant growth at this point. However, no large-scale convecting layers formed either above nor below the fingers. In all experiments, the transport of mass was between one and two orders of magnitude greater than mass diffusion would be for equivalent, but stable, systems. The results of measurement of the finger velocity and lengths, as well as mass flux will be presented in detail.

Accuracy and Computational Efficiency in 3D Dispersion via Lattice Boltzmann: Models for Double-Diffusive Fingering and Dispersion in Rough Fractures.

Harlan W. Stockman [Sandia National Laboratories]

In the presence of buoyancy, multiple diffusion coefficients, and porous media, the dispersion of solutes can be remarkably complex. The lattice Boltzmann (LB) method is ideal for modeling double-diffusive dispersion, and dispersion of solutes in flow through rough fractures; simple code optimizations yield simulation rates up to ~3 million site updates per second on inexpensive, single-CPU systems. Yet, LB models of solute fingers or slugs can suffer from peculiar numerical conditions (e.g., denormal generation) that degrade computational performance by factors of 6 to 100. We will discuss solutions for common LB performance issues, and use two examples to illustrate limits of the method.

Double-diffusive convection drives "salt-fingering", a process thought responsible for mixing of fresh-cold and warm-salty waters in many coastal regions. Fingering experiments are typically performed in Hele-Shaw cells, and can be modeled with the 2D (pseudo-3D) LB method originally described by Holme and Rothman or Flekkoy et al. However, the 2D models cannot capture Taylor-Aris dispersion from the cell walls, and this dispersive component can be surprisingly large, even with "slowly-moving" fingers. We compare 2D and true 3D fingering models against observations from laboratory experiments.

Dispersion of solute in a thin duct is often approximated with dispersion between infinite parallel plates. However, Doshi, Daiya and Gill (DDG) showed that for a smooth-walled duct, this approximation is in error by a factor of ~8. This error is significant for modeling contaminant transport in fractured rock, because in short-term laboratory experiments, it is extremely difficult to distinguish sorption from anomalous dispersion. But in the presence of wall roughness (found in all real fractures), the DDG phenomenon can be diminished, and the Taylor-Aris approximation may actually be more accurate than the DDG solution. We examine the source of the error, discuss the problems inherent in modeling the phenomenon with LB, and provide preliminary estimates of dispersion between rough-walled fractures.

The Role of Fracture Intersections in the Flow and Transport Properties of Rock

Stephen R. Brown [New England Research]
Harlan W. Stockman [Geochemistry Department, Sandia National Laboratories]
Arvind Caprihan [New Mexico Resonance]

Many studies have shown that fluid flow and solute transport occur mainly through channels within individual fractures. Additionally, select fractures of a network may take most of the flow, thus forming a larger-scale channel structure. This multi-level system of channels allows solutes to travel much farther and faster than might otherwise be expected from the mean velocity or for uniform flow in constant width fractures. Fluids or the solutes they contain, which can interact chemically with the wall rock, are in contact with smaller areas of the fracture surfaces and for less time than for uniform flow.

We propose to physically model and analyze several configurations of flow and transport through fracture intersections. We will utilize a combination of quantitative measurements, visual and magnetic resonance imaging (MRI) observations of flow through real rough-walled fractures, and numerical modeling via lattice Boltzmann (BGK) methods. This project will provide needed fundamental understanding, since at this time it is not known whether intersections enhance or inhibit flow either perpendicular to or along them, whether or not the surface roughness of the fractures comprising an intersection and thus the channels within them are correlated, and how multiple phases behave as they meet an intersection.