H21J-01 INVITED
Front roughness and averaged saturation for two-phase flow in heterogeneous porous media
An important characterization criterion for displacement of one fluid by another, immiscible one in porous media, is the morphology of the fluid-fluid interface. The interface morphology on the pore scale is determined by the interplay between capillary, gravity and viscous forces and by the structure of the pore space. Interface criteria on the pore scale cannot necessarily be transferred to the Darcy scale. This is in particular true in heterogeneous media, where the structure of material interfaces on the large scale may determine the flow process. Pore scale instabilities may, for example, appear as stabilized on the large scale due to large scale structures. The properties of displacement fronts in heterogeneous media on the large scale and their upscaled description on a scale, where heterogeneities are averaged out, can for some flow regimes be predicted approximately using homogenization and stochastic theory. One important criterion is the growth rate of the averaged front. For viscous dominated displacement (e.g. Langlo and Espedal, 1995) and for displacement with capillary barriers (Pruess, 1996) a pseudo-dispersive behavior of the growth of the averaged front has been discussed. This presentation discusses predictions of large scale front behavior obtained with homogenization and stochastic theory, where capillary forces and viscous forces are taken into account. The theoretical predictions are compared to observations of displacement fronts in Darcy scale heterogeneous media on the lab scale in quasi-two-dimensional sand tanks. Fluid content was measured using optical methods and the front properties were analyzed for different flow regimes and structures. The front shows a different behavior than the spatially averaged fluid content. While the front is in most cases stable after some time, the width of the distribution of the averaged fluid content continues to grow due to pore-scale and macroscopic trapping events. Langlo, P. and M.S. Espedal, Advances in Water Resources 17, 297-316, 1995. Pruess, K., Transport in Porous Media 24, 1-33, 1996.
H21J-02
Experimental Examination of Localized-Bursts of Fluid Advancement During Immiscible Drainage in Porous Media
This talk will describe experiments of immiscible two-phase drainage in a translucent porous medium, at low injection speeds. Air displaced the water by irregular bursts of motion, suddenly invading small portions of the hydrophilic medium. These periods of activity, followed by dormancy, are similar to descriptions of systems at a self-organized critical point, where a slight disturbance may induce an avalanche of activity. While the apparent relationship between self-organized criticality and invading mass-bursts has been investigated with numerical simulations, very few experimental studies have examined this phenomenon. The fractal characteristics of the invading air structure at breakthrough were examined as well. With static (box-counting) calculations of the invaded air mass and through an evaluation of the time-dependent motion of the invading mass two different fractal evaluation methods were performed. Results were compared with prior two-phase numerical studies in porous media. A power-law scaling exponent determined from invasion percolation modeling was shown to be well suited to describing the structure of the invading fluid. To examine the applicability of self-organized criticality predictions to the invading fluid movement, a new image analysis procedure was developed to identify the location of individual bursting events during the drainage experiments. The predictions of self-organized criticality, namely the scaling of the occurrence of bursts to the mass of the bursts and a spatio-temporal randomness of different sized bursts, are also examined. Bursts of a wide range of sizes are shown to occur throughout the porous medium, over both time and space. The mass distribution of burst sizes is shown to be well described by self-organized criticality predictions, with an experimentally determined scaling exponent, τ ~ 1.53, which is quite similar to previous numerically derived values. Keywords: Self-organized criticality, fractal scaling exponents, mass-avalanches, interface depinning, Haines jumps.
H21J-03
DEVELOPMENT AND PRELIMINARY APPLICATION OF HIGH-RESOLUTION ENDOSCOPIC PIV FOR QUANTIFICATION OF FLOW STRUCTURE WITHIN A PORE SPACE
Most natural rivers have beds of loose, cohesionless sediment that form a porous bed, thus permitting significant interactions between the free flow above the bed and that within the pore spaces. Many unresolved problems in channel engineering and ecohydraulics are related to an incomplete understanding of this interstitial flow. For example, the mechanisms of pollutant transport and prediction of river bed morphodynamics may be strongly influenced by flow occurring within the pore spaces. While this lack of understanding has been widely acknowledged, the direct experimental investigation of flow within the pore spaces has been restricted by the practical difficulties in collecting such data. This has also created drawbacks in the numerical modeling of pore flow as there remains a dearth of robust experimental data with which to validate such models. In order to help address these issues, we present details of a new endoscopic PIV system designed to tackle some of the challenges highlighted above. The work presented in this paper is also being used to validate a numerical model that is being developed as part of this project. A fully endoscopic PIV system has been developed to collect velocity and turbulence data for flow within the pore space of a gravel bed. The system comprises a pulsed Nd:YAG laser that provides high intensity illumination for single exposure pairs of images on a high-resolution digital camera. The use of rigid endoscopes for both the laser light source and camera allows measurement of quasi-instantaneous flow fields by high-resolution PIV images (2352*1728 pixels). In the first instance, the endoscopic PIV system has been used to study flow within an artificial pore space model constructed from 38 and 51 mm diameter spheres, used to represent a simplified version of a natural gravel-bed river. Across-correlation processing approach has been applied to the PIV images and the processing parameters have been optimized for the experimental conditions. A series of instantaneous two-dimensional flow fields in a simple pore space has been reconstructed permitting quantification of the mean flow. A not symmetric flow structure has been highlighted showing the strong dependence of flow on the bed geometry and presence of the free surface. Preliminary results will be discussed here in order to highlight the critical aspects of the technique. Illumination from the laser endoscope must be optimized in terms of angle of divergence, uniformity and stability, with any source of irregular illumination causing strong reflections from the surface of the spheres resulting in saturation of huge image areas. The preliminary results obtained demonstrate the utility of the fully endoscopic PIV technique for investigation of flow structure in pore spaces. Further developments of the technique will include improving light uniformity, removing reflections from images and increasing the illuminated portion of the pore space area.
H21J-04
Spreading in Two-Phase Buckley-Leverett Flow due to Heterogeneity
We consider idealised immiscible two phase displacement flow (Buckley-Leverett) in a heterogeneous porous medium. In particular, we consider two cases – (a) horizontal flow subjected to temporal fluctuations and (b) vertical flow with buoyancy. Using perturbation and stochastic methods we analytically derive a large scale 'mixing' (spreading) parameter for these Buckley Leverett flows. In analogy with previous work in passive scalar spreading, this 'mixing' effect can be quantified by an effective large scale dispersion term. While temporal fluctuations enhance mixing for a passive conservative tracer, we illustrate in case (a) that for multiphase flow they do not always do so. For the vertical case (b) buoyancy can act as a stabilizing or destabilizing influence competing with viscous instabilities and heterogeneity. This makes the quantification of spreading more difficult. However, our solution still works well for many cases and provides useful insight into others. In order to validate the analytical models, a series of numerical solutions was conducted. This project is motivated by a desire to understand the influence of heterogeneities on multiphase flow with a specific ultimate application to CO2 sequestration.
H21J-05
The Influence of Unconformities Along the Layer Interface on Capillary Barrier Flow
Under unsaturated conditions the water flow in sediments is largely influenced by capillary forces. Especially if layers of fine grained sand overlay coarser layers of sand and gravel. The fine soil layer stores infiltrating water (capillary forces), acts like a drainage layer in sloping systems and thus is used to divert laterally the water under unsaturated conditions. This effect is used in waste technology as a barrier to downward flow. By far most of the present experiments with this respect were investigating undisturbed, straight construction of the interface between the two layers. Sedimentological unconformities in natural soils or uneven settlements of underlying waste are disturbing this distinct construction. These unconformities along the layer interface may change the flow pattern and cause vertical breakthrough. The experiments presented here are aimed to quantify the influence of interface discontinuities on the capillary flow. In the experimental set up a capillary layer (0.35 m sand) and capillary block (0.18 m gravel) were placed in an experimental tank of 6 m length, 1 m high, and 0.6 m width, with a slope of 11.3°. The tank is subdivided in 12 separately measurable drainage compartments, which enables the identification and quantification of local breakthrough. Inflow, outflow at all 14 segments, soil water tension (13 tensiometers), soil moisture (4 TDR probes) were automatically monitored. In addition tracers (NaCl and Amidorhodamine G) were used to visualize the flow pattern and determine hydraulic parameters. In a first set of experiments (3) the interface between sand and gravel were partially covered by a plastic membrane with variable openings. The second setup included two pillows filled with water, which were placed in the gravel during the construction each on the left and the right side of the tank, in a distance of 0.42 m from the upper end. In all setups the inflow rate was stepwise increased until reaching the lateral drainage capacity. Analysis of water content and out flow rates show specific drainage capacities of the material combination until breakthrough occurs. The different setups show however a heterogenous distribution of drainage paths from the beginning of the experiment. At a critical irrigation rate (229 l/m/d), discontinuities were created. We registered some water in the drainage compartments and locally tensiometers indicated saturation in the gravel. This shows the influence of discontinuities at the interface on the infiltration of water. Breakthrough however occurs only in a small percentage of the outflow (less than 1 per cent). It is occurring on both sides of the capillary barrier but preferentially on the left side, upstream and downstream from the pillow. The increase of the irrigation shows a nonlinear increase of the breakthrough, but the breakthrough never turned out to be stable as the irrigation and the outflow. Thus it appears that preferential path ways are created in the initially unsaturated sand and continued under increase of saturation. These can be traced by the water potential isographs and were finally visualized by the tracer tests.
H21J-06
Avalanches and non-Gaussian fluctuations of the velocity of imbibition fronts
We present an experimental study of the velocity fluctuations of a viscous fluid interface during forced-flow imbibition within a model porous medium. Our high resolution set-up shows that the invading fronts display an intermittent behavior signature of a burst-like dynamics. In order to characterize the scaling features of this intermittency -the local pinnings and depinnings of the front- we compute the local waiting time fluctuations of the interface during its propagation. Avalanches -defined as clusters of large local velocities- follow robust power-law distributions (with exponential cut-offs), both in size S and duration D. Moreover, the anisotropic shape of the avalanche clusters provides an estimate of the local roughness exponent of the interface. Finally, when the mean (spatially averaged) velocity of the fronts is measured on window sizes comparable to its correlation length, the velocity fluctuations follow a Generalized Gumbel distribution, whose skewness increases as the measuring window and/or the injection flow rate are reduced, offering the effective number of degrees of freedom probed in our experiment.
H21J-07
Experimental and Theoretical Study of Hydrodynamics of Groundwater Flow and solute transport in a Karst Aquifer
Sandbox experiment and numerical simulation are developed to study groundwater flow and solute transport in a Karst aquifer, which is composed of limestone matrix and conduits. In the sandbox experiment, a screen made pipe, used to represent the conduit, in a sandbox is surrounded by the glass-beads, which is used to represent matrix. The water and solute can be exchanged between the matrix and conduit according to the hydraulic and chemical gradients between the two domains. In the mathematical model, a two-zone model is developed to describe the flow in the two domains. The model uses the Darcy equation in the matrix domain and Stokes equation in the conduit domain. On the interface between the two domains, Beaver-Joseph interface conditions are proposed. Convection-dispersion equation is used to describe solute transport in the matrix domain. Finite elementary method is developed for the numerical simulation. The numerical simulations are consistent with experimental results. The developed method makes a solid step towards quantitative study of groundwater flow and solute transport in Karst aquifers.