H13K-01 INVITED
Alternative Measures of Dispersion Applied to PTV Experiments
Steady flow in a corrugated pore is studied via Particle Tracking Velocimetry. The pore is constructed from a sequence of closed parallel cylindrical tubes welded together in plane which are then sliced down the lateral mid- plane and the lower complex is laterally shifted relative to the upper complex. Flow is induced in the lateral direction normal to the axis of the tubes. The a-time, Ta, finite-size Lyapunov exponent, ëa, and the real- space self and distinct part of the intermediate scattering functions, Gs and Gd, and the pair density function, Gp, are computed from the data. Particle trajectories, velocity maps and streamlines show the pore has two prominent recirculation zones and a main flow region. The first passage time pdf of tagged particles past a plane transverse to the mean flow illustrates how particles are delayed by recirculation zones. The delay caused by fluid element folding is manifested in single particle statistics such as the first passage time and the slowing increase in horizontal evolution of Gs. Gp describes initial particle distribution and allows areas in the flow domain trapping particles to be identified and visualized. Gd shows the evolution of the average separation of pairs of particles and when examined in a recirculation zone, it evolves little because of fluid element rotation. ëa gives information on what transpires at a fixed scale and provides an estimate of the rate at which particles initially separated by a distance x separate to a distance ax as opposed to Gd which allows one to view changes over time. At small separations, ë1.3 approaches a constant and for intermediate separations it scales as x-0.8.
H13K-02
An Example of Non-Fickian Dispersion in Porous Media Explained by Heterogeneous Microscale Matrix Diffusion
We report a set of single well injection withdrawal tracer tests (SWIWTT) and transmission tracer tests (TTT) at laboratory scale in high porosity limestone using newly developed equipment. Tracer concentration breakthrough curves (BTC) are measured over 4 to 5 orders of magnitude allowing us to precisely characterize the non-Fickean dispersion behavior. Using the SWIWTT for distinctly different exploration volume and the TTT performed through the core corresponding to the same level in the borehole, we interpret the non-Fickean dispersion behavior in term of mobile-immobile mass transfers due to diffusion in the microporosity. All the BTC are similar and do not display the usual single slope power law concentration decrease C(t) ~ t-γ corresponding to the conventional MIM mass transfer model. At intermediate time t1<t<t2 , when t1 is larger than the advection characteristic time, the concentration decreases roughly as C(t) ~ t-2. Then, at large times (t> t2) the asymptotic decrease is C(t) ~ t-1.5. Analyzing the BTC set using both CTRW approach and memory function approach, we explain the measured BTC by a dual slope transition time distribution that denotes, in term of MIM mass transfer model, a dual control of the retention time probability of the tracer in the immobile domain. The origin of these distinctly different characteristic times of retention, which appears to be independent of the scale, is difficult to solve by conventional analysis of the medium. To test the assumption that the heterogeneity of the microporosity controls this unusual non-Fickean behavior, we performed numerical diffusion experiments using X-ray microtomography to quantify the mobile-immobile interface geometry and the immobile microposisity distribution. Result shows that, a memory function similar to the one required for fitting the BTC set is obtained by the numerical diffusion experiment as soon as the heterogeneity of the immobile domain is taken into account. We conclude that, for limestone reservoirs, the strong non-Fickean dispersion behavior is explained by matrix diffusion only, and the unusual dual slope pretension time is controlled by the microscale heterogeneity of the diffusivity in the rock matrix.
H13K-03
Particles Tracking in Transparent Matched Index of Refraction Porous Media
An inexpensive non-invasive three-dimensional particle tracking velocimetry system was designed and constructed to investigate tracer particles' movement in a match-index-refraction (MIR) porous medium. This flow visualization experiment was carried out by releasing and recording neutrally-buoyant tracer particles in both homogeneous and heterogeneous MIR materials. Particles were released and tracked in the two materials and a three-dimensional trajectory of each particle was recorded using two video camcorders. This technique consisted of using images from two cameras which were placed orthogonal to the main axis of the porous material flow cell. The particle trajectories were obtained based on image processing and via Three-Dimensional Particle Tracking (3DPT) technique. In this technique a Lagrangian analysis was used, and the coordinates and the velocity components of each tracer particle were accurately determined. The experiment's results have shown the following main conclusions: 1) the particle's trajectory and spreading are affected by the size of the tracer particles and are sensitive to their initial locations; 2) small-scale heterogeneity may enhance the early-time dispersion while large-scale heterogeneity may control the late-time asymptotic dispersion; 3) an effective porosity (ne) may exist in the heterogeneous medium which may be significantly smaller than the total porosity and ne should be viscosity-dependent. For the same porous medium, the higher the viscosity, the smaller the effective porosity; 4) the distributions of the longitudinal velocities were found to be lognormal while the distribution of the transverse velocities was found to be Gaussian.
H13K-04
Significance of Pre-Asymptotic Dispersion in Porous Media
When chemically neutral tracer particles flow in a porous medium, the interplay of advection and diffusion (described by Peclet number, Pe) causes their spreading that is traditionally described by dispersion coefficients, D. Dispersion coefficients are defined by σ2 = 2Dt, where σ2 is the variance of the solute position and t is the time. In the asymptotic limit D is constant and can be used in an averaged advection- dispersion equation. However, it is highly important to recognize that, until the velocity field is fully sampled, the particle transport is non-Gaussian and D possesses temporal or spatial variation. We study spatial and temporal probability density functions of tracer particles by using a Lagrangian pore-scale network model that incorporates flow and diffusion in 2D and 3D network lattices representative of Berea sandstone. The pre-asymptotic and asymptotic dispersion are quantitatively described by the probability density functions and dispersion coefficients. The subtleties arising from comparison with the 2D lattice model that accurately predicts NMR, laser fluorescence and the classic breakthrough data for the experimental dependence of the longitudinal dispersion coefficient, DL, on Pe are discussed. We show that, even in a statistically homogeneous medium where there is no spatial correlation of pore size, thousands of pores must be traveled before Gaussian behaviour is reached. This applies to the studies where there is a 100-fold range of velocities; in natural systems the heterogeneities at the larger scales will significantly increase this range thus significantly delaying the asymptotic approach to Gaussian behaviour. As a consequence, the asymptotic behaviour might not be reached at the reservoir scale. This opens up the question on how appropriate is the use of averaged advection-dispersion equation with constant dispersion coefficients in reservoir simulation.
H13K-05
A numerical study of transverse dispersion and variable density flow in porous media
A two-dimensional laboratory-scale model is used to study the nonlinear behavior of density gradients on transverse dispersion. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersion. Changing salt concentration significantly affects fluid properties which involves a non-linearity in the modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from tracer case, due to the spatial variation of permeability, described by statistical parameters, at the local-scale. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and the limitations of the nonlinear model of Hassanizadeh and Leijnse (1995) in heterogeneous porous media are investigated.
H13K-06
Physical and Numerical Modeling of Buoyant Groundwater Plumes
In coastal states, the injection of treated wastewater into deep saline aquifers offers a disposal alternative to ocean outfalls and discharge directly into local waterways. The density of treated wastewater is similar to that of freshwater but is often much lower than the ambient density of deep aquifers. This significant density contrast can cause upward buoyant movement of the wastewater plume during and after injection. Since some wastewater treatment plants inject more than 100 MGD of this treated wastewater, it is of the utmost importance to be able to not only determine the fate and transport rates of the plume, but to be able to best determine locations for monitoring wells for early detection of possible problems. In this study, both physical and numerical modeling were undertaken to investigate and understand buoyant plume behavior and transport. Physical models using a 2D cross-sectional Plexiglas tank filled with glass beads were carried out under different ambient density scenarios. The experiments consisted of injection of a freshwater pulse-source bubble into a fully saline tank. The injection occurred in an initially static system with no ambient flow. In the scenarios, the freshwater plume migrated vertically upward until reaching the top of the tank. Fingers developed because of the heterogeneity of the density dependent flow field. The vertical velocities and transport patterns of these plumes were compared to one another to investigate variances due to different ambient water densities. Using the finite-difference numerical code SEAWAT to simulate variable density flow, the experiments were numerically modeled and compared with the physical model results. Due to the sensitivity of this problem to numerical resolution, results from three different grids were compared to determine a reasonable compromise between computer runtimes and numerical accuracy. Furthermore, a comparison of advection solvers was undertaken to identify the best solver to use for this specific problem. This involved a comparison between finite- difference, total variation diminishing and mixed Eulerian-Langrangian methods. From these scenarios, the Method of Characteristics (MOC) advection solver with the fine resolution grid (0.1 cm x 0.1 cm x 2.7 cm cells) resulted in a simulation that was in good agreement with the physical experiments. This model was determined to be the base-case problem for further sensitivity analysis. To further verify both the physical and numerical model, SUTRA_MS was also used for comparison. Dimensionless analysis of the flow and transport governing equations was undertaken to determine important physical problem parameters. From these derived dimensionless numbers, it was hypothesized that density, hydraulic conductivity and dispersivity should all play important roles in this problem. A parameter sensitivity analysis was performed using the numerical model base-case. The parameters investigated were hydraulic conductivity, ambient groundwater density, longitudinal dispersivity and injection volume. It was determined that the problem was most sensitive to ambient density, hydraulic conductivity and dispersivity changes as hypothesized, with all three affecting both vertical mass transfer rates, plume fingering and mixing between the fresh and saline waters. The sensitivity to injection volume was not seen to be an important parameter, except for the obvious effect of change in size of the plume.
H13K-07
Connecting Soil Pores to the Field: Uranium Transport Experiments at the Intermediate Scale
An overlying goal of reactive transport modeling (RTM) is to explicitly couple the chemical behavior of a specific contaminant with the hydrology and the geochemical conditions in a given aquifer. Chemical behaviors can include dissolution/precipitation, microbial degradation, redox transformation and sorption/desorption. By combining the chemistry with the hydrology, a more accurate and robust model of what is occurring in the sub- surface should emerge. However, a major obstacle for RTM is how to ‘up-scale' the chemical information collected in laboratories to a field setting. In this presentation we report on experiments that are taking place at the intermediate scale (between lab and field scales) which are designed to elucidate methodologies to ‘link' pore- and field-scale processes. Two intermediate scale tanks (2.44 m x 1.22 m x 7.6 cm, and 2.44m x 0.61m x 7.6cm) have been constructed and two separate packings of uranium contaminated sediment from the Naturita Uranium Mill Tailings Remedial Action (UMTRA) site have been completed. The first packing, in the larger of the two tanks, was physically homogenous using only the <2mm fraction of sediment. In the second, smaller tank, physical heterogeneity was introduced by splitting the <2mm fraction into 0-0.250mm and 0.250mm-2mm fractions. These two size fractions were packed in alternating layers of different thicknesses. In both tanks, samples for uranium and water quality analysis as well as measurements of pressure head were taken through bulkhead fittings installed through the wall of each tank. In the larger tank a bromide tracer test has been completed to determine hyrdrologic parameters for this sediment. Uranium distribution within the tanks was found to vary with pH, alkalinity, dissolved calcium and the rate of release of U from the different particle size categories and the nature of the heterogeneity distribution. In the larger of the two tanks, effluent uranium concentrations ranged from 7.26microM at early time points, and decreased to ~1.5microM as the tank began to exhibit tailing behavior. The spatial gradients of the major chemical constituents were generally smooth, but were variable both as a function of time and space. Kinetic hindrances to uranium desorption were exhibited during stop flow events; these hindrances may be either physical or chemical in nature.