A Chaotic-Dynamical Conceptual Model to Describe Fluid flow and Contaminant Transport in a Fractured Vadose zone

(1) To determine if and when dynamical chaos theory can be used to investigate infiltration of fluid and contaminant transport in heterogeneous soils and fractured rocks. (2) To introduce a new approach to the multiscale characterization of flow and transport in fractured basalt vadose zones and to develop physically based conceptual models on a hierarchy of scales. The following activities are indicative of the success in meeting the project s objectives: A series of ponded infiltration tests, including (1) small-scale infiltration tests (ponded area 0.5 m2) conducted at the Hell s Half Acre site near Shelley, Idaho, and (2) intermediate-scale infiltration tests (ponded area 56 m2) conducted at the Box Canyon site near Arco, Idaho. Laboratory investigations and modeling of flow in a fractured basalt core. A series of small-scale dripping experiments in fracture models. Evaluation of chaotic behavior of flow in laboratory and field experiments using methods from nonlinear dynamics; Evaluation of the impact these dynamics may have on contaminant transport through heterogeneous fractured rocks and soils, and how it can be used to guide remediation efforts; Development of a conceptual model and mathematical and numerical algorithms for flow and transport that incorporate (1) the spatial variability of heterogeneous porous and fractured media, and (2) the description of the temporal dynamics of flow and transport, both of which may be chaotic. Development of appropriate experimental field and laboratory techniques needed to detect diagnostic parameters for chaotic behavior of flow. This approach is based on the assumption that spatial heterogeneity and flow phenomena are affected by nonlinear dynamics, and in particular, by chaotic processes. The scientific and practical value of this approach is that we can predict the range within which the parameters of flow and transport change with time in order to design and manage the remediation, even when we can not predict the behavior at any point or time

WRRCTMR No.55 Numerical Modelling of Liquid Waste Injection into Porous Media Saturated with Density-Stratified Fluid: A Progress Report

Waste effluent injected into an aquifer saturated with denser ambient brackish or salt water experiences a buoyant lift. As a result, the effluent migrates both outward from the well and upward in response to the combined effects of injection head and buoyant force. After the injection process has begun, several phenomena can affect the density, shape, and distribution in space and time of the resulting buoyant plume. The most important of these include convection and mechanical dispersion and molecular diffusion. Previous sandbox and Hele-Shaw laboratory modelling work have provided a basic qualitative understanding of buoyant plume movement in a porous medium. However, these laboratory models cannot correctly simulate dispersion phenomena which may have significant effects on buoyant plume movement and distribution. Consequently, it is necessary to mathematically model the problem using coupled sets of partial differential equations which take into account the effects of dispersion and diffusion, as well as convection. For this problem, there are four unknowns (density, concentration, velocity, and pressure), requiring four equations. The four governing equations are: a motion equation (Darcy's law), a continuity equation, a dispersion equation, and an equation of state. In addition, boundary and initial conditions must be stipulated. In this study, two sets of boundary conditions are used: the first consists of conditions identical to those in the sandbox model studies, and the second models the geology of a specific prototype area. The resulting governing equations and boundary and initial conditions are numerically solved by both the finite difference and the finite element methods. Finally, the numerical models are calibrated with the results of the sandbox model studies mentioned previously. This report describes in detail formulation of the governing equations and the initial and boundary conditions, and preliminary finite difference modelling work completed to date.U.S. Department of the Interior OWRT Project NO. A-071-HI Grant/Contract No. 14-34-0001-702

WRRCTR No.125 Numerical Modeling of Liquid Waste Injection into a Two-Phase Fluid System

The injection of liquid wastes into a groundwater environment saturated with density-stratified fluid is simulated by a finite-difference numerical model. The fluid transport equation is simultaneously solved with the convective-dispersion equation for salinity. The migration of the injected liquid waste effluent is then tracked by solving a second convective-dispersion equation for an ideal tracer dissolved in the effluent. The convective-dispersion equation for the ideal tracer is solved with the flow velocities obtained from the simultaneous solution of the fluid transport and the salinity convective-dispersion equations. The equations are solved for the two-dimensional case of a line of injection wells set close together parallel to the coastline. Total length of the line of injection wells is considered to be much longer than the distance to the ocean so that any vertical cross section taken normal to the coastline will appear the same. Results are presented in a time-series of contour maps in the vertical plane: one map for each time-step, with lines of equal concentration for the salinity (isochlors); and the effluent tracer (isopleths). The more concentrated effluent is found to migrate vertically upward around the injection well due to buoyant force, while dilute effluent solutions migrate horizontally, displaying very little buoyant rise.Office of Water Research and Technology, U.S. Dept. of Interior Grant/Contract No. A-071-HI 14-34-0001-7025, 7026, 801

The fractional-order governing equation of Lévy motion

A governing equation of stable random walks is developed in one dimension

WRRCTR No.96 Waste Injection into the Hawaiian Ghyben-Herzberg Aquifer: A Laboratory Study Using a Sand-Packed Hydraulic Model

Injection of wastes into the Hawaiian subsurface environment presents unique problems because the waste effluents normally are injected into the salt or brackish water underlying the fresh Ghyben-Herzberg lens. Because the waste water commonly has approximately the same density as fresh water, in addition to any ambient groundwater flow effects, a buoyant uplift is produced which causes the injected waste to move upward and outward from the injection point as a buoyant plume. A laboratory sand-packed hydraulic model was used to study the mechanics of buoyant plume movement, and the entrainment of salt water by the plume. Simulated waste effluent was injected into a density-stratified aquifer system under static groundwater conditions, and the effects on plume mechanics of varying several different injection parameters, such as injection depth, injection rate, type of injection source, density of receiving water, etc., were observed. The laboratory studies indicated that although several of the injection parameters (most notably depth of the injection with respect to the saltfresh interface) have an effect on the details of the injection process and the plume movement and configuration, none of the injection parameters exerts a truly significant control on the ultimate fate of the injected plume. That is, for the conditions stipulated in this study, the injection plumes always migrated well up into the freshwater lens, regardless of variations in any of the several injection parameters. Furthermore, these experiments showed little evidence of entrainment of the surrounding salt water into the injected buoyant plumes, which strongly suggests that the principal means of plume movement is by mass displacement rather than by mixing processes.U.S. Department of the Interior Grant Agreement Nos.: 14-31-0001-5011, 14-31-0001-5068 OWRT Project No. B-038-H

WRRCTR No.107 A Laboratory Study of Waste Injection Into a Ghyben-Herzberg Groundwater System Under Dynamic Conditions

Injection of wastes into a Ghyben-Herzberg groundwater system presents unique problems because the waste effluents are normally injected into the salt or brackish water underlying the fresh Ghyben-Herzberg lens. Because the waste water commonly has approximately the same density as fresh water, in addition to any ambient groundwater flow effects, a buoyant uplift is produced which causes the injected waste to move upward and outward from the injection point as a buoyant plume. A laboratory sand-packed hydraulic model was used to study the mechanics of buoyant plume movement and the entrainment of salt water by the plume. Simulated waste effluent was injected into a density-stratified aquifer system under dynamic groundwater conditions, and the effects on plume mechanics of varying several different injection parameters, such as injection depth and rate, type of injection source, strength of the ambient flow field, and density of ambient perceiving water, were observed. In every experiment conducted during this study, a buoyant plume of injected effluent, which was clearly distinct from the president aquifer liquids, formed and rose vertically into the lower portion of the freshwater lens, where it was subjected to the freshwater flow field and migrated downgradient with the fresh water, still keeping its identity as a distinct plume of injected effluent. Three of the injection parameters exerted significant control on the movement of the injection plumes. The rate of effluent injection and the strength of the ambient freshwater flow field significantly influenced both the vertical and upgradient dimensions of the plumes, and also appeared to influence downgradient mixing of the plume with the ambient fresh water; and the depth of effluent injection, with respect to the relative density of the resident liquids, influenced the upgradient migration of the plumes. Although there was some initial evidence of salt water entrainment within the salt zone injection plumes, it was a transient phenomenon, and little evidence of salt water entrainment was observed once the plumes reached steady-state conditions. Downgradient dilution of the effluent plumes by the ambient fresh water was apparent, however, and increased with downgradient distance from the injection well.U.S. Department of the Interior, Water Resources Grant/Contract No. 14-31-0001-3511 Project No. B-043-H

Non-Fickian Ionic Diffusion Across High-Concentration Gradients

A non-Fickian physico-chemical model for electrolyte transport in high-ionic strength systems is developed and tested with laboratory experiments with copper sulfate as an example electrolyte. The new model is based on irreversible thermodynamics and uses measured mutual diffusion coefficients, varying with concentration. Compared to a traditional Fickian model, the new model predicts less diffusion and asymmetric diffusion profiles. Laboratory experiments show diffusion rates even smaller than those predicted by our non-Fickian model, suggesting that there are additional, unaccounted for processes retarding diffusion. Ionic diffusion rates may be a limiting factor in transporting salts whose effect on fluid density will in turn significantly affect the flow regime. These findings have important implications for understanding and predicting solute transport in geologic settings where dense, saline solutions occur