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Neuman, Shlomo P. (8)Evans, Daniel D. (3)Warrick, Arthur W. (3)Baker, Victor (2)Harshbarger, John W. (2)Mac Nish, Robert (2)Myers, Donald E. (2)Cady, Ralph. (1)Davis, Donald R. (1)View MoreTypes
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Multiscale anaylses of permeability in porous and fractured media

Hyun, Yunjung. (The University of Arizona., 2002)

It has been shown by Neuman [1990], Di Federico and Neuman [1997, 1998a,b] and Di Federico et al. [1999] that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework, which views hydraulic conductivity as a random fractal characterized by a power variogram. Any such random fractal field is statistically nonhomogeneous but possesses homogeneous spatial increments. When the field is statistically isotropic, it is associated with a power variogram γ(s) = Cs²ᴴ where C is a constant, s is separation distance, and If is a Hurst coefficient (0 < H< 1). If the field is Gaussian it constitutes fractional Brownian motion (fBm). The authors have shown that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian vario grams of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale. Low- and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. In this dissertation, I investigate the effects of domain and support scales on the multiscale properties of random fractal fields characterized by a power variogram using real and synthetic data. Neuman [1994] and Di Federico and Neuman [1997] have concluded empirically, on the basis of hydraulic conductivity data from many sites, that a finite window of length-scale L filters out (truncates) all modes having integral scales λ larger than λ = μL where μ ≃ 1/3. I confii in their finding computationally by generating truncated fBm realizations on a large grid, using various initial values of μ, and demonstrating that μ ≃ 1/3 for windows smaller than the original grid. My synthetic experiments also show that generating an fl3m realization on a finite grid using a truncated power variogram yields sample variograms that are more consistent with theory than those obtained when the realization is generated using a power variogram. Interpreting sample data from such a realization using wavelet analysis yields more reliable estimates of the Hurst coefficient than those obtained when one employs variogram analysis. Di Federico et al. [1997] developed expressions for the equivalent hydraulic conductivity of a box-shaped support volume, embedded in a log-hydraulic conductivity field characterized by a power variogram, under the action of a mean uniform hydraulic gradient. I demonstrate that their expression and empirically derived value of μ ≃ 1/3 are consistent with a pronounced permeability scale effect observed in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. I then investigate the compatibility of single-hole air permeability data, obtained at the ALRS on a nominal support scale of about 1 m, with various scaling models including fBm, fGn (fractional Gaussian noise), fLm (fractional Lévy motion), bfLm (bounded fractional Lévy motion) and UM (Universal Multifractals). I find that the data have a Lévy-like distribution at small lags but become Gaussian as the lag increases (corresponding to bfLm). Though this implies multiple scaling, it is not consistent with the UM model, which considers a unique distribution. If one nevertheless applies a UM model to the data, one obtains a very small codimension which suggests that multiple scaling is of minor consequence (applying the UM model to permeability rather than log-permeability data yields a larger codimension but is otherwise not consistent with these data). Variogram and resealed range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Resealed range analysis shows that the data are not compatible with an fGn model. I conclude that the data are represented most closely by a truncated fBm model.

An adaptive multi-dimensional Eulerian-Lagrangian finite element method for simulating advection-dispersion.

Cady, Ralph. (The University of Arizona., 1989)

Advection-dispersion is generally solved numerically with methods that treat the problem from one of three perspectives. These are described as the Eulerian reference, the Lagrangian reference or a combination of the two that will be referred to as Eulerian-Lagrangian. Methods that use the Eulerian-Lagrangian approach incorporate the computational power of the Lagrangian treatment of advection with the simplicity of the fixed Eulerian grid. A modified version of a relatively new adaptive Eulerian-Lagrangian finite element method is presented for the simulation of advection-dispersion. Advection is solved by an adaptive technique that automatically chooses a local solution technique based upon a criterion involving the spatial variation of the gradient of the concentration. Moving particles (the method of characteristics; MOC) are used to define the concentration field in areas with significant variation of the concentration gradient. A modified method of characteristics (MMOC) called single-step reverse particle tracking is used to treat advection in areas with fairly uniform concentration gradients. As the simulation proceeds, the adaptive technique, as needed to maintain solution accuracy and optimal simulation efficiency, adjusts the advection solution process by inserting and deleting moving particles to shift between MMOC and MOC. Dispersion is simulated by a finite element formulation that involves only symmetric and diagonal matrices. Despite evidence from other investigators that diagonalization of the mass matrix may lead to poor solutions to advection-dispersion problems, this method seems to allow "lumping" of the mass matrix by essentially decoupling advection and dispersion. Based on tests of problems with analytical solutions, the method seems capable of reliably simulating the entire range of Peclet numbers with Courant numbers that range to 15.

New taxonomy of clastic sedimentary structures and a procedure for its use in the simulation of groundwater flow

Mock, Peter Allen. (The University of Arizona., 1997)

This work describes a new taxonomy for elastic, sedimentary porous media. The taxonomy is synthesized for the investigation and characterization of ground-water flow from accumulating developments in the genetic analysis of elastic, sedimentary depositional structures. Genetic analysis recognizes spatial associations of elastic, sedimentary structures imposed during genesis. The taxonomy is a nested hierarchy of discrete elastic, sedimentary structures distinguished by the bounding surfaces created during their emplacement and rearrangement. The investigation and characterization of a specific ground-water flow system in elastic, sedimentary porous media can be improved by imposing a structural context on lithologie observations, geophysical measurements, head measurements, and hydraulic conductivity estimates. Globally-valid and transferable descriptions of structures in the taxonomy from modern exposures, outcrops, and densely sampled subsurface systems are modified to fit site-specific geologic observations and measurements. A specific procedure is developed for applying the taxonomy in the investigation and analysis of ground-water flow. The procedure quantitatively measures the hydraulic validity of alternative geologic interpretations of site-specific data under the taxonomy. The application of the taxonomy and procedure to a typical set of data types, densities, and quality is illustrated with data from a site of ground-water contamination investigation.

The hydro-mechanics of the ground water system in the southern portion of the Kaibab Plateau, Arizona

Huntoon, Peter W. (The University of Arizona., 1970)

The elevated Kaibab plateau in northern Arizona has an area of 88 0 square miles and lies adjacent to the Grand Canyon of the Colorado river. It is composed of a sequence of lithified Paleozoic rocks that are approximately 4000 feet thick and consist of marine sediments that contain very little permeability. The ground water system of the plateau has two principal components: 1) circulation through unfractured stratified rocks that range up to a few tens of miles wide and 2) fault controlled drains. In unfractured zones, most of the ground water circulation takes place in the upper 900 feet of the section. The water drains laterally through these rocks toward fault zones or seep faces along the canyon walls. Approximately 40 percent of the plateau surface (330 square miles) drains to canyon seeps. Fault zones provide laterally and vertically continuous large capacity conduits through the plateau. These function as drains for the ground water system as well as floodways for storm pulses that enter the faults directly from the surface. Fracturing has controlled the development of extensive karst networks in limestones that lie near the base of the Paleozoic section. These systems drain to 10 groups of karst springs that discharge an average of approximately 100 cubic feet of water per second. The karst springs drain approximately 60 percent of the plateau surface (550 square miles). The springs in Tapeats amphitheater on the west side of the plateau discharge from the extensive West Kaibab fault zone and account for approximately 70 percent of the measurable water leaving the plateau. This group of three springs drains about 40 percent of the plateau surface (380 square miles). Development of ground water supplies does not appear to be economically tenable in the unfractured portions of the plateau because the permeabilities of the rocks are very small and the depth to the small quantities of available water exceed 500 feet. Production from the large fault controlled drainage networks is equally unattractive. Although the occurrence of water is certain, the large supplies are more than 2800 feet below the land surface and exist in finite channels along the fault zones. These would be difficult to penetrate with conventional drilling methods.

A farm package for MODFLOW-2000 : simulation of irrigation demand and conjunctively managed surface-water and ground-water supply

Schmid, Wolfgang. (The University of Arizona., 2004)

A new Farm Package (FMP) was developed for using the U.S. Geological Survey's groundwater modeling program, MODFLOW-2000 (MF2K), to estimate irrigation water allocations to irrigation settings. The FMP dynamically integrates irrigation water demand, surface-water & groundwater supply, and return flow from excess irrigation. Routed surface-water delivery is optional, and can be simulated by coupling FMP with the Streamflow Routing Package (SFR1). MF2K with FMP and SFR1 allows estimating the allocation of surface-water and groundwater to farms for the following applications: (1) historic and future simulations, (2) water rights issues and operational decisions, (3) non-drought and drought situations. Irrigation demand, supply, and return flow are partly subject to head-dependent sinks and sources such as transpiration uptake from groundwater (formulated by FMP) and leakage between the conveyance system and the aquifer (formulated by SFR1). A steady state transpiration uptake, varying with changing water level, is stepwise linearly approximated by FMP. This was validated by ensembles of variably saturated soil column models using HYDRUS2D for different soil types, values of potential transpiration, and root zone depths. A restriction of transpiration uptake is proportional to a reduction of the active root zone. It is approximated in FMP by an analytical solution, which determines inactive ranges of the root zone with pressure heads typical for conditions of anoxia or wilting. At steady state, the transpiration uptake equaled the flux across the water table (plus the irrigation flux, if applied). Therefore, changes in soil water storage are assumed negligible. Based on this assumption, the irrigation flux required is determined in FMP by subtracting transpiratory components from natural sources (groundwater, precipitation) from a maximum transpiration uptake. This transpiratory irrigation requirement is calculated for each finite difference cell, and increased sufficiently to compensate for evaporative losses and for inefficient use. Accumulating the resulting cell delivery requirement over all cells in a farm yields the total farm delivery requirement, which is to be satisfied with surface- or groundwater. Five economic and non-economic drought response policies can be applied, if the potential supply of surface- and groundwater is insufficient to meet the crop demand. The code was verified by a hypothetical example problem run in 55 scenarios (5 drought policy scenarios x 11 parameter-group scenarios). Among all sources and sinks in a cumulative volumetric budget, 'farm well discharge,' and particularly 'farm net recharge,' were most sensitive to changes in drought policies or changes of parameters.

Estimating bank storage and evapotranspiration using soil physical and hydrological techniques in a gaining reach of the San Pedro River, Arizona

Whitaker, Martha Patricia Lee. (The University of Arizona., 2000)

Bank storage is defined as a volume of water that periodically infiltrates a river's banks during increases in stream stage. It is a potentially critical variable for accurately modeling the water budget in semi-arid riparian systems, but is particularly difficult to assess and quantify. It is especially essential for understanding ground-water/surface-water interactions. In collaboration with other projects, a field-scale vadose monitoring effort took place in the San Pedro Riparian National Conservation Area (SPRNCA), Arizona. The San Pedro River flows north from Mexico into the United States, and SPRNCA is a 60 km stretch of U.S.-protected ecosystem north of the border. In addition to a progressive climate of ecological conservation, hydrological research that leads to an improved understanding of the water budget will ultimately improve the prospects for improved water policy decisions. Soil moisture, stream stage, and soil tension data were collected for over 8 consecutive months in both 1997 and 1998, and the data were used as input into a software program called HYDRUS-2D (§imiinek et al. 1996), which models two-dimensional, variably saturated flow. Field-collected data and subsequent modeling efforts suggest that the effects of bank storage were estimated to contribute approximately 8.5% of the river's total flow for 147 days in 1997. Accordingly, bank storage and its effects should be considered in future water-balance simulations of stream-aquifer interaction, and of the San Pedro River in particular. In addition, model estimates of root water uptake match favorably with other estimates of evapotranspiration in the cottonwood-willow forest gallery of the SPRNCA.

Numerical inverse interpretation of pneumatic tests in unsaturated fractured tuffs at the Apache Leap Research Site

Vesselinov, Velimir Valentinov. (The University of Arizona., 2000)

A three-dimensional stochastic numerical inverse model has been developed for characterizing the properties of unsaturated fractured medium through analysis of singleand cross-hole pneumatic tests. Over 270 single-hole [Guzman et al., 1996] and 44 cross-hole pneumatic tests [Illman et al., 1998; Inman, 1999] were conducted in 16 shallow vertical and slanted boreholes in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS), Arizona. The single-hole tests were interpreted through steady-state [Guzman et al., 1996] and transient [Illman and Neuman, 2000b] analytical methods. The cross-hole tests were interpreted by analytical type-curves [Illman and Neuman, 2000a]. I describe a geostatistical analysis of the steady-state single-hole data, and numerical inversion of transient single-hole and cross-hole data. The geostatistical analysis of single-hole steady-state data yields information about the spatial structure of air permeabilities on a nominal scale of 1 m. The numerical inverse analysis of transient pneumatic test data is based on the assumption of isothermal single-phase airflow through a locally isotropic, uniform or non-uniform continuum. The stochastic inverse model is based on the geostatistical pilot point method of parameterization [de Marsily, 1978], coupled with a maximum likelihood definition of the inverse problem [Carrera and Neuman, 1986a]. The model combines a finite-volume flow simulator, FEHM [Zyvoloski et al., 1997], an automatic mesh generator, X3D [Trease et al., 1996], a parallelized version of an automatic parameter estimator, PEST [Doherty et al., 1994], and a geostatistical code, GSTAT [Pebesma and Wesseling, 1998]. The model accounts directly for the ability of all borehole intervals to store and conduct air through the system; solves the airflow equations in their original nonlinear form accounting for the dependence of air compressibility on absolute air pressure; can, in principle, account for atmospheric pressure fluctuations at the soil surface; provides kriged estimates of spatial variations in air permeability and air-filled porosity throughout the tested fractured rock volume; and is applied simultaneously to pressure data from multiple borehole intervals as well as to multiple cross-hole tests. The latter amounts to three-dimensional stochastic imaging, or pneumatic tomography, of the rock as proposed by Neuman [1987] in connection with cross-hole hydraulic tests in fractured crystalline rocks near Oracle, Arizona. The model is run in parallel on a supercomputer using 32 processors. Numerical inversion of single-hole pneumatic tests allows interpreting multiple injection-step and recovery data simultaneously, and yields information about air permeability, air-filled porosity, and dimensionless borehole storage coefficient. Some of this cannot be accomplished with type-curves [Inman and Neuman, 2000b]. Air permeability values obtained by my inverse method agree well with those obtained by steady-state and type-curve analyses. Both stochastic inverse analysis of cross-hole data and geostatistical analysis of single-hole data, yield similar geometric mean and similar spatial pattern of air permeability. However, I observe a scale effect in both air permeability and air-filled porosity when I analyze cross-hole pressure records from individual monitoring intervals one by one, while treating the medium as being uniform; both pneumatic parameters have a geometric mean that is larger, and a variance that is smaller, than those obtained by simultaneous stochastic analysis of multiple pressure records. Overall, my analysis suggests that (a) pneumatic pressure behavior of unsaturated fractured tuffs at the ALRS can be interpreted by treating the rock as a continuum on scales ranging from meters to tens of meters; (b) this continuum is representative primarily of interconnected fractures; (c) its pneumatic properties nevertheless correlate poorly with fracture density; and (d) air permeability and air-filled porosity exhibit multiscale random variations in space.

Recharge characteristics of an effluent dominated stream near Tucson, Arizona

Lacher, Laurel Jane,1964- (The University of Arizona., 1996)

Almost 90% of the treated sewage effluent processed by the two treatment plants serving the greater Tucson area is available for passive recharge through the Santa Cruz River streambed north of Tucson. In the absence of any major disturbance of the effluent channel, the recharge capacity of the streambed materials decreases over time as microbial activity, and possibly suspended sediments settling out of solution, act to clog the surficial sediments under the effluent stream. Effluent stream transmission-loss measurements made over the period from November 1994 to August 1995 provided data used to determine the average vertical hydraulic conductivity of the low-flow channel in the study reach through simulations using the computer model known as KINEROS2. Saturated hydraulic conductivity (KSAT) served as the calibration parameter in the model. The appropriate KSAT value was chosen for each set of field data by matching the observed and simulated downstream hydrographs for the study reach. KSAT values were corrected for viscosity changes resulting from changing average daily surface water temperatures over the study period. Saturated hydraulic conductivity values for the effluent stream channel ranged from a maximum of 37 mm/hr in January, 1995, following several major winter storms, to a minimum of 11 mm/hr in August, 1995, after a nearly six-month interstorm period. The saturated hydraulic conductivity values decay exponentially with time after the last major winter storm. The mathematical model describing this decay may be used to estimate effluent recharge rates under similar future meteorological and climatological conditions.

Prediction of transient flow in random porous media by conditional moments

Tartakovsky, Daniel. (The University of Arizona., 1996)

This dissertation considers the effect of measuring randomly varying local hydraulic conductivity K(x) on one's ability to predict transient flow within bounded domains, driven by random sources, initial head distribution, and boundary functions. The first part of this work extends the steady state nonlocal formalism by Neuman and Orr [1992] in order to obtain the prediction of local hydraulic head h(x, t) and Darcy flux q(x, t) by means of their ensemble moments (c) and (c)conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation which contains a nonlocal in space and time term called a "residual flux". As a result, (c) is nonlocal and non-Darcian so that an effective hydraulic conductivity K(c) does not generally exist. It is shown analytically that, with the exception of several specific cases, the well known requirement of "slow time-space variation" in uniform mean hydraulic gradient is essential for the existence of K(c). In a subsequent chapter, under this assumption, we develop analytical expressions for the effective hydraulic conductivity for flow in a three dimensional, mildly heterogeneous, statistically anisotropic porous medium of both infinite extent and in the presence of randomly prescribed Dirichlet and Neumann boundaries. Of a particular interest is the transient behavior of K(c) and its sensitivity to degree of statistical anisotropy and domain size. In a bounded domain, K(c) (t) decreases rapidly from the arithmetic mean K(A) at t = 0 toward the effective hydraulic conductivity corresponding to steady state flow, K(sr), K(c), exhibits similar behavior as a function of the dimensionless separation distance ρ between boundaries. At ρ = 0, K(c) = K(A) and rapidly decreases towards an asymptotic value obtained earlier for an infinite domain by G. Dagan. Our transient nonlocal formalism in the Laplace space allows us to analyze the impact of other than slow time-variations on the prediction of (c),. Analyzing several functional dependencies of mean hydraulic gradient, we find that this assumption is heavily dependent on the (relaxation) time-scale of the particular problem. Finally, we formally extend our results to strongly heterogeneous porous media by invoking the Landau-Lifshitz conjecture.

Fluid flow and solute transport through three-dimensional networks of variably saturated discrete fractures

Rasmussen, T. C. (The University of Arizona., 1988)

Methodologies for estimating hydraulic and solute transport properties of unsaturated, fractured rock are developed. The methodologies are applied to networks of discrete fractures for the purpose of estimating steady fluid flow rates and breakthrough curves of entrained solutes. The formulations employ the boundary integral method to discretize the outer rim of each fracture and to solve a two dimensional flow equation within fracture planes. A three dimensional variant of the two dimensional boundary integral method is used to calculate flow through a permeable matrix with embedded permeable fractures. Exterior and interior surfaces are discretized using boundary elements to account for flow between fractures and the matrix, and between the matrix and fractures and the exterior boundaries. Synthetic fracture networks are created using planar fractures of finite areal extent embedded within a three dimensional rock matrix for the purpose of performing sensitivity studies of network hydraulic conductivity with respect to geometric parameters, such as fracture orientation and density. Results of the sensitivity studies show that: (1) The global hydraulic conductivity is linearly dependent on the product of fracture transmissivity and density for fractures of which fully penetrate the rock volume; (2) The effect of correlation between fracture length and transmissivity is to increase the global hydraulic conductivity; and (3) Results using a three dimensional coupled fracture— matrix flow regime compare favorably with analytic results. Flow through variably saturated fracture networks is modeled by assuming a constant capillary head within individual fractures. A free surface is found using an iterative procedure which locates nodal points at the intersection of constant total head and pressure head contours. The simulated free surface compares favorably with an approximate analytic solution and with laboratory results. Simulations indicate the presence of zones of water under both positive and negative pressure, as well as regions of air—filled voids. Travel times and breakthrough curves are determined by integrating the inverse velocity over a streamline, and then summing over all streamlines. For the fracture network examined, travel times decrease with decreasing fracture saturation. The effects of retardation and matrix diffusion are also examined.

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