The purpose of this investigation was to test the existing methods of correlating pipe-line data on dilatant fluids in a laminar flow, to gather pertinent physical properties of dilatant fluids, and to propose a theory for the mechanism of dilatancy. In order that the correlation for flow of dilatant fluids in conduits could be tested it was necessary to build a flow apparatus from which pressure drops and flow rates could be measured, to develop viscometric equipment such that flow curves could be determined at shearing conditions similar to those in the flow tests, and to uae the data from the two sources to calculate the variables of interest: the friction factor, f, and the modified Reynolds number, R'_e. A flow apparatus suitable for the purpose outlined was constructed from 1-1/4 inch, Schedule 40 galvanized pipe with motive power provided by a Moyno pump, was provided with temperature control and calming sections, and was provided with a ten foot test section. Flow curves were determined independently with a specially constructed cone and plate viscometer. Provisions were made to determine pressure drop over the fittings: coupling, glove valve, and 90 degree elbow. Dilatant fluids consisting of corn starch suspended in the liquids water, ethylene glycol, and glycerine with values of flow behavior index, n from 1.15-2.50 flowing in laminar flow between R’_e of 12-410 were studied. Results of the investigation showed that the Metzner-Reed correlation method could be used in correlating dilatant, laminar flow. Equivalent resistances of fittings, expressed as equivalent diameters of pipe, were found not to match those found in the literature for Newtonian fluids, except that for the case of couplings the value was negligible for both fluid types. Rather, much lower values were found for the case of flow through a globe valve, and the value found for the 90 degree elbow was strongly dependent on the flow rate. A cone and plate viscometer was used to study the dependency of the Power Law parameters on temperature for a starch suspension in glycerine and ethylene glycol. The parameter n was found to be independent of temperature over the 80-130° F range of temperature studied. Conversely, K varied with temperature in a manner described by an Arrhenius equation and its rate of change with temperature roughly paralleled that of the glycerine. A theory of the basic mechanism responsible for the phenomenon of dilatancy was presented and discussed, and its relation to the Power Law Model established. / Ph. D.

This dissertation develops an analytical-numerical approach to deterministically predict the space-time evolution of concentrations in heterogeneous geologic media conditioned on measurements of hydraulic conductivities (transmissivities) and/or hydraulic heads. Based on the new conditional Eulerian-Lagrangian transport theory by Neuman, we solve the conditional transport problem analytically at early time, and express it in pseudo-Fickian form at late time. The stochastically derived deterministic pseudo-Fickian mean concentration equation involves a conditional, space-time dependent dispersion tensor. The latter not only depends on properties of the medium and the velocity but also on the available information, and can be evaluated numerically along mean "particle" trajectories. The transport equation lends itself to accurate solution by standard Galerkin finite elements on a relatively coarse grid. This approach allows computing without using Monte Carlo simulation and explicitly the following: Concentration variance/covariance (uncertainty), origin of detected contaminant and associated uncertainty, mass flow rate across a "compliance surface", cumulative mass release and travel time probability distribution across this surface, uncertainty associated with the latter, second spatial moment of conditional mean plume about its center of mass, conditional mean second spatial moment of actual plume about its center of mass, conditional co-variance of plume center of mass, and effect of non-Gaussian velocity distribution. This approach can also account for uncertainty in initial mass and/or concentration when predicting the future evolution of a plume, whereas almost all existing stochastic models of solute transport assume the initial state to be known with certainty. We illustrate this approach by considering deterministic and uncertain instantaneous point and nonpoint sources in a two-dimensional domain with a mildly fluctuating, statistically homogeneous, lognormal transmissivity field. We take the unconditional mean velocity to be uniform, but allow conditioning on log transmissivity and hydraulic head data. Conditioning renders the velocity field statistically nonhomogeneous with reduced variances and correlation scales, renders the predicted plume irregular and non-Gaussian, and generally reduces both predictive dispersion and uncertainty.

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.

No description available.

Variabilities of hydraulic and solute transport properties of soil are examined at three scales: pore-scale, sample volume-scale, and field-scale. Undisturbed soil cores were taken at 19 subsites spaced logarithmically along a 150 m line transect in a Groseclose mapping unit near Blacksburg; Virginia. Three core sizes were taken at each subsite at the soil surface and 0.5 m depth. 'Small' cores were-40x54 mm; 'medium' cores were 60X100 mm; and 'large' cores were 100x150 mm. Macropore effects on solute transport were evaluated using monocontinuum and bicontinuum models. Bicontinuum-predicted solute breakthrough curves (BTC) closely agreed with observed BTC data with mean errors of reduced concentrations </- 0.05 for 97% of the samples, Monocontinuum predicted BTC's had comparable fits with 80% of the samples having mean errors </- 0.07. The simpler monocontinuum model was chosen for estimating dispersion coefficients for all samples on the basis that seven percent error in concentration is acceptable for the purpose of making field predictions in light of high spatial variability. Sample volume did not significantly affect the low variation (coefficients of variation, (CV) of 7-20%) soil properties bulk density or moisture retention characteristics in Ap or Bt horizons. Large cores are recommended for assessing high variation (CV of 60-280%) fluid transport parameters, saturated hydraulic conductivity (Ks), pore water velocity and dispersion coefficients (D) since they yielded less variance than the smaller cores. Ranges of about 25 m were determined for log-transformed Ks and D from semivariograms. Monte Carlo simulations were used to predict field-average BTC's. / Master of Science

[Truncated abstract] To date, many subsurface contaminant modelling studies have focused on increasing model complexity and measurement requirements to improve model accuracy and widen model application. However, due to the highly complex and heterogeneous nature of flow in the subsurface, the greater benefit in model development may lie in decreasing complexity by identifying key processes and parameters, simplifying the relationships that exist between them, and incorporating these relationships into simple models that recognise or quantify the inherent complexity and uncertainty. To address this need, this study aims to identify and isolate the key processes and parameters that control dense nonaqueous phase liquid (DNAPL) and aqueous phase migration through single, onedimensional fractures. This is a theoretical representation which allows the study of processes through conceptual and mathematical models. Fracture systems typically consist of multiple two-dimensional fractures in a three-dimensional network; however, these systems are computationally and conceptually demanding to investigate and were outside of the scope of this study. This work initially focuses on DNAPL migration in single, one-dimensional fractures. The similitude techniques of dimensional and inspectional analysis are performed to simplify the system and to develop breakthrough time scale factors. This approach relies heavily on the limitations of the equation used for the analysis and on the difficulty in representing variable aperture scenarios. The complexity of the conceptual model is then increased by embedding the fracture in a two-dimensional, porous matrix. ... These tools can be readily applied by the field investigator or computer modeller to make order-of-magnitude estimates of breakthrough times, reduce or target measurement requirements, and lessen the need to employ numerical multiphase flow models. To determine the implications of the results found in the one-dimensional studies to applications at the field scale, the complexity of the conceptual model was increased to a single, two-dimensional, planar fracture embedded in a three-dimensional porous matrix. The focus of this study was not DNAPL breakthrough times but the relative importance and interaction of different mass transport processes and parameters on plume migration and evolution. Observations clearly show that estimates of the size, location and concentration of the plume is highly dependent on the geologic media, the temporal and spatial location and resolution of measurements, and on the history, mass and location of the DNAPL source. In addition, the processes controlling mass transport (especially matrix diffusion and back diffusion) act in combination at the field scale in ways not always expected from an analysis of processes acting individually at smaller spatial and temporal scales. Serious concerns over the application of the common '1% Rule of Thumb' to predict DNAPL presence and the use of remediation efforts that rely largely on natural attenuation are raised. These findings have major implications for the field worker and computer modeller, and any characterisation, monitoring or remediation program development needs to be sensitive to these findings.