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Quantitative Methods for Reservoir Characterization and Improved Recovery: Application to Heavy Oil Sands

Description: The first twelve months of the project focused on collecting data for characterization and modeling. In addition, data from Coalinga Field was analyzed to define the fractal structure present in the data set. The following sections of the report parallel the first four subtasks of the investigation were: (1) Collect and Load Property Data from Temblor Outcrops in California, (2) Collect and Load Property Data from Temblor Reservoir Sands, West Coalinga Field, California, (3) Collect and Load Property Data from Continuous Upper Cretaceous Outcrops in Utah, and (4) Define Fractal Structure in the Data Sets and Apply to Generating Property Representations.
Date: November 29, 2001
Creator: Castle, James W. & Molz, Fred J.
Partner: UNT Libraries Government Documents Department

Frequency-dependent viscous flow in channels with fractal rough surfaces

Description: The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to {infinity} (but has a finite cutoff), and the universal scaling of the dynamic permeability, k({omega}), needs modification. We performed accurate numerical computations of k({omega}) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k({omega}) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations.
Date: May 1, 2010
Creator: Cortis, A. & Berryman, J.G.
Partner: UNT Libraries Government Documents Department

Characterizing soil preferential flow using iodine--starch staining experiments and the active region model

Description: Thirteen iodine-starch staining experiments with different boundary conditions and measurement scales were conducted at two sites to study preferential flow processes in natural unsaturated soils. Digital imaging analyses were implemented to obtain the corresponding preferential flow patterns. The test results are used to evaluate a recently proposed active region model in terms of its usefulness and robustness for characterizing unsaturated flow processes at field scale. Test results provide useful insights into flow patterns in unsaturated soils. They show that flow pattern depends on the top boundary condition. As the total infiltrating-water depth increased form 20 mm to 80 mm for the 100 x 100 cm{sup 2} plots, the corresponding flow pattern changed from few preferential flow paths associated with a relatively small degree of stained coverage and a small infiltration depth, to a pattern characterized by a higher stained coverage and a larger infiltration depth, and to (finally) a relatively homogeneous flow pattern with few unstained area and a much larger infiltration depth. Test results also show that the preferential flow pattern became generally more heterogeneous and complex for a larger measurement scale (or size of infiltration plot). These observations support the general idea behind the active region model that preferential flow pattern in unsaturated soils are dynamic and depend on water flow conditions. Further analyses of the test results indicate that the active-region model is able to capture the major features of the observed flow pattern at the scale of interest, and the determined parameter values do not significantly depend on the test conditions (initial water content and total amount of infiltrating water) for a given test site. This supports the validity of the active region model that considers that parameter to be a property of the corresponding unsaturated soil. Results also show that some intrinsic relation seems to ...
Date: March 1, 2009
Creator: Sheng, Feng; Wang, Kang; Zhang, Renduo & Liu, Hui-Hai
Partner: UNT Libraries Government Documents Department

Dimensions in Random Constructions.

Description: We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Date: May 2002
Creator: Berlinkov, Artemi
Partner: UNT Libraries

Quantization Dimension for Probability Definitions

Description: The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances have been minimized. In this dissertation we give a short history of quantization as well as some basic facts. We develop a generalized framework for the quantization dimension which extends the current theory to include a wider range of probability measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area could lead to new results in another. It would also be expected that the results in this dissertation would extend to all probabilities for which a quantization dimension function exists. The cases considered here include probabilities generated by conformal iterated function systems (and include self-similar probabilities) and also probabilities generated by graph directed systems, which further generalize the idea of an iterated function system.
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Date: December 2001
Creator: Lindsay, Larry J.
Partner: UNT Libraries

The use of fractally-designed waveforms in electroforming

Description: Pulsed electrodeposition offers the potential for superior control of deposit properties because of the additional control variables available. However, optimization of pulsed deposition processes is a challenge because of the complexity. E.g., the tendency of electroforms to acquire irregularities such as dendritic growths or other morphological instabilities, creates the need for methods to control these undesirable phenomena. One such method is periodic reverse pulses. Optimization of periodic reverse processes is not simple and can lead to local solutions that do not optimize all properties simultaneously. One method for global optimization that might, for example, control surface irregularities on several size scales, uses a periodic reverse design based on fractal time series. This incorporates deplating pulses of several lengths within one self- similar waveform. The properties of fractals permit control of highly complex designs with a small number of input variables. The creation of such waveforms, their properties, and their use in a lead- plating process are described. Speculation on the potential for further application of this method is offered. 26 figs, 11 refs.
Date: March 1, 1996
Creator: Bullock, J.S.; Lawson, R.L. & Kirkpatrick, J.R.
Partner: UNT Libraries Government Documents Department

A macroscopic relationship for preferential flow in the vadose zone: Theory and Validation

Description: Preferential flow commonly observed in unsaturated soils allows rapid movement of solute from the ground surface or vadose zone to the groundwater, bypassing a significant volume of unsaturated soil and increasing the risk of groundwater contamination. A variety of evidence indicates that complex preferential flow patterns observed from fields are fractals. This paper discusses a macroscopic rela-tionship for modeling preferential flow in the vadose zone. Conceptually, the flow domain can be di-vided into active and inactive regions. Flow occurs preferentially in the active region (characterized by fractals), and inactive region is simply bypassed. The portion of the active region was found to be a power function of saturation. The validity of this macroscopic relationship is demonstrated by its consistency with field observations and the related numerical experiments.
Date: February 15, 2010
Creator: Liu, H.H. & Zhang, R.D.
Partner: UNT Libraries Government Documents Department

The effect of resist on the transfer of line-edge roughness spatial metrics from mask to wafer

Description: Mask contributors to line-edge roughness (LER) have recently been shown to be an issue of concern for both the accuracy of current resist evaluation tests as well the ultimate LER requirements for the 22-nm production node. More recently, it has been shown that the power spectral density of the mask-induced roughness, is markedly different than that of intrinsic resist roughness and thus potentially serves as a mechanism for distinguishing mask effects from resist effects in experimental results. Further considering stochastic resist effects, however, demonstrates that such a test would only be viable in cases where the resist effects are completely negligible in terms of their contribution to the total LER compared to the mask effects. The results presented here lead us to the surprising conclusion that it is indeed possible for mask contributors to be the dominant source of LER while the spatial characteristics of the LER remain indistinguishable from the fractal characteristics of resist-induced LER.
Date: May 1, 2009
Creator: Naulleau, Patrick & Gallatin, Gregg
Partner: UNT Libraries Government Documents Department

Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems

Description: In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS). For example, if the IFS is finite and conformal, then the Hausdorff and packing dimensions of the limit sets agree and the corresponding Hausdorff and packing measures are positive and finite. Moreover, the map which takes the IFS to its dimension is continuous. Developing on previous work, we show that the map which takes a finite conformal IFS to the numerical value of its packing measure is continuous. In the context of self-similar sets, we introduce the super separation condition. We then combine this condition with known density theorems to get a better handle on finding balls of maximum density. This allows us to extend the work of others and give exact formulas for the numerical value of packing measure for classes of Cantor sets, Sierpinski N-gons, and Sierpinski simplexes.
Date: August 2017
Creator: Reid, James Edward
Partner: UNT Libraries

Nonlinear extensions of a fractal-multifractal approach for environmental modeling

Description: We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.
Date: October 15, 2008
Creator: Cortis, A.; Puente, C.E. & Sivakumar, B.
Partner: UNT Libraries Government Documents Department

Bells Galore: Oscillations and circle-map dynamics from space-filling fractal functions

Description: The construction of a host of interesting patterns over one and two dimensions, as transformations of multifractal measures via fractal interpolating functions related to simple affine mappings, is reviewed. It is illustrated that, while space-filling fractal functions most commonly yield limiting Gaussian distribution measures (bells), there are also situations (depending on the affine mappings parameters) in which there is no limit. Specifically, the one-dimensional case may result in oscillations between two bells, whereas the two-dimensional case may give rise to unexpected circle map dynamics of an arbitrary number of two-dimensional circular bells. It is also shown that, despite the multitude of bells over two dimensions, whose means dance making regular polygons or stars inscribed on a circle, the iteration of affine maps yields exotic kaleidoscopes that decompose such an oscillatory pattern in a way that is similar to the many cases that converge to a single bell.
Date: October 15, 2008
Creator: Puente, C.E.; Cortis, A. & Sivakumar, B.
Partner: UNT Libraries Government Documents Department

Scale dependency of the effective matrix diffusion coefficient

Description: It has been recognized that matrix diffusion is an important process for retarding solute transport in fractured rock. Based on analyses of tracer transport data from a number of field tests, we demonstrate for the first time that the effective matrix-diffusion coefficient may be scale dependent and generally increases with test scale. A preliminary theoretical explanation of this scale dependency is also presented, based on the hypothesis that solute travel paths within a fracture network are fractals.
Date: May 30, 2003
Creator: Liu, H. H.; Bodvarsson, G. S. & Zhang, G.
Partner: UNT Libraries Government Documents Department

Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids

Description: Using effective medium theory we demonstrate that the thermal conductivity of nanofluids can be significantly enhanced by the aggregation of nanoparticles into clusters. The enhancement is based purely on conduction and does not require a novel mechanism. Predictions of the effective medium theory are in excellent agreement with detailed numerical calculations on model nanofluids involving fractal clusters and show the importance of cluster morphology on thermal conductivity enhancements.
Date: August 10, 2006
Creator: Prasher, R; Evans, W; Fish, J; Meakin, P; Phelan, P & Keblinski, Pawel
Partner: UNT Libraries Government Documents Department

Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Description: In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
Date: May 2005
Creator: Coiculescu, Ion
Partner: UNT Libraries

Small-angle and surface scattering from porous and fractal materials.

Description: We review the basic theoretical methods used to treat small-angle scattering from porous materials, treated as general two-phase systems, and also the basic experimental techniques for carrying out such experiments. We discuss the special forms of the scattering when the materials exhibit mass or surface fractal behavior, and review the results of recent experiments on several types of porous media and also SANS experiments probing the phase behavior of binary fluid mixtures or polymer solutions confined in porous materials. Finally, we discuss the analogous technique of off-specular scattering from surfaces and interfaces which is used to study surface roughness of various kinds.
Date: September 18, 1998
Creator: Sinha, S. K.
Partner: UNT Libraries Government Documents Department

On the geometry of two-dimensional slices of irregular level sets in turbulent flows

Description: Isoscalar surfaces in turbulent flows are found to be more complex than (self-similar) fractals, in both the far field of liquid-phase turbulent jets and in a realization of Rayleigh-Taylor-instability flow. In particular, they exhibit a scale-dependent coverage dimension, D{sub 2}((lambda)), for 2-D slices of scalar level sets, that increases with scale, from unity, at small scales, to 2, at large scales. For the jet flow and Reynolds numbers investigated, the isoscalar-surface geometry is both scalar-threshold- and Re-dependent; the level-set (coverage) length decreases with increasing Re, indicating enhanced mixing with increasing Reynolds number; and the size distribution of closed regions is well described by lognormal statistics at small scales. A similar D{sub 2}((lambda)) behavior is found for level-set data of 3-D density-interface behavior in recent direct numerical-simulation studies of Rayleigh-Taylor-instability flow. A comparison of (spatial) spectral and isoscalar coverage statistics will be disc
Date: March 20, 1998
Creator: Catrakis, H.J.; Cook, A.W.; Dimotakis, P.E. & Patton, J.M.
Partner: UNT Libraries Government Documents Department

Fractal funcitons and multiwavelets

Description: This paper reviews how elements from the theory of fractal functions are employed to construct scaling vectors and multiwavelets. Emphasis is placed on the one-dimensional case, however extensions to IR{sup m} are indicated.
Date: April 1, 1997
Creator: Massopust, P.R.
Partner: UNT Libraries Government Documents Department

Reservoir characterization of Pennsylvanian sandstone reservoirs

Description: The overall objectives of this work are: (i) to investigate the importance of various qualities and quantities of data on the optimization of water flooding performance; and (ii) to study the application of newly developed, geostatistical techniques to analyze available production data to predict future prospects of infill drilling. Specifically to satisfy our first objective, we will study the feasibility of applying fractal geometry concepts to characterize individual formations; develop a three-dimensional conditional simulation program to define reservoir properties at various scales; establish a method to integrate the data collected at various scales including the well test and the core data; and to investigate the utility of outcrop data in describing subsurface reservoir details. To satisfy the second objective, we will investigate various techniques to utilize the production data, including initial potential and the production decline, in proposing a possible location for a future infill well. The techniques investigated will include geostatistical analyses. The study will be restricted to Pennsylvanian sandstones reservoirs commonly found in Oklahoma.
Date: March 1, 1995
Creator: Kelkar, B.G.
Partner: UNT Libraries Government Documents Department

Multifractal analysis and modeling of one- and two-dimensional data with discrete wavelet transforms, isotropic or not

Description: The authors compare several ways of uncovering multifractal properties of data in 1D and 2D using wavelet transforms. The WTMM or (Continuous) Wavelet Transform Maximum Modulus method has been extensively documented and widely applied by Dr. Alain Arneodo`s (Bordeaux) group, to the point where their successes have overshadowed simpler techniques that use the Discrete WT. What the latter lack in robustness is gained in efficiency, thus enabling virtually real-time multifractal analysis of data as it is collected. Another advantage of DWT-based approaches is that tensor products of dyadic and triadic branching schemes enable a straightforward attack on strong anisotropy in natural and artificial 2D random fields.
Date: December 1998
Creator: Davis, A. B.
Partner: UNT Libraries Government Documents Department

Fractal Analysis of Fracture Systems: Topical report, September 3, 1996

Description: A fractal analysis of outcrop fracture patterns was undertaken in the Valley and Ridge study area. Use of pavement style investigations such as those conducted by Barton and Hsieh (1989) was not a feasible form of analysis in either Appalachian study areas. Large exposures of bedding plane surfaces are limited, particularly at the Plateau site; hence, fracture studies were concentrated in the Middle and Elkhorn Mountain areas of the Valley and Ridge. The area is complexly deformed, which presented difficulty in the design of a controlled experiment. While bedding plane exposures were found, it was not possible to find comparable exposures of the same lithologic unit in the different structural areas represented at the site. In such instances, therefore, lithologic factors could not be separated from structural factors in the interpretation of variations in fractal dimension. Comparisons of fractal behavior in a common lithologic interval were possible to some extent using one-dimensional analysis of bed-normal fracture plane intersections. However, even in this case, the distribution of exposure was the limiting factor.
Date: December 31, 1997
Creator: Wilson, T.
Partner: UNT Libraries Government Documents Department

Frontier orbital symmetry control of intermolecular electron transfer. Final report, September 15, 1988--December 31, 1994

Description: This report discusses the following topics: the recovery of intermolecular transfer parameters from fluorescence quenching in liquids; photoinduced intramolecular electron transfer in flexible donor/space/acceptor systems containing an extended unsaturated spacer; electron transfer sensitized reaction; the recovery of solute and fractal dimensions from electron transfer quenching data; and frontier orbital symmetry control of back electron transfer.
Date: July 1, 1997
Creator: Stevens, B.
Partner: UNT Libraries Government Documents Department

Fractal Approach in Petrology: Combining Ultra-Small Angle (USANA) and Small Angle Neutron Scattering (SANS)

Description: Ultra small angle neutron scattering instruments have recently covered the gap between the size resolution available with conventional intermediate angle neutron scattering and small angle neutron scattering instruments on one side and optical microscopy on the other side. Rocks showing fractal behavior in over two decades of momentum transfer and seven orders of magnitude of intensity are examined and fractal parameters are extracted from the combined USANS and SANS curves.
Date: October 14, 1999
Creator: LoCelso, F.; Triolo, F.; Triolo, A.; Lin, J.S.; Lucido, G. & Triolo, R.
Partner: UNT Libraries Government Documents Department