Browsing by Subject "Propagation"
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Item Bispectral analysis of nonlinear acoustic propagation(2011-05) Gagnon, David Edward; Hamilton, Mark F.; Wochner, Mark S.Higher-order spectral analysis of acoustical waveforms can provide phase information that is not retained in calculations of power spectral density. In the propagation of high intensity sound, nonlinearity can cause substantial changes in the waveform as frequency components interact with one another. The bispectrum, which is one order higher than power spectral density, may provide a useful measure of nonlinearity in propagation by highlighting spectral regions of interaction. This thesis provides a review of the bispectrum, places it in the context of nonlinear acoustic propagation, and presents spectra calculated as a function of distance for numerically propagated acoustic waveforms. The calculated spectra include power spectral density, quad-spectral density, bispectrum, spatial derivative of the bispectrum, bicoherence, and skewness function.Item Experimental investigation of geomechanical aspects of hydraulic fracturing unconventional formations(2014-08) Alabbad, Emad Abbad; Olson, Jon E.Understanding the mechanisms that govern hydraulic fracturing applications in unconventional formations, such as gas-bearing shales, is of increasing interest to the petroleum upstream industry. Among such mechanisms, the geomechanical interactions between hydraulic fractures and pre-existing fractures on one hand, and simultaneous multiple hydraulic fractures on the other hand are seen of high importance. Although the petroleum engineering and related literature contains a number of studies that discusses such topics of hydraulic fracture interactions, there still remain some aspects that require answers, validations, or further supporting data. Particularly, experimental evidence is fairly scarce and keenly needed to solidify the understanding of such complex applications. In this work, the investigation methodology uses a series of hydraulic fracturing laboratory tests performed on synthetic rocks made of gypsum-based cements such as hydrostone and plaster in various experimental set ups. Those laboratory tests aim to closely investigate hydraulic fracture intersection with pre-existing fractures by assessing some factors that govern its outcomes. Specifically, the roles of the pre-existing fracture cementation, aperture, and relative height on the intersection mode are examined. The results show dominant effect of the cement-fill type relative to the host-rock matrix in determining whether hydraulic fracture crossing the pre-existing interface may occur. Similarly, hydraulic fracture height relative to the height of the pre-existing fracture may dictate the intersection results. However, the intersection mode seems to be insensitive of the pre-existing fracture aperture. Moreover, simultaneous multi-fracture propagation is examined and found to be impacted by the interference of the stresses induced from each fracturing source on neighboring fracturing sources. Such stress interference increases as the number of the propagating hydraulic fractures increase. While hydraulic fractures initiating from fracturing sources located in the middle of the fracturing stage seem to have inhibited propagation, outer hydraulic fractures may continue propagating with outward curvatures. Overall, the experimental results and analyses offer more insights for understanding hydraulic fracture complexity in unconventional formations.Item A general poro-elastic model for pad-scale fracturing of horizontal wells(2015-12) Manchanda, Ripudaman; Sharma, Mukul M.; Espinoza, David N; McClure, Mark W; Olson, Jon E; Roussel, Nicolas PEconomic production of oil and gas from tight rocks requires horizontal well drilling with multiple hydraulic fractures along the length of the horizontal wells. Multiple horizontal wells are drilled and fractured close to each other to increase the recovery of oil and gas from a single location or pad. Interference between fractures in a horizontal well pad is commonly observed in the field. There is no clear understanding of the impact of various operational and reservoir parameters on the observed interference. This inter-well interference can occur through the creation of complex fracture networks and/or poro-elastic stress changes. In this research, the development of a poro-elastic numerical simulator was undertaken to evaluate hydraulic fracturing practices in pad-scale scenarios. The primary motivation was to assess the impact of various operational parameters such as fracture spacing, well spacing and fracture sequencing on the geometry of the created fractures. Two approaches were used to understand the problem at hand. In the first approach, static fractures were simulated in 3-D and the impact of their stress shadow on subsequent fractures was studied. It was observed that fracture spacing, injection volume, and time between successive fractures were the most important parameters that could be used to optimize the creation of fractures in a well. Formation properties such as Young’s modulus and horizontal stress contrast modified the magnitude and spatial extent of the stress shadow and the extent of stress reorientation. It was shown that stage spacing, well spacing and fracture sequencing together with fracture designs (volume of sand pumped and fluids used) can be adjusted to obtain non-intersecting, transverse fractures that efficiently drain the reservoir. A hypothesis, time dependent closure of induced unpropped fractures, was presented to explain why zipper fracturing often outperforms conventional sequential fracturing. The hypothesis was tested and confirmed with a field data set made available to us by Shell from the Eagle Ford shale. In the second approach, a novel finite volume based 3-D, geomechanical, field-scale numerical simulator was developed to simulate propagation of multiple fractures simultaneously in a poro-elastic reservoir. This provided a more realistic model of the pad-scale fracturing process. The ability of the model to perform realistic pad-scale simulations was demonstrated for a variety of field situations such as multi-cluster multi-stage fracturing, infill-well fracturing, re-fracturing, mini-frac analysis and fracture network simulations. The inclusion of poro-elastic effects and reservoir heterogeneity in the model allowed us to examine the effects of reservoir depletion on fracture geometry in refraced and infill wells.Item Mittag-Leffler moments and weighted L∞ estimates for solutions to the Boltzmann equation for hard potentials without cutoff(2016-05) Tasković, Maja; Martínez Gamba, Irene, 1957-; Pavlović, Nataša; Caffarelli, Luis A.; Chen, Thomas; Figalli, Alessio; Morrison, Philip J.; Vasseur, Alexis F.In this thesis we study analytic properties of solutions to the spatially homogeneous Boltzmann equation for collision kernels corresponding to hard potentials without the angular cutoff assumption, i.e. the angular part of the kernel is non-integrable with prescribed singularity rate. We study behavior in time of such solutions for large velocities i.e. their tails. We do this in two settings - L¹ and L∞. In the L¹ setting, we study Mittag-Leffler moments of solutions of the Cauchy problem under consideration. These moments, obtained by integrating the solution against a Mittag-Leffler function, are a generalization of exponential moments since Mittag-Leffler functions asymptotically behave like exponential functions. Mittag-Leffler moments can be also represented as infinite sums of renormalized polynomial moments. However, instead of considering renormaliztion by integer factorials that would lead to classical exponential moments, we renormalize by Gamma functions with non-integer arguments. By analyzing the convergence of partial sums sequences of these infinite sums, we prove the propagation and generation in time of Mittag-Leffler moments. In the case of propagation, orders of these moments depend on the singularity rate of the angular collision kernel. In the case of generation, the orders depend on the potential rate of the kernel. The proof uses a subtle combination of angular averaging and angular singularity cancellation, to show that partial sums satisfy an ordinary differential inequality with a negative term of the highest order while controlling all positive terms, whose solutions are uniformly bounded in time and number of terms. These techniques apply to both generation and propagation of Mittag-Leffler moments, with some variations depending on the case. In the L∞ setting, we prove that solutions to the Boltzmann equation that satisfy propagation in time of weightedL¹ bounds also satisfy propagation in time of weighted L∞ bounds. To emphasize that the propagation in time of weighted L∞ bounds relies on the propagation in time of weighted L¹ bounds, we express our main result using certain general weights. Consequently we apply the main result to cases of exponential and Mittag-Leffler weights, for which propagation in time of weighted L¹ bounds holds. Hence we obtain propagation in time of exponentially or Mittag-Leffler weighted L∞ bounds on the solution.Item Propagation success of grapevines (Vitis vinifera L.) infected with Xylella fastidiosa(2009-05) Krawitzky, Michael; Montague, David T.; Hellman, Edward H.; Woodward, Jason E.; Appel, DavidPierce's disease of grapes, caused by the xylem-limited bacterium Xylella fastidiosa Wells, is typically fatal to varieties of Vitis vinifera L. The objective of this study was to investigate rooting success of asexually propagated cuttings taken from X. fastidiosa infected grapevines and determine if rooted cuttings could survive and produce viable plants for vineyard establishment. Cuttings were taken January 2008 from dormant V. vinifera cv. Merlot and cv. Cabernet Sauvignon grapevines located in the Hill Country and Gulf Coast regions of Central Texas. Prior to our research, symptoms of Pierce's disease were recorded on each grapevine in each vineyard using a Symptomatic Reliability Index. At the conclusion of six weeks, cuttings were uprooted and evaluated. Rooting percentage, number of roots, root length, root rating, number of shoots, and shoot length, were recorded for each cutting. Rooting data indicates symptomatic and asymptomatic X. fastidiosa infected grapevines have the ability to be propagated asexually through cuttings. To confirm the presence of X. fastidiosa, rooted cuttings were tested with Enzyme-Linked ImmunoSorbent Assay and Real-time Polymerase Chain Reaction. Results revealed several asymptomatic and symptomatic cuttings positive for X. fastidiosa. This experiment demonstrated grapevine cuttings infected with X. fastidiosa can be propagated to produce healthy looking nursery plants that could be sold as clean nursery stock.Item Simulating refracturing treatments that employ diverting agents on horizontal wells(2013-08) Bryant, Stephen Andrew; Sharma, Mukul M.The use of hydraulic fracturing has increased rapidly and is now a necessary technique for the development of shale oil and gas resources. However, production rates from these plays typically exhibit high levels of decline. After one year, rates often decrease by over fifty percent. Refracturing – the process of hydraulically fracturing a well that has previously been fractured – is a proposed technique designed to offset these high decline rates and provide a sustainable increase in production. Benefits from refracturing can occur due to a variety of reasons, including the extension of fracture length, the increase in fracture conductivity or the reorientation of the fracture into new areas of the reservoir. In this thesis, the simulation of refracturing treatments on horizontal wells with the use of a diverting agent is described. Diverting agents are used to distribute flow more evenly along the wellbore and to replace the use of costly downhole equipment employed to isolate sections of the wellbore. When diverting agent is deposited, a cake forms with an associated permeability. Flow is diverted from the fractures with high amounts of diverting agent because the larger cake results in a greater resistance to flow. The diverting agent cake breaks down with time at reservoir temperature so that production is uninhibited. Two different models are used to account for the application of diverting agent. One assumes the diverting agent cake forms in the perforation tunnel and the other assumes it forms in the fracture. The propagation of competing fractures is calculated using a computer code developed at the University of Texas called UTWID. In both models, the simulations showed successful diversion of flow. Previously understimulated fractures – that is, shorter fractures or fractures that would grow less preferentially under normal fracturing treatments – grew at a faster pace after pumping of the diverting agent. A sensitivity analysis was conducted on several of the key refracturing design parameters, and the interdependence of the parameters was demonstrated. The simulations support the concept that diverting agents can be used to more evenly stimulate the entire length of the lateral.Item Simulation of Hydraulic Fractures and their Interactions with Natural Fractures(2012-10-19) Sesetty, VarahanareshModeling the stimulated reservoir volume during hydraulic fracturing is important to geothermal and petroleum reservoir stimulation. The interaction between a hydraulic fracture and pre-existing natural fractures exerts significant control on stimulated volume and fracture network complexity. This thesis presents a boundary element and finite difference based method for modeling this interaction during hydraulic fracturing process. In addition, an improved boundary element model is developed to more accurately calculate the total stimulated reservoir volume. The improved boundary element model incorporates a patch to calculate the tangential stresses on fracture walls accurately, and includes a special crack tip element at the fracture end to capture the correct stress singularity the tips The fracture propagation model couples fluid flow to fracture deformation, and accounts for fracture propagation including the transition of a mechanically-closed natural fractures to a hydraulic fracture. The numerical model is used to analyze a number of stimulation scenarios and to study the resulting hydraulic fracture trajectory, fracture aperture, and pressures as a function of injection time. The injection pressure, fracture aperture profiles shows the complexity of the propagation process and its impact on stimulation design and proppant placement. The injection pressure is observed to decrease initially as hydraulic fracture propagates and then it either increases or decreases depending on the factors such as distance between hydraulic fracture and natural fracture, viscosity of the injected fluid, injection rate and also other factor that are discussed in detail in below sections. Also, the influence of flaws on natural fracture in its opening is modeled. Results shows flaws that are very small in length will not propagate but are influencing the opening of natural fracture. If the flaw is located near to one end tip the other end tip will likely propagate first and vice versa. This behavior is observed due to the stress shadowing effect of flaw on the natural fracture. In addition, sequential and simultaneous injection and propagation of multiple fractures is modeled. Results show that for sequential injection, the pressure needed to initiate the later fractures increases but the geometry of the fractures is less complicated than that obtained from simultaneous injection under the same fracture spacing and injection. It is also observed that when mechanical interaction is present, the fractures in sequential fracturing have a higher width reduction as the later fractures are formedItem Single station Doppler tracking for satellite orbit prediction and propagation(2015-05) Dykstra, Matthew C.; Fowler, Wallace T.; Lightsey, E. GlennPresently, there are two main methods of launching a cube satellite into Earth orbit. The first method is to purchase a secondary payload slot on a major launch vehicle. For the second method, the satellite must first be transported via a major launch vehicle to the International Space Station. From there, the satellite is loaded into one of two deployment mechanisms, and deployed at a specified time. In each case, the satellite's initial orbit is not accurately known. For ground operators this poses a problem of position uncertainty. In order to solve this problem, a satellite tracking algorithm was developed to use an initial two-line element set for coarse orbit prediction, followed by Doppler measurements for continuous processing and updating. The system was tested using simulated data. The analysis showed that this low-cost, scalable system will satisfy the tracking requirements of many cube satellite missions, including current missions at the University of Texas.Item Space object translational and rotational state prediction and sensitivity calculation(2016-12) Hatten, Noble Ariel; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Bettadpur, Srinivas V; Jones, Brandon A; Weisman, Ryan MWhile computing power has grown monumentally during the space age, the demands of astrodynamics applications have more than kept pace. Resources are taxed by the ever-growing number of Earth-orbiting space objects (SOs) that must be tracked to maintain space situational awareness (SSA) and by increasingly popular but computationally expensive tools like Monte Carlo techniques and stochastic optimization algorithms. In this dissertation, methods are presented to improve the accuracy, efficiency, and utility of SO state prediction and sensitivity calculation algorithms. The dynamical model of the low Earth orbit regime is addressed through the introduction of an upgraded Harris-Priester atmospheric density model, which introduces a smooth polynomial dependency on solar flux. Additional modifications eliminate singularities and provide smooth partial derivatives of the density with respect to SO state, time, and solar conditions. The numerical solution of the equations of motion derived from dynamics models is also addressed, with particular emphasis placed on six-degree-of-freedom (6DOF) state prediction. Implicit Runge-Kutta (IRK) methods are applied to the 6DOF problem, and customizations, including variable-fidelity dynamics models and parallelization, are introduced to maximize efficiency and take advantage of modern computing architectures. Sensitivity calculation -- a necessity for SSA and other applications -- via RK methods is also examined. Linear algebraic systems for first- and second-order state transition matrix calculation are derived by directly differentiating either the first- or second-order form of the RK update equations. This approach significantly reduces the required number of Jacobian and Hessian evaluations compared to the ubiquitous augmented state vector approach for IRK methods, which can result in more efficient calculations. Parallelization is once again leveraged to reduce the runtime of IRK methods. Finally, a hybrid special perturbation/general perturbation (SP/GP) technique is introduced to address the notoriously slow speed of fully coupled 6DOF state prediction. The hybrid method uses a GP rotational state prediction to provide low-fidelity attitude information for a high-fidelity 3DOF SP routine. This strategy allows for the calculation of body forces using arbitrary shape models without adding attitude to the propagated state or taking the small step sizes often required by full 6DOF propagation. The attitude approximation is obtained from a Lie-Deprit perturbation result previously applied to SOs in circular orbits subject to gravity-gradient torque and extended here to SOs in elliptical orbits. The hybrid method is shown to produce a meaningful middle ground between 3DOF SP and 6DOF SP methods in the accuracy vs. efficiency space.