Hydraulic fracturing is an important and abundant process in both industrial applications and natural environments. The current work is the first systematic quantitative study of the effect of interaction in and between complex hydraulic fractures at different spatial scales. A mathematical model, based on the boundary collocation method, has been developed. The model has been employed for a typical field case, a highly segmented vein. This vein is well-mapped, and therefore, represents a well constrained example. The computed apertures are compared to the measured apertures. By using the simplest constitutive model, based on an ideal elastic material, and including the effect of interaction between the segments, it was possible to obtain an excellent match at all considered scales. It was also shown that the concept of effective fracture, as currently accepted in the literature, is not always applicable and may lead to unbounded inaccuracy. Unfortunately, in most cases, very little (if any) directly measured data on fracture and material properties is available. An important example of such a weakly constrained case, involving hydraulic fracturing, is diking beneath the seafloor at mid-oceanic ridges. In this study, it is shown that the commonly accepted scenario of a dike propagating from the center of the pressurized magma chamber to the ocean floor is not consistent with conventional fracture mechanics due to the fact that the chamber has the shape of a thin lens. Even at such a large scale (i.e., a kilometer or more), the mechanical principles of elastic interaction appear to be applicable. Since diking is likely to generate a region of high permeability near its margin, in addition to heat, the ongoing hydrothermal activity becomes localized. Our modeling suggests the probable positions of the propagating dikes. Consequently, comparing the observed locations of hydrothermal sites with respect to that of the magma chamber could be useful for constraining the mechanisms of magma lens evolution.

This dissertation focuses mainly on three topics: (1) mixed-mode branching and segmentation of hydraulic fractures in brittle materials, (2) hydraulic fracture propagation in particulate materials, and (3) hydraulic fracturing in water flooding conditions. Mixed-mode loading is one of the primary causes of fracture branching and segmentation in brittle materials. We conducted the first laboratory experiments on the mixed mode I+III hydraulic fracturing. We found that a KIII/KI ratio as small as ~1% is sufficient for fracture front segmentation. In reality, such a small mode III component is always expected, for example, due to the small deviations of the fracture shape from planar. Thus, we concluded that fracture segmentation is likely to accompany growth of most, if not all, real hydraulic fractures. We also proposed a theoretical model that captures the main features of experimental observations and indicates the importance of the hydraulic effect of segmentation. Particulate materials often exhibit pronounced non-linear behavior and yielding even at relatively small loads. In order to adequately describe hydraulic fracturing in particulate materials with low or no cohesion, plasticity at the crack tip must be explicitly considered. We investigated the shear band mechanism of strain localization at the fracture front. This mechanism takes into account the fact that cohesionless material can not bear tension, and is in compression everywhere, including near the fracture front. To verify the shear band hypothesis, we conducted numerical simulations of the plastic deformation at the tip of a fracture in particulate material with strain softening. Our model describes the shear bands by properly placed and oriented dislocations. The model results are consistent with experimental observations. Water flooding, which in certain important cases, can result in processes resembly hydraulic fracturing by a low-viscosity fluid with extremely high leak-off. It is difficult to simulate this process in the laboratory. To investigate the fracture initiation mechanism in water flooding conditions, we conducted a numerical simulation of fluid injection into particulate material by using the discrete element code PFC2D. We also considered an analytical model of cavity initiation based on the fluidization mechanism. The estimates given by this model fit remarkably well with the numerical simulation results.

This investigation carried out the analysis of fracture conductivity in a tight reservoir using laboratory experiments, by applying the procedure known as the dynamic fracture conductivity test. Considering the large number of experiments necessary to evaluate the effect of each parameter and the possible interaction of their combinations, the schedules of experiments were planned using a fractional factorial design. This design is used during the initial stage of studies to identify and discharge those factors that have little or no effect. Finally, the most important factors can then be studied in more detail during subsequent experiments. The objectives of this investigation were focused on identifying the effect of formation parameters such as closure stress, and temperature and fracture fluid parameters such as proppant loading over the final conductivity of a hydraulic fracture treatment. With the purpose of estimating the relation between fracture conductivity and the design parameters, two series of experiments were performed. The first set of experiments estimated the effects of the aliases parameters. The isolated effect of each independent parameter was obtained after the culmination of the second set of experiments. The preliminary test results indicated that the parameters with major negative effect over the final conductivity were closure stress and temperature. Some additional results show that proppant distribution had a considerable role over the final fracture conductivity when a low proppant concentration was used. Channels and void spaces in the proppant pack were detected on these cases improving the conductivity of the fracture, by creating paths of high permeability. It was observed that with experiments at temperatures around 250 degrees F, the unbroken gel dried up creating permeable scales that resulted in a significant loss in conductivity. The results of this investigation demonstrated that dynamic fracture conductivity test procedure is an excellent tool to more accurately represent the effects of design parameters over the fracture conductivity. These results are also the first step in the development of a statistical model that can be used to predict dynamic fracture conductivity.

In the scope of the study, prismatic roughness elements with different longitudinal spacing and arrangements have been tested in a rectangular flume in order to reveal their effects on fundamental characteristics of a hydraulic jump. Two basic roughness types with altering arrangements have been tested. Roughness elements of the first type extends through the channel width against the flow with varying length and pitch ratios for different arrangements. The second type is of staggered essence and produced by piecing the roughness elements defined in the initial type into three parts which are equal in length. The doublet formed from the pieces on the sides is shifted to the consequent row to make two successive roughness rows encapsulate the channel span completely. Staggered roughness type is formed with the repetition of this arrangement along the flume. Independent of their type and arrangement, the entirety of roughness elements are embedded in the channel bed in order to avoid their protuberance into the flow, based on the presumption that the crests of the roughness elements levelled with the channel inlet would be less exposed to caving effects of flow than the protruding elements. In the study, influence of the proposed roughness elements on the fundamental engineering concerns as the length, height (tail water depth) and energy dissipation capacity of hydraulic jumps has been questioned in the light of empirical work and related literature on forced and smooth hydraulic jumps. At the final stage of the study, it was concluded that both strip and staggered roughness have positive effects on the characteristics of hydraulic jump given above. 3-7% more energy dissipation was observed in jumps on rough beds compared to classical hydraulic jumps. For tailwater dept reduction, whereas strip roughness provided 5-13%, staggered roughness led to 7-15% tailwater depth reduction compared to classical hydraulic jump. While strip roughness reduced jump length around 40%, 35-55% reduction was observed with staggered roughness when compared to classical hydraulic jump.

Waterhammer is an unsteady hydraulic problem which is commonly found in closed conduits of hydropower plants, water distribution networks and liquid pipeline systems. Due to either a malfunction of the system or inadequate operation conditions, pipeline may collapse or burst erratically resulting in substantial damages, and human losses in some cases. In this thesis, time dependent flow situations in the penstocks of small hydropower plants are investigated. A software, HAMMER, that utilizes method of characteristics for solving nonlinear differential equations of transient flow is used in the study. In two case studies, various operation conditions such as load rejection, load acceptance and instant load rejection are studied. The parameters and situations affecting pressure and turbine speed rises are investigated. Computed and available measured values are found to be very close. Also, differences between waterhammer responses of the Francis and Pelton turbines are revealed. Finally, specific protective measures are suggested to either diminish and/or avoid the harmful effects of waterhammer problems in small hydropower plants.

All pipeline systems are susceptible to water hammer that can cripple critical infrastructure. One effective method to relieve excessive waterhammer pressures in pipelines is to use air chambers. This study aims to develop an empirical procedure for the quick analysis of penstock-turbine systems to determine dimensions and operating conditions of air-chambers that can effectively diminish the transient phenomena after sudden changes of flow rate in the system. A numerical study has been carried out by obtaining repeated solutions for variable system parameters using a commercial software. The relief brought by air chambers is found to approach to an asymptotic value for increasing chamber volumes. It is possible to determine the required chamber volume for a given discharge to limit the waterhammer pressures at a prescribed level in a given penstock-turbine system using the charts produced in the study.

In practice, baffle blocks and sills are commonly being used to stabilize the location of a hydraulic jump and shorten the length of a stilling basin. On the other hand, gravels, corrugations and rectangular prismatic roughnesses which cover the entire length of the basin or placed in a staggered manner may be an alternative. The objective of this study is to determine the effects of these roughness elements on the characteristics of hydraulic jumps such as conjugate depth, jump length and energy dissipation using experimental data collected from the previous studies. The investigations show that the roughness elements have positive effects on the characteristics of hydraulic jumps. The tailwater depth reduction compared to classical jump is 2-10%. The length of the jump is reduced about by 30-50% by prismatic roughness elements, 40% by corrugations, and 30% by gravels. The roughness elements induce 3-15% more energy dissipation than that of classical jump. Therefore, these types of bed roughness elements should be considered as an effective alternative of accessory devices such as baffle blocks and sills.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 190-192). Also available on the Internet.

Thesis (Ph. D.)--Brigham Young University. Dept. of Civil and Environmental Engineering, 2004. / Includes bibliographical references (p. 223-229).

Hydraulic fracturing is an important stimulation method for producing unconventional gas reserves. Natural fractures are present in many low-permeability gas environments and often provide important production pathways for natural gas. The production benefit from natural fractures can be immense, but it is difficult to quantify. The Mesaverde Group in the Piceance Basin in Colorado is a gas producing reservoir that has low matrix permeability but is also highly naturally fractured. Wells in the Piceance Basin are hydraulically fractured, so the production enhancements due to natural fracturing and hydraulic fracturing are difficult to decouple. In this thesis, dipole sonic logs were used to quantify geomechanical properties by combining stress equations with critically-stressed faulting theory. The properties derived from this log-based evaluation were used to numerically model hydraulic fracture treatments that had previously been pumped in the basin. The results from these hydraulic fracture models, in addition to the log-derived reservoir properties were used to develop reservoir models. Several methods for simulating the reservoir were compared and evaluated, including layer cake models, geostatistical models, and models simulating the fracture treatment using water injection. The results from the reservoir models were compared to actual production data to quantify the effect of both hydraulic fractures and natural fractures on production. This modeling also provided a framework upon which completion techniques were economically evaluated. / text