In this work, we present methodologies for optimization of hydraulic fracturing design under uncertainty specifically with reference to the thick and anisotropic reservoirs in the Lower Tertiary Gulf of Mexico. In this analysis we apply a stochastic programming framework for optimization under uncertainty and apply a utility framework for risk analysis. For a vertical well, we developed a methodology for making the strategic decisions regarding number and dimensions of hydraulic fractures in a high-cost, high-risk offshore development. Uncertainty is associated with the characteristics of the reservoir, the economics of the fracturing cost, and the fracture height growth. The method developed is applicable to vertical wells with multiple, partially penetrating fractures in an anisotropic formation. The method applies the utility framework to account for financial risk. For a horizontal well, we developed a methodology for making the strategic decisions regarding lateral length, number and dimensions of transverse hydraulic fractures in a high-cost, high-risk offshore development, under uncertainty associated with the characteristics of the reservoir. The problem is formulated as a mixed-integer, nonlinear, stochastic program and solved by a tailored Branch and Bound algorithm. The method developed is applicable to partially penetrating horizontal wells with multiple, partially penetrating fractures in an anisotropic formation.

Currently microseismic monitoring is widely used for fracture diagnosis. Since the method monitors the propagation of shear failure events, it is an indirect measure of the propped fracture geometry. Our primary interest is in estimating the orientation and length of the ‘propped’ fractures (not the created fractures), as that is the primary driver for well productivity. This thesis presents a new Low Frequency Electromagnetic Induction (LFEI) method that has the potential to estimate the propped length, height, orientation of hydraulic fractures, and vertical distribution of proppant within the fracture. The proposed technique involves pumping electrically conductive proppant (which is currently available) into the fracture and then using a specially built logging tool to measure the electromagnetic response of the formation. Results are presented for a proposed logging tool that consists of three sets of tri-directional transmitters and receivers at 6, 30 and 60 feet spacing respectively. The solution of Maxwell’s equations shows that it is possible to use the tool to determine both the orientation and the length of the fracture by detecting the location of these particles in the formation after hydraulic fracturing. Results for extensive sensitivity analysis are presented in this thesis to show the effect of different propped lengths, height and orientation of planar fractures in a shale environment. Multiple numerical simulations, using a state-of-the-art electromagnetic simulator (FEKO) indicate, as this work show, that we can detect and map fractures up to 250 feet in length, 0.2 inches wide, and with a 0 to 45 degree of inclination with respect to the wellbore. Special cases such as proppant banking, non-symmetrical bi-wing fractures, and wells with steel casing in place were studied. / text

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / The propagation of hydraulic fractures with tortuosity is investigated. Tortuosity is the complicated fracture geometry that results from asperities at the fluid-rock interface and, if present, from contact regions. A tortuous hydraulic fracture can either be open without contact regions or partially open with contact regions. We replace the tortuous hydraulic fracture by a two-dimensional symmetric model fracture that accounts for tortuosity. A modified Reynolds flow law is used to model the tortuosity in the flow due to surface roughness at the fracture walls. In order to close the model, the linear and hyperbolic crack laws which describe the presence of contact regions in a partially open fracture are used. The Perkins-Kern-Nordgren approximation in which the normal stress at the crack walls is proportional to the half-width of the symmetric model fracture is used. A Lie point symmetry analysis of the resulting governing partial differential equations with their corresponding boundary conditions is applied in order to derive group invariant solutions for the half-width, volume and length of the fracture. For the linear hydraulic fracture, three exact analytical solutions are derived. The operating conditions of two of the exact analytical solutions are identified by two conservation laws. The exact analytical solutions describe fractures propagating with constant speed, with constant volume and with fluid extracted at the fracture entry. The latter solution is the limiting solution of fluid extraction solutions. During the fluid extraction process, fluid flows in two directions, one towards the fracture entry and the other towards the fracture tip. It is found that for fluid injection the width averaged fluid velocity increases approximately linearly along the length of the fracture. This leads to the derivation of approximate analytical solutions for fluid injection working conditions. Numerical solutions for fluid injection and extraction are computed. The hyperbolic hydraulic fracture is found to admit only one working condition of fluid injected at the fracture entry at a constant pressure. The solution is obtained numerically. Approximate analytical solutions that agree well with numerical results are derived. The constant pressure solutions of the linear and hyperbolic hydraulic fracture are compared. While the hyperbolic hydraulic fracture model is generally considered to be a more realistic model of a partially open fracture, it does not give information about fluid extraction. The linear hydraulic fracture model gives various solutions for di erent working conditions at the fracture entry including fluid extraction.

Successful development of shale gas reservoirs is highly dependent on hydraulic fracture treatments. Many questions remain in regards to the geometry of the created fractures. Production data analysis from some shale gas wells quantifies a much smaller stimulated pore volume than what would be expected from microseismic evidence and reports of fracturing fluids reaching distant wells. In addition, claims that hydraulic fracturing may open or reopen a network of natural fractures is of particular interest. This study examines hydraulic fracturing of shale gas formations with specific interest in fracture geometry. Several field cases are analyzed using microseismic analysis as well as net pressure analysis of the fracture treatment. Fracture half lengths implied by microseismic events for some of the stages are several thousand feet in length. The resulting dimensions from microseismic analysis are used for calibration of the treatment model. The fracture profile showing created and propped fracture geometry illustrates that it is not possible to reach the full fracture geometry implied by microseismic given the finite amount of fluid and proppant that was pumped. The model does show however that the created geometry appears to be much larger than half the well spacing. From a productivity standpoint, the fracture will not drain a volume more than that contained in half of the well spacing. This suggests that for the case of closely spaced wells, the treatment size should be reduced to a maximum of half the well spacing. This study will provide a framework for understanding hydraulic fracture treatments in shale formations. In addition, the results from this study can be used to optimize hydraulic fracture treatment design. Excessively large treatments may represent a less than optimal approach for developing these resources.

This dissertation presents three inter-related studies. Chapter 2 presents a study of scaling of crack propagation in rubber sheets. Two different scaling laws for supersonic and subsonic cracks were discovered. Experiments and numerical simulations have been conducted to investigate subsonic and supersonic cracks. The experiments are performed at 85 °C to suppress strain-induced crystallites that complicate experiments at lower temperature. Calibration experiments were performed to obtain the parameters needed to compare with a theory including viscous dissipation. Both experiments and numerical simulations support supersonic cracks, and a transition from subsonic to supersonic is discovered in the plot of experimental crack speed curves versus extension ratio for different sized samples. Both experiments and simulations show two different scaling regimes: the speed of subsonic cracks scales with the elastic energy density while the speed of supersonic cracks scales with the extension ratio. Crack openings have qualitatively different shapes in the two scaling regimes. Chapter 3 describes a theory of oscillating cracks. Oscillating cracks are not seen very widely, but observed in rubber and gels. A theory has been proposed for the onset of oscillation in gels, but the oscillation of cracks in rubber has not been explained. This study provides a theory able to describe both rubber and gels and recover the experimental phase diagram for oscillating cracks in rubber. The main new idea is that the oscillations of cracks follow from basic features of fracture mechanics and are independent of details of the crack equation of motion. From the fact that oscillations exist, one can deduce some conditions on forms that equations of motion can take. A discrete model of hydraulic fracture is mentioned in Chapter 4. Hydraulic fracturing is a stimulation treatment wherein fluids are injected into reservoirs under high pressure to generate fractures in reservoirs. In this study, a lattice-based pseduo-3D model is developed to simulate hydraulic fracturing. This mode has been validated via a comparison with the KGD model. A series of pilot simulations was systematically tested for complex geometries under more realistic operation conditions, including flexible boundary conditions, randomness in elastic properties of shales and perforations. The simulation results confirm that perforation is likely to increase the complexity of fracture networks; the results also suggest that the interference between neighboring fractures is key to fracture network formation. / text

Thesis (Ph.D.)--Memorial University of Newfoundland. / Typescript. Restricted until November 1997. Bibliography: leaves [125]-133. Also available online.

Thesis (M.S.)--West Virginia University, 2010. / Title from document title page. Document formatted into pages; contains ix, 38 p. : col. ill., maps (some col.). Includes abstract. Includes bibliographical references (p. 36-37).

Thesis (M. Sc.)--University of Hong Kong, 2005.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

In conjunction with horizontal drilling, hydraulic fracturing or fracking has enabled the recovery of natural gas from low permeable shale formations. In addition to water, these fracking fluids employ proppants and up to 38 different chemical additives to improve the efficiency of the process. One important class of additives used in hydraulic fracturing is biocides. When applied appropriately, they limit the growth of harmful microorganisms within the well, saving energy producers 4.5 billion dollars each year. However, biocides or their harmful daughter products may return to the surface in produced water, which must then be appropriately stored, treated and disposed of. Little is known about the effect of mineral-fluid interactions on the fate of the biocides employed in hydraulic fracturing. In this study, we employed laboratory experiments to determine changes in the persistence and products of these biocides under controlled environments. While many minerals are present in shale formations, pyrite, FeS2(s) is particularly interesting because of its prevalence and reactivity. The FeII groups on the face of pyrite may be oxidized to form FeIII phases. Both of these surfaces have been shown to be reactive with organic compounds. Chlorinated compounds undergo redox reactions at the pyrite-fluid interface, and sulfur-containing compounds undergo exceptionally strong sorption to both pristine and oxidized pyrite. This mineral may significantly influence the degradation of biocides in the Marcellus Shale. Thus, the overall goal of this study was to understand the effect of pyrite on biocide reactivity in hydraulic fracturing, focusing on the influence of pyrite on specific functional groups. The first specific objective was to demonstrate the effect of pyrite and pyrite reaction products on the degradation of the bromine-containing biocide, DBNPA. On the addition of pyrite to DBNPA, degradation rates of the doubly brominated compound were found to increase significantly. DBNPA is proposed to undergo redox reactions with the pyrite surface, accepting two-electrons from pyrite, and thus becoming reduced. The primary product is the monobrominated analogue of DBNPA, 2-monobromo-3-nitrilopropionamide (or MBNPA). The surface area-normalized first-order initial degradation rate constant was found to be 5.1 L.m-2day-1. It was also determined that the dissolution and oxidation products of pyrite, FeII, S2O32- and SO42- are unlikely to contribute to the reduction of the biocide. Taken together, the results illustrate that a surface reaction with pyrite has the ability to reduce the persistence of DBNPA, and as a consequence change the distribution of its reaction products. The second objective was to quantify the influence of water chemistry and interactions with pyrite on the degradation of the sulfur-containing biocide. Dazomet readily hydrolyzes in water due to the nucleophilic attack of hydroxide (OH-) anions. Thus the half-life of dazomet during the shut-in phase of hydraulic fracturing will decrease with increasing pH: 8.5 hours at pH 4.1 to 3.4 hours at pH 8.2.Dazomet degradation was rapidly accelerated upon exposure to the oxidized pyrite surface, reacting five times faster than hydrolysis in the absence of pyrite at a similar pH. The products measured were identical to those identified on hydrolysis (methyl isothiocyanate and formaldehyde) and no dissolved iron was detected in solutions. This suggests that the dithiocarbamate group in dazomet was able to chemisorb onto the oxidized pyrite surface, shifting the electron density of the molecule which resulted in accelerated hydrolysis of the biocide. The third objective explored the reactivity of various biocide functional groups due to the addition of pyrite. Several elimination mechanisms were identified, and tied to the reactivity of the specific functional group involved. The addition of pyrite led to accelerated degradation of dibromodicyanobutane. This is because the bromine (-Br) group is easily reduced. For methylene bis(thiocyanate), hydrolysis was a noteworthy elimination mechanism since the thiocyanate (-SCN) functionality is a good leaving group. Benzisothiazolinone and methyl isothiazolinone were stable at low pH due to the stabilizing donor-acceptor interactions between the organic biocides’ carbonyl (–C=O) groups and salts in the solution. This body of work has illustrated that pristine pyrite can undergo redox reactions with brominated biocides used in hydraulic fracturing, reducing their persistence and altering the product distribution. This will change the efficacy and the risks associated with the use of these biocides in shales containing pyrite, particularly at lower pH where organic compounds are more stable to hydrolysis. However, at higher pH hydrolysis becomes more important, and additional studies will need to be conducted to investigate the pyrite contribution under these conditions. Conversely, the FeIII surface groups on oxidized pyrite can catalyze the hydrolysis of dazomet and may do so for other labile, sulfur-containing biocides as well. Overall, this research has shown that the physicochemical properties (such as the acid dissociation constant and the standard reduction potential) that govern the environmental reactivity of a molecule can be used to anticipate its reactivity in hydraulic fracturing.