Proppant flowback in fractures under confining pressures is not well understood and difficult to reproduce in a laboratory setting. Improper management of proppant flowback leads to flow restrictions near the well bore, poor fracture conductivity and costly production equipment damage. A simple, scalable model is developed using a discrete element method (DEM) particle simulator, to simulate representative cubic volumes consisting of fracture openings, fracture walls and the confining formation. The effects of fracture width, confining stress, fluid flow velocity and proppant cohesion are studied for a variety of conditions. Fracture width is found to be dependent on confining stress and fluid flow velocity while proppant production is also dependent on cohesion. Three regimes are observed, with complete fracture evacuation occurring at high flow rates and low confining stresses, fully packed fractures occurring at high confining stresses and open but mostly evacuated fractures occurring in-between. From these observations, a recommended flowback rate can be estimated for a given set of conditions. A slow and controlled well flowback is recommended to improve proppant pack stability. The rate ramp-up time is dependent on the leak-off coefficient. / text

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D.Sc. / Please refer to full text to view abstract

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa, in fulfilment of the requirements for the degree of Master of Science. 21 March 2016. / The problem of turbulent hydraulic fracturing is considered. Despite it being a known phenomenon, limited mathematical literature exists in this field. Prandtl’s mixing length model is utilised to describe the eddy viscosity and a mathematical model is developed for two distinct cases: turbulence where the kinematic viscosity is sufficiently small to be neglected and the case where it is not. These models allow for the examination of the fluid’s behaviour and its effect on the fracture’s evolution through time. The Lie point symmetries of both cases are obtained, and a wide range of analytical and numerical solutions are explored. Solutions of physical significance are calculated and discussed, and approximate solutions are constructed for ease of fracture estimation. The non-classical symmetries of these equations are also investigated. It was found that the incorporation of the kinematic viscosity within the modelling process was important and necessary. / MT2016

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Thesis (M.S.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains xii, 99 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 53-54).

A sizable amount of literature exists analyzing the effect of confining stress on fracture conductivity in sandstones. This thesis attempts to answer similar questions with regard to shale formations. The low Young’s Moduli and Brinell hardness values characteristic of many prospective shale formations may lead to a great deal of embedment and fines production which can drastically reduce fracture conductivity. Furthermore, shales exhibit sensitivity to aqueous fluids which may cause them to be weakened in the presence of certain fracturing fluids. Previous work analyzing shale fluid sensitivity has failed to preserve the shales’ formation properties by allowing the shale to dry out. This paper presents a study of propped fracture conductivity experiments at reservoir temperature and pressure using various North American shale reservoir cores. Exposure to the atmosphere can alter the mechanical properties of the shale by either drying or hydrating the samples, so care was taken to preserve these shales in their native state by maintaining constant water activity (relative humidity). Variations in applied closure stress and aqueous fluid exposure were analyzed and in certain cases altered the propped fracture conductivity by crushing proppant, embedding the proppant into the fracture face, and producing fines. The damage to fracture conductivity is correlated to mineralogy for the various shale samples. These findings show that a one-size-fits-all frac design will not work in every shale formation, rather a tailored approach to each shale is necessary. In the future, the results of this work will be analyzed alongside easier to perform Brinell hardness tests, swelling tests, and other characterization techniques incorporated into the UT Shale Characterization Protocol. Correlations were developed to relate the simpler tests to the fracture conductivity experiments which yield a straight forward method to determine the role embedment and fluid sensitivity have on post treatment fracture conductivity in shales. The UT Shale characterization Protocol can then be used to optimize the design and execution of fracing treatments. / text

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.

Acid fracture conductivity and the effect of key variables in the etching process during acid fracturing can be assessed at the laboratory scale. This is accomplished by using an experimental apparatus that simulates acid injection fluxes comparable to those in actual acid fracture treatments. After acid etching, fracture conductivity is measured at different closure stresses. This research work presents a systematic study to investigate the effect of temperature, rock-acid contact time and initial condition of the fracture surfaces on acid fracture conductivity in the Austin Chalk formation. While temperature and rock-acid contact are variables normally studied in fracture conductivity tests, the effect of the initial condition of the fracture surface has not been extensively investigated. The experimental results showed that there is no significant difference in acid fracture conductivity at high closure stress using smooth or rough fracture surfaces. In addition, we analyzed the mechanisms of acid etching and resulting conductivity creation in the two types of fracture surfaces studied by using surface profiles. For smooth surfaces, the mechanism of conductivity creation seems connected to uneven etching of the rock and roughness generation. For rough surfaces, acid conductivity is related to smoothing and deepening of the initial features on the sample surface than by creating more roughness. Finally, we compared the experimental results with Nirode-Kruk correlation for acid fracture conductivity.

Thesis (M.S. - Hydrology and Water Resources)--University of Arizona. / Includes bibliographical references (leaves 201-204).