Diss.: University of Duisburg-Essen, 2009. / Includes bibliographical references (p. [127]-134).

Diss.: Berlin, Humboldt-University, 2009. / Includes bibliographical references (p. 159-168).

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006u. / Nemhauser, George L., Committee Chair ; Ahmed, Shabbir, Committee Member ; Bartholdi, John J., Committee Member ; Takriti, Samer, Committee Member ; Gu, Zonghao, Committee Member.

Thesis (Ph. D.)--Washington State University, August 2006. / Includes bibliographical references.

Wong Man Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 60-63). / Abstracts in English and Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Thesis Assessment Committee --- p.iii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Our Work and Motivation --- p.1 / Chapter 1.2 --- Literature Review --- p.3 / Chapter 1.3 --- Thesis Structure --- p.5 / Chapter 2 --- Preliminary --- p.6 / Chapter 2.1 --- Calculus for Volume of Sphere --- p.6 / Chapter 2.2 --- Fractional Programming and Dinkelbach's Algorithm --- p.7 / Chapter 2.3 --- Nonlinear Programming and Interior Point Algorithm --- p.8 / Chapter 2.4 --- Second Order Cones and Conic Programming --- p.10 / Chapter 3 --- The Probability Model --- p.12 / Chapter 3.1 --- Derive the Chance Constraint --- p.12 / Chapter 3.2 --- Single Cluster Model --- p.18 / Chapter 3.3 --- Multi-clusters Model --- p.21 / Chapter 4 --- The Downside Risk Model --- p.24 / Chapter 4.1 --- Derive the Downside Risk Measure --- p.24 / Chapter 4.2 --- Calculate the First and Second Derivative of the Downside Risk --- p.27 / Chapter 4.3 --- Single Cluster Model and Numerical Algorithm --- p.29 / Chapter 4.4 --- Multi-clusters Model --- p.34 / Chapter 5 --- The Conditional Value-at-Risk Model --- p.37 / Chapter 5.1 --- Derive the Conditional Value at Risk --- p.37 / Chapter 5.2 --- Single Cluster Model and Numerical Algorithm --- p.41 / Chapter 5.3 --- Multi-clusters Model --- p.47 / Chapter 6 --- Numerical Results --- p.51 / Chapter 6.1 --- Data Set --- p.51 / Chapter 6.2 --- The Probability Model --- p.53 / Chapter 6.3 --- The Downside Risk Model --- p.53 / Chapter 6.4 --- The CVaR Model --- p.56 / Chapter 7 --- Conclusions --- p.58 / Bibliography --- p.60

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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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.

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