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<b><span style="font-size:16.0pt">Poroelastic Solutions of Hydraulic Fracturing Problems Using Fast Multipole Boundary Element Method<o:p></o:p></span></b></p>
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<b><span style="font-size:16.0pt"><o:p> </o:p></span></b></p>
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<b><span style="font-size:11.0pt;mso-ascii-font-family:Calibri;mso-fareast-font-family:
"Times New Roman";mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black;background:white">PhD Dissertation Defense by:
</span></b><span style="font-size:11.0pt;mso-ascii-font-family:Calibri;mso-fareast-font-family:
"Times New Roman";mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black;background:white">Ali Rezaei<b><o:p></o:p></b></span></p>
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<b><span style="font-size:11.0pt;mso-ascii-font-family:Calibri;mso-fareast-font-family:
"Times New Roman";mso-hansi-font-family:Calibri;mso-bidi-font-family:Calibri;
color:black;background:white">Petroleum Engineering Department</span></b><span style="font-family:"Times New Roman",serif;mso-fareast-font-family:"Times New Roman""><o:p></o:p></span></p>
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<b><span style="font-size:16.0pt"><o:p> </o:p></span></b></p>
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<b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;
color:black">Defense Date:</span></b><span style="font-size:11.0pt;font-family:
"Calibri",sans-serif;color:black"> Friday, August 3<sup>rd</sup>, 2018 <b>Time: </b>2:00 pm <b>Location: </b>Room
124, ERP Building 9</span><span style="font-family:"Calibri",sans-serif;color:black"><o:p></o:p></span></p>
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<b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;
color:black">Committee Members:</span></b><span style="font-size:11.0pt;
font-family:"Calibri",sans-serif;color:black"> Dr. Mohamed Soliman (Chair), Dr. Ganesh Thakur, </span><span style="font-family:"Calibri",sans-serif;
color:black">Dr.
Guan Qin</span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;
color:black">,
</span><span style="font-family:"Calibri",sans-serif;color:black">Dr. S.M. Farouq Ali, Dr. Giorgio Bornia, Dr. Mehdi Rafiee, and Dr. Stephen Morse<o:p></o:p></span></p>
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<o:p> </o:p></p>
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<o:p> </o:p></p>
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<o:p> </o:p></p>
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Hydraulic fracturing (HF) of horizontal wells is an essential part of any unconventional field development activity. Hence, understanding the behavior of this process in horizontal wells is extremely important. A comprehensive study on the behavior of hydraulic
fractures is highly dependent on the mathematical formulation of the problem, assumptions that are made to make the problem tractable, and numerical method that is utilized to solve the corresponding equations. Although the host medium of hydraulic fractures
is porous and saturated, this problem is often solved using elasticity equations and adding a leak off or other parameters in an un-coupled fashion to the model. This approach ignores the fully-coupled essence of the hydraulic fracturing problem and often
gives inaccurate results. On the other hand, adding the necessary details makes the model inefficient when degree of freedom (DOF) increases. Another complexity that exists in hydraulic fracturing problems is movement of the boundary, which makes it difficult
to re-mesh the domain that is required by most of the domain-based numerical methods after propagation. The objective of this study is to develop a comprehensive yet efficient model to investigate the behavior of hydraulic fractures in poroelastic media. The
theory of poroelasticity together with displacement discontinuity method, and an efficient fast multipole algorithm are utilized to develop an efficient hydraulic fracture model. The main contribution of this research can be categorized in two parts, namely
implementation and application. In the first part, solutions that are obtained by the fast multipole algorithm is compared to the conventional fully-poroelastic displacement discontinuity method. Also, the applicability of the fast multipole method in a fully-coupled
displacement discontinuity algorithm is established. On the application side, the model is used to study several problems such as refracturing of a horizontal well, fracturing of an infill well in a partially depleted reservoir, and problems including randomly
distributed fractures. <o:p></o:p></p>
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