Hydraulic fracture with Darcy and non-Darcy flow in a porous medium

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dc.contributor.authorNchabeleng, Mathibele Willy
dc.date.accessioned2017-05-26T12:17:50Z
dc.date.available2017-05-26T12:17:50Z
dc.date.issued2017
dc.descriptionA dissertation submitted to the Faculty of Science,University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. December 2016.en_ZA
dc.description.abstractThis research is concerned with the analysis of a two-dimensional Newtonian fluid-driven fracture in a permeable rock. The fluid flow in the fracture is laminar and the fracture is driven by the injection of a Newtonian fluid into it. Most of the problems in litera- ture involving fluid flow in permeable rock formation have been modeled with the use of Darcy's law. It is however known that Darcy's model breaks down for flows involv- ing high fluid velocity, such as the flow in a porous rock formation during hydraulic fracturing. The Forchheimer flow model is used to describe the non-Darcy fluid flow in the porous medium. The objective of this study is to investigate the problem of a fluid-driven fracture in a porous medium such that the flow in the porous medium is non-Darcy. Lubrication theory is applied to the system of partial di erential equations since the fracture that is considered is thin and its width slowly varies along its length. For this same reason, Perkins-Kern-Nordgren approximation is adopted. The theory of Lie group analysis of differential equations is used to solve the nonlinear coupled sys- tem of partial differential equations to obtain group invariant solutions for the fracture half-width, leak-o depth and length of the fracture. The strength of fluid leak-off at the fracture wall is classi ed into three forms, namely, weak, strong and moderate. A group invariant solution of the traveling wave form is obtained and an exact solution for the case in which there is weak fluid leak-off at the interface is found. A dimensionless parameter, F0, termed the Forchheimer number was obtained and investigated. Nu- merical results are obtained for both the case of Darcy and non-Darcy flow. Computer generated graphs are used to illustrate the analytical and numerical results.en_ZA
dc.description.librarianMT2017en_ZA
dc.format.extentOnline resource (x, 109 leaves)
dc.identifier.citationNchabeleng, Mathibele Willy (2017) Hydraulic fracture with Darcy and non-Darcy flow in a porous medium, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/22740>
dc.identifier.urihttp://hdl.handle.net/10539/22740
dc.language.isoenen_ZA
dc.subject.lcshFluid mechanics--Mathematical models
dc.subject.lcshRocks--Permeability
dc.subject.lcshHydraulic fracturing
dc.subject.lcshPorous materials
dc.titleHydraulic fracture with Darcy and non-Darcy flow in a porous mediumen_ZA
dc.typeThesisen_ZA
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