Fracturing rock with untra high pressure waterFitt, A.D. and Fowkes, N.D. and Mason, D.P. and Myers, T.G. and Moss, E.A. and Cheng, J. (2006) Fracturing rock with untra high pressure water. Mathematics in Industry Study Groups in South Africa > MISGSA 2006: University of the Witwatersrand (23rd - 27th January 2006). Full text available as:
Abstract/SummaryModelling issues are considered for the process of cracking rock in mines using ultra high pressure water. The elevated pressures are caused by the ignition of a propellant and may be as large as 1000MPa. We first consider time, length and pressure scales and then derive a model for the propagation of a two-dimensional crack. A number of aspects of this model are considered and similarity solutions and behaviour near the crack tip are investigated. Consideration is given to a simplified model where the elastic component of the interaction between the rock and the fluid is handled using an elementary closure law: in this case much progress may be made and closed-form solutions may be determined. Conditions are also identified where a model based on “impulsive” lubrication theory is appropriate. However, this leads to a very challenging problem. Finally, some other ways of extending the model to include (for example) fluid leak-off into the rock are discussed.
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