A formulation for the flow of a power law non-Newtonian fluid in a porous-permeable medium represented by a nonlinear partial differential equation is presented. This governing equation is transformed into a nonlinear ordinary differential equation whose solution is expanded as a Lie series. As an application to hydraulic fracturing, the problem of a Newtonian reservoir fluid being displaced by an injected non-Newtonian fluid is discussed. The resulting moving boundary problem is solved, resulting in explicit solutions for the respective pressure distributions and the displacement of the moving interface. The presented solutions provide a firm theoretical basis for fluid loss characterization in the porous-permeable reservoir.

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