In hydraulic fracturing, a mixture of proppant and fluid is injected into the fracture to maintain the opening of the fracture during and after the operation. A model for describing the distribution of proppant in a propagating hydraulic fracture is developed in this study. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant -laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracture. A finite element analysis is developed and implemented in a computer program (GYCO-PT) to carry out the calculations. In order to ensure the accuracy of the computed results and produce a more robust method capable of full simulation, a grid generation scheme is developed and incorporated into the computer program. The grid scheme encompasses unstructured Delaunay triangulation with the convection, insertion and redistribution of nodal points. The behavior of the fracture and the grid depend on the distribution of the in-situ stresses. Four examples covering different types of in-situ stress distribution are carried out to demonstrate the distribution of proppant and the construction of the grid for the hydraulic fracture.
- Pub Date:
- January 1994