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Numerical Modeling of Fluid Flow and Proppant Transport in Hydraulic Fracture Using Extended Finite Element Method

Hosseini, Navid | 2020

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52804 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza; Shad, Saeed
  7. Abstract:
  8. Transport phenomena in porous media play important role in many areas of subsurface hydrology, geo-physics, environment, energy and petroleum. The work in the field of numerical modeling of fractured porous media is yet an open area of research. The classic finite element method (FEM) has some limitations in modeling of discontinuities like fracture. FEM mesh should conform with the geometry of the fracture. Presence of fracture imposes discontinuity in pressure field of fluid phases and displacement field of solid phase (rock). To represent the fractures, the extended finite element method (X-FEM) can be used in which the standard finite element approximation of the field variables is enriched by appropriate enrichment functions. Hence, the presence of the fractures is modeled by adding enriched degrees of freedom assigned to elements cut by the fractures. As a result, mesh could be regular and independent of the position of the fractures. The governing equations include the mass conservation law for fluid phases and linear momentum equation for solid phase which should be applied in both matrix and fracture domains. The mass exchange between the fracture and the surrounding matrix is considered in the integral form (weak form) of the governing equations. In this study, different transport phenomena such as two-phase fluid flow, density-driven solute transport, proppant transport in hydraulic fracture are modeled and some problems are investigated in order to validate the proposed models. In two-phase fluid flow, the robustness of the proposed computational model is demonstrated through several numerical examples, and the effects of crack orientation, capillary pressure function, and existence of short cracks on the pattern of fluid flow are investigated. The pre-existing short fractures, which are distributed randomly in the porous medium, contribute to the increase of the effective permeability tensor and are modeled with an “equivalent continuum model”. It is shown that the developed model provides a correct prediction of flow pattern for different crack configurations.In density-driven solute transport, several numerical examples of dense brine transport in a water aquifer are studied to validate the proposed method; moreover, the effects of different parameters of the fracture (such as aperture, interconnectivity) and matrix medium (such as permeability, diffusion) are investigated. In addition, it is shown that the developed model provides an accurate prediction of subsurface hydrology for a field-scale closed desert basin.In proppant transport inside hydraulic fracture, several numerical examples of typical hydraulic fracturing problems are simulated to investigate the overall behavior of the fracture propagation in the case of tip screen-out formation; moreover, the influence of different parameters of the proppant (such as injection concentration, size) and matrix medium (such as permeability) on the fracture characteristics is examined. The results show when the proppnat is added to the injection fluid, the facture propagtion rate decreases, and the pressure at the wellbore begins to increase. Moreover, when the tip screen-out occurs, the fracture growth ceases, and further slurry pumping yields to an increase in the fracture aperture. Moreover, as the proppant plug region extends, the fluid pressure within the fracture tip drops so that the fracture tends to close
  9. Keywords:
  10. Hydraulic Fracturing ; Extended Finite Element Method ; Density Dependet Flow ; Two Phase Fluid Flow ; Proppant Transport ; Crack Tip Screen-Out

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