Sharif Digital Repository

In this paper, a coupled hydro-mechanical formulation is developed for the simulation of interaction between hydraulic fractures and natural discontinuities within saturated porous media. The momentum balance equation of the bulk together with the momentum balance and continuity equations of the fluid phase are employed to obtain the fully coupled set of governing equations. The hydro-fracture is modeled for fluid flow using the Darcy law. The natural discontinuity on the other hand is modeled for both opening and closing modes which induce fluid flow and/or contact behavior along the crack edges. The discontinuity in the displacement field is incorporated by using the Heaviside enrichment... 

In this paper, the eXtended Finite Element Method (X-FEM) is developed in pressure-sensitive plasticity of powder compaction process. In X-FEM, the need for mesh adaption to discontinuity interface is neglected and the process is accomplished by employing additional functions, which are added to approximate the displacement field of the elements located on the interface. The double-surface cap plasticity model is employed within the X-FEM framework in numerical simulation of powder material. The plasticity model includes a failure surface and an elliptical cap, which closes the open space between the failure surface and hydrostatic axis. The moving cap expands in the stress space according... 

An explicit dynamics extended finite element method (X-FEM) is applied to the problems with material interfaces. To this end, the available X-FEM element mass matrix lumping techniques have been identified and assessed. It is shown that all the methods have their own limitations and are not general enough to handle the enrichment functions specifically developed for the elements with material interfaces. Hence, a general element mass matrix lumping technique has been introduced which exactly preserves the kinetic energies of the basic rigid body and enrichment modes. The idea is borrowed from the previously published method for a specific range of enrichment functions and extended to... 

In the extended finite element method (FEM), the transition elements between the enriched and standard elements, which are generally referred as the blending, or partially enriched elements, are often crucial for a good performance of the local partition of unity enrichments. In these elements, the enrichment function cannot be reproduced exactly due to the lack of a partition of unity, and blending elements produce unwanted terms into the approximation that cannot be compensated by the standard final element part of the approximation. In this paper, some optimal X-FEM-type methods reported in literature are employed to study the performance of blending elements in large plastic deformation... 

In this paper, the interaction between the fluid-driven fracture and frictional natural fault is modeled using an enriched-FEM technique based on the partition of unity method. The intersection between two discontinuities is modeled by introducing a junction enrichment function. In order to model the fluid effect within the fracture, the fluid pressure is assumed to be constant throughout the propagation process. The frictional contact behavior along the fault faces is modeled using an X-FEM penalty method within the context of the plasticity theory of friction. Finally, several numerical examples are solved to illustrate the accuracy and robustness of proposed computational algorithm as... 

In this paper, the extended finite element method is presented for large elasto-plastic deformation of continuum problems. The X-FEM computational algorithm is presented in the framework of Lagrangian description in order to model the arbitrary interfaces in large deformations. In X-FEM, the material interface is represented independently of element boundaries and the process is accomplished by partitioning the domain with several tetrahedral sub-elements whose Gauss points are used for integration of the domain of elements. The interface between two bodies is modeled by using the X-FEM technique and applying a modified level set enrichment function. In order to simulate the nonlinear... 

In this paper, a computational model is developed for the simulation of hydro-fracture growth in naturally layered impervious media using the extended finite element method (X-FEM). The equilibrium equation of the bulk is solved in conjunction with the hydro-fracture inflow and continuity equations using the staggered Newton method. The hydro-fracture inflow is governed by the lubrication theory, where the permeability of the fracture is incorporated by taking advantage of the cubic law. The Eigen-function expansion method is utilised in order to develop enrichment functions suited for the asymptotic stress field in the vicinity of the singular points. An energy release rate-based criterion... 

In this paper, an extended finite element method is presented for simulation of interaction between hydraulic fracturing and natural fractures in saturated porous media. The well-known u−p formulation is employed in order to obtain the fully coupled set of governing equations. Natural faults are modeled for both opening and closure modes where the fluid inflow and contact conditions are considered at the interface, respectively. The Darcy law is employed in conjunction with an aperture dependent permeability for the fracture channel to describe the interfacial inflow. The contact constraints of both the solid and fluid phases are imposed using the Penalty method. The Heaviside and modified... 

In this paper, a numerical model is developed based on the X-FEM technique to simulate the proppant transport and tip screen-out in hydraulic fracturing. The governing equations are based on the momentum balance and mass conservation of the fluid. The hydro-mechanical coupling between the fracture and surrounding porous medium is fulfilled through the weak form of the governing equations. The fluid inflow within the fracture is modeled using the one-dimensional mass conservation of the injected slurry and proppant along the fracture, in which the viscosity of the slurry is dependent on the proppant concentration. The transition from the Poiseuille to Darcy flow regime is incorporated into... 

In this paper, a numerical model is developed based on the X-FEM technique to simulate the transport of dense solute in a single fluid phase through the fractured porous media. The governing equation is based on the mass conservation law which is applied to the fluid phase and the solute in both matrix and fracture domain. The integral governing equations of the mass exchange between the fracture and the surrounding matrix is derived. The extended finite element method (X-FEM) is applied by employing appropriate enrichment functions to model the fractured porous domain. The superiority of the X-FEM is that the FE mesh is not necessary to be conformed to the fracture geometry, so the regular... 

In this paper, a fully coupled numerical model is developed based on the X-FEM technique to simulate the reactive acid transport in fractured porous media. The porous medium consists of the solid and fluid phases, in which the fluid phase includes water and acid components, and chemical reactions can be occurred between acid component and solid phase at the solid–fluid interfaces. The governing equations include the mass and momentum conservation laws for fluid phase, and the advective–diffusive transport of acid component that must be solved to obtain the primary unknowns, including the pore fluid pressure, acid concentration, and fluid velocity vector. Applying the...