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Utilizing improved production methods have been always challenging in upstream industries. Nowadays, hydraulic fracturing is one of the most prestigious mechanical methods. Application of this method is in wells with low productivity index. Hydraulic fracturing efficiency depends on various factors, such as fracture geometry, fluid composition, and stress distribution. But some of them would be ignored, such as fracture geometry, which is neglected due to nongravity and lack of investigation of DFN statistical population assumption. The authors develop a more comprehensive methodology based on fracture geometry and aim to model one of the gas reservoirs in Iran that is naturally fractured by... 

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin... 

In this paper, the crack growth simulation is presented in saturated porous media using the extended finite element method. The mass balance equation of fluid phase and the momentum balance of bulk and fluid phases are employed to obtain the fully coupled set of equations in the framework of u - p formulation. The fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well-known cubic law. The spatial discritization is performed using the extended finite element method, the time domain discritization is performed based on the generalized Newmark scheme, and the non-linear system of equations is solved using the... 

Modeling the water flow in cohesive fracture is a fundamental issue in the crack growth simulation of cracked concrete gravity dams and hydraulic fracture problems. In this paper, a mathematical model is presented for the analysis of fracture propagation in the semi-saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double-nodded zero-thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The modified crack permeability is applied in fracture propagation based on the data obtained from experimental... 

In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double-nodded zero-thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the... 

hydraulic fracturing is one of the most prestigious mechanical methods which used as a facile production rate improvement method. Application of this method is in wells with low productivity index. Hydraulic fracturing efficiency depends on various factors, like fracture geometry, fluid composition and stress distribution. But some of them would be ignored. Such as fracture geometry which is neglected due to non-gravity and lack of investigation of DFN statistical population assumption. In this paper we develop a more comprehensive methodology based on fracture geometry, we aim to model one of the gas reservoirs which is naturally fractured, by using well-known commercial software. Based on... 

Creating hydraulically induced fractures in oil/gas reservoirs is one of the methods for Enhanced Oil Recovery (EOR) that has been applied extensively in petroleum industry in recent years. Despite its popularity, the design process of Hydraulic Fracture treatment is mostly empirical based on the previous experiences gained in the oil-rich formation. The reason lies in the complexities involved in the Hydraulic Fracture process including interacting effects of fluid(s) flowand solid deformations, injection of non-Newtonian fluids in the porous media, leak-off of the injected fluid into the formation, complex geometry of the induced fracture in the intact or naturally fractured rock,... 

In this paper, an enriched finite element technique is presented to simulate the mechanism of interaction between the hydraulic fracturing and frictional natural fault in impermeable media. The technique allows modeling the discontinuities independent of the finite element mesh by introducing additional DOFs. The coupled equilibrium and flow continuity equations are solved using a staggered Newton solution strategy, and an algorithm is proposed on the basis of fixed-point iteration concept to impose the flow condition at the hydro-fracture mouth. The cohesive crack model is employed to introduce the nonlinear fracturing process occurring ahead of the hydro-fracture tip. Frictional contact is... 

In this paper, a fully coupled numerical model is developed for the modeling of the hydraulic fracture propagation in porous media using the extended finite element method in conjunction with the cohesive crack model. The governing equations, which account for the coupling between various physical phenomena, are derived within the framework of the generalized Biot theory. The fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well-known cubic law. By taking the advantage of the cohesive crack model, the nonlinear fracture processes developing along the fracture process zone are simulated. The spatial discretization... 

Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi-analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element-free Galerkin (EFG) mesh-less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity... 

Diffusivity equation which can provide us with the pressure distribution, is a Partial Differential Equation (PDE) describing fluid flow in porous media. The quadratic pressure gradient term in the diffusivity equation is nearly neglected in hydrology and petroleum engineering problems such as well test analysis. When a compressible liquid is injected into a well at high pressure gradient or when the reservoir possess a small permeability value, the effect of ignoring this term increases. In such cases, neglecting this parameter can result in high errors. Previous models basically focused on numerical and semi-analytical methods for semi-infinite domain. To the best of our knowledge, no... 

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, 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... 

It is generally accepted that a hydraulically induced fracture in the reservoir is approximately a plane fracture perpendicular to the direction of the in situ minor principal stress. However, field observations, in some cases, do not support the above traditional assumption. This is especially true when hydraulic fracturing technique is applied to the uncemented porous materials such as oil sands. In this article, the pattern of hydraulically induced fractures in oil sands and other geomaterials is discussed. Field observations and experimental investigation results are combined with the outcomes of the numerical simulations of hydro-fracturing in oil sands conducted by the authors to...