Download or read book Precise Numerical Implementation of Pseudo three dimensional Models for Hydraulic Fractures written by Michael Edward Mear and published by . This book was released on 1983 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pseudo three Dimensional Models of Hydraulic Fracture Propagation written by Mark Edward Mear and published by . This book was released on 1983 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Simulation in Hydraulic Fracturing Multiphysics Theory and Applications written by Xinpu Shen and published by CRC Press. This book was released on 2017-03-27 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expansion of unconventional petroleum resources in the recent decade and the rapid development of computational technology have provided the opportunity to develop and apply 3D numerical modeling technology to simulate the hydraulic fracturing of shale and tight sand formations. This book presents 3D numerical modeling technologies for hydraulic fracturing developed in recent years, and introduces solutions to various 3D geomechanical problems related to hydraulic fracturing. In the solution processes of the case studies included in the book, fully coupled multi-physics modeling has been adopted, along with innovative computational techniques, such as submodeling. In practice, hydraulic fracturing is an essential project component in shale gas/oil development and tight sand oil, and provides an essential measure in the process of drilling cuttings reinjection (CRI). It is also an essential measure for widened mud weight window (MWW) when drilling through naturally fractured formations; the process of hydraulic plugging is a typical application of hydraulic fracturing. 3D modeling and numerical analysis of hydraulic fracturing is essential for the successful development of tight oil/gas formations: it provides accurate solutions for optimized stage intervals in a multistage fracking job. It also provides optimized well-spacing for the design of zipper-frac wells. Numerical estimation of casing integrity under stimulation injection in the hydraulic fracturing process is one of major concerns in the successful development of unconventional resources. This topic is also investigated numerically in this book. Numerical solutions to several other typical geomechanics problems related to hydraulic fracturing, such as fluid migration caused by fault reactivation and seismic activities, are also presented. This book can be used as a reference textbook to petroleum, geotechnical and geothermal engineers, to senior undergraduate, graduate and postgraduate students, and to geologists, hydrogeologists, geophysicists and applied mathematicians working in this field. This book is also a synthetic compendium of both the fundamentals and some of the most advanced aspects of hydraulic fracturing technology.

Download or read book Numerical Modeling of Complex Hydraulic Fracture Development in Unconventional Reservoirs written by Kan Wu and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Successful creations of multiple hydraulic fractures in horizontal wells are critical for economic development of unconventional reservoirs. The recent advances in diagnostic techniques suggest that multi-fracturing stimulation in unconventional reservoirs has often caused complex fracture geometry. The most important factors that might be responsible for the fracture complexity are fracture interaction and the intersection of the hydraulic and natural fracture. The complexity of fracture geometry results in significant uncertainty in fracturing treatment designs and production optimization. Modeling complex fracture propagation can provide a vital link between fracture geometry and stimulation treatments and play a significant role in economically developing unconventional reservoirs. In this research, a novel fracture propagation model was developed to simulate complex hydraulic fracture propagation in unconventional reservoirs. The model coupled rock deformation with fluid flow in the fractures and the horizontal wellbore. A Simplified Three Dimensional Displacement Discontinuity Method (S3D DDM) was proposed to describe rock deformation, calculating fracture opening and shearing as well as fracture interaction. This simplified 3D method is much more accurate than faster pseudo-3D methods for describing multiple fracture propagation but requires significantly less computational effort than fully three-dimensional methods. The mechanical interaction can enhance opening or induce closing of certain crack elements or non-planar propagation. Fluid flow in the fracture and the associated pressure drop were based on the lubrication theory. Fluid flow in the horizontal wellbore was treated as an electrical circuit network to compute the partition of flow rate between multiple fractures and maintain pressure compatibility between the horizontal wellbore and multiple fractures. Iteratively and fully coupled procedures were employed to couple rock deformation and fluid flow by the Newton-Raphson method and the Picard iteration method. The numerical model was applied to understand physical mechanisms of complex fracture geometry and offer insights for operators to design fracturing treatments and optimize the production. Modeling results suggested that non-planar fracture geometry could be generated by an initial fracture with an angle deviating from the direction of the maximum horizontal stress, or by multiple fracture propagation in closed spacing. Stress shadow effects are induced by opening fractures and affect multiple fracture propagation. For closely spaced multiple fractures growing simultaneously, width of the interior fractures are usually significantly restricted, and length of the exterior fractures are much longer than that of the interior fractures. The exterior fractures receive most of fluid and dominate propagation, resulting in immature development of the interior fractures. Natural fractures could further complicate fracture geometry. When a hydraulic fracture encounters a natural fracture and propagates along the pre-existing path of the natural fracture, fracture width on the natural fracture segment will be restricted and injection pressure will increase, as a result of stress shadow effects from hydraulic fracture segments and additional closing stresses from in-situ stress field. When multiple fractures propagate in naturally fracture reservoirs, complex fracture networks could be induced, which are affected by perforation cluster spacing, differential stress and natural fracture patterns. Combination of our numerical model and diagnostic methods (e.g. Microseismicity, DTS and DAS) is an effective approach to accurately characterize the complex fracture geometry. Furthermore, the physics-based complex fracture geometry provided by our model can be imported into reservoir simulation models for production analysis.

Download or read book Development of a Three dimensional Semi analytical Propagation Model for Non symmetric Hydraulic Fractures written by Jose Ignacio Rueda and published by . This book was released on 1994 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Modeling of Complex Hydraulic Fracture Propagation in Layered Reservoirs with Auto optimization written by Jiacheng Wang (Ph. D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic fracturing brings economic unconventional reservoir developments, and multi-cluster completion designs result in complex hydraulic fracture geometries. Therefore, accurate yet efficient modeling of the propagation of multiple non-planar hydraulic fractures is desired to study the mechanisms of hydraulic fracture propagation and optimize field completion designs. In this research, a novel hydraulic fracture model is developed to simulate the propagation of multiple hydraulic fractures with proppant transport in layered and naturally fractured reservoirs. The simplified three-dimensional displacement discontinuity method (S3D DDM) is enhanced to compute the hydraulic fracture deformation and propagation with analytical fracture height growth and vertical width variation. Using a single row of DDM elements, the enhanced S3D DDM hydraulic fracture model computes the fully 3D geometries with a similar computational intensity to a 2D model. Then an Eulerian-Lagrangian proppant transport model is developed, where the slurry flow rate and pressure are solved within the Eulerian regime, and the movement of solid proppant particles is solved within the Lagrangian regime. The adaptive proppant gridding scheme in the model allows a smaller grid size at the earlier fracturing stage for higher resolution and a larger grid size at the later fracturing stage for higher efficiency. Besides the physical model, an optimization module that utilizes advanced optimization algorithms such as genetic algorithm (GA) and pattern search algorithm (PSA) is proposed to automatically optimize the completion designs according to the preset targets. Numerical results show that hydraulic fracture propagation is under the combined influence of the in-situ stress, pumping schedule, natural fractures, and cluster placement. Hence, numerical simulation is needed to predict complex hydraulic fracture geometries under various geologic and completion settings. The complex hydraulic fracture geometries, together with fracturing fluid and proppant properties, also affect proppant placement. Moreover, the stress contrast at layer interfaces can cause proppant bridging and form barriers on the proppant transport path. The optimized completion designs increase effective hydraulic and propped areas, but they vary depending on the optimization targets. The developed hydraulic fracture model provides insights into the hydraulic fracturing process and benefits unconventional reservoir development

Download or read book Hydraulic Fracture Modeling written by Yu-Shu Wu and published by Gulf Professional Publishing. This book was released on 2017-11-30 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic Fracture Modeling delivers all the pertinent technology and solutions in one product to become the go-to source for petroleum and reservoir engineers. Providing tools and approaches, this multi-contributed reference presents current and upcoming developments for modeling rock fracturing including their limitations and problem-solving applications. Fractures are common in oil and gas reservoir formations, and with the ongoing increase in development of unconventional reservoirs, more petroleum engineers today need to know the latest technology surrounding hydraulic fracturing technology such as fracture rock modeling. There is tremendous research in the area but not all located in one place. Covering two types of modeling technologies, various effective fracturing approaches and model applications for fracturing, the book equips today’s petroleum engineer with an all-inclusive product to characterize and optimize today’s more complex reservoirs. Offers understanding of the details surrounding fracturing and fracture modeling technology, including theories and quantitative methods Provides academic and practical perspective from multiple contributors at the forefront of hydraulic fracturing and rock mechanics Provides today’s petroleum engineer with model validation tools backed by real-world case studies

Download or read book Hydraulic Fracture Optimization with a Pseudo 3D Model in Multi layered Lithology written by Mei Yang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic Fracturing is a technique to accelerate production and enhance ultimate recovery of oil and gas while fracture geometry is an important aspect in hydraulic fracturing design and optimization. Systematic design procedures are available based on the so-called two-dimensional models (2D) focus on the optimization of fracture length and width, assuming one can estimate a value for fracture height, while so-called pseudo three dimensional (p-3D) models suitable for multi-layered reservoirs aim to maximize well production by optimizing fracture geometry, including fracture height, half-length and width at the end of the stimulation treatment. The proposed p-3D approach to design integrates four parts: 1) containment layers discretization to allow for a range of plausible fracture heights, 2) the Unified Fracture Design (UFD) model to calculate the fracture half-length and width, 3) the PKN or KGD models to predict hydraulic fracture geometry and the associated net pressure and other treatment parameters, and, finally, 4) Linear Elastic Fracture Mechanics (LEFM) to calculate fracture height. The aim is to find convergence of fracture height and net pressure. Net pressure distribution plays an important role when the fracture is propagating in the reservoir. In multi-layered reservoirs, the net pressure of each layer varies as a result of different rock properties. This study considers the contributions of all layers to the stress intensity factor at the fracture tips to find the final equilibrium height defined by the condition where the fracture toughness equals the calculated stress intensity factor based on LEFM. Other than maximizing production, another obvious application of this research is to prevent the fracture from propagating into unintended layers (i.e. gas cap and/or aquifer). Therefore, this study can aid fracture design by pointing out: (1) Treating pressure needed to optimize fracture geometry, (2) The containment top and bottom layers of a multi-layered reservoir, (3) The upwards and downwards growth of the fracture tip from the crack center.

Download or read book Numerical Modeling of Nonlinear Problems in Hydraulic Fracturing written by Endrina Rivas and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic fracturing is a stimulation technique in which fluid is injected at high pressure into low-permeability reservoirs to create a fracture network for enhanced production of oil and gas. It is the primary purpose of hydraulic fracturing to enhance well production. The three main mechanisms during hydraulic fracturing for oil and gas production which largely impact the reservoir production are: (1) fracture propagation during initial pad fluid injection, which defines the extent of the fracture; (2) fracture propagation during injection of proppant slurry (fluid mixed with granular material), creating a propped reservoir zone; and (3) shear dilation of natural fractures surrounding the hydraulically fractured zone, creating a broader stimulated zone. The thesis has three objectives that support the simulation of mechanisms that lead to enhanced production of a hydraulically-fractured reservoir. The first objective is to develop a numerical model for the simulation of the mechanical deformation and shear dilation of naturally fractured rock masses. In this work, a two-dimensional model for the simulation of discrete fracture networks (DFN) is developed using the extended finite element method (XFEM), in which the mesh does not conform to the natural fracture network. The model incorporates contact, cohesion, and friction between blocks of rock. Shear dilation is an important mechanism impacting the overall nonlinear response of naturally fractured rock masses and is also included in the model--physics previously not simulated within an XFEM context. Here, shear dilation is modeled through a linear dilation model, capped by a dilation limiting displacement. Highly nonlinear problems involving multiple joint sets are investigated within a quasi-static context. An explicit scheme is used in conjunction with the dynamic relaxation technique to obtain equilibrium solutions in the face of the nonlinear constitutive models from contact, cohesion, friction, and dilation. The numerical implementation is verified and its convergence illustrated using a shear test and a biaxial test. The model is then applied to the practical problem of the stability of a slope of fractured rock. The second objective is to develop a numerical model for the simulation of proppant transport through planar fractures. This work presents the numerical methodology for simulation of proppant transport through a hydraulic fracture using the finite volume method. Proppant models commonly used in the hydraulic fracturing literature solve the linearized advection equation; this work presents solution methods for the nonlinear form of the proppant flux equation. The complexities of solving the nonlinear and heterogeneous hyperbolic advection equation that governs proppant transport are tackled, particularly handling shock waves that are generated due to the nonlinear flux function and the spatially-varying width and pressure gradient along the fracture. A critical time step is derived for the proppant transport problem solved using an explicit solution strategy. Additionally, a predictor-corrector algorithm is developed to constrain the proppant from exceeding the physically admissible range. The model can capture the mechanisms of proppant bridging occurring in sections of narrow fracture width, tip screen-out occurring when fractures become saturated with proppant, and flushing of proppant into new fracture segments. The results are verified by comparison with characteristic solutions and the model is used to simulate proppant transport through a KGD fracture. The final objective is to develop a numerical model for the simulation of proppant transport through propagating non-planar fractures. This work presents the first monolithic coupled numerical model for simulating proppant transport through a propagating hydraulic fracture. A fracture is propagated through a two-dimensional domain, driven by the flow of a proppant-laden slurry. Modeling of the slurry flow includes the effects of proppant bridging and the subsequent flow of fracturing fluid through the packed proppant pack. This allows for the simulation of a tip screen-out, a phenomenon in which there is a high degree of physical interaction between the rock deformation, fluid flow, and proppant transport. Tip screen-out also leads to shock wave formation in the solution. Numerical implementation of the model is verified and the model is then used to simulate a tip screen-out in both planar and non-planar fractures. An analysis of the fracture aperture, fluid pressure, and proppant concentration profiles throughout the simulation is performed for three different coupling schemes: monolithic, sequential, and loose coupling. It is demonstrated that even with time step refinement, the loosely-coupled scheme fails to converge to the same results as the monolithic and sequential schemes. The monolithic and sequential algorithms yield the same solution up to the onset of a tip screen-out, after which the sequential scheme fails to converge. The monolithic scheme is shown to be more efficient than the sequential algorithm (requiring fewer iterations) and has comparable computational cost to the loose coupling algorithm. Thus, the monolithic scheme is shown to be optimal in terms of computational efficiency, robustness, and accuracy. In addition to this finding, a robust and more efficient algorithm for injection-rate controlled hydraulic fracturing simulation based on global mass conservation is presented in the thesis.

Download or read book Three Dimensional Numerical Model of Hydraulic Fracturing in Fractured Rock Masses written by B. Damjanac and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Three-Dimensional Numerical Model of Hydraulic Fracturing in Fractured Rock Masses.

Download or read book Reservoir Stimulation written by Michael J. Economides and published by . This book was released on 2000-06-23 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sets forth a rationalisation of stimulation using reservoir engineering concepts, and addresses topics such as formation characterisation, hydraulic fracturing and matrix acidizing. Formation damage, which refers to a loss in reservoir productivity, is also examined comprehensively.

Download or read book Solving Three dimensional Problems in Natural and Hydraulic Fracture Development written by Farrokh Sheibani and published by . This book was released on 2013 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many fracture models are based on two-dimensional plane strain approximations, accurately predicting fracture propagation geometry requires accounting for the three-dimensional aspects of fractures. In this study, we implemented 3-D displacement discontinuity (DD) boundary element modeling to investigate the following intrinsically 3-D natural or hydraulic fracture propagation problems: the effect of fracture height on lateral propagation of vertical natural fractures, joint development in the vicinity of normal faults, and hydraulic fracture height growth and non-planar propagation paths. Fracture propagation is controlled by stress intensity factor (SIF) and its determination plays a central role in LEFM. The DD modeling is used to evaluate SIF in Mode I, II and III at the tip of an arbitrarily-shaped embedded crack by using crack-tip element displacement discontinuity. We examine the accuracy of SIF calculation is for rectangular, penny-shaped, and elliptical planar cracks. Using the aforementioned model for lateral propagation of overlapping fractures shows that the curving path of overlapping fractures is strongly influenced by the spacing-to-height ratio of fractures, as well as the differential stress magnitude. We show that the angle of intersection between two non-coincident but parallel en-echelon fractures depends strongly on the fracture height-to-spacing ratio, with intersection angles being asymptotic for "tall" fractures (large height-to-spacing ratios) and nearly orthogonal for "short" fractures. Stress perturbation around normal faults is three-dimensionally heterogeneous. That perturbation can result in joint development at the vicinity of normal faults. We examine the geometrical relationship between genetically related normal faults and joints in various geologic environments by considering a published case study of fault-related joints in the Arches National Park region, Utah. The results show that joint orientation is dependent on vertical position with respect to the normal fault, the spacing-to-height ratio of sub-parallel normal faults, and Poisson's ratio of the media. Our calculations represent a more physically reasonable match to measured field data than previously published, and we also identify a new mechanism to explain the driving stress for opening mode fracture propagation upon burial of quasi-elastic rocks. Hydraulic fractures may not necessarily start perpendicular to the minimum horizontal remote stress. We use the developed fracture propagation model to explain abnormality in the geometry of fracturing from misaligned horizontal wellbores. Results show that the misalignment causes non-planar lateral propagation and restriction in fracture height and fracture width in wellbore part.

Download or read book Development of a Numerical Simulator for Three dimensional Hydraulic Fracture Propagation in Heterogeneous Media written by R. D. Barree and published by . This book was released on 1984 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Modeling and Finite Element Analysis of Three dimensional Hydraulic Fractures in Layered Media written by Tae Soo Lee and published by . This book was released on 1989 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Brittle Fracture Propagation with Application to Hydraulic Fracture written by Benjamin Grossman-Ponemon and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The breaking apart of brittle materials via fracture is ubiquitous in engineering applications and in nature. A hydraulic fracture is one driven by pressurized fluid, which is an important tool in the energy industry and a fundamental physical process in the study of volcanoes. Three major challenges in simulating brittle fracture propagation are (a) constructing discretizations of the problem geometry which account for crack paths that are not known a priori, (b) correctly modeling crack evolution, especially when the relative speeds of individual crack tips or points along a crack front are ambiguous in the context of Griffith's theory of fracture, and (c) accurately computing the singularities in the stress fields which can adversely affect convergence rates of standard numerical methods. Further, hydraulic fracture simulations require a suitable mesh of the crack geometry in order to account for the fluid flow within. In this thesis, three contributions to the problem of brittle (possibly hydraulic) fracture simulation are presented. The first is a method to simulate curvilinear hydraulic fractures under plane-strain or axisymmetric loading conditions. Discretizing the problem geometry is addressed through Universal Meshes, a novel technique to construct conforming triangulations by perturbing a limited number of nodes in a single background (universal) mesh. The conforming triangulation also provides a mesh of the crack surface by segments, and hence the Finite Element Method is used to simultaneously approximate the displacements within the rock and the pressure of the fracturing fluid. The method is benchmarked through a convergence study, a comparison with near-surface experiments, and the study of a hydraulic fracture propagating in a narrow channel. The method is then applied to a problem in volcanology: the growth of magma-filled dikes away from a depressurizing magma chamber. The fully-coupled simulations are used to make predictions about the growth rate of the dike as a function of time and about the pressure in the magma chamber as a function of the dike length. The second contribution is a method to compute the stress intensity factors along the front of a three-dimensional crack. In Linear Elastic Fracture Mechanics, the stress intensity factors are used to predict the onset of crack growth and direction of said growth. However, numerical schemes to calculate these factors in three dimensions often result in oscillatory values, which may not improve under mesh refinement. The presented method formulates functionals which are derived from the interaction integral, and that, when applied to the exact displacement field, yield weighted integrals of the stress intensity factors along the crack front. Through careful analysis of the functionals and the method, conditions under which the method is guaranteed to converge are derived. The method is validated on several crack configurations from the literature. The final contribution in this thesis addresses the challenge of predicting crack advancement in the absence of inertial effects, in particular the ambiguous crack velocities for cases in two dimensions with multiple crack tips or for cases in three dimensions. A model for crack evolution is proposed which extends Griffith's theory for quasi-static growth to account for supercritical propagation, and which resolves the crack speed ambiguity. Algorithms to apply the method in two- and three-dimensional cases are presented, and these algorithms are demonstrated on various examples.

Download or read book New numerical approaches to model hydraulic fracturing in tight reservoirs with consideration of hydro mechanical coupling effects written by Lei Zhou and published by Cuvillier Verlag. This book was released on 2014-03-20 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, two new numerical approaches for hydraulic fracturing in tight reservoir were developed. A more physical-based numerical 3D-model was developed for simulating the whole hydraulic fracturing process including fracture propagation, closure and contact as well as proppant transport and settling. In this approach rock formation, pore and fracture systems were assembled together, in which hydro-mechanical coupling effect, proppant transport and settling as well as their influences on fracture closure and contact were fully considered. A combined FDM and FVM schema was used to solve the problem. Three applications by using the new approach were presented. The results illustrated the whole hydraulic fracturing process well and seemed to be logical, which confirmed the ability of the developed approach to model the in-situ hydraulic fracturing operation from injection start till fully closure. In order to investigate the orientation problem of hydraulic fracturing in tight reservoir, a new approach for simulating arbitrary fracture propagation and orientation in 2D was developed. It was solved by a hybrid schema of XFEM and FVM. Three numerical studies were illustrated, which proved the ability of the developed approach to solve the orientation problem in field cases.

Download or read book A 3D Hydro mechanical Discrete Element Model for Hydraulic Fracturing in Naturally Fractured Rock written by Efthymios Papachristos and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic fracturing is at the core of a number of naturally occurring and induced phenomena and crucial for a sustainable development of energy resource production. Given its crucial role this process has been given increasing attention in the last three decades from the academic world. Nonetheless a number of very significant aspects of this process have been systematically overlooked by the community. Two of the most notable ones are the inability of the vast majority of existing models to tackle at once the propagation of hydraulic fractures in realistic, fractured rocks-masses where hydraulic fracturing is a competing dipole mechanism between fracturing of the intact rock and re-activation of exiting fracture networks. Another essential aspect of this process is that it is intrinsically three-dimensional which is neglected by most models. To tackle this vital problem taking into account these pivotal aspects, a fully coupled hydro-mechanical model based on the discrete element method has been developed. The rock mass is here represented by a set of discrete elements interacting through elastic-brittle bonds that can break to form cracks inside the simulated medium. Theses cracks can coalesce to form fractures. A finite volume scheme is used to simulate the fluid flow in between these discrete elements. The flow is computed as a function of the pore space deformation in the intact medium and of the cracks' aperture in the fractures. Furthermore, the natural fractures are modelled explicitly and present mechanical and hydraulic properties different from the rock matrix. Employing this model in an intact numerical specimen, single fluid injection and multiple closely spaced sequential injections, enabled the description the full spatio-temporal evolution of HF propagation and its impact on quantitative indexes used in description of hydraulic fracturing treatments, such as fractured volume, fracture intensity and down-the-hole pressure for different control parameters and in-situ stress-fields. Moreover, injections from perforation slots which are not well aligned to the minimum stress plane showed possible creation of percolating non-planar hydraulic fractures of low connectivity, which can be troublesome for proppant placement. Also, strong interactions between closely spaced HF were highlighted by tracking the local principal stress rotation around the injection zones, emphasizing the importance of stress shadow effects. Optimization solutions are proposed for multiple treatments from a non-perfectly aligned wellbore. Finally, interaction between a single hydraulic fracture and a single natural fracture of varying properties and orientations was studied using the proposed model. The evolution of the hydraulic fracture and the global response of the specimen were recorded in a way comparable to existing experimental data to bridge the experimental and numerical findings. Persistent natural fractures appeared to be barriers for the hydraulic fracture if their conductance is high compared to the matrix conductivity or if their stiffness is significantly low compared to the rock matrix rigidity. Low stiffness in non-persistent defects might also cause a bifurcation of the main hydraulic fracture due to the local stress field perturbation around the defect and ahead of the hydraulic fracture tip. Furthermore, high approach angles and differential stresses seemed to favour crossing of the natural fracture while low angles enable shear slippage or dilation on the part of the plane which is not affected by the local stress perturbation.