Analysis of Hydraulic Fracture Propagation in Fractured Reservoirs

Analysis of Hydraulic Fracture Propagation in Fractured Reservoirs PDF Author: Arash Dahi Taleghani
Publisher:
ISBN:
Category : Gas reservoirs
Languages : en
Pages : 0

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Book Description
Large volumes of natural gas exist in tight fissured reservoirs. Hydraulic fracturing is one of the main stimulating techniques to enhance recovery from these fractured reservoirs. Although hydraulic fracturing has been used for decades for the stimulation of tight gas reservoirs, a thorough understanding of the interaction between induced hydraulic fractures and natural fractures is still lacking. Recent examples of hydraulic fracture diagnostic data suggest complex, multi-stranded hydraulic fracture geometry is a common occurrence. The interaction between pre-existing natural fractures and the advancing hydraulic fracture is a key condition leading to complex fracture patterns. Large populations of natural fractures that exist in formations such as the Barnett shale are sealed by precipitated cements which could be quartz, calcite, etc. Even though there is no porosity in the sealed fractures, they may still serve as weak paths for fracture initiation and/or for diverting the path of the growing hydraulic fractures. Performing hydraulic fracture design calculations under these complex conditions requires modeling of fracture intersections and tracking fluid fronts in the network of reactivated fissures. In this dissertation, the effect of the cohesiveness of the sealed natural fractures and the intact rock toughness in hydraulic fracturing are studied. Accordingly, the role of the pre-existing fracture geometry is also investigated. The results provide some explanations for significant differences in hydraulic fracturing in naturally fractured reservoirs from non-fractured reservoirs. For the purpose of this research, an extended finite element method (XFEM) code is developed to simulate fracture propagation, initiation and intersection. The motivation behind applying XFEM are the desire to avoid remeshing in each step of the fracture propagation, being able to consider arbitrary varying geometry of natural fractures and the insensitivity of fracture propagation to mesh geometry. New modifications are introduced into XFEM to improve stress intensity factor calculations, including fracture intersection criteria into the model and improving accuracy of the solution in near crack tip regions. The presented coupled fluid flow-fracture mechanics simulations extend available modeling efforts and provide a unified framework for evaluating fracture design parameters and their consequences. Results demonstrate that fracture pattern complexity is strongly controlled by the magnitude of in situ stress anisotropy, the rock toughness, the natural fracture cement strength, and the approach angle of the hydraulic fracture to the natural fracture. Previous studies (mostly based on frictional fault stability analysis) have concentrated on predicting the onset of natural fracture failure. However, the use of fracture mechanics and XFEM makes it possible to evaluate the progression of fracture growth over time as fluid is diverted into the natural fractures. Analysis shows that the growing hydraulic fracture may exert enough tensile and/or shear stresses on cemented natural fractures that they may be opened or slip in advance of hydraulic fracture tip arrival, while under some conditions, natural fractures will be unaffected by the hydraulic fracture. A threshold is defined for the fracture energy of cements where, for cases below this threshold, hydraulic fractures divert into the natural fractures. The value of this threshold is calculated for different fracture set orientations. Finally, detailed pressure profile and aperture distributions at the intersection between fracture segments show the potential for difficulty in proppant transport under complex fracture propagation conditions. Whether a hydraulic fracture crosses or is arrested by a pre-existing natural fracture is controlled by shear strength and potential slippage at the fracture intersections, as well as potential debonding of sealed cracks in the near-tip region of a propagating hydraulic fracture. We introduce a new more general criterion for fracture propagation at the intersections. We present a complex hydraulic fracture pattern propagation model based on the Extended Finite Element Method as a design tool that can be used to optimize treatment parameters under complex propagation conditions.

Analysis of Hydraulic Fracture Propagation in Fractured Reservoirs

Analysis of Hydraulic Fracture Propagation in Fractured Reservoirs PDF Author: Arash Dahi Taleghani
Publisher:
ISBN:
Category : Gas reservoirs
Languages : en
Pages : 0

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Book Description
Large volumes of natural gas exist in tight fissured reservoirs. Hydraulic fracturing is one of the main stimulating techniques to enhance recovery from these fractured reservoirs. Although hydraulic fracturing has been used for decades for the stimulation of tight gas reservoirs, a thorough understanding of the interaction between induced hydraulic fractures and natural fractures is still lacking. Recent examples of hydraulic fracture diagnostic data suggest complex, multi-stranded hydraulic fracture geometry is a common occurrence. The interaction between pre-existing natural fractures and the advancing hydraulic fracture is a key condition leading to complex fracture patterns. Large populations of natural fractures that exist in formations such as the Barnett shale are sealed by precipitated cements which could be quartz, calcite, etc. Even though there is no porosity in the sealed fractures, they may still serve as weak paths for fracture initiation and/or for diverting the path of the growing hydraulic fractures. Performing hydraulic fracture design calculations under these complex conditions requires modeling of fracture intersections and tracking fluid fronts in the network of reactivated fissures. In this dissertation, the effect of the cohesiveness of the sealed natural fractures and the intact rock toughness in hydraulic fracturing are studied. Accordingly, the role of the pre-existing fracture geometry is also investigated. The results provide some explanations for significant differences in hydraulic fracturing in naturally fractured reservoirs from non-fractured reservoirs. For the purpose of this research, an extended finite element method (XFEM) code is developed to simulate fracture propagation, initiation and intersection. The motivation behind applying XFEM are the desire to avoid remeshing in each step of the fracture propagation, being able to consider arbitrary varying geometry of natural fractures and the insensitivity of fracture propagation to mesh geometry. New modifications are introduced into XFEM to improve stress intensity factor calculations, including fracture intersection criteria into the model and improving accuracy of the solution in near crack tip regions. The presented coupled fluid flow-fracture mechanics simulations extend available modeling efforts and provide a unified framework for evaluating fracture design parameters and their consequences. Results demonstrate that fracture pattern complexity is strongly controlled by the magnitude of in situ stress anisotropy, the rock toughness, the natural fracture cement strength, and the approach angle of the hydraulic fracture to the natural fracture. Previous studies (mostly based on frictional fault stability analysis) have concentrated on predicting the onset of natural fracture failure. However, the use of fracture mechanics and XFEM makes it possible to evaluate the progression of fracture growth over time as fluid is diverted into the natural fractures. Analysis shows that the growing hydraulic fracture may exert enough tensile and/or shear stresses on cemented natural fractures that they may be opened or slip in advance of hydraulic fracture tip arrival, while under some conditions, natural fractures will be unaffected by the hydraulic fracture. A threshold is defined for the fracture energy of cements where, for cases below this threshold, hydraulic fractures divert into the natural fractures. The value of this threshold is calculated for different fracture set orientations. Finally, detailed pressure profile and aperture distributions at the intersection between fracture segments show the potential for difficulty in proppant transport under complex fracture propagation conditions. Whether a hydraulic fracture crosses or is arrested by a pre-existing natural fracture is controlled by shear strength and potential slippage at the fracture intersections, as well as potential debonding of sealed cracks in the near-tip region of a propagating hydraulic fracture. We introduce a new more general criterion for fracture propagation at the intersections. We present a complex hydraulic fracture pattern propagation model based on the Extended Finite Element Method as a design tool that can be used to optimize treatment parameters under complex propagation conditions.

Hydraulic Fracture Modeling

Hydraulic Fracture Modeling PDF Author: Yu-Shu Wu
Publisher: Gulf Professional Publishing
ISBN: 0128129999
Category : Technology & Engineering
Languages : en
Pages : 568

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Book Description
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

The Combined Finite-Discrete Element Method

The Combined Finite-Discrete Element Method PDF Author: Antonio A. Munjiza
Publisher: John Wiley & Sons
ISBN: 0470020172
Category : Technology & Engineering
Languages : en
Pages : 348

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Book Description
The combined finite discrete element method is a relatively new computational tool aimed at problems involving static and / or dynamic behaviour of systems involving a large number of solid deformable bodies. Such problems include fragmentation using explosives (e.g rock blasting), impacts, demolition (collapsing buildings), blast loads, digging and loading processes, and powder technology. The combined finite-discrete element method - a natural extension of both discrete and finite element methods - allows researchers to model problems involving the deformability of either one solid body, a large number of bodies, or a solid body which fragments (e.g. in rock blasting applications a more or less intact rock mass is transformed into a pile of solid rock fragments of different sizes, which interact with each other). The topic is gaining in importance, and is at the forefront of some of the current efforts in computational modeling of the failure of solids. * Accompanying source codes plus input and output files available on the Internet * Important applications such as mining engineering, rock blasting and petroleum engineering * Includes practical examples of applications areas Essential reading for postgraduates, researchers and software engineers working in mechanical engineering.

Fracture Propagation in Naturally Fractured Reservoirs

Fracture Propagation in Naturally Fractured Reservoirs PDF Author: Hunjoo Peter Lee
Publisher:
ISBN:
Category :
Languages : en
Pages : 378

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Book Description
Investigations of hydrocarbons in tight formations require understanding of hydraulic fracturing in order to optimize the production and recovery of oil and natural gas. The classic description of hydraulic fracture is a single bi-wing planar feature, however, field observations show that hydraulic fracture growth in naturally fractured formations like shale is complex. Lack of knowledge concerning the remote stress impact and the interaction with planes of weakness on a fracture propagation trajectory leads to inaccurate predictions of the fracture geometry and the surface area required for the production estimation. Most studies in engineering mechanics extended the standard mixed-mode fracture propagation models, based on the near tip approximations, to include the impact of the tensile crack-parallel stress on the fracture propagation path. However, for fractures in the subsurface, the remote stress is compression, and internal fluid pressure or frictional stress become important in the near-tip stress field and the propagation trajectory. The Modified Maximum Tangential Principal Stress criterion (MMTPS-criterion) was introduced to address and evaluate the remote and internal crack stresses in the propagation path. The predictions of the fracture propagation angles by the MMTPS-criterion agreed with published experimental results of fractures propagating under both tensile and compressive external loads. In addition, the predictions matched well with uniaxial compression tests on hydrostone samples with the critical radial distance, defined by the process zone size, for open fractures that satisfy the Small Scale Yielding conditions. For short open fractures, a larger critical radial distance was required to correspond with the experimental results. The MMTPS-criterion was also capable of predicting lower propagation angles for closed cracks with higher friction coefficients. Preexisting discontinuities in shale, including natural fractures and bedding, act as planes of weakness that divert fracture propagation. To investigate the influences of weak planes on hydraulic fracture propagation, I performed Semi-Circular Bend (SCB) tests on Marcellus shale core samples containing calcite-filled natural fractures (veins). The approach angle of the induced fracture to the veins and the thickness of the veins had a strong influence on propagation. As the apprach angle became more oblique to the induced fracture plane, and as the vein got thicker, the induced fracture was more likely to divert into the vein. Microstructural analysis of tested samples showed that the induced fracture propagated in the middle of the vein rahter than the interface between vein and the rock matrix. Cleavage planes and fluid inclusion trails in the vein cements exerted some control on the fracture path. By combining the experimental results with theoretical fracture-mechanics arguments, the fracture toughness of the calcite veins was estimated to range from 0.99 MPa [square root of m] to 1.14 MPa [square root of m], depending on the value used for the Young's modulus of the calcite vein material. Measured fracture toughness of unfractured Marcellus shale was 0.64 MPa [square root of m]. A Discrete Element Method (DEM) based numerical modeling software, Particle Flow Code in three-dimensions (PFC3D), was utilized to reproduce and analyze the experimental results of Marcellus shale samples. The trend of numerical results correlated with the interaction feature of the experimental results for various approach angel and thickness (i.e., aperture) of the vein. Further sensitivity analysis on vein properties indicated that veins with lower stranght and higher stiffness contribute to more fracture diversion than veins with higher strenght and lower stiffness. Additionally, parallel bond breakages in the model show that microcracks were generated inside the vein before the induced fracture encountered the vein especially for the veins with higher stiffnesses when compared to the rock matrix. Most of the bond failure mode inside the vein and the induced fracture was tensile rather that shear mode.

The Effect of Cemented Natural Fractures on Hydraulic Fracture Propagation

The Effect of Cemented Natural Fractures on Hydraulic Fracture Propagation PDF Author: Weiwei Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 368

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Book Description
Microseismic events, which are generated during hydraulic fracturing treatments, suggest that a complicated fracture network develops in many naturally−fractured unconventional reservoirs. Deformation along weak planes, such as cemented natural fractures, has been proposed as one of the possible reasons for fracture network complexity. Cemented natural fractures widely exist in shale reservoirs. They are diverse in composition and size, depending on the burial condition, the composition of the rock matrix, and the geochemical environment. The interaction between cemented natural fractures with hydraulic fractures generated as part of the reservoir stimulation are thought to impact hydraulic fracture propagation. Previous studies mostly treated natural fractures as frictional interfaces without considering the actual cement fillings. In this study, I analyzed the effect of cemented natural fractures on hydraulic fracture propagation by considering natural fracture thickness, mechanical properties and rock−cement interface bond strength. Firstly, I conducted a series of semi−circular bend (SCB) tests and corresponding numerical simulations to study the interaction between hydraulic and natural fractures. The SCB tests are attractive in general because of their simple setup with consistent results. The experimental results also served as a validation for numerical model. Two drawbacks of the SCB tests include that the test is unconfined and there is no fluid component. Numerical modeling can then be applied to extend results beyond these shortcomings. Synthetic hydrostone samples with embedded inclusions of different mechanical properties were used to mimic rock with cemented natural fractures. Experimental results identified several parameters that could be used to explain hydraulic fractures interaction with cemented natural fractures. The SCB test conditions that promoted fracture crossing were near−orthogonal approach angles, small natural fracture thicknesses, and strong rock−cement interfaces. Such conditions in a reservoir would promote long hydraulic fractures and less complicated fracture networks. In contrast, the SCB test conditions that caused fracture diverting were more oblique approach angles, large natural fracture thicknesses, and weak rock−cement interfaces, resulting in short hydraulic fractures and more complicated fracture networks. The SCB tests using synthetic rock samples provided insights into the hydraulic fracture propagation in naturally−fractured reservoirs. Through the numerical modeling with the finite element code in Abaqus, the impact of fluid driven fracturing on fracture−fracture interaction was investigated. Fracture propagation in two dimensions was modeled using the cohesive elements and anisotropic compressive remote stress conditions. Results suggest that if the natural fracture thickness is considered, the commonly used fracture crossing/diverting criterion will overestimate the hydraulic fracture crossing scenario. Factors including modulus contrast and coefficient of friction also influence hydraulic fracture interaction with natural fractures. An application of this work is the case of how bedding−parallel veins will affect hydraulic fracture height growth. Such natural fractures are abundant in the unconventional resource play in the Vaca Muerta formation in Argentina. When the rock−cement coefficient of friction is around 0.4−0.5, which most likely represents shale reservoirs, hydraulic fracture crossing behavior is affected by the modulus contrast between natural fractures and host rock as well as the natural fracture thickness.

Unconventional Reservoir Geomechanics

Unconventional Reservoir Geomechanics PDF Author: Mark D. Zoback
Publisher: Cambridge University Press
ISBN: 1107087074
Category : Business & Economics
Languages : en
Pages : 495

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Book Description
A comprehensive overview of the key geologic, geomechanical and engineering principles that govern the development of unconventional oil and gas reservoirs. Covering hydrocarbon-bearing formations, horizontal drilling, reservoir seismology and environmental impacts, this is an invaluable resource for geologists, geophysicists and reservoir engineers.

Numerical Modeling of Complex Hydraulic Fracture Propagation in Layered Reservoirs with Auto-optimization

Numerical Modeling of Complex Hydraulic Fracture Propagation in Layered Reservoirs with Auto-optimization PDF Author: Jiacheng Wang (Ph. D.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
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

Geomechanics and Hydraulic Fracturing for Shale Reservoirs

Geomechanics and Hydraulic Fracturing for Shale Reservoirs PDF Author: Yu Wang
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1618968963
Category : Art
Languages : en
Pages : 383

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Book Description
This book is intended as a reference book for advanced graduate students and research engineers in shale gas development or rock mechanical engineering. Globally, there is widespread interest in exploiting shale gas resources to meet rising energy demands, maintain energy security and stability in supply and reduce dependence on higher carbon sources of energy, namely coal and oil. However, extracting shale gas is a resource intensive process and is dependent on the geological and geomechanical characteristics of the source rocks, making the development of certain formations uneconomic using current technologies. Therefore, evaluation of the physical and mechanical properties of shale, together with technological advancements, is critical in verifying the economic viability of such formation. Accurate geomechanical information about the rock and its variation through the shale is important since stresses along the wellbore can control fracture initiation and frac development. In addition, hydraulic fracturing has been widely employed to enhance the production of oil and gas from underground reservoirs. Hydraulic fracturing is a complex operation in which the fluid is pumped at a high pressure into a selected section of the wellbore. The interaction between the hydraulic fractures and natural fractures is the key to fracturing effectiveness prediction and high gas development. The development and growth of a hydraulic fracture through the natural fracture systems of shale is probably more complex than can be described here, but may be somewhat predictable if the fracture system and the development of stresses can be explained. As a result, comprehensive shale geomechanical experiments, physical modeling experiment and numerical investigations should be conducted to reveal the fracturing mechanical behaviors of shale.

Numerical Investigation of Interaction Between Hydraulic Fractures and Natural Fractures

Numerical Investigation of Interaction Between Hydraulic Fractures and Natural Fractures PDF Author: Wenxu Xue
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
Hydraulic fracturing of a naturally-fractured reservoir is a challenge for industry, as fractures can have complex growth patterns when propagating in systems of natural fractures in the reservoir. Fracture propagation near a natural fracture (NF) considering interaction between a hydraulic fracture (HF) and a pre-existing NF, has been investigated comprehensively using a two dimensional Displacement Discontinuity Method (DDM) Model in this thesis. The rock is first considered as an elastic impermeable medium (with no leakoff), and then the effects of pore pressure change as a result of leakoff of fracturing fluid are considered. A uniform pressure fluid model and a Newtonian fluid flow model are used to calculate the fluid flow, fluid pressure and width distribution along the fracture. Joint elements are implemented to describe different NF contact modes (stick, slip, and open mode). The structural criterion is used for predicting the direction and mode of fracture propagation. The numerical model was used to first examine the mechanical response of the NF to predict potential reactivation of the NF and the resultant probable location for fracture re-initiation. Results demonstrate that: 1) Before the HF reaches a NF, the possibility of fracture re-initiation across the NF and with an offset is enhanced when the NF has weaker interfaces; 2) During the stage of fluid infiltration along the NF, a maximum tensile stress peak can be generated at the end of the opening zone along the NF ahead of the fluid front; 3) Poroelastic effects, arising from fluid diffusion into the rock deformation can induce closure and compressive stress at the center of the NF ahead of the HF tip before HF arrival. Upon coalescence when fluid flows along the NF, the poroelastic effects tend to reduce the value of the HF aperture and this decreases the tension peak and the possibility of fracture re-initiation with time. Next, HF trajectories near a NF were examined prior to coalesce with the NF using different joint, rock and fluid properties. Our analysis shows that: 1) Hydraulic fracture trajectories near a NF may bend and deviate from the direction of the maximum horizontal stress when using a joint model that includes initial joint deformation; 2) Hydraulic fractures propagating with higher injection rate or fracturing fluid of higher viscosity propagate longer distance when turning to the direction of maximum horizontal stress; 3) Fracture trajectories are less dependent on injection rate or fluid viscosity when using a joint model that includes initial joint deformation; whereas, they are more dominated by injection rate and fluid viscosity when using a joint model that excludes initial joint deformation.

Hydraulic Fracture Modeling in Naturally Fractured Reservoirs

Hydraulic Fracture Modeling in Naturally Fractured Reservoirs PDF Author: Kaustubh Shrivastava
Publisher:
ISBN:
Category :
Languages : en
Pages : 239

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Book Description
Hydraulic fracturing of horizontal wells is one of the key technological breakthroughs that has led to the shale revolution. Hydraulic fracturing models are used to engineer hydraulic fracture design and optimize production. Typically, hydraulic fracturing models treat hydraulic fractures as planar, bi-wing fractures. However, recent core-through investigations have suggested that during hydraulic fracturing in naturally fractured reservoirs, complex hydraulic fracture geometries can be created due to the interaction of the growing hydraulic fracture with natural fractures. This limits the application of planar fracture models for optimizing hydraulic fracturing design in naturally fractured reservoirs. In this research, we present a novel three-dimensional displacement discontinuity method based hydraulic fracturing simulator that allows us to model hydraulic fracture growth in the presence of natural fractures along with proppant transport in an efficient manner. The model developed in this dissertation is used to investigate the interaction of a hydraulic fracture with natural fractures and study the transport of proppant in the resulting complex fracture networks. This investigation gives us novel insight into the influence of fracture geometry and stress interference on the final distribution of proppant in fracture networks. Based on this investigation, suggestions are made to improve proppant transport in complex fracture networks. In order to correctly capture the effect of natural fractures on fracture growth, knowledge about the distribution of natural fractures in the reservoir is imperative. Typically, little is known about the in-situ natural fracture distribution, as direct observation of the reservoir is not possible. A novel technique of synthetic coring is developed to create a discrete fracture network (DFN) from core data, and it is used to create a DFN based on the Hydraulic Fracturing Test Site #1 data. Hydraulic fracture propagation is modeled in the created DFN, and the results are compared with field observations. As the reservoir may contain thousands of natural fractures, simulations in a realistic DFN can be computationally very expensive. In order to reduce the computational requirements of the simulator, we present a novel predictor step based on the local linearization method that provides a better initial guess for solving the fluid-solid interaction problem. This is shown to reduce computational time significantly. A novel technique, Extended Adaptive Integral Method, to speed up the simulator is developed. The method uses an effective medium to represent the interaction between displacement discontinuity elements and reduces the order of complexity of solving the geomechanical system of equations from O(N2) to O(NlogN). The novel formulation of this method is presented, and sensitivity studies are conducted to show the improvement in computational efficiency