Download or read book Mathematical and Numerical Modeling of Hydraulic Fractures for Non Newtonian Fluids written by and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical and Numerical Modeling of Hydraulic Fractures for Non Newtonian Fluids written by Monika Perkowska and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Theoretical and Numerical Simulation of Non Newtonian Fluid Flow in Propped Fractures written by Liangchen Ouyang and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The flow of non-Newtonian fluids in porous media is important in many applications, such as polymer processing, heavy oil flow, and gel cleanup in propped fractures. Residual polymer gel in propped fractures results in low fracture conductivity and short effective fracture length, sometimes causing severe productivity impairment of a hydraulically fractured well. Some residual gels are concentrated in the filter cakes built on the fracture walls and have much higher polymer concentration than the original gel. The residual gel exhibits a higher yield stress, and is difficult to remove after fracture closure. But non-Newtonian fluid has complicated rheological equation and its flow behavior in porous media is difficult to be described and modeled. The Kozeny-Carman equation, a traditional permeability-porosity relationship, has been popularly used in porous media flow models. However, this relationship is not suitable for non-Newtonian fluid flow in porous media. At first, I studied polymer gel behavior in hydraulic fracturing theoretically and experimentally. I developed a model to describe the flow behavior of residual polymer gel being displaced by gas in parallel plates. I developed analytical models for gas-liquid two-phase stratified flow of Newtonian gas and non-Newtonian residual gel to investigate gel cleanup under different conditions. The concentrated gel in the filter cake was modeled as a Herschel-Buckley fluid, a shear-thinning fluid following a power law relationship, but also having a yield stress. Secondly, I used a combination of analytical calculations and 3D finite volume simulation to investigate the flow behavior of Herschel-Bulkley non-Newtonian fluid flow through propped fractures. I developed the comprehensive mathematical model, and then modified the model based on numerical simulation results. In the simulations, I developed a micro pore-scale model to mimic the real porous structure of flow channel in propped fractures. The correlation of pressure gradient and superficial velocity was investigated under the influence of primary parameters, such as yield stress, power law index, and consistency index. I also considered the effect of proppant packing arrangement and proppant diameter. The Herschel-Bulkley model was used with an appropriate modification proposed by Papanastasiou to avoid the discontinuity of the apparent viscosity and numerical difficulties. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151731

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 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 Mechanics written by Peter Valkó and published by . This book was released on 1995 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the theoretical background of one of the most widespread activities in hydrocarbon wells, that of hydraulic fracturing. A comprehensive treatment of the basic phenomena includes: linear elasticity, stresses, fracture geometry and rheology. The diverse concepts of mechanics are integrated into a coherent description of hydraulic fracture propagation. The chapters in the book are cross-referenced throughout and the connections between the various phenomena are emphasized. The book offers readers a unique approach to the subject with the use of many numerical 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 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 An Integrated Peridynamics finite Volume Based Multi phase Flow Geomechanics and Hydraulic Fracture Model written by Shivam Agrawal and published by . This book was released on 2019 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydraulic fracturing in unconventional reservoirs exhibits several interesting phenomena including the interaction of hydraulic fractures with multi-scale heterogeneities such as natural fractures, stress/barrier layers, bedding planes, shale laminations, and mineralogy. Moreover, hydraulic fractures originating from different clusters or stages in a multi-stage, multi-cluster treatment interact among themselves. Mathematical models, with various degrees of numerical complexity, are developed for gaining better insights into the physics governing these phenomena. Peridynamics-based hydraulic fracturing model developed by Ouchi (2016) has been demonstrated to capture all of these phenomena. However, its major drawback is that it is computationally expensive. In this dissertation, we have extended the capabilities of the model to multi-phase flow and made it significantly faster by coupling it with the less expensive Finite Volume Method. The single-phase peridynamics flow model for slightly compressible, Newtonian fluids has been generalized for multiphase, multicomponent flow of compressible, non-Newtonian fluids. The generalized flow model has been coupled with the fracturing model and compared with laboratory experiments performed under low confining stresses. The extended model is also applied to simulate the growth of fractures from a new (child) well in the presence of depleted regions created by production from the fractures of an old (parent) well under high confining stresses. The interaction of a hydraulic fracture (HF) with a natural fracture (NF) is investigated. Remote shear failure of the NF due to the pororelastic stress changes caused by the propagating HF are considered. Consistent with the experiments, the remote shear failure is shown to result in the bending of the HF towards the NF before intersecting with it. Accounting for the effects of remote shear failure and poroelasticity, numerical crossing criteria for the HF-NF interaction are developed. The hydraulic fracturing model based on peridynamics (PD) theory is coupled with the less expensive Finite Volume Method (FVM), following the PD-FEM coupling method proposed by Galvanetto et al. (2016). Significant improvements in computational performance are achieved by the coupled model relative to the pure PD-based model, without compromising the unique original capabilities. By monitoring material damage in remote heterogeneous regions, a workflow for estimating the extent of the Stimulated Reservoir Volume (SRV) around a primary hydraulic fracture is developed. A sensitivity study for the effects of elastic properties of the formation, injection rate, and the reservoir fluid type on SRV extent is presented

Download or read book FEFLOW written by Hans-Jörg G. Diersch and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e.g., multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e.g., flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).

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 Numerical Modeling of Hydraulic Fracture Propagation Using Thermo hydro mechanical Analysis with Brittle Damage Model by Finite Element Method written by Kyoung Min and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Better understanding and control of crack growth direction during hydraulic fracturing are essential for enhancing productivity of geothermal and petroleum reservoirs. Structural analysis of fracture propagation and impact on fluid flow is a challenging issue because of the complexity of rock properties and physical aspects of rock failure and fracture growth. Realistic interpretation of the complex interactions between rock deformation, fluid flow, heat transfer, and fracture propagation induced by fluid injection is important for fracture network design. In this work, numerical models are developed to simulate rock failure and hydraulic fracture propagation. The influences of rock deformation, fluid flow, and heat transfer on fracturing processes are studied using a coupled thermo-hydro-mechanical (THM) analysis. The models are used to simulate microscopic and macroscopic fracture behaviors of laboratory-scale uniaxial and triaxial experiments on rock using an elastic/brittle damage model considering a stochastic heterogeneity distribution. The constitutive modeling by the energy release rate-based damage evolution allows characterizing brittle rock failure and strength degradation. This approach is then used to simulate the sequential process of heterogeneous rock failures from the initiation of microcracks to the growth of macrocracks. The hydraulic fracturing path, especially for fractures emanating from inclined wellbores and closed natural fractures, often involves mixed mode fracture propagation. Especially, when the fracture is inclined in a 3D stress field, the propagation cannot be modeled using 2D fracture models. Hence, 2D/3D mixed-modes fracture growth from an initially embedded circular crack is studied using the damage mechanics approach implemented in a finite element method. As a practical problem, hydraulic fracturing stimulation often involves fluid pressure change caused by injected fracturing fluid, fluid leakoff, and fracture propagation with brittle rock behavior and stress heterogeneities. In this dissertation, hydraulic fracture propagation is simulated using a coupled fluid flow/diffusion and rock deformation analysis. Later THM analysis is also carried out. The hydraulic forces in extended fractures are solved using a lubrication equation. Using a new moving-boundary element partition methodology (EPM), fracture propagation through heterogeneous media is predicted simply and efficiently. The method allows coupling fluid flow and rock deformation, and fracture propagation using the lubrication equation to solve for the fluid pressure through newly propagating crack paths. Using the proposed model, the 2D/3D hydraulic fracturing simulations are performed to investigate the role of material and rock heterogeneity. Furthermore, in geothermal and petroleum reservoir design, engineers can take advantage of thermal fracturing that occurs when heat transfers between injected flow and the rock matrix to create reservoir permeability. These thermal stresses are calculated using coupled THM analysis and their influence on crack propagation during reservoir stimulation are investigated using damage mechanics and thermal loading algorithms for newly fractured surfaces. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/150961

Download or read book Mechanics of Hydraulic Fracturing written by Xin-rong Zhang and published by John Wiley & Sons. This book was released on 2023-01-05 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics of Hydraulic Fracturing Comprehensive single-volume reference work providing an overview of experimental results and predictive methods for hydraulic fracture growth in rocks Mechanics of Hydraulic Fracturing: Experiment, Model, and Monitoring provides a summary of the research in mechanics of hydraulic fractures during the past two decades, plus new research trends to look for in the future. The book covers the contributions from theory, modeling, and experimentation, including the application of models to reservoir stimulation, mining preconditioning, and the formation of geological structures. The four expert editors emphasize the variety of diverse methods and tools in hydraulic fracturing and help the reader understand hydraulic fracture mechanics in complex geological situations. To aid in reader comprehension, practical examples of new approaches and methods are presented throughout the book. Key topics covered in the book include: Prediction of fracture shapes, sizes, and distributions in sedimentary basins, plus their importance in petroleum industry Real-time monitoring methods, such as micro-seismicity and trace tracking How to uncover geometries of fractures like dikes and veins Fracture growth of individual foundations and its applications Researchers and professionals working in the field of fluid-driven fracture growth will find immense value in this comprehensive reference on hydraulic fracturing mechanics.

Download or read book Mechanics of Hydraulic Fracturing written by Ching H. Yew and published by Gulf Professional Publishing. This book was released on 2014-09-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised to include current components considered for today's unconventional and multi-fracture grids, Mechanics of Hydraulic Fracturing, Second Edition explains one of the most important features for fracture design — the ability to predict the geometry and characteristics of the hydraulically induced fracture. With two-thirds of the world's oil and natural gas reserves committed to unconventional resources, hydraulic fracturing is the best proven well stimulation method to extract these resources from their more remote and complex reservoirs. However, few hydraulic fracture models can properly simulate more complex fractures. Engineers and well designers must understand the underlying mechanics of how fractures are modeled in order to correctly predict and forecast a more advanced fracture network. Updated to accommodate today's fracturing jobs, Mechanics of Hydraulic Fracturing, Second Edition enables the engineer to: - Understand complex fracture networks to maximize completion strategies - Recognize and compute stress shadow, which can drastically affect fracture network patterns - Optimize completions by properly modeling and more accurately predicting for today's hydraulic fracturing completions - Discusses the underlying mechanics of creating a fracture from the wellbore - Enhanced to include newer modeling components such as stress shadow and interaction of hydraulic fracture with a natural fracture, which aids in more complex fracture networks - Updated experimental studies that apply to today's unconventional fracturing cases

Download or read book Numerical Modeling of Fluid driven Hydraulic Fracturing and J integral Analysis written by Shijun Wei and published by . This book was released on 2020 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper numerically investigates inelastic behavior of sandstone for better understanding of hydraulic fracture propagation in georeservoirs. Although many numerical, theoretical, and experimental studies investigated hydraulic fracturing, not enough emphasis has been given to the inelastic behavior of rock prior and during the hydraulic fracture propagation. Current practice widely uses linear elastic fracture mechanics (LEFM) principles for prediction of hydraulic fracturing in weak sandstone. However, discrepancies between LEFM models and filed or laboratory results indicate presence of plastic deformation, such as are for example micro-cracks or acoustic emission cloud data. Therefore, this study uses J-integral for obtaining hydraulic fracture propagation criteria under the elastic-plastic stress-strain state. J-integral is calculated on the path around a DEM model in two-dimensions. A synthetic rock mass modeled in DEM has an advantage of time-stepping and stress-strain redistribution which leads to micro-cracks represented by broken bonds between DEM particles, and therefore models well elastoplastic behavior. The relationship between far-field stress magnitudes and breakdown pressures, process zone length and calculated J-integral values are presented. The relationship between crack driving forces and applied stresses is investigated to better understand the plasticity effects. The influence of stiffness of sandstone on breakdown pressures and J-integral values are also studied. Overall, results show that LEFM is not applicable for describing fracture propagation at higher confinement stresses. Inelastic J-integral increases dramatically with rock confinement, especially its plastic portion.

Download or read book Numerical Model of Massive Hydraulic Fracture Final Report SYMFRAC1 written by and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This project has involved development of a hydraulic fracture simulator which calculates fracture height as a function of distance from the wellbore in a situation in which a payzone is bounded by two zones in which the minimum in-situ stress is higher (the fracture is vertical). The fracture must be highly elongated (length/height ratio approximately greater than 4) and variations in elastic modulus across zones are ignored. First, we describe the leakoff and spurt loss calculations employed in the modeling. Second, we discuss a revised version of the vertically symmetric simulator (bounding zone stresses equal). The addition of non-Newtonian flow and leakoff (including spurt loss) is described in detail. An illustrative result is given. Third, we describe in detail the vertically asymmetric simulator (bounding zone stresses not equal). To illustrate the last results, we present design calculations for a 30,000 gallon fracture, which was the first stimulation in the Multi-Well Experiment. The 80 ft fracture interval in the Paludal zone has at its upper edge a 520 psi stress contrast, and at its lower edge a 1195 psi contrast. Computed fracture height growth above and below the perforated interval, bottomhole pressure, and width profiles in vertical sections are displayed. Comparison is made with diagnostic measurements of fracture length, height, and bottomhole pressure. The appropriate computer codes are included in this report. 21 references, 11 figures, 4 tables.

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