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 of Fluid Flow Proppant Transport and Fracture Propagation in Hydraulic Fractures for Unconventional Reservoirs written by Yatin Suri and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Rock Characterisation Modelling and Engineering Design Methods written by Xia-Ting Feng and published by CRC Press. This book was released on 2013-05-17 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rock Characterisation, Modelling and Engineering Design Methods contains the contributions presented at the 3rd ISRM SINOROCK Symposium (Shanghai, China, 1820 June 2013). The papers contribute to the further development of the overall rock engineering design process through the sequential linkage of the three themes of rock characterisation, model

Download or read book Fractured Porous Media written by Pierre M. Adler and published by Oxford University Press, USA. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.

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 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 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 Flow and Transport Through and Deformation of Rough Fractures written by Lichun Wang and published by . This book was released on 2015 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding physical, chemical, and mechanical processes and properties of a single fracture is fundamental to many processes on Earth, particularly hydrogeological phenomena across many scales. However, classical and widely used theories governing flow and transport processes are founded on the parallel plates model; this ignores the complex morphology of natural fracture. To fill this gap, I have investigated the role of fracture morphology on flow (permeability), transport (dispersion coefficients and other surrogate parameters), and mechanical (stiffness) properties through complementary theoretical analysis and computational experiments. The collection of single fractures used in this dissertation included natural fractures mapped through high-resolution x-ray computed tomography and synthetic ones generated through a model which produces fractures with fractal properties. I developed a modified Local Cubic Law (MLCL) allowing for fracture roughness, tortuosity, and weak inertial force to improve the prediction of fluid flow process. The validation of the MLCL was tested by comparing volumetric flux from solving the Navier-Stokes equations to that from the MLCL. Secondly, the effect of fracture roughness on the non-Fickian or anomalous transport was studied through an ensemble of 2D direct transport simulations. Moreover, I was able to show, analyze, and predict the transition from non-Fickian to Fickian transport by developing a quasi-3D particle tracking algorithm. Finally, I developed a fracture deformation model. The co-evolving permeability and stiffness were then determined through the MLCL and strain-stress relationship based on the deformation model. Through my dissertation research, I confirm that the classical LCL fails to predict bulk permeability or volumetric flux (errors up to 41%). The MLCL performs better in characterizing local and effective fluid flow processes, with only 4% error. Moreover, I find out that fracture roughness leads to non-Fickian transport, and that the degree of non-Fickian behavior depends directly on the fracture roughness. Additionally, I theoretically derive asymptotic time and lengths scales for distinguishing non-Fickian from Fickian transport for the simplified Poiseuille and Hagan-Poiseuille flow fields. The increasing scales drives non-Fickian transitioning into Fickian transport even though the presence of persistent intermittent velocity structure. Lastly, I show that scaling between fracture permeability and normal stiffness depends on both fracture roughness and aperture correlation length, indicating a potentially universal model that can describe this behavior.

Download or read book Modeling and Analysis of Fluid Driven Fracture Propagation Under the Plane Strain Condition written by Young Hoon Kim and published by . This book was released on 2013 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of fracture propagation driven by the pressure of the fluid flow between the fracture surfaces has been of considerable interest for understanding natural geological phenomena such as the formation of volcanic dikes and developing hydraulic fracturing technologies for industrial applications. Man-made hydraulic fracturing has been most commonly used for stimulation of oil and gas reservoirs to increase hydrocarbon production, stimulation of geothermal reservoirs, remediation of soil and groundwater aquifers, injection of wastes, goafing and fault reactivation in mining, and measurement of underground in situ stresses. Computational modeling and simulation of fluid driven fracture propagation in realistic geological formation has been a challenging problem because of various complexities including formation heterogeneities and the use of highly nonlinear engineered fluids. At present, one of the main obstacles for the robust industrial application of the simulating technology is the computational efficiency and stability. The objective of this study is to investigate the numerical efficiency and stability of various algorithms that can be potentially used in modeling of fluid driven fracture propagation. For simplicity, we have focused on fracture propagation in the plane strain condition. The fracture is assumed to in homogeneous linear elastic medium and modeled using displacement discontinuity boundary element method (DDBEM). The nonlinear power-law fluid flow is modeled using conventional lubrication theory. The coupled equations are then discretized using zero order elements for its efficiency. The coupled equations become increasingly stiff and difficulty to solve when the power law indices become smaller. Various numerical algorithms such as Newton iteration with line search, trust-region and quasi-Newton method are investigated and compared. We have also extended the model to the fluid driven non-planar fracture propagation. A numerical crack propagation criterion based on the minimum local shear stress under mixed loading condition is proposed and compared with conventional theoretical and numerical criteria. The new crack propagation criterion provides more accurate and smooth crack initiation paths. Finally we have studied the geomechanics interaction between two simultaneous fluid driven fractures. The results provided some useful inputs for optimal design of multiple stage and multiple fracturing treatments along horizontal wells currently adopted by the oil and gas industry for the economical recovery of unconventional resources such as shale gas and oil.

Download or read book Numerical Simulation of Fracture Pattern Development and Implications for Fluid Flow written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Simulation of Two phase Flow in Discrete Fractures Using Rayleigh Ritz Finite Element Method written by Sandeep P. Kaul and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.

Download or read book Fluid Flow in Fractured Rocks written by Robert W. Zimmerman and published by John Wiley & Sons. This book was released on 2023-12-19 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: FLUID FLOW IN FRACTURED ROCKS "The definitive treatise on the subject for many years to come" (Prof. Ruben Juanes, MIT) Authoritative textbook that provides a comprehensive and up-to-date introduction to fluid flow in fractured rocks Fluid Flow in Fractured Rocks provides an authoritative introduction to the topic of fluid flow through single rock fractures and fractured rock masses. This book is intended for readers with interests in hydrogeology, hydrology, water resources, structural geology, reservoir engineering, underground waste disposal, or other fields that involve the flow of fluids through fractured rock masses. Classical and established models and data are presented and carefully explained, and recent computational methodologies and results are also covered. Each chapter includes numerous graphs, schematic diagrams and field photographs, an extensive reference list, and a set of problems, thus providing a comprehensive learning experience that is both mathematically rigorous and accessible. Written by two internationally recognized leaders in the field, Fluid Flow in Fractured Rocks includes information on: Nucleation and growth of fractures in rock, with a multiscale characterization of their geometric traits Effect of normal and shear stresses on the transmissivity of a rock fracture and mathematics of fluid flow through a single rock fracture Solute transport in rocks, with quantitative descriptions of advection, molecular diffusion, and dispersion Fluid Flow in Fractured Rocks is an essential resource for researchers and postgraduate students who are interested in the field of fluid flow through fractured rocks. The text is also highly suitable for professionals working in civil, environmental, and petroleum engineering.

Download or read book MULTIDIMENSIONAL NUMERICAL SIMULATION OF FLUID FLOW IN FRACTURED POROUS MEDIA written by and published by . This book was released on 1980 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Simulation of Multiphase Fluid Flow in Naturally Fractured Reservoirs written by Kuriyit Nakornthap and published by . This book was released on 1982 with total page 476 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 Rock Fractures and Fluid Flow written by National Research Council and published by National Academies Press. This book was released on 1996-08-27 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific understanding of fluid flow in rock fracturesâ€"a process underlying contemporary earth science problems from the search for petroleum to the controversy over nuclear waste storageâ€"has grown significantly in the past 20 years. This volume presents a comprehensive report on the state of the field, with an interdisciplinary viewpoint, case studies of fracture sites, illustrations, conclusions, and research recommendations. The book addresses these questions: How can fractures that are significant hydraulic conductors be identified, located, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? Among other topics, the committee provides a geomechanical understanding of fracture formation, reviews methods for detecting subsurface fractures, and looks at the use of hydraulic and tracer tests to investigate fluid flow. The volume examines the state of conceptual and mathematical modeling, and it provides a useful framework for understanding the complexity of fracture changes that occur during fluid pumping and other engineering practices. With a practical and multidisciplinary outlook, this volume will be welcomed by geologists, petroleum geologists, geoengineers, geophysicists, hydrologists, researchers, educators and students in these fields, and public officials involved in geological projects.

Download or read book Unconventional Reservoir Geomechanics written by Mark D. Zoback and published by Cambridge University Press. This book was released on 2019-05-16 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.