Semi Analytical Modeling Of Fluid Flow And Solid Deformation In Heterogeneous Reservoirs Using Universal Boundary Integral Approaches

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Semi-Analytical Modeling of Fluid Flow and Solid Deformation in Heterogeneous Reservoirs Using Universal Boundary Integral Approaches

Author : Lei Xiao
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)

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Book Synopsis Semi-Analytical Modeling of Fluid Flow and Solid Deformation in Heterogeneous Reservoirs Using Universal Boundary Integral Approaches by : Lei Xiao

Download or read book Semi-Analytical Modeling of Fluid Flow and Solid Deformation in Heterogeneous Reservoirs Using Universal Boundary Integral Approaches written by Lei Xiao and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Canadian oil and gas industry, heavy oil and unconventional reservoirs play a vital role in sustaining the production of crude oil and face tremendous technical challenges of enhancing recovery while reducing environmental footprints. Among various development technologies, the cold heavy oil production with sand (CHOPS) and hydraulic fracturing techniques have been widely applied in Western Canadian basins to unlock the unconsolidated heavy oil and tight formation reservoirs, respectively. Both technologies are proved to be efficient during the primary production period; however, they suffer sharp production decline and low recovery factor. Moreover, during the enhanced oil recovery (EOR) phase, the existence of wormholes and fractures will cause conformance problems and early polymer injection breakthrough. Therefore, better understanding of the wormholes distributions in CHOPS reservoirs and more reliable description of fractures in tight formations become crucial for Canadian operators to design EOR pilots and operate full field applications. Reservoir characterization and modeling of CHOPS reservoirs with wormholes and fractured tight formations face numerous technical issues due to the existence of wormholes and fractures, which make the system no longer homogeneous and cause more complex problems in fluid flow and solid deformation. The boundary element method (BEM), which has been widely applied to solve for fluid flow and solid deformation problems, however, is limited to homogeneous systems. To inherit the merits of BEM such as near-analytical accuracy and negligible space and time subdivision, this research aims at developing boundary integral approaches, as extensions of BEM, to heterogeneous reservoirs with arbitrary wormhole distributions, realistic fracture morphologies, and variation of geological facies. Moreover, field operators have observed that the in-situ stress state will be altered during hydraulic fracturing with associated stress shadow effects. The depletion-induced stress changes will also cause fracture closure and stress reorientation. Accordingly, the boundary integral approaches are further extended to solve for depletion-induced stress change due to poroelastic and mechanical effects in a heterogeneous reservoir with arbitrary distribution of porosity and permeability. The universal boundary integral approaches, which include the integration of various fundamental solutions along boundaries, have been proposed in this study. The developed boundary integral approaches are benchmarked by comparing with analytical solutions and numerical simulations. Representative cases are also presented to analyze complicated heterogeneous problems. Applications of the universal boundary integral approaches for heterogeneous systems are exemplified in the areas of wormhole coverage estimation, pressure and rate transient analysis of heterogeneous reservoirs, spatial-temporal stress evolution of multi-stage fractured horizontal wells, and evaluation of refracturing upside.

Unsteady-state Fluid Flow

Author : E.J. Hoffman
Publisher : Elsevier
ISBN 13 : 0080543456
Total Pages : 484 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Unsteady-state Fluid Flow by : E.J. Hoffman

Download or read book Unsteady-state Fluid Flow written by E.J. Hoffman and published by Elsevier. This book was released on 1999-07-02 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ubiquitous examples of unsteady-state fluid flow pertain to the production or depletion of oil and gas reservoirs. After introductory information about petroleum-bearing formations and fields, reservoirs, and geologic codes, empirical methods for correlating and predicting unsteady-state behavior are presented. This is followed by a more theoretical presentation based on the classical partial differential equations for flow through porous media.Whereas these equations can be simplified for the flow of (compressible) fluids, and idealized solutions exist in terms of Fourier series for linear flow and Bessel functions for radial flow, the flow of compressible gases requires computer solutions, read approximations. An analysis of computer solutions indicates, fortuitously, that the unsteady-state behavior can be reproduced by steady-state density or pressure profiles at successive times. This will demark draw down and the transition to long-term depletion for reservoirs with closed outer boundaries.As an alternative, unsteady-state flow may be presented in terms of volume and surface integrals, and the methodology is fully developed with examples furnished. Among other things, permeability and reserves can be estimated from well flow tests.The foregoing leads to an examination of boundary conditions and degrees of freedom and raises arguments that the classical partial differential equations of mathematical physics may not be allowable representations. For so-called open petroleum reservoirs where say water-drive exists, the simplifications based on successive steady-state profiles provide a useful means of representation, which is detailed in the form of material balances. Unsteady-State Fluid Flow provides:• empirical and classical methods for correlating and predicting the unsteady-state behavior of petroleum reservoirs• analysis of unsteady-state behavior, both in terms of the classical partial differential equations, and in terms of volume and surface integrals• simplifications based on successive steady-state profiles which permit application to the depletion of both closed reservoirs and open reservoirs, and serves to distinguish drawdown, transition and long-term depletion performance.

Semi-analytical Modelling of Fluid Flow in Unconventional Fractured Reservoirs Including Branch-fracture Permeability Field

$Download Semi-analytical Modelling of Fluid Flow in Unconventional Fractured Reservoirs Including Branch-fracture Permeability Field PDF Online Free$

Author : Ayon Kumar Das
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (131 download)

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Book Synopsis Semi-analytical Modelling of Fluid Flow in Unconventional Fractured Reservoirs Including Branch-fracture Permeability Field by : Ayon Kumar Das

Download or read book Semi-analytical Modelling of Fluid Flow in Unconventional Fractured Reservoirs Including Branch-fracture Permeability Field written by Ayon Kumar Das and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing demand for energy and unavailability of new viable energy resources have played a crucial role in the persistent exploitation of unconventional resources through multistage hydraulic fracturing. Currently, standard modelling approaches idealize a fractured media as an interplay of several homogeneous continuum of normal diffusive characteristics. However, evolved branch-fractures generate a space with extreme heterogeneity around primary fracture plane. The precise characterization of these branch-fractures is imperative for well performance analysis along with subdiffusive behaviour of unconventional matrices. This study presents two semi-analytical models that account for the branch-fracture permeability field and subdiffusion. The first model, Induced Branch-fracture Subdiffusive Flow model (SIBFF), accounts for exponential permeability field concept and subdiffusive transport behaviour of matrices. Compared to the earlier analytical models, the SIBFF model accounts for more comprehensive transport mechanisms and medium properties. The other model, Fractal Branch-fracture model, couples fractal porosity/permeability distribution of branch-fracture and subdiffusion to account for more detailed description of stimulated reservoir volume (SRV) and unfractured inner region. The wellbore pressure solution is derived by discretizing the reservoir into several flow regions and imposing both flux and pressure continuity at the interface between contiguous segments. The inclusion of permeability field and fractional flux law introduces important complexities to the mathematical model that are carefully resolved by implementing Bessel functions and Laplace transformation (LT). Finally, the solution is inverted to time domain using Gaver-Wynn-Rho (GWR) algorithm. This study also assessed the applicability of four numerical inversion methods and found GWR method more suitable and predictive. The sensitivity of important model parameters is presented. Results were verified analytically and validated against Niobrara and Eagleford field data. It is shown that the models could be implemented to quantify the efficiency of a stimulation job, to decide on the necessity of re-fracturing a formation and to analyze horizontal well performance with better predictive capability. The proposed models could further be employed to characterize different flow regimes for unconventional reservoirs.

Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs

Author : Myron B. III. Allen
Publisher : Springer Science & Business Media
ISBN 13 : 3642822134
Total Pages : 219 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs by : Myron B. III. Allen

Download or read book Collocation Techniques for Modeling Compositional Flows in Oil Reservoirs written by Myron B. III. Allen and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This investigation is an outgrowth of my doctoral dissertation at Princeton University. I am particularly grateful to Professors George F. Pinder and William G. Gray of Princeton for their advice during both my research and my writing. I believe that finite-element collocation holds promise as a numer ical scheme for modeling complicated flows in porous media. However, there seems to be a "conventional wisdom" maintaining that collocation is hopelessly beset by oscillations and is, in some way, fundamentally inappropriate for multiphase flows. I hope to dispel these objections, realizing that others will remain for further work. The U. S. National Science Foundation funded much of this study through grant number NSF-CEE-8111240. TABLE OF CONTENTS ABSTRACT ;; FOREWORD ;; ; CHAPTER ONE. THE PHYSICAL SYSTEM. 1.1 Introduction. 1 1.2 The reservoir and its contents. 5 1.3 Reservoir mechanics. 9 1.4 Supplementary constraints. 18 1.5 Governing equations. 26 CHAPTER TWO. REPRESENTING FLUID-PHASE BEHAVIOR. 39 2.1 Thermodynamics of the fluid system. 40 2.2 Standard equation-of-state methods. 45 2.3 Maxwell-set interpolation.

Computer Modeling of Free-Surface and Pressurized Flows

Author : M. Hanif Chaudhry
Publisher : Springer Science & Business Media
ISBN 13 : 9401109648
Total Pages : 737 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Computer Modeling of Free-Surface and Pressurized Flows by : M. Hanif Chaudhry

Download or read book Computer Modeling of Free-Surface and Pressurized Flows written by M. Hanif Chaudhry and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computers are widely used for the analysis, design, and operation of water resource projects. This gives accurate results, allowing the analysis of complex systems which may not have been possible otherwise, and the investigation and comparison of several different alternatives in a short time, thereby reducing the project costs, optimizing design, and efficient utilization of resources. This volume compiles an edited version of the lecture notes specially prepared by 14 well-known European and North American researchers. Part I deals with free-surface flows. Governing equations are derived and their solution by the finite-difference, finite-element, and boundary-integral methods are discussed. Then, turbulence models, three-dimensional models, dam-break flow models, sediment transport models, and flood routing models are presented. Part II is related to the modeling of steady and transient pressurized flows. Governing equations for both single and two-component flows are derived and numerical methods for their solution are presented. The modeling of water quality in pipe networks, of cooling water systems, and slow and rapid transients is then discussed.

Mathematical Modeling for Flow and Transport Through Porous Media

Author : Gedeon Dagan
Publisher : Springer Science & Business Media
ISBN 13 : 9401721998
Total Pages : 293 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Mathematical Modeling for Flow and Transport Through Porous Media by : Gedeon Dagan

Download or read book Mathematical Modeling for Flow and Transport Through Porous Media written by Gedeon Dagan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this paper is to present some new and general results, ap plicable to the the equations of two phase flow, as formulated in geothermal reservoir engineering. Two phase regions are important in many geothermal reservoirs, especially at depths of order several hundred metres, where ris ing, essentially isothermal single phase liquid first begins to boil. The fluid then continues to rise, with its temperature and pressure closely following the saturation (boiling) curve appropriate to the fluid composition. Perhaps the two most interesting theoretical aspects of the (idealised) two phase flow equations in geothermal reservoir engineering are that firstly, only one component (water) is involved; and secondly, that the densities of the two phases are so different. This has led to the approximation of ignoring capillary pressure. The main aim of this paper is to analyse some of the consequences of this assumption, especially in relation to saturation changes within a uniform porous medium. A general analytic treatment of three dimensional flow is considered. Pre viously, three dimensional modelling in geothermal reservoirs have relied on numerical simulators. In contrast, most of the past analytic work has been restricted to one dimensional examples.

Multi-scale Phenomena in Complex Fluids

Author : Thomas Y. Hou
Publisher : World Scientific
ISBN 13 : 9814273252
Total Pages : 379 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Multi-scale Phenomena in Complex Fluids by : Thomas Y. Hou

Download or read book Multi-scale Phenomena in Complex Fluids written by Thomas Y. Hou and published by World Scientific. This book was released on 2009 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Scale Phenomena in Complex Fluids is a collection of lecture notes delivered during the ªrst two series of mini-courses from "Shanghai Summer School on Analysis and Numerics in Modern Sciences," which was held in 2004 and 2006 at Fudan University, Shanghai, China. This review volume of 5 chapters, covering various fields in complex fluids, places emphasis on multi-scale modeling, analyses and simulations. It will be of special interest to researchers and graduate students who want to work in the field of complex fluids.

Modeling and Simulation of Fluid Flow in Naturally and Hydraulically Fractured Reservoirs Using Embedded Discrete Fracture Model (EDFM)

Download Modeling and Simulation of Fluid Flow in Naturally and Hydraulically Fractured Reservoirs Using Embedded Discrete Fracture Model (EDFM) PDF Online Free

Author : Mahmood Shakiba
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (91 download)

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Book Synopsis Modeling and Simulation of Fluid Flow in Naturally and Hydraulically Fractured Reservoirs Using Embedded Discrete Fracture Model (EDFM) by : Mahmood Shakiba

Download or read book Modeling and Simulation of Fluid Flow in Naturally and Hydraulically Fractured Reservoirs Using Embedded Discrete Fracture Model (EDFM) written by Mahmood Shakiba and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and simulation of fluid flow in subsurface fractured systems has been steadily a popular topic in petroleum industry. The huge potential hydrocarbon reserve in naturally and hydraulically fractured reservoirs has been a major stimulant for developments in this field. Although several models have found limited applications in studying fractured reservoirs, still more comprehensive models are required to be applied for practical purposes. A recently developed Embedded Discrete Fracture Model (EDFM) incorporates the advantages of two of the well-known approaches, the dual continuum and the discrete fracture models, to investigate more complex fracture geometries. In EDFM, each fracture is embedded inside the matrix grid and is discretized by the cell boundaries. This approach introduces a robust methodology to represent the fracture planes explicitly in the computational domain. As part of this research, the EDFM was implemented in two of The University of Texas in-house reservoir simulators, UTCOMP and UTGEL. The modified reservoir simulators are capable of modeling and simulation of a broad range of reservoir engineering applications in naturally and hydraulically fractured reservoirs. To validate this work, comparisons were made against a fine-grid simulation and a semi-analytical solution. Also, the results were compared for more complicated fracture geometries with the results obtained from EDFM implementation in the GPAS reservoir simulator. In all the examples, good agreements were observed. To further illustrate the application and capabilities of UTCOMP- and UTGEL-EDFM, a few case studies were presented. First, a synthetic reservoir model with a network of fractures was considered to study the impact of well placement. It was shown that considering the configuration of background fracture networks can significantly improve the well placement design and also maximize the oil recovery. Then, the capillary imbibition effect was investigated for the same reservoir models to display its effect on incremental oil recovery. Furthermore, UTCOMP-EDFM was applied for hydraulic fracturing design where the performances of a simple and a complex fracture networks were evaluated in reservoirs with different rock matrix permeabilities. Accordingly, it was shown that a complex network is an ideal design for a very low permeability reservoir, while a simple network results in higher recovery when the reservoir permeability is moderate. Finally, UTGEL-EDFM was employed to optimize a conformance control process. Different injection timings and different gel concentrations were selected for water-flooding processes and their impact on oil recovery was evaluated henceforth.

Hydrodynamics of Free Surface Flows

Author : Jean-Michel Hervouet
Publisher : John Wiley & Sons
ISBN 13 : 9780470319635
Total Pages : 360 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Hydrodynamics of Free Surface Flows by : Jean-Michel Hervouet

Download or read book Hydrodynamics of Free Surface Flows written by Jean-Michel Hervouet and published by John Wiley & Sons. This book was released on 2007-06-13 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: A definitive guide for accurate state-of-the-art modelling of free surface flows Understanding the dynamics of free surface flows is the starting point of many environmental studies, impact studies, and waterworks design. Typical applications, once the flows are known, are water quality, dam impact and safety, pollutant control, and sediment transport. These studies used to be done in the past with scale models, but these are now being replaced by numerical simulation performed by software suites called “hydro-informatic systems”. The Telemac system is the leading software package worldwide, and has been developed by Electricité de France and Jean-Michel Hervouet, who is the head and main developer of the Telemac project. Written by a leading authority on Computational Fluid Dynamics, the book aims to provide environmentalists, hydrologists, and engineers using hydro-informatic systems such as Telemac and the finite element method, with the knowledge of the basic principles, capabilities, different hypotheses, and limitations. In particular this book: presents the theory for understanding hydrodynamics through an extensive array of case studies such as tides, tsunamis, storm surges, floods, bores, dam break flood waves, density driven currents, hydraulic jumps, making this a principal reference on the topic gives a detailed examination and analysis of the notorious Malpasset dam failure includes a coherent description of finite elements in shallow water delivers a significant treatment of the state-of-the-art flow modelling techniques using Telemac, developed by Electricité de France provides the fundamental physics and theory of free surface flows to be utilised by courses on environmental flows Hydrodynamics of Free Surface Flows is essential reading for those involved in computational fluid dynamics and environmental impact assessments, as well as hydrologists, and bridge, coastal and dam engineers. Guiding readers from fundamental theory to the more advanced topics in the application of the finite element method and the Telemac System, this book is a key reference for a broad audience of students, lecturers, researchers and consultants, right through to the community of users of hydro-informatics systems.

New Trends In Fluid And Solid Models - Proceedings Of The International Conference In Honour Of Brian Straughan

Author : Michele Ciarletta
Publisher : World Scientific
ISBN 13 : 9814465909
Total Pages : 196 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis New Trends In Fluid And Solid Models - Proceedings Of The International Conference In Honour Of Brian Straughan by : Michele Ciarletta

Download or read book New Trends In Fluid And Solid Models - Proceedings Of The International Conference In Honour Of Brian Straughan written by Michele Ciarletta and published by World Scientific. This book was released on 2009-09-29 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the 1st Conference on New Trends in Fluid and Solid Models provide an overview of results and new models in fluid dynamics and, in general, in continuum mechanics. The contributions refer in particular to models in continuum mechanics, phase transitions, qualitative analysis for ODEs or PDEs models, Stability in fluids and solids, wave propagation, discontinuity and shock waves, and numerical simulations.

Modeling Steam Assisted Gravity Drainage in Heterogeneous Reservoirs Using Different Upscaling Techniques

Author : Dhananjay Kumar
Publisher :
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.:/5 (892 download)

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Book Synopsis Modeling Steam Assisted Gravity Drainage in Heterogeneous Reservoirs Using Different Upscaling Techniques by : Dhananjay Kumar

Download or read book Modeling Steam Assisted Gravity Drainage in Heterogeneous Reservoirs Using Different Upscaling Techniques written by Dhananjay Kumar and published by . This book was released on 2014 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents different methods that improve the ability to relate the flow properties of heterogeneous reservoirs to equivalent anisotropic flow properties in order to predict the performance of the Steam Assisted Gravity Drainage (SAGD) process. Process simulation using full scale heterogeneous reservoirs are inefficient and so the need arises to develop equivalent anisotropic reservoirs that can capture the effect of reservoir heterogeneity. Since SAGD is highly governed by permeability in the reservoir, effective permeability values were determined using different upscaling techniques. First, a flow-based upscaling technique was employed and a semi-analytical model, derived by Azom and Srinivasan, was used to determine the accuracy of the upscaling. The results indicated inadequacy of flow-based upscaling schemes to derive effective direction permeabilities consistent with the unique flow geometry during the SAGD process. Subsequently, statistical upscaling was employed using full 3D models to determine relationships between the heterogeneity variables: k[subscript italic v]/k[subscript italic h], correlation length and shale proportion. An iterative procedure coupled with an optimization algorithm was deployed to determine optimal k[subscript italic v] and k[subscript italic k] values. Further regression analysis was performed to explore the relationship between the variables of shale heterogeneity in a reservoir and the corresponding effective properties. It was observed that increased correlation lengths and shale proportions both decrease the dimensionless flow rates at given dimensionless times and that the semi-analytical model was more accurate for cases that contained lower shale proportions. Upscaled heterogeneous values inputted into the semi-analytical model resulted in underestimation of oil flow rate due to the inability to fully account for the impact of reservoir barriers and the configuration of flow streamlines during the SAGD process. Statistical upscaling using geometric averaging as the initial guess was used as the basis for developing a relationship between correlation length, shale proportion and k[subscript italic v]/k[subscript italic h]. The initial regression models did not accurately predict the anisotropic ratio because of insufficient data points along the regression surface. Subsequently a non-linear regression model that was 2nd order in both length and shale proportion was calibrated by executing more cases with varying levels of heterogeneity and the regression model revealed excellent matches to heterogeneous models for the prediction cases.

Fluid Flow and Transport in Porous Media, Mathematical and Numerical Treatment

Author : Zhangxin Chen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821856314
Total Pages : 540 pages
Book Rating : 4.8/5 (563 download)

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Book Synopsis Fluid Flow and Transport in Porous Media, Mathematical and Numerical Treatment by : Zhangxin Chen

Download or read book Fluid Flow and Transport in Porous Media, Mathematical and Numerical Treatment written by Zhangxin Chen and published by American Mathematical Soc.. This book was released on 2002 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research papers written and edited by prominent researchers working with the mathematical and numerical treatment of fluid flow and transport in porous media. Papers are based on talks given at a 2001 Joint AMS-IMS-SIAM Summer Research Conference held at Mount Holyoke College (South Hadley, MA). Topics cover a variety of subjects such as network flow modeling, contemporary numerical methods, parallel computation, optimization, multiscale phenomena, upscaling,uncertainty reduction, well treatment, and media characterization. The material addresses many problems originating from the applied geosciences and focuses on their common state-of-the-art mathematical and numerical treatment. This work is particularly pertinent to those working in oil exploration andother industrial applications. The book serves as an excellent reference work for all geoscientists, mathematicians, physicists, and engineers working in this research area

A Systems Description of Flow Through Porous Media

Author : Jan Dirk Jansen
Publisher : Springer Science & Business Media
ISBN 13 : 3319002600
Total Pages : 130 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis A Systems Description of Flow Through Porous Media by : Jan Dirk Jansen

Download or read book A Systems Description of Flow Through Porous Media written by Jan Dirk Jansen and published by Springer Science & Business Media. This book was released on 2013-05-23 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text forms part of material taught during a course in advanced reservoir simulation at Delft University of Technology over the past 10 years. The contents have also been presented at various short courses for industrial and academic researchers interested in background knowledge needed to perform research in the area of closed-loop reservoir management, also known as smart fields, related to e.g. model-based production optimization, data assimilation (or history matching), model reduction, or upscaling techniques. Each of these topics has connections to system-theoretical concepts. The introductory part of the course, i.e. the systems description of flow through porous media, forms the topic of this brief monograph. The main objective is to present the classic reservoir simulation equations in a notation that facilitates the use of concepts from the systems-and-control literature. Although the theory is limited to the relatively simple situation of horizontal two-phase (oil-water) flow, it covers several typical aspects of porous-media flow. The first chapter gives a brief review of the basic equations to represent single-phase and two-phase flow. It discusses the governing partial-differential equations, their physical interpretation, spatial discretization with finite differences, and the treatment of wells. It contains well-known theory and is primarily meant to form a basis for the next chapter where the equations will be reformulated in terms of systems-and-control notation. The second chapter develops representations in state-space notation of the porous-media flow equations. The systematic use of matrix partitioning to describe the different types of inputs leads to a description in terms of nonlinear ordinary-differential and algebraic equations with (state-dependent) system, input, output and direct-throughput matrices. Other topics include generalized state-space representations, linearization, elimination of prescribed pressures, the tracing of stream lines, lift tables, computational aspects, and the derivation of an energy balance for porous-media flow. The third chapter first treats the analytical solution of linear systems of ordinary differential equations for single-phase flow. Next it moves on to the numerical solution of the two-phase flow equations, covering various aspects like implicit, explicit or mixed (IMPES) time discretizations and associated stability issues, Newton-Raphson iteration, streamline simulation, automatic time-stepping, and other computational aspects. The chapter concludes with simple numerical examples to illustrate these and other aspects such as mobility effects, well-constraint switching, time-stepping statistics, and system-energy accounting. The contents of this brief should be of value to students and researchers interested in the application of systems-and-control concepts to oil and gas reservoir simulation and other applications of subsurface flow simulation such as CO2 storage, geothermal energy, or groundwater remediation.

Analytical Modeling of Multi-Fractured Horizontal Wells in Heterogeneous Unconventional Reservoirs

Author : Jie Zeng
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)

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Book Synopsis Analytical Modeling of Multi-Fractured Horizontal Wells in Heterogeneous Unconventional Reservoirs by : Jie Zeng

Download or read book Analytical Modeling of Multi-Fractured Horizontal Wells in Heterogeneous Unconventional Reservoirs written by Jie Zeng and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current analytical models for multi-fractured horizontal wells (MFHW) generally neglect reservoir heterogeneity, typical seepage characters of unconventional reservoir, partially penetrating fracture and various fracture damage mechanisms. In this thesis, three linear flow models have been developed to facilitate pressure and rate behavior analysis of shale, tight sand and unconventional reservoir with damaged fractures. These models are validated by comparing with KAPPA Ecrin and are more accurate than previous linear flow models in modeling partially penetrating cases. Field data are analyzed and results prove the reliability of these models. The first model is for heterogeneous shale reservoir with multiple gas transport mechanisms. It subdivides the reservoir into seven parts, namely, two upper/lower regions, two outer regions, two inner regions, and hydraulic fracture region. Fracture interference is simulated by locating a no-flow boundary between two adjacent fractures. The locations of these boundaries are determined based on the boundary's pressure to satisfy the no-flow assumption. Adsorption/desorption, gas slippage and diffusion effects are included for rigorous modeling of flow in shale. Sensitivity analysis results suggest that larger desorption coefficient causes smaller pressure and its derivative as a larger proportion of gas is desorbed in formation and contributes to productivity. The influences of other parameters, such as matrix II permeability, matrix block size, secondary fracture permeability, hydraulic fracture conductivity, and fracture pattern are also discussed. The second model is for heterogeneous tight sand reservoir with threshold pressure gradient (TPG). The linear flow sub-regions are the same as those of the first model. TPG and pressure drop within the horizontal wellbore are included. Simulation results suggest that TPG affects middle-late time behaviors. Greater TPG results in higher pressure drop and accelerates production decline. But this influence is marginal when TPG is small. Effects of other parameters, such as formation permeability, fracture length, conductivity, and wellbore storage are also investigated. The third model is for heterogeneous reservoir with various fracture damage. In this model, the following possible fracture damage situations are discussed: (1) choked fracture damage (2) partially propped fracture, (3) fracturing fluid leak-off damage, (4) dual or multiple damage effects. Simulation results indicate that choked frature damage influences early-mid time performance. Partially propped section within fracture dominates formation linear flow regime. Only severe matrix impairment near fracture face can have noticeable effects on pressure and rate response. A new parameter, skin factor ratio, is applied to describe the relative magnitude of multiple damage mechanisms. Reservoir heterogeneity and fracture damage make the pressure and rate behaviors deviate significantly from undamaged one but one can distinguish major damage mechanisms even in heterogeneous reservoir.

Modelling Water Flow in Unsaturated Porous Media

Author : Adam Szymkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 364223559X
Total Pages : 254 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Modelling Water Flow in Unsaturated Porous Media by : Adam Szymkiewicz

Download or read book Modelling Water Flow in Unsaturated Porous Media written by Adam Szymkiewicz and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on two issues related to mathematical and numerical modelling of flow in unsaturated porous media. In the first part numerical solution of the governing equations is discussed, with particular emphasis on the spatial discretization of highly nonlinear permeability coefficient. The second part deals with large scale flow in heterogeneous porous media of binary structure. Upscaled models are developed and it is shown that the presence of material heterogeneities may give rise to additional non-equilibrium terms in the governing equations or to hysteresis in the averaged constitutive relationships.

Constructive Modeling Of Structural Turbulence And Hydrodynamic Instabilities

Author : Oleg Mikhailovich Belotserkovskii
Publisher : World Scientific
ISBN 13 : 9814470376
Total Pages : 489 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Constructive Modeling Of Structural Turbulence And Hydrodynamic Instabilities by : Oleg Mikhailovich Belotserkovskii

Download or read book Constructive Modeling Of Structural Turbulence And Hydrodynamic Instabilities written by Oleg Mikhailovich Belotserkovskii and published by World Scientific. This book was released on 2009-01-05 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an original approach in the research of structural analysis of free developed shear compressible turbulence at high Reynolds number on the base of direct numerical simulation (DNS) and instability evolution for ideal medium (integral conservation laws) with approximate mechanism of dissipation (FLUX dissipative monotone “upwind” difference schemes) and does not use any explicit sub-grid approximation and semi-empirical models of turbulence. Convective mixing is considered as a principal part of conservation law.Appropriate hydrodynamic instabilities (free developed shear turbulence) are investigated from unique point of view. It is based on the concept of large ordered structures with stochastic core of small scale developed turbulence (”turbulent spot”). Decay of “turbulent spot” are simulated by Monte Carlo method. Proposed approach is based on two hypotheses: statistical independence of the characteristic of large ordered structures (LOS) and small-scale turbulence (ST) “and” weak influence of molecular viscosity (or more generally, dissipative mechanism) on properties of large ordered structures.Two versions of instabilities, due to Rayleigh-Taylor and Richtmyer-Meshkov are studied detail by the three-dimensional calculations, extended to the large temporal intervals, up to turbulent stage and investigation turbulent mixing zone (TMZ).The book covers both the fundamental and practical aspects of turbulence and instability and summarizes the result of numerical experiments conducted over 30 years period with direct participation of the author.In the book are cited the opinions of the leading scientists in this area of research: Acad. A S Monin (Russia), Prof. Y Nakamura (Japan, Nagoya University) and Prof. F Harlow (USA, Los-Alamos).

Modeling Shallow Water Flows Using the Discontinuous Galerkin Method

Author : Abdul A. Khan
Publisher : CRC Press
ISBN 13 : 1482226014
Total Pages : 218 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Modeling Shallow Water Flows Using the Discontinuous Galerkin Method by : Abdul A. Khan

Download or read book Modeling Shallow Water Flows Using the Discontinuous Galerkin Method written by Abdul A. Khan and published by CRC Press. This book was released on 2014-03-03 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.