Application Of Convolution And Average Pressure Approximation For Solving Non Linear Flow Problems
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Application Of Convolution And Average Pressure Approximation For Solving Non Linear Flow Problems
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Author : Mansur Zhakupov
language : en
Publisher:
Release Date : 2006
Application Of Convolution And Average Pressure Approximation For Solving Non Linear Flow Problems written by Mansur Zhakupov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
The accurate description of fluid flow through porous media allows an engineer to properly analyze past behavior and predict future reservoir performance. In particular, appropriate mathematical models which describe fluid flow through porous media can be applied to well test and production data analysis. Such applications result in estimating important reservoir properties such as formation permeability, skin-factor, reservoir size, etc. "Real gas" flow problems (i.e., problems where the gas properties are specifically taken as implicit functions of pressure, temperature, and composition) are particularly challenging because the diffusivity equation for the "real gas" flow case is strongly non-linear. Whereas different methods exist which allow us to approximate the solution of the real gas diffusivity equation, all of these approximate methods have limitations. Whether in terms of limited applicability (say a specific pressure range), or due to the relative complexity (e.g., iterative character of the solution), each of the existing approximate solutions does have disadvantages. The purpose of this work is to provide a solution mechanism for the case of time-dependent real gas flow which contains as few "limitations" as possible. In this work, we provide an approach which combines the so-called average pressure approximation, a convolution for the right-hand-side non-linearity, and the Laplace transformation (original concept was put forth by Mireles and Blasingame). Mireles and Blasingame used a similar scheme to solve the real gas flow problem conditioned by the constant rate inner boundary condition. In this work we provide solution schemes to solve the constant pressure inner boundary condition problem. Our new semi-analytical solution was developed and implemented in the form of a direct (non-iterative) numerical procedure and successfully verified against numerical simulation. Our work shows that while the validity of this approach does have its own assumptions (in particular, referencing the right-hand-side non-linearity to average reservoir pressure (similar to Mireles andBlasingame)), these assumptions are proved to be much less restrictive than those required by existing methods of solution for this problem. We believe that the accuracy of the proposed solution makes it universally applicable for gas reservoir engineering. This suggestion is based on the fact that no pseudotime formulation is used. We note that there are pseudotime implementations for this problem, but we also note that pseudotime requires a priori knowledge of the pressure distribution in the reservoir or iteration on gas-in-place. Our new approach has no such restrictions. In order to determine limits of validity of the proposed approach (i.e., the limitations imposed by the underlining assumptions), we discuss the nature of the average pressure approximation (which is the basis for this work). And, in order to prove the universal applicability of this approach, we have also applied this methodology to resolve the time-dependent inner boundary condition for real gas flow in reservoirs.
Application Of Convolution Theory For Solving Non Linear Flow Problems
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Author : Thomas Joseph Mireles
language : en
Publisher:
Release Date : 1995
Application Of Convolution Theory For Solving Non Linear Flow Problems written by Thomas Joseph Mireles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Numerical Ship Hydrodynamics
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Author : Lars Larsson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-30
Numerical Ship Hydrodynamics written by Lars Larsson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-30 with Technology & Engineering categories.
This book assesses the state-of-the-art in computational fluid dynamics (CFD) applied to ship hydrodynamics and provides guidelines for the future developments in the field based on the Gothenburg 2010 Workshop. It presents ship hull test cases, experimental data and submitted computational methods, conditions, grids and results. Analysis is made of errors for global (resistance, sinkage and trim and self-propulsion) and local flow (wave elevations and mean velocities and turbulence) variables, including standard deviations for global variables and propeller modeling for self-propulsion. The effects of grid size and turbulence models are evaluated for both global and local flow variables. Detailed analysis is made of turbulence modeling capabilities for capturing local flow physics. Errors are also analyzed for head-wave seakeeping and forward speed diffraction, and calm-water forward speed-roll decay. Resistance submissions are used to evaluate the error and uncertainty by means of a systematic verification and validation (V&V) study along with statistical investigations. Post-workshop experimental and computational studies are conducted and analyzed for evaluation of facility biases and to draw more concrete conclusions regarding the most reliable turbulence model, appropriate numerical methods and grid resolution requirements, respectively.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1974
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mechanics, Applied categories.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1972
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Aeronautics categories.
Star
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Author :
language : en
Publisher:
Release Date : 1973
Star written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Aeronautics categories.
Theories Of Turbulence
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Author : Martin Oberlack
language : en
Publisher: Springer
Release Date : 2014-05-04
Theories Of Turbulence written by Martin Oberlack and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.
The term "turbulence” is used for a large variety of dynamical phenomena of fluids in motion whenever the details of the flow appear to be random and average properties are of primary interest. Just as wide ranging are the theoretical methods that have been applied towards a better understanding of fluid turbulence. In this book a number of these methods are described and applied to a broad range of problems from the transition to turbulence to asymptotic turbulence when the inertial part of the spectrum is fully developed. Statistical as well as nonstatistical treatments are presented, but a complete coverage of the subject is not attempted. The book will be of interest to scientists and engineers who wish to familiarize themselves with modern developments in theories of turbulence. The fact that the properties of turbulent fluid flow are addressed from very different points of view makes this volume rather unique among presently available books on turbulence.
An Introduction To Turbulent Flow
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Author : Jean Mathieu
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-26
An Introduction To Turbulent Flow written by Jean Mathieu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-26 with Science categories.
Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. An Introduction to Turbulent Flow, first published in 2000, offers a solid grounding in the subject of turbulence, developing both physical insight and the mathematical framework needed to express the theory. It begins with a review of the physical nature of turbulence, statistical tools, and space and time scales of turbulence. Basic theory is presented next, illustrated by examples of simple turbulent flows and developed through classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by spectral analysis and its applications. The final chapter introduces the numerical simulation of turbulent flows. This well-balanced text will interest graduate students in engineering, applied mathematics, and the physical sciences.
Petroleum Abstracts
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Author :
language : en
Publisher:
Release Date : 1992
Petroleum Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Petroleum categories.
Seismic Applications Of Acoustic Reciprocity
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Author : J.T. Fokkema
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Seismic Applications Of Acoustic Reciprocity written by J.T. Fokkema and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
The seismic applications of the reciprocity theorem developed in this book are partly based on lecture notes and publications from Professor de Hoop. Every student Professor de Hoop has taught knows the egg-shaped figure (affectionately known as "de Hoop's egg") that plays such an important role in his theoretical description of acoustic, electromagnetic and elastodynamic wave phenomena. On the one hand this figure represents the domain for the application of a reciprocity theorem in the analysis of a wavefield and on the other hand it symbolizes the power of a consistent wavefield description of this theorem. The roots of the reciprocity theorem lie in Green's theorem for Laplace's equation and Helmholtz's extension to the wave equation. In 1894, J.W. Strutt, who later became Lord Rayleigh, introduced in his book The Theory of Sound this extension under the name of Helmholtz's theorem. Nowadays it is known as Rayleigh's reciprocity theorem. Progress in seismic data processing requires the knowledge of all the theoretical aspects of the acoustic wave theory. The reciprocity theorem was chosen as the central theme of this book as it constitutes the fundaments of the seismic wave theory. In essence, two states are distinguished in this theorem. These can be completely different, although sharing the same time-invariant domain of application, and they are related via an interaction quantity. The particular choice of the two states determines the acoustic application, in turn making it possible to formulate the seismic experiment in terms of a geological system response to a known source function. In linear system theory, it is well known that the response to a known input function can be written as an integral representation where the impulse response acts as a kernel and operates on the input function. Due to the temporal invariance of the system, this integral representation is of the convolution type. In seismics, the temporal behaviour of the system is dealt with in a similar fashion; however the spatial interaction needs a different approach. The reciprocity theorem handles this interaction by identifying one state with the spatial impulse function, also known as the Green's function, while the other state is connected with the actual source distribution. In general, the resulting integral representation is not a spatial convolution. Moreover, the systematic use of the reciprocity theorem leads to a hierarchical description of the seismic experiment in terms of increasing complexity. Also from an educational point of view this approach provides a hierarchy and the student learns to break down the seismic problem into constituent partial solutions. This book should contribute to the understanding that the reciprocity theorem is a powerful tool in the analysis of the seismic experiment.