Unsteady State Fluid Flow

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.

Due to recent and continuing advances in computational fluid dynamics, programs are now available for speedy and detailed treatment of problems involving nonstationary fluid dynamics. Explains the basic ideas underlying the use of unsteady fluid flow and explores new ideas, processes and devices taking place in this rapidly developing field. Covers such diverse topics as tidal wave power, wind energy conversion systems, and thrust-augmenting pulsed ejectors. Offers numerous illustrated examples and applications to both inspire and challenge the reader.

Most of the fundamental concepts of unsteady viscous flows have been known since the early part of the century. However, the past decade has seen an unprecedented number of publications in this area. In this monograph I try to connect materials of earlier contributions and synthesize them into a comprehensive entity. One of the main purposes of a monograph, in my opinion, is to fit together in a comprehensive way scattered contributions that provide fragmented information to the readers. The collection of such contributions should be presented in a unified way; continuity of thought and logical sequence of the presentation of ideas and methods are essential. The reader should be able to follow through without having to resort to other references, something that is unavoidable in the case of a research paper or even a review paper. Many of the solutions discussed in the literature address specific practical problems. In fact, in the process of collecting information, I discovered independent lines of investigations, dealing with the same physical problem, but inspired by different practical applications. For example, I found that two groups of investigators have been studying independently the response of a viscous layer to a harmonic external disturbance. One group is con cerned with mass transport and the transport of sediment over the bottom of the ocean, and the other is interested in the aerodynamics of lifting surfaces in harmonically changing environments.

Computation of Unsteady Internal Flows provides an in-depth understanding of unsteady flow modeling and algorithms. This understanding enables suitable algorithms and approaches for particular fields of application to be selected. In addition, the understanding of the behavior of algorithms gained allows practitioners to use them more safely in existing codes, enabling meaningful results to be produced more economically. Features of Computation of Unsteady Internal Flows: Specialized unsteady flow modeling algorithms, their traits, and practical tips relating to their use are presented. Case studies considering complex, practically significant problems are given. Source code and set-up files are included. Intended to be of a tutorial nature, these enable the reader to reproduce and extend case studies and to further explore algorithm performances. Mathematical derivations are used in a fashion that illuminates understanding of the physical implications of different numerical schemes. Physically intuitive mathematical concepts are used. New material on adaptive time stepping is included. £/LIST£ Audience: Researchers in both the academic and industrial areas who wish to gain in-depth knowledge of unsteady flow modeling will find Computation of Unsteady Internal Flows invaluable. It can also be used as a text in courses centered on computational fluid dynamics.

This book provides a unifying framework for understanding and computing unsteady flow and transport in shallow one-dimensional open-water systems.

This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.

An introduction to the mechanics of unsteady fluid flow and energy transfer. This text/reference explains the fundamentals of thermofluid mechanics and presents methods useful in creative analysis and experimentation. Includes coverage of bulk flow and propagative behavior of hydrostatic waves, disturbance and wave propagation, unsteady multidimensional flows and uniform systems, and system normalization. Contains many graphs and tables for quick estimates of thermofluid system behavior and response.

From the reviews: "Researchers in fluid dynamics and applied mathematics will enjoy this book for its breadth of coverage, hands-on treatment of important ideas, many references, and historical and philosophical remarks." Mathematical Reviews