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Basniev K.S. et al. Mechanics of Fluid Flow

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Basniev K.S. et al. Mechanics of Fluid Flow
K.S.Basniev, Nikolay M. Dmitriev, George V. Chilingar and Misha Gorfunkle. — Scrivener Publishing LLC., John Wiley & Sons, Inc., 2012. 568 p. — ISBN 978-1-118-38506-7.
The mechanics of fluid flow is a fundamental engineering discipline explaining both natural phenomena and human-induced processes, and a thorough understanding of it is central to the operations of the oil and gas industry.
This book, written by some of the world’s best-known and respected petroleum engineers, covers the concepts, theories, and applications of the mechanics of fluid flow for the veteran engineer working in the field and the student, alike. It is a must-have for any engineer working in the oil and gas industry.
Contents
Preface
Fundamentals of the Mechanics of Continua
Basic Concepts of the Mechanics of Continua
Introduction
Continuity hypothesis
Movement of continuous medium: description techniques
Local and substantive derivative
Scalar and vector fields
Forces and stresses in the continuous medium. Stress tensor
Conservation Laws. Integral and Differential
Equations of Continuous Medium
Integral parameters of a continuous medium and the conservation laws
Time differentiation of the integral taken over a movable volume
Continuity equation (law of mass conservation)
Motion equation under stress
Law of variation of kinetic momentum. Law of pairing of tangential stresses
The law of conservation of energy
Theorem of variation of kinetic energy
Heat flow equation
Continuous medium motion equations
Continuous Medium Deformation Rate
Small particle deformation rate. Helmholtz theorem
Tensor of the deformation velocity
Physical meaning of the deformation velocity tensor components
Tensor surface of a symmetric second-rank tensor
Velocity circulation. Potential motion of the liquid
Liquids
Mathematical model of ideal fluid
Mathematical model of ideal incompressible fluid
Viscous fluid. Stress tensor in viscous fluid
Motion equations of viscous fluids
Mathematical model of a viscous incompressible flui
The work of internal forces. Equation of the heat inflow
Basics of the Dimensionality and Conformity Theory
Systems of units. Dimensionality
Dimensionality formula
Values with independent dimensionalities
Π-theorem
Conformity of physical phenomena, modeling
Parameters determining the class of phenomena
Examples of application of the Π-theorem
Contraction of equations to dimensionless format
Hydromechanics
Hydrostatics
Liquids and gas equilibrium equations
Equilibrium of a liquid in the gravitational field
Relative quiescence of fluid
Static pressure of liquid on firm surfaces
Elements of buoyancy theory
Flow of Ideal Fluid
Euler's equations in the Gromeko-Lamb format
Bernoulli's integral
cular forms of Bernoulli's integral
Simple applications of Bernoulli's integral
Cauchy-Lagrange's integral
Thomson's theorem
Helmholtz equation
Potential flow of an incompressible fluid
Flow around the sphere
Applications of the momentum law
Parallel-Plane Flows of Ideal Incompressible Fluid
Complex-valued potential of flow
Examples of parallel-plane potential flows
Conformous reflection of flows
Zhukovsky's transform
Flow-around an arbitrary profile
Forces acting on a profile under the stationary flow
Flow of Viscous Incompressible Fluid in Prismatic Tubes
Equations descring straight-line motion of a viscous incompressible fluid in prismatic tubes
Straight-line flow between two parallel walls
Straight-line flow within axisymmetric tubes
Equation of transient-free circular motion of a viscous fluid
Flow between two revolving cylinders
Turbulent Flow of Fluids in Pipes
Reynolds'experiments
Averaging the parameters of turbulent flow
Reynolds'equations
Semi-empiric turbulency theory by L. Prandtl
Application of the dimensionality theory to the construction of semi-empirical turbulence theories
Logarithmic law of velocity distribution
Experimental studies of hydraulic resistance
Hydraulic Calculation for Pipelines
Bernoulli's equation for a viscous fluid flow
Types of head loss
Designing simple pipelines
Designing complex pipelines
Pipelines performing under vacuum
Fluid's Outflow from Orifices and Nozzles
Outflow from a small orifice
Outflow through nozzles
Outflow of fluid at variable head
Non-Stationary Flow of Viscous Fluid in Tubes
Equations of the non-stationary fluid flow in tubes
Equation of non-stationary flow for slightly-compressible fluid in tubes
Equations of non-stationary gas flow in tubes at low subsonic velocities
Integrating equations of non-stationary fluid and gas flow using the characteristics technique
Integrating linearized equations of non-stationary flow using Laplace transformation
Examples of computing non-stationary flow in tubes
Hydraulic shock
Effect of flow instability on force of friction
Laminar Boundary Layer
Equations of the boundary layer
Blasius problem
Detachment of the boundary layer
Unidimensional Gas Flows
Sound velocity
Energy conservation law
Mach number. Velocity factor
Linkage between the flow tube's cross-section area and flow velocity
Gas outflow through a convergent nozzle
De Laval's nozzle
Gas-dynamic functions
Shock waves
Computation of gas ejector
Transient-free gas flow in tubes
Shukhov's equation
Laminar Flow of Non-Newtonian Fluids
Simple shear
Classification of non-Newtonian fluids
Viscosimetry
Fluid flow in an infinitely-long round tube
Rotational fluid flow within a ring gap
Integral technique in viscosimetry
Hydraulic resistance factor
Additional remarks to the calculation of non-Newtonian fluids flow in tubes
Two-Phase Flow in Pipes
Equations of the conservation laws
Equations of two-phase mixture flow in tubes
Transformation of equations of two-phase flow in pipes
Flow regimes
Absolute open flow of a gas-condensate well
Oil and Gas Subsurface Hydromechanics
Main Definitions and Concepts of Fluid and Gas Flow Darcy's Law and Experiment
Specifics of fluid flow in natural reservoirs
Basic model concepts of the subsurface liquid and gas hydrodynamics
Reservoir properties of porous bodies. Porosity, specific surface area
Darcy's experiment and Darcy's law. Permeability. The concept of "true" average flow velocity
and flow velocity
Applicability limits of Darcy's law. Analysis and interpretation of experimental data
Nonlinear laws of filtration
Structural model of porous media
Darcy's law for anisotropic media
Mathematical Models of Uniphase Filtration
Introductory notes. The concept of the mathematical model of a physical process
Mass conservation laws in a porous medium
Differential equation of fluid flow
Closing equations. Mathematical models of isothermal filtration
Filtration model of incompressible viscous fluid under Darcy's law in a non-deformable reservoir
Gas filtration model under Darcy's law. Leibensohn's function
Uniphase filtration models in non-deformable reservoir under non-linear filtration laws
Correlation between fluid parameters and porous medium parameters with pressure
Unidimensional Transient-Free Filtration of Incompressible Fluid and Gas in an Uniform Porous Medium
Schematics of unidimensional filtration flows
Rectiliner-parallel filtration of incompressible fluid
Radial-plane filtration of incompressible fluid
Radial-spherical filtration of incompressible fluid
Filtration similarity between incompressible liquid and gas
Unidimensional filtration flow of ideal gas
Parallel-plane filtration flow of real gas under Darcy's law
Radial-plane filtration flow of incompressible liquid and gas under binomial filtration law
Radial-plane filtration flow on incompressible liquid and gas under the exponential filtration law
Unidimensional Filtration of Incompressible Liquid and Gas in a Nonuniform Reservoirs Under Darcy's Law
Major types of reservoir nonuniformities
Rectilinear-parallel flow within nonuniformly-laminated reservoir
Rectilinear-parallel flow in zonally-nonuniform bed
On the calculation of continuously-nonuniform reservoirs
Radial-plane flow in a nonuniformly stratified reservoir
Rectilineal-parallel flow in a nonuniformly stratified reservoir
Flat Transient-Free Filtration Flows
Major definitions and concepts
Potential of a point source and sink on an isotropic plane. Superposition method
Liquid flow to a group of wells with the remote charge contour
Liquid inflow to a well in the reservoir with a rectilinear charge contour
Liquid inflow to a well in the reservoir near the impermeable boundary
Liquid inflow to a well positioned eccentrically in a round reservoir
On the use of superposition technique at the gas filtration
Fluids inflow to infinite well lines and ring well rows
Non-Stationary Flow of an Elastic Fluid in an Elastic Reservoir
Elastic reservoir drive
Calculation of elastic fluid reserves of a reservoir
Mathematical model of the elastic fluid non-stationary filtratio in an elastic porous medium
Derivation of the differential equation of the elastic fluid filtration in an elastic porous medium under Darcy's law
Unidimensional filtration flows of an elastic fluid. Point-solutions of the piezo-conductivity equation. Main equation of the elastic drive theory
Rectilinear-parallel filtration flow of an elastic fluid
Rectilinear-parallel filtration flow of an elastic fluid. The main equation of the elastic filtration regime theory
Approximate solution techniques of the elastic drive problems
Method of sequential change of stationary states
Pirverdian's technique
Integral relationships technique
"Averaging" technique
Elastic fluid flow to an aggregate well
Non-Stationary Flow of Gas in a Porous Medium
Mathematical model of non-stationary gas filtration
Linearization of Leibensohn's equation and the main solution of linearized equation
Point solution of an automodel problem on axisymmetric gas flow to a well with a constant flow-rate
Solution of the problem of gas flow to a well using sequential change of stationary states technique
Solution of the gas flow to well problem using averaging technique
Application of superposition principle to problems of non-stationary gas filtration
Approximate solution of gas production from closed reservoir problems using the material balance equation
Filtration of Non-Newtonian Liquid
Viscoplastic liquid: filtration law and mathematical model
Rectilinear-parallel filtration flow for the viscoplastic liquid
Rectilinear-parallel filtration flow of viscoplastic liquid in a nonuniformly-laminated reservoir
Radial-plane filtration flow of viscoplastic liquid
Non-stationary filtration flow of viscoplastic liquid
Formation of bypass zones in the process oil-by-water displacement
Specifics of viscoplastic liquid filtration in anisotropic porous media
Liquid and Gas Flow in Fractured and Fractured-Porous Media
Specifics of filtration in fractured and fractured-porous media
Filtration laws in fractured media
Permeability vs. pressure in fractured and fractured-porous media
On the fluid crossflow in fractured-porous media
Derivation of differential equations for liquids and gas flow within the fractured and fractured-porous media
Stationary unidimensional liquids and gas filtration in a fractured and fractured-porous reservoir
Non-stationary liquid and gas flow in fractured and fractured-porous reservoirs
Appendix A
References
Subject Index
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