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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

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

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

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

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

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

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

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

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

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

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

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

Bernoulli's equation for a viscous fluid flow

Types of head loss

Designing simple pipelines

Designing complex pipelines

Pipelines performing under vacuum

Outflow from a small orifice

Outflow through nozzles

Outflow of fluid at variable head

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

Equations of the boundary layer

Blasius problem

Detachment of the boundary layer

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

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

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

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

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

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

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

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

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

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

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

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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