Fluid Mechanics for Petroleum Engineers (eBook)

Front Cover 1
Fluid Mechanics for Petroleum Engineers 4
Copyright Page 5
Contents 10
Chapter 1. Flow properties of fluids 13
1.1 The fluid state 13
1.2 The continuum model of fluids 14
1.3 Variables of state 15
1.4 Conductivity coefficients 21
Chapter 2. Kinematics 23
2.1 Eulerian and Lagrangian description of fluid motion 24
2.2 The velocity field 29
2.3 The acceleration field 34
2.4 Motion of an infinitesimal fluid particle 37
2.5 Rotational motion, vorticity field 39
2.6 Relationships between the acceleration- and the vorticity fields 42
2.7 The transport theorem: the material derivative of a volume integral over a volume of flowing fluid 44
Chapter 3. Balance equations 47
3.1 The principle of conservation of mass 47
3.2 The balance of momentum 50
3.3 The balance of angular momentum 55
3.4 The balance of kinetic energy 58
3.5 The principle of conservation of energy 62
3.6 The balance of entropy 64
3.7 Mechanical equilibrium of fluids 66
Chapter 4. Perfect fluid flow 71
4.1 The perfect fluid 71
4.2 Euler's equation 72
4.3 The Bernoulli equation 78
4.4 Simple applications of the Bernoulli equation 82
4.5 The Cauchy—Lagrange integral of Euler's equation 90
4.6 Kelvin's vortex theorem 93
4.7 The law of conservation of energy for perfect fluid flow 94
4.8 The Vázsonyi— Crocco equation 99
4.9 Small perturbations at the speed of sound 102
4.10 Dynamical similarity of ideal gas flows 105
4.11 Critical flow variables 107
4.12 Variation in area for isentropic flow 110
4.13 High velocity gas flow in pipes with friction 116
Chapter 5. Shock waves in compressible flow 124
5.1 Shock surfaces 124
5.2 Kinematics of motion of singular surfaces: the speed of displacement 128
5.3 Weak singular surfaces in compressible flow 133
5.4 Discontinuous balance equations at a shock surface 135
5.5 Balance equations at a shock surface 138
5.6 Changes in the variables of state across a shock surface 141
5.7 Speed of propagation of shock surfaces 145
5.8 The jump in the variables of state as a function of the Mach number 147
5.9 Shock surfaces in steady supersonic planar flow 149
Chapter 6. Laminar flow 158
6.1 The flow of viscous fluids 158
6.2 The Navier—Stokes equation 160
6.3 The balance of kinetic energy for laminar flow 163
6.4 The balance of internal energy for laminar flow 165
6.5 Dynamical similarity 171
6.6 Some general properties of incompressible viscous flow 177
6.7 Steady incompressible flow in a cylindrical pipe 179
6.8 Steady incompressible laminar flow in annuli 183
6.9 Elementary boundary-layer theory 185
6.10 Resistance of a solid sphere in laminar flow 191
6.11 Free convection 196
Chapter 7. Turbulent flow 203
7.1 The nature of turbulent motion 203
7.2 Reynolds’s equation: the balance of momentum for turbulent flow 205
7.3 The balance of kinetic energy for turbulent flow 209
7.4 Determination of the apparent turbulent shear stress according to the mixing length theory 214
7.5 Turbulent flow through pipes 217
7.6 Turbulent boundary-layer flow 224
7.7 Turbulent flow in annuli 232
Chapter 8. One-dimensional pipe flow 238
8.1 One-dimensional approximation for flow in pipes 238
8.2 Basic equations for one-dimensional flow in pipes 239
8.3 Criteria for laminar, transitional and turbulent flow 247
8.4 Head loss in straight cylindrical pipes 250
8.5 Head losses resulting from fittings 260
8.6 Pressure loss of a low velocity gas flow 276
8.7 Flow in pipes with mechanical energy addition 280
8.8 Flow in pipes with heat exchange 282
8.9 Pressure waves in one-dimensional pipe flow 288
Chapter 9. Non-Newtonian fluid flow 298
9.1 Specific types of flow behavior 298
9.2 Laminar flow of pseudoplastic fluids in pipes 311
9.3 Bingham fluid flow in pipes 318
9.4 Unsteady viscoelastic fluid flow in a cylindrical pipe 322
9.5 The Rabinowitsch equation 324
9.6 Laminar flow of thixotropic fluids in pipes 327
9.7 Pseudoplastic fluid flow in annuli 335
9.8 Turbulent flow of non-Newtonian fluids in pipes 342
Chapter 10. Flow of multiphase mixtures 349
10.1 Properties of multiphase mixtures 349
10.2 The continuity equation for multiphase mixtures 353
10.3 The momentum equation for multiphase mixtures 357
10.4 The mechanical energy equation for multiphase flow 364
10.5 The total energy equation for multiphase flow 369
10.6 Characteristic flow patterns 371
10.7 Holdup relations for two-phase flow 382
10.8 Determination of pressure losses for two-phase flow in pipes 387
Literature 401
Subject index 409