Foreword ........................................................ 7
CHAPTER I. FLUID FLOW MODELS ................................... 15
1.0 Single-phase and two-phase fluid flow models .............. 18
2.0 The transformation of ML model equations .................. 33
3.0 The MLT model for the case of constant residual
saturation ................................................ 48
4.0 Non-isothermal flow of immiscible fluids with variable
residual saturations (the MLT model) ...................... 51
5.0 The combination of well and reservoir flows of viscous
incompressible fluids ..................................... 54
6.0 A formation flow model of waxy, high gas content oil
displacement .............................................. 60
7.0 Formation flow of two immiscible inhomogeneous fluids ..... 63
CHAPTER II. ANALYTICAL AND ONE-DIMENSIONAL MODELS OF THERMAL
TWO-PHASE FLOW ................................................. 68
1.0 Boundary-value problems for ordinary differential
equations ................................................. 70
2.0 Numerical and analytical methods of investigation of
thermal two-phase flow problems ........................... 81
3.0 Analytical problems of thermal two-phase flow in the
case of variable residual saturations ..................... 96
4.0 The qualitative properties of analytical MLT model
solutions ................................................ 107
5.0 An analytical solution of flow equations for two
non-linear viscous fluids ................................ 125
6.0 Validation of the use of a specific approximate method
in two-phase non-isothermal flow ......................... 133
7.0 Combination of the principal models of two-phase fluid
flow ..................................................... 139
8.0 One-dimensional flow of two interpenetrating viscous
incompressible fluids .................................... 152
CHAPTER III. MULTIDIMENSIONAL NUMERICAL MODELS OF SUBSURFACE
FLOW DYNAMICS ................................................. 168
1.0 Convergence of finite-difference schemes for a Navier-
Stokes model with velocity - pressure variables .......... 170
2.0 Numerical realization of Navier-Stokes model in
multiply connected domain in velocity - flow function
variables ................................................ 190
3.0 Implementing the method of splitting into underlying
physical processes in complex geometrical regions ........ 204
4.0 Numerical simulation of the oil displacement process
based of N.E. Zhukovsky model ............................ 216
5.0 Numerical model to find formation pressure ............... 223
6.0 Convective warm-up of an inhomogeneous porous medium ..... 236
7.0 The splitting of physical processes under non-
isothermal two-phase fluid flow in a porous medium ....... 245
8.0 Flow of two immiscible inhomogeneous fluids in porous
media .................................................... 254
9.0 Numerical solution of the problem of two-dimensional
two-phase flow ........................................... 262
10.0 Geological and mathematical models of the reservoir ...... 271
References .................................................... 293
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