Modelling Emergency Situations in the Drilling of Deep Boreholes

Contents
Preface
Chapter 1
	1.1. Technical aspects of deep-drilling problems
	1.2. Abnormal phenomena accompanying deep-drilling processes
	1.3. Mathematical aspects of deep-drilling string mechanic issues
	References to Chapter 1
Chapter 2
	2.1 Basic relations of quasi-static equilibrium and vibrations of rotating, twisted drill strings with internal fluid flows
	2.2 Singularly perturbed equations in boundary value problems of the deep drilling string mechanics
	2.3 Procedure for constructing bifurcation solutions
	2.4 The bifurcation states of the vertical rotating strings
	2.5 DS buckling according to the forms of spiral wavelets
	2.6 Two-point boundary value problems of drill strings buckling
	2.7 Multipoint boundary value problems of bifurcation buckling of drill strings with centralisers
	2.8 Analysis of quasi-static equilibrium stability of drill strings using integrated calculation schemes
	References to Chapter 2
Chapter 3
	3.1 Technical and applied aspects of the problem of the prestressed rotating tubular rods with internal fluid flows
	3.2 Spiral progressive waves in infinite twisted tubular rotating rods with internal fluid flows
	3.3. Small free bending vibrations of rotating drill strings
	References to Chapter 3
Chapter 4
	4.1 Self-oscillating systems and methods of their analysis
	4.2 Mathematical aspects of the problem of self-oscillation of deep-drilling strings
	4.3. Hopf bifurcations in problems of torsional self-oscillations of deep drilling strings
	4.4. Torsional oscillations of composite drill strings
	4.5. Self-excitation of torsional vibrations of deep drill strings in a viscous liquid medium
	References to Chapter 4
Chapter 5
	5.1. Existing models of drill string whirling vibrations
	5.2. The main aspects of the whirling model based on the effects of friction and nonholonomic rolling of the bit
	5.3. The problem of Celtic stone mechanics and its analogy with bit rolling dynamics
	5.4. Friction model of elastic oscillations of the system during rolling of a spherical bit on the spherical surface of the well bottom
	5.5. Analysis of frictional whirling vibrations of the system
	5.6. Kinematic (nonholonomic) model of the spherical bit whirling on the spherical surface of the well bottom
	5.7. Analysis of elastic vibrations of the system using the nonholonomic model of the bit rolling
	5.8. Friction and nonholonomic rolling of the spherical bit on the ellipsoidal surface of the well bottom
	5.9. The frictional rolling of ellipsoid bit on the bottom surface of a well
	5.10. The analogy between the rolling dynamics of the ellipsoid bit and rattleback rotation
	5.11. Dynamics of elastic bending of a drill string with the bit in the shape of an elongated ellipsoid
	5.12. Dynamics of elastic bending of a drill string with the bit in the shape of a flattened ellipsoid
	5.13. Elastic oscillations of the drill string for nonholonomic rolling of an ellipsoid bit on the surface of the well bottom
	References to Chapter 5
Chapter 6
	6.1 Features of modern technologies of oil and gas fuel extraction and problems of mechanics of elastic bending of drill strings in curvilinear boreholes
	6.2 Mathematical aspects of the problem of forced elastic bending of the drill string in the channel of a curvilinear borehole
	6.3 Stiff string drag and torque model of DS bending in curvilinear boreholes
	6.4. Modelling resistance forces in a well with localised harmonic imperfections
	6.5 Modelling resistance forces in a well with localised spiral imperfections
	6.6 Simulation of energy-saving regimes of tripping in/out operations in a well with geometric imperfections
	6.7 Method for minimising resistance force in the interfacing areas of the borehole curvilinear segments
	References to Chapter 6
Chapter 7
	7.1. State of the problem of drill string stability in a curvilinear borehole
	7.2. Buckling of a drill string in a directional channel of a rectilinear borehole
	7.3 Buckling of a drill string in a borehole channel with a circular outline
	7.4. Global analysis of drill string buckling in a curvilinear well
	References to Chapter 7
Index