Physics for Geologists, Second edition

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Force 25 Figure 2.4 Density current. The head of flow is due to the work required to displace the static water. Figure 2.5 Diagrammatic section of a stable and an unstable sequence. A less dense substance (lighter ornament) overlying a denser substance is stable, and there is a force tending to make them horizontal. Denser over less dense is unstable, and the less dense will tend to rise above the denser. had been depleted by production. This was called 'wall-sticking' or 'differential sticking'. It was due to the lateral pressure gradient or discon- tinuity between the mud in the hole and the depleted fluid pressures of the reservoir (Figure 2.6); and it could hold the pipe against the wall of the hole, cushioned in the filter cake that forms around the hole in permeable rocks, with great force. The stuck point, in oil field jargon, was not usually the bottom of the pipe, at the drill collars, but higher. To free the pipe, one would first pull on it (in those days, not now) -the strength of pull being limited by the tensile strength of the pipe. The question was, how hard could the pipe be pulled without its parting? The answer is not as simple as it seems. The weight of steel pipe is reduced by the weight of the mud displaced, but what is the weight of the pipe above the stuck point? If the force of buoyancy acts on the pipe above the stuck point, the pipe could be pulled that much harder because it is the tension in the pipe that is limited. If the force of buoyancy does not act on the pipe above the stuck point, as was commonly Copyright 2002 by Richard E. Chapman
26 Force Figure 2.6 Wall-sticking in horizontal section through the borehole. The pressure of the mud holds the pipe to a depleted reservoir, sealed by the mud cake (the cake of mud formed by filtration of the solids in the mud as a result of the greater energy of the mud in the hole). believed at that time, the pipe could only be pulled to its nominal tensile strength (less a safety margin). This problem has been called the 'drill-pipe fallacy'. Consider the forces acting on an open-ended pipe hanging freely in a borehole filled with mud. Let us take the following values of the parameters for the pipe and mud: Length of pipe: 3 000 m. Weight of pipe: 263.6N m-I, displacing 3.33 x lop3 m3 m-I, in mud of mass density 1500 kgmP3. The cross- sectional area of the pipe is 3.3 x m2. The pressure exerted by the mud at the bottom of the pipe is pgd = 1 500 x 9.8 x 3 000 = 44 x lo6 Pa, or 44 MPa. This is providing an upward force of 147 kN on the bottom of the pipe, equivalent to the weight of about 550m of the pipe in air. Drill pipe is stacked in the mast or derrick of a drilling rig in lengths of about 30 m. These pipes have a visible bend, so it is clear that 550 m could not stand on end but would buckle. But it does not buckle in the borehole, so either the physical interpretation is wrong or there are factors that have not been taken into account. Alternatively, the 3 km of pipe displaces 10 m3 of mud that weighs 1 500 x 10 x 9.8 = 147000N or 147 kN, so the weight of the pipe in the mud is 791 - 147 = 644 kN. The effective weight is 215 N m-l, and the tensile load on the pipe varies continuously from its total effective weight at the top to zero at the bottom, the whole length of the pipe being in tension. Buoyancy, like weight, must be a body force - the difference between the effects of the body force of gravity on materials of two different densities. What would happen if you plugged the bottom of the pipe and so prevented its filling with mud as you lowered it into the borehole? Copyright 2002 by Richard E. Chapman
Page 1 and 2: Physics for Geologists Second editi
Page 3 and 4: Copyright 2002 by Richard E. Chapma
Page 5 and 6: ... vlii Contents Polarization 47 L
Page 7 and 8: Figures Copyright 2002 by Richard E
Page 9 and 10: Tables Copyright 2002 by Richard E.
Page 11 and 12: xiv Preface waves diminishes with d
Page 13 and 14: xvi Preface provides. This book is
Page 15 and 16: xviii Acknowledgements to K. Whaler
Page 17 and 18: xx Symbols mass refractive index bu
Page 19 and 20: 2 Basic concepts Table 1.1 Dimensio
Page 21 and 22: 4 Basic concepts Table 1.2 Basic SI
Page 23 and 24: 6 Basic concepts pascal (Pa) and si
Page 25 and 26: 8 Basic concepts all the relevant d
Page 27 and 28: 10 Basic concepts relating them by
Page 29 and 30: 2 Force The dimensions of force are
Page 31 and 32: 14 Force The ratio of the Moon's ac
Page 33 and 34: 16 Force Figure 2.1 The sum of the
Page 35 and 36: 18 Force When a motorcycle takes a
Page 37 and 38: 20 Force Figure 2.3 Torque is the p
Page 39 and 40: 22 Force How does momentum differ f
Page 41: 24 Force the weights - that is, the
Page 45 and 46: 3 Gravity Universal gravity When di
Page 47 and 48: 30 Gravity are significant to geolo
Page 49 and 50: 32 Gravity Figure 3.2 The tractive,
Page 51 and 52: 34 Gravity Mean sea level It might
Page 53 and 54: 36 Gravity The benefits of space fl
Page 55 and 56: 38 Gravity Figure 3.6 Profile of th
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
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Electricity and magnetism 77 Figure
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Electricity and magnetism 79 rivett
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Electricity and magnetism 8 1 defin
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Electricity and magnetism 83 is kno
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9 Stress and strain Pressure, p, is
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Stress and strain 87 than some natu
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These three elastic constants are r
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Stress and strain 91 Figure 9.1 New
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Stress and strain 93 Figure 9.2 Com
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Stress and strain 95 Figure 9.3 Ide
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Fracture Stress and strain 97 We fo
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Stress and strain 99 from which we
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10 Sea waves The nature of water wa
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Sea waves 103 Figure 10.1 Wave moti
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Sea waves 105 refraction by islands
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Acoustics: sound and other waves 10
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Acoustics: sound and other waves 10
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12 Fluids and fluid flow Introducti
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Fluids and fluid flow 1 13 Figure 1
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Fluids and fluid flow 115 Figure 22
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Fluids and fluid flow 117 and the f
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water above a vertical thickness h
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Fluids and fluid flow 121 where V i
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Fluids and fluid flow 123 ardentes,
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Fluids and fluid flow 125 Figure 12
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- 14 $ 12 E 10 K .- 3 8 r cll + 6 0
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Fluids and fluid flow 129 the liqui
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Some dangers of mathematical statis
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Appendix 139 What would happen if y
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Notes 141 and since x is very large
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References Allum, J. A. E. (1966) P
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References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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