Mechanisms of sediment compaction responsible for oil field subsidence

MECHANISMS

OF SEDIMENT COMPACTION

_{RESPONSIBLE FOR}

OIL FIELD SUBSIDENCE.

A thesis _{submitted to the} University _{of London}

(University _{College London)}

for _{the degree of Doctor of Philosophy}

in the Department of Geological

Sciences.

by

Michael Anthony Addis

October 1987

to my parents

for all their

encouragement

Abstract

During the _{production of a hydrocarbon reservoir,} the _compaction of weakly cemented sedimentary materials can result from increases in

effective stress, and lead to surface _subsidence. Such a phenomenon has recently been observed _{in the oil and gas bearing} chalk fields in the Central North _{Sea. In order to evaluate the compaction potential}

of sedimentary materials during _{exploitation of a} reservoir,

laboratory _{experiments- were performed on chalks and clays. These} experiments _{were predominantly'Ký} (zero lateral _strain) tests.

The tests _{were performed in a high pressure triaxial cell, the} development _{of which continued throughout the experimental 'programme.}

Tests _{performed on chalks from the Central North Sea, and from two} onshore sites in _{southern -England showed similar} deformational

trends. _{The analyses of these results concentrated on the variables}

of testing and the _{possible errors resulting} from the _{use of} laboratory _{data in the modelling}

of field situations. The analyses of the tests _also include _{a comparison between the experimental methods} and the interpretation _of the _{results of} this _{study and those of}

other workers on the _{subject of reservoir compaction.} A parametric

description _{of the compaction of chalk is presented as a summary to} these tests.

w

Two compaction tests _{on clay samples} from the Central North Sea were also undertaken. The clays _{were uncemented} and show contrasting

behaviour _{to the chalks. These tests were performed to evaluate the} amount of compaction likely to _occur in the overburden of a hydrocarbon _{reservoir during production.}

The results of the deformational trends obtained from this study

are compared to those obtained by other workers, with particular reference to the changes in physical parameters during compaction.

This follows _a literature _survey into hydrocarbon _reservoir compaction.

The K0 tests _performed in this _{study are thought to represent} the condition of sediment burial in _{a tectonically} inactive basin. This

subject is briefly reviewed, _and the _{relevance of} the _results presented earlier discussed in terms _of the _{prediction of stresses}

existing _within differing lithologies.

The analysis _of the _{results have been performed using parameters} commonly used in _{soil mechanics, this seemed to be appropriate for} the deformations _undergone

by the materials _{used in this study.}

Acknowledgements

During _{the period of research the author has been in receipt of a} Natural Environment Research _{Grant, whibh is duly acknowledged.}

During the three _{years of research the author has been associated} with three colleges in the University _{of London.} The first two years

of the research were _{performed while a student at} the Geology Department _{of King's College, now sadly "mergered" in outer London.} The final _{year was spent as a student}

of University College. During the three _{years, the experimental" work was performed in the}

soil laboratories _{in the Department 'of Civil Engineering,}

at Imperial College. As _{such I am indebted to many}

people from the three institutions _{to numerous to mention. I would however like to thank} the _{chief technicians from King's}

and University College, Mr. J Congram and Mr. _{R Dudman respectively, for}

ensuring relatively few hickups _{along the way.}

I would especially like _{to thank the technical staff of the soil} laboratories _{who have provided}

excellent support to this study, with much input into the _equipment design _{and construction, as well as} many other subject _areas. I am sure that _without their _expertise,

help _{and patience this study would}

not have been possible. Mr. S. Ackerley, _{Mr. L. Spall, Mr. G. Keefe, Mr. A. Bolsher and Mr. R. Hare}

are gratefully _{acknowledged. I would also like} to thank Mrs. E. Gibbs for _{all her help, and for her forgiveness during times of oil leaks.} Particular _{thanks are given to Mr. S. Ackerley whose enthusiasm,}

general _willingness to do the impossible _{and his patience with an} ignorant _{geologist is gratefully}

appreciated.

Technical help _{was also provided by Mr. T. Osbourne and Mr. S. at}

University College _{and Mr. R. Giddons in the Department of geological} sciences, Imperial college _{who are duely} thanked. During the initial set up of the apparatus the help of Mr. B. Clarke in the Engineering Geology _section in Imperial College _{was sought and willingfully}

obtained on many occasions; Iwould like to express my thanks for his help _{and advice.}

My period of work at the soils

laboratory,

Imperial

College

_{was a}

true _{education and} I _must thank _{my colleagues} in this _group for answering my many questions _patiently., regardless of the elementary

nature of these, _{and for} their _{encouragement} during this study. My many thanks *go to Mr A. J. Bond, Dr. G. T. Dounias, Mr. D. French, Mr.

J. Hellings, _{Mrs. G. N. Georgiannou Lesas, Dr. M. Maccarini, Mr. M.} Mahmoud, Dr. J. Maswoswe, Mr. D. L. Nyaoro, Dr. E. Ovando-Shelley, Mr. D. Schreiner, _{Dr. S. Shibuya and Mr. D. Toll, Mrs. T. Tika}

Vaffilikos. _{I would also like to thank Dr. M. Maccarini for our many} discussions _{on the behaviour of cemented materials and his ready} exchange of ideas. The help _{of Mr.} D. Toll _{and use of his computer} expertise and software. for the _{calculation of results} is _gratefully

appreciated. Use of software developed by Mr. A. J. Bond for the 3-dimensional _{plots is also gratefully appreciated by the author.}

I am very grateful

_{to have been able to work at the soil mechanics}

laboratories, _{and as such I must thank the head of the soil mechanics} section, Prof. J. B. Burland for this _opportunity. I would also like to express my gratitude to the academic _staff of the section, Dr. R. J. Chandler, Prof. _{J. N. Hutchinson, Dr. R. Jardine,} Dr. S. Leroueil

(visiting _{academic), Dr. D. M. Potts, Prof. A. W. Skempton, Dr. P.} R. Vaughan and particularly Dr. A. E. Skinner, for _{many stimulating}

and enlightening discussions.

Many thanks _{go to the Norwegian Petroleum} Directorate for _allowing

me the opportunity of working on samples obtained from the North Sea. I would _especially like to thank Mr. K. Tonstad, Mr. 0. P. Berget _and Mr. P. E. Overli, for _{many fruitful} discussions.

Colleagues

_at

King's

College

_{and University}

College

_are

_also

thanked for _all their _{support and help in very many ways, my thanks} go to Dr. H. Chen, Mr. M. J. Leddra, Mr A. Goldsmith, and Miss N. A. Yassir. _{I am especially grateful to Miss N. A. Yassir} for _correcting

my grammar _-a most unenviable task, many thanks. At this point I would like to express _{my gratitude} to my numerous co-tenants/

colleagues for their _{patience with} the _author during the _period of research, _{as well as} for their _welcome distractions _{and excellent}

company, these include Mr. H. Davies, Miss K. Jeffr*ey, Miss K. Lewin, Mr. J. Morris, _{Mr. A. Pritchard, Mr. M. Shaw, Dr. J. Williams, and} Miss M. White.

It only remains for me to thank my supervisor,

Dr. M. E. Jones for

his help _{and encouragement, and for directing me towards a very} interesting _{area of study. His support is acknowledged and} appreciated _especially in times _{of critisism} from the author.

I would finally like _{to express my appreciation to my family and} especially-to my parents, _{who have always encouraged and supported}

me, not only through this _{period of research,} but through _{my whole} education, the good and not so good times. My thanks _{are insufficient}

to express my gratitude.

Contents

Title

Abstract

Acknowledgements Contents

List-of figures List _{of tables}

... i

... 111

... viii

... Xl

... xvi Glossary _{of terms}

Chapter 1 Introduction

... xviii

... 1 Chapter 2 Aspects _{of compaction}

... 8 2.1 Introduction

... 8 2.2 _{The principle of effective stress}

... 10 2.3 Undrained _{pore pressure response}

... 18 2.3.1 _{Sample saturation}

... 20 2.4 One dimensional _{consolidation}

... 21 2.5 Representations _{of stress states in sediments}

... 24

2.5.1

_{Stress paths}

...

24

2.5.2

_Critical

_state

_model

...

28

2.6

_Mechanical

_behaviour

_{of chalks}

...

34

2.6.1

Behaviour

_{of bonded particulate}

_materials

...

34

2.6.2

_{Stress-strain}

_{characteristics}

_{of weakly}

cemented _{sedimentary materials ...} 39 2.6.3 _{Compaction of chalk}

... 42 2.6.3. _{i Normal consolidation}

... 42 2.6.3. ii _{Secondary consolidation/creep}

... 49 2.6.3. _{iii Summary of salient points}

... 50 2.7 Strain _{rate effects}

... 50 2.8 Effects _{of temperature on consolidation}

... 59 Chapter 3 Experimental _{methodology and materials}

... 66 3.1 Introduction

... 66 3.2 _{The coefficient of earth pressure at rest}

... 68 3.2.1 _Introduction

... 68 3.2.2 Relationships _{of Ko}

... 71 3.2.2. _{i Ko} 0' _relationship

... 71 3.2.2.11 _{K° --V relationship}

... 73 3.2.3 Laboratory _{determination of K}

... 74 3.2.3.1 _{Requirements for the K° test}

... 74 3.2.3. ii _{Methods of measuring K° during}

zero lateral

_strain

tests

_...

75

3.2.3. iii

_{Recommendations for lateral}

_strains

during K tests _... 77 3.2.4 K _{at high stresses}

.. "... 78 3.2°. 4. i Previous _{high pressure K experiments}

... 78 3.2.4. _{ii K derived from angles o? internal}

friction

...

79

3.3

_{Constant rate of strain}

tests

_...

80

3.3.1

Introduction

...

80

3.3.2

Interpretation

_{of the CRS test}

_...

81

3.4 Compaction tests in the high _{pressure oedometer}

... 90 3.5 Materials _{used in this study ...} 91

3.5.1

Introduction

...

91

3.5.2

_{The geology of chalk}

...

91

3.5.2.1

General description

_...

91

3.5.2. _ii Ekofisk _{area chalk}

... 94 3.5.2. iii Pegwell _{Bay chalk}

... 97

3.5.2. iv Butser Hill

_chalk

_...

100

3.5.3 North _{Sea clays}

... 104 Chapter 4 Discussion _{of the results}

... 108 4.1 Introduction

... 108 4.2 _{The effect of porosity variations on}

the compaction of chalk _... 108

4.3 _{strain rate effects on compaction}

... 125 4.4 The influence _{of sample shape on the}

compaction behaviour _... 141

4.5 Temperatures _{effects on compaction}

... 148 4.6 Hydrostatic _{to uniaxial strain conversion}

... 162 4.7 Time dependancy _{of the compaction}

... 169 4.8 _{The nature of compaction of chalk}

... 177

-

4.8.1

Particle

degradation

during-compaction

_...

183

4.8.1. _{i low magnification}

... 186

4.8.1. ii high magnification

_...

189

4.9 Yield _{and failure surface of chalk}

... 192 4.10 Compaction _{of chalk: Summary}

... 196

Chapter 5

Discussion

_{of the clay tests}

...

214

5.1

Introduction

...

214

5.2

_{The compaction test on sample NSC2.20}

...

215

5.3

_{The compaction test on sample NSC3.20}

...

220

5.4

Discussion

...

223

Chapter 6 Hydrocarbon _{reservoir compaction and}

associated _{ground subsidence ...} 226 6.1 Introduction

... 226 6.2 Hydrocarbon _{reservoir compaction}

... 227 6.2.1 Theoretical _{approach to reservoir compaction}

... 228 6.2.1. _{i Conversion of hydrostatic strain data}

to uniaxial _{strains ...} 230 6.2. l. ii Empirical _{approaches of reservoir}

compaction _... 236

6.2.2 _{Changes in physical parameters during}

compaction _... 243

6.2.2. _{i The variation in permeability with} increasing _{effective stress}

... 243 6.2.2. _{ii Variation in compressibilities of}

reservoir

materials

_...

249

6.2.3

Time-dependant

_deformation

_{in reservoir}

compaction

_...

_""..

256

6.3 Examples _{of subsidence in oil and gas fields}

... 261 6.4 Discussion

... 267 Chapter 7 The state _{of stress during burial of sediments}

... 274

7.1 Introduction

7.2 Vertical _stress

7.3 Horizontal _stress Chapter 8 Conclusions

References

... 274

... 274

... 276

... 284

... 291

Appendix 1 Description _{and development of the triaxial cell} ... 310

A1.1 The triaxial _cell ... 310

A1.2 The heating _system ... 314

A1.3 The drainage _system ... 315

A1.3.1

_{New high pressure volume gauge}

...

318

Al. 3.2 _{Medium pressure volume gauge} ... 323

A1.4 _{The radial strain belt} ... 325

Al. 5 Control

_{of the tests}

...

329

A1.6 Future _{apparatus development} ... 330

Al. 7 _{Data acquisition} ... 331

Appendix 2 _{High pressure oedometer} ... 333

A2.1 Description _{of the high pressure oedometer} ... 333

A2.2 Drainage _system ... 336

A2.3 _{The heating system} ... 336

Appendix. 3 _{Sample preparation and test procedure} ... 338

A3.1 _{Sample preparation} ... 338

A3.1.1 _Chalk ... 338

A3.1.2 _Clay ... 342

A3.2 _{Test procedure} ... 343

A3.2.1

_{K tests}

...

343

A3.2. l. i

Applying

_{back pressure}

...

343

A3.2. l. ii Shearing following

K loading

...

344

A3.2.2

_Triaxial

_{compression tests}

0

...

344

Appendix 4 Calibrations _{of the equipment and transducers} ... 345

A4.1 Calibration _{of the triaxial cell} ... 345

A4.1.1 _{Ram friction} ... 345

A4.. 1.2 _{Ram shortening} ... 350

A4.2 Transducer _calibrations ... 352

Appendix A5.1 A5.2 A5.3 A5.4 A5.5 A5.6 A5.7 5 Chalk _test results North _{Sea chalks} Strain _rates Sample shape Butser Hill _chalks Hydrostatic _test Drained _{shear tests} Undrained _{shear tests} ... 358

... 358

... 413

... 458

... 480

... 537

... 539

... 547

Appendix 6 Equipment _{specifications} ... 558

A6.1- Specifications

_{for the components of the triaxial}

cell

heating

_{s ystem}

_...

558

A6.2 Specifications _{of components of the drainage system} .... 559

A6.3 Strain _{gauges used on the radial strain} belt ... 560

List _{of figures}

Fig. 2.1 The frictionless dashpot _{analogy of compaction}

illustrating two different _{effective stress} increases _. 14 Fig. 2.2 Stress _paths for hydrostatic _{and drained} loading tests

in 3-dimensional _{principle effective stress space ...} 25 Fiq. 2.3 Stress _paths for hydrostatic _{and drained} loading tests

in maximum and minimum principle effective stress space 25 Fig. 2.4 Mohr diagram _construction for _stress presentation... 27

Fig. 2.5 Comparison _{of stress paths and failure} lines in t-s'

and q-p' stress space _{""... """"""} 27 Fig. 2.6 Diagrams _{showing the shape of the Critical} State line

(After _{Atkinson and Bransby, 1978)}

... 29 Fig. 2.7 _{The Roscoe surface as defined} by drained _{and undrained}

loading _tests (After _{Atkinson and Bransby,} 1978) _... 31 Fig. 2.8 The shape of the Hvorslev _{surface, plotted on normalised}

axes to eliminate volume changes between different

samples (After Atkinson and Bransby, 1978) _... 31 Fig. 2.9 _{An undrained section through the Critical} State diagram

(After _{Atkinson and Bransby, 1978)}

... 33 Fig. 2.10 The Critical _{State diagram illustrating the stress}

dependance _{of volume reduction for uncemented sediments} (After _{Atkinson and Bransby, 1978)}

... 33

Fig. 2.11 Coulombic yield envelope with a terminating

_{end cap ...}

35

Fig.

2.12 A Generalised

_cementation

_yield

_{envelope (After}

Sangrey,

1972)

_...

37

Fig. 2.13 Model of yield _{envelope components} in cemented soil (After _{Uriel and Serrano, 1973)}

... """ 37 Fig. 2.14 Brittle _{and ductile yield} in triaxial tests _{on dry}

samples of Bath Stone (After Elliott and Brown, 1985) _. 41 Fig. 2.15 The trend _{of decreasing} initial _{permeability with}

porosity for pure chalks (After Scholle, 1977) _... 48 Fig. _{2.16 Time effects} during _{consolidation} (After Mesri _and

Godlewski, 1977) _... 54

Fig. 2.17 Time effects

on the compression of a sediment subjected

to reloading (After Bjerrum, 1967) _... 56 Fig. 3.1 K _{stress paths} for _{overconsolidated clays}

(ýfter

_Lerouiel

_{et. al.,}

₁₉₈₃₎

""""".

"...

70

Fig. 3.2 Triaxial _{cell with} inner _cell for _maintaining K

conditions (After Bishop, Webb and Skinner, 1969) _... 76

Fig. 3.3 Effect _{of stress} interval _{on the Wissa analysis ...} 86

Fig. 3.4 Effect _{of stress} interval _{on the Lee analysis ...} 88

Fig. 3.5

X-ray diffraction

trace of Pegwell Bay chalk ...

99

Fig. 3.6 X-ray diffraction trace _{of Butser} Hill chalk _... 102

Fig. 3.7 XRD for _clay test NSC2.20 (Depth 1200m) _... 105

Fig. 3.8 XRD for _clay test NSC3.20 (Depth 1850m) _... 106

Fig. 4.1

Yield strength

for EC5.20, EC6.20, and EC9.20 ...

109

Fig. 4.2 Yield _{point vs porosity} for K tests _{on Central} North Sea chalks ° _... 110

Fig. 4.3 Comparison _{of yield point vs porosity results with} data presented by Jones (1985) _... 111

Fig. 4.4a Young's _{modulus vs porosity} for K tests _{on Central}

North Sea chalks

.0

...

113

Fig. 4.4b Comparison _{of Young's modulus vs porosity'results with} data presented by Jones (1985) ... 114

Fig. 4.5

_{Yield point vs Young's modulus for Central North}

Sea chalks

_...

115

Fig. 4.6a Uniaxial _{compressibility variation of Central} North Sea chalks with increasing _{vertical effective} stress _... 116

Fig. 4.6b Pre-yield

_{M variation}

_{with porosity}

for Central

Fig. 4.7 _{K0 vs porosity for Central North Sea chalks ...} 119

Fig. 4.8 _{0"3' vs 0"1' plot for three Central} North Sea chalks _.... 120

Fig. 4.9 _{Trend of with with de/dp'} for Central North Sea chalks 120 Fig. 4.10 _{Void ratio variation with maximum effective stress} for Central _{North Sea chalks ... """} 122 Fig. 4.11 Shifted _{void ratio vs maximum effective stress plots} for Central North _{Sea chalks ... ". "...} 123

Fig. _{4.12 Comparison of the compaction trend shown in Fig.} 4.11

with published

trends.

_...

124

Fig. 4.13a Effect

_{of strain}

_{rate on e-log p' plot}

for PB1.20

_....

126

Fig. 4.13b Analysis

_{of strain}

_{rate variation}

in PB1.20

_...

126

Fig. 4.14 _and-4.15 Comparison _{of three strain rate experiments ..} 128 Fig. 4.16 Comparison _{of tests} PB5.20 and PB6.20 _... 129

Fig. 4.17

, a011-Normal consolidation axial strain for samples

tested _{at different strain rates ...} 135 Fig. 4.18 Variation _{of CJ}

lnc' with strain rate for Pegwell

Bay chalks _... 136

Fig. 4.19 Normalised _{stress-strain plots} for _{samples of Pegwell}

Bay samples tested at different strain rates _... 138 Fig. 4.20 Normalised _{stress-adjusted strain plots} for _samples

tested _{at different strain rates ...} 139 Fig. 4.21 Normalised _{stress-normal consolidation axial strain}

plots for samples tested at different strain rates _.... 140 Fig. 4.22 Effect _{of sample shape on K0 deformation}

... 143 Fig. 4.23 Normalised _{stress - adjusted strain plots} for _samples

of different H/D ratios _{and strain} rates _... 146 Fig. 4.24 Normalised _stress

- normal consolidation axial strain plot for samples _{of different} H/D ratios and strain

rates _... 147

Fig. 4.25 Comparison _{of BH14.60 and BH17.60}

... 150 Fig. 4.26 Comparison _{of BH14.60, BH16.100, and BH18.20}

... 154 Fig. 4.27 Temperature _{experiments shifted to the same initial}

void ratio _... 156

Fig. 4.28 Normalised

_stress

_{- axial}

_strain

_{from yield,}

_stress

normalised

to the yield point for the

temperature

experiments _... 158

Fig. 4.29 Normalised _{stress - normal consolidation strain} for the

temperature

_experiments

_...

159

Fig. 4.30 Normalised _{stress - normal consolidation strain} for

BH14.60 and BH17.60 _... 160

Fig. 4.31 Normalised _{stress - normal consolidation strain} for

Butser _{Hill chalks tested at 20°C ...} 161

Fig. 4.32 Stress-strain

_{curves for uniaxial}

_{and hydrostatic}

tests

163

Fig. 4.33 Uniaxial

_strain

_{from BH5.20 vs unconverted and converted}

hydrostatic

_strain

data from BH6.20

_...

165

Fig. 4.34 Enlarged low strain

area of Fig. 4.33

_...

166

Fig. 4.35 Stress _{- strain curves} for _uniaxial, hydrostatic, converted hydrostatic, and curve construction

after Johnson and Rhett _... 168 Fig. 4.36 _{The effect of temperature variations on Cv and K ...} 171 Fig. 4.37 Absolute _{permeability vs maximum effective stress} for

temperature _variation tests

... 172 Fig. 4.38 _{Cv and K reduction} for Central North Sea chalks _... 174

Fig. 4.39 _{The effect of grain crushing} during K. tests _on

sands (After Schmidt, 1967) _... 179 Fig. 4.40 _e- log p' plot for _{the oedometer} test _{performed on}

Butser Hill _chalk

... 180 Fig. 4.41 Undrained _{pore pressure response of incremental} loads

in the oedometer test _{on Butser} Hill _{chalk ...} 182 Fig. 4.42a Uniaxial _{compressibility of sands (After} Roberts,

1969)

...

185

Fig. 4.42b Uniaxial

_{compressibility'of}

_carbonate

_sediments

(After _{Valent et. al., 1982)}

... 185 Fig. 4.43 Yield _{envelope and failure line for Butser Hill chalks 194} Fig. 4.44 Young's _{modulus vs porosity for K0 tests on three}

chalks

_...

197

Fig. 4.45 Yield point vs porosity

for K0 tests

_{on three chalks}

..

198

Fig. 4.46 Yield point vs Young's modulus for K° tests on

three _chalks

... 199 Fig. 4.47 Deviatoric _{stress vs change in void ratio during the}

elastic deformation _{of K and drained shear} tests _on Butser Hill _chalk 0

... 201 Fig. 4.48 Stress _{paths for four K0 tests on Butser} Hill _chalks

.. 204 Fig. 4.49 Analysis _{of the pore collapse deformation} for K° tests

on Butser Hill _{chalks ".. """.. """"""} 205 Fig. 4.50 Variation _{of pore collapse deformation with yield point}

for _{K0 tests on Central North Sea chalks}

... 206 Fig. 4.51 Variation _{of the size of the pore collapse} deformation

in q-p' space for Central North Sea chalks _... 206 Fig. 4.52 Trends _{of void ratio with mean effective stress} for

normally consolidated deformation of Central North Sea

chalks _... 208

Fig. _{4.53 Shifted compaction curves for Central North Sea chalks} 209 Fig. 4.54 _{K0 stress path in q-p'-e space}

... 210 Fig. 4.55 Diagrammatic _{K0 stress path} for _{chalk ...} 211

Fig. 5.1 K0 test _{of North Sea clay NSC2.20}

... 216 Fig. 5.2 Ko test _{of North Sea clay NSC3.20}

... 221 Fig. 6.1 Permeability _reduction in Danian _{outcrop chalk} due to

stress increases (After Simon et. al., 1982) _... 246 Fig. 6.2a Reduction _{of permeability with porosity} in K tests _on

Central North _{Sea chalks} o... 247

Fig. 6.2b Reduction _{of permeability with porosity} in K tests _on

two chalks from southern England °... 247 Fig. 6.3 Effect _{of stress history on My of sand (After} Mess,

1978)

... 252 Fig. 6.4 Uniaxial _{compressibility variation with} increasing

stress for Central North Sea chalk _{samples ...} 253 Fig. 6.5 Comparison _{of uniaxial compressibilities obtained from}

outcrop _{chalk samples and North} Sea samples _... 254 Fig. 6.6 Consolidation _{of clay layers of various thicknesses}

resulting from an instantaneous _stress increase (After

van der Knaap and van der Vlis, 1967) _... 259 Fig. 7.1 Variation _{of ratios of horizontal to vertical stress}

with depth reported

in the literature

(After

Brown and

Hoek, 1978)

... 281 Fig. A1.1 The high _{pressure triaxial cell}

... 311 Fig. _{A1.2 Sample set up in the triaxial cell}

... 313 Fig. A1.3 Diagrammatic _{illustration of the drainage system}

... 316 Fig. _{A1.4 High pressure volume gauge}

... 319 Fig. A1.5 Calibrations _{of the high pressure volume gauge at}

various back pressures _{... """"""} 322 Fig. A1.6 Calibration _{of the medium pressure volume gauge at}

the working _{back pressure ...} 325

Fig. _{A1.7 Cross section through the pad of the radial strain} belt 326 Fig., Al. 8 Stability-of _{the second radial strain} belt

... 328 Fig. _{A2.1 The high pressure hydraulic oedometer}

... 334 Fig. _{A4. la Increase of ram friction with ram displacement - Low}

cell pressures _... 346

Fig. A4. lb Increase _{of ram friction with ram displacement - Medium}

cell pressures _... 347

Fig. A4.2 Variation _{of ram friction with cell pressure}

... 348

Fig. _{A4.3 3-D plot of ram friction} in the triaxial _{cell ...} 349

Fig. _{A4.4 Ram and sample pedestal shortening} during _axial loading 351 Fig. A4.5 Output _{of the first radial strain} belt _{with cell} pressure _... 355

Fig. A4.6 Apparent _{change, in} diameter _{of sample due to the} pressure sensitivity _{of radial} strain belts _... 356

Plates Plate 3.1. _{-Oil saturated Butser Hill chalk showing}

heterogeneities

_{due to burrows and borings}

...

103

Plate 4.1 -Low magnification SEMs- of untested (4273) and tested (4277) _{Pegwell Bay chalk} ... 187

Plate 4.2 Collapse _{of foraminifera tests, SEM 4276} ... 188

Plate 4.3 _{High magnification SEMs of untested (4264) and}

tested

(4269): Pegwell Bay chalk

...

190

Plate 4.4

_{Back scatter}

_{images of samples in plate 4.3 ...}

₁₉₁

Plate A1.1

The triaxial

_cell

...

312

Plate Al. 2 The medium pressure volume gauge and. intensifier

_....

324

Plate A3.1 Equipment _{used during sample preparation} ... 339

List _{of tables} Table 2.1 Compressibility _{data from van Kooten} ... 16

Table 2.2 Correction _{values obtained from Table 2.1} ... 16

Table 2.3 Compressibility _{data from Heiberg} ... 17

Table 2.4 Reported _{properties of chalk.} ... 44

Table 2.5 Strain _{rate dependance of various materials} ... 52

Table _{3.1 Some reported relationships between Ko and 0' ...} 72

Table 3.2 Details

_{of Central}

_{North Sea chalk samples tested ...}

96

Table 3.3 XRD data of the two clay samples tested

_...

107

Table 4.1 Summary of the results of the North Sea chalk samples _. 122

Table 4.2 Summary of the results

of the strain

rate tests

_...

133

Table _{4.3 Summary of the results of the sample shape tests ...} 142 Table _{4.4 Summary of the results of temperature variation} tests _. 153 Table 4.5 Viscosity _{and density changes of water with} temperature 173 Table _{4.6 Summary of the results of the drained} loading tests _... 193 Table 6.1 Uniaxial _{compressibilities of sandstones and limestones}

(After _{Geertsma, 1973)}

... 250 Table _{6.2 The main examples of subsidence} due to hydrocarbon

production _... 266

Table 7.1 Variation _{of horizontal stress with} depth, _calculated

from hydraulic fracturing data (From Breckels _{and van} Eekelen, 1981)

... 278 Table 7.2 Variation _{of horizontal stress with} depth, _calculated

from formation _{integrity tests} (from _{Breckels and van} Eekelen, ₁₉₈₁₎

... 279 Table A1.1 Calibrations _{of the new high pressure volume gauge ... 322} Table A4.1 Calibration _{coefficients for transducers used with the}

triaxial _cell

... 353 Table _{A5.1 Summary of the North Sea samples used in K0 tests}

.... 360 Table A5.2 Summary of the samples used in the strain rate tests _. 415 Table A5.3 Summary of the samples used in the sample shape tests 459 Table _{A5.4 Summary of the samples used in the temperature}

variation

tests

_...

481

Table A5.5 Summary of the samples used in drained shear tests ... 541

0

Glossary _{of terms}

The following list is _{a glossary of} the _main terms used in this thesis, _other terms _{used are defined} in the discussion.

A Skempton's _{pore pressure parameter.} B Skempton's _{pore pressure parameter.} C Compressibility-of _{mineral grains.}

C Coefficient _{of secondary consolidation.} Lb Rock bulk _{compressibility.}

C Coefficient _{of volume compressibility.} Cf _{Pore compressibility}

C Uniaxial _{compressibility} (= Mv). Cm _{Rock matrix compressibility.}

Cr Skeleton _{compressibility.}

Cs Coefficient _{of consolidation.} Dv Depth

e void ratio.

E Young's _modulus.

f Fractional _porosity.. G _{Shear modulus.}

H Height/Depth.

k Hydraulic _conductivity (cm/sec).

K Coefficient _{of permeability} (Darcies). K Coefficient _{of earth pressure at rest.} To _{K for incremental stress changes.}

K° K° for elastic deformations.

Konc for _{normal consolidation deformations} (Normal is used to describe _{materials which exist} at higher than _{experienced previously, and free of} cementation.

KK for _{pore collapse deformations.} M°pc =°q/p'

Mv

Uniaxial

_{compressibility}

(= Cm)

n

Measure of non-linearity

_{of elasticity.}

p'

Mean effective

stress.

PO Pore pressure of the formation.

Pon ° Normal pore pressure gradient (9.79kPa/m). gq, Shear stress/deviatoric stress.

t

Ellapsed

time.

T _{Time constant} (= C

. t/H2) U. _{Pore pressure.} v

U _{Pore pressure} difference _{across the sample.} Vh Volume.

0( _{Thermal expansivity.}

P _{Ratio of rock matrix to bulk compressibility.} 6 Density.

E

_Strain.

0'

_{Angle of internal}

_friction

O

_{Total stress.}

IT, Effective _stress. Q' _{Rate of effective}

stress _change. Poisson's _ratio

consolidation

stress

levels

any effects

of

CHAPTER 1

INTRODUCTION

This thesis _presents the _{results of a experimental study of} the volume reduction which occurs in sedimentary rocks when pore fluid

is expelled. In nature loss _{of pore} fluid _{from a sediment may result} either because of the increased loading due to burial in sedimentary

basins _{or reduction} in _{pore pressures} during _production from reservoirs. The reduction in pore volume which occurs _{as a result of}

fluid _{withdrawal during exploitation of oil fields and aquifer}

systems, is analogous to natural dewatering, _{and relevant aspects of} this _{subject are} therefore _{discussed both from an engineering and a} geological standpoint. The work _contained herein is based _{on an} experimental programme _{of one-dimensional compaction} tests (zero lateral _strain deformation _{experiments) performed in a high pressure} triaxial _cell. A drainage _{system, a heating facility and special}

control systems for the tests _{performed, were} developed for the triexial _{cell and refined during the testing programme.}

The testing _{programme required samples of a weak sedimentary rock} that _{was porous and cemented. The chalk, which has been shown by} previous workers (Blanton, 1981; Jones _{and Addis,} 1985b) to exhibit

mechanical _{characteristics} typical _{of most porous cemented sediments} was selected for this _purpose. The chalks tested initially were

sampled from cores _recovered from the Central North Sea and were of varying _porosities. These early _{experiments were then supplemented} by a series of deformation tests _performed on samples of outcrop

chalk from two onshore sites in southern England. These experiments

on samples with the same porosity were performed to evaluate the effects of different test procedures on the mechanical characteristics exhibited by the North Sea samples. The experimental

study of the chalks enabled the construction of a model for chalk behaviour during _{one-dimensional compaction.} Two compaction tests _on

Tertiary _{clays, cored} from the _{same area of} the North Sea as the chalk samples, were also performed. These results provide an

interesting _{comparison with the chalk compaction} data, because _unlike the chalk the clays were uncemented.

Porosity decrease _{in sediments has been studied in geology since} the _{earliest days of the subject, and has received the attention of} many notable geologists. The methodology behind these _{early studies}

has been to _{correlate porosity with age of strata using outcrop} materials. Later studies incorporated _{samples recovered} from drilling

operations. From these _{studies, plots of} decreasing _{porosity with} increasing depth have _{been produced} (Rieke _{and Chilingarian, 1974;} Selley, 1978; Baldwin _{and Butler, 1985).}

The _{experimental study of porosity decrease with increasing}

applied stress was initiated in the 1930's. The main expansion of this _{study occured} in _the 1950's, _with the _realisation that _pore volume decrease significantly _affected the _prediction of volumes of oil in place, in hydrocarbon _{reservoir productivity} calculations,

Hall _"(1953). Since _{then, geological work has mainly concentrated on} this'aspect _{of volume decrease in sediments and rocks.} Also, _{a number} of _{experimental engineering studies} have extended low pressure soil mechanics theory to the high _{pressures encountered} in _reservoir engineering _{- these} have proved to be interesting geologically.

The reduction in _{pore volume of sediments} during burial _{can be}

effectively split into two _{main mechanisms:} i) _{consolidation,} the reduction in pore volume by intergranular _slip and grain rearrangement, with little _{alteration, of the constituent} grains, and ii) _cementation, the bonding _{of the sediment,} through filling _{of the} pore volume, with mineral material. The former mechanisms have been widely studied at low pressures in the engineering discipline of soil

mechanics, but relatively few studies have been performed _at high pressures. As a result, there is very little information on the

consolidation behaviour of sediments at high pressures, though some notable. contributions _exist (Rieke _and Chilingarian, 1974). The

second mechanism, _{volume reduction} through _cementation leads to an increase in _{the competency of a unit of strata, increasing its} lithification, _{and has normally been attributed to a pressure} solution mechanism. Pressure _solution is the dissolution _{occurring at} compressed points _{of intergranular contacts, with reprecipitation of} the dissolved _{material in areas of relatively low compressive}

stress. This differs from _{cementation of near}

surface sediments, _which is generally due to deposition _{of salts precipitating} from pore fluids,

commonly accompanied by _mineral breakdown in _{weathered parent} materials. Pressure _solution is very dependent _{upon chemical} factors which alter the solubility _{of the solid material} in the transporting

medium, whereas consolidation, _{as a volume change mechanism,} has rarely been related to the _{chemistry of sediments.} Another

fundamental. _{difference between the two mechanisms is the time} dependency _{associated with them: consolidation has mainly been}

investigated _{by engineers over the time}

scale of decades, whereas cementation _{of sediments} is _{normally considered as a geological}

process, _{occurring over a considerably} longer _{period, of} time. Cementation _{due to pressure solution is a very slow process, and it}

can only be tested 'at very slow strain rates. The excessively long times _{required to undertake} laboratory _{studies of pressure solution,}

has meant that it _{has been predominantly studied} from _{a theoretical}

or descriptive standpoint. (see Addis and Jones (1985) for a brief review of the literature).

The work presented in this thesis _{applies soil mechanics} theory to the _{problem of compaction of a weak rock under conditions of}

increasing _{overburden stress.} This increase in the _effective overburden stress could result _naturally from the progressive burial

of a sediment, or from the increase in _{effective stress} due to drawdown _{of pore pressure "during production of a subsurface}

reservoir. A model of sediment behaviour is _{used as a framework} for the study; this _{is presented in Chapter 2. The experimental work has} mainly concentrated _{on the study of one-dimensional compaction and} consolidation _{of the chalk.} Those factors _which have been thought to affect the compaction _of the _chalk have been investigated _as independent _{variables. This study has also explored in detail the} stress path followed by the sample during _compaction (Chap. 3), _and demonstrates _{how sample volume change is dependent on the magnitude} of all components _{of the applied stress system.} This'has been ignored in _{some of} the _{previous studies which have considered porosity} decrease in _{sediments, during high pressure compaction experiments}

(Rieke _{and Chilingarian, 1974). -The results of this part of the study} indicate _{that a knowledge of both the magnitude of the stresses} acting _{at depth} in sedimentary basins, _{and the manner in which} these

stresses _{vary as the lithology}

changes, is essential to understanding

the _{compaction of the different sediment units. Such knowledge is} also _required to _understand the _{generation of overpressures} (pore pressures in sediments _{and rocks, which are} in _{excess of} the

hydrostatic _{gradient). Without such a knowledge a full understanding}

of the structures in, _{or associated with sedimentary} basins _cannot be obtained.

Analyses _{of the results in terms of the consolidation parameters} described in Chapter 3, involves _{the acceptance of assumptions}

implicite in Terzaghi's _{consolidation theory, these assumptions may} not be valid for chalk or for _{other materials at high pressures.} This is discussed in detail _{in the text} (Chaps. _{2 and 3). The reduction in} pore volume due to consolidation _{will affect} the _{permeability of a}

sediment. This is _{obviously an important} factor both in terms _of consolidation of naturally buried _{sediments, where low permeabilities}

will resist further _{volume change, and in the case of compacting oil} reservoirs, where _a loss _{of permeability will} have _significant

economic consequences. Permeability _{was measured-} in the _samples tested during _{this study while the samples}

were deforming; this method of permeability _{measurement has not been- performed at high} pressures previously. The results indicate _{that measurement of the} permeability using this test _method (Chap. _{3) may be a more useful} and more time _efficient technique than the incremental _methods generally employed. The possible _errors involved in _applying these new testing techniques _{are discussed} in Chapter 3.

Chapter 4 discusses _{the results of the chalk deformation tests} presented in App. 5, _{with emphasis on the variables} influencing

compaction, _{and relates} the _results to _{similar published work,} wherever _possible. After discussing the _{variables affecting} the

compaction _{of. chalk,} the nature _{and mechanisms of the compaction are} discussed. _{The chapter is terminated by a discussion of deformation}

of the chalk in terms _{of the soil model described earlier} in, Chapter 2. Chapter 5 is _{a brief description of the two clay samples tested}

from the Central North Sea, to _which the _{chalk experiments can be} compared. The tests were each of approximately 6 weeks duration, but

because _{of the low sample permeability,} they _{did not attain} the large strains developed during the deformation of the chalk samples. Because _{of the difficulties encountered} in testing the clay samples,

the _{results are not} discussed in _{any great} detail, _{and should} be treated _{semi-quantitatively.}

Chapters, 6 _and 7, _{are predominantly} literature _{reviews of} hydrocarbon _{reservoir compaction and the analysis of in-situ stresses}

in basins, _{respectively. Initially in Chapter} 6, _{the methods} previously used to calculate reservoir compactions and subsidence

deformations _{are reviewed. The results from this study are compared} with those reported in the _{reservoir engineering} literature. The

chapter is concluded _{with a review of the reported cases of reservoir} subsidence. Chapter 7 is _{a brief} discussion _of the _{state of stress} which might exist in tectonically inactive _sedimentary basins.

The last _{section of this thesis (Chap. 8) presents the conclusions}

of the study, with emphasis _{on the nature of chalk compaction and on} the methodology of K0 testing _{at high pressures.}

Due to the dual _{application of soil mechanics and reservoir} compaction theories in this _study, the thesis is deliberately

separated into the two parts; the former is a discussion of relevant soil mechanics theory _{and analyses predominantly} used to interpret

the _{results of} the _{experimental programme, whilst the} latter

considers _{reservoir compaction} theories _{of sediment volume change as} well _as the _{geological applications of} the _{results of} the

experimental _work. The two sections _{are seperated} by the discussion

of the results (which _{are presented} individually in the App. 5). This was done because the two subject _{areas were} difficult to combine,

which in turn is due to the different _{approaches employed} in the analysis of deformational _{volume change.}

CHAPTER 2

ASPECTS OF COMPACTION

2.1) INTRODUCTION

. This chapter discusses and reviews those aspects of soil mechanics theory _{which are applicable} to the _{problems of compaction} in _oil

reservoirs, compaction during _sediment burial _and to the _work presented later in this thesis. The chapter is _sub-divided, treating

separately the various _{aspects of soil mechanics which are discussed.} These are:

a) the principle of effective _stress;

b) undrained pore pressure response to loading;

c) one-dimensional

consolidation;

d) representation of stress _states in sediments; e) mechanical behaviour _{of cemented sediments;}

f) strain rate effects; _and

g) the affect

of temperature

_{on consolidation.}

The first three _{subjects consider the effective stress acting on a} sedimentary material; the first _{section reviewing} the _{applicability}

of Terzaghi's effective _{stress equation} to a material with compressible _grains. The undrained _{pore pressure response} to, loading,

describes _{the build up of pore pressure during undrained loading of a} test _{specimen. Undrained loading occurred during initial stressing}

of the _sample in the first tests _performed in this _study (App. 1), and in the oedometer test. The one-dimensional consolidation equation

formulated _{by Terzaghi describes the pore pressure} (and _{hence the}

effective stress) distribution in a drained _{saturated material which} has been loaded. _{The pore pressure under this condition varies with} both time _{and position} in the _{sediment considered.} The Terzaghi

consolidation equation or equivalent equations have been used as a basis for the _{constant rate of strain consolidation analyses}

discussed in Chapter 3. This discussion _{on the consolidation equation} is designed to bring _{to the attention of the reader, assumptions}

implicite in the original formulation _{of Terzaghi} (1943), _{and, as a} result, in the constant _{rate of strain consolidation analyses.} Other consolidation equations _are discussed briefly for _comparative purposes.

The fourth _{section in this chapter, discusses the different}

representations of _{stress states -} in _sediments. The type _{of axes} commonly used to represent the state _{of stress in sediments and rocks} are compared graphically, to assist those _{readers unfamiliar with the} notation which is _{used to represent} the _{results of this study. The} second part of this _section then briefly discusses the Critical State model commonly _used in _{soil mechanics.} This thesis _{employs the} notation normally _{associated with} this _model. The model illustrates

how the void ratio _{or porosity is related to the stress system acting} on the sample.

The fifth _{section briefly describes the mechanical behaviour}

exhibited by cemented sedimentary _{materials, e. g. sensitive clays and} residual _{soils, which can be considered to have analogous,}

- but not identical _{behaviour, to weak rocks: like the chalks tested in this} study. The introduction _of the _mechanical behaviour _{of 'these} low pressure _analogs to-porous _{sedimentary rocks,} is necessary due to the

limited _{high pressure experimental}

work that has been published for weakly _cemented rocks. In this _section information from _{weak rocks}