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Terrestrial Heat Flow Studies in Eastern Africa

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Terrestrial Heat Flow Studies in Eastern Africa TERRESTRIAL HEAT FLOW STUDIES IN EASTERN AFRICA AND THE NORTH SEA A Thesis By Thomas Richard Evans Submitted for the Degree of Doctor of Philosophy to the University of London The Geology Department Imperial College London, U.K. November, 1975 - Terrestrial Heat Flow Studies in Eastern Africa and the North Sea Abstract A detailed feasibility study of the use of oil exploration borehole temperatures and cutting samples as primary data in the computation of heat flow forms the major part of this work. The temperature data consists entirely of bottom hole temperatures (BHTs) measured by commercial logging companies during breaks in drilling. Conductivity samples were largely drill cuttings. The thermal disturbance due to drilling and the consequent non- equilibrium state existing during temperature logging is discussed. Theoretical models and practical examples suggest that BHT derived geothermal gradients are, on average, unlikely to be more than 10-15 percent in error and thus are suitable for heat flow determinations. A rigorous study of the reliability of conductivity values obtained from measurements on drill cuttings is presented. An empirical relation between the thermal conductivity measured at laboratory temperatures to its in-situ temperature value was derived from a large number of experi- mental measurements in the range 10-90°C. Sixty-eight heat flow values of variable quality were computed from all available oil exploration wells in the coastal sedimentary basins of the Sudan, Somalia, Ethiopia, Kenya, and Tanzania. Eight new Red Sea results considerably extend the heat flow coverage from the zone of axial 2 spreading in this young proto-ocean. The results, averaging 113 m1Pm , are consistent with a lithospheric spreading model. Two previously unknown -2 thermal anomalies are reported; a low, mean 44 mW.m , iin the Eastern Ogaden 2 region of Ethiopia and Somalia and a high, mean 89 miPm , in the Garissa region of Kenya. A regional assessment of the heat flow was made by a trend surface analysis of the data and that of the surrounding seas. One dimensional modelling indicates that the lithosphere may be sufficiently thick beneath the Ogaden to impede plate motion; shallow partial melt zones are postulated under the Red Sea shelf and the Garissa region. Two dimensional modelling suggests that the Ogaden and Garissa anomalies could arise from heat pro- duction—conductivity contrast structures within the crust. Three heat flow values are presented for the North Sea; their pre- ferred mean is 63 mW•m-2. Extensive conductivity measurements were combined with detailed geothermal gradient and sedimentary structure maps to produce heat flow profiles. One dimensional modelling indicates an 80 kilometre thick litho- sphere beneath the North Sea. A two dimensional model of a salt dome emphasizes the importance of local structure on heat flow determinations made in oil exploration boreholes. The mechanisms of subsidence for both Eastern Africa and the North Sea are discussed and evaluated in the context of the tectonic setting and surface heat flow of these two regions. - iV - Table of Contents Page 1 Introduction 7 Chapter 1 Temperature Measurements 7 1.1 Introduction 8 1.2 The Drilling of an Oil Exploration Well; a Description of the Resulting Thermal Disturbance 12 1.3 Temperature Measurements Routinely Made in Oil Exploration Wells 19 1.4 Model One to Predict Temperature Variations Resulting from Drilling Disturbances — The Continuous Line Heat Source 23 1.5 Model Two to Predict Temperature Variations Due to Drilling Disturbances - The Region Bounded Internally by the Continuous Cylinder Heat Source 29 1.6 The Time Required for a Borehole to Return to Thermal Equilibrium - Practical Examples 42 1.7 Other Sources of Possible Error in The Temperature Measurements 47 1.8 The Error in the Determination of The Geothermal Gradient From Oil. Exploration Borehole BHTs page 54 1.9 Regional Geothermal Gradient Studies and Their Significance 55 1.10 Suggestions for Future Research 57 Chapter 2 Thermal Conductivity Measurements 57 2.1 Introduction 58 2.2 The Measurement of Thermal Conductivity 60 2.3 The Divided Bar 68 2.4 Calibration of the Divided Bar 72 2.5 The Preparation and Measurement of Discs 73 2.6 The Calculation of the Contact Resistance 77 2.7 The Measurement of Rock Chips - Theory 79 2.8 The Measurement of Rock Chips - Practice 83 2.9 The Calculation of Nonporous and Porous Conductivities with a Direct Comparison with Discs 89 2.10 Porosity Determinations From Commercial Well Logs - vi - Page 99 2.11 Comparison of Porosity Determinations From Various Logs 105 2.12 Measurement of Soluble Rock Chips 108 2.13 The Repeatibility of Disc and Chip Conductivity Measurements 111 2.14 Interlab Checks and Fluid Comparisons 115 2.15 Errors in the Determination of Thermal Conductivity - an Assessment 126 2.16 Predicting Thermal Conductivities From Other Known Rock Properties 129 2.17 Suggestions for Future Research 131 Chapter 3 The Calculation of and The Corrections Applied to the Heat Flow Values 131 3.1 Introduction 132 3.2 The Calculation of Heat Flow - Methods 135 3.3 The Topographic Correction 138 3.4 The Climatic Correction 147 3.5 The Uplift and Erosion or Downwarp and Sedimentation Correction 153 3.6 The Correction of Thermal Conductivity Data for In-Situ Pressure vii - Page 158 3.7 The Correction of Thermal Conductivity Data for In—Situ Temperature 175 3.8 Estimation of Parameters in the Calculation of Heat Flow 180 3.9 The Computation and Correction of Heat Flow Values — Computer Use, Data Presentation and Errors 185 3.10 Recommendations for Future Research 186 Chapter 4 Eastern Africa Heat Flow Results and Interpretation 186 4.1 Introduction 188 4.2 The Regional Geology of Eastern Africa (South of 15°N) 195 4.3 Regional Geophysical Studies of Eastern Africa (South of 15°N) 201 4.4 The Central and Southern Red Sea Regions 204 4.5 Plate Tectonics of Eastern Africa and the Surrounding Seas 208 4.6 Previous Heat Flow Studies in Eastern Africa and the Surrounding Seas 211 4.7 New Heat Flow Data from Eastern Africa 229 4.8 Heat Production Measurements Ea at 232 4.9 Coastal Red Sea Heat Flow 245 4.10 The Guban Region Heat Flow 252 4.11 The Darror and Nogal Valley Region Heat Flow 264 4.12 The Obbia Embayment Region Heat Flow 270 4.13 The Eastern Ogaden Region Heat Flow 283 4.14 The Benadir Coast Region Heat Flow 295 4.15 The Mandera-Lugh Basin Region Heat Flow 301 4.16 The South-West Somalia Basin Region Heat Flow 307 4.17 The Lamu Embayment Region Heat Flow 317 4.18 The Coastal Tanzania Region Heat Flow 324 4.19 Trend Surface Analysis of Heat Flow Data Between 10°S, 15°N, and 35°E, 70°E 338 4.20 Heat Flow and the Subsidence of the Eastern Africa Continental Margin 343 4.21 Crust and Upper Mantle Temperature Profiles page 352 4.22 Two Dimensional Crust and Upper Mantle Temperature Models 360 Chapter 5 Preliminary Heat Flow Studies in The North Sea 360 5.1 Introduction 360 5.2 The Geology of the North Sea Basin • 366 5.3 Geophysical Studies of the North Sea 368 5.4 North-West European Heat Flow 378 5.5 Crust and Upper Mantle Thermal Profiles 386 5.6 Heat Flow and the Subsidence of the North Sea Intracratonic Basin 388 5.7 The Effect of Local Structure on Heat Flow Determination 391 Chapter 6 Conclusions 391 6.1 Objectives 392 6.2 Significant Results 394 6.3 Suggestions for Future Research 396 List of References - x - Page 432 Omissions from Reference List 433 Appendix 1 A Discussion of the Paper by E.C. Bullard (1947) entitled 'The Time Necessary For A Borehole To Attain Temperature Equilibrium' 436 Appendix 2 Equations and Tables for the Unit Functions T(td), Q(td) and q(td) 439 Appendix 3 Derivation of the Nonporous Rock Conductivity From the Maxwell Spheres Relation 442 Appendix 4 Solution of the Subsidiary Heat Equation for the Semi-Infinite Region Moving With a Velocity, u. 446 Appendix 5 Tabulation of Eastern Africa Tempera- ture and Conductivity Data 487 Appendix 6 Tabulation of North Sea Temperature and Conductivity Data Inside Back Cover Pocket 'North Sea Geothermal Gradients', a Paper by T.R. Evans and N.C. Coleman (1974) Inside Back Cover Pocket 'Heat Flow and Heat Production in North-East Africa', a Paper by T.R. Evans and H.Y. Tammemagi (1974) - xi - List of Figures Page Number Title 4 0.1 Sedimentary Basins and Shelves of The World 10 1.1(a) Schematic of Circulating Fluid in Oil Exploration Well 10 1.1(b) Drill Pipe Temperatures During Circulation 11 1.1(c) Circulating Temperatures 11 1.1(d) Temperature versus Time (During and Post Circulation) 13 1.2 Flowline Temperatures (An Example) 15 1.3 Examples of Continuous Temperature Logs 16 1.4 Typical Log Heading 18 1.5 Comparison of BHT and Flowline Temperatures 28 1.6(a) Graphical Representation of Equation 1.21 28 1.6(b) Graphical Representation of Equation 1.22 28 1.6(c) Contour Integral Path for Equation 1.31 Pa a Number Title 33 1.7(a) Cylinder Model Dimensionless Tempera- ture Disturbance versus the ratio of Shut In to Total Time 34 1.7(b) Line Source and Cylinder Models - Comparison of Dimensionless Temperature Disturbance 36 1.8(a) Examples of the Return to Thermal Equilibrium in Oil Exploration Wells 37 1.8(b) Examples of the Return to Thermal Equilibrium in Oil Exploration Wells 39 1.9 Dimensionless Temperature Disturbance versus Dimensionless Time 43 1.10(a) Critical Gradients for Onset of Convection in a Borehole 43 1.10(b) Example of Well Disturbed by Water Flow 45 1.10(c) Example of Temperatures Disturbed by Gas Flow 45 1.10(d) Example of Temperature
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