Formulas and Calculations for Drilling Operations, Second Edition

<p>Preface xiii</p>
<p>1 Standard Formulas and Calculations 1</p>
<p>1.01 Abrasion Index 1</p>
<p>1.02 Acid Number 3</p>
<p>1.03 Acidity and Alkalinity 3</p>
<p>1.04 Annular Velocity 4</p>
<p>1.05 Antoine Equation 5</p>
<p>1.06 API Gravity – Kilograms per Liter/Pounds per Gallon 5</p>
<p>1.07 Barrel – Conversion to other Units. 15</p>
<p>1.08 Bernoulli s Principle 15</p>
<p>1.09 Brine 16</p>
<p>1.10 Bubble Point and Bubble Point Pressure 16</p>
<p>1.11 Buoyancy, Buoyed Weight, and Buoyancy Factor 18</p>
<p>1.12 Capacity 19</p>
<p>1.12.1 Hole (Pipe, Tubing) Capacity (in barrels per one linear foot, bbl/ft) 20</p>
<p>1.12.2 Annular Capacity 20</p>
<p>1.12.3 Annular Volume</p>
<p>1.13 Capillary Number 21</p>
<p>1.14 Capillary Pressure 21</p>
<p>1.15 Cementation Value 22</p>
<p>1.16 Composite Materials 23</p>
<p>1.17 Compressibility 23</p>
<p>1.18 Darcy s Law 25</p>
<p>1.19 Dew Point Temperature and Pressure 26</p>
<p>1.20 Displacement 27</p>
<p>1.21 Effective Weight 28</p>
<p>1.22 Flow Through Permeable Media 29</p>
<p>1.22.1 Productivity Index 29</p>
<p>1.22.2 Steady–State Flow 29</p>
<p>1.22.3 Linear Flow 39</p>
<p>1.22.4 Spherical Flow 39</p>
<p>1.23 Flow Through Porous Media 39</p>
<p>1.24 Flow Velocity 40</p>
<p>1.25 Fluid Saturation 41</p>
<p>1.26 Formation Volume Factor – Gas 41</p>
<p>1.27 Formation Volume Factor – Oil 42</p>
<p>1.28 Friction 42</p>
<p>1.28.1 Coefficient of Friction 42</p>
<p>1.28.2 Types of Friction 43</p>
<p>1.28.3 Friction and Rotational Speed 43</p>
<p>1.29 Gas Deviation Factor 43</p>
<p>1.30 Gas Solubility 44</p>
<p>1.31 Gas–Oil Ratio 44</p>
<p>1.32 Geothermal Gradient 45</p>
<p>1.33 Hole Capacity 45</p>
<p>1.34 Horsepower 50</p>
<p>1.35 Hydrostatic Pressure 51</p>
<p>1.36 Isothermal Compressibility of Oil 51</p>
<p>1.37 Marx–Langenheim Model 52</p>
<p>1.38 Material Balance 53</p>
<p>1.39 Modulus of Elasticity 55</p>
<p>1.40 Oil and Gas Originally in Place 55</p>
<p>1.41 Oil Recovery Factor 56</p>
<p>1.42 Permeability 57</p>
<p>1.43 Poisson s Ratio 57</p>
<p>1.44 Porosity 59</p>
<p>1.45 Pressure Differentials 61</p>
<p>1.46 Productivity Index 62</p>
<p>1.47 PVT Properties 62</p>
<p>1.47.1 Specific Gravity and Molecular Weight 62</p>
<p>1.47.2 Isothermal Compressibility 62</p>
<p>1.47.3 Undersaturated Oil Formation Volume Factor 63</p>
<p>1.47.4 Oil Density 63</p>
<p>1.47.5 Dead Oil Viscosity 63</p>
<p>1.47.6 Undersaturated Oil Viscosity 63</p>
<p>1.47.7 Gas/Oil Interfacial Tension 63</p>
<p>1.47.8 Water/Oil Interfacial Tension 63</p>
<p>1.48 Reserves Estimation 65</p>
<p>1.49 Reservoir Pressure 65</p>
<p>1.50 Resource Estimation 67</p>
<p>1.51 Reynold s Number 67</p>
<p>1.52 Saturated Steam 67</p>
<p>1.53 Standard Oilfield Measurements 68</p>
<p>1.54 Twist 69</p>
<p>1.55 Ultimate Tensile Strength 70</p>
<p>1.56 Volume Flow Rate 70</p>
<p>1.57 Volumetric Factors 71</p>
<p>1.58 Yield Point 72</p>
<p>2 RIG Equipment 73</p>
<p>2.01 API Casing Grades 73</p>
<p>2.02 Block Efficiency Factor 74</p>
<p>2.03 Blocks and Drilling Line 74</p>
<p>2.04 Crown Block Capacity 75</p>
<p>2.05 Derrick Load 76</p>
<p>2.06 Energy Transfer 77</p>
<p>2.07 Engine Efficiency 78</p>
<p>2.08 Line Pull Efficiency Factor 79</p>
<p>2.09 Mud Pump 79</p>
<p>2.09.1 Volume of Fluid Displaced 80</p>
<p>2.09.2 Volumetric Efficiency 80</p>
<p>2.09.3 Pump Factor 81</p>
<p>2.10 Offshore Vessels 81</p>
<p>2.10.1 Terminology 82</p>
<p>2.10.2 Environmental Forces 83</p>
<p>2.10.3 Riser Angle 83</p>
<p>2.11 Rotary Power 85</p>
<p>2.12 Ton–Miles Calculations 85</p>
<p>2.12.1 Round–Trip Ton Miles Calculations 86</p>
<p>2.12.2 Drilling Ton–Miles Calculations 86</p>
<p>2.12.3 Coring Ton–Miles Calculations 86</p>
<p>2.12.4 Casing Ton–Miles Calculations 86</p>
<p>3 Well Path Design 89</p>
<p>3.01 Average Curvature–Average Dogleg Severity 89</p>
<p>3.02 Bending Angle 89</p>
<p>3.03 Borehole Curvature 90</p>
<p>3.03.1 General Formula 90</p>
<p>3.03.2 Borehole Radius of Curvature 90</p>
<p>3.04 Borehole Torsion 91</p>
<p>3.04.1 General Method 91</p>
<p>3.04.2 Cylindrical Helical Method 91</p>
<p>3.05 Horizontal Displacement 92</p>
<p>3.06 Magnetic Reference and Interference 93</p>
<p>3.07 Tool Face Angle 94</p>
<p>3.08 Tool Face Angle Change 96</p>
<p>3.09 Tortuosity 97</p>
<p>3.09.1 Absolute and Relative Tortuosity 97</p>
<p>3.09.2 Sine Wave Method 98</p>
<p>3.09.3 Helical Method 99</p>
<p>3.09.4 Random Inclination Azimuth Method 99</p>
<p>3.09.5 Random Inclination Dependent Azimuth Method 100</p>
<p>3.10 Types of Wellpath Designs 100</p>
<p>3.11 Vertical and Horizontal Curvatures 100</p>
<p>3.12 Wellbore Trajectory Uncertainty 101</p>
<p>3.13 Wellpath Length Calculations 103</p>
<p>4 Fluids 105</p>
<p>4.01 Acidity–Alkalinity 105</p>
<p>4.02 Base Fluid Water–Oil Ratios 106</p>
<p>4.03 Common Weighting Materials 107</p>
<p>4.04 Diluting Mud 108</p>
<p>4.05 Drilling Fluid Composition 109</p>
<p>4.06 Equivalent Mud Weight 110</p>
<p>4.07 Fluid Loss 110</p>
<p>4.08 Marsh Funnel 112</p>
<p>4.09 Mud Rheology 112</p>
<p>4.10 Mud Weighting 114</p>
<p>4.11 Plastic Viscosity, Yield Point, and Zero–Sec Gel 116</p>
<p>4.11.1 Bingham, Plastic Model 116</p>
<p>4.11.2 Shear Stress and Shear Rate 117</p>
<p>4.11.3 Power Law 117</p>
<p>4.12 Reynolds Number and Critical Velocity 118</p>
<p>4.13 Slip Velocity 118</p>
<p>5 Hydraulics 121</p>
<p>5.01 Basic Calculations 121</p>
<p>5.01.1 Critical Velocity 121</p>
<p>5.01.2 Pump Calculations 121</p>
<p>5.02 Bingham Plastic Model 122</p>
<p>5.03 Bit Hydraulics 124</p>
<p>5.03.1 Common Calculations 124</p>
<p>5.03.2 Optimization Calculations 125</p>
<p>5.03.2.1 Limitation 1 Available Pump Horsepower 126</p>
<p>5.03.2.2 Limitation 2 Surface Operating Pressure 126</p>
<p>5.04 Critical Transport Fluid Velocity 127</p>
<p>5.05 Equivalent Circulating Density 127</p>
<p>5.06 Equivalent Mud Weight 127</p>
<p>5.07 Gel Breaking Pressure 128</p>
<p>5.08 Hole Cleaning Cuttings Transport 128</p>
<p>6 Tubular Mechanics 131</p>
<p>6.01 API Casing and Liners Weight, Dimensions, Capacity, and Displacement 131</p>
<p>6.02 API Drill Pipe Capacity and Displacement 134</p>
<p>6.03 Bending Stress Ratio 135</p>
<p>6.04 Buckling Force 135</p>
<p>6.05 Drag Force 136</p>
<p>6.06 Drill Collar Length 137</p>
<p>6.07 Fatigue Ratio 138</p>
<p>6.08 Length Change Calculations 138</p>
<p>6.09 Maximum Permissible Dogleg 139</p>
<p>6.10 Pipe Wall Thickness and other Dimensions 140</p>
<p>6.11 Slip Crushing 140</p>
<p>6.12 Stress 145</p>
<p>6.12.1 Radial Stress 145</p>
<p>6.12.2 Tangential Stress 145</p>
<p>6.12.3 Longitudinal Stress 145</p>
<p>6.12.4 Stress Ratio 146</p>
<p>6.13 Tension 146</p>
<p>6.14 Torque 146</p>
<p>7 Drilling Tools 149</p>
<p>7.01 Backoff Calculations 149</p>
<p>7.02 Downhole Turbine 152</p>
<p>7.03 Jar Calculations 153</p>
<p>7.03.1 Force Calculations for Up Jars 153</p>
<p>7.03.2 Force Calculations for Down Jars 153</p>
<p>7.04 Overpull/Slack–off Calculations 155</p>
<p>7.05 Percussion Hammer 157</p>
<p>7.06 Positive Displacement Motor (PDM) 157</p>
<p>7.07 Rotor Nozzle Sizing 157</p>
<p>7.08 Stretch Calculations 159</p>
<p>8 Pore Pressure and Fracture Gradient 161</p>
<p>8.01 Formation Pressure 161</p>
<p>8.01.1 Hubert and Willis Correlation 161</p>
<p>8.01.2 Matthews and Kelly Correlation 162</p>
<p>8.01.3 Eaton s Correlation 163</p>
<p>8.01.4 Christman s Correlation 163</p>
<p>8.02 Leak–off Pressure 163</p>
<p>9 Well Control 165</p>
<p>9.01 Accumulators 165</p>
<p>9.02 Driller s Method 166</p>
<p>9.03 Formulas Used in Kick and Kill Procedures 167</p>
<p>9.04 Hydrostatic Pressure Due to the Gas Column 168</p>
<p>9.05 Kill Methods 168</p>
<p>9.06 Kill Mud Weight 169</p>
<p>9.07 Leak–off Pressure 170</p>
<p>9.08 Length and Density of the Kick 171</p>
<p>9.08.1 Length of the Kick 171</p>
<p>9.08.2 Density of the Kick 171</p>
<p>9.08.3 Type of Kick 172</p>
<p>9.08.4 Kick Classification 172</p>
<p>9.08.5 Kick Tolerance 173</p>
<p>9.09 Maximum Allowable Annular Surface Pressure 174</p>
<p>9.10 Riser Margin 175</p>
<p>10 Drilling Problems 177</p>
<p>10.01 Differential Sticking Force 177</p>
<p>10.01.1 Method 1 178</p>
<p>10.01.2 Method 2 178</p>
<p>10.01.3 Method 3 179</p>
<p>10.02 Hole Cleaning Slip Velocity Calculations 179</p>
<p>10.02.1 Chien Correlation 179</p>
<p>10.02.2 Moore Correlation 180</p>
<p>10.02.3 Walker–Mays Correlation 180</p>
<p>10.03 Increased Equivalent Circulating Density (ECD) Due to Cuttings 181</p>
<p>10.04 Keyseating 182</p>
<p>10.05 Lost Circulation 183</p>
<p>10.06 Common Minerals and Metals Encountered During Drilling Operations 185</p>
<p>10.07 Mud Weight Increase Due to Cuttings 185</p>
<p>10.08 Pressure Loss in the Drill String 186</p>
<p>10.09 Spotting Fluid Requirements 187</p>
<p>11 Cementing 189</p>
<p>11.01 API Classification of Cement 189</p>
<p>11.02 Cement: Physical Properties of Additives 191</p>
<p>11.03 Cement Plug 192</p>
<p>11.04 Cement Slurry Requirements 194</p>
<p>11.05 Contact Time 195</p>
<p>11.06 Gas Migration Potential 195</p>
<p>11.07 Hydrostatic Pressure Reduction 196</p>
<p>11.08 Portland Cement Typical Components 197</p>
<p>11.09 Slurry Density 198</p>
<p>11.10 Yield of Cement 198</p>
<p>12 Well Cost 199</p>
<p>12.01 Drilling Cost 199</p>
<p>12.02 Expected Value 200</p>
<p>12.03 Future Value 200</p>
<p>12.04 Price Elasticity 201</p>
<p>13 Appendices 203</p>
<p>Glossary 243</p>
<p>Bibliography and Information Sources 273</p>
<p>About the Author 277</p>
<p>Index 279</p>