Formulas and Calculations for Petroleum Engineering

1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Biographies of authors - p. xxv 6. Foreword - p. xxvii 7. Acknowledgement - p. xxix 8. Chapter 1: Reservoir engineering formulas and calculations - p. xxix 9. Abstract - p. 1 10. 1.1 API gravity - p. 3 11. 1.2 Average permeability for linear flow—Layered beds - p. 3 12. 1.3 Average permeability for linear flow—Series beds - p. 4 13. 1.4 Average permeability for parallel-layered systems - p. 4 14. 1.5 Average permeability in radial systems - p. 4 15. 1.6 Average temperature of a gas column - p. 5 16. 1.7 Calculation of fractional flow curve - p. 5 17. 1.8 Capillary number - p. 6 18. 1.9 Capillary pressure - p. 6 19. 1.10 Characteristic time for linear diffusion in reservoirs - p. 6 20. 1.11 Cole plot - p. 7 21. 1.12 Communication between compartments in tight gas reservoirs - p. 7 22. 1.13 Communication factor in a compartment in tight gas reservoirs - p. 7 23. 1.14 Compressibility drive in gas reservoirs - p. 8 24. 1.15 Correction factor—Hammerlindl - p. 8 25. 1.16 Critical rate for horizontal Wells in edge-water drive reservoirs - p. 8 26. 1.17 Crossflow index - p. 9 27. 1.18 Cumulative effective compressibility—Fetkovich - p. 10 28. 1.19 Cumulative gas production—Tarner's method - p. 10 29. 1.20 Cumulative oil production—Undersaturated oil reservoirs - p. 11 30. 1.21 Deliverability equation for shallow gas reservoirs - p. 11 31. 1.22 Dimensionless pressure—Kamal and Brigham - p. 11 32. 1.23 Dimensionless radius of radial flow—Constant-rate production - p. 12 33. 1.24 Dimensionless time—Myhill and Stegemeier's method - p. 12 34. 1.25 Dimensionless time for interference testing in homogeneous reservoirs—Earlougher - p. 13 35. 1.26 Dimensionless vertical well critical rate correlations—Hoyland, Papatzacos, and Skjaeveland - p. 13 36. 1.27 Dimensionless wellbore storage coefficient of radial flow—Constant-rate production - p. 13 37. 1.28 Effective compressibility in undersaturated oil reservoirs—Hawkins - p. 14 38. 1.29 Effective wellbore radius of a horizontal well—Method 1—Anisotropic reservoirs - p. 14 39. 1.30 Effective wellbore radius of a horizontal well—Method 1—Isotropic reservoirs - p. 15 40. 1.31 Effective wellbore radius of a horizontal well—van der Vlis et al. method - p. 16 41. 1.32 Effective wellbore radius of a well in presence of uniform-flux fractures - p. 16 42. 1.33 Effective wellbore radius to calculate slant well productivity—van der Vlis et al. - p. 16 43. 1.34 Estimation of average reservoir pressure—MDH method - p. 17 44. 1.35 Formation temperature for a given gradient - p. 17 45. 1.36 Fraction of the total solution gas retained in the reservoir as free gas - p. 17 46. 1.37 Fractional gas recovery below the critical desorption pressure in coal bed methane reservoirs - p. 18 47. 1.38 Free gas in place - p. 18 48. 1.39 Gas adsorbed in coal bed methane reservoirs - p. 19 49. 1.40 Gas bubble radius - p. 19 50. 1.41 Gas cap ratio - p. 19 51. 1.42 Gas cap shrinkage - p. 20 52. 1.43 Gas drive index in gas reservoirs - p. 20 53. 1.44 Gas expansion factor - p. 20 54. 1.45 Gas expansion term in gas reservoirs - p. 21 55. 1.46 Gas flow rate into the wellbore - p. 21 56. 1.47 Gas flow under laminar viscous conditions - p. 22 57. 1.48 Gas formation volume factor - p. 22 58. 1.49 Gas hydrate dissociation pressure - p. 22 59. 1.50 Gas material balance equation - p. 23 60. 1.51 Gas produced by gas expansion - p. 23 61. 1.52 Gas saturation—Water-drive gas reservoirs - p. 24 62. 1.53 Gas solubility in coalbed methane reservoirs - p. 24 63. 1.54 Geertsma's model for porosity/transit-time relationship - p. 25 64. 1.55 Geothermal gradient - p. 25 65. 1.56 Hagen Poiseuille equation - p. 26 66. 1.57 Hagoort and Hoogstra gas flow in tight reservoirs - p. 26 67. 1.58 Hammerlindl method for gas in place - p. 26 68. 1.59 High-pressure region gas flow rate - p. 27 69. 1.60 Horizontal well breakthrough time—With gas cap or bottom water - p. 27 70. 1.61 Horizontal well critical rate correlation—Chaperon - p. 28 71. 1.62 Horizontal well critical rate correlations—Efros - p. 28 72. 1.63 Horizontal well critical rate correlations—Giger and Karcher - p. 29 73. 1.64 Horizontal well critical rate correlations—Joshi method for gas coning - p. 29 74. 1.65 Hydrocarbon pore volume occupied by evolved solution gas - p. 30 75. 1.66 Hydrocarbon pore volume occupied by gas cap - p. 30 76. 1.67 Hydrocarbon pore volume occupied by remaining oil - p. 31 77. 1.68 Hydrostatic pressure - p. 31 78. 1.69 Incremental cumulative oil production in undersaturated reservoirs - p. 31 79. 1.70 Ineffective porosity - p. 32 80. 1.71 Initial gas cap - p. 32 81. 1.72 Initial gas in place for water-drive gas reservoirs - p. 32 82. 1.73 Injectivity index - p. 33 83. 1.74 Instantaneous gas-oil ratio - p. 33 84. 1.75 Interporosity flow coefficient - p. 34 85. 1.76 Interstitial velocity - p. 34 86. 1.77 Isothermal compressibility of oil—Vasquez-Beggs correlation—P > Pb - p. 34 87. 1.78 Isothermal compressibility of oil—Villena-Lanzi correlation—P < Pb - p. 35 88. 1.79 Isothermal compressibility of water—Osif correlation - p. 35 89. 1.80 Kerns method for gas flow in a fracture - p. 35 90. 1.81 Klinkenberg gas effect - p. 36 91. 1.82 Kozeny equation - p. 36 92. 1.83 Kozeny-Carman relationship - p. 36 93. 1.84 Leverett J-function - p. 37 94. 1.85 Line-source solution for damaged or stimulated wells - p. 37 95. 1.86 Low-pressure region gas flow rate for non-circular drainage area - p. 38 96. 1.87 Material balance for cumulative water influx—Havlena and Odeh - p. 38 97. 1.88 Maximum height of oil column in cap rock - p. 39 98. 1.89 Modified Cole plot - p. 39 99. 1.90 Modified Kozeny-Carman relationship - p. 39 100. 1.91 Normalized saturation - p. 40 101. 1.92 Oil bubble radius of the drainage area of each well represented by a circle - p. 40 102. 1.93 Oil density—Standing's correlation - p. 41 103. 1.94 Oil formation volume factor—Standing's correlation - p. 41 104. 1.95 Oil formation volume factor—Beggs-standing correlation—P < Pb - p. 41 105. 1.96 Oil formation volume factor—Beggs-standing correlation—P > Pb - p. 42 106. 1.97 Oil in place for undersaturated oil reservoirs without fluid injection - p. 42 107. 1.98 Oil in place in saturated oil reservoirs - p. 43 108. 1.99 Oil lost in migration - p. 43 109. 1.100 Oil saturation at any depletion state below the bubble point pressure - p. 44 110. 1.101 Original gas in place - p. 44 111. 1.102 Payne method for intercompartmental flow in tight gas reservoirs - p. 44 112. 1.103 Performance coefficient for shallow gas reservoirs - p. 45 113. 1.104 Poisson's ratio - p. 45 114. 1.105 Pore throat sorting - p. 46 115. 1.106 Pore volume occupied by injection of gas and water - p. 46 116. 1.107 Pore volume through squared method in tight gas reservoirs - p. 46 117. 1.108 Porosity determination—IES and FDC logs - p. 47 118. 1.109 Produced gas-oil ratio - p. 47 119. 1.110 Productivity index for a gas well - p. 48 120. 1.111 Pseudo-steady state productivity of horizontal Wells—Method 1 - p. 48 121. 1.112 Pseudo-steady state productivity of horizontal Wells—Method 2 - p. 49 122. 1.113 Pseudo-steady state productivity of horizontal wells—Method 3 - p. 50 123. 1.114 Pseudo-steady state radial flow equation - p. 50 124. 1.115 Relative permeability—Corey exponents - p. 51 125. 1.116 Remaining gas in place in coalbed methane reservoirs - p. 51 126. 1.117 Roach plot for abnormally pressured gas reservoirs - p. 52 127. 1.118 Rock expansion term in abnormally pressured gas reservoirs - p. 52 128. 1.119 Shape factor—Earlougher - p. 52 129. 1.120 Solution gas oil ratio—Beggs-standing correlation—P < Pb - p. 53 130. 1.121 Solution gas oil ratio—Standing's correlation - p. 53 131. 1.122 Solution gas water ratio - p. 54 132. 1.123 Somerton method for formation permeability in coalbed methane reservoirs - p. 54 133. 1.124 Specific gravity of gas hydrate forming components - p. 54 134. 1.125 Time to reach the semi-steady state for a gas well in a circular or square drainage area - p. 55 135. 1.126 Time to the end of infinite-acting period for a well in a circular reservoir - p. 55 136. 1.127 Torcaso and Wyllie's correlation for relative permeability ratio prediction - p. 55 137. 1.128 Total compressibility - p. 56 138. 1.129 Total pore volume compressibility - p. 56 139. 1.130 Transmissibility between compartments - p. 57 140. 1.131 Transmissibility of a compartment - p. 57 141. 1.132 Transmissivity - p. 57 142. 1.133 Trapped gas volume in water-invaded zones - p. 58 143. 1.134 Two-phase formation volume factor - p. 58 144. 1.135 Underground fluid withdrawal—Havlena and Odeh - p. 59 145. 1.136 Vertical well critical rate correlations—Craft and Hawkins method - p. 59 146. 1.137 Vertical well critical rate correlations—Hoyland, Papatzacos, and Skjaeveland—Isotropic reservoirs - p. 60 147. 1.138 Vertical well critical rate correlations—Meyer, Gardner, and Pirson—Simultaneous gas and water coning - p. 60 148. 1.139 Vertical well critical rate correlations—Meyer, Gardner, and Pirson—Water coning - p. 61 149. 1.140 Vertical well critical rate correlations—Meyer, Gardner, and Pirson—Gas coning - p. 61 150. 1.141 Viscosibility - p. 62 151. 1.142 Viscosity of crude oil through API - p. 62 152. 1.143 Viscosity of dead oil—Standing's correlation - p. 62 153. 1.144 Viscosity of dead-oil—Egbogah correlation—P < Pb - p. 63 154. 1.145 Viscosity of live oil—Beggs/Robinson correlation - p. 63 155. 1.146 Viscosity of oil—Vasquez/Beggs correlation—P > Pb - p. 63 156. 1.147 Viscosity of water at atmospheric pressure—McCain correlation - p. 64 157. 1.148 Viscosity of water at reservoir pressure—McCain correlation - p. 64 158. 1.149 Volume of gas adsorbed in coalbed methane reservoirs - p. 64 159. 1.150 Volumetric heat capacity of a reservoir - p. 65 160. 1.151 Water breakthrough correlation in vertical wells—Bournazel and Jeanson - p. 65 161. 1.152 Water breakthrough correlations in vertical wells—Sobocinski and Cornelius - p. 66 162. 1.153 Water content of sour gas - p. 66 163. 1.154 Water cut—Stiles - p. 67 164. 1.155 Water-drive index for gas reservoirs - p. 67 165. 1.156 Water-drive recovery - p. 68 166. 1.157 Water expansion term in gas reservoirs - p. 68 167. 1.158 Water formation volume factor—McCain correlation - p. 68 168. 1.159 Water influx—Pot aquifer model - p. 69 169. 1.160 Water influx constant for the van Everdingen and Hurst unsteady-state model - p. 69 170. 1.161 Water two-phase formation volume factor - p. 70 171. 1.162 Waxman and Smits model—Clean sands - p. 70 172. 1.163 Welge extension—Fractional flow - p. 70 173. Chapter 2: Drilling engineering formulas and calculations - p. 70 174. Abstract - p. 71 175. 2.1 Accumulator capacity - p. 73 176. 2.2 Accumulator precharge pressure - p. 74 177. 2.3 Amount of additive required to achieve a required cement slurry density - p. 74 178. 2.4 Amount of cement to be left in casing - p. 75 179. 2.5 Amount of mud required to displace cement in drillpipe - p. 75 180. 2.6 Angle of twist—Rod subjected to torque - p. 75 181. 2.7 Annular capacity between casing and multiple strings of tubing - p. 76 182. 2.8 Annular capacity between casing and multiple tubing strings - p. 76 183. 2.9 Annular velocity—Using circulation rate in Gpm - p. 77 184. 2.10 Annular velocity—Using pump output in bbl/min - p. 77 185. 2.11 Annular velocity for a given circulation rate - p. 78 186. 2.12 Annular velocity for a given pump output - p. 78 187. 2.13 Annular volume capacity of pipe - p. 78 188. 2.14 API water loss calculations - p. 79 189. 2.15 Area below the casing shoe - p. 79 190. 2.16 Axial loads in slips - p. 79 191. 2.17 Beam force - p. 80 192. 2.18 Bit nozzle pressure loss - p. 80 193. 2.19 Bit nozzle selection—Optimized hydraulics for two and three jets - p. 81 194. 2.20 Borehole torsion—Cylindrical helical method - p. 82 195. 2.21 Bottomhole annulus pressure - p. 83 196. 2.22 Bottomhole assembly length required for a desired weight on bit - p. 83 197. 2.23 Bulk density of cuttings—Using the mud balance - p. 83 198. 2.24 Bulk modulus using Poisson's ratio and Young's modulus - p. 84 199. 2.25 Buoyancy weight - p. 84 200. 2.26 Buoyancy factor - p. 85 201. 2.27 Buoyancy factor using mud weight - p. 85 202. 2.28 Calculations for the number of feet to be cemented - p. 85 203. 2.29 Calculations required for spotting pills - p. 86 204. 2.30 Capacity formulas—bbl/ft - p. 87 205. 2.31 Capacity formulas—gal/ft - p. 88 206. 2.32 Capacity of tubulars and open-hole - p. 88 207. 2.33 CO2 solubility in oil and oil-mud emulsifiers - p. 88 208. 2.34 Combined solubility—Hydrocarbon gas, CO2, and H2S—in each of the mud components - p. 89 209. 2.35 Control drilling—Maximum drilling rate - p. 89 210. 2.36 Conversion of pressure into the mud weight - p. 90 211. 2.37 Cost per foot during drilling - p. 90 212. 2.38 Cost per foot of coring - p. 91 213. 2.39 Critical annular velocity and critical flow rate - p. 91 214. 2.40 Critical flow rate for flow regime change - p. 92 215. 2.41 Critical velocity for change in flow regime - p. 92 216. 2.42 Crown block capacity - p. 93 217. 2.43 Current drag force—Offshore - p. 93 218. 2.44 Curvature radius for a borehole - p. 94 219. 2.45 Cutting slip velocity - p. 94 220. 2.46 Cuttings produced per foot of hole drilled—bbls - p. 94 221. 2.47 Cuttings produced per foot of hole drilled—lbs - p. 95 222. 2.48 D—Exponent - p. 95 223. 2.49 Depth of a washout—Method 1 - p. 96 224. 2.50 Depth of a washout—Method 2 - p. 96 225. 2.51 Derrick efficiency factor - p. 96 226. 2.52 Difference in pressure gradient between the cement and mud - p. 96 227. 2.53 Differential hydrostatic pressure between cement in the annulus and mud inside the casing - p. 96 228. 2.54 Dilution of a mud system - p. 96 229. 2.55 Direction of dip - p. 96 230. 2.56 Directional curvature for a deviated well - p. 99 231. 2.57 Downward force or weight of casing - p. 99 232. 2.58 Drill pipe or drill collar capacity - p. 99 233. 2.59 Drill pipe or drill collar displacement and weight - p. 100 234. 2.60 Drill string design—Drill pipe length for bottomhole assembly - p. 100 235. 2.61 Drilled gas entry rate - p. 101 236. 2.62 Drilling cost per foot - p. 101 237. 2.63 Drilling ton miles—Coring operation ton miles - p. 102 238. 2.64 Drilling ton miles—Drilling/connection ton miles - p. 102 239. 2.65 Drilling ton miles—Round trip ton miles - p. 102 240. 2.66 Drilling ton miles—While making short trip ton miles - p. 103 241. 2.67 Drilling ton miles—Setting casing ton miles - p. 103 242. 2.68 Duplex pump factor - p. 104 243. 2.69 Duplex pump output—Using liner diameter - p. 104 244. 2.70 Duplex pump output—Using rod diameter - p. 104 245. 2.71 Duplex pump output by using liner and rod diameters - p. 105 246. 2.72 Dynamically coupled linear flow—Formation invasion - p. 105 247. 2.73 Effective weight during drilling - p. 106 248. 2.74 Effective wellbore radius for finite-conductivity fractures - p. 106 249. 2.75 Effective wellbore radius in infinite-conductivity fractures - p. 107 250. 2.76 Efficiency of block and tackle system - p. 107 251. 2.77 Equivalent area of pipe subject to uniform axial force - p. 108 252. 2.78 Equivalent circulating density - p. 108 253. 2.79 Equivalent density of a wellbore fluid - p. 109 254. 2.80 Equivalent formation water resistivity from SP log - p. 109 255. 2.81 Equivalent mud weight—Deviated well - p. 109 256. 2.82 Equivalent mud weight—Vertical well - p. 110 257. 2.83 Evaluation of centrifuge - p. 110 258. 2.84 Evaluation of hydrocyclone - p. 111 259. 2.85 Fluid volume required to spot a plug - p. 111 260. 2.86 Force applied to stretch material - p. 112 261. 2.87 Force exerted by the fluid on the solid surface of flow through an annulus - p. 112 262. 2.88 Friction factor in drill pipe - p. 113 263. 2.89 Front displacement of a particle in the reservoir—Formation invasion - p. 113 264. 2.90 Gas migration velocity - p. 114 265. 2.91 Gas solubility in a mud system - p. 114 266. 2.92 Gas/mud ratio - p. 114 267. 2.93 Gel strength—Optimal solid removal efficiency - p. 115 268. 2.94 Gel strength—Solid control efficiency - p. 115 269. 2.95 Gel strength—Solids build-up in system - p. 116 270. 2.96 Height of cement in the annulus - p. 116 271. 2.97 Hydraulic horsepower - p. 116 272. 2.98 Hydraulics analysis - p. 117 273. 2.99 Hydromechanical specific energy - p. 118 274. 2.100 Hydrostatic pulling - p. 118 275. 2.101 Hydrostatic pulling wet pipe out of the hole - p. 119 276. 2.102 Hydrostatic pressure in annulus due to slug - p. 119 277. 2.103 Hydrostatic pressure decrease at total depth caused by gas-cut mud - p. 119 278. 2.104 Impact force—Nozzle hydraulic analysis - p. 120 279. 2.105 Impringing jet - p. 120 280. 2.106 Increase mud density by barite - p. 121 281. 2.107 Increase mud density by calcium carbonate - p. 121 282. 2.108 Increase mud density by hematite - p. 121 283. 2.109 Increase volume by barite - p. 122 284. 2.110 Increase volume by calcium carbonate - p. 122 285. 2.111 Increase volume by hematite - p. 122 286. 2.112 Initial volume required to achieve a volume with barite - p. 123 287. 2.113 Initial volume required to achieve a volume with calcium carbonate - p. 123 288. 2.114 Initial volume required to achieve a volume with hematite - p. 124 289. 2.115 Injection/casing pressure required to open valve - p. 124 290. 2.116 Input power of a pump—Using fuel consumption rate - p. 124 291. 2.117 Jet velocity—Nozzle hydraulic analysis - p. 125 292. 2.118 Kick analysis—Influx - p. 125 293. 2.119 Kick analysis—Formation pressure with well shut-in on a kick - p. 126 294. 2.120 Kick analysis—Maximum pit gain from a gas kick in water-based mud - p. 126 295. 2.121 Kick analysis—Maximum surface pressure from a gas kick in water-based mud - p. 126 296. 2.122 Kick analysis—Shut-in drill pipe pressure - p. 127 297. 2.123 Kick analysis—Height of influx - p. 127 298. 2.124 Kill weight mud determination—Moore equation - p. 127 299. 2.125 Kinetic friction - p. 128 300. 2.126 Laser specific energy - p. 128 301. 2.127 Lateral load imposed on a casing centralizer—Cementing - p. 129 302. 2.128 Lateral load imposed on a casing centralizer with a dogleg—Cementing - p. 129 303. 2.129 Linear annular capacity of pipe - p. 129 304. 2.130 Linear capacity of pipe - p. 130 305. 2.131 Load to break cement bond—Cementing - p. 130 306. 2.132 Mass rate of flow through annulus - p. 131 307. 2.133 Matching conditions at the cake-to-rock interface—Formation invasion - p. 131 308. 2.134 Maximum allowable mud weight - p. 131 309. 2.135 Maximum drilling rate—Larger holes - p. 132 310. 2.136 Maximum equivalent derrick load - p. 132 311. 2.137 Maximum length of a slanted well in a given reservoir thickness - p. 133 312. 2.138 Maximum length of drillpipe for a specific bottomhole assembly - p. 133 313. 2.139 Maximum recommended low-gravity solids - p. 133 314. 2.140 Maximum recommended solids fractions in drilling fluids - p. 134 315. 2.141 Maximum weight on bit - p. 134 316. 2.142 Mechanical energy balance for wellbore fluids - p. 134 317. 2.143 Mechanical specific energy - p. 135 318. 2.144 Mud rheology—Herschel and Buckley law - p. 135 319. 2.145 Mud rheology—Power-law model—Consistency index - p. 136 320. 2.146 Mud rheology—Power-law model—Power-law index - p. 136 321. 2.147 Mud rheology—Power-law - p. 136 322. 2.148 Mud rheology calculations—Bingham plastic model - p. 137 323. 2.149 Mud weight increase required to balance pressure - p. 137 324. 2.150 Mud weight reduction by dilution—Water/diesel/any liquid - p. 137 325. 2.151 Mudcake growth equation—Formation invasion - p. 138 326. 2.152 Mudcake growth equation-2—Formation invasion - p. 138 327. 2.153 Mudcake permeability—Formation invasion - p. 139 328. 2.154 New pump circulating pressure - p. 139 329. 2.155 Nozzle area calculation - p. 139 330. 2.156 Number of sacks of cement required - p. 140 331. 2.157 Number of sacks of cement required for a given length of plug - p. 141 332. 2.158 Number of sacks of lead cement required for annulus - p. 141 333. 2.159 Number of sacks of tail cement required for casing - p. 141 334. 2.160 Open-ended displacement volume of pipe - p. 142 335. 2.161 Overall efficiency—Diesel engines to mud pump - p. 142 336. 2.162 Overall power system efficiency - p. 143 337. 2.163 Penetration rate—Drill-rate model—Alternative equation - p. 143 338. 2.164 Penetration rate—Drill-rate model—Basic equation - p. 143 339. 2.165 Percentage of bit nozzle pressure loss - p. 144 340. 2.166 Plastic viscosity—Bingham plastic model - p. 144 341. 2.167 Plug length to set a balanced cement plug - p. 145 342. 2.168 Polar moment of inertia - p. 145 343. 2.169 Polished rod horsepower—Sucker-rod pump - p. 145 344. 2.170 Pore-pressure gradient—Rehm and McClendon - p. 146 345. 2.171 Pore-pressure gradient—Zamora - p. 146 346. 2.172 Pressure analysis—Pressure by each barrel of mud in casing - p. 147 347. 2.173 Pressure analysis—Surface pressure during drill stem test - p. 147 348. 2.174 Pressure gradient - p. 147 349. 2.175 Pressure required to break circulation—Annulus - p. 148 350. 2.176 Pressure required to break circulation—Drill string - p. 148 351. 2.177 Pressure required to overcome gel strength of mud inside the drill string - p. 148 352. 2.178 Pressure required to overcome mud's gel strength in annulus - p. 149 353. 2.179 Pump calculation—Pump pressure - p. 149 354. 2.180 Pump calculations—Power required - p. 149 355. 2.181 Pump displacement - p. 150 356. 2.182 Pump flow rate - p. 150 357. 2.183 Pump head rating - p. 151 358. 2.184 Pump output—gpm - p. 151 359. 2.185 Pump output triplex pump - p. 151 360. 2.186 Pump pressure/pump stroke relationship - p. 152 361. 2.187 Radial force related to axial load—Cementing - p. 152 362. 2.188 Range of load—Sucker-Rod pump - p. 152 363. 2.189 Rate of fuel consumption by a pump - p. 153 364. 2.190 Rate of gas portion that enters the mud - p. 153 365. 2.191 Relationship between traveling block speed and fast line speed - p. 153 366. 2.192 Rock removal rate - p. 154 367. 2.193 Rotating horsepower - p. 154 368. 2.194 Side force at bit in anisotropic formation - p. 155 369. 2.195 Sinusoidal buckling - p. 155 370. 2.196 Slurry density for cementing calculations - p. 155 371. 2.197 Solids analysis—High-salt content muds - p. 156 372. 2.198 Solids analysis low-salt content muds - p. 157 373. 2.199 Spacer volume behind slurry required to balance the plug - p. 157 374. 2.200 Specific gravity of cuttings by using mud balance - p. 158 375. 2.201 Stripping/snubbing calculations—Breakover point between stripping and snubbing - p. 158 376. 2.202 Stripping/snubbing calculations—Height gain and casing pressure from stripping into influx - p. 159 377. 2.203 Stripping/snubbing calculations—Maximum Allowable surface pressure governed by casing burst pressure - p. 159 378. 2.204 Stripping/snubbing calculations—Maximum allowable surface pressure governed by formation - p. 160 379. 2.205 Stripping/snubbing calculations—Minimum surface pressure before stripping - p. 160 380. 2.206 Stripping/snubbing calculations—Constant BHP with a gas bubble rising - p. 161 381. 2.207 Stroke per minute required for a given annular velocity - p. 161 382. 2.208 Stuck pipe calculations—Method-1 - p. 161 383. 2.209 Stuck pipe calculations—Method-2 - p. 162 384. 2.210 Subsea considerations—Adjusting choke line pressure loss for higher mud weight - p. 162 385. 2.211 Subsea considerations—Casing burst pressure-subsea stack - p. 162 386. 2.212 Subsea considerations—Choke line pressure loss - p. 163 387. 2.213 Subsea considerations—Maximum allowable mud weight—Subsea stack from leakoff test - p. 163 388. 2.214 Subsea considerations—Casing pressure decrease when bringing well on choke - p. 164 389. 2.215 Subsea considerations—Velocity through choke line - p. 164 390. 2.216 Surface test pressure required to frac the formation - p. 164 391. 2.217 Total amount of solids generated during drilling - p. 165 392. 2.218 Total heat energy consumed by the engine - p. 165 393. 2.219 Total number of sacks of tail cement required - p. 166 394. 2.220 Total water requirement per sack of cement - p. 166 395. 2.221 Triplex pump factor - p. 166 396. 2.222 Upward force acting at the bottom of the casing shoe - p. 167 397. 2.223 Vertical curvature for deviated wells - p. 167 398. 2.224 Viscous shear stress at the outer mudcake boundary - p. 167 399. 2.225 Volume of cuttings generated per foot of hole drilled - p. 168 400. 2.226 Volume of dilution water or mud required to maintain circulating volume - p. 168 401. 2.227 Volume of fluid displaced for duplex pumps - p. 168 402. 2.228 Volume of fluid displaced for single-acting pump - p. 169 403. 2.229 Volume of fluid displaced for triplex pump - p. 169 404. 2.230 Volume of liquid (oil plus water) required to prepare a desired volume of mud - p. 170 405. 2.231 Volume of slurry per sack of cement - p. 170 406. 2.232 Volumes and strokes—Annular volume - p. 171 407. 2.233 Volumes and strokes—Drill string volume - p. 171 408. 2.234 Volumes and strokes—Total strokes - p. 171 409. 2.235 Weight of additive per sack of cement - p. 172 410. 2.236 Weighted cementing calculations - p. 172 411. Chapter 3: Well test analysis formulas and calculations - p. 172 412. Chapter 4: Production engineering formulas and calculations - p. 202 413. Abstract - p. 203 414. 4.1 Acid penetration distance (acidizing) - p. 204 415. 4.2 Additional pressure drop in the skin zone - p. 205 416. 4.3 Additive crystalline salt amount to increase the density—Method I (single-salt systems) - p. 205 417. 4.4 Additive crystalline salt amount to increase the density—Method II (single-salt systems) - p. 206 418. 4.5 Additive crystalline salt and water amount to increase the density—Method I (two-salt systems) - p. 206 419. 4.6 Annulus pressure loss due to friction during hydraulic fracturing (laminar flow) - p. 207 420. 4.7 Annulus pressure loss due to friction during hydraulic fracturing (turbulence flow) - p. 207 421. 4.8 Approximate ideal counterbalanced load - p. 208 422. 4.9 Average downstroke load (sucker-rod pump) - p. 208 423. 4.10 Average fracture width (acidizing) - p. 208 424. 4.11 Average permeability of a hydraulically fractured formation - p. 209 425. 4.12 Average specific weight of the formation (hydraulic fracturing) - p. 209 426. 4.13 Average upstroke load (sucker-rod pump) - p. 210 427. 4.14 Average wellbore fluid density (completion and workover fluids) - p. 210 428. 4.15 Capacity ratio of a hydraulically fractured surface - p. 210 429. 4.16 Choke discharge coefficient - p. 211 430. 4.17 Close-ended displacement volume of pipe - p. 211 431. 4.18 Convective mass transfer for laminar flow (acidizing) - p. 212 432. 4.19 Convective mass transfer for turbulent flow (acidizing) - p. 212 433. 4.20 Correct counterbalance (sucker-rod pump) - p. 213 434. 4.21 Corresponding reciprocal rate (post-fracture production—Constant Bottomhole flowing conditions) - p. 213 435. 4.22 Damaged/undamaged zone productivity comparison (acidizing) - p. 214 436. 4.23 Density of brine (completion and workover fluids) - p. 214 437. 4.24 Dimensionless fracture width for linear vertical fracture (Geertsma & Klerk) - p. 214 438. 4.25 Downhole operating pressure (hydraulic fracturing) - p. 215 439. 4.26 Entrance hole size (perforation) - p. 215 440. 4.27 Equivalent skin factor in fractured wells - p. 216 441. 4.28 Filter cake on the fracture (acidizing) - p. 216 442. 4.29 Flow coefficient during drawdown - p. 217 443. 4.30 Flow rate through orifice - p. 217 444. 4.31 Flow through fracture in response to pressure gradient - p. 217 445. 4.32 Formation fluid compressibility (acidizing) - p. 218 446. 4.33 Fracture area of a hydraulically fractured formation - p. 218 447. 4.34 Fracture coefficient of a hydraulically fractured reservoir - p. 219 448. 4.35 Fracture fluid coefficient for reservoir-controlled liquids - p. 219 449. 4.36 Fracture fluid coefficient for viscosity-controlled liquids - p. 220 450. 4.37 Fracture geometry (acidizing) - p. 220 451. 4.38 Fracture gradient (hydraulic fracturing) - p. 220 452. 4.39 Fracture-fluid invasion of the formation (acidizing) - p. 221 453. 4.40 Frictional pressure drop (Economides and Nolte) - p. 221 454. 4.41 Gas velocity under sonic flow conditions (through choke) - p. 222 455. 4.42 Hydraulic fracture efficiency - p. 222 456. 4.43 Hydraulic horse power for a hydraulic fracturing operation - p. 223 457. 4.44 Ideal fracture conductivity created by acid reaction (acidizing) - p. 223 458. 4.45 Incremental density in any wellbore interval (completion and workover fluids) - p. 223 459. 4.46 Initial rate following a hydraulic fracturing operation - p. 224 460. 4.47 Injection pressure for hydraulic fracturing - p. 224 461. 4.48 Lifetime of a hydraulically fractured well - p. 225 462. 4.49 Mass of rock dissolved per unit mass of acid (acidizing) - p. 225 463. 4.50 Mass transfer in acid solutions by Fick’s law (acidizing) - p. 225 464. 4.51 Maximum treatment pressure (hydraulic fracturing) - p. 226 465. 4.52 Mechanical resistant torque (PCP) - p. 226 466. 4.53 Minimum polished rod load (sucker rod pump) - p. 226 467. 4.54 Peclet number for fluid loss (acidizing) - p. 227 468. 4.55 Perforation friction factor - p. 227 469. 4.56 Perforation friction pressure - p. 228 470. 4.57 Perforation hole size (perforation) - p. 228 471. 4.58 Perforation length in formation - p. 228 472. 4.59 Perforation penetration ratio (formation of interest/reference formation) - p. 229 473. 4.60 Perforation skin factor - p. 229 474. 4.61 Pore growth function (acidizing) - p. 230 475. 4.62 Pressure drop across perforations in gas wells - p. 230 476. 4.63 Pressure drop across perforations in oil wells - p. 231 477. 4.64 Pressure loss due to perforations during hydraulic fracturing - p. 232 478. 4.65 Pressure loss due to perforations during hydraulic fracturing—2 - p. 232 479. 4.66 Principal stress due to petro-static pressure (hydraulic fracturing) - p. 232 480. 4.67 Productivity index (for generating composite IPR curve) - p. 233 481. 4.68 Productivity ratio - p. 233 482. 4.69 Productivity ratio calculation of a hydraulically-fractured formation - p. 234 483. 4.70 Pseudo skin factor due to partial penetration (Brons and Marting method) - p. 234 484. 4.71 Pseudo-skin factor due to partial penetration (Yeh and Reynolds correlation) - p. 235 485. 4.72 Pseudo-skin factor due to partial penetration (Odeh correlation) - p. 235 486. 4.73 Pseudo-skin factor due to partial penetration (Papatzacos correlation) - p. 235 487. 4.74 Pseudo-skin factor due to perforations - p. 237 488. 4.75 Quantifying formation damage and improvement - p. 238 489. 4.76 Recommended underbalanced environment for perforation - p. 239 490. 4.77 Reynolds number for acid flow into the fracture (acidizing) - p. 239 491. 4.78 Reynolds number for fluid loss (acidizing) - p. 239 492. 4.79 Sand weight needed to refill a hydraulically fractured reservoir volume - p. 240 493. 4.80 Shape factor expressed as skin factor for vertical wells - p. 240 494. 4.81 Single-phase gas flow (subsonic) - p. 240 495. 4.82 Single-phase liquid flow through choke - p. 241 496. 4.83 Skin factor - p. 241 497. 4.84 Skin factor by Hawkins method - p. 242 498. 4.85 Skin factor due to partial penetration - p. 242 499. 4.86 Skin factor due to reduced crushed-zone permeability - p. 243 500. 4.87 Skin factor for a deviated well - p. 243 501. 4.88 Slope of Semilog plot for bottom-hole flowing pressure vs time for drawdown test - p. 244 502. 4.89 Sucker rod—Peak polished rod load - p. 244 503. 4.90 Suspension property of static fluids (completion and workover fluids) - p. 245 504. 4.91 Tangential annular flow of a power law fluid - p. 245 505. 4.92 Temperature at choke outlet - p. 246 506. 4.93 The z component of the force of the fluid on the wetted surface of the pipe - p. 246 507. 4.94 Total skin in partially depleted wells for a buildup test - p. 246 508. 4.95 Velocity distribution in the annular slit of a falling-cylinder viscometer - p. 247 509. 4.96 Velocity distribution in the narrow annular region in annular flow with inner cylinder moving axially - p. 247 510. 4.97 Velocity distribution of flow through an annulus - p. 248 511. 4.98 Velocity of fluid in annulus - p. 248 512. 4.99 Velocity of fluid in pipe - p. 249 513. 4.100 Viscous force acting on the rod over the narrow annular region - p. 249 514. 4.101 Volume capacity of pipe - p. 250 515. 4.102 Volume of fluid loss per unit area measured in a dynamic test (acidizing) - p. 250 516. 4.103 Volume of fluid loss per unit area measured in a static test (acidizing) - p. 250 517. 4.104 Volume of rock dissolved per unit volume of acid (acidizing) - p. 251 518. 4.105 Water quantity that dilutes the original brine with assumed density (two-salt systems) - p. 251 519. 4.106 Weight of crystalline CaCl2 and CaBr2 salt addition to brine (two-salt systems) - p. 252 520. 4.107 Well flowing pressure (line-source solution by including skin factor) - p. 252 521. 4.108 Well flowing pressure under Pseudo-steady state flow for non-circular reservoirs - p. 253 522. 4.109 Wellbore pressure loss due to friction during hydraulic fracturing (laminar flow) - p. 253 523. 4.110 Wellbore pressure loss due to friction during hydraulic fracturing (turbulence flow) - p. 254 524. 4.111 Wellbore storage - p. 254 525. 4.112 Wellbore storage due to fluid level - p. 254 526. 4.113 Wellhead pressure (multiphase flow across the choke) - p. 255 527. 4.114 Workover operations (maximum allowed tubing pressure) - p. 255 528. 4.115 Young Modulus by using sonic travel time (acidizing) - p. 256 529. Chapter 5: Fluid flow and transport phenomena formulas and calculations - p. 256 530. Abstract - p. 257 531. 5.1 Archimedes number - p. 258 532. 5.2 Average number of collisions to reduce neutron energy - p. 259 533. 5.3 Average velocity of a falling film with variable viscosity - p. 259 534. 5.4 Average velocity of flow through a circular tube - p. 260 535. 5.5 Average velocity of flow through an annulus - p. 260 536. 5.6 Average velocity of fluids in flow of two adjacent immiscible fluids - p. 261 537. 5.7 Average velocity over the cross section of a falling film - p. 261 538. 5.8 Blowdown time in unsteady gas flow - p. 262 539. 5.9 Boltzmann equation - p. 262 540. 5.10 Boussinesq approximation—Buoyancy - p. 262 541. 5.11 Brinkman number - p. 263 542. 5.12 Buckingham Reiner equation - p. 263 543. 5.13 Calculation of mass flow rate - p. 264 544. 5.14 Calculation of momentum flux - p. 264 545. 5.15 Combined momentum flux tensor - p. 265 546. 5.16 Combined radiation and convection - p. 265 547. 5.17 Compressible flow in a horizontal circular tube - p. 265 548. 5.18 Compton scattering - p. 266 549. 5.19 Correction factor for stagnant film according to the penetration model - p. 266 550. 5.20 Darcy Weisbach equation (head loss form) - p. 267 551. 5.21 Darcy Weisbach equation (pressure loss form) - p. 267 552. 5.22 Dean number - p. 267 553. 5.23 Deborah number - p. 268 554. 5.24 Decay of thermal neutrons - p. 268 555. 5.25 Determination of the controlling resistance - p. 269 556. 5.26 Determination of the diameter of a falling sphere - p. 269 557. 5.27 Diffusion from an instantaneous point source - p. 270 558. 5.28 Diffusion in a moving film - p. 270 559. 5.29 Diffusion in polymers - p. 270 560. 5.30 Diffusion Into a falling liquid film (gas absorption) - p. 271 561. 5.31 Diffusion of low-density gases with equal mass - p. 271 562. 5.32 Diffusion potential - p. 272 563. 5.33 Diffusion through a non-isothermal spherical film - p. 272 564. 5.34 Diffusion through a stagnant film - p. 273 565. 5.35 Diffusion through a stagnant gas film - p. 273 566. 5.36 Diffusion through cleat spacing in coalbed methane reservoirs - p. 273 567. 5.37 Diffusion with a heterogeneous chemical reaction - p. 274 568. 5.38 Diffusion with a homogeneous chemical reaction - p. 274 569. 5.39 Diffusion, convection, and chemical reaction - p. 275 570. 5.40 Drag coefficient - p. 275 571. 5.41 Drag force - p. 275 572. 5.42 Draining of a cylindrical tank - p. 276 573. 5.43 Draining of a spherical tank - p. 276 574. 5.44 Eckert number - p. 277 575. 5.45 Effective emissivity of a hole - p. 277 576. 5.46 Effective thermal conductivity for a solid with spherical inclusions - p. 277 577. 5.47 Efflux time for draining a conical tank - p. 278 578. 5.48 Ekman number - p. 278 579. 5.49 Elimination of circulation in a rising gas bubble - p. 279 580. 5.50 Energy emitted from the surface of a black body - p. 279 581. 5.51 Estimation of diffusivity of liquids - p. 279 582. 5.52 Estimation of self diffusivity at high density - p. 280 583. 5.53 Estimation of the viscosity of a pure liquid - p. 280 584. 5.54 Euler number - p. 281 585. 5.55 Fanning friction factor (laminar flow) - p. 281 586. 5.56 Fanning's friction factor (turbulent flow) - p. 282 587. 5.57 Fick's law of binary diffusion - p. 282 588. 5.58 Film condensation on vertical pipes - p. 282 589. 5.59 Film condensation on vertical tubes - p. 283 590. 5.60 Film thickness of a falling film on a conical surface - p. 284 591. 5.61 Flow in a liquid-liquid ejector pump - p. 284 592. 5.62 Flow in a slit with uniform cross flow - p. 285 593. 5.63 Flow near a corner - p. 285 594. 5.64 Flow of power law fluid through a narrow slit - p. 286 595. 5.65 Fluid kinetic force in conduits - p. 286 596. 5.66 Fluid kinetic force in flow around submerged objects - p. 286 597. 5.67 Form drag - p. 287 598. 5.68 Free air correction—Gravity survey - p. 287 599. 5.69 Free batch expansion of a compressible fluid - p. 288 600. 5.70 Free convection heat transfer from a vertical plate - p. 288 601. 5.71 Friction drag - p. 288 602. 5.72 Friction factor for creeping flow around a sphere - p. 289 603. 5.73 Friction factor in flow around submerged objects - p. 289 604. 5.74 Friction factor in flow through conduits - p. 290 605. 5.75 Friction factor in packed column (laminar) - p. 290 606. 5.76 Friction factor in packed column (turbulant) - p. 290 607. 5.77 Galilei number - p. 291 608. 5.78 Gas absorption from rising bubbles for creeping flow - p. 291 609. 5.79 Gas absorption through bubbles - p. 292 610. 5.80 Gas absorption with chemical reaction in an agitated tank - p. 292 611. 5.81 Gas absorption with rapid reaction - p. 293 612. 5.82 Gas mass rate flow in compressible tube flow - p. 293 613. 5.83 Graetz number - p. 293 614. 5.84 Graham equation viscosity ratio - p. 294 615. 5.85 Grash of number - p. 294 616. 5.86 Hagen number - p. 295 617. 5.87 Hagen-Poiseuille equation - p. 295 618. 5.88 Influence of changing interfacial area on mass transfer - p. 296 619. 5.89 Knudsen flow - p. 296 620. 5.90 Krieger Dougherty equation viscosity ratio - p. 296 621. 5.91 Laminar flow along a flat plate (approximate solution) - p. 297 622. 5.92 Laminar flow of an incompressible power-law fluid in a circular tube - p. 297 623. 5.93 Laplace number - p. 298 624. 5.94 Lewis number - p. 298 625. 5.95 Mach number - p. 298 626. 5.96 Manning formula - p. 299 627. 5.97 Marangoni number - p. 299 628. 5.98 Mass absorption (attenuation) coefficient - p. 300 629. 5.99 Mass flow rate as a function of the modified pressure drop in a network of tubes - p. 300 630. 5.100 Mass flow rate in a rotating cone pump - p. 300 631. 5.101 Mass rate of flow - p. 301 632. 5.102 Mass rate of flow in a squared duct - p. 301 633. 5.103 Mass rate of flow of a falling film - p. 302 634. 5.104 Mass rate of flow through a circular tube - p. 302 635. 5.105 Mass transfer for creeping flow around a gas bubble - p. 303 636. 5.106 Mass transfer to drops and bubbles - p. 303 637. 5.107 Maximum flow rate (Vogel's equation) - p. 303 638. 5.108 Maximum velocity of a falling film - p. 304 639. 5.109 Maximum velocity of flow through a circular tube - p. 304 640. 5.110 Maximum-velocity Vz-maximum of a falling film - p. 305 641. 5.111 Method for separating helium from natural gas - p. 305 642. 5.112 Modified capillary number - p. 306 643. 5.113 Modified Van Driest equation - p. 306 644. 5.114 Momentum flux distribution of flow through a circular tube - p. 306 645. 5.115 Momentum flux distribution of flow through an annulus - p. 307 646. 5.116 Momentum flux profile of fluids in flow of two adjacent immiscible fluids - p. 307 647. 5.117 Momentum fluxes for creeping flow into a slot - p. 308 648. 5.118 Mooney equation viscosity - p. 308 649. 5.119 Non-Newtonian flow in annulus - p. 309 650. 5.120 Nusselt number - p. 309 651. 5.121 Ohnesorge number - p. 310 652. 5.122 Potential flow around a cylinder - p. 310 653. 5.123 Prandtl number - p. 310 654. 5.124 Pressure distribution in a creeping flow around a sphere - p. 311 655. 5.125 Pressure drop per length of the adsorption unit - p. 311 656. 5.126 Pressure loss due to sudden enlargement - p. 312 657. 5.127 Reynolds number - p. 312 658. 5.128 Schmidt number - p. 313 659. 5.129 Sherwood number - p. 313 660. 5.130 Slit flow in Bingham fluid - p. 313 661. 5.131 Smoluchowski equation - p. 314 662. 5.132 Stanton number - p. 314 663. 5.133 Stefan number - p. 315 664. 5.134 Stokes number - p. 315 665. 5.135 Strouhal number - p. 315 666. 5.136 Taylor dispersion (axial dispersion coefficient) - p. 316 667. 5.137 Taylor equation viscosity - p. 316 668. 5.138 Taylor number - p. 317 669. 5.139 Theory of diffusion in colloidal suspensions - p. 317 670. 5.140 Toricelli equation - p. 317 671. 5.141 Total force of the fluid on the sphere in a creeping flow around a sphere - p. 318 672. 5.142 Velocity distribution in a creeping flow around a sphere - p. 318 673. 5.143 Velocity distribution of a falling film with variable viscosity - p. 319 674. 5.144 Velocity distribution of flow through a circular tube - p. 319 675. 5.145 Velocity profile of fluids in flow of two adjacent immiscible fluids - p. 319 676. 5.146 Viscosity by a falling-cylinder viscometer - p. 320 677. 5.147 Winsauer equation - p. 320 678. Chapter 6: Well log analysis, geophysics, petrophysics formulas, and calculations - p. 321 679. Chapter 7: Petroleum economics formulas and calculations - p. 358 680. Chapter 8: Phase behavior and thermodynamics formulas and calculations - p. 376 681. Chapter 9: Petroleum engineering laboratory formulas and calculations - p. 398 682. Chapter 10: Enhanced oil recovery and geothermal formulas and calculations - p. 414 683. Chapter 11: Geomechanics and fracturing formulas and calculations - p. 442 684. Chapter 12: Facilities and process engineering formulas and calculations - p. 476 685. Index - p. 509