THE PRACTICE OE RESERVOIR ENGINEERING - UniTrento
EVELOPMENTS IN R PETROLEUM SCIENCE THE PRACTICE OE RESERVOIR ENGINEERING (REVISED EDITION) L.P. Dake
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CONTENTS :.nuU„vnl M Foreword to the revised edition Preface In Memoriam Nomenclature Chapter 1. I N T R O D U C T I O N TO RESERVOIR ENGINEERING 1.1. Activities i n reservoir engineering (a) Observations (b) Assumptions (c) Calculations (d) Development decisions 1 Z- Basic themes of the text (a) Simplicity (b) What works and what does not — and why? (c) Analytical methods (d) Offshore versus onshore developments - i The role o f reservoir engineers l A Technical responsibilities of reservoir engineers (a) .Appraisal b i End of appraisal . Development - -. r h \ sical principles of reservoir engineering ' : 1 IT vii ix xiii xxi T H E APPRAISAL OF O I L A N D GAS FIELDS . :::on r - \ olume-temperature fluid properties for o i l . P V T parameters r l i n g reservoir fluids : ratory experiments -.r arison of laboratory and field P V T data :or \ olatile o i l systems : r. of the stock tank o i l initially i n place v.2ation/equity determination -.mally in place ( O I I P ) . X tank o i l initially i n place ( S T O I I P ) - '. erable reserves ibIeoU - - gas initially i n place ( O I I P ) a plotting ? ;: Gas field appraisal :he repeat formation tester . ng the repeat formation tester . . testing 1 sj 1 1 2 3 4 4 4 5 6 7 T 17 18 19 19 26 28 29 29 29 29 33 37 40 43 44 45 46 47 48 49 50 51 53 58 63 66
xvi ,,, Contents 2.10. Extended well testing References Chapters. MATERIAL BALANCE APPLIED TO OILFIELDS 70 72 73 3.1. 3.2. 73 74 75 75 78 81 82 85 86 86 87 Introduction Derivation of the cumulative material balance for o i l reservoirs (a) Left-hand side (underground withdrawal — rb) (b) Right-hand side (expansion plus water influx) 3.3. Necessary conditions for application of material balance 3.4. Solving the material balance (knowns and unknowns) 3.5. Comparison between material balance and numerical simulation modelling 3.6. The opening move in applying material balance 3.7. Volumetric depletion fields LTv ;'. (a) Depletion above the bubble point Exercise 3.1: Material balance applied to an undersaturated volatile oilfield Exercise 3.2: Identification o f the drive mechanism and calculation of the S T O I I P for a depletion type reservoir (b) Depletion below the bubble point (solution gas drive) Exercise 3.3: Application of the Muskat material balance i n history matching and prediction of solution gas drive 3.8. Water influx calculations (a) Carter-Tracy water influx calculations (b) Aquifer "fitting" using the method of Havlena-Odeh Exercise 3.4: History matching using the Carter-Tracy aquifer model and the "fitting" technique of Haviena and Odeh (c) History matching w i t h numerical simulation models 3.9. Gascap drive Exercise 3.5: Application o f material balance to the early production performance of a gascap drive field 3.10. Compaction drive Exercise 3.6: Compaction drive 3.11. Conclusion References (iHirler 4. 4.1. 4.2. OILWELL TESTING 1 .' L . Introduction Essential observations i n well testing (a) Rate, pressure, time (b) Core/log data (c) RI'T, pressure-depth profiles (d) Geological model (c) Drive mechanism (f) I'VT liuid properties (g) Well completion (It) Eqiiipmcnl (i) Icsts in neighbouring wells 4.3. Well Icsling lilcialure 4.4. The pill pose of well testing (a) Appraisal well testing (b) Devclopmenl well testing 4.5. Basic, radial How equation (a) Radial diitiisivily equation (b) Invesligalioii o i Ihe validity o f linearizing the basic radial flow equation by the method ! I. of deletion o i Icrms ( (intents 4.6. 1.7. 'I.K. 4.9. 4.10. 4.11. 4.12. 4.13. 4.14. 92 98 4.15. 106 110 110 Ill 4.16. 112 116 117 4.17. 119 124 128 133 134 137 137 138 138 139 141 142 142 143 143 143 144 145 147 147 152 154 154 156 4.18. iif Constant terminal rate solution of the radial diffusivity equation 159 (a) Bounded reservoir conditions 161 (b) Steady-state condition 165 The transient constant terminal rate solution of the radial diffusivity equation 168 Difficulties in application o f the constant terminal rate solution of the radial diffusivity equation 176 Superposition o f C T R solutions 177 Single-rate drawdown test 180 (a) Inspection of the flowing pressure 181 (b) Time derivative of drawdown pressures 182 Pressure buildup testing (general description) 183 Miller, Dyes, Hutchinson ( M D H ) pressure buildup analysis 185 Horner pressure buildup analysis 190 Some practical aspects of appraisal well testing 196 (a) Determination of the initial pressure 196 (b) Afterflow 196 Exercise 4.1: Pressure buildup test: infinite acting reservoir 199 Practical difficulties associated with Horner analysis 205 (a) Flowing time/superposition 206 (b) The meaning o f p * 210 The influence of fault geometries on pressure buildups in appraisal well testing 212 (a) General description 212 (b) Single fault , . , , 213 Exercise 4.2: Pressure buildup test: single fault analysis '.' 217 (c) Some general considerations in defining fault positions 223 (d) Definition o f more complex fault geometries 228 Application of the exponential integral 230 (a) Example: interference between oilfields 231 Pressure support during appraisal well testing 235 (a) Pressure buildup performance 236 (b) Dimensioniess pressure-radius of investigation 238 (c) Miller, Dyes, Hutchinson interpretation ,,.*, ,(,. (A) Horner interpretation (e) Variable skin factor (well clean-up) Exercise 4.3: Pressure buildup test: steady-state flow condition 4.19. Weil testing i n developed fields (a) Pressure buildup analysis method of H o r n e r - M B H for bounded reservoir systems . . (b) Pressure buildup analysis method of M D H - D i e t z for bounded reservoir systems . . . (c) Buildup analysis for systems with constant pressure or mixed boundary conditions . . 241 245 246 253 254 258 260 (d) Example well test (e) Practical difficulties i n testing development wells (f) Relationship between weiibore and numerical simulation grid block pressures (g) Afterflow (h) Extended well testing (i) Radius o f investigation 4.20. Multi-rate flow testing (a) Two-rate flow testing (b) Example well test (c) Selective inflow performance (SIP) testing 4.21. L o g - l o g type curves (a) Conventional type-curve interpretation (b) Time derivative type curves (c) Practical aspects 264 271 273 275 275 277 279 280 284 288 290 290 294 296 . . . .
Contents 4.22. Conclusions (a) The elusive straight line (b) Saving money in well testing (c) Identification of the correct early straight line References 299 299 300 304 307 Chapters. 311 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 0 *:' 5.8. WATERDRIVE Introduction Planning a waterfiood . (a) Purpose (b) Permeability (c) O i l viscosity (d) O i l volatility (e) Overpressures (f) Reservoir depth Engineering design of waterdrive projects (a) Production plateau rate (b) Number of production/injection wells (c) Surface production/injection facilities Exercise 5.1: Topsides facilities design for an offshore waterdrive field The basic theory o f waterdrive i n one dimension (a) Rock relative permeabilities (b) Mobility ratio (c) Fractional flow (d) The Buckiey-Leverett displacement theory (e) Weige displacement efficiency calculations (f) Input of rock relative permeabilities to numerical simulation and analytical reservoir models (g) Laboratory experiments The description of waterdrive in heterogeneous reservoir sections (a) Reservoir heterogeneity (b) Recipe for evaluating vertical sweep efficiency in heterogeneous reservoirs Waterdrive under segregated flow conditions (vertical equilibrium) (a) Basic description (b) Data requirements and interpretation for input to the generation of pseudo-relative permeabilities (c) Catering for the presence of edge water i n V E flooding (d) V E displacement i n a homogeneous acting reservoir Exercise 5.2: Water-oil displacement under the vertical equilibrium condition Exercise 5.3: The influence of distinctive permeability distributions on the vertical sweep efficiency for Ihc VE-flooding condition Waterdrive in scclions across which there is a tola! lack of pressure equilibrium (a) Reservoir eiiviroiitnent (b) Data iet iiiiemenls and interpretation for input in the generation of pseudo-relative permealiililies (c) Stiles inelhod (d) Dykstra-Parsons melliod (e) Weilworkovers Exercise 5.4: History matching and prediction ol' a waterdrive field performance using the method of Stiles ' Exercise 5.5: Dykstra-Parsons displacement calculations The numerical simulation of waterdrive (a) Purpose 311 312 312 315 316 317 320 323 324 324 326 327 330 336 337 339 341 345 348 355 362 366 366 369 373 373 375 384 386 388 398 405 405 409 411 413 416 416 423 427 427 (Yiilcnis xix ( I t ) Generation of pseudo-relative permeabilities using cross-sectional simulation modelling (c) A r e a i numerical simulation modelling 'I i hc examination of waterdrive performance (a) Starting point (b) Natural waterdrive (c) Prediction (d) Perturbations i n the fractional flow (e) Example — N o r t h Sea Waterdrive Field (1) Example — the East Texas Field (g) The influence of operational activity (h) Comment Id Dit'ficult waterdrive fields (a) Field A (b) Field B (c) The overall management of waterdrive fields Kik-rences 429 435 436 440 441 442 443 443 448 454 457 458 458 463 469 470 (IHIJ,ICT6. GAS RESERVOIR E N G I N E E R I N G 6.1. 6.2. 473 Introduction P V T requirements for gas-condensate systems (a) Equation of state (b) Surface/reservoir volume relationships (c) Constant volume depletion ( C V D ) experiments (d) Gas compressibility and viscosity (e) Semi-empirical equations of state (EOS) 6.3. Gas field volumetric material balance (a) Appropriateness i n application (b) Haviena-Odeh interpretation (e) p/Z-interpretation technique (d) Example field (c) Gas field development li I The dynamics of the immiscible gas-oil displacement (a) Mobility ratio (b) Heterogeneity/gravity (c) Displacement condition Exercise 6.1: Immiscible gas drive i n a heterogeneous reservoir under the V E condition 6,.5. Dry gas recycling i n retrograde gas-condensate reservoirs (a) M o b i l i t y ratio (b) Heterogeneity/gravity (c) Vertical sweep efficiency Exercise 6.2: Generation of pseudo-relative permeabilities for dry gas recycling . . . . Kcicicnces 473 473 475 476 477 479 479 481 481 483 485 489 500 506 507 508 513 Suhiect Index 537 I I 517 523 524 526 529 530 535
-i The role of reservoir engineers s j T l A Technical responsibilities of reservoir engineers 17 (a) .Appraisal 18 bi End of appraisal 19 . Development 19 - -. rh\ sical principles of reservoir engineering 26 ' 28 : THE APPRAISAL OF OIL AND GAS FIELDS 29 1 . :::on 29 IT r-\ olume-temperature fluid properties for oil 29 . PVT parameters 29 .
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