Hydraulic Fracturing Short Course, Texas A&M University College Station 2005

1. Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Modeling, Monitoring, Post-Job Evaluation, Improvements

2. 3D

3. P3D and 3D Models • FracPro (RES, Pinnacle Technologies) • FracCADE (Dowell) • Stimwin (Halliburton) and PredK (Stim-Lab) • TerraFrac • StimPlan • MFrac

4. Dimensionless Form of Nordgren Model tD(xfD) : inverse of xfD(tD) xD = 0 (wellbore) xD = xfD (tip)

5. Propagation Criterion of the Nordgren Model • Net pressure zero at tip • Once the fluid reaches the location, it opens up immediately • Propagation rate is determined by “how fast the fluid can flow

6. Other Propagation Criteria • (Apparent) Fracture Toughness • Dilatancy • Statistical Fracture mechanics • Continuum Damage mechanics

7. KIC KI hf pn xf (Rf) Fracture Toughness Criterion Stress Intensity Factor KI =pnxf1/2

8. CDM What is the time needed for D to start at D = 0 and grow to D = 1 ?

9. CDM Propagation Criterion Combined Kachanov parameter:

10. P3D • Pseudo 3 D Models: Extension of Nordgren’s differential model with height growth • Height criterion • Equilibrium height theory • or Assymptotic approach to equilibrium • Plus some “tip” effect

11. y wellbore element tip element x 3D (Finite Element Modeling)

12. KIC pn Fracture Toughness Criterion • Fluid flow in 2 D • Fluid loss according to local opening time • Propagation: Jumps • Stress Intensity Factor KI > KIC ?

13. Data Need for both P3D and 3D: • Layer data • Permeability, porosity, pressure • Young’s modulus, Poisson ratio, Fracture toughness • Minimum stress • Fluid data • Proppant data • Leakoff calculated from fluid and layer data

14. Design Tuning Steps • Step Rate test • Minifrac (Datafrac, Calibration Test) • Run design with obtained min (if needed) and leakoff coefficient • Adjust pad • Adjust proppant schedule

15. Step rate test Bottomhole pressure Injection rate Time

16. Propagation pressure Bottomhole pressure Two straight lines Injection rate Step rate test

17. 6 Fall-off (minifrac) 3 ISIP 4 Closure 5 Reopening 6 Forced closure 7 Pseudo steady state 8 Rebound 1 5 2 3 4 8 Injection rate Bottomhole pressure Injection rate 2nD injection cycle 1st injection cycle 7 shut-in flow-back Time

18. Pressure fall-off analysis(Nolte)

19. g-function dimensionless shut-in time area-growth exponent where F[a, b; c; z] is the Hypergeometric function, available in the form of tables and computing algorithms

20. g-function

21. Pressure fall-off Fracture stiffness

22. Fracture Stiffness(reciprocal compliance) Pa/m

23. g Shlyapobersky assumption • No spurt-loss bN mN Ae from intercept pw g=0

24. a=4/5 a=2/3 a=8/9 PKN KGD Radial p p x h 8 R Leakoff ( ) ( ) ( ) f f f - - - m m m coefficient, N N N p 3 t E ' 4 t E ' 2 t E ' e e e C L ¢ ¢ 2 E V ¢ Fracture 3 E V E V = i x = = 3 i x i R ( ) ( ) ( ) Extent f p - f 2 p - f h b p - h b p 8 b p f N C f N C N C V V V Fracture = - = - = - i w i i w w p Width e e e x h x h 2 R f f f f f 2 - - 2 . 830 C t 2 . 956 C t L e L e - 2 . 754 C t L e p w x h w x h Fluid 2 e f f e f f w R h = h = Efficiency e f e e 2 V V h = i i e V i Vi: injected into one wing Nolte-Shlyapobersky

25. 1: g-function plot of pressure 2: get parameters bN and mN 3 Calculate Rf (fracture extent -radius) 4 Calculate CLAPP (apparent leakoff coeff) 5 Calculate wL (leakoff width) 6 Calculate we (end-of pumping width) 7 Calculate h (fluid efficiency)

26. Computer Exercise 3-1 Minifrac analysis

27. Example Permeable (leakoff) thickness, ft, 42 Plane strain modulus, E' (psi), 2.0E+6 Closure Pressure, psi, 5850

28. Output

29. From "apparent" to "real“ (radial)

30. Redesign • Run the design with new leakoff coefficient (That is why we do minifrac analysis)

31. Monitoring • Calculate proppant concentration at bottom (shift) • Calculate bottomhole injection pressure, net pressure • Calculate proppant in formation, proppant in well • Later: Add and synchronize gauge pressure

32. Nolte-Smith plot Wellbore screenout Log net pressure Tip screenout Normal frac propagation Unconfined height growth Log injection time

33. Post-Job Logging • Tracer Log • Temperature Log • Production Log

34. Available Techniques for Width and Height • Measured Directly • Formation Micro Scanner • Borehole Televiewer • Based on Inference • Temperature Logging • Isotopes (fluid, proppant) • Seismic Methods, Noise Logging • Tiltmeter techniques • Spinner survey Radius of penetration

35. ScSb IrTracerlog

36. Tiltmeter Results after Economides at al. Petroleum Well Construction

37. Pressure Match with 3D Simulation

38. 0.25 5000 0.20 4000 0.15 3000 Propped Width - in Conductivity (Kfw) - md.ft 0.10 2000 0.05 1000 0 0 0 50 100 150 200 250 Fracture Half-Length - ft 3D Simulation Texaco E&P FracCADE OCS-G 10752 #D-12 Actual 05-23-1997 Flow Capacity Profiles Propped Width (ACL) Conductivity - Kfw *Mark of Schlumberger

39. Well Testing: The quest for flow regimes

40. Design Improvement in a Field Program • Sizing • Pad volume for “generic” design • More aggressive or defensive proppant schedule • Proppant change (resin coated, high strength etc.) • Fluid system modification (crosslinked, foam) • Proppant carrying capacity • Leakoff • Perforation strategy changes • Forced closure, Resin coating, Fiber reinforcement, Deformable particle

41. Example: Tortuous Flow Path • Analysis of the injection rate dependent element of the treating pressure • Does proppant slug help? • Does limited entry help? • Does oriented perforation help? • Extreme: reconsidering well orientation: e.g. S shaped

42. Misalignment

43. smax smax Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342 From overbalanced perforation From underbalanced perforation

44. High Viscosity slugs

45. Proppant Slugs

46. Case Study: Effect of Non-Darcy Flow • Forcheimer Equation • Cornell & Katz

47. Non-Darcy Flow • Dimensionless Proppant Number is the most important parameter in UFD Effective Proppant Pack Permeability

48. Non-Darcy Flow • Effective Permeability keff is determined through an iterative process Drawdown is needed to calculate velocity • Reynolds Number

49. Non-Darcy Flow Coefficient (b) • Several equations have been developed mostly from lab measurements (empirical equations) • General form of b equation where b is 1/m and k is md