Source: Economides and Nolte: Reservoir Stimulation 3 rd Ed.

1. Hydraulic FracturingShort Course,Texas A&M University College Station 2005Fracture Design Fracture Dimensions Fracture ModelingPeter P. Valkó

2. Source: Economides and Nolte: Reservoir Stimulation 3rd Ed.

3. Frac Design Goals

4. Well or Reservoir Stimulation? • Near wellbore region and/or bulk reservoir? • Acceleration versus increasing reserve? • Low permeability • Medium permeability • High permeability • Coupling of goals • Frac&pack

5. Hydraulic Fracturing Design and Evaluation • Why do we create a propped fracture? • How do we achieve our goals? • Data gathering • Design • Execution • Evaluation

6. Fractured Well Performance • Relation of morphology to performance • Streamline view • Flow regimes, Productivity Index, Pseudo-steady state Productivity Index, skin and equivalent wellbore radius

7. Well- Fracture Orientation • MATCH • Vertical well - Vertical fracture • Horizontal well – longitudinal fracture • MISMATCH (Choke effect) • Horizontal well with a transverse vertical fracture • Vertical well intersecting a horizontal fracture

8. Principle of least resistance Least Principal Stress Least Principal Stress Horizontal fracture Vertical fracture

9. Mismatch (Choked fracture) • Typical mismatch situations: • Horizontal well with a transverse vertical fracture • Vertical well intersecting a horizontal fracture

10. Vertical Fracture - Vertical well • Bypass damage Original skin disappears • Change streamlines Radial flow disappears Wellbore radius is not a factor any more • Increased PI can be utilized Dp or q

11. sH,min sH,min xf sH,max Longitudinal Vertical Fracture -Horizontal well Can it be done?

12. Hydraulic Fracture sH,max sH,max D xf sH,min Transverse Vertical Fractures - Horizontal Well Radial converging flow in frac

13. Fracture Morphology source: Economides at al.: Petroleum Well Construction

14. Main questions • Which wellbore-fracture orientation is favorable? • Which can be done? • How large should the treatment be? • What part of the proppant will reach the pay? • Width and length (optimum dimensions)? • How can it be realized?

15. Prod Eng 101 • Transient vs Pseudo-steady state • Productivity Index • Skin

16. Pseudo-steady state Productivity Index Production rate is proportional to drawdown, defined as average pressure in the reservoir minus wellbore flowing pressure Drawdown Circular: Dimensionless Productivity Index

17. Hawkins formula Damage penetration distance

18. Wellbore radius 0.328 ft Permeability impairment Damage penetration 0.5 ft Exercise 1 Calculate the skin factor due to radial damage if Solution of Exercise 1 Note that any "consistent" system of units is OK.

19. Exercise 2 Assume pseudo-steady state and drainage radius re = 2980 ft in Exercise 1. What portion of the pressure drawdown is lost in the skin zone? What is the damage ratio? What is the flow efficiency? Solution 2 The fraction of pressure drawdown in the skin zone is given by (Since we deal only with ratios, we do not have to convert units.): Therefore 31 % of the pressure drawdown is not utilized because of the near wellbore damage. The damage ratio is DR = 31 % The flow efficiency is FE = 69 %.

20. Assume that the well of Exercise 2 has been matrix acidized and the original permeability has been restored in the skin zone. What will be the folds of increase in the Productivity Index? (What will be the folds of increase in production rate assuming the pressure drawdown is the same before and after the treatment?) Solution 3 We can assume that the skin after the acidizing treatment becomes zero. Then the folds of increase is: The Productivity Index increase is 44 % , therefore the production increase is 44 % . Exercise 3

21. Exercise 4 Assume that the well of Exercise 2 has been fracture treated and a negative pseudo skin factor has been created: sf = -5. What will be the folds of increase in the Productivity Index with respect to the damaged well? Solution 4 The ratio of Productivity Indices after and before the treatment is The Productivity Index will increase 260 % .

22. wp h 2Vfp 2xf Fully penetrating vertical fracture: Relating Performance to Dimensions

23. 2 xf w fracture conductivity no name Dimensionless fracture conductivity Dimensionless fracture conductivity

24. Accounting for PI: sf and f and r’w sf is pseudo skin factor used after the treatment to describe the productivity • JD is a function of what? • half-length, • dimensionless fracture conductivity • Drainage radius, re • sf is a function of what? • half-length, • dimensionless fracture conductivity • wellbore radius, rw

25. Pseudo-skin, equivalent radius, f-factor or Prats Cinco-Ley

26. rw wellbore radius, m (or ft) r'w Prats’ equivalent wellbore radius due to fracture, m (or ft) Cinco-Ley-Samanieggo factor, dimensionless sf the pseudo skin factor due to fracture, dimensionless Prats' dimensionless (equivalent) wellbore radius Notation But JD is the best

27. Example Assume rw = 0.3 ft and A= 40 acre

28. Dimensionless Productivity Index, sf and f and r’w or Prats Cinco-Ley

29. ye = xe 2 xf xe Penetration Ratio Dimensionless Fracture ConductivityProppant Number

30. The following models, graphs and correlations are valid for low to moderate Proppant Number, Nprop • OK, so what IS the Proppant Number? • The weighted ratio of propped fracture volume to reservoir volume. The weight is 2kf/k . • A more rigorous definition will be given later. • The following models are valid for Nprop <=0.1 ! (The case when the boundaries do not distort the streamline structure (with respect to lower proppant numbers.)

31. 1.0 0.1 0.01 100 0.1 1.0 10 Prats' Dimensionless Wellbore Radius

32. 4 3 2 f 1 0 0.1 1 10 100 1000 CfD Cinco-Ley and Samaniego graphf (CfD)= sf + ln(xf/rw) use f = ln(2) for CfD > 1000

33. Infinite or finite conductivity fracture • Note that after CfD > 100 (or 30), nothing happens with f. • Infinite conductivity fracture. • Definition: finite conductivity fracture is a not infinite conductivity fracture (CfD < 100 or 30) • (Other concept: uniform flux fracture, we will learn later.)

34. Proppant Number - Various ways to look at it Nprop= const means fixed proppant volume

35. Fig 1: JD vs CfD (moderate Nprop)

36. Fig 2: JD vs CfD (large Nprop)

37. OPTIMIZATION

38. Struggle for propped volume: w and xf 2Vfp = 2h wp xf 2Vfp = 2h wp xf Optimal length and width

39. The Key Parameter is the Proppant Number Medium perm High perm Frac&Pack

40. The Key Parameter is the Proppant Number Low perm Massive HF Medium perm

41. Let us read the optimum from the JD Figures! dimensionless fracture conductivity (for smaller Nprop) penetration ratio (for larger Nprop)

42. Optimum for low and moderate Proppant Number CfDopt=1.6

43. Optimum for large Proppant Number

44. Tight Gas and Frac&Pack: the extremes Tight gas k << 1 md (hard rock) High permeability k >> 1 md (soft formation)

45. FracPi

46. Exercise No 1 Determine the "folds of increase" if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 0.5 md permeability. Assume all proppant goes to pay. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. Determine the optimal fracture length and propped width.

47. 1: Proppant Number 2: Max Folds of Increase 40,000 lbm proppant, specific gravity 2.6, pack porosity 0.35 packed volume is 40,000/62.4/2.6/(1-0.35) = 380 ft3 Folds of Increase FracPi 0.467 0.0768 FOI: 6.8 with respect to skin 5 FOI: 3.8 with respect to skin=0

48. Optimum frac dimensions • The volume of two propped wing is • 2V1wp = 380 ft3 • If the proppant number is not too large: the optimal fracture half-length is • The propped width is

49. Computer Exercise: High Perm Determine the optimal fracture length and propped width if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 50 md permeability. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. (Assume all proppant goes to pay.)

50. Computer Exercise: Tight gas Determine the optimal fracture length and propped width if 40,000 lbm proppant (pack porosity 0.35, specific gravity 2.6, permeability 60,000 md) is to be placed into a 65 ft thick formation of 0.01 md permeability. The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5. (Assume all proppant goes to pay.)