Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Fracture Dimensions Peter P. Valkó

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

2. Proppant Placement

3. Proppant Placement Concepts • From dynamic width (hydraulic) to propped width (after frac closes on proppant) • Areal proppant concentration • Added proppant concentration • Max added proppant conc • Proppant (placement) efficiency

4. Proppant Transport: Settling • Settling causes problems • proppant efficiency decreases (proppant leaves pay layer) • screenout danger • No settling in “perfect” transport fluid • Viscosity (rheology) and density difference (Foams: visc good, dens: bad)

5. Design Logics • Height is known (see height map) • Amount of proppant to place is given (from NPV) • Target length is given (see opt frac dimensions) • Fluid leakoff characteristics is known • Rock properties are known • Fluid rheology is known • Injection rate, max proppant concentratrion is given • How much fluid? How long to pump? How to add proppant?

6. Key concept: Width Equation • Fluid flow creates friction • Friction pressure is balanced by injection pressure • Net pressure is positive • Fracture width is determined by net pressure and characteristic dimension (half length or half height) • The combination of fluid mechanics and solid mechanics

7. Two approximations: • Perkins-Kern-(Nordgren) • Vertical plane strain • characteristic half-length ( c ) is half height, h/2 • elliptic cross section • Kristianovich-Zheltov - (Gertsmaa-deKlerk) • Horizontal plane strain • characteristic half length ( c ) is xf • rectangular vross section

8. Perkins-Kern-Nordgren PKN Kristianovich-Zheltov Geertsma-De-Klerk KGD Width Equations (consistent units) width: w, wo, wwell,o viscosity: m inj. rate (1 wing): qi half-length: xf plain-strain modulus: E' height: hf

9. PKN Power-Law Width Equation • With equivalent viscosity at average shear rate • the maximum width at the wellbore is Power Law fluid K: Consistency (lbf/ft2)·sn n: Flow behavior index

10. Material balance +Width Equation 2qi Vi = qi te xf Vfe = Vi - Vlost Average w(xf) qi hf A Lost: spurt +leakoff

11. Pumping time, fluid volume, proppant schedule: Design of frac treatments Pumping time and fluid volume: Injected = contained in frac + lost length reached, width created Proppant schedule: End-of-pumping concentration is uniform, mass is the required Given: Mass of proppant, target length, frac height, inj rate, rheology, elasticity modulus, leakoff coeff, max-possible-proppant-added-conc

12. Pumping time, slurry volume (1 wing) 1 Calculate the wellbore width at the end of pumping from the PKN (Power Law version) 2 Convert max wellbore width into average width 3 Assume a k = 1. 5 and solve the mat balance for inj time, (selecting sqrt time as the new unknown) 4 Calculate injected volume 5 Calculate fluid efficiency

13. Nolte’s power law proppant schedule: C/C e 1 y = x e Nolte's proposition: select fpad=e slurry V/V 0 1 i f x pad 1 0

14. Proppant schedule calculation 1 Calculate the Nolte exponent of the proppant concentration curve 2 Calculate the pad volume and the time needed to pump it 3 The required max proppant concentration, ce should be (mass/slurry-volume) 4 The required proppant concentration (mass/slurry-volume) curve 5 Convert it to “added proppant mass to volume of clean fluid” (mass/clean-fluid-volume)

15. 2qi Vi = qi te Vfe = Vi - Vlost 2D design: hf is given A hf hp Lost: spurt +leakoff rp= hp /hf Gross and Net Height

16. Ex_2: Frac Design • Pay: 45 ft Gross: 67.5 ft (Gross = hf) • Proppant mass (2wing) = 100,000 lbm is available • 2/3 will go to pay layer • Slurry injection rate (2qi) = 30 bpm • Created fracture height is 67.5 ft • E' = 2.08 106 psi • Power Law rheology: • K' = 0.022 lbf/(ft2 sec0.63) and n' = 0.63 • Leakoff coefficient (w.r.t. perm zone) CL,p = 0.003 ft/min1/2 • Spurt loss is negligible • Blender can do max 12 ppga

17. Proppant mass for (two wings), lbm 100,000 Sp grav of proppant material (water=1) 2.65 Porosity of proppant pack 0.35 Proppant pack permeability, md 60,000 Formation permeability, md 0.5 Permeable (leakoff, net) thickness, ft 45 Well Radius, ft 0.328 Well drainage radius, ft 3000 Pre-treatment skin factor 0 Fracture height, ft 67.5 Plane strain modulus, E’ , psi 2.08×106 Slurry injection rate (2 wings, liq+prop), bpm 30 Rheology, K' (lbf/ft2)×sn' 0.0220 Rheology, n' 0.63 Leakoff coefficient in perm layer, ft/min0.5 0.003 Spurt loss coefficient, Sp, gal/ft2 0

18. Ex_2 Proppant placement efficiency is 66.7% The fracture height is 1.5 times the pay layer thickness, therefore approximately 66,700 lbm proppant will be placed into the pay (2 wings). The mass of proppant in one wing will be 50,000 lbm from which 33,300 lbm will be in the pay layer.

19. Ex_2 Modified Target Proppant mass placed (2 wing), lb 100,000 Proppant in pay, (2 wing) lb 66,700 Proppant number, Np 0.117 Dimensionless PI, JDact 0.48 Dimensionless fracture cond, CfD 1.6 Half length, xf, ft 718 Propped width, wp, inch 0.115 Post treatment pseudo skin factor, sf -6.3 Folds of increase of PI 4.0

20. Ex_2 Input in Consistent Units (SI)

21. Ex_2 Modified (Apparent) Leakoff Coefficient is 2/3-rd of CL,p The fracture height is 1.5 times the pay layer The apparent leakoff coefficient will be only CL = 0.667 CLp = 0.787×10-4 m/s0.5

22. Ex_2 Pumping time, slurry volume (1 wing) 1 Calculate the wellbore width at the end of pumping from the PKN (Power Law version) 2 Convert max wellbore width into average width

23. Ex_2 Pumping time, slurry volume (cont’d) 3 Assume a k = 1. 5 and solve the mat balance for inj time, The positive root of the quadratic equation is x = 43.4 s0.5 therefore the injection time is te = 43.42 s = 31.4 min. 4 Once the injection time is known, calculate the injected slurry volume (1 wing)

24. Ex_2 Efficiency Volume of 1 wing at end of pumping: 5 Fluid efficiency:

25. Ex_2 Proppant concentration at end of pumping This concentration is mass proppant per volume of slurry. We want this to be the proppant concentration everywhere in the fracture at the end of pumping. This should be the proppant concentration in the last injected slurry stage. In terms of added proppant to clean liquid this is 1133 kg added to 1 m3 clean liquid, 70.8 lbm added to 1 ft3 clean fluid that is 9.3 ppga (lbm proppant added to 1 gallon clean fluid)

26. Ex_2 Proppant schedule Nolte exponent Pad Propp concentration This is kg proppant in 1 m3 of slurry Convert it “propp-added-to-clean”

27. Ex_2 Stages at end of pumping (after PWC) Proppant Settling 9 lb/gal 6 to 9 lb/gal 2 to 9 lb/gal 1 lb/gal concentrated to 9 lb/gal 3 to 9 lb/gal

29. 35 10 9 30 8 25 7 6 20 5 15 gallon liquid ca, lbm prop added to 4 Liquid injection rate, bpm 3 10 2 5 1 0 0 0 10 20 30 40 Pumping time, min Ex_2 Proppant Roadmap

30. Stages

31. Design Outcome • Constraints allow optimum placement of the given amount of proppant • Some improvement is necessary • Consider higher quality proppant • Better fluid loss control • Better rheology • Larger allowable proppant concentration • Optimum placement is not possible with traditional method: consider tip screenout design

32. Additional Concerns During Design

33. Tip Screenout vs. Near-well Screenout • Screenout in the near-wellbore region: Proppant cannot enter to the main body of the fracture (oftentimes in Austin chalk) • Screenout at tip: Length control • Two concepts: • Enough width for a single proppant • Enough width for the actual number of proppant grains

34. Width to accept proppant • At the end of pad stage the created width has to be at least 2-3 times the proppant diameter • At the end of pumping the proppant reaches only that part which has a width at least 2-3 times the proppant diameter • Propped length less than hydraulic length

35. Width ratio criterion • Considering material coordinate, • Accounting for fluid loss • Calculate ratio of (Dry width) to (Dynamic width) • Criterion: cannot exceed critical value (about 0.5)

36. Net Pressure Prediction (PKN) • Net pressure is proportional to width • Width from width equation (PKN) • Convert it to pn • Basic uses: • Feedback to height containment • Hydraulic horsepower calculation

37. Hydraulic Horsepower Energy: (Power)  (Time) Power = (Pumping Pressure) (Injection rate) (Pumping Pressure) = Minimum Stress + Net Pressure + Friction Losses - Hydrostatic Pressure Friction Losses : in tubulars, through perforations and possibly in near wellbore tortuous flow path

38. On-site Tuning of Design During Job Execution

39. Main Tasks During Execution • Zonal Isolation, Cement Integrity • Perforation strategy • Pumping through tubing, casing, both • Safety considerations: wellhead, casing, tubing • Formation breakdown and Step rate test • Calibration test (Minifrac) • Pad and Proppant schedule tuning • Pumping • Monitoring: Tip screenout - near-well/well screenout • Flush • Forced closure • Cleanup

40. Perforation and Execution Strategy • For thin layer: Perforate the whole interval • For thick or multilayer formation • Danger: non uniform coverage • Solution: Ball sealers, Limited entry or Staged • Limited entry • Few perforations in small groups • High perforation friction loss • Uniform coverage • Staged (from bottom to top)

41. 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

42. Introducing… HF2DPKN

43. Input Parameters • Proppant mass for (two wings), lbm • This is the single most important decision variable of the design procedure • Sp gravity of proppant material (from 2.6 to 3.5) • Porosity of proppant pack (e.g. 0.35) • Proppant pack permeability, md • One of the most important design parameters. Retained permeability including fluid residue and closure stress effects, might be reduced by a factor as large as 10 in case of non-Darcy flow in the frac Realistic proppant pack permeability would be in the range from 10,000 to 100,000 md for in-situ flow conditions. Values provided by manufacturers such, as 500,000 md for a “high strength” proppant should be considered with caution. • Max prop diameter, Dpmax, inch • From mesh size, for 20/40 mesh sand it is 0.035 in.

44. Input Parameters cont'd • Formation permeability, md • Permeable (leakoff) thickness, ft • Wellbore Radius, ft • Well drainage radius, ft • Needed for optimum design. (Do not underestimate the importance of this parameter!) • Pre-treatment skin factor • Can be set zero, it does not influence the design. It affects only the "folds of increase" in productivity, because it is used as basis. • Fracture height, ft • Usually greater than the permeable height. One of the most critical design parameters. Might come from lithology information, or can be adjusted iteratively related to the frac length. • Plane strain modulus, E' (psi) • Hard rock: about 106 psi, soft rock 105 psi or less.

45. Input Parameters cont'd • Slurry injection rate (two wings, liq+ prop), bpm • Rheology, K' (lbf - secn'/ft2) • Rheology, n' • Leakoff coefficient in permeable layer, ft/min0.5 • The leakoff coefficient outside the permeable layer is considered zero. If the frac height to permeable layer ratio is high, the apparent leakoff coefficient calculated from this input will be much lower than the input for this parameter. If the leakoff is significant outside the net pay, you may want to adjust this parameter when you adjust fracture height. • Spurt loss coefficient, Sp, gal/ft2 • The spurt loss in the permeable layer. Outside the permeable layer the spurt loss is considered zero. See the remark above.

46. Input Parameters, cont'd • Max possible added proppant concentration, lbm/gallon fluid (ppga) • The most important equipment constraint. Some current mixers can provide more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maximum technically possible concentration. • Multiply optimum length by factor • This design parameter can be used for sub-optimal design. Play! • Multiply pad by factor • Play (if necessary)! • (More input for TSO, Cont Damage Mech, etc.)

47. Summary • Keep in mind the goals • Allocate resources according to significance • Realize need for compromise: • Limited data • Limited understanding of physics • Sensitivity to the uncertainty in data • Find the optimum complexity of model • Do sensitivity analysis • Make decisions top - down

48. Computer Exercise 2-1: Medium perm design example

49. Computer Exercise 2-2: Tight gas design example

50. Computer Exercise 2-3: High perm Frac&pack example