1. Hydraulic Fracturing. Short Course,. Texas A&M University
Hydraulic Fracturing Short Course, Texas A&M University College Station Fracture Dimensions Peter P. Valkó
Fracture Dimensions 2004

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

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 1 i f
pad x 1

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

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' = psi
Power Law rheology:
K' = lbf/(ft2 sec0.63) and n' = 0.63
Leakoff coefficient (w.r.t. perm zone) CL,p = 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
Proppant pack permeability, md 60,000
Formation permeability, md 0.5
Permeable (leakoff, net) thickness, ft 45
Well Radius, ft
Well drainage radius, ft
Pre-treatment skin factor 0
Fracture height, ft
Plane strain modulus, E’ , psi ×106
Slurry injection rate (2 wings, liq+prop), bpm 30
Rheology, K' (lbf/ft2)×sn'
Rheology, n'
Leakoff coefficient in perm layer, ft/min
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
Dimensionless PI, JDact
Dimensionless fracture cond, CfD 1.6
Half length, xf, ft
Propped width, wp, inch
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 = 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 = s = 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. This is kg proppant in 1 m3 of slurry
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. Ex_2 Proppant Roadmap 35 9 30 8 25 7 6 20 Liquid injection rate, bpm5 10 15 20 25 30 35 40
Pumping time, min
Liquid injection rate, bpm 1 2 3 4 6 7 8 9
ca, lbm prop added to
gallon liquid

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
Fracture Dimensions 2004

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 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