1. Modeling, Monitoring, Post-Job Evaluation, Improvements
Hydraulic Fracturing Short Course, Texas A&M University College Station 2005
Modeling, Monitoring, Post-Job Evaluation, Improvements
Tamu Frac Modelling 2004

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

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

12. Fracture Toughness Criterion
Fluid flow in 2 D
Fluid loss according to local opening time
Propagation: Jumps
Stress Intensity Factor KI > KIC ? pn
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. Step rate test Propagation pressure Two straight lines
Injection rate
Bottomhole pressure
Propagation pressure
Two straight lines

17. Fall-off (minifrac) Bottomhole pressure Injection rate Injection rate
3 ISIP
4 Closure
5 Reopening
6 Forced closure
7 Pseudo steady state
8 Rebound 1 5 2 3 4 8 6
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 where F[a, b; c; z] is the Hypergeometric 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. Shlyapobersky assumption
No spurt-loss bN mN
Ae from intercept pw g
g=0

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

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
Time, min
BH Injection rate, bpm
BH Pressure, psi
Include into inj volume
Include into g-func fit
0.0
9.9 1
1.0
21.8
9.9
0.0 1
21.95
22.15

28. Output Slope, psi -4417 Intercept, psi 13151 Injected volume, gallon
9044
Frac radius, ft
39.60
Average width, inch
Fluid efficiency
Apparent leakoff coefficient (for total area), ft/min^0.5
Leakoff coefficient in permeable layer, ft/min^0.5

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. Normal frac propagation
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. Sc Sb Ir Tracer log

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

37. Pressure Match with 3D Simulation

38. 3D Simulation FracCADE Flow Capacity Profiles 50 100 150 200 250
Texaco E&P
OCS-G #D-12
Actual
Flow Capacity Profiles 50
100
150
200
250
Fracture Half-Length - ft
0.05
0.10
0.15
0.20
0.25
Propped Width - in
1000
2000
3000
4000
5000
Conductivity (Kfw) - md.ft
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. Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342
smax
From
overbalanced perforation
From
underbalanced perforation
Tamu Frac Modelling 2004

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 Reynolds Number
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

50. SPE 90195
Optimum FractureTreatment Design Minimizes the Impact of Non-Darcy Flow Effects
Henry D. Lopez-Hernandez, SPE, Texas A&M University, Peter. P. Valko, SPE, Texas A&M University, Thai T. Pham, SPE, El Paso Production

51. Case Study: Reynolds number

52. Case Study: Proppant number

53. Case Study: Max possible JD

54. Case Study: Optimum frac length

55. Case Study: Optimum frac width

56. Summary Increasing role of evaluation
Integration of reservoir engineering, production engineering and treatment information
Cost matters
Expensive 3D model does not substitute thinking
Still what we want to do is increasing JD
Tamu Frac Modelling 2004