1. PTA Based After Closure Analysis Gives
Insight to Permeability and SRV Behavior
Bob Bachman, CGG - Taurus Reservoir Solutions

2. Outline
1. Can we see SRV like behavior in a DFIT Test ?
2. Overlaying DFITS from multiple wells
• Can we relate production data to DFIT’s ?
3. After Closure Analysis – Do we need specialized plots ?
2

3. 1) Stimulated Reservoir Volume (SRV)
Characteristics
• Zone of Increase Permeability around Fracture
• SRV is retained permeability after a fracture job
• Should be visible during a DFIT
• If Rate High enough ?!
• Late Time
• Not Pressure Dependent Leak-off (PDL)
• PDL behavior disappears during the closure process
• Early Time
3

4. Rate Normalized
Bourdet Derivative
Kinner=0.1 md
Kinner=1.0 md
Kinner=10 md
Kouter=0.001 md
End of unit slope
Starting to see the
true value of the
outer permeability
1/1
Kinner
Kouter
Kinner=0.01 md
Radial Flow – Composite Permeability
Log Deriv DP over Q versus Delta Time
SPE 174454
Radial Composite – Bourdet Derivative
0 – 1 – 0 Slope
4

5. Vertical Well
Linear Flow
Composite Permeability Concept
Kinner
High Permeability
Due to Influence of Fracture
Kouter
Static Fracture
SPE 174454
Linear Composite – Bourdet Derivative
½ – 1 – ½ Slope
5

6. Vertical Well
Nolte Flow
Composite Permeability Concept
Kinner
High Permeability
Due to Influence of Fracture
Kouter
Open Fracture
SPE 174454
Nolte Composite – Bourdet Derivative
3/2 – 1 – 3/2 Slope
6

7. SPE 163825
Tip Extension ?
7
Combination
G Function Plot
Flow Period DT (minutes) Rate (m3/min) Rate (stb/min)
1 0.75 0.30 1.88
2 0.30 0.50 3.14
3 0.20 0.41 2.59
4 4.13 0.40 2.53
5 14.60 0.50 3.18
Total 19.98

8. Tip Extension ?
8
DT Derivative Plot
SPE 163825
Flow Period DT (minutes) Rate (m3/min) Rate (stb/min)
1 0.75 0.30 1.88
2 0.30 0.50 3.14
3 0.20 0.41 2.59
4 4.13 0.40 2.53
5 14.60 0.50 3.18
Total 19.98
1/4

9. -½
3/2
1/1
-1/1
End Nolte Flow at 1.0 days
Composite Permeability at End
This is what an SRV looks like
9
SPE 163825
Flow Period DT (minutes) Rate (m3/min) Rate (stb/min)
1 0.75 0.30 1.88
2 0.30 0.50 3.14
3 0.20 0.41 2.59
4 4.13 0.40 2.53
5 14.60 0.50 3.18
Total 19.98

10. Composite Permeability
10
DT Derivative Plot
SPE 163825
Flow Period DT (minutes) Rate (m3/min) Rate (stb/min)
1 0.75 0.30 1.88
2 0.30 0.50 3.14
3 0.20 0.41 2.59
4 4.13 0.40 2.53
5 14.60 0.50 3.18
Total 19.98
0

11. 1) Conclusions
Stimulated Reservoir Volume (SRV) Characteristics
• Look for late time unit slopes on Bourdet derivative
• Tip Extension at late time does not happen
• Replaced with ‘Composite Permeability’ Idea
11

12. 2) Overlaying DFITS from Multiple Wells
• Background PTA overlay theory
• Single Well/Multiple Tests
• Can we compare wells based on DFITS ?
• Multi Well/Single Tests
12

13. Radial Flow during a Buildup Bourdet log-log
Derivative Plot
Permeability Decreasing as
position of zero slope line
moves up
0
13

14. Permeability Decreasing as
position of zero slope line
moves up
Divide Derivative by Rate
Prior to Shut-in to Compare
different tests
14
Comparing Different Tests
Example - Sequential Injection/Fall-off Tests

15. Formation Linear Flow/Radial Flow during a BU
Bourdet log-log Derivative Plot
15

16. Decreasing xf*k0.5
As position of ½ slope
line moves up and to
the left
16
Formation Linear Flow/Radial Flow during a BU
Bourdet log-log Derivative Plot

17. Even if no radial flow
one can still calculate
maximum permeability
17
Formation Linear Flow/Radial Flow during a BU
Bourdet log-log Derivative Plot

18. 18
3/2 1/1

19. 0
Definitely closed and rolling over
towards linear flow/radial flow
Permeability likely similar to Well
Duvernay #2
19

20. -½
20
Duvernay Oil Wells – Liquid Prod Profiles

21. Duvernay Oil Wells – Liquid Prod Profiles
21

22. 2) Conclusions
Overlaying DFITS from Multiple wells
• PTA based Mini-frac interpretations have advantages
• Rate normalized derivative plot overlays are key
• Allows direct comparison of tests from different wells
• Useful even when complex flow regimes occur
• Permeability can be ‘estimated’ even when a rigorous analysis is not possible
• Example shows that 2 wells with similar estimated permeability have
similar production behavior
22

23. 3) After Closure Analysis
Sparky Oil Well - Alberta
• Examine different extrapolation techniques for Pi
23

24. End HRTS, DT=0.09125, G=6.62
BHP=19,098, Grad=14.0 (Closure)
Combination
G Function Plot
24

25. ½
-3/2
PTA based Bourdet Derivative
with Primary Pressure Derivative
(PPD) Plot
0
1) End HRTS, DT=0.09125, G=6.62
BHP=19,098, Grad=14.0 (Closure)
2) End Linear Flow, DT=1.02439, G=25.56
3) Radial Flow at end
BHP=14,181, Grad=10.4
25
-2/1

26. Linear Soliman/Craig
ACA Plot
0
Extrapolation
P*=12,100, Grad= 8.9 kPa/m
26

27. Linear Superposition
Time Plot
0
Extrapolation
P*=12,100, Grad= 8.9 kPa/m
27

28. Radial Soliman/Craig
ACA Plot
0
Extrapolation
P*=12,900, Grad= 9.5 kPa/m
28

29. Radial Superposition
Time Plot
0
Extrapolation
P*=12,900, Grad= 9.5 kPa/m
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30. 3) Conclusions
Linear/Radial Superposition Time Plots
Generalized ACA Plots
• Has been used in PTA Analysis for 50+ years
• Accounts for rate variations
• No ‘Impulse Assumption’
• Use with the derivative plot
• Why do we need specialized plots?
• PTA techniques only work when Shut-In times are short compared to
injection times ?! (Dake – “Practice of Reservoir Engineering”)
• This is INCORRECT
• PTA works on all time scales
• Specialized plots are not necessary
30

31. Thank you
Questions?
31

32. Radial Superposition Time (tsr)
as pumping time becomes small
1 Injection Period + 1 Fall-off
• 𝑡 𝑠𝑟 = ln(
𝑡 𝑝+∆𝑡
∆𝑡
) = ln(1 +
𝑡 𝑝
∆𝑡
) =
𝑡 𝑝
∆𝑡
-
1
2
(
𝑡 𝑝
∆𝑡
) 2+ …
• lim
𝑡 𝑝→0
𝑡 𝑠𝑟 = lim
𝑡 𝑝→0
𝑡 𝑝
∆𝑡
−
1
2
(
𝑡 𝑝
∆𝑡
) 2+ … =
𝑡 𝑝
∆𝑡
• For radial flow with short pumping time a plot of Pressure versus 1/Dt
or 1/(tp + Dt) is equivalent to a Horner Plot. This is the Radial
Soliman/Craig plot
32