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PTA Based After Closure Analysis Gives
Insight to Permeability and SRV Behavior
Bob Bachman, CGG - Taurus Reservoir Solutions
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
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
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 TimeSPE 174454
Radial Composite – Bourdet Derivative
0 – 1 – 0 Slope4
Vertical WellLinear FlowComposite Permeability Concept
Kinner
High Permeability
Due to Influence of Fracture
Kouter
Static Fracture
SPE 174454
Linear Composite – Bourdet Derivative
½ – 1 – ½ Slope
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Vertical WellNolte FlowComposite 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
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SPE 163825
Tip Extension ?
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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
Tip Extension ?
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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
-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
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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
Composite Permeability
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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
1) ConclusionsStimulated 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
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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
Radial Flow during a Buildup Bourdet log-log Derivative Plot
Permeability Decreasing as position of zero slope line moves up
0
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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 TestsExample - Sequential Injection/Fall-off Tests
Formation Linear Flow/Radial Flow during a BU Bourdet log-log Derivative Plot
15
Decreasing xf*k0.5
As position of ½ slope line moves up and to the left
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Formation Linear Flow/Radial Flow during a BU Bourdet log-log Derivative Plot
Even if no radial flow one can still calculate maximum permeability
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Formation Linear Flow/Radial Flow during a BU Bourdet log-log Derivative Plot
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3/2 1/1
0
Definitely closed and rolling over towards linear flow/radial flowPermeability likely similar to Well Duvernay #2
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-½
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Duvernay Oil Wells – Liquid Prod Profiles
Duvernay Oil Wells – Liquid Prod Profiles
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2) ConclusionsOverlaying 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
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3) After Closure AnalysisSparky Oil Well - Alberta• Examine different extrapolation techniques for Pi
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End HRTS, DT=0.09125, G=6.62BHP=19,098, Grad=14.0 (Closure)
Combination
G Function Plot
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½
-3/2
PTA based Bourdet Derivative
with Primary Pressure Derivative
(PPD) Plot
0
1) End HRTS, DT=0.09125, G=6.62BHP=19,098, Grad=14.0 (Closure)2) End Linear Flow, DT=1.02439, G=25.563) Radial Flow at endBHP=14,181, Grad=10.4
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-2/1
Linear Soliman/Craig
ACA Plot
0
ExtrapolationP*=12,100, Grad= 8.9 kPa/m
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Linear Superposition
Time Plot
0
ExtrapolationP*=12,100, Grad= 8.9 kPa/m
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Radial Soliman/Craig
ACA Plot
0
ExtrapolationP*=12,900, Grad= 9.5 kPa/m
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Radial Superposition
Time Plot
0
ExtrapolationP*=12,900, Grad= 9.5 kPa/m
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3) ConclusionsLinear/Radial Superposition Time PlotsGeneralized 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
Thank you
Questions?
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Radial Superposition Time (tsr)as pumping time becomes small1 Injection Period + 1 Fall-off
• 𝑡𝑠𝑟 = ln(𝑡𝑝+∆𝑡
∆𝑡) = ln(1 +
𝑡𝑝
∆𝑡) =
𝑡𝑝
∆𝑡-1
2(𝑡𝑝
∆𝑡) 2+ …
• lim𝑡𝑝→0
𝑡𝑠𝑟 = lim𝑡𝑝→0
𝑡𝑝
∆𝑡−
1
2(𝑡𝑝
∆𝑡) 2+ … =
𝑡𝑝
∆𝑡
• For radial flow with short pumping time a plot of Pressure versus 1/Dtor 1/(tp + Dt) is equivalent to a Horner Plot. This is the Radial Soliman/Craig plot
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