3. Pressure Transient Analysis (1)
• General production/injection tests
– Static reservoir properties only (do not change with time)
• Much larger field of testing than mini-frac analysis
• Goals of PTA
– Initial pressure
– Permeability
– Static Fracture properties
3
4. Pressure Transient Analysis (2)
• Why not use it in mini-frac analysis ?
– Past: New flow regimes to consider
– Special cases not handled
• PDL, HRTS, tip extension
– Today: No significant issues
4
5. PTA Approach - Assume Radial Flow
• Drawdown
• Build-up
C
td
Pd
t
tCP
)(
)(
...)ln(
C
td
Pd
t
tt
tt
t
tCP
er
er
p
p
er
er
)(
)(
...)ln(
ter is the Agarwal equivalent time
with a radial basis function
1 - Drawdown
2 - Build-up
5
10. Early Time Slope = 0.5
Late Time Slope = -0.5
Middle Time = Variable
-½½
Plot hinders flow regime
identification process
DT log-log
derivative plot
td
Pd
t
)(
td
10
Linear Flow Analytical
Solution Case
Holistic Method
11. Even though radial basis
function used there is no
great distortion for linear
flow
That is why radial basis
function is used almost
exclusively in PTA
½
½
Linear Flow Analytical
Solution Case
Bourdet log-log
derivative plot
td
11
PTA Method
12. Mini-Frac in Oilsands/Caprocks
• Goals
– Determine closure stress
• Pump-in/Fall-off tests only
• Unique features to oilsands/caprock testing
– Multi-Zone
– Multi-Cycle
• Attempt to get repeatability within a zone
12
14. Mini-Frac Theory
• Nolte (1979)
– The first rigorous approach to mini-frac analysis
– Came up with ‘G Time’ concept
• Applies during a fall-off and while a fracture is open
• Generalized to ‘Nolte Flow’
p
d
t
t
t
14
)()0( 1 dtGCpDTpPDP
1)1(
3
16
)( 5.15.1
ddd tttG
15. Traditional G Function Method
• Traditional interpretation
• Go right to ‘special plots’
15
16. First Attempts at Closure Picks
Deviation from straight line is closure
as a new post-closure flow regime begins
16
17. PTA Based Method
• Recent interpretation technique from 2011 to the
present
17
18. Early Time Slope = 1
Late Time Slope = 1.5
1/1
3/2
Nolte Flow Analytical
Solution Case
Bourdet log-log
derivative plot
-1/2
0
td
18
PTA Method
19. Example 1 - Constant Leak-off Case
• Tight Oil Well (not oilsand)
• From SPE 160169
– Reappraisal of the G Time Concept in Mini-Frac
Analysis
19
20. pfoc = 8400 kPa
Combination G
Function plot
20
Holistic Method – Plot 1
21. Cross over of ‘Middle’
and ‘Late’ ½ Slope
Delta Time = 0.28
Days
pfoc = 8300 kPa
½
½
-½
DT log-log
derivative plot
21
Holistic Method – Plot 2
25. Example 2 - Tip Extension
• From SPE 107877
– Holistic Fracture Diagnostics:
Consistent Interpretation of Prefac Injection Tests
Using Multiple Analysis Methods
25
26. Ever increasing GdP/dG
And no flattening of dP/dG
indicate fracture may not
have closed
Combination G
Function plot
26
Holistic Method – Plot 1
28. Late time unit slope
No ¼ slope so no
bilinear flow
Apparent ¼ slope in ‘DT
derivative’ is artifact of
not using the Bourdet
derivative
What causes late time
unit slope?
It is not Nolte Flow
1/1
-1/1
Bourdet log-log
derivative plot
With PPD
28
PTA Method
29. 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
29
PTA Method
30. Approximate end of constant slope
Starting to see the true value of the outer
permeability
Constant slope not seen if perm contrast <100
Kouter=0.001 md
Kinner=0.1 md
Kinner=1.0 md
Kinner=10 md
Kinner=0.01 md
30
DT Normalized Bourdet Derivative
31. Nolte Flow/Formation Linear Flow
Composite Permeability Concept
for a Vertical Well
Kinner
High Permeability
Due to influence of
fracture
Kouter
Fracture
31
32. Example 3 - Tip Extension
• Deep Oilsand Formation
– High permeability
– High viscosity fluid
32
33. Ever increasing GdP/dG
And no flattening of dP/dG
indicate fracture may not
have closed
Combination G
Function plot
33
Holistic Method – Plot 1
34. 1/4
End of ½ slope at DT=0.00038 days
Ever increasing derivative at end indicates
fracture may not have closed (holistic theory)
½
34
DT log-log
derivative plot
Holistic Method – Plot 2
35. -¾ slope
Slope between
-½ and -3/2
End Fracture Linear
Flow at DT=0.0075 days
½
1/1
Bourdet log-log
derivative plot
With PPD
35
PTA Method
36. Bourdet derivative and
specialized derivative
function
1/DT * dDP/dTer
Giving zero slope
when Bourdet
Derivative has unit
slope
End of Unit Slope for Bourdet
Derivative
At DT=0.025 days
Latest time fracture may be open is
at DT=0.025 days
0
1/1
36
DT Normalized
Bourdet Derivative
37. Earliest possible closure time
End fracture linear flow
DT=0.0075 days
Fracture not closed yet
according to Holistic theoryLatest possible closure time
composite permeability theory
DT=0.025 days
In oilsands allowable Maximum
Operating Pressure (MOP) for thermal
projects is directly related to closure
pressure of the cap rocks
37
Comparative Closure Picks
38. Example 4 – G*dp/dG Overreliance
• McMurray Oilsand
– High permeability
– High viscosity
38
41. Ambiguous as no Nolte Flow
Some analysts would pick
closure at the blue circles
G = 0.95
P = 1600 kPa
Gradient = 13.4 kPa/m
41
Combination G
Function plot
Holistic Method – Plot 1
42. ½
End ¼ slope line
DT= 0.007 days
P = 1503 kPaa
Gradient = 12.6 kPaa/m
1/4
42
DT log-log
derivative plot
Holistic Method – Plot 2
43. End Linear DT=0.0008 days
P = 2040 kPaa
Gradient = 17.1 kPaa/m
½
-½
-½
43
Bourdet log-log
derivative plot
With PPD
PTA Method
44. Conclusions
• G-Function analysis of mini-fracs can give
erroneous results (or no results)
• PTA is a more universal analysis method
• PTA method identifies two new flow regimes
– Pre-closure linear flow
– Composite permeability
• Tip extension as conventionally defined does not
occur
44
