Pressure & Rate transient Analysis

1. Medhat (Med) Kamal
Emeritus Fellow
Society of Petroleum Engineers
Distinguished Lecturer Program
www.spe.org/dl
Pressure & Rate
Transient Analysis

2. 2018-2019
Transient Data have been Used since the1920’s
Johnston Well Tester
3 After SLB Oil Field Review

3. 2018-2019
Steady State Data Has Some Information
4
𝑞 =
0.00707 𝑘ℎ 𝑝𝑒 − 𝑝𝑤
𝜇 𝑙𝑛
𝑟𝑒
𝑟𝑤
+ 𝑠
Cannot separate flow capacity and skin

4. -1 0 1 2
Superposition Time Function
130
180
230
Pressure
[psi]
Pressure
change,
psi
Time, hr
0.1 1 10 100
2018-2019
Transient Data is Rich in Information
Slope m
Estimation of kh
Dp(1hr)=>skin
a
t
m
p
p wf
i +

=
− log








+
−
=
D s
r
c
k
m
hr
p
w
t
wf 8686
.
0
2275
.
3
log
)
1
( 2

kh
B
q
m

6
.
162
=
5 After CVX Well Testing School

5. 6
©Alain
C.
Gringarten
2017
6
2017
Well Testing Interpretation history
After A. Gringarten SPE ATWE Dubai 2014
0
100
200
300
400
500
600
700
Year
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
Number
of
publications
with
“well
testing”
Horizontal
wells
Electronic
gauges
Permanent
gauges
Hardware/Completion
MHF
IKVF
MDT
Multiple-fraced
horizontal wells
800
SPE
Oil price in 2015 $
One-Petro
Horner
Derivatives
Methodology
Type
Curve
Analysis
MDH MBH
Commercial
Software
Interpretation methods
IOC
Shell, Gulf Oil Corp,
The Atlantic Refining Co…)
UNIVERSITIES
Texas A&M, Stanford
Henry J. Ramey, et al.
SERVICE
Flopetrol
Schlumberger
NICHES
Stanford, Imperial,
Chevron, Shale
SEVERAL
Kappa,
ARCO, etc.
DEVELOPERS
GROUNDWATER
Theis (1935),
Jacob (1947),
Hantush (>1947)
Stehfest Single well
Deconvolution
Laplace
transform
Green’s
functions
Mathematical tools
Multiwell
Deconvolution
Pulse
Testing Numerical
Well
Testing
DFIT
Falloff
Testing
Multiphase
Testing
DDI
Numerical
Analysis

6. Pressure and Rate Transient Analysis
Discussion Topics:
1. Recent
developments in
characterizing
conventional and
unconventional
reservoirs
2. Practical use of
recent changes to
develop reservoir
models, their
advantages and
limitations
Desired Outcome:
• Knowledge of the new capabilities of using transient data
• Use of the new capabilities in reservoir management
Key Messages:
1. Transient data rich information source
2. Steady and continuous progress in
technology
3. Development of technology due to:
• Changes in types of reservoirs / their
stages of development
• New tools
• Interpretation technology
4. New developments are enhancing reservoir
management
2018-2019
7

7. Discussion Topics
2018-2019
8
 PTA & RTA Integration
 Unconventional Reservoirs
 Resources
 Characterization and Management
 Testing Under Multiphase Flow Conditions
 Average Reservoir Pressure
 Directional Permeability
 Numerical Well Testing
 Data Analytics and Machine Learning in Pressure
and Rate Transient Analysis

8. Rate Time (Production Data) Analysis
Fetkovich Composite Type Curves
 Applicable to both the transient part of the data and
the boundary dominated flow period
1E-4 1E-3 0.01 0.1 1 10
1E-3
0.01
0.1
1
Fetkovich type curve plot: qDd and QDd vs tDd
Analytical Empirical
transient decline
re/rw
b
∞
∞
10
10
1
0
0
1
2018-2019
After CVX Well Testing School
9

9. Pressure Transient Analysis versus
Production Data Analysis
10
(typically geological boundaries)
(dynamic boundaries)
Production Data Analysis
(PDA)
2018-2019
After CVX Well Testing School

10. PTA-PDA (RTA) Workflow
11
QA/QC data
• Measurement methods & conditions
• Reliability of data
• Synchronization of pressure and rate
Pressure Transient Analysis
• Overlay log-log plots of all shut-in
periods
• Consistent transient behavior?
Change of properties? Boundaries?
• Analytical model match
• If needed for complex reservoirs,
numerical model match
Forecast well
performance
Report
Production Data
Analysis
• Review rate data accuracy
• If surface gauge, convert
pressure to bottom-hole
condition
• Boundaries detected?
• Use PTA results and regular
shape to estimate well drainage
area (analytical)
• If needed, transfer PTA
numerical model to match long-
term data
• Calculate average pressure
trend
•Sensitivity study
•Work-over suggestion
2018-2019
After CVX Well Testing School

11. Unconventional Resources
2018-2019
12

12. Drawdown Behavior of Multiple Transverse
Fractured Well (MTFW)
10,000-Year Transients
2018-2019
After B. Song SPE 144031
13

13. Management of Unconventional
Resources
2018-2019
14
 Three Major Items:
Diagnostic Fracture Injection Test
(DFIT)
Decline Curve Analysis*
Rate Transient Analysis*
*Usually done on groups of wells

14. DFIT - Schematic of Fracture Injection Test
2018-2019
15

15. Management of Unconventional
Resources
2018-2019
16
 Decline Curve Analysis
Arps Equations (Constant BHP, Boundary-
Dominated Flow)
Power-law Exponential (Log-Log Linear then
constant D Parameter)
Stretched Exponential Function (Transient not
BDF, EUR is bounded)
Duong Model (Practically Long Linear Flow)
Weibull Growth Model (More Physically
Appropriate)

16. Comparison of Field Flow Rate for DCA
Models – Example 1
2018-2019
After Mishra SPE 161092
17

17. Comparison of Field Flow Rate for DCA
Models – Example 2
2018-2019
After Mishra SPE 161092
18

18. Management of Unconventional
Resources
2018-2019
19
 Uncertainty Assessment
Alternative Models Fit Data
Model Averaging
Generalized Likelihood / Uncertainty
Estimate (GLUE)
Maximum Likelihood Bayesian Model
Averaging

19. Management of Unconventional
Resources
2018-2019
20
 Rate Transient Analysis
Linear Flow Diagnostics
Stimulated Reservoir Volume (SRV) Flow
Diagnostics
History Matching
Performance Prediction and Estimated
Ultimate Recovery (EUR)

20. Management of Unconventional
Resources
2018-2019
21
 Workflow
 Accessing Data
 Quality Control
 Diagnostic Analysis and
Well Grouping
 Representative Wells
 DCA / RTA & Production
Forecast of
Representative Wells
 Generalizing
Representative Wells
Forecast to Other Wells

21. Analysis of Transient Tests Under
Multiphase Flow Conditions
22
 Effective Oil Permeability
 Effective Water Permeability
 Relative Permeability Ratio
mh
μ
B
q
k
w
w
w
w
6
.
162
=
w
o
k
k
mh
μ
B
q
k
o
o
o
o
6
.
162
=
-5 -4 -3 -2 -1
Superposition Time
1000
1200
1400
Pressure
[psia]
Semi-Log plot: p [psia] vs Superposition Time
IARF
Time
Pressure
1E-4 1E-3 0.01 0.1 1 10 100
Time [hr]
1
10
100
Pressure
[psi]
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
IARF
Time
Pressure
Semi-Log Plot
Log-Log Plot
2018-2019
After Kamal & Pan SPE 113903
22

22. Water Saturation Curve
23
 From relative permeability curves, calculate ko/kw vs. Sw
 Use ko/kw value from well test analysis to calculate value of water
saturation
2018-2019
After Kamal & Pan SPE 113903
23

23. Relative Permeability Curve
24
 Use saturation of dominate phase to calculate relative permeability of that
phase
 Calculate absolute permeability or
0
0.2
0.4
0.6
0.8
1
0.0 0.2 0.4 0.6 0.8 1.0
K
ro
and
K
rw
Sw
Kro and Krw vs. Sw
Kro
Krw
rw
w
k
k
k =
ro
o
k
k
k =
2018-2019
After M. Kamal SPE 113903
24

24. Typhoon Field Tests
25
2018-2019
After Kamal & Pan 113903
25
3000
4000
5000
6000
2500
5000
2500
5000
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2007
Jan Feb
2008
Pressure [psia], Gas Rate [Mscf/D], Liquid Rate [STB/D] vs Time [ToD]
BU#2
BU#3
BU#22
BU#6
BHP = 5,228
4000
BHP = 6,261
Pressure - psia
Gas rate – Mscf/D
Oil rate – STB/D
Time
2000
4500
Production History
P>Pb P<Pb

25. Typhoon Field Buildup Data
26
2018-2019
After Kamal & Pan 113903
26
1E-4 1E-3 0.01 0.1 1 10 100 1000
10
100
1000
build-up #2
build-up #3
build-up #6
build-up #22 (ref)
Log-Log plot: dp and dp' normalized [psi] vs dt
Time - hour
dP
–
psi,
dP/dlnt
ko
eff when P>Pb
ko
eff when P<Pb
BU#3
Keff Kr abs K abs K
md md md
oil 73.60 0.56 130 130
gas 2.44 0.02 123
ko/kg 30.16
Sg 0.11 0
BU#22

26. 2018-2019
After A. Dastan SPE 159568
27
Why is Accurate Important?
p
p < p*
p > p*

27. Case Study: The Agbami Field
2018-2019
After A. Dastan SPE 159568
28
❑ Nigeria, Deep Water, ~800
MM recoverable bbls.
❑ Crestal gas and peripheral
water injection.
❑ Average pressure calculated
for each well to:.
❑ Help with the calibration
of the model.
❑ Improve forecasting and
optimization.

28. Calculation of Average Pressure Type
Curve in the Agbami Field
2018-2019
After A. Dastan SPE 159568
29
Length
Length
▪ Use simulator to
calculate pave for a
particular drainage
shape.
▪ pave calculated at the
beginning of buildup
Step 1: Calculate Drainage Shape & Area
Step 2: Transfer the model to simulator
Step 3: Simulate to obtain p and pbar.

29. 2018-2019
After A. Dastan SPE 159568
30
Remarks:
- pave ~ p* for small
tp
- pave significantly
different than p* for
long tp
-Type curves can
be used to define
shape factors.
Type Curve for a Specific Well and
Drainage Area Shape

30. 2018-2019
After A. Dastan SPE 159568
31
Change of Average Pressure Over Time
in the Agbami Field
The decrease in average
pressure slows down due to
injection wells.
As the cumulative production
time increases, the deviation
of average pressure from p*
also increases.

31. Calculation of Directional Permeability from
Transient Tests
Requirements
• At least three sets of interwell transient tests at
different azimuth angels
• Individual pair of interwell test (interference/pulse)
has been analyzed
How
• Mathematical matrix operation
kmax
q
kmin
Well 1
(0,0)
Well 2
(x1,y1)
Well 3
(x2,y2)
Well 4
(x3,y3)
y
x
r1
r2
r3
( )   j
ij
eff
xy
yy
xx
i R
M
k
k
k
k
=
k




=










−1
2

2
xy
yy
xx
eff
k
k
k
=
k −

Well location
coordinate matrix
Individual interwell test
analysis result tensor
( ) ( )
( ) ( )







 −
=





 +
−
−
+





 +
−
+
+
xy
xx
xy
yy
xx
yy
xx
xy
yy
xx
yy
xx
k
k
k
k
k
k
k
k
=
k
k
k
k
k
k
=
k
max
2
2
min
2
2
max
arctan
4
2
1
4
2
1
q
2018-2019
After Y. Pan SPE 181437
32

32. Field Application
2018-2019
After Y. Pan SPE 181437
33
Korolev Field
• Carbonate oil field, Kazakhstan
• Pilot to investigate IOR
opportunities
Transient Data
• Effective surveillance plan in
place
• Well designed and executed
well tests
• All 12 wells with single-well
buildup tests
• Extensive interwell transient
tests
• Wide range of diffusivity (k/Φ)
P-6
P-7
P-11
P-2
P-1
P-3
P-8
P-5
P-9
P-10
P-12
P-4
k/ > 1000 md
500< k/ <1000 md
100< k/ <500 md
k/ < 100 md

33. P-1
P-11
P-5
P-7
P-4
P-9
P-3
P-2
P-12
P-10
P-6
P-8
Korolev Field
Directional Permeability Map
• Directional permeabilities are
calculated at well locations with at
least three interwell transient tests at
different azimuth angles
• They are in well-spacing scale
Dominant Fracture Trend
• Geological interpretive model of
fractures parallel and perpendicular
to the strike of depositional margin of
carbonate buildup
Effective Fracture Orientations
• Interpreted from borehole image
logs
• Rose diagrams show strike of
effective fractures
5%
5%
kmax/kmin from interwell tests
fracture strike from image logs
Interpreted dominant fracture trend
2018-2019
After Y. Pan SPE 181437
34

34. Select grid size
History match with WT data
Well test analysis
0.01 0.1 1 10 100
100
1000
Log-Log plot: dp and dp' [psi] vs dt [hr]
Well test information
9000
10000
11000
0 100 200 300
0
625
History plot (Pressure [psia], Liquid Rate [STB/D] vs Time [hr])
Extract test influence area
Full-field simulation model
Update full-field model
Verify production history
Update coarse full-field model
Numerical Well Testing
Tengiz Field Example
After M. Kamal SPE 95905
35

35. Machine Learning Based Pressure-Rate Deconvolution
 Features are handcrafted based on analytical pressure transient solutions.
 Model is trained on multirate q-p data, then pressure is deconvolved by
feeding a constant rate input to the trained model.
The machine learning approach was shown to identify the reservoir
models successfully from the multirate data, and it outperformed
conventional industry methods developed by von Schroeter et al. and
Levitan et al. when noise or outliers were contained in the data for
deconvolution
Deconvolution
2018-2019
After Liu and Horne 2012, Tian and Horne 2015, and Tian 2018
36

36. Machine Learning Based Well Productivity Estimation
 Train on q-p data → virtual shut-in → predict BHP → well productivity
index PI60
 The calculation is performed on real-time data by the operator.
9/30/12 5/24/17
Red: PI60 prediction by Machine Learning
Blue:PI60 calculated by PTA of actual shut-in data
Machine learning based productivity index (PI) calculation offsets need for shut-
ins. PI calculated by machine learning (red) captures well performance trends
quite well compared to actual shut-ins (blue).
After Sankaran et al. 2017
37 2028-2019

37. Summary
2018-2019
38
 Transient data is rich in information about the
reservoir and wells
 Developments in this area of technology started
in the 1920’s and continue at increasing pace
until now.
 Developments continue to address changes in
produced reservoir types and well completions
and use advancements in measurement tools
and computer technology

38. Summary
2018-2019
39
 Key developments in use of transient data
include:
 Integration of PTA and RTA
 Characterization of Unconventional Reservoirs
 Analysis under Multiphase Flow Conditions
 Average Reservoir Pressure
 Directional Permeability
 Numerical Well Testing
 Reservoir characterization from transient
(dynamic) data should be an integral part of field
management

39. Society of Petroleum Engineers
Distinguished Lecturer Program
www.spe.org/dl 40
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