Capacitance Resistance Model Update
Larry W. Lake
The University of Texas at Austin
Outline
• Introduction
• The Model
• Validation
• Updates of Technology
Prior and Current Work
• Belkis Refunjol
• Jorge S’Antana Pizarro (Petrobros)
• Isolda Griffiths (Shell)
• Alejandro Albertoni (Nytec)
• Pablo Gentil (Galp)
• Ali Al-Yousif (Aramco)
• Danial Kaviani (TAMU)
• Thang Bui (TAMU)
• Xming Liang
• Morteza Sayarpour (Chevron)
• Sami Kaswas (ExxonMobil)
• Daniel Weber (Shell)
• Tom Edgar, ChE
• Leon Lasdon, IROM
• Tad Patzek, PGE
• Alireza Mollaei, PGE
• Anh Phoung Nguyen, ChE
• Fei Cao, PGE
• Wenle Wang, PGE
• Jong Suk Kim, ChE
Past Present
What others say about modeling…
• Bratvold and Bickel…Two types
– Verisimilitude- the appearance of reality
– Cogent- enables decisions
• Haldorsen….the progress of ideas
– Youth= simple, naïve
– Adolescence=complex, naïve
– Middle age=complex, sophisticated
– Maturity= simple, sophisticated
Hypothesis
• Characteristics of a reservoir can be
inferred from analyzing production
and injection data only
Boundary Conditions
• Must be injection project
• Rates are most abundant data type
• Rates must vary
• No geologic model required
• Input, output in a spreadsheet
Outline
• Introduction
• The Model
• Validation
• Updates of technology
q(t) q(t0)e(
t t0
) I(t) 1 e
(t t0
)
ctVp
pwf,t pwf,0
t t0
1 e(
t t0
)
CRM Continuity Equation
ctVp
dp
dt i(t) q(t)
dq(t)
dt
1
q(t)
1
i(t) J
dpwf
dt
ctVp
J
Ordinary Differential Equation:
Continuity:
Solution:
q(t) i(t)
BHP Injection Primary
q(t) J p pwf
Production Rate:
Signal Response
Production response to an injection signal
Connectivity
τij = 1 day
fij = 0%
Connectivity
τij = 1 day
fij = 100%
Connectivity
τij = 6 days
fij = 100%
Connectivity
ij = 6 days
fij = 65%
Capacitance-Resistance Model (CRMT)
k
tt
kk Ieeqq
11
q(t) I(t) J
Vc pt
Time constant
f2j
f6j
f4j
f3j
f5j
jf1j
f11 f12
f13
I6
I1
I2
I3
I4 I5
qj(t)
Capacitance-Resistance Model (CRMP)
ik
n
i
ij
tt
kjjk Ifeeqqi
jj
1
1 1
j
pt
jJ
Vc
11
pn
j
ijf
Time constant
Inter-well connectivity or gain
Drainage volume
around a producer
Capacitance-Resistance Model (CRMIP)
Ii(t)
qj(t)
fij
ij
ij
pt
ijJ
Vc
11
pn
j
ijf
Time constant
Inter-well connectivity or gain
i
ijij
n
i
ikij
tt
kijjk Ifeeqq1
1 1
Gains >0.5
Mature West Texas Waterflood
Injector
Producer
Gains > 0.5
Gains >0.4
Mature West Texas Waterflood
Injector
Producer
Gains >0.3
Mature West Texas Waterflood
Gains > 0.3 Injector
Producer
Gains >0.2
Mature West Texas Waterflood
Gains > 0.2
Injector
Producer
Outline
• Introduction
• The Model
• Validation
• Updates to technology
Validation
How do we scientifically validate
geoscience hypotheses?
Remember:
Characteristics of a reservoir can be inferred
from analyzing production and injection data
only
Recognizing testable hypotheses can be subtle and
requires practice. To do it, ask “how would one test this
hypothesis”.
– If the duck is lighter than this woman, then she is
a witch.
Validation
Field Injectant Independent Data Agree
Synfields Water Simulation Very well
Snyfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
SWCFU Water Anecdotal fractures Reasonably
NSF I Water Structure Well
NBDU Gas Tracer data Fairly well
Will. Basin Water Acoustic impedance Reasonably
SELU Water Oil in tank Maybe
Characteristics of a reservoir can be inferred from
analyzing production and injection data only
Outline
• Introduction
• The Model
• Validation
• Updates to Technology
Updates to Technology
• Input data screening (Cao, 2011)
• New graphical methods (Wang, 20110
• Integrated CRM (error intervals) (Kim, 2011)
• Extension to primary recovery (Nguyen, 2011)
• Extension to subsidence problem (Wang, 2011)
Possible Data Problems
• Missing flowing
pressures, flow rates
• Unexplained
discontinuous changes
• Inconsistencies with
rates, pressures
• Wrong water
production data
• Unknown operational
changes
0
500
1000
1500
2000
2500
3000
0 10 20 30 40 50 60 70 80 90pro
duct
ion r
ate
(rb/d
ay)
Time, month
Example 1
oil production
total production
water production
gas production
Data Issues Remedies
• Get to know data set
• Replace with averages
• Restart CRM
• Outlier detection
• Fill in blanks with CRM
Remove outliers
Maximize NPV of future oil recovery
Warm start
Gainfit
Remove
inactive wells Remove gains
based on distance
Remove small
gains
Gainfit #2 Calculate residuals
and replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residuals
and remove outliers Fracfit #2
Reservoir
model
Model Fit and Prediction Algorithm
~2.5 hrs
computation
time
Remove outliers
Maximize NPV of future oil recovery
Warm start
Gainfit
Remove
inactive wells Remove gains
based on distance
Remove small
gains
Gainfit #2 Calculate residuals
and replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residuals
and remove outliers Fracfit #2
Reservoir
model
Model Fit and Prediction Algorithm
<1 min
computation
time
Remove outliers
Maximize NPV of future oil recovery
Warm start
Gainfit
Remove
inactive wells Remove gains
based on distance
Remove small
gains
Gainfit #2 Calculate residuals
and replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residuals
and remove outliers Fracfit #2
Reservoir
model
Model Fit and Prediction Algorithm
<10 min
computation
time
Updates to Technology
• Input data screening (Cao, 2011)
• New graphical methods
• Integrated CRM (error intervals)
• Extension to primary recovery
• Extension to subsidence problem
Well connectivity for time interval 11/06/2006-
07/29/2007
P1
P2
P3
P4
P5
P6 P7
P8
P9
P10
P11
P12
P13
P14 P15
P16
P17
P18
P19
P20
P21
P22
P23
P24
P25
P26
P27 P28
P29
P30
P31
P32
P33
P34
P35
P36
P37
P38
P39
P40 P42 P43
P44
P45
P46
P47
P48
P49
P50
P51
P52
P53
P54 P55
P56
P57
P59
P60 P61
P62 P63
P64 P65
P66
P67
P68
P71
P72
P73
P74
P75
P76
P77
P78
P79
P80
P81
P82
P84
P85
P86
P88
P89
P91
P93
P94
P95
P96
P97
P98
P99
P100
P101 P102
P103 P104
P105
P106
P107
P108
P109
P110
P111
P112
P115
P116
P117
P118
P119
P120
P121
P122
I1
I2
I3
I4
I6
I7
I14
I15
I18
I19 I21
I22 I23
I24
I25
I26
I28
I29
I30
I31
I32
I33
I34
I35
I36
I37
I38
I39
I40
I41
I42
I43
I44
I45
I46
I47 I48
I49
I50
I51
I52
I53
I54
I55
I56
I57
I58
I59 I61
I62
I63
I64
I65
I66
I67
I68
I69
I70
I71
I75
I76
I77
I78
I79
I80
I81
I82
I83 I84
I85
I86
I87
I88 I89
I90 I91
I92 I93 I94
I95
I96
I97
I98 I99
I100
I101
I102 I103
I104
I105
I106
I107
I108
I109
I110
I111
I112
I113
I115
0.85 - 1
0.75 - 0.85
0.65 - 0.75
0.55 - 0.65
0.45 - 0.55
0.35 - 0.45
0.25 - 0.35
0.15 - 0.25
0 - 0.15
•For gain>0.2
•Gain vector sum for time interval 11/06/2006-
07/29/2007
5
10
15
30
210
60
240
90
270
120
300
150
330
180 0
Gain Orientation from 11/06/2006-07/29/2007
5
10
15
20
30
210
60
240
90
270
120
300
150
330
180 0
Gain Orientation from 08/13/2007-06/29/2008
5
10
15
30
210
60
240
90
270
120
300
150
330
180 0
Gain Orientation from 06/29/2008-06/28/2009
Gain Orientation Histogram
for Different Time Periods
Updates to Technology
• Input data screening (Cao, 2011)
• New graphical methods
• Integrated CRM (error intervals)
• Extension to primary recovery
• Extension to subsidence problem
Integrated Capacitance Resistive Model for
Primary Recovery
HYPOTHESIS In primary recovery, reservoir properties such as pore
volume, reservoir pressure, productivity index, producer-
producer interaction can be inferred from production data
ADVANTAGES A quick, simple diagnostic tool for engineer
No additional cost
No well shut-in required as to measure productivity
index, reservoir pressure
OUTCOME Reservoir property estimates (volume, pressure, etc.)
Future production forecast
Support production planning (number of wells, production
rate schedule, producing life)
ICR Model
•Reservoir 3
•Reservoi
r 2 •Reservoi
r 1
•Well
1
•Well
2
•Well
3
•Known - Production rates –
q
• - Bottom hole
pressure – Pwf
• - Initial average
pressure – Pi(0)
• - Cumulative
production - Np
i
pi
i
iwfiipt
i
i
i
ipt NPPVcqJ
Vc)0()(
•Unknown - Pore Volume
– Vp
• - Productivity
Index – J
•Assumption: ct is
constant
•
•Assumptions
•No gas
•No volatile oil
•No aquifer
ICR Model Validation
• ICR has been tested to on different fields to consider the effects of Field size Permeability Initial oil saturation Heterogeneity Number of producers, producers start at different times
ICR results – CMG synthetic field
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
2.5E+07
3.0E+07
3.5E+07
4.0E+07
4.5E+07
12/6/1999 3/15/2000 6/23/2000 10/1/2000 1/9/2001 4/19/2001
Dynamic pore volume Vp (bbl)
P1
P2
P1+P2
Actual pore volume 37.7e6 bbl
ICR Case Study – Oman field
•Estimated dynamic pore volumes
•Estimated productivity index over time
Updates to Technology
• Input data screening (Cao, 2011)
• New graphical methods
• Integrated CRM (error intervals)
• Extension to primary recovery
• Extension to subsidence problem
Contents
Synfield-1 (Streak case) Confidence limits by linear regression
Synfield-2 (Complete sealing barrier)
Synfield-3 (Partially sealing barrier)
Synfield-4 (Wells in random locations)
• ICR Model Applied on Synfields:
• Summary
• Future Work
•40
• CRM Introduction
•Application of the ICR
model for Secondary
Recovery
• qjk, Iik, and pwf,jk are assumed to be constant over the time step
length (t)
• qj0 is the actual production rate of producer j at k=0
- Fully model driven
• Parameters to be determined by nonlinear regression are
- fij is the connectivity between injector i and producer j
- j is the time constant of producer j
- Jj is the productivity index of producer j
Nonlinear CRMP (CRM-Producer
Based)
1
/ /
( 1)ˆ ˆ 1j j
j kjknit t wf wf
jk j k ij ik j j
i
p pq q e e f I J
t
•(4)
•Weight on the rate at previous time
•Weight on the injection signals at current time
•41 •Application of the ICR
model for Secondary
Recovery
• Least Mean Squares(LMS) parameters estimation
(5)
• Constraints
for all i (6)
for all i and j (7)
Equation 7 ensures that injected water does not adversely affects the
reservoir production.
Objective Function and Constraints of CRM
2
1 1
ˆmint Pn n
obs
jk jk
k j
z q q
1
1jn
ij
j
f
, 0ij jf
•42 •Application of the ICR
model for Secondary
Recovery
CRMP vs. ICR model
•43
• using cumulative
quantities
• using instantaneous
quantities
1
/ /
( 1)ˆ ˆ 1j j
j kjknit t wf wf
jk j k ij ik j j
i
p pq q e e f I J
t
-3.00E+06
-2.00E+06
-1.00E+06
0.00E+00
1.00E+06
2.00E+06
3.00E+06
50 70 90
To
tal w
ate
r in
jec
ted
or
liq
uid
p
rod
uc
ed
(rb
)
Time periods (month)
Independent variables used for the ICR model
W4
-Np4
W1
W2
W3
W5
0
500
1000
1500
2000
2500
3000
50 60 70 80 90 100
Wate
r in
jecti
on
rate
s (
rb/d
ay)
Time periods (month)
Independent variables used for the CRMP
I1
I2
I3
•* Reservoir barrel
(rb)
•Application of the ICR
model for Secondary
Recovery
0
, 0 , ,
1
ink k k
p j j jk j ij i j j wf j wf j
i
N q q f CWI J p p
•where
• NP,j is the cumulative total liquid
production from a producer j
• CWIi is the cumulative water injection
into a injector i
Schematics of Convex Function with Constraints which form Convex Sets
Convex optimization problem: Minimize: f(x1,x2)
Subject to: gi(x1,x2) ≤ 0 i=1, 2, … , m
f(x1,x2)
x2 x1
•Global minimum
•without constraints
•Global minimum
•With constraints
•g1(x1,x2
)
•g2(x1,x2
) •g3(x1,x2
)
•g4(x1,x2
)
Streak Case – Inverted 5-Spot Pattern
•2480 ft
• Square reservoir (2480 ft by 2480 ft)
• 5 water injectors & 4 producers
• Isotropic and homogeneous reservoir
• - except 2 high permeability channels
• Water flood for 100 months (8.33 years)
• Fitting periods from 58th to 100th month
• Number of fitting periods is 42
• Radial distance limit of 4000 ft
• CRMP used
•
•
•45
•2480 ft
•(Same example as in Sayarpour, 2008)
•Application of the ICR
model for Secondary
Recovery
ICR Model Results ICR model is comparable to the CRMP
•46
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
I01 I02 I03 I04 I05
fi1
P01-fi1
fi1_nonlinear
fi1_linear_Np
0.00
0.05
0.10
0.15
0.20
0.25
I01 I02 I03 I04 I05
fi2
P02-fi2
fi2_nonlinear
fi2_linear_Np
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
I01 I02 I03 I04 I05
fi3
P03-fi3
fi3_nonlinear
fi3_linear_Np
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
I01 I02 I03 I04 I05
fi4
P04-fi4
fi4_nonlinear
f4_linear_Np
•Application of the ICR
model for Secondary
Recovery
ICR Model Results ICR model is comparable to the CRMP
•47 •Application of the ICR
model for Secondary
Recovery
0
5
10
15
20
25
30
P1 P2 P3 P4
Tau
s (
day)
Time Constants
Tau_CRMP Tau_ICR
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
P1 P2 P3 P4
R2
Fit Qualities
R2_CRMP R2_ICR
fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)
P1 (j=1) 0.8961 0.5926 0.1981 0.2515 0.1625 5.16
P2 (j=2) 0.0357 0.0351 0.0402 0.2047 0.0330 13.64
P3 (j=3) 0.0199 0.1808 0.0856 0.0400 0.1660 12.27
P4 (j=4) 0.0586 0.1992 0.6634 0.5511 0.5929 10.60
•48
0.00E+00
5.00E+05
1.00E+06
1.50E+06
2.00E+06
2.50E+06
3.00E+06
3.50E+06
4.00E+06
50 60 70 80 90 100
Np
(rb
)
Time period (month)
P01
Data
Linear_Npk0.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
4.50E+05
5.00E+05
50 60 70 80 90 100
Np
(rb
)
Time period (month)
P02
Data
Linear_Npk
0.00E+00
1.00E+05
2.00E+05
3.00E+05
4.00E+05
5.00E+05
6.00E+05
7.00E+05
8.00E+05
50 60 70 80 90 100
Np
(rb
)
Time period (month)
P03
Data
Linear_Npk0.00E+00
5.00E+05
1.00E+06
1.50E+06
2.00E+06
2.50E+06
3.00E+06
50 60 70 80 90 100
Np
(rb
)
Time period (month)
P04
Data
Linear_Npk
ICR Model Results NP(t) vs time
•Application of the ICR
model for Secondary
Recovery
•49
ICR Model Results q(t) vs time
•Application of the ICR
model for Secondary
Recovery
95% Confidence Intervals – ICR Model Narrow error bars show the estimates are trustworthy
•50 •Application of the ICR
model for Secondary
Recovery
• Confidence limits calculated by the linear model (ICR) is smaller than
those calculated by the nonlinear model (CRMP).
•51
95% Confidence Intervals – ICR Model Narrow error bars show the estimates are trustworthy
•Application of the ICR
model for Secondary
Recovery
0
5
10
15
20
25
30
P1 P2 P3 P4
Ta
us
(d
ay) Time Constants
Tau_CRMP Tau_ICR
•52
Synfield-2: Complete Sealing Barrier
•Application of the ICR
model for Secondary
Recovery
fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)
P1 (j=1) 1.0000 0.0000 0.0000 0.0000 0.0000 8.359
P2 (j=2) 0.0000 0.0000 0.9995 1.0000 0.0000 33.04
P3 (j=3) 0.0000 0.7461 0.0001 0.0000 0.5002 25.98
P4 (j=4) 0.0000 0.2539 0.0005 0.0000 0.4996 22.89
•ICR parameters for Synfield-2
•Synfield-2 is a homogeneous isotropic reservoir (k=50
md and =0.2) and consists of three compartments that
do not communicate to each other because of the
presence of fault seals.
• The ICR model is able to detect the presence of
no-flow boundaries.
•53
Synfield-2: Complete Sealing Barrier q(t) vs time
•Application of the ICR
model for Secondary
Recovery
•54
Synfield-3: Partially Sealing Barrier
•Application of the
ICR model for
Secondary Recovery
•ICR parameters for Synfield-3
fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)
P1 (j=1) 0.0326 0.4670 0.0409 0.0827 0.1257 27.79
P2 (j=2) 0.6286 0.0737 0.3560 0.4568 0.1410 13.84
P3 (j=3) 0.1000 0.3550 0.1717 0.1470 0.3659 13.45
P4 (j=4) 0.2388 0.1043 0.4314 0.3135 0.3674 13.40
•Synfield-3 is a homogeneous isotropic reservoir
(k=50 md and =0.2) with a partially sealing barrier
(navy diagonal blocks).
The presence of transmissibility barrier could be
inferred by low gains calculated from the ICR model.
•55
Synfield-3: Partially Sealing Barrier q(t) vs time
•Application of the
ICR model for
Secondary Recovery
•56
Synfield-4: Wells in Random Locations
•Application of the ICR
model for Secondary
Recovery
•Synfield-4 is a homogeneous isotropic reservoir (k=50 md
and =0.2).
•57
Synfield-4: Relationship between the
interwell-distance and interwell-
connectivity (gain)
•Application of the ICR
model for Secondary
Recovery
The results show that as the distance between interwell-pairs increases, the well
connectivity tends to decrease.
fij = -0.0003(ft-1)*dij (ft)+ 0.402 for 110 ft < dij < 959 ft
Distance (ft) fij (ICR) fij(CRMP)
110 0.5409 0.5321
198 0.4294 0.4091
260 0.1968 0.2977
310 0.4837 0.2868
388 0.2401 0.2314
426 0.2068 0.2010
426 0.2751 0.2510
442 0.1270 0.1418
493 0.0444 0.1646
510 0.3100 0.4077
527 0.2742 0.2643
543 0.3502 0.3413
576 0.1253 0.1250
650 0.2059 0.2369
677 0.1246 0.1226
745 0.0861 0.1439
806 0.2895 0.2504
815 0.2756 0.2323
860 0.2457 0.1878
959 0.1687 0.1722
y = -0.0003x + 0.402 R² = 0.3681
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 200 400 600 800 1000 1200
f ij
Distance between well-pair (ft)
Gains vs Distance (CRMP)
fij_CRMPLinear (fij_CRMP)
y = -0.0003x + 0.401 R² = 0.2487
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 200 400 600 800 1000 1200
f ij
Distance between well-pair (ft)
Gains vs Distance (ICR Model)
fij_ICRLinear (fij_ICR)
•58
Synfield-4: q(t) vs time
•Application of the ICR
model for Secondary
Recovery
Updates to Technology
• Input data screening (Cao, 2011)
• New graphical methods
• Integrated CRM (error intervals)
• Extension to primary recovery
• Extension to subsidence problem
Comparison of Actual and Model
Subsidence
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 365 730 1095 1460 1825
Su
rface s
ub
sid
en
ce
(ft
)
Average subsidence vs. time
Actual average cumulative
subsidence
Model average cumulative
subsidence
•Elapsed days between 12/31/2003-9/16/2008 (days)
• Dr. Edgar (Principal advisor)
• Dr. Lake (Co-advisor)
• Lab mates
Acknowledgment
•61
• This work was supported by the
sponsors of the Center for Petroleum
Asset Risk Management (CPARM) at UT
Austin
•Application of the ICR
model for Secondary
Recovery
Future Work
• Working spreadsheet
– Couple to GAMS
– Excel vs. MATLAB
– Multiplotting (visualization)
• Integrate with DA/VOI approaches
• Propagating error/uncertainty
• More validation (oil in tank)
• Extend to primary recovery
• Fluid allocation studies (conformance)
• Optimize to produce more oil
• Add EOR model(s)
Gardner Hype Curve
The Gardner Group 63 Jim Honefenger (P.E. Moseley & Associates, Inc.)
Validation
Field Injectant Independent Data Agree
Synfields Water Simulation Very well
Snyfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
SWCFU Water Anecdotal fractures Reasonably
NSF I Water Structure Well
NBDU Gas Tracer data Fairly well
SELU Water Oil in tank Msybe
Characteristics of a reservoir can be inferred from
analyzing production and injection data only
Williston Basin Field
ObjectiveÊfunction actualÊrate modelÊrate 2
FittingÊwindow
Producers
F fittingÊwindow,modelÊparameters
öqj t qj t;modelÊparameters 2
ttFirst
tLast
j1
Np
modelÊparameters
CRMT
j, fij CRMP
ij, fij CRMIP
fittingÊwindow int ervalÊwithÊnoÊexternalÊchanges
Basic Definitions
RProducer
2 1ScatterÊofÊproducerÊrateÊaboutÊmodel
ScatterÊofÊproducerÊrateÊaboutÊmean
Basic Definitions
R j2
fittingÊint erval
1
öqj t qj t;modelÊparameters 2
ttFirst
tLast
öqj t qj 2
ttFirst
tLast
Steady-State Connectivity Map
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Better CO2
Performance
Interwell Connectivity
Two Equally Viable Solutions
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 10 days
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 30 days
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 90 days
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 180 days
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 365 days
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 2 years
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
After 4 years
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Transient Interwell Connectivity
4 years <<
0
20
40
60
80
0 20 40 60 80 100
Producer
Water Injector
Carbon Dioxide Injector 0 1,000 ft
Gains >0.5
Mature West Texas Waterflood
Injector
Producer
Gains > 0.5
Gains >0.4
Mature West Texas Waterflood
Injector
Producer
Gains >0.3
Mature West Texas Waterflood
Gains > 0.3 Injector
Producer
Gains >0.2
Mature West Texas Waterflood
Gains > 0.2
Injector
Producer
Mature West Texas Waterflood
0 50 100 150 200 250-1.5
-1
-0.5
0
0.5
1
Producer Number
R-squared Value
R-squared
Producer Number
•109,252
•103,042
•Confidence band
for regression
line
•39,956 bbl •~
$2,800,000
Oil Rate vs. Cumulative Oil Production
Producer 184 – Good Fit
0 20 40 60 80 100 12020
40
60
80
100
120
140
160
180
200
Month
bbl/day
Historic Total Production
Modeled Total Production
R2 = 0.961
err = 0.146 Bbl/
day
Month
Producer 127 – Good Fit
0 20 40 60 80 100 1200
100
200
300
400
500
600
Month
bbl/day
Historic Total Production
Modeled Total Production
R2 = 0.696
err = 0.037
outliers
Bbl/
day
Month
Producer 74 – Poor Fit
0 20 40 60 80 100 1200
20
40
60
80
100
120
140
160
180
Month
bbl/day
Historic Total Production
Modeled Total Production
R2 = -1.03
err = 0.143
Bbl/
day
Month
Producer 201 – Poor Fit
0 20 40 60 80 100 1200
200
400
600
800
1000
1200
Month
bbl/day
Historic Total Production
Modeled Total Production
R2 = 0.793
err = 6.58
Bbl/
day
Month
Gain Map
712000
714000
716000
718000
720000
722000
724000
726000
728000
475000 480000 485000 490000 495000 500000
ft
ft
Injector
Producer
P210
I 58
P103
Producer 210 (large distance)
0 20 40 60 80 100 1200
100
200
300
400
500
600
Month
bbl/day
Historic Total Production
Modeled Total Production
093.0
882.0R 2
err
Bbl/
day
0 20 40 60 80 100 1200
50
100
150
Month
bbl/day
Historic Total Production
Modeled Total Production
Producer 103 (skipped over)
110.0
635.0R 2
errBbl/
day
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Injector Number
Fraction of Injection Lost
Injector Number
Lost Injection
1 f
ijj1
Np
Time Constants
1
10
100
1000
10000
100000
1
11
21
30
42
56
75
87
10
1
11
1
12
3
13
3
14
2
15
3
16
3
17
5
18
4
19
5
20
5
21
6
22
5
23
4
Producer Number
Tim
e C
on
sta
nt
(da
ys
)
...
.... Before Outlier Removal
After Outlier Removal
Reservoir A
CRM Fit – Total Field
0 20 40 60 80 100 1202.5
3
3.5
4
4.5
5
5.5
6x 10
4
Month
bbl/day
Historic Injection
Historic Total Production
Modeled Total Production
R2 = 0.956 Bbl/
day
Month
Future Injection
• Historic Period – 131 Active Injectors
• Prediction Period – 97 Active Injectors
• Injection has been concentrated in fewer wells (37
injectors shut-in)
• 27.3% of historic field injection from injectors shut-
in throughout prediction period
Appraisal and
Conceptual
Analysis
GATE GATE Evaluate
Alternatives GATE
Define
Selected
Alternative
GATE Execute Operate
Inevitable
Dis-
appointment
Portfolio
Optimization
Uncertainty
Updating
Concept Selection & Development Optimization
Real Options
Portfolio Management and
Project Selection
Addressing Risks Throughout the E&P Asset Lifecycle
VOI; Impact
of Estimates
& Methods
Financial Risk
Management
Cost and Schedule Estimating; Execution Risk Management
HSE Risk Management
Real-Time Optimization
and Risk Management
Valuing Price
Forecasts
Capital
Allocation w/
Uncertain
Arrivals
FUTURE:
Life Cycle
Assessments
Contracting
Strategies
(lump sum v
cost plus?)
MPD &
Blowouts;
Drlg Safety;
Offshore
Spills
Simple Model
Development
Optimal Injection and Predicted Oil Production for
the Field
0 20 40 60 80 100 120 140 160 180 200 2
3
4
5
6 x 10
4
Month
bb
l/d
ay
Historic
Optimal
0 20 40 60 80 100 120 140 160 180 200 500
1000
1500
2000
2500
3000
Month
bb
l/d
ay
Historic Oil Production
Predicted Oil Production
Extrapolated Oil Production
Injection Shares
0 20 40 60 80 100 120 1400
0.5
1
1.5
2
2.5
3
3.5
Injector Number
Percent of Total Field Injection
Historic Share
Predicted Share
Injector Number
Percent of
Total
0 50 100 150 200 2500
0.5
1
1.5
2
2.5
Producer Number
Percent of Field Oil Production
Historic Share
Predicted Share
Production Shares
P112 P195
Producer Number
Percent of
Total
Retrodiction
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