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Reservoir Characterization From Production and Injection Fluctuations
Larry W. LakeThe University of Texas at Austin
Larry_Lake@mail.utexas.edu
Outline
• Introduction• The Model• Applications of the Model
– Synthetic Fields (Synfields)
– Field Applications• Uses of the Model• Validation
Prior and Current Work
• Belkis Refunjol
• Jorge S’Antana Pizarro
(Petrobras)
• Isolda Griffiths (Shell)
• Alejandro Albertoni (Nexen)
• Pablo Gentil (ENI)
• Ali Al-Yousif (Aramco)
• Danial Kaviani (TAMU)
• Thang Bui (TAMU)• Xming Liang
• Morteza Sayarpour (Chevron)
• Sami Kaswas (Exxon)
• Tom Edgar, ChE
• Leon Lasdon, IROM
• Jerry Jensen (U.Calgary)• Alireza Mollaei, PGE• Ahn Phoung Nguyen, ChE• Fei Cao, PGE• Jacob McGregor, PGE• Jong Suk Kim, ChE• Wenle Wang, PGE
PastPresent
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
• Everything done in a spreadsheet
Outline
• Introduction• The Model• Applications of the Model
– Synthetic Fields (Synfields)
– Field Applications• Uses of the Model• Validation
q(t) = q(t0)e−(
t− t0τ
)+ I(t) 1− e
−(t− t0τ
)⎛
⎝
⎜⎜
⎞
⎠
⎟⎟− ctVp( ) pwf,t − pwf,0
t − t0
⎡
⎣⎢⎢
⎤
⎦⎥⎥
1− e−(
t− t0τ
)⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
CRM Continuity Equation
ctVpdpdt
= i(t) − q(t)
dq(t)dt
+1τ
q(t) = 1τ
i(t) − Jdpwf
dt
τ =ctVp
J
Ordinary Differential Equation:
Continuity:
Solution:
q(t)i(t)
BHPInjectionPrimary
q(t) = J p − pwf( )Production Rate:
Signal Response
Production response to an injection signal
Connectivity
τij = 1 dayfij = 0%
Connectivity
τij = 1 dayfij = 100%
Connectivity
τij = 6 daysfij = 100%
Connectivity
τij = 6 daysfij = 65%
Capacitance-Resistance Model (CRMT)
( ) k
tt
kk Ieeqq ⎟⎠⎞⎜
⎝⎛ −+=
Δ−Δ−−
ττ 11
τ
q(t)I(t) JVc pt=τ
Time constant
f2j
f6j
f4j
f3j
f5j
jτf1j
f11f12
f13
I6
I1I2
I3
I4I5
qj(t)
Capacitance-Resistance Model (CRMP)
( ) ik
n
iij
tt
kjjk Ifeeqqi
jj ∑=
Δ−Δ−
− ⎟⎠
⎞⎜⎝
⎛ −+=1
1 1 ττ
j
ptj J
Vc⎟⎟⎠
⎞⎜⎜⎝
⎛=τ
11
≤∑=
pn
jijf
Time constant
Inter-well connectivity or gain
Drainage volume around a producer
Capacitance-Resistance Model (CRMIP)
Ii(t)
qj(t)
fij
τij
ij
ptij J
Vc⎟⎟⎠
⎞⎜⎜⎝
⎛=τ
11
≤∑=
pn
jijf
Time constant
Inter-well connectivity or gain
( )∑=
Δ−Δ−
− ⎥⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ −+=i
ijijn
iikij
tt
kijjk Ifeeqq1
1 1 ττ
Steady-State Connectivity Map
0
0
0
0
0
0 20 40 60 80 100
ProducerWater InjectorCarbon Dioxide Injector 0 1,000 ft
Better CO2 Performance
Interwell ConnectivityTwo Equally Viable Solutions
Transient Interwell Connectivity After 10 days
Transient Interwell Connectivity After 30 days
Transient Interwell Connectivity After 90 days
Transient Interwell Connectivity After 180 days
Transient Interwell Connectivity After 365 days
Transient Interwell Connectivity After 2 years
Transient Interwell Connectivity After 4 years
Transient Interwell Connectivity 4 years <<
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 > 0.3Injector
Producer
Gains >0.2
Mature West Texas WaterfloodGains > 0.2
Injector
Producer
Mature West Texas WaterfloodR-squared
Producer Number
Time Constants
Reservoir A
Producer 184 – Good Fit
R2 = 0.961
err = 0.146Bbl/day
Month
Producer 127 – Good Fit
R2 = 0.696
err = 0.037
outliers
Bbl/day
Month
Producer 74 – Poor Fit
R2 = -1.03
err = 0.143
Bbl/day
Month
Producer 201 – Poor Fit
R2 = 0.793
err = 6.58Bbl/day
Month
CRM: Oil Fractional-Flow Model
fo(t) =qo
qo + qw=
11+ WOR(t)
qo(t) = fo(t)q(t)
fo(t) = 1
1+ a CWI(t)( )b
log 1fo(t)
− 1⎛
⎝⎜⎞
⎠⎟= loga + blog CWI(t)( )
Outline
• Introduction• The Model• Applications of the Model
– Synthetic Fields (Synfields)
– Field Applications• Uses of the Model• Validation
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
Optimal Injection and Predicted Oil Production for the Field
0 20 40 60 80 100 120 140 160 180 2002
3
4
5
6x 10
4
Month
bbl/d
ay
HistoricOptimal
0 20 40 60 80 100 120 140 160 180 200500
1000
1500
2000
2500
3000
Month
bbl/d
ay
Historic Oil ProductionPredicted Oil ProductionExtrapolated Oil Production
Injection Shares
Injector Number
Percent of Total
Production Shares
P112 P195
Producer Number
Percent of Total
Gardner Hype Curve
The Gardner Group40Jim Honefenger (P.E. Moseley & Associates, Inc.)
Outline
• Introduction• The Model• Applications of the Model
– Synthetic Fields (Synfields)
– Field Applications• Uses of the Model• Validation
Validation
Just how do we scientifically validategeoscience 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.
Synfield Cases
• Heterogeneity• Large compressibility• Fractures• Barriers• Anisotropy• Partial completions• Large shut in times• Changing BHP• All agree with imposed geology
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Characteristics of a reservoir can be inferred from analyzing production and injection data only
Retrodiction
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Synfields Water Retrodiction Very well
Characteristics of a reservoir can be inferred from analyzing production and injection data only
Chihuido Field
• Good correlation• Inferred faults are in yellow•Gains and time constants reproduce known geological features
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Synfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
Characteristics of a reservoir can be inferred from analyzing production and injection data only
SWCF Flow Capacity
75167519
7523
7524
From Al-Yousef (2006)
Homogeneous
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Synfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
SWCFU Water Anecdotal fractures Reasonably
Characteristics of a reservoir can be inferred from analyzing production and injection data only
North Sea Field II
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Synfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
SWCFU Water Anecdotal fractures Reasonably
NSF II Water Structure Well
Characteristics of a reservoir can be inferred from analyzing production and injection data only
North Buck Draw Comparison
• CM τ correlates with tracer breakthrough time
0
5
10
15
20
300 5 10 15 20 25 35Tracer Breakthrough Time (months)
Spea
rman
or C
M T
ime
(mon
ths)
SpearmanCMLinear (CM)
Validation
Field Injectant Independent Data AgreeWith Data
Synfields Water Simulation Very well
Snyfields Water Retrodiction Very well
Chuido Water Faults from seismic Reasonably
SWCFU Water Anecdotal fractures Reasonably
NSF II Water Structure Well
NBDU Gas Tracer data Fairly well
Characteristics of a reservoir can be inferred from analyzing production and injection data only
Williston Basin Field
Validation
Field Injectant Independent Data AgreeWith Data
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
Characteristics of a reservoir can be inferred from analyzing production and injection data only
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)
Remove outliers
Maximize NPV of future oil recovery
Warm start Gainfit
Removeinactive wells
Remove gainsbased on distance
Remove smallgains
Gainfit #2 Calculate residualsand replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residualsand 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
Removeinactive wells
Remove gainsbased on distance
Remove smallgains
Gainfit #2 Calculate residualsand replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residualsand 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
Removeinactive wells
Remove gainsbased on distance
Remove smallgains
Gainfit #2 Calculate residualsand replace outliers Gainfit #3
Gainfit #1
Fracfit #1 Calculate residualsand remove outliers Fracfit #2
Reservoir model
Model Fit and Prediction Algorithm
<10 min computation
time
Appraisal and Conceptual
AnalysisGATE GATEEvaluate
Alternatives GATE
Define Selected
AlternativeGATEExecute 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
Gain MapInjector
Producer
P210
I 58
P103
Producer 210 (large distance)
093.0882.0R 2
==
err
Bbl/day
Producer 103 (skipped over)
110.0635.0R 2
==
errBbl/day
Injector Number
Lost Injection
1− fij
j=1
Np∑
CRM Fit – Total Field
R2 = 0.956Bbl/day
Month
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