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8/3/2019 Review of Tracer Transport Models for Reservoir Characterization
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Review of Tracer Transport Models for
Reservoir Characterization
SPE ATW Tracer Technology for Reservoir
Management, 22-24 June 2010Ibrahim Kocabas, Chemical Engineering Department
American University of Sharjah, UAE
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OUTLINE
1. Tracers for Reservoir Description
2. Modeling of Tracer Transport
1. Simple homogeneous system models
2. Simple heterogeneous system models
3. Complex systems models-Analytical
4. Numerical Models
3. Conclusions
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Information From Interwell Tracers
1. Delineation of Flow Barriers
2. Directional Flow Trends
3. Volumetric Sweep at breakthrough
4. Continuity of Sands and Shales
5. Characterization of Faults
6. Pattern Balancing
7. Identification ofOffending Injectors
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Preferential Flow Paths
Peaks are proportional to layer flow
capacitance, khw
BT time is controlled by pore volume
Tailing is controlled by heterogeneity
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Flow Barriers
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Characterizing Faults
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Directional Flow Trends
8/3/2019 Review of Tracer Transport Models for Reservoir Characterization
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Offending Injectors
8/3/2019 Review of Tracer Transport Models for Reservoir Characterization
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Pattern Balancing
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Modeling Equations
t
CqCuCD
x
x!
)(. *
JJJ
t
CqCur
rrr
CDr
rr xx!
xx
xx
xx )(*
11 JJJ
t
Cq
x
Cu
x
CD
xx!
xx
xx *
2
2
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Theoretical Studies
Linear TransportOgata and Banks : Purely Linear CD
Avdonin: Coupled Single Fracture & Matrix
Coats and Smith: Flowing and immobile mediaCorrea et al: Flowing and immobile media
Radial transport
Raimondy, Hoopes and Harleman: Radial CD, simplified
Tang and Peaceman: Purely radial CD
Falade : Radial CD with reaction
Ramirez et al: Radial CD flowing and immobile media
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Theoretical Studies
Pattern Flow in Layered SystemsAbbaszadeh and Brigham
Models based on reservoir geology
Numerical simulatorsFinite difference models
Streamline simulators
Interpretations:
Nonlinear regression on analytical models
Assisted history matching via simulators
Inverse modeling via simulators
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Theoretical StudiesTransport in Homogeneous Systems: Convection,
pure dispersion and flow geometry influence
Ogata and Banks Tang and Babu
!
D
DDD
D
DD
D
t
txerfcx
t
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2exp
221
+!
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o
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v
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XXX
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4)(
221
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Fluid Mechanics Control
0)1( 2
2
!x
x
x
x
x
x
x
x
D
D
D
D
D
mD
D
D
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C
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C
t
C
t
C[[
mDDmD CCt
C!
x
x P[)1(
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Theoretical StudiesTransport in heterogeneous systems
Coats and Smith and also Correa et al.:
Falade and also Ramirez et. al.:
)(2))( 22
1
2/22
sfrsrKvs
sfrsrC DDvv
vDD
D +
!
!
2
))((411exp1 D
Dx
sfss
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Baldwin: Pattern Flow approximately linear
transport
!
!
222
1
22
1
WE
xxerfc
x
xxerfcCD
dispersion is superimposed on standard deviation
Practical Applications
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Practical applications:
Baldwins Work
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Abbaszadeh and
Brigham Work
Practical Applications
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Abbaszadeh and Brigham ModelField test interpretation identifies nine
non-communicating layers
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A second Field Example: Excellent match
with 2 layers but kh
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Reasoning for kh< kh actual
Abbaszadeh explanation: there must be a
subset of layers having disproportionate
contribution to flow
Streamline simulation people: geological
model is neglected. That means there may
be 1. Areal permeability variations 2.
Crossflow 3. Vertical permeability variations4. Correlated permeability variations
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If those possibilities are included streamline
simulation will reproduce profiles with
actual kh values (Illiasov )
.
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Conclusions: Pros and Cons
Abbaszadeh: considers pattern, mobility ratio,
heterogeneity (with constant dispersion), and
layering
Unresolved issues: Areal heterogeneity,
fractures, faults, permeability streaks, two
phase, layer communication etc
Inverse Theory and Streamline Simulation :
areal heterogeneity, layer communication,
two phase, permeability streaks and so on
honoring a priori geological model.
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Practical Applications
Problems with Inverse Theory:
Results are non unique
# of unknowns >> number of data points
Numerical dispersion, oscillation, grid
size/slug size
Simulating Interfaces between Faults and
Matrix or High K streaks with matrix
Relatively time consuming
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Conclusions: Practical
ApplicationsProblems with All Models:
Failing to include wellbore and facilities
storage effects vertical profiling is impossible due to
sampling practices
Selected injection is costly and unpracticed Information is limited to that is inferred from
given equations and not actual conditions of
tests in the field