Review of Tracer Transport Models for Reservoir Characterization

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


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Offending Injectors


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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

txerfc

C

2exp

221

+!

Dt

o

D

v

DD drr

vC X

XXX

4exp

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

x

C

x

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

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sfrsrKvs

sfrsrC DDvv

vDD

D +

!

!

2

))((411exp1 D

Dx

sfss

C [


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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



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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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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

Documents

Review of Tracer Transport Models for Reservoir Characterization