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PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP

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Greaves & Patel studied the flow of Xanthan in Elginshire sandstone ... Greaves & Patel. a = 7.6. Cannella et al. a = 4.8. Same networks...similar rheologies ... – PowerPoint PPT presentation

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Title: PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP


1
PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP
  • Pore Scale Modeling of Single-Phase
  • Non-Newtonian Flow

Xavier Lopez Martin Blunt
Imperial College of Science, Technology
and Medicine, London
10th January 2003
2
IMPERIAL COLLEGE CONSORTIUM
Acknowledgements
  • BHP
  • UK Department of Trade and Industry EPSRC
  • Enterprise Oil
  • Gaz de France
  • Japan National Oil Corporation
  • PDVSA-Intevep
  • Schlumberger
  • Shell
  • Statoil

3
Contents
  • Introduction
  • Single-phase Background
  • Network Model
  • Results
  • Conclusions
  • Future Work

4
Introduction
Effects of non-Newtonian rheology on flow in
porous media.
  • EOR

5
Introduction
Effects of non-Newtonian rheology on flow in
porous media.
  • EOR
  • Fracturing in injection wells

6
Introduction
Effects of non-Newtonian rheology on flow in
porous media.
  • EOR
  • Fracturing in injection wells
  • Water blocking in producing wells

7
Introduction
Effects of non-Newtonian rheology on flow in
porous media.
8
Single-phase Flow Background
9
Single-phase Flow Background
Relating bulk and in situ properties
10
Single-phase Flow Background
Relating bulk and in situ properties
  • Porous medium representation
  • Average radius R depending on medium properties
    (K, F, tortuousity)
  • Define porous medium shear rate

11
Single-phase Flow Background
Relating bulk and in situ properties
a Correction Factor
  • Experiments

Values in the literature 1 lt a lt 15 Requires
experimental determination !!
12
Network Model
  • Berea
  • Permeability 3D
  • Porosity 24.02
  • Average connection number 4.19
  • 12349 Pores, 26146 Throats
  • Triangular Shape 92.27
  • Throat size 1.8 113 µm
  • Pore size 7.24 147 µm
  • Sand pack
  • Permeability 101D
  • Porosity 34.6
  • Average connection number 5.46
  • 3567 Pores, 9923 Throats
  • Triangular Shape 94.7
  • Grain size 100- 425 µm

13
Network Model
Cope with non-Newtonian rheology
Truncated power-law
14
Network Model
Cope with non-Newtonian rheology
Base on single circular tube expression
Initial guess for viscosity
Solve pressure field
In each pore and throat
15
Network Model
Equivalent Radius
Capillary bundle based on medium properties
(e.g. from Savins)
Network approach based on conductance
(our approach)
16
Network Model
Underlying assumptions
  • Power law behavior across the entire cross
    section of each element (then cut-offs)
  • No visco-elastic effects
  • No adsorption
  • No polymer exclusion (excluded volume)
  • Newtonian viscosity plateaux

17
Results
Sand pack comparisons
Hejri et al studied the flow of Xanthan in sand
packs
Input rheology
18
Results
Sand pack comparisons
19
Results
Sand pack comparisons
Permeability Difference Hejri et al
experiment 893mD Our sand-pack 101D
re-scale all the network lengths by
20
Results
Sand pack comparisons
21
Results
Sand pack comparisons
Permeability Difference Hejri et al
experiment 893mD Our sand-pack 101D
re-scale all the network lengths by For
simplicity we re-scale the velocity
22
Results
Sand pack comparisons
Vogel Pusch studied the flow of biopolymer in
sand packs
23
Results
Sandstone comparisons
Greaves Patel studied the flow of Xanthan in
Elginshire sandstone
24
Results
Sandstone comparisons
Cannella et al studied the flow of Xanthan in
Berea sandstone
25
Conclusions
Capillary bundle model
Simplebut does not have genuine predictive
capabilities.
Vogel Pusch a 1.34
Hejri et al a 0.98
Sand pack
?
Same networkssimilar rheologies
Cannella et al a 4.8
Greaves Patel a 7.6
Sandstone
?
26
Conclusions
Our model
  • Our approach allows predictions to be made for 2
    types of network with no empirical correction
    needed.
  • Experimental evidence of pore blocking ?
  • Lower Newtonian plateau apparent

27
Future Work
28
PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP
  • Pore Scale Modeling of Single-Phase
  • Non-Newtonian Flow

Xavier Lopez Martin Blunt
Imperial College of Science, Technology
and Medicine, London
10th January 2003
29
Dimensionless pressure drop measurements for
different contraction ratios, after Rothstein
McKinley 18.
30
Multi-phase flow, NEWTONIAN and NON-NEWTONIAN
Newtonian Case
Non-Newtonian Case
  • Water relative permeability reduction

31
Multi-phase flow, NEWTONIAN and NON-NEWTONIAN
Newtonian Case
Non-Newtonian Case
  • Water relative permeability reduction

32
Network code results
Newtonian Case
  • until sufficient pressure drop is achieved.

Non-Newtonian Case
33
Network code results
Newtonian Case
  • until sufficient pressure drop is achieved.

Non-Newtonian Case
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