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Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP
Pore Scale Modeling of Single-Phase
Non-Newtonian Flow
Xavier LopezMartin Blunt
Imperial College of Science, Technology and Medicine, London 10th January 2003
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
IMPERIAL COLLEGE CONSORTIUM• BHP• UK Department of Trade and Industry & EPSRC• Enterprise Oil• Gaz de France• Japan National Oil Corporation• PDVSA-Intevep• Schlumberger• Shell• Statoil
Acknowledgements
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Contents
IntroductionSingle-phase BackgroundNetwork ModelResultsConclusionsFuture Work
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Introduction
Effects of non-Newtonian rheology on flow in porous media.
• EOR
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Introduction
Effects of non-Newtonian rheology on flow in porous media.
Pre Treatment: Flow restricted by radial geometry
Post Treatment: Increased productivity through fractures
• EOR
• Fracturing in injection wells
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Introduction
Effects of non-Newtonian rheology on flow in porous media.
• EOR
• Fracturing in injection wells
• Water blocking in producing wells
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Introduction
Effects of non-Newtonian rheology on flow in porous media.
Treatment fluid is pumped from surface without mechanical isolation.
Fluid invades all zones
Treatment fluid provide weak gel through physical interactions.
Back flow of oil disrupts and disperses treatment fluid, while flow of water is inhibited.
Production is dominated by water from high permeability channel
Treatment fluid gels permanently to isolate watered out layer
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Single-phase Flow Background
“Xanthan”
Xanthomonas campestris (E415)M.P. Escudier et al. / J. Non-Newtonian Fluid Mech. 97 (2001) 99–124
Viscometric viscosity of xanthan gum solutions together with Carreau–Yasuda (—)Cross (– – – –) model fits & experimental points.
Shear rate (s-1)
Vis
c os i
ty (
Pa.
s)
0
1. nC
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Single-phase Flow Background
Relating bulk and in situ properties
Shear rate,
Visc
osity
,
= f () ?
Characteristic length: absK
= f (v)
Velocity, v
Visc
osity
,
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Single-phase Flow Background
Relating bulk and in situ properties
• Porous medium representation
Capillary bundle approach
“Average radius R” depending on medium properties (K, Φ, tortuousity…)
Define “porous medium” shear rate
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Single-phase Flow Background
Relating bulk and in situ properties
• Experiments
Shear rate, (s-1)
Effe
ctiv
e Vi
scos
ity,
(mPa
.s)
Rheology of Xanthan FLOCON 4800MX after Fletcher et al
α: Correction Factor
αValues in the literature:
1 < α < 15
Requires experimental determination !!
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
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
Network Model
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
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Network Model
Cope with non-Newtonian rheology
01;.; n
eff CMinMax
Truncated power-law
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Network Model
Cope with non-Newtonian rheology
Initial guess for viscosity
Solve pressure field
In each pore and throat
Relate pressure drop to effective viscosity
Update viscosity
n
n
beff LC
PR
n
nC
1
..2
.
4
13.
Base on single circular tube expression
R ???
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Network Model
Equivalent Radius
Capillary bundle: based on medium properties
..8 abs
equ
KR (e.g. from Savins)
41
/.8
tpNNconduc
equ
GR
Network approach: based on conductance
(our approach)
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
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
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sand pack comparisonsHejri et al studied the flow of Xanthan in sand packs
Input rheology
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sand pack comparisons
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sand pack comparisons
Permeability Difference:
* Hejri et al experiment: 893mD
* Our sand-pack: 101D
re-scale all the network lengths by netnetK
K
expexp
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sand pack comparisons
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
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 netnet
netscaledre
K
Kqq
expexp
netnetK
K
expexp
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sand pack comparisonsVogel & Pusch studied the flow of biopolymer in sand packs
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Sandstone comparisonsGreaves & Patel studied the flow of Xanthan in Elginshire sandstone
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Results
Cannella et al studied the flow of Xanthan in Berea sandstone
Sandstone comparisons
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Conclusions
Capillary bundle model
Simple…but does not have genuinepredictive capabilities.
Sand pack
Sandstone
Vogel & Pusch
α = 1.34Hejri et al
α = 0.98
Greaves & Patel
α = 7.6Cannella et al
α = 4.8
Same networks…similar rheologies
?
?
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
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
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Future Work
Single-phase flow• Variations of alpha • Elasticity• Depleted layers effects• More complex rheology
Multi-phase flow• Relative permeability• Constant Q • Wettability effects
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP
Pore Scale Modeling of Single-Phase
Non-Newtonian Flow
Xavier LopezMartin Blunt
Imperial College of Science, Technology and Medicine, London 10th January 2003
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
R
v
T
TD
process
materiale
2R <v>
Dimensionless pressure drop measurements for different contraction ratios, after Rothstein & McKinley [18].
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Water relative permeability reduction…
Newtonian Case
Krw,N(S)Kro, N(S)
Non-Newtonian Case
Krw, NN(S, )P Delta P = 1 Pa
Krw, NN(S, )P Delta P = 10 Pa
Krw, NN(S, )P Delta P = 100 Pa
Multi-phase flow, NEWTONIAN and NON-NEWTONIAN
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Newtonian Case
Non-Newtonian Case
Krw, N(S)
Krw, NN(S, )P Delta P = 1 Pa
Krw, NN(S, )P Delta P = 10 Pa
Krw, NN(S, )P Delta P = 100 Pa
Water relative permeability reduction…
Multi-phase flow, NEWTONIAN and NON-NEWTONIAN
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Network code results:…until sufficient pressure drop is achieved.
Newtonian Case
Krw,N(S)Kro, N(S)
Non-Newtonian Case
Krw, NN(S, ) Delta P = 100 PaP
Krw, NN(S, ) Delta P = 300 PaP
Krw, NN(S, ) Delta P = 105 PaP
Krw, NN(S, ) Delta P = 104 PaP
Krw, NN(S, ) Delta P = 103 PaP
Krw, NN(S, ) Delta P = 600 PaP
Imperial College , PETROLEUM ENGINEERING AND ROCK MECHANICS GROUP 10th January 2003
Network code results:…until sufficient pressure drop is achieved.
Newtonian Case
Non-Newtonian Case
Krw, NN(S, ) Delta P = 100 PaP
Krw, NN(S, ) Delta P = 300 PaP
Krw, NN(S, ) Delta P = 105 PaP
Krw, NN(S, ) Delta P = 104 PaP
Krw, NN(S, ) Delta P = 103 PaP
Krw, NN(S, ) Delta P = 600 PaP
Krw,N(S)