imperial college, petroleum engineering and rock mechanics group 10 th january 2003 petroleum...

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 CONSORTIUM• BHP• UK Department of Trade and Industry & EPSRC• Enterprise Oil• Gaz de France• Japan National Oil Corporation• PDVSA-Intevep• Schlumberger• Shell• Statoil

Acknowledgements


Contents

IntroductionSingle-phase BackgroundNetwork ModelResultsConclusionsFuture Work


Introduction

Effects of non-Newtonian rheology on flow in porous media.

• EOR


Introduction


Pre Treatment: Flow restricted by radial geometry

Post Treatment: Increased productivity through fractures

• EOR

• Fracturing in injection wells


Introduction


• EOR

• Fracturing in injection wells

• Water blocking in producing wells


Introduction


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


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



Relating bulk and in situ properties

Shear rate,

Visc

osity

,

= f () ?

Characteristic length: absK

= f (v)

Velocity, v

Visc

osity

,




• Porous medium representation

Capillary bundle approach

“Average radius R” depending on medium properties (K, Φ, tortuousity…)

Define “porous medium” shear rate




• 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 !!


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


Network Model

Cope with non-Newtonian rheology

01;.; n

eff CMinMax

Truncated power-law


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 ???


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)


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


Results

Sand pack comparisonsHejri et al studied the flow of Xanthan in sand packs

Input rheology


Results

Sand pack comparisons


Results


Permeability Difference:

* Hejri et al experiment: 893mD

* Our sand-pack: 101D

re-scale all the network lengths by netnetK

K

expexp


Results



Results


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


Results

Sand pack comparisonsVogel & Pusch studied the flow of biopolymer in sand packs


Results

Sandstone comparisonsGreaves & Patel studied the flow of Xanthan in Elginshire sandstone


Results

Cannella et al studied the flow of Xanthan in Berea sandstone

Sandstone comparisons


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

?

?


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


Future Work

Single-phase flow• Variations of alpha • Elasticity• Depleted layers effects• More complex rheology

Multi-phase flow• Relative permeability• Constant Q • Wettability effects


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


R

v

T

TD

process

materiale

2R <v>

Dimensionless pressure drop measurements for different contraction ratios, after Rothstein & McKinley [18].


Water relative permeability reduction…

Newtonian Case

Krw,N(S)Kro, N(S)

Non-Newtonian Case

Krw, NN(S, )P Delta P = 1 Pa



Multi-phase flow, NEWTONIAN and NON-NEWTONIAN


Newtonian Case

Non-Newtonian Case

Krw, N(S)




Water relative permeability reduction…

Multi-phase flow, NEWTONIAN and NON-NEWTONIAN


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







Network code results:…until sufficient pressure drop is achieved.

Newtonian Case

Non-Newtonian Case







Krw,N(S)

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