Efectos de Mojabilidad

PERMPERMIn the name of God

PorePore--Scale Modelling ofScale Modelling ofThreeThree--Phase Flow and Phase Flow and

the Effects of Wettability and the Effects of Wettability and Displacement PathDisplacement Path

Mohammad PiriMohammad Piri Dr. Matthew JacksonDr. Matthew Jackson Prof. Martin BluntProf. Martin Blunt

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AcknowledgmentsAcknowledgments

Gas de FranceGas de France BHPBHP Enterprise OilEnterprise Oil SchlumbergerSchlumberger StatoilStatoil Japan National Oil Cooperation (JNOC)Japan National Oil Cooperation (JNOC) Department of Trade and Industry (DTI)Department of Trade and Industry (DTI)

We thank the Members of the Imperial College Consortium on Pore-Scale Modelling for Financial Support:

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3 mm3 mm

3 mm

ApproachApproach Model with Same Geometry & TwoModel with Same Geometry & Two--Phase Physics as my Colleague Phase Physics as my Colleague

Uses (Statoils Network)Uses (Statoils Network)

A Realization of Berea SandstoneA Realization of Berea Sandstone Porosity = 24.02 %

Cube Size = 3 mm*3mm*3mm

No. of Pores=26146

No. Throats=12349

Coordination Number=1 to 19

Pore Inscribed Radius= 3.62 to 73.54 (um)

Throats Inscribed Radius= 0.90 to 56.85 (um)

Clay Volume=5.7%

Triangular Shape (Irregular & Equilateral)=92.27 %

Rectangular Shape=6.51 %

Circular Shape=1.22 %

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Gas InjectionGas Injection

DepressurisationDepressurisation

Solution Gas DriveSolution Gas Drive

Gravity DrainageGravity Drainage

Thermal FloodingThermal FloodingWhere:

Hard to Measure 3Hard to Measure 3--Phase Kr Phase Kr

Empirical Correlations are Unreliable & Unphysical Empirical Correlations are Unreliable & Unphysical

(At Low Oil Saturation)(At Low Oil Saturation)

Why Three_Phase Flow ?Why Three_Phase Flow ?

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PhysicallyPhysically--Based ApproachBased Approach Realistic Model Tuned to or Predicting TwoRealistic Model Tuned to or Predicting Two--Phase Data is Phase Data is

Used to Predict ThreeUsed to Predict Three--Phase ResultsPhase Results

Guide to Construct New Empirical ModelsGuide to Construct New Empirical Models

LookLook--up Tables in Simulation Modelsup Tables in Simulation Models

Understanding 3Understanding 3--Phase Physics for the Design of Recovery Processes Phase Physics for the Design of Recovery Processes

Directly in a Dynamic UpDirectly in a Dynamic Up--scaling Approachscaling Approach

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Solid

Solid

Solid

owowwsos cos+=

gwgwwsgs cos+=

gogoosgs cos+=

owowgogogwgw coscoscos +=

3-Fluid-Phase System:

3 Contact Angles

1 Constraint Between Them

2 Independent Values of Contact Angles

n-Fluid-Phase System:

n(n-1)/2 Contact Angles

(n-1)(n-2)/2 Constraint Between Them

(n-1) Independent Values of Contact Angles

Oil Gas

Water

OilWater

Gas

ow

go

gw

ow

go

gw

*

Wettability and Contact AnglesWettability and Contact Angles

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Wettability and Contact AnglesWettability and Contact Angles(Cont. )(Cont. )Implications for Multiphase Processes:Implications for Multiphase Processes:

1. Consider a Three1. Consider a Three--Phase WaterPhase Water--wet System Where Oil Spreads wet System Where Oil Spreads on Water:on Water:

Which is often used to estimate an interfacial tension betwWhich is often used to estimate an interfacial tension between two liquids een two liquids from two surface tensions.from two surface tensions.

2. Consider a Three2. Consider a Three--Phase OilPhase Oil--wet System:wet System:

00

=

=

go

ow

gogwow =

At ambient conditions, typical Interfacial Tensions for water/nAt ambient conditions, typical Interfacial Tensions for water/n--alkane system: alkane system:

mmNow /50=mmNgo /20=

180ow deg. owgogogwgw = coscos

0cos gw deg.

*

*

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The analysis above for Oil-wet systems suggests :

Gas is not the most non-wetting phase in the presence of water

Gas doesnt occupy the largest pore spaces

Lower gas relative permeabilities in the presence of water than in the presence of Oil

Water reduces the effective mobility of gas leading to a more stable and economically favorable displacement process.

Wettability and Contact AnglesWettability and Contact Angles(Cont. )(Cont. )

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Configuration D

Configuration D

Configuration G

Configuration F

/2gwGas Invasion

into Water

GasWaterOil

Displacement PhysicsDisplacement Physics

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Water Layer

Collapsing

Configuration E

Configuration E Configuration J

Configuration I Configuration G

Configuration F

/2>gw

/2gw

/2

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Configuration B Configuration H

/2goGas Invasion into Oil

Oil Layer Collapsing

Displacement PhysicsDisplacement Physics(Cont.)(Cont.)

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Configuration G

Configuration F

Configuration C

Oil Layer

Collapsing

Configuration C Configuration I

Gas Invasion into Water

Gas Invasion into Water

Oil Layer

Collapsing

/2gw


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New ConfigurationsNew Configurations


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Use Empirical Expressions for Layer Use Empirical Expressions for Layer ConductanceConductance

Test for Trapping of all Three PhasesTest for Trapping of all Three Phases

Simulate any Sequence of Oil, Water and Gas Simulate any Sequence of Oil, Water and Gas InjectionInjection

Relative PermeabilityRelative Permeability

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0

10000

20000

30000

40000

50000

60000

70000

0 0.2 0.4 0.6 0.8 1

Pc(pa)- by Paal-Eric

Pc(pa)- by Mohammad

Pc(pa)- by Per

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

krw-by Paal-Eric

kro-by Paal-EricKrw-by Mohammad

Kro-by Mohammad

Krw-by PerKro-by Per

Reassuring that Three Independent Codes

Give the Same Results.

Sw (frac.) Sw (frac.)

Kr

Pcow(pa)

Kro

Krw

TwoTwo--Phase ResultsPhase Results

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0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.20 0.40 0.60 0.80 1.00

Sg (frac.)

Kr

0.0

10000.0

20000.0

30000.0

40000.0

50000.0

60000.0

70000.0

80000.0

90000.0

0.00 0.20 0.40 0.60 0.80 1.00

Pc (pa)

Sg (frac.)

Pcgo

Pcgw

Results for The Berea Sandstone Network (Random)Results for The Berea Sandstone Network (Random)

Kro

Krg

ThreeThree--Phase ResultsPhase Results

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FieldScale

CoreScale

CoreScale

PoreScale

Laboratory

Upscaling

Traditional STraditional Statictatic Linking of Linking of Length Length ScalesScales

SelfSelf--ConsistencyConsistency

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Dynamic Pore to Core-Scale Simulation

SelfSelf--ConsistencyConsistency(Cont.)(Cont.)

Gas Oil and water

Krg, Krw, KroPcow, Pcgw, Pcgo

Sg, Sw, SoSg, Sw, So

n

n+1 n+1n+1

nn

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NetworkModel

Simulator

So Sw

Sg

So Sw

Sg

?

S

Kr

S

Kr


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So Sw

Sg

Sg, Sw, Son nn

Sg, Sw, Son+1 n+1n+1

Sg, Sw, Son nn

Find smallest contrast insaturations between timesteps|Sw -Sw | |So -So | |Sg -Sg |

Fill capillary tubeFill tube with lowest Pcgo

(lowest Pg)

Calculate Sg, Sw, SoClose to FD values?

Yes - STOP

No

Find largest contrast insaturations between timesteps

Sg > Sg gas into oilSg < Sg oil into gas

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Find largest contrast insaturations between timesteps

Decide on displacement

Find smallest contrast insaturations between timesteps|Sw -Sw | |So -So | |Sg -Sg |

Fill capillary tube based upon Pc

Calculate Sg, Sw, SoClose to FD values?

Yes - STOP

No

So Sw

Sg



Sg, Sw, Son nn

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WAG FloodingWAG Flooding

Gas Injection into DifferentGas Injection into Different SwiSwi

Secondary vs. Tertiary Gas Secondary vs. Tertiary Gas InjectionInjection

ApplicationsApplications

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Couple Pore Scale Network Model to 3D Simulator to Capture a Physically Based Kr for the Correct Displacement Path

Possibly on Selected Region

PorePore--toto--CoreCore--toto--Field SimulationField Simulation

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ConclusionsConclusions

Definitive ThreeDefinitive Three--Phase ModelPhase Model

Preliminary Relative Permeability and Capillary Preliminary Relative Permeability and Capillary Pressure ResultsPressure Results

Working on Coupling a PoreWorking on Coupling a Pore--Scale Network Scale Network Model with LargerModel with Larger--Scale SimulationScale Simulation

Efectos de Mojabilidad

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