In the name of God

Three-Phase Flow in Mixed-Wet Porous Media

Mohammad PiriMohammad Piri

Prof. Martin BluntProf. Martin Blunt

Petroleum Eng. and Rock Mechanics (PERM) Research Group Department of Earth Science and Engineering

Imperial College

Acknowledgments

Enterprise OilEnterprise Oil StatoilStatoil ShellShell BHPBHP Gas de FranceGas de France PDVSA – Intevep PDVSA – Intevep SchlumbergerSchlumberger Japan National Oil Corporation (JNOC)Japan National Oil Corporation (JNOC) Department of Trade and Industry Department of Trade and Industry

(DTI)(DTI)

We Thank the Members of the Imperial College Consortium on Pore-Scale Modelling for Their Generous and Continued Support of our Research:

Outline Why Three-Phase Flow and Physically-Based Network

Modelling ?

Model We Use

Three-Phase Physics • Layer Formation • Wettability and Contact Angles

• Three-Phase Generic Configurations

• Network of Displacements for Every Type of Possible Two and Three

Phase Processes – Example, Water-Wet System

Network Modelling and Some of Its Complications• How to Choose the Right Displacement at Each Time?

• Single, Double and Multiple Displacements and Their Volume Errors• Relative Permeability Computation• Connectivity and Clustering and How Important They Are !

Three-Phase Results

Applications, Future Works and Conclusions

Why Three_Phase Flow ?

Gas Injection in Oil ReservoirsGas Injection in Oil Reservoirs

DepressurisationDepressurisation

Solution Gas DriveSolution Gas Drive

Gravity DrainageGravity Drainage

Thermal FloodingThermal Flooding

Steam InjectionSteam Injection

NAPL Migration in the Unsaturated ZoneNAPL Migration in the Unsaturated Zone

NAPL Flow in the Saturated Zone in the Presence of NAPL Flow in the Saturated Zone in the Presence of Gas Gas

We Face with Three Phase Systems at Following Processes:

Very Difficult to to Measure 3-Phase Relative Very Difficult to to Measure 3-Phase Relative

Permeabilities Particularly for Whole Range of O/W, Permeabilities Particularly for Whole Range of O/W, G/WG/W

and G/O Contact Anglesand G/O Contact Angles

Empirical Correlations have Little or No Physical BasisEmpirical Correlations have Little or No Physical Basis

Enormously Reduces the Uncertainty Associated with Enormously Reduces the Uncertainty Associated with the the

Assessment of Gas Injection ProjectsAssessment of Gas Injection Projects

Significantly Improves our Understanding of Three-Significantly Improves our Understanding of Three-Phase Phase

Physics for the Design of Recovery Processes Physics for the Design of Recovery Processes

Guide to Construct New Empirical ModelsGuide to Construct New Empirical Models

Directly in a Dynamic Up-scaling ApproachDirectly in a Dynamic Up-scaling Approach

Why Physically-Based Three-Phase Network Models ?

A Realization of Berea Sandstone (A Realization of Berea Sandstone (Statoil’s Statoil’s Network)Network)

Porosity = 24.02 %Porosity = 24.02 %

Cube Size = 3 mm*3mm*3mmCube Size = 3 mm*3mm*3mm

No. of Pores=12349No. of Pores=12349

No. of Throats=26146No. of Throats=26146

Coordination Number=1 to 19Coordination Number=1 to 19

Pores Inscribed Radius= 3.62 to 73.54 (um)Pores Inscribed Radius= 3.62 to 73.54 (um)

Throats Inscribed Radius= 0.90 to 56.85 (um)Throats Inscribed Radius= 0.90 to 56.85 (um)

Clay Volume=5.7%Clay Volume=5.7%

Triangular Shape (Irregular & Equilateral)=92.27 %Triangular Shape (Irregular & Equilateral)=92.27 %

Rectangular Shape=6.51 %Rectangular Shape=6.51 %

Circular Shape=1.22 %Circular Shape=1.22 %

Model We Use

Configuration E Configuration F Configuration G Configuration H

Configuration C Configuration DConfiguration A Configuration B

Two and Three-Phase Generic Configurations

GasWaterOil

Configuration J Configuration KConfiguration I Configuration L

Configuration NConfiguration M Configuration oConfiguration P

Two and Three-Phase Generic Configurations(Cont.)

GasWaterOil

WF= Water Flooding

GI = Gas Injection

PD = Primary Drainage

OI = Oil Injection

/ = OR

C

D

E

A B

F

G

H

K

J

I

L MN

F

E

O

P

C

D

WF

PD

WF

WF

WF

WF

GI

GI

GI

WF

GI

GI/OI

GI

GI/WF

GI/WF

GI OI

WF/O

I

WF/O

I

OI

WF/OI

WF/O

I

WF

WF/O

I

GI/WF

WF/OI

WF

GI/WF

WF WF

GI/WF

WF

GI GI

A B

C E

G

I

Displacements Network

PD,WF and GI in Strongly Water-Wet Systems

Configuration CConfiguration A Configuration B

Configuration EConfiguration G

Primary Drainage

Water Flooding

Gas Injection

Configuration I

Layer Collapsing

gw

go Gas Injection

GasWaterOil

How to Choose Right Disp. Each Time?1. A capillary pressure between any two phases is defined as:

jiCij PPP

2. The capillary pressure required to do Piston-Like, Snap-off or Layer Collapsing events that leads to configuration change is calculated using pore inscribed radius, right contact angle, corner angle(s) and interfacial tension.

3. Calculated capillary pressures are placed in one of six following sorted lists corresponding to what phase displaces what phase : Water to Gas, Water to Oil, Gas to Oil, Gas to Water, Oil to Water, Oil to Gas4. In every list we favour the event that needs lower pressure of displacing phase. This corresponds to the event with the lowest capillary pressure in Drainage processes and the highest capillary pressure in Imbibition processes.

5. During injection of phase I, it displaces either phase J or K at each time (i.e. event). To find which of these should be done at every time:

5-A) Find the most favourable event in I to J and I to K lists

5-B) Between the two most favourable events the one that needs lower

I pressure is favoured

How to Choose Right Disp. Each Time?

Example:

Gas injection after water flooding in a strongly oil-wet system:

Pcgw1

Pcgw2

Pcgw3

.

.

.

Pcgwn

Pcgo1

Pcgo2

Pcgo3

.

.

.

Pcgon

Pg1=Pw+Pcgw1

Pcgw = Pg - Pw

Pgn=Po+Pcgon

Pcgo = Pg - Po

Gas Invasion into Oil Imbibition

Process

Gas Invasion into water Drainage

Process

If Pg1<Pgn do G/W

Else do G/OAscending

Ascending

Single Displacements

1. Both Displacing and Displaced Phases Need to be Connected to Either Inlet or Outlet

2. There is no Volume Error

Gas Injection into Oil in a Strongly Water-wet System (Drainage Process)

Gas

Oil

Double Displacements and Volume Error

1. Only the First and the Third Phases are Connected to Either Inlet or Outlet in the case of Double Displacements

2. There is Volume Error that Needs to be Dealt With

3. Multiple Displacements Involving More Than One Intermediate Stage are Also Possible if Two Phases are Trapped.

Gas Injection into Oil in a Strongly Oil-wet System

Gas into Water is an Imbibition Process

Water into Oil is a Drainage Process

GasOil

Water

= Circular Cross Section

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

Use Theoretical and Empirical Use Theoretical and Empirical Expressions to Calculate Layer, Corner Expressions to Calculate Layer, Corner and Centre Conductance and Centre Conductance

Relative Permeability

Pore I

Pore J

IJL

)( ,,,

, JiIiIJ

IJiIJi PP

L

gq (I)

Ji

J

Ii

I

ti

t

IJi

IJ

g

L

g

L

g

L

g

L

,,,, 2

1(II)

Connectivity and Clustering(Cont.)

Inlet

Outlet

Cluster is Connected

*

Dead End

Periodic Boundary Condition

Cluster Connectivity(Cont.)

The pore that displacement is happening in it

Clusters with different phases surrounding the pore

Using phase connectivity could be very time consuming because:

1. For every single displacement connectivity of both displacing and displaced phases need to be checked

2. For double and multiple displacements we need to define the trapped and connected clusters

3. It is necessary to know the connectivity of all the site-phases in the network in order to calculate the relative permeabilities

How can we deal with this?

Before displacement

1 Check whether the pore allows clusters with the same fluids to be connected to each other through its sites

2 If yes store “ Connected “ else “ Not-Connected “

After displacement

4 Check whether the pore allows clusters with the same fluids to get connected to each other through its sites

5 If yes store “ Connected “ else “ Not-Connected “

6 Compare the connection of clusters with same fluids before and after the displacement and decide whether to check the continuity of clusters to inlet or outlet, based on the type of displacement and their flags before the displacements.

Cluster Connectivity(Cont.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Sw (frac.)

Kro

Krw

Dr. Paal-Eric OerenMohammad Piri

Per Valvatne

Two-Phase Results

Reassuring that Three Independent Codes

Give the Same Results.

0

10000

20000

30000

40000

50000

60000

70000

0 0.2 0.4 0.6 0.8 1

Pcow

Sw (frac.)

Tertiary Gas Injection, Strongly Water-wet System

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Oil Saturation (frac.)

Oil

Re

lati

ve

Pe

rme

ab

ility

TGI, Soi = 0.60

TGI, Soi = 0.665

TGI, Soi = 0.53

SGI, Soi=0.745

Tertiary Gas Injection, Strongly Water-wet System(Cont.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Gas Saturation (frac.)

Ga

s R

ela

tiv

e P

erm

ea

bil

ity

TGI, Soi = 0.53TGI, Soi = 0.60

TGI, Soi = 0.665SGI, Soi=0.745

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Water Saturation (frac.)

Wa

ter

Re

lati

ve

Pe

rme

ab

ilit

y

TGI, Soi = 0.53

TGI, Soi = 0.60

TGI, Soi = 0.665

Tertiary Gas Injection, Strongly Water-wet System(Cont.)

Tertiary Gas Injection, Strongly Oil-wet System

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Oil Saturation (frac.)

Oil

Re

taiv

e P

erm

ea

bil

ity

Soi=0.665, Teta_ow=180.0 deg.

Soi = 0.665, Teta_ow=60.0 deg.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Gas Sauration (frac.)

Ga

s R

ela

tiv

e P

erm

ea

bil

ity

Soi=0.665, Teta_ow=180.0 deg.

Soi = 0.665, Teta_ow=60.0 deg.

Tertiary Gas Injection, Strongly Oil-wet System

WAG Flooding, Water-wet System

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Oil Saturation (frac.)

Oil

Re

lati

ve

Pe

rme

ab

ilit

y

First WF Soi=0.745 to So=0.264TGI from Soi=0.662 to So=0.543Second WF from Soi=0.543 to So=0.185TGI from Soi=0.662 to So=0.514Second WF from Soi=0.514 to So=0.157 TGI from Soi=0.662 to So=0.056TGI from Soi=0.662 to So=0.597Second WF from Soi=0.597 to So=0.219TGI from Soi=0.662 to So=0.636Second WF from Soi=0.636 to So=0.238

Effects of Initial Oil Saturation on Second Water Flooding

WAG Flooding, Water-wet System

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Oil Saturation (frac.)

Oil

Rel

ativ

e P

erm

eabi

lity

First WF Soi=0.745 to So=0.264TGI from Soi=0.64 to So=0.52Second WF from Soi=0.52 to So=0.185TGI from Soi=0.616 to So=0.526Second WF from Soi=0.526 to So=0.2 TGI from Soi=0.662 to So=0.528Second WF from Soi=0.528 to So=0.179TGI from Soi=0.687 to So=0.504Second WF from Soi=0.504 to So=0.157Secondary Gas InjectionTGI from Soi=0.590 to So=0.523Second WF from Soi=0.522 to So=0.222

WAG FloodingWAG Flooding

Gas Injection into Different SoiGas Injection into Different Soi

Secondary vs. Tertiary Gas Secondary vs. Tertiary Gas InjectionInjection

Applications

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

Solution Gas Drive Solution Gas Drive

Future Work

Conclusions

Three-Phase ModelThree-Phase Model

Relative Permeability and Capillary Relative Permeability and Capillary Pressure ResultsPressure Results

Working on Coupling a Pore-Scale Working on Coupling a Pore-Scale Network Model with Larger-Scale Network Model with Larger-Scale Simulation and Including More PhysicsSimulation and Including More Physics