flow visualization & pore network simulation of immiscible/ miscible displacement with gravity...

Flow Visualization & Flow Visualization & Pore Network Simulation ofPore Network Simulation of

Immiscible/ Miscible Displacement Immiscible/ Miscible Displacement with Gravity Domination with Gravity Domination

M. HaghighiM. Haghighi09/09/0909/09/09

Table of ContentsTable of Contents

EOR Process with Gravity DominationEOR Process with Gravity Domination

Darcy Law Is Not EnoughDarcy Law Is Not Enough

Experimental ResultsExperimental Results

Modelling ResultsModelling Results

Future WorkFuture Work

EOR Process with EOR Process with Gravity DrainageGravity Drainage

GAGDGAGD

SAGDSAGD

Downdip Gas InjectionDowndip Gas Injection

Updip Gas InjectionUpdip Gas Injection

Gas Injection In Fractured ReservoirsGas Injection In Fractured Reservoirs

CO2 GAGD (Jadhawar & Sarma)CO2 GAGD (Jadhawar & Sarma)

SAGDSAGD

Downdip Gas InjectionDowndip Gas Injection

Gravity Drainage In Fractured ReservoirsGravity Drainage In Fractured Reservoirs

Reservoir SimulationReservoir Simulation

Diffusivity Equation (Mass Balance and Diffusivity Equation (Mass Balance and Darcy Equation)Darcy Equation)

Relative Permeability Concept (Buckley-Relative Permeability Concept (Buckley-Leverett equation for immiscible Leverett equation for immiscible displacement) displacement)

EOR EfficiencyEOR Efficiency

Microscopic Displacement Efficiency Microscopic Displacement Efficiency

××

Macroscopic Displacement EfficiencyMacroscopic Displacement Efficiency

Microscopic Displacement Microscopic Displacement EfficiencyEfficiency

Flow Mechanism at Pore ScaleFlow Mechanism at Pore Scale

Pore GeometryPore Geometry

Pore StructurePore Structure

WettabilityWettability

DispersionDispersion

DiffusionDiffusion

Macroscopic Displacement Macroscopic Displacement EfficiencyEfficiency

Areal Sweep EfficiencyAreal Sweep Efficiency

Vertical Sweep EfficiencyVertical Sweep Efficiency

Large Scale Reservoir HeterogeneitiesLarge Scale Reservoir Heterogeneities

Well PatternWell Pattern

Darcy Law is not enoughDarcy Law is not enough(at (at Pore Scale)Pore Scale)

Pore Scale Flow MechanismsPore Scale Flow Mechanisms

Film FlowFilm Flow

Meniscus MovementMeniscus Movement

Corner FlowCorner Flow

Wettability AlterationWettability Alteration

Fluid SpreadingFluid Spreading

Darcy Law Is Not EnoughDarcy Law Is Not Enough(In (In Pore Network)Pore Network)

Viscous FingeringViscous Fingering

Invasion PercolationInvasion Percolation

Diffusion Limited AggregationDiffusion Limited Aggregation

Fractal CharacteristicsFractal Characteristics

DLADLA

Lenormand et al.Lenormand et al.

Research Tools at Pore ScaleResearch Tools at Pore Scale

Flow Visualization using Glass MicromodelFlow Visualization using Glass Micromodel

Pore Network SimulationPore Network Simulation

Glass Etched Micromodels

1) Preparing the pattern of porous media

2) Elimination of the protection-layer of the mirror

3) Covering the mirror with photo resist laminate

4) Exposing the covered mirror to UV light

5) Elimination of not-lightened parts using a developer

6) Etching the glass with HF

7) Fusing the etched glass with a plain glass

Experimental Set-upExperimental Set-up

Pore Network Modeling

Simple solution to the momentum equations in each pore throat.

Mass conservation at each pore: 0 throatsj

iji qQ

)(,, ij

jiji PP

gq

1. A discrete view of the porous medium (pores and pore throats)

Pores provide volume & interconnectivity

Pore throats provide resistance to flow.

2. Solution to various transport problems using conservation equations.

Solution of the Fluid Flow in the NetworkSolution of the Fluid Flow in the Network

Fluid Flow EquationsFluid Flow Equations

a) One Phase (Oil):a) One Phase (Oil):

b) Two-Phase (Oil & Gas):b) Two-Phase (Oil & Gas):

)( oil

j

oil

i

oil

ij

oil

ij gq ghP oiloiloil

)( cjiijij Pgq

Nodes with Oil-Gas Front:

cii PPP

Node

c

oil

i

gas

i PPP

Pgas= Constant= Patm

Continuity (Mass Balance) Eq. For Each Oily Node:

j

oil

ijq 0

Writing Continuity Eq. for all Nodes, We have a linear set of equations:

)],,([]].[[ gasog

c PHgPDPG

Conductances:

g =0.5GA2/μ , circular cross section g = 0.5623GA2/μ , square cross section g = 3R2A/20μ , triangular cross section

At = πR2 , circular cross section At = 4R2 , square cross section At =R2/4G , triangular cross section

2P

AG

2

232313

2

23

231

)1(1)1(sin12

tan)sin1(

cc A

AffA

Ag

Film Conductance:

Gas-Oil DisplacementGas-Oil Displacement

ing

ed

q

Vt

edttted qtVV .1

Generalization of Continuity Eq. for Different Fluid Configurations

)(...)()(411 44

4

11

4

1ijogjiij

kijogjiijijij

kij hgPPghgPPggq

kkk

Example: If All Adjacent Nodes of Node i Are Oily Nodes:

441144114321......)( ijogijijogijjijjijiijijijij hgghggPgPgPgggg

Example: If One of the Adjacent Nodes of Node i be Occupied by Gas:

4

1

4

1

0)(k

ijijk

ij kkkgq

4422111

44224321

...)(

...)(

ijogijijogijijogCatmij

jijjijiijijijij

hgghgghgPPg

PgPgPgggg

ij

34 Different Fluid Gonfigurations → 34 Different Continuity Equations

Pore LevelPore LevelDisplacement MechanismsDisplacement Mechanisms

2-Phase Displacement Mechanisms2-Phase Displacement Mechanisms

a) Drainage a) Drainage

b) Imbibitionb) Imbibition

c) Counter-Current Drainagec) Counter-Current Drainage

3-Phase Displacement Mechanisms3-Phase Displacement Mechanisms

a) Double Drainagea) Double Drainage

b) Double Imbibitionb) Double Imbibition

ijC

jgas

ioil Og

PPP ijC

jgas

ioil Og

PPP ijC

jgas

ioil Og

PPP

ij

C

j

gas

i

oil OgPPP

k k

j

oil

i

oil

ij

oil

ij

oilkkk PPgq 0)(

ijC

jgas

ioil Og

PPP

ij

C

j

gas

i

oil OgPPP

JOil

IJCg

IOil PPPP

og

Model AssumptionsModel Assumptions

≈≈1010-6 -6 → Viscous forces are negligible→ Viscous forces are negligible

≈ ≈ 1609 > 101609 > 10-4 -4 → Gravity forces are very important→ Gravity forces are very important

capN

ij

ji gLB

2)(

Future WorkFuture Work

Micible Co2 Flooding with Gravity Micible Co2 Flooding with Gravity Domination Using Glass-etched Domination Using Glass-etched Micromodel and Pore network ModellingMicromodel and Pore network Modelling

Miscible Co2 Flooding with Miscible Co2 Flooding with Gravity Domination Gravity Domination

Establishing Flow Visualization LabEstablishing Flow Visualization Lab Performing Miscible Displacement TestsPerforming Miscible Displacement Tests Developing Pore Network Model for Developing Pore Network Model for Miscible DisplacementMiscible DisplacementIdentifying Controlling parametersIdentifying Controlling parametersPerforming Experimental in Core ScalePerforming Experimental in Core ScalePerforming Process OptimizationPerforming Process OptimizationUpscalingUpscaling

End End

Any Questions?Any Questions?

flow visualization & pore network simulation of immiscible/ miscible displacement with gravity...

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