Flow Visualization &
Pore Network Simulation of
Immiscible/ Miscible Displacement
with Gravity Domination
M. Haghighi
09/09/09
Table of Contents
EOR Process with Gravity Domination
Darcy Law Is Not Enough
Experimental Results
Modelling Results
Future Work
EOR Process with
Gravity Drainage
GAGD
SAGD
Downdip Gas Injection
Updip Gas Injection
Gas Injection In Fractured Reservoirs
CO2 GAGD (Jadhawar & Sarma)
SAGD
Downdip Gas Injection
Gravity Drainage In Fractured Reservoirs
Reservoir Simulation
Diffusivity Equation (Mass Balance and
Darcy Equation)
Relative Permeability Concept (BuckleyLeverett equation for immiscible
displacement)
EOR Efficiency
Microscopic Displacement Efficiency
×
Macroscopic Displacement Efficiency
Microscopic Displacement
Efficiency
Flow Mechanism at Pore Scale
Pore Geometry
Pore Structure
Wettability
Dispersion
Diffusion
Macroscopic Displacement
Efficiency
Areal Sweep Efficiency
Vertical Sweep Efficiency
Large Scale Reservoir Heterogeneities
Well Pattern
Darcy Law is not enough
(at Pore Scale)
Pore Scale Flow Mechanisms
Film Flow
Meniscus Movement
Corner Flow
Wettability Alteration
Fluid Spreading
Darcy Law Is Not Enough
(In Pore Network)
Viscous Fingering
Invasion Percolation
Diffusion Limited Aggregation
Fractal Characteristics
DLA
Lenormand et al.
Research Tools at Pore Scale
Flow Visualization using Glass Micromodel
Pore 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-up
Experimental Results
Experimental Results
Experimental Results
Experimental Results
Experimental Results
Experimental Results
Experimental Results
Pore Network Modeling
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.
Mass conservation at each pore:
Simple solution to the
momentum equations in each
pore throat.
Qi 
 qij  0
j throats
qi , j 
gi, j

( Pj  Pi )
Pi  Pi    Pc
Solution of the Fluid Flow in the Network
Conductances:
Fluid
Flow Equations
Nodes
with Oil-Gas
Front:
g a)
=0.5GA
, (Oil):
circular cross
section
One2/μPhase
g = 0.5623GA2/μg a,s square
cross Node
section
oil
oil , 
oil
oil section
P(i oilP
g = 3R2A/20μqP
triangular
cross
i  g
c

)
ij
G
ij
i
j
 o il  P o il   o il gh
A Pgas= Constant= Patm
P2
b)
Two-Phase
(Oil Balance)
& Gas): Eq. For Each Oily Node:
Continuity
(Mass
At = πR2 , circular cross section
oil
At = 4R2 , square
cross
section
q
0
ij (
q

g

ij
ij
2
j
At =R /4G , triangular
crossisectionj

 Pc )
Writing
Film Conductance:
Continuity Eq. for all Nodes,
We have a linear set of
equations:
3
2
2
g
A1 (1  sin  ) tan 3

og
gas
A2 
2
12Ac sin  (1   3 ) c1  f1 3  (1  f 2 3 )

A

c 

2
[G].[ P]  [ D ( P ,  gH , P )]
Gas-Oil Displacement
Generalization of Continuity Eq.
for Different Fluid Configurations
4 Different Continuity Equations
34 Different Fluid
Gonfigurations
→
3
V
Ved Nodes
t.qiedAre Oily Nodes:
t  t Vof
1 tNode
Example: If Allqing
Adjacent
t  
ed
( g ij1  g ij2  g ij3  g ij4 ) Pi  g ij1 Pj1  ...  g ij4 Pj4  g ij1  og ghij1  ...  g ij4  og ghij4
4
q
k 1
4
ijk
  g ijk ( ijk )  g ij1 ( Pi  Pj1   og ghij1 )  ... g ij 4 ( Pi  Pj 4   og ghij4 ) 
k 1
Example: If One of the Adjacent Nodes of Node i be Occupied by Gas:
4
q
k 1
4
ijk
  g ijk ( ijk )  0 
k 1
( g ij1  g ij2  g ij3  g ij4 ) Pi  g ij2 Pj2  ...  g ij4 Pj4 
g ij1 ( Patm  PCij   og ghij1 )  g ij2  og ghij2  ...  g ij4  og ghij4
1
j
Poili 
 Pgas
 PCijOg
Pore Level
Displacement Mechanisms
2-Phase Displacement Mechanisms
a) Drainage
b) Imbibition
c) Counter-Current Drainage
3-Phase Displacement Mechanisms
a) Double Drainage
b) Double Imbibition
j
Poili  Pgas
 PCij
Og
j
Poili  Pgas
 PCij
Og
POilI  Pg  PCIJog  POilJ
 q   g
ijk
oil
k
k
ijk
oil
( Poili  Poilj )  0
k
Model Assumptions
N cap
B



(  i   j ) gL2
 ij
≈10-6 → Viscous forces are negligible
≈ 1609 > 10-4 → Gravity forces are very important
Experimental Results
Future Work
Micible Co2 Flooding with Gravity
Domination Using Glass-etched
Micromodel and Pore network Modelling
Miscible Co2 Flooding with
Gravity Domination
Establishing Flow Visualization Lab
Performing Miscible Displacement Tests
Developing Pore Network Model for
Miscible Displacement
Identifying Controlling parameters
Performing Experimental in Core Scale
Performing Process Optimization
Upscaling
End
Any Questions?