development of a 1d isothermal surfactant flooding simulator
DESCRIPTION
This presentation discussed in depth on the modeling and numerical solutions to surfactant flooding processes for enhanced oil recovery.TRANSCRIPT
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Adsorption and Dispersion in EOS CompositionalFlow
Akmal Aulia, G01059
EOR Centre, Petroleum Engineering, UT PetronasSupervisor: Prof. Dr. Noaman El-Khatib
December 20th, 2010
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Outline
Background
Literature Review
Methodology
Extension
Research Progress
Summary
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Background
Is my surfactant flooding project economical?
Loss of surfactants due to adsorption
Loss of slug stability due to dispersion
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Background
Is my surfactant flooding project economical?
Loss of surfactants due to adsorption
Loss of slug stability due to dispersion
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Problem Description
Based on given fluid and rock properties, is the projecteconomical?
How can I evaluate the economical feasibilities? - simulation,other quantitative methods?
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Problem Description
Based on given fluid and rock properties, is the projecteconomical?
How can I evaluate the economical feasibilities? - simulation,other quantitative methods?
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Problem Description
Many uses Compositional Models to simulate ChemicalFlooding processes
IFT, Mobility, Relative Permeability, Residual Saturations, areaffected by compositions
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Problem Description
Many uses Compositional Models to simulate ChemicalFlooding processes
IFT, Mobility, Relative Permeability, Residual Saturations, areaffected by compositions
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Objective of the Study
To investigate the effects of adsorption and dispersion oncompositional dynamics in surfactant flooding processes.
(possible extension?) To explore compositional paths undervarious heterogeneity distributions.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Objective of the Study
To investigate the effects of adsorption and dispersion oncompositional dynamics in surfactant flooding processes.
(possible extension?) To explore compositional paths undervarious heterogeneity distributions.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
1.1. Problem Description1.2. Objective1.3. Scope of Study
Scope of Study
1-dimensional
isothermal
core scale
capillary pressure neglected
2 phase (aqueous, oleic), 3 components (surfactant, water,oil)
no gas
homogenous, heterogeneous (possible extension)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Progress in Compositional Simulation
AU YR AD DP EOS DIM Gas? PHS
Nolen 1973 -√
LE-RK 3D√
-Pope 1978 Lang.
√- 1D
√-
Coats 1980 - - RK 3D√
3El-Khatib 1985
√ √- 1D - 2
Porcelli 1994 - - - 1D - 2Branco 1995 - -
√1D
√3
Bidner 1996√ √
- 1D - 2Wang 1997 - - PR 3D
√-
Coats 1998 - - PR, SRK 3D√
3Coats 2000 - - flash 1D,3D
√3
UTCHEM 2000√ √
- 3D√
2,3Bidner 2002
√ √- 1D - 2
GPAS 2005 Lang. -√
3D - 3Chen 2007
√ √PR 3D
√3
Najafabadi 2009√ √
PR 3D - 3Hustad 2009 - - - 1D,2D,3D
√3
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A glimpse on the Finite Difference Method (FDM)
f : x → u, x ∈ <. Let h = x − a and u′(x) = ddx (u(x)). The Taylor
expansion of u(x + h) and u(x − h) for 2nd order,
u(x + h) = u(x) + hu′(x) +h2
2!u′′(x) + O(h3) (1)
u(x − h) = u(x)− hu′(x) +h2
2!u′′(x)− O(h3) (2)
can yield the approximations of u′(x)
u′(x) =u(x + h)− u(x − h)
2h(3)
u′(x) =u(x + h)− u(x)
h(4)
u′(x) =u(x)− u(x − h)
h(5)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A glimpse on the Finite Difference Method (FDM)
In terms of grids, (du
dx
)i
=ui+1 − ui−1
2h(6)(
du
dx
)i
=ui+1 − ui
h(7)(
du
dx
)i
=ui − ui−1
h(8)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Explicit FDM
Let,dP
dt=∂2P
∂x2(9)
or,Pt = Pxx (10)
for short. Thus, discretized EXPLICITLY as:
Pn+1i − Pn
i
4t=
Pni+1 − 2Pn
i + Pni−1
(4x)2(11)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Explicit FDM
Solve EXPLICITLY discretized equation as,
Pn+1i = Pn
i +4t
(4x)2(Pn
i+1 − 2Pni + Pn
i−1) (12)
Therefore, use PAST information to obtain FUTURE information.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Implicit FDM
Recall,Pt = Pxx (13)
IMPLICIT discretization reads,
Pn+1i − Pn
i
4t=
Pn+1i+1 − 2Pn+1
i + Pn+1i−1
(4x)2(14)
Therefore, use FUTURE and PAST information to obtainFUTURE information.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Implicit FDM
To solve for the IMPLICIT scheme, is to solve A*x=b such that Ais a matrix and x,b are vectors. Example,
1 + r − r2 0 0
− r2 1 + r − r
2 00 − r
2 1 + r − r2
0 0 − r2 1 + r
P2
P3
P4
P5
=
f1 − kI
f2f3
f4 − kB
Tools needed for solving: Thomas algorithm, Choleskydecomposition, Conjugate Gradient, Preconditioned ConjugateGradient
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
Newton-Raphson
For single variable,
x = xold −f
f ′(15)
For multiple variables,
x = xold + p (16)
J · p = −f (17)
where (for example, 2 variables),
J =
[∂f1/∂x1 ∂f1/∂x2
∂f2/∂x1 ∂f2/∂x2
]
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
Nomenclature:
S j =volume of phase j
pore volume(18)
c li =
volume of component i in phase j
volume of phase l(19)
Ci =∑
j
S lc ji [=]
total volume of component i
pore volume(20)
Γi =adsorbed volume of component i
pore volume(21)
Kl = dispersion coefficient of phase l (22)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
For i ∈ {p, c} the continuity equations for each species read,
φ∂Ci
∂t+
∂
∂x
∑l∈L
c li u
l − ∂
∂x
∑l∈L
S lKl ∂c li
∂x= −∂Γi
∂t(23)
The adsorption expression is,
Γc = φαLapc (24)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
Summing the continuity equations for all i ∈ Cyields the Overall Continuity Equation (pressure equation)
∂
∂x
(λ∂Pa
∂x
)=
∂
∂t
(∑i∈C
Γi
)− ∂
∂x
(λo ∂PC
∂x
)(25)
Note: Dispersion terms collapses by summation. The dispersionterm reads,
KDm
=1
Fφ+ 1.75
Udp
Do(26)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
Restriction relations:For i ∈ {p, c},
Ci =∑l∈L
S lc li (27)
For l ∈ {o, a}, ∑i∈C
c li = 1 (28)
For all i and l, ∑l∈L
S l = 1 (29)∑i∈C
Ci = 1 (30)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
Supporting expressions:For l = a only,
ul = −Kk lr
µl
∂P l
∂x(31)
For all i and l ,
u = −λ∂Pa
∂x− λo ∂PC
∂x(32)
PC = Po − Pa (33)
u = uo + ua (34)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
The Compositional Model: Bidner et al, 1994-2002
The unknown variables are,
ul = 2 (35)
u = 1 (36)
P l = 2 (37)
S l = 2 (38)
c li = 6 (39)
Ci = 3 (40)
TOTAL UNKNOWNS = 16 (41)
Note: 16 Unknowns vs 13 Equations !!!
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
DOF=3. How to make it 0 ?
Bidner et al use equilibrium ratios,
Lapc =
cap
cac
(42)
Lowc =
cow
coc
(43)
Kc =coc
cac
(44)
- EOS can yield more accurate compositions (Chen, 2006, 2007).- Recent work (Roshafenkr, Li, and Johns 2008) describe a fewexperimental efforts for phase behavior – a most likely feasibleoption.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A note about Roshafenker, Li, and Johns (UT Austin)
Yinghui Li wrote a thesis about the method
Roshafenkr, Li, and Johns wrote a paper (2008) on themethod
They said that the future study is to include their phasebehavior modeling methods on compositional simulators.
This is how this research can contribute; a continuation oftheir research.
At a glance; method basically requires few experimentalsamplings.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A note about Roshafenker, Li, and Johns (UT Austin)
Yinghui Li wrote a thesis about the method
Roshafenkr, Li, and Johns wrote a paper (2008) on themethod
They said that the future study is to include their phasebehavior modeling methods on compositional simulators.
This is how this research can contribute; a continuation oftheir research.
At a glance; method basically requires few experimentalsamplings.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A note about Roshafenker, Li, and Johns (UT Austin)
Yinghui Li wrote a thesis about the method
Roshafenkr, Li, and Johns wrote a paper (2008) on themethod
They said that the future study is to include their phasebehavior modeling methods on compositional simulators.
This is how this research can contribute; a continuation oftheir research.
At a glance; method basically requires few experimentalsamplings.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A note about Roshafenker, Li, and Johns (UT Austin)
Yinghui Li wrote a thesis about the method
Roshafenkr, Li, and Johns wrote a paper (2008) on themethod
They said that the future study is to include their phasebehavior modeling methods on compositional simulators.
This is how this research can contribute; a continuation oftheir research.
At a glance; method basically requires few experimentalsamplings.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
2.1. Progress in Compositional Simulation2.1. Finite Difference Method2.2. Explicit FDM2.3. Implicit FDM2.4. Newton-Raphson2.5. Compositional Model
A note about Roshafenker, Li, and Johns (UT Austin)
Yinghui Li wrote a thesis about the method
Roshafenkr, Li, and Johns wrote a paper (2008) on themethod
They said that the future study is to include their phasebehavior modeling methods on compositional simulators.
This is how this research can contribute; a continuation oftheir research.
At a glance; method basically requires few experimentalsamplings.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
A glimpse on IMPECS
Using FDM,- IMplicit Pressure- Explicit Concentrations + Saturations
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
The IMPECS algorithm: Bidner (2002)
For each time step, for all gridblocks:
STEP 1: Calculate Pa IMPLICITLY.
STEP 2: Calculate Po .
STEP 3: Calculate u, ua, uo .
STEP 4: Calculate Cc ,Cp via continuity equations,EXPLICITLY.
STEP 5: Calculate Cw , cji , S
j via restriction relations.
STEP 6: Evaluate errors:
M∑m=1
|(Ci )k+1m − (Ci )
km| (45)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
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5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
Mobility calculations
σ for Type II (-) can be described as a function of compositions,
F =1− e−
√Pi (c
oi −ca
i )2
1− e−√
2
log σ = log F + (1− Lapc) log σH +
G1
G1 + G2La
pc ; Lapc ≤ 1
log σ = log F +G1
(1 + LapcG2)
; Lapc > 1
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
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5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
Mobility calculations
Once σ is found, we can compute the capillary number:
Nvc =µaHuIN
σ(46)
Which leads to the residual saturations as a function of Nvc ,
S jr
S jrH=
1, if Nvc < 10(1/T j
1)−T j2 ;
T j1
[log(Nvc) + T j
2
], if 10(1/T j
1)−T j2 ≤ Nvc ≤ 10−T j
2 ;
0, if Nvc > 10−T j2 .
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
Mobility calculations
k lr = k l0
r
(S l − S lr
1− S lr − S l ′r
)e l
; l 6= l ′ (47)
k l0r = (1− k l0H
r )
(1− S l ′r
S l ′rH
)+ k l0H
r (48)
e l = (1− e lH)
(1− S l ′r
S l ′rH
)+ e lH (49)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
3.1. On IMPECS3.1. IMPECS algorithm3.2. Mobility calculations
Mobility calculations
along with, (my supervisor suggested other averaging method)
µl = c lwµ
aHeα1(c lp+c l
s) + c lpµ
oHeα1(c lw +c l
s) + c lsα3e
α2(c lw +c l
p) (50)
we can write mobility as,
λ = λo + λa =Kko
r
µo+
Kkar
µa(51)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Checkpoints
- Thomas Algorithm (with Fortran 95)- Cholesky Decomposition (with Fortran 95)- Crank-Nicholson Scheme (with Fortran 95) - Conjugate Gradient- Jacobi-Preconditioned Conjugate Gradient (with Fortran 9)- IMPECS solver (with Fortran 90, some progress on debugging)- Multivariable Newton-Raphson (with Fortran 90)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part I
Recall,
Lapc =
cap
cac
(52)
Lowc =
cow
coc
(53)
Kc =coc
cac
(54)
Lapc , Lo
wc , and Kc are the swelling parameter, solubilizationparameter, and equilibrium ratio between the two phases,respectively.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part II
Also recall,
Cc =∑l∈L
S jc lc
= Sacac + Soco
c
= Sacac + (1− Sa)Kcc
ac (55)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part III
Similary for Cp,
Cp = Sacap + Soco
p
= SaLapcc
ac + (1− Sa)(1− co
c − cow )
= SaLapcc
ac + (1− Sa)(1− Kcc
ac − Lo
wccoc )
= SaLapcc
ac + (1− Sa)(1− Kcc
ac − LwcoKcc
ac )
= SaLapcc
ac + (1− Sa)(1− Kcc
ac (1 + Lo
wc))
(56)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part IV
Thus, we can set up a 2 equations - 2 unknown adaptive NR as,
f1(Sa, cac ) = Saca
c + (1− Sa)Kccac − Cc (57)
f2(Sa, cac ) = SaLa
pccac + (1− Sa) ·
(1− Kccac (1 + Lo
wc))− Cp (58)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part V
−→x k+1 = −→x k − J−1−→f k (59)
where,
−→x k =
[Sa
cac
]k
−→f k =
[x1
x2
]k
=
[f1(Sa, ca
c )
f2(Sa, cac )
]k
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part VI
and,
J =
∂f1∂x1
∂f1∂x2
∂f2∂x1
∂f2∂x2
k
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part VII
where,
∂f1∂x1
= cac (1− Kc) (60)
∂f1∂x2
= Sa(1− Kc) + Kc (61)
∂f2∂x1
= cac (La
pc + Kc(1 + Lowc))− 1 (62)
∂f2∂x2
= Sa(Lapc + Kc(1 + Lo
wc))
−Kc(1 + Lowc) (63)
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part VIII
However, constraints must be defined → enhanced adaptivity!
!"#$%&!"#&
!"#$%&!"'& %(!"'&
Figure: Description of the Adaptive Newton-Raphson.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part IX
Mathematically,
(Sa)k+1 =
(Sa)k + Sar
2, if (Sa)k+1 < Sar
(Sa)k + (1− Sor )
2, if (Sa)k+1 > (1− Sor )
(Sa)k+1, otherwise.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Note on the Implementing Adaptive NR Method: Part X
and,
(cac )k+1 =
(cac )k + 0
2, if (ca
c )k+1 < 0
(cac )k + 1
2, if (ca
c )k+1 > 1
(cac )k+1, otherwise.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Fortran Results Part I
Table: Compositional Simulator’s Input Parameters
Parameter Assigned Value Units Description
uIN 10−4 cm/s input flowrate
SorH, SarH 0.35 res. sat. at high IFTPIN, POUT 1 atm endpoint Pressuresφ 0.24 porosity
CINs 0.1 overall surfactant conc.
CINp 0 overall oil conc.
L 100 cm core (porous media) lengthK 0.5 Darcy permeability
ko0Hr , ka0H
r 1, 0.2 Rel. Permeability at high IFT
µoH , µaH 5, 1 cP phase viscosities
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
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Fortran Results Part II
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.1
1 2 3 4 5
n=1
n=2
n=3
Figure: Aqueous phase pressures across grid at different timesteps.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
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5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Fortran Results Part III
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5
n=1
n=2
n=3
Figure: Surfactant phase composition (aqueous phase) across grid atdifferent timesteps.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Fortran Results Part IV
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5
n=1
n=2
n=3
Figure: Surfactant phase composition (oleic phase) across grid atdifferent timesteps.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Fortran Results Part V
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5
n=1
n=2
n=3
Figure: Aqueous phase saturation across grid at different timesteps.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Fortran Results Part VI
Figure: Oleic phase saturation across grid at different timesteps.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Achievements - 3 semesters residency
Published 2 journal articles:Akmal Aulia and Noaman El-Khatib, ”Mathematical Description of the Implementation of the AdaptiveNewton-Raphson Method in Compositional Porous Media Flow,” International Journal of Basic andApplied Sciences IJBAS-IJENS Vol. 10 No. 06 ISSN: 2077-1223 (accepted with minor revision).
Akmal Aulia, Tham Boon Keat, Muhammad Sanif M., Noaman El-Khatib, and Mazuin Jasamai, ”SmartOilfield Data Mining for Reservoir Analysis,” International Journal of Engineering and TechnologyIJET-IJENS Vol. 10 No. 06 ISSN: 2077-1185 (accepted).
and 2 conference papers:Akmal Aulia and Noaman El-Khatib, ”Mathematical modeling of Adsorption and Dispersion in ChemicalFlood EOS Compositional Flow”, ICIPEG 2010, 15-17 June 2010, Kuala Lumpur, Malaysia
Akmal Aulia, Tham Boon Keat, Muhammad Sanif Bin Maulut, Noaman El-Khatib, and Mazuin Jasamai,”Mining Data from Reservoir Simulation Results”, ICIPEG 2010, 15-17 June 2010, Kuala Lumpur, Malaysia
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
4.1. Checkpoints4.2. Recent Publications4.3. Gantt Chart
Gantt Chart
Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Literature Review
Model Development
Model Discretization
Code Development
Debug
Analytical Solutions with MOC
Publications
Dissertation Writing
Submit Dissertation
2009 2010Items
2 Conference Papers, 2 Journal Articles
2011
attempt 1 more journal
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Summary
The importance of IMPECS in solving coupled PDE.
The importance of Newton-Raphson methods in many aspectof IMPECS.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Summary
The importance of IMPECS in solving coupled PDE.
The importance of Newton-Raphson methods in many aspectof IMPECS.
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow
1. Background2. Literature Review
3. Methodology4. Research Progress
5. Summary
Thank you for coming! Questions and Comments?
Akmal Aulia, G01059 Adsorption and Dispersion in EOS Compositional Flow