submarine gas hydrate reservoir simulations – a gas ... · submarine gas hydrate reservoir...
TRANSCRIPT
Submarine Gas Hydrate Reservoir Simulations – A Gas/ Liquid Fluid Flow Model for Gas Hydrate Containing Sedimen ts
Stefan Schlüter, Georg Janicki, Torsten Hennig, Görge DeerbergFraunhofer UMSICHT, Oberhausen (Germany)
COMSOL Conference 2014, Cambridge (UK)
What are gas hydrates?
Gas molecules
Water molecules
Water
Tem
pera
ture
Gas
© J
en
s G
rein
ert IFM GEOMAR
Petrobras
Fraunhofer UMSICHT
Idea of the SUGAR project
© IFM
GEO
MA
R
• CO2 hydrate stable at lower pressure / higher temperature
• replacing CH4 by CO2
• simultaneous production of CH4
and storage of CO2
• sustainable energy supply system
Reservoir model principles
Phases
• 3 solid phases: sediment, methane hydrate, CO2 hydrate
• 2 fluid phases: gas phase, water (liquid) phase
• (1 supercritical phase: supercritical CO2 – not implemented yet)
Components
• 2 gas phase components: methane, carbon dioxide
• 3 components solved in water: sea salt, methane, carbon dioxide
Pressure equation: advanced 2-phase Darcy model
Energy equation: flow through porous solid, hydrate extensions, latent heats, pressure work
Reservoir Model – Pressure/Saturation Equation
Continuity equations:
Saturation:
Convection splitted form:
( ) ( )
( ) ( )
( )
( )
G G G G G
L L L L L
MH MH MH
CH CH CH
S st
S st
S st
S st
φ ρ ρ
φ ρ ρ
φ ρ
φ ρ
∂+∇⋅ =
∂∂
+∇⋅ =∂∂
=∂∂
=∂
u
u
1S sS
t t
ρ ρφ φ
ρ ρ ρ
∂ ∂ ∇+ +∇⋅ + ⋅ =
∂ ∂u u
1
j j
j
S
jS
ε ε
ε φ= = =−
volume fraction of phase
sediment free volume fraction
Euler/Euler
Reservoir Model – Pressure/Saturation Equation
Density derivatives:
General form:
Darcy equation:
Phase summation:
, , ,
1 1 1, ,
k k
k
kT y P y P TP T y
ρ ρ ρχ β ϕ
ρ ρ ρ
∂ ∂ ∂ = = − = ∂ ∂ ∂
1,k
k k kk k
yP TP T y
t t t t
ρ ρχ β ϕ χ β ϕ
ρ ρ
∂∂ ∂ ∂ ∇= − + = ∇ − ∇ + ∇
∂ ∂ ∂ ∂∑ ∑
( ) ( )with , ,rel
f rel H L
kP k f S SΛ ρ Λ
η= − ∇ + = =u K g
k
k k kk k
yS P T sS P T y
t t t tφ φ χ β ϕ χ β ϕ
ρ
∂∂ ∂ ∂ + − + +∇⋅ + ⋅ ∇ − ∇ + ∇ = ∂ ∂ ∂ ∂ ∑ ∑u u
1 , 0j
jj j
SS
tφ∂
= =∂
∑ ∑
Reservoir Model – Pressure/Saturation Equation
Insertion in general form and summation over phases leads to general pressure equation:
Capillary pressure:
Calculation pressure:
( )( )
( ) , ,
,
, , ,
j
j j f j j jj j
f j j j j j k j k j jjk
j k j
j j k j f j j j k j k jj j jkj
PS P
t
P T y P
q yTS T y
t t
φ χ Λ ρ
Λ χ ρ β ϕ
φ β ϕ Λ ρ β ϕρ
∂+∇⋅ − ∇ +
∂
− ∇ + − ∇ + ∇ ∇ =
∂ ∂ + − − ∇ − ∇ ∂ ∂
∑ ∑
∑ ∑
∑ ∑ ∑ ∑
K g
K g
K g
with ( , )C G L C H LP P P P f S S= − =
( )1 1 1
,2 2 2L G L C G C
P P P P P P P P P= + → = − = +
Reservoir Model – Pressure/Saturation Equation
COMSOL coefficient form PDE:
( )( )
( ) ( ) ( )
0,
0 2,
2
L L G G MH CH H
L L L
C
f G L L L G G
f L G
f L C
f L L
L
f
P S S S Su d
S S
P
cP
φ χ χ χ
φ χ φ
Λ Λ ρ Λ ρ ΛΛ Λ
γΛ ε
Λ ρ
Λ χ
β
+ + + = =
∇ − − + + + = = ∇ − − +
+−
=
K gK
KK g
K( )( )( )( )
( )( )
,
,
0,
0
L C L L S L S
G G C G G C G C
f L L C L L
P P T c
P P T y f
P P T
ρ β ϕ
Λ χ ρ β ϕ
Λ χ ρ β
∇ −∇ + − ∇ + ∇ + ∇ +∇ + − ∇ + ∇ = − ∇ −∇ + − ∇
g
g
K g
…
…
( )2
2
u ue d c u u u au f
ttα γ β
∂ ∂+ +∇⋅ − ∇ − + + ∇ + =∂∂
artificial diffusion for SL
Reservoir Model – Energy Equations
Summation over single phase energy equations with
Pressure work:
Latent heats: (heats of formation)
( ) ( )
( ) ( )( )
( ) ( )( )
( ) ( )( )
, ,
, ,
, ,
,1 1 0
G
G G P G G G G f G G G G P G G P
L
L L P L L L L f L L L L L P L L L
H
MH MH P MH CH CH P CH MH MH CH CH H H
S
S P S S S
TS c S T P c T q
t
TS c S T P S c T q
t
TS c S c S S T q
t
Tc T
t
φ ρ φ Λ ρ ρ
φ ρ φ Λ ρ ε ρ
φ ρ ρ φ
φ ρ φ
∂+∇⋅ − ∇ − ∇ + ∇ =
∂
∂+∇⋅ − ∇ − ∇ + + ∇ ∇ =
∂
∂+ −∇⋅ + ∇ =
∂
∂− +∇⋅ − − ∇ =
∂
K g
K g
ɺ
ɺ
ɺ
λλλλ
λλλλ
λ λλ λλ λλ λ
λλλλ
( )( )1G
P G G G f G G G G G G
Pq S T P T P
tφ β Λ ρ β
∂= + ∇ + − ∇
∂K gɺ
( )H MH MH CH CHq R h R h= − ∆ + ∆ɶ ɶɺ
G L H ST T T T= = =
real gasbehaviour
Reservoir Model – Single Component Equations
Gas phase component, molar fraction conservative form
Liquid phase component, molar concentration conservative form
( ), ,
1
1
( )
1( )
effi
G G i G G G i G G i G i G i G
n
G G k n k
G G G G kkG G
yS y S S y y q
t t
S P M M yTS S
t S t t t M t
φ ρ φ ρ φ ρ ρ
φ ρ φ ρ χ β ϕ−
=
∂ ∂+ +∇⋅ − ∇ + =
∂ ∂
∂ ∂ − ∂∂ ∂ = + − + − ∂ ∂ ∂ ∂ ∂ ∑
uɶ ɶ ɶ ɶ ɶ
ɶ ɶ
ɶ ɶɶ
δδδδ
( )( )( ),
, , , , ,
i L effL
L i L L i L i L f L L L L i L i L
c SS c S c P S c q
t tφ φ φ Λ ρ ε∂ ∂
+ +∇⋅ − ∇ − ∇ + + ∇ =∂ ∂
K gδδδδ ɶ
Reservoir Model – Gas Hydrate Equations
Methane and Carbon Dioxide hydrate saturation
Hydrate kinetics (linearized partial pressure kinetic)
MH G C MH
MH MH MH
MH
CH G C CH
CH CH CH
CH
S P P sTS
t t t t
S P P qTS
t t t t
φ φ χ βρ
φ φ χ βρ
∂ ∂ ∂ ∂ + − − = ∂ ∂ ∂ ∂
∂ ∂ ∂ ∂ + − − = ∂ ∂ ∂ ∂
( )
( )
*
*
1
1
MH
MH MH MH M G MH
CH
CH CH CH C G CH
NR k a y P P
V t
NR k a y P P
V t
∂= = −
∂
∂= = −
∂
COMSOL Implementation
COMSOL Multiphysics implementation essentials
� 3D and 2D axisymmetric models
� Coefficient Form PDE + Heat Transfer in Porous Media
� Discretization/Stabilization as default
� Fully Coupled solution, Direct linear solver (PARDISO)
� Pressure Dirichlet boundary condition given as Weak Constraint
� Initial time step 10 s, maximum time step 5 · 106 s
� maximum mesh size = 15 m, fine meshing at the well
Methods for gas hydrate decomposition
Depressurization
Thermal stimulation
Additives
Field production plan
1000 m 1000 m 1000 m 1000 m
1000 m
1000 m
1000 m
1000 m
500 m
500m
1/8 well
1/8 well
Injection well
Production well
45°
45°
t = 15 years
Case Study I – Methane production by DepressurizationP0 = 92 bar T0 = 10,0°C Sh0 = 0,40 Hres = 20 m
Case Study I – Methane production by Depressurization
Case Study II – Depressurization of Multi-Layer Reser voir
smoothing
5 Layers a‘ 4 m in height
Case Study II – Depressurization of Multi-Layer Reser voir
„Fingering“ Effect
Case Study II – Depressurization of Multi-Layer Reser voir
„Fingering“ Effect
SUGAR project – case studies
More case studies developed with COMSOL:
� Injection of Carbon Dioxide with parallel Methane production (2 wells)
� Reservoir simulations for the Ulleung Basin, South Korea (UGBH 2.6)
� Simulation cases for process safety and reservoir integrity issures
� Production upriser pipe simulations (1D / 2Ph Euler Equations)
Summary
State
• Development of a gas hydrate reservoir model in COMSOL Multiphysics
• Usage of the Coefficient Form PDE tool of the Mathematics branch
• Highly nonlinear model, needs the fully coupled approach with direct solution
• Simulation of important reservoir production cases were successful
Outlook
• New 3. project phase starts in October 2014
• Field development simulations in preparation of a real field test
• Production safety simulations
FRAUNHOFER UMSICHTProcess Technology / Modeling & Simulation
Thank you for your attention!
Contact:Fraunhofer UMSICHTOsterfelder Strasse 3D-46047 Oberhausen (Germany)E-Mail: [email protected]: http://www.umsicht.fraunhofer.de
Dr.-Ing. S. SchlüterTelefon: +49 208 8598 1126E-Mail: [email protected]