This document summarizes a reservoir simulation model for gas hydrate sediments developed by Fraunhofer UMSICHT. The model includes: 1) Equations describing multiphase fluid flow and heat transfer through porous media, accounting for gas, water, methane hydrate, and CO2 hydrate phases. 2) A COMSOL implementation using coefficient form PDEs coupled to heat transfer in porous media. 3) Methods for simulating gas hydrate decomposition including depressurization, thermal stimulation, and additives. 4) A proposed field production plan involving depressurization through vertical wells.

1. Submarine Gas Hydrate Reservoir Simulations – A Gas/Liquid
Fluid Flow Model for Gas Hydrate Containing Sediments
Stefan Schlüter, Georg Janicki, Torsten Hennig, Görge Deerberg
Fraunhofer UMSICHT, Oberhausen (Germany)
COMSOL Conference 2014, Cambridge (UK)

2. What are gas hydrates?
Gas molecules
Water molecules
Water
Temperature
Gas
©
Jens
Greinert
IFM GEOMAR
Petrobras
Fraunhofer UMSICHT

3. Idea of the SUGAR project
©
IFM
GEOMAR
• CO2 hydrate stable at
lower pressure / higher temperature
• replacing CH4 by CO2
• simultaneous production of CH4
and storage of CO2
• sustainable energy supply system

4. 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

5. 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 s
t
S s
t
S s
t
S s
t
φ ρ ρ
φ ρ ρ
φ ρ
φ ρ
∂
+∇⋅ =
∂
∂
+∇⋅ =
∂
∂
=
∂
∂
=
∂
u
u
1
S s
S
t t
ρ ρ
φ φ
ρ ρ ρ
∂ ∂ ∇
+ + ∇⋅ + ⋅ =
∂ ∂
u u
1
j j
j
S
j
S
ε ε
ε φ
= = =
−
volume fraction of phase
sediment free volume fraction
Euler/Euler

6. Reservoir Model – Pressure/Saturation Equation
Density derivatives:
General form:
Darcy equation:
Phase summation:
, , ,
1 1 1
, ,
k k
k
k
T y P y P T
P T y
ρ ρ ρ
χ β ϕ
ρ ρ ρ
 
   
∂ ∂ ∂ 

 
  
 
= = − = 
  
  
  
 
  

∂ ∂ ∂
     
1
,
k
k k k
k k
y
P T
P T y
t t t t
ρ ρ
χ β ϕ χ β ϕ
ρ ρ
∂
∂ ∂ ∂ ∇
= − + = ∇ − ∇ + ∇
∂ ∂ ∂ ∂
∑ ∑
( ) ( )
with , ,
rel
f rel H L
k
P k f S S
Λ ρ Λ
η
= − ∇ + = =
u K g
k
k k k
k k
y
S P T s
S P T y
t t t t
φ φ χ β ϕ χ β ϕ
ρ
   
∂
∂ ∂ ∂ 
 



+ − + + ∇⋅ + ⋅ ∇ − ∇ + ∇ =


 
  



∂ ∂ ∂ ∂  
 
∑ ∑
u u
1 , 0
j
j
j j
S
S
t
φ
∂
= =
∂
∑ ∑

7. 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 j
j j
f j j j j j k j k j j
j
k
j k j
j j k j f j j j k j k j
j j j
k
j
P
S P
t
P T y P
q y
T
S T y
t t
φ χ Λ ρ
Λ χ ρ β ϕ
φ β ϕ Λ ρ β ϕ
ρ
∂
+ ∇⋅ − ∇ +
∂
 


− ∇ + − ∇ + ∇ ∇ =

 
 
 
 
∂  
∂ 
 



+ − − ∇ − ∇ 
 
 
  
 ∂ ∂  


 
∑ ∑
∑ ∑
∑ ∑ ∑ ∑
K g
K g
K g
with ( , )
C G L C H L
P P P P f S S
= − =
( )
1 1 1
,
2 2 2
L G L C G C
P P P P P P P P P
= + → = − = +

8. 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 S
u d
S S
P
c
P
φ χ χ χ
φ χ φ
Λ Λ ρ Λ ρ Λ
Λ Λ
γ
Λ ε
Λ ρ
Λ χ
β
 
  + + + 


 
 
 
= =
 
 
 
 


  
   
 
 
∇ 
 
 

− − + +
 


   


+ 

 
  

 
  
= = 
  

  
 
 ∇

 


   

− − +

 


 


 
  
 
+
−
=
K g
K
K
K 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 u
e d c u u u au f
t
t
α γ β
∂ ∂
+ + ∇⋅ − ∇ − + + ∇ + =
∂
∂
artificial diffusion for SL

9. 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
T
S c S T P c T q
t
T
S c S T P S c T q
t
T
S c S c S S T q
t
T
c 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
λ
λ
λ
λ
λ
λ
λ
λ
λ λ
λ λ
λ λ
λ λ
λ
λ
λ
λ
( )( )
1
G
P G G G f G G G G G G
P
q S T P T P
t
φ β Λ ρ β
∂
= + ∇ + − ∇
∂
K g
ɺ
( )
H MH MH CH CH
q R h R h
= − ∆ + ∆
ɶ ɶ
ɺ
G L H S
T T T T
= = =
real gas
behaviour

10. Reservoir Model – Single Component Equations
Gas phase component, molar fraction conservative form
Liquid phase component, molar concentration conservative form
( )
, ,
1
1
( )
1
( )
eff
i
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 k
k
G G
y
S y S S y y q
t t
S P M M y
T
S S
t S t t t M t
φ ρ φ ρ φ ρ ρ
φ ρ φ ρ χ β ϕ
−
=
∂ ∂
+ + ∇ ⋅ − ∇ + =
∂ ∂
 
 
∂ ∂ − ∂
∂ ∂ 
 
 

 
= + − + − 

  


 
∂ ∂ ∂ ∂ ∂ 
  
 
∑
u
ɶ ɶ ɶ ɶ ɶ
ɶ ɶ
ɶ ɶ
ɶ
δ
δ
δ
δ
( )
( )
( )
,
, , , , ,
i L eff
L
L i L L i L i L f L L L L i L i L
c S
S c S c P S c q
t t
φ φ φ Λ ρ ε
∂ ∂
+ + ∇⋅ − ∇ − ∇ + + ∇ =
∂ ∂
K g
δ
δ
δ
δ ɶ

11. 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 s
T
S
t t t t
S P P q
T
S
t t t t
φ φ χ β
ρ
φ φ χ β
ρ
 
 
∂ ∂ ∂ ∂ 
 
 

 
+ − − =


  


 
∂ ∂ ∂ ∂ 
  
 
 
 
∂ ∂ ∂ ∂ 
 
 

 
+ − − =


  


 
∂ ∂ ∂ ∂ 
  
 
( )
( )
*
*
1
1
MH
MH MH MH M G MH
CH
CH CH CH C G CH
N
R k a y P P
V t
N
R k a y P P
V t
∂
= = −
∂
∂
= = −
∂

12. 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

13. Methods for gas hydrate decomposition
Depressurization
Thermal stimulation
Additives

14. 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°

15. t = 15 years
Case Study I – Methane production by Depressurization
P0 = 92 bar T0 = 10,0°C Sh0 = 0,40 Hres = 20 m

16. Case Study I – Methane production by Depressurization

17. Case Study II – Depressurization of Multi-Layer Reservoir
smoothing
5 Layers a‘ 4 m in height

18. Case Study II – Depressurization of Multi-Layer Reservoir
„Fingering“ Effect

19. Case Study II – Depressurization of Multi-Layer Reservoir
„Fingering“ Effect

20. 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)

21. 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

22. FRAUNHOFER UMSICHT
Process Technology / Modeling & Simulation
Thank you for your attention!
Contact:
Fraunhofer UMSICHT
Osterfelder Strasse 3
D-46047 Oberhausen (Germany)
E-Mail: info@umsicht.fraunhofer.de
Internet: http://www.umsicht.fraunhofer.de
Dr.-Ing. S. Schlüter
Telefon: +49 208 8598 1126
E-Mail: stefan.schlueter@umsicht.fraunhofer.de