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: info@umsicht.fraunhofer.deInternet: http://www.umsicht.fraunhofer.de

Dr.-Ing. S. SchlüterTelefon: +49 208 8598 1126E-Mail: stefan.schlueter@umsicht.fraunhofer.de