mechanical and numerical modeling of gas hydrate …mtig.uniroma2.it/presentazioni/sanchez.pdf ·...

Mechanical and Numerical Modeling of Gas

Hydrate Bearing Sediments

Marcelo Sánchez

Zachry Department of Civil Engineering Texas A&M University (USA)

Xuerui (Gary) Gai


Ajay Shastri


J. Carlos Santamarina

King Abdullah University of Science and Technology (Saudi Arabia)

Outline

Brief introduction to Hydrate Bearing Sediments (HBS)

Basic components of the proposed coupled THCM framework

for HBS

Simple benchmarks involving HBS

HBS mechanical modeling

Validation

Final remarks

Gas hydrates are solid ice-like

materials that consists of guest

gas molecules encased in a water

matrix.

Hydrate bearing sediments are

typically found in:

marine sediments

permafrost

Methane hydrates sediments are

highly compacted (stable) under

deposit conditions and are likely

to behave as bonded

sedimentary soils

Water + Methane CH4 = Methane hydrate

Gas Hydrate Bearing Sediments (HBS)

Soga et al. (2006)

(Kvenvolden and Lorenson, 2001; www.pet.hw.ac.uk; Ballough et al.]

(USGS,

[gigaton] )

Relevance:

methane recovery, energy resource

instability (boreholes and slopes)

effect on submarine infrastructure

climate change

CO2 sequestration

Gas Hydrate Bearing Sediments (HBS)

T

Heat conduction

H

Water and gas flow

M

Fluid density

Fluid viscosity

Heat convection

Thermal conductivity

Specific heat

Effec

tive

str

ess

Suct

ion

chan

ges

Por

osity

Therm

al strainsPorosity

T

Heat conduction

T

Heat conduction

H

Water and gas flow

H

Water and gas flow

MM

Fluid density

Fluid viscosity

Heat convection


Specific heat

Effec

tive

str

ess

Suct

ion

chan

ges

Por

osity

Therm

al strainsPorosity

Fluid density

Fluid viscosity

Heat convection


Specific heat

Fluid density

Fluid viscosity

Heat convection


Specific heat

Effec

tive

str

ess

Suct

ion

chan

ges

Por

osity

Effec

tive

str

ess

Suct

ion

chan

ges

Por

osity

Therm

al strainsPorosity

Therm

al strainsPorosity Stress-strain

THERMAL

o Heat conduction

o Heat advection (liquid water

and gas)

o Phase changes latent heat

MECHANICALo Net/effective stresses

o Gsa/water pressure

o Temperature

HYDRAULIC

o Liquid flow

o Gas flow

o Air dissolution in water

o Air diffusion in water

o Phase changes

o Gas diffusion

o Gas generation and

transport

THM Coupled Phenomena

Heating

Depressurization

Phase Boundary

Methane Hydrate

Chemical

Inhibition

Ice -Liquid Water

Phase Boundary

HBS – Coupled Phenomena and Phase Boundaries

Hydrate Dissociation

Numerical Code

CODE_BRIGHT computational code

Coupled analysis in geological media

Interaction with the atmosphere

Finite element in space

o 1D, 2D and 3D elements

o Monolithic coupling

o Full Newton-Raphson

Finite difference in time

o Implicit time discretisation scheme

o Automatic time advance

o Mass conservative approach for mass

balance equations

User-friendly pre/post processing of data

Olivella et al. (1996)

Solid

Gas

Liquid

Three phases:

• solid (s) : mineral

• liquid (l ) : water + air dissolved

• gas (g ) : mixture of dry air and

water vapour

Three species:

• mineral (-) : the mineral is

coincident with solid

• water (w ) : as liquid or evaporated

in the gas phase

• air (a ) : dry air, as gas or

dissolved in the liquid phase

Phases and species

Coupled THM Formulation

Governing equations

Balance equations

Constitutive equations

Equilibrium restrictions

pores liquid gas

total total

V V V

V V

1liquid liquid

l g

pores liquid gas

V VS S

V V V

Solid

Liquid

Gas

Hydrate

Vv

Vs

Methane

(+ water

vapor)

Water (+ dissolved

methane)

Mineral

Water + methane

Ice Water - solid

Three main species:

mineral

water (w)

methane (m)

The species are found in five phases:

solid particles (s)

liquid (l)

gas (g)

hydrates (h)

ice (i)

g l h ivV V V VV

V V

, , ,v

VS l g h i

V 1l g h iS S S S

Water

Soil particle

Gas

Hydrate

Solid

Hydrate

Liquid or ice

Gas

Phases Species

HBS - Species and Phases

Water in liquid:

Net flow of water in

liquid:

Net flow of water in

hydrate:

Water in

hydrate

S

h hS

w

lj

w

hj

mass of water in total flows external supplydivergence

liquid, hydrate and ice (& gas) phases of water of watert

Mass Balance of Water

w w w w

h h i i h i

porosity external supplymass of water in liquid, total flows of waterhydrate and ice phases of water

[( S S S ) ] .[ ] ft

j j j

Water

Soil particle

Gas

Hydrate

Solid

Hydrate

Liquid or ice

Net flow of water in icew

ijWater in ice:

i iS

HBS - Mass Balance Equations

Sediment

Liquid

Hydrate

Gas

Mass of water ( Pl )

w

h h i i h h i i

mass water per unit volume w in liquid w in hydrate w in ice

[( S S S ) ] .[ S S S ] ft

q v v v

m

g g h h g g g g h h

m in hydratem in gasmass of methane per unit volume

S 1 S .[ S 1 S ] ft

q v v

energy per unit volume of the hydrate bearing sediment

s s g g g h h h i i i c g g g g h h h

transport in transtransport in g

e 1 e S e S e S e S . .[e ( S ) e ( S ) e St

i q v q v vE

i i i s s

port in h transport in i transport in s

e S e (1 ) ] f v v

Momentum ( u )

Energy ( T )

Mass of methane ( Pg )

b 0

Water

Soil particle

Gas

Hydrate

Solid

Hydrate

Liquid

or ice

Gas

Mass of solid ()

s s

mass mineral m in solidper unit volume

[ 1 ] [ 1 ] 0t

v

Mass of solute (ci)

s

s s s s l l

mass s per s in liquid s in liquidnon advectiveunit volume

flux of s

(C S ) .[ C C C S ] ft

D q v

Mathematical Formulation

HBS – Balance Equations

EQUATION VARIABLE NAME VARIABLE

Constitutive Equations

Fourier’s law conductive heat flux ic

Darcy´s law liquid and gas advective flux ql , qg

Retention curve liquid degree of saturation Sl , Sg

Fick’s law vapour and air non-advective fluxes igw , il

m

Mechanical model stress tensor

Phase density liquid density l

Gases law methane density g

Equilibrium Restrictions

Hydrate

dissociation/formation

Hydrate Saturation Sh

Ice thaw/formation Ice Saturation Si

Henry’s law Methane dissolved mass fraction wla

Psychrometric law

HBS - Constitutive Equations and Equilibrium Restrictions

Table 2: Specific Energy and Thermal Transport – Selected Values

Phases

Mass

Density

[kg/m-3

]

Specific Energy Thermal

Conductivity

[W/(m.K)] Expression

Latent heat

L [J/g]

Specific heat

c [J/(g K)]

liquid (water) 998 oe c T T - 4.2 0.58

ice 917 i fuse i oe L c T T 334

fusion 2.1 2.3

gas (methane) gas law

(see text) g g oe c T T -

1.9 V=const

2.5 P=const

0.05

(P-dependenta)

hydrate 910 h diss h oe L c T T 339

dissociation 2.1

0.6

(T-dependentb)

mineral 2650 s s oe c T T - 0.7 quartz 8 quartz

- 0.8 calcite 3 calcite

o

6 1808.5 KPa.s 2.1 10 exp

T

3

g-6

g

P 280 KPa.s 10.3 10 1 0.053

MPa T

1

hbs s h h i i g g1 S S S S

2

o T

P T 277 K1 1

B 5.6

HBS - Phases Properties and Phase Change

HBS – Coupled Phenomena and Phase Boundaries

PT Paths: Four Regions

Phase boundaries for methane hydrate (H), gas (G), water (W) & ice (I).

0

5

10

15

270 275 280 285 290

Press

ure [M

Pa]

Temperature [K]

0

5

10

15

270 275 280 285 290 295 300

Press

ure [M

Pa]

Temperature [K]

0

5

10

15

270 275 280 285 290

Press

ure [M

Pa]

Temperature [K]

0

5

10

15

270 275 280 285 290 295 300

Press

ure [M

Pa]

Temperature [K]

0

5

10

15

265 270 275 280 285 290 295 300

Press

ure [M

Pa]

Temperature [K]

0

5

10

15

265 270 275 280 285 290 295 300

Press

ure [M

Pa]

Temperature [K]

Pressure-Temperature paths

Hydrate formation



Hydrate Dissociation - Heating

Cementation Pore Filling Supporting Matrix

HBS – Mechanical Behavior at Constant Sh

Masui et al. (2008)Masui et al. (2005)

Shearing Hydrate damage Hydrate dissociation Sediment collapse

HBS – Mechanical Behavior During Dissociation Under Stress

Hyodo et al. (2014) Santamarina et al. (2015)

Some previous developments

Mohr–Coulomb based model

Rutqvist and Moridis (2007)

Klar, Soga and Ng (2010)

Based on an elasto–viscoplastic framework

Kimoto, Oka, Fushita and Fujiwaki (2007).

Kimoto, Oka, Fushita (2010)

Modified Cam-Clay based model

Sultan and Garziglia (2011)

Uchida, Soga and Yamamoto (2012)

HBS – Mechanical Behavior

The mechanical behavior of HBS depends on

Hydrate concentration

Pore habit

Stress level

Stress history

HBS – Mechanical Behavior

Hydrates in soils

contribute to support the external applied stresses,

the strain partition concept is used to compute this contribution;

alter the mechanical behavior of sediments, e.g. provide hardening and

dilation enhancement

a critical state model for the sediment to account for these effects.

Strain partition concept

Vs

Vf

Vh

v v v

ss h hC q q q

ss h hC

v v

h ss q q

h ss

h hC S

HBS – Mechanical Model

1h

hC

ε ε

Hydrate Model

0

L

h h hh he σ Dε εD

20

L

e

Proposed by Pinyol et al. (2007) for clayed cemented materials

1

( ) 0

r L

L hr r e u

Sediment Model

pd : hardening

enhancementF

2

2 ' '

2

2

9n

b ss ss ss

n

dc

aF q p p p p

M

Final Stress-Strain Relationships2 2

'

1 1 1h

h h h

h h h

ss h C h h

C C C

C Cd d dC

C

σ D D ε d σ

d hp C

HBS – Mechanical Model

' '

1h

h

h

ss

C

Cd d d

σ σ σ

Effect of Hydrate Saturation – Constant Sh

Experimental data from Hyodo et al. (2013)

HBS – Mechanical Model Validation

Synthetic Samples – Triaxial Conditions

Experimental data from Masui et al. (2005)

Effect of Pore Habit – Constant Sh


Synthetic Samples – Triaxial Conditions

Natural Samples – Triaxial Conditions

Experimental data from Joneda et al. (2015)


Effect of Hydrate Saturation – Constant Sh

Experimental data from Hyodo et al. (2014)

Already dissociated sediment

Dissociation induced at a=1%Dissociation induced at a=5%.


Effect of Hydrate Dissociation

Synthetic Samples – Triaxial Conditions - Sh~48%

Experimental data from Santamarina et al. (2015)

Natural Samples – Oedometric Conditions



Sh~18% Sh~74%

Oedometric Conditions



Code verification

Maximum gas production from HBS by depressurization

Analytical solution – Cylindrical radial flow - Steady state conditions

r

2 1

2

1

2 ( )

ln( )

kH h hq

r

r

1*

**

*

1

*

Sed w

HBS farSed w

HBS far

k h h

k h hk h h

k h h

w farr r r

* *

*

*

2 2

lnln

Sed w HBS far

far

w

k H h h k H h h

rr

rr

Code verification



1N

HBS sed hk k S

• 2D axisymmetric model

• A single vertical well producing

• Very fine grid (2503 elements)

kHBS=1x10-12 m2

Sh=0.5

=0.40

L= 1.20 km

h=0.40 m

rw=0.1m

Code verification



Gas Production in-situ by Heating

1000m Hea

tin

g

Time = 0 Time = 300 Time= 500 Time = 1000

Hydrate

Concentration

Temperature

D=150m D=150m D=150m D=150m

Hea

tin

g


Hydrate

Concentration

Temperature

D=150m D=150m D=150m D=150m

Gas Production in-situ by Depressurization

Dep

ress

uri

zati

on


Liquid

Pressure

Hydrate

Concentration

Temperature

D=150m D=150m D=150m D=150m

1000mD

epre

ssuri

zati

on


Liquid

Pressure

Hydrate

Concentration

Temperature

D=150m D=150m D=150m D=150m

In this work we present a coupled THCM formulation for modeling the

behavior of gas hydrates bearing sediments.

The proposed approach incorporates the fundamental physical and chemical

phenomena that control de behavior of gas hydrates bearing sediments.

The FE program CODE_BRIGHT has been adapted to incorporate the main

balance and constitutive equations related to problems involving gas hydrate

sediments.

An advanced mechanical model for HBS has been proposed and validated.

Cases studies, at actual scale, modeling the different strategies for gas

(methane) production has been analyzed, showing the potential of the

proposed approach to model these kinds of problems

Summary and conclusions

The authors would like to acknowledge the financial support from:

NETL (National Energy Technology Laboratory),

DOE (Department of Energy, US).

Project: THCM Coupled Model For Hydrate-Bearing Sediments: Data Analysis

and Design of New Field Experiments (Marine and Permafrost Settings)

Award No.: DE-FE0013889.

Acknowledgements

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