Decoupling and block preconditioning for sedimentary basin simulations

Marie - Curie Fellowship

Description

Niveau: Supérieur, Doctorat, Bac+8
DECOUPLING AND BLOCK PRECONDITIONING FOR SEDIMENTARY BASIN SIMULATIONS IN TEMIS3D ROBERT SCHEICHL y , ROLAND MASSON z , AND JOHANNES WENDEBOURG x Abstra t. The simulation of sedimentary basins aims at re onstru ting its histori al evolution in order to provide quantitative predi tions about phenomena leading to hydro arbon a umula- tions. The kernel of this simulation is the numeri al solution of a omplex system of time dependent, three-dimensional partial dierential equations (PDE) of mixed paraboli -hyperboli type. A dis- retisation (Finite Volumes + Impli it Euler) and linearisation (Newton) of this system leads to very ill- onditioned, strongly non-symmetri and large systems of linear equations with three unknowns per mesh element, i.e. pressure, geostati load, and hydro arbon saturation. The pre onditioning whi h we will present for these systems onsists in three stages. First of all the equations for pressure and saturation are lo ally de oupled on ea h element. This de oupling aims not only at redu ing the oupling, but also at on entrating in the \pressure blo k the ellipti part of the system whi h is then in the se ond stage pre onditioned by eÆ ient methods like AMG. The third step nally onsists in \re oupling the equations (e.

• mathemati al


• per mesh


• ally


• ase


• pre onditioning


• al ulated


• unknowns per


• onstru ting

Sujets

• Fellowship
• Mathématiques appliquées

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 11
• Langue: English

Extrait

olution
DECOUPLING
ran
AND
simplied
BLOCK
in
PRECONDITIONING
history
F
la
OR
for
SEDIMENT
Institut
AR
of
Y

BASIN

SIMULA
y
TIONS
ecome
IN
tire
TEMIS3D
the

Beicip-F
R
out
OBER
erogen
T
olution
SCHEICHL
v
y
basin
,
o
R
pro
OLAND

MASSON
ran
z
of
,
a
AND
burial,
JOHANNES
assessmen
WENDEBOUR
de
G
(IFP)
x
ol.

to
The

sim
,
ulation
and
of
ide-
sedimen
,
tary
w
basins
ey
aims
in
at
del

p
its
is
historical
the
ev

olution
y
in
Math
order
rance.
to
rance.
pro
part
vide
future
quan
jor
titativ
should
e

predictions
on
ab
oten
out
in
phenomena
a
leading
ed
to
du
h
b
ydro



on
tary

titativ
ula-
h
tions.
presen
The
lithology
k
kness,
ernel

of
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this
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sim
to
ulation
and
is
of
the
ard
n
solution
umerical
w
solution
Therefore
of

a
the

).
system

of
transfer,
time
generation,
dep
and
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ard
t,
la
three-dimensional
during
partial
w
dieren
F
tial
Mathematical
equations
7A
(PDE)
Informatique
of

mixed

parab

olic-h

yp
has
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in
olic
the
t
t
yp
v
e.
all
A

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the
(Finite

V

olumes
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Implicit
a
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and
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olution
of
The
this
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y
leads
ran
to

v
mark
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its

represen
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aims
and
historical
large
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systems
in
of
vide
linear
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equations
leading
with

three
Giv
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y
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p
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erature,
mesh
ux,
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total
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t
i.e.
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pressure,
throughout

the
load,
w
and
lik
h
the
ydro
the

its
on
the
saturation.
h
The

preconditioning
time.
whic
er,
h
this
w
problem
e
y
will
our
presen
an
t
del
for
kw
these
to
systems
of

b
in
full
three
the
stages.
h
First
generation,
of
of
all
media,
the
ulti-phase
equations
and
for
mi-
pressure

and
time
saturation
er
are
er
lo
history




on
w

the
h
wship
elemen
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Univ
This
Bath,

UK
aims
z
not
tique
only
ematiques
at
Institut

du
the
Rueil-Malmaison,

Division
but
Institut
also
du
at
Rueil-Malmaison,

basins
trating
b
in
an
the
tegral
\pressure
in
blo
exploration

presen
k"
and
the
reser-
elliptic
oirs
part
almost
of
ma
the
oil
system
Ideally
whic
basin
h
ulator
is
span
then
en
in
pro
the
of

ro
stage
k
preconditioned
h
b

y
generation,

migration
t
to
metho
p
ds
tial
lik
and
e
t
AMG.
trap
The
tegrit
third
throughout
step
ev
nally
of

basin.
in

\recoupling"
TEMIS3D
the
elop
equations
b
(e.g.
the
Blo
F


k
P
Gauss-Seidel,
etrole

and
binativ
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e
y

subsidiary
hniques,.
ranlab
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ts
.
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).
to
In
It
almost
at
all
the
our
ev
n
of
umerical
sedimen
tests
basin
on
order
real
pro
test
quan
problems
e
from
ab

phenomena
studies
to
w
ydro
e
on
observ
ulations.
ed
en
a
t-da

maps
erable
the

of
of
,
the
ymetry
CPU-time
temp
for
thic
the
heat
linear
k
solv
and
er,

up
ten
to
(TOC)
a
\paleogeological"

describing
4.3
distributions
with
the
resp
of
ect
basin
to
e
ILU(0)
ould
preconditioning
ally

e
h

is
ev
used
of
at
basin
the
of
momen
geometry
t
and
in
migration
TEMIS3D
the
).
ydro
The
ons
p
kw

in
of
Ho
the
ev
preconditioner
the
sho
of
ws
in
no
erse
degradation
is
with
a
resp
b
ect
ond
to
means.
the
only
n
extremely
um
mo
b
is
er

of
ard
elemen
time
ts,

the
geometry
size
the
of
(
the
ack-stripping
time
The
step,
mo
high

migration
pro
ratios,
of
or
ydro
strong
on
heterogeneities
heat
and

anisotropies
the
in
orous
the
pressure
p
m
orous
Darcy
media.
w
Key
oil
w
gas
ords.
gration
three-dimensional
then
m
forw
ultiphase
in
Darcy
adding
o
y
w,
after

y
of
using
p

orous

media,
the
n
k-stripping
umerical

solution,
This
blo
ork

as
k
through
preconditioning,
Marie-Curie

ello
m
HPMI-CT-1999-00012.
ultigrid
Departmen
AMS
of
sub
Sciences,

ersit

of
65F10,
BA2
65M99,
Y,
65Y20,
(
74F10,
).
74S10,
Division
76T99
Scien
1.
et
In

tro
Appliqu

ees,
In
F


t
P
y
etrole,
ears
F
the
x
3D
Geologie{Geo
mo
himie,
delling
F
and

sim
P
ulation
etrole,
of
F
sedimen-
1
tary
2

R.
tativ
SCHEICHL,
erature.
R.
ery
MASSON,
oil
AND
non-linear
J.
linearisation
WENDEBOUR
x
G

Th
tirely
us,
V
a
A
3D
,

us
study
the
is
A

A
osed
is
of
its
three
hniques
ma
nev
jor
the
steps:

3D
elemen
blo


elemen
k
a
building
solution
and

mesh
a

a

A
k-stripping,
A
and

forw
usually
ard
robust
sim
d
ulation

(see
to
Sc
and
hneider
in
et
literature
al.
v
℄
idea
for
Behie
an
V
example
equations
of
the

(1.1)
h
x
a
a

unkno
study).
load,
The
w
3D
equations
blo
fo

nonlinear
k
on
building
as
step,
of
usually
and

will
out
equations
b
x
y
A
the
A
geologist,
0

1
in
2
preparing
(1.1)
the
strongly

an
data,
of
i.e.
nd
in
b
dening
er
a
and

b
t
b
3D
from
blo
with

at
k
this
whic
problem,
h
but
represen
strong
ts
the
the
ulation.
studied
strategy
area
elop
and
Edw
in
[4
assem
Wheeler
bling
First
with
saturation
this
linear
blo
equations

onds
k
matrix
a
!
set
b
of
time
geological
of
maps.
in
It
p
also
(pressure,

orosit
in
saturation),
dening
b
a
of
3D
the
mesh
w
on
on
the
the
blo
and

no
k
e
whic
temp
h
en.
will
the
usually
equations