Reservoir Simulation: State of the Art

by
Keith
of
A
H.
Michigan.
was
a
teaching
research
and
was
SPE
After
senior
1961-66
-k
Coats,
1969–
associate
70
chemical
engineer
professor
Dlstinaukhed
of
Lecturer
Introduction
The
of
and
of
some
why
resemoir
model,
two
through
used.
petroleum
on
summarizes
sections
reservok
of
and
by
The
two
computer
to
these
used
sections
today,
with
and
The
are
the
sharp
addressed
in
processes:
to
ing,
a summary.
Ii
History
a broad
pmcticed
in the
reservoir
since
the
1930’s.
to
recove~
consisted
largely
dimensional
reservoir
or
methods).
of
term
as
analytical
solution
a major
of
Imge
transient,
two-
advancement
of
multiphase
advancement
rapid
evolution
of
and
for
in
large
recove~
equations
is on
examining
and
related
(2-
of
by
and
mathematical
finite-difference
equations.
During
devoted
black-oil
simulated
the
1960’s,
largely
reservoir
to two-phase
reservoir
essentially
problems.
were
simulation
efforts
gas/water
and
Recove~
methods
limited
to
depletion
were
numerical
allowed
andlor
increased
stability
numerical
AUGUST
1982
of AIME
of
to
reduction
thermal
methods
effects
and
1970’s
concept
the
the
to
as
each
emphasis
equations
these
of
today
and
techniques.
resulted
in many
model
methods.
more
in the
to represent
Thus,
1970’s
solution
had
single-model
tuning
These
complex
formulations
advances
recove~
computing
the
to simple
costs
formulations
through
and
efficiency
of
methods.
three-phase
Simulation
or
0deh7
Models—A
gives
subdivision
En@wm
(IFT)
in simulation
of
of
addition
orber
developed
reduced
the
influence
degradation,
pertinent
simulation
simplicity
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the
solution
processes
the
recovery
the
was
behavior.
of
advances
flow
characterize
sinwlato~
tension
fine
oil)
complex
In
and
schemes.
during
significant
and
from
and
comfortable
the
behavior.
phase
flooding,
and
and
and
that
pressure
immiscible
adsorption
assumptions
Research
the
digital
numerical
of
3D),
porous
possible
high-speed
systems
allowed
processes
and
(gas
mcdla,
pilot
stirnulationlflood-
under
were
new
relatively
in porous
a departure
new
they
A
field
chemic,al
water
agents,
proliferation
these
because
hot
kinetics,
models
programs
of
to unravel
equilibrium
caused
of
model
trends
of
,depletion
interracial
individual
These
made
large-scale,
and
reaction
The
early
relatively
cost
of
enhance&remvery
in simple
phase
chemical
effects,
in the
into
heterogeneous
was
development
solving
emulsifying
finite-difference
flow
This
computers
1,2 zero-
of
displacement
flow
reflect
a
markedly.
funding
floodlng,
chemical
complex
thrcedlmensional
media.
methods
alternative
common
oil
multiphase
calculations
one-dimensional
evolved
programs,
sets
aid
and
became
methods
computer
describing
‘.4
of
changed
two-component
rnulticomponent
(to
of
these
physics
@e
‘cost
governmental
pa~ial
or
a stmggle
temperature,
of
calculations.
“simulation”
represented
engineering
use
~ethods,
balances,
predictive
sophisticated
the
economics
1960,
Bqckley-f_everett5J
The
~etroleum
by
of
to operating
the
simulation
behavior
replaced
been
performance
compare
Before
material
1960’s,
of
has
is simply
predict
recovery
(ID)
beginnin~
.Simulation
calculations
forecast
simulation
concept
reduces
and
combustion.
of
hydrocarbon
sense,
to
steani
in-situ
most
appealed
pictu~
prices
to miscible
and
a
addressing
This
conventional
understanding
A Brief
the
oil
led
beyond
maintenance
He
to develop
of
has
during
7966–70.
Nominatin.a
possible
a prolifemtiim
CO z injection,
examples
the
potentially,
and
This
bats
Co,
maintenance.
deregulation
led
on
capable
and,
1961,
during
it significantly
1970’s,
rise
extended
is used
served
to
Research
Texas.
alyays
usage,
and
Dining
7959
encountered.
because
development
of
It was
model
and
projects
in
questions
a section
simulation
sections
and
problems
training
U.
model
genetal
from
Production
the
maintenance.
toward
simulation
performance
simulation),
pertinent
why
reservoir
and
descriptive
of
memoir
of
cur~ntly
a discussion
typical
second
a
at
simulation
single,
mechanisms
developments
technology
models.
followed
The
recent
of
the
recovery
is
Michigan
Esso
simulation
companies
a brief
description
describe
discussions
the
simulation
Following
model
of
with
englneertng
reservoir
This
U.
the
associate
single
current
a simulation
a general
methodology.
past
the
simulation.
“of whit
or
discusses
by
in
and
model
is to describe
dkcussion
simulation
simulator
(i.e.,
paper
it is needed
of
simulation
and
this
development
requires
histoty
at
research
pressure
propose
level
engineering
and
grid
blocks.
an
6f
Brief
excellent
a simulation
of
He
a reservoir
then
shows
Description
description
model,
into
that
of
He
a“ 2the
the
conceptual
illustmtes
or
3D
network
simulation
the
of
model
1633
I-
DIMENSIONAL
saturation
PVT
and
Temperature.
associated
with
First,
overall
DIMENSIONAL
ptessure
tests
vs.
Second,
fluid
volume
factors,
obtained
perforated
3-DIMENSIONAL
m
Fig.
output
rate
on
of
each
end
Internal
manipulation
resemoir
pressme
cumulative
and
2-,
by
3D grids
and
are
balance
grid
equation
block
and
its
respectively)
law
concept.
or
four
the
Reservoir
fluid
and
throughout
properties
for
the
of
reservoir
porosity
relative
1634
2-,
are
denoted
visualize
grid
top
surface
is a set
mtmcrical
differential
either
In
of
011
in the
block
from
side
each
grid
positive
vary
formation
aids
dip.
and
reservoir
to anotbe~
also
vary
flow
and
fluid
with
solution
masom
in
sands
la~e
with
To
opposed
amenable
for
this
arc
capillmy
(2)
a
to
mobiliz&
are
and
vs.
oil
widely
really
black
mechanisms
depletion
of
drive
and
of
model
pressure
we
loosely
phenomena
that
Some
of
the
accounts
OF
these
first
for
oil
maintenance
JOURNAL
the
This
of
gasloil
to the
pefieabdit
and
dkcussion,
from
oil
in heterogeneous
mobilization,
in simulation
or
drainage
rec?ve~
variation
OIL
by
differences,
normal
important
compositional
distincb
oil
caused
a declining
wateffloods
different
matrix.
naturalIy
density
generally
in this
expulsion
porous
or
upward
an
(1)
fluid
in oil
the
above
are:
gmvity
d~inage,
vefiical
recoverable
not
The
of
lateral
processes
includes
(1)
nonlinearity
pressure
to
be
accommodate
mechanism,
permeability
.geomet~;
and
as
can
most
recoveV
Simple
injected
causing
to
basic
results
through
imbibition,
direction,
used
reservoirs
(3)
oil/gas)
from
water
The
four
from
imbibition.
Gravity
drainage
and
Mechanisms
advancing”’bottomwater
Fkily,
average
gas,
are
The
and
and
well
compositional,
decline
flow’
by
an
oil,
capillaty
gas
each
and
mechanisms.
oil
pressure
recovexy
oil,
displacement,
by
mechanism
time
partial-difference
(4)
gives
rates
models
flood
water.
below
recovexy
of
equations
The
oil
from
spatial
computations.
Oil-Recovery
black
subsequent
downward
uniform
are
and
and
for
the
of
and
(water/oil
contact.
assumed
However,
and
(PI’s),
time.
recovering
is displaced
locations,
include
results
simulation
(2)
with
encroaching
practice,
as pressure,
block
heterogeneity—variable
permeability
N
expansion
these
vs.
chemical
and
its
are
well
instantaneous
field
expansion,
formation
injection/production
of
oil-recovery
for
drainage,
and
period.
model
irregular
of
on
and
as
viscosities
results
and
of
types
mechanisms
~lative
indices
step
and
different
thermal,
cases,
time
of
used
of
distributions,
WOR
Models
ty~s
widely
fluid
permeability
one
3D
block
reseti.oir
block
grid
interior
two
z directions.
block.
grid
each
B and
and
from
describe
“3D grids
an
neighbrms,
as
each
by
The
by
are
solution.
and
and
composition,
requiring
partial
a reservoir.
such
simulation
A simulation
set
of
can
for
or
rilativi”perineability
such
each
2-3
thi
the
vary
1-,
by
1-,
Different
represented
properties
a given
properties
(in
reflecting
properties
and
temperature,
analytical
to
between
six
material
phase
are
six
position,
each
blocks
x, y,
depths
porosity,
equations
its
in the
areal
during
One
with
subsea
fluid
or
nefghbo~
block
with
four,
volumetric
ra@
1 illustrates
grids.
grid
the
for
flow
a portion
2D
3D
of
phase
two,
Fig.
familiar
written
modified
representing
1- and
the
adjacent
Darcy’s
the
3,4
The
block.
two
basically
Laborato~
injectivity/productivity)
total
Simulation
equations
com
3.
specified.
injectionlproduction
well
Geological
and
Finally,
satiation
and
welk
such
and
calculated
and
GOR
(for
at the
1—1-,
or
pressure
producing
be
grid
relationships.
productivity
must
each
tables.
estimates
gas,
(1)
capiIky
logs
1 and
tests.
intervals,
Model
fluid
or
properties,
Iaboratoty
schedules
for
pressure
solution
input
(3)
and
items
yield
PVT
by
elevation
capilkmy
of
include
specification,
involving
for
samples
and
types
data
functions
work
core
three
size
and
is necessary
on
digital
arithmetic
permeability
saturation
permeability
rate
grid
relative
petmphysical
analyses
-
(4)
highspeed
of
requires
porosity,
and
fluid
composition,
require
amo~t
description
(2)
permeability,
and
the
of
pressure,
solutions.
resemoir
geomehy,
block,
CROSS-SECTION
the
nonfinearhy
of
models
of
model
simulation
(3)
functions
The
because
data.
and
as
computers
A
2-
relationshi~
properties
y.
enhancedadd
a fifth
defined
create
term
or
phenomena
four.
the
recovery
four
by
basic
natural
(e.g.,
PETROLEUM
TECHNOLOGY
waterflooding).
T’Ms
rcsemoim
phases
gas
with
oil
of
The
basic
models
which
model
the
Some
to
black
oil
gas
condensate’
and
properties
bubble-
vsry
or
(&y
or
mobilize
enriched)
oil
phase
by
or by
of
dynamic
(multiple-contact)
injection
of
by
CO
swelliig.
~ “into
Helms
mechanisms
The
G+/oil
in
as
from
comelations
and
an
or,
more
miscible
simulators
in-situ
combustion
where
oil
viscosity
are
applied
processes
is mobilized
pruducing
by
water
oil
with
increased
by
the
PVT
(2)
phase
to the
more
gas
of
oil
the
phase
subsequent
mobile
[usually
correlations
to
pmpties
as
phase,
above
distillation.
and
500”F
Thermal
describe
fmm
of
(3)
include
oil
piessuti,
gas
of
recovery
and
flood
(surfactant),
and
watedlooding
In
reduce
oillwater
and
to water
xnd/or
flouding,
IFT,
oil
well
tilckened
water.
impmved
oil
by
oil
Results
The
a.kemtion,
interactions
but
are
and
involve
such
lowering
effective
increasing
propelled
bank
of
C02
thought
the
slug
toward
tie
pulymer-
flooding
to
emulsification.
complicated
adsorption,
are
include
models
performance
of
by
simulation
and
injectkn
rate,
of
in cyclic
stimulation
and
per
cycle
for
gas
steam
flooding
case
and
spacing.
A number
models
have
been
rate
to OPtimize
to overcome
studies
and
questions
injected
pressure
the
level,
and
issues
quality
and
One
optimal
question.
time
periods
production.
of
steam-injection
published.
addceased
steam
steam..
soak,
of
simulate
stimulaticm
the
to
19
to
of
and
~quired
in reservoir
injected
of
a C02
and
rates
injection,
introduces
and
recycling
USefUl
used
injection,
The
using
C02
applied
the
and
CO ~
are
heterogeneity.
concerns
oil
model
by
of
by
injected
on
Graze
injection
operating
with
level,
injection
These
to effects
loss
surface
composition
and
steam
thk
from
time
is also
relate
gas
simulation
steam
of
of
recove~
fluids.
cyclic
In
inclusion
IFT,
inj.+tcd
are
in
recove~
a compositional
of
aud
steamflooding.
N2
breakthrough
arc
combustion
of
in cases
applied
of
of
oil
reservoir
not
10 Chemical
ion
of
10ss
depletion
of
CO ~ /water
for
low
fluid/fluid
effects
arc
miscibility.
facilities
aud
most
only
reduction
field
18 Modeling
Thermal
into
or
of produced
size
in-situ
surfactant
responsible
alkaline
as
the
plus
fixed-composition
or
compositional
production
pattern
water
oil
g The
the
gas
for
of pressure.
C02
application
include
design
greatly
solublizing
bank.
mechanisms
in
by
used
They
tie
effects
a function
of
project
gmtegies.
the
are
(reinfection
RangeIy
as
micelIar
surfactants
are
a graded
recovery
prucesses
by
thereby
an
normally
clearly
1982
reducing
(2)
17 describe
leveI.
Polymer
recovexy
by
micellar
mobilized
understood
oil
ratio
forming
polymer,
(caustic).
improves
micelles
production
include
alkaline
mobili~
parneabfiity
viscosity.
models
drive
or
vs.
previously,
during
and
vaporization
composition
Chemical
water
(1)
drupout
and
injection
composition.
oil/water
and
prcssme
phase
stated
to estimate
composition,
in estimating
and
water
flank
vs.
is invalid.
cycling
by
dso
as
resexvoim
PVT
gas
Gf rate,
waterfhding,
gas
two-component,
liquid
with
teinpem”mti,
to pattern
(7)
the
weIl
intervals,
of
models
partial
Zana
cracking
completion
aa a functiGn
desirability
black-oil
by
oil
oil
(260”C)]
models
N-component
functions
the
(1)
and
but,
studies
caused
full.or
dktillation
of
to estimate
recove~:
a natural
repmaentation
or
of
mGdels
augmenting
aud
purpoacs
facilities),
reduction
15 aud
(5)
opposed
drilling,
reservoir
injection
Heam
used
oil
well
coning
rste,
as
where
state
a
applications
black-oil
are
on
(2)
water
Compositional
of
field
13 and
m]ection.
thcae
are
of
et al.
and
frequently
injection
infi!l
water
of
reservoirs
(1)
temperature,
components
AUGUST
(6)
discussion
recent
parameter
spacing,
peripheral
Oil
an
with
reaewois.
these
(4)
11 give
14 describe
Harpde
different
simulation
McCulloch
16 describe
models
of
of
a
operuting
of
a geneml
misuse.
for
to
altered
Herbeck
uses
in Ref.
complex
of
and
the
models.
et al.
or
and
equations
in heavy-oil
primarily
hydrocarbon
mc!dfluid
simulation
~covery
(forecasting),
economics
12 gives
and
papers
and
(K-values)
to steam
intermediate
nettability
of
condensate
Th&mal
flooding
use
andlor
(EOS).
and
Coats
simulatkm
gas
mixture.
frum
examples.
(3)
composition-dependent
recently,
of
floodlng.
equilibrium
and
Staggs
pattern
reservoir
N-component
and
pressure-
mobilize
description
describes
mom)
Usad
rccove~
dkcussion
gas
(3)
on
to cGmpare
methods.
BIack-oiI
to
reduction
excellent
C02
properties
to
(m
to estimate
scheme
recove~
effect
mobife
Are
excellent
below
and
reservoir
effects
and
Kllough
or
(single-$ontact)
viscosity
model
content
phase
calculated
oil
oil
an
compositional
hydrocarbon
an
by
gives
active
outright
mow
three-
is used
producing
the
rather
reservoir
the
miscibility;
2 and
Med.mism
into
6il
nonequilibrium
a black-oil
evaluate
of
is injtild.
presswe
of
existing
number
compositions
with
vaporization
attainment
for
a volatile
phase
injection
into
to the
phases
of
significantly
(2)
accmunt
processes
oil
snd
Models
simulation
conditions,
of” constantaud
whete
dewpoint;
and
Compositional
depletion
reservoir
phase,
here
recovery
gas
(1)
gas
water.
in addition
assumption
are:
phase
discussed
simulate
immiscible
examples
gas
types
the
Simulation
Resemoir
given
gas
in the
in
mechanisms.
used
composition,
oil
oil.
mechanisms
recovery
are
of
shear,
flow.
of
presumes
and
viscous
phase
gas
Why
content
oil
and
mobilization
snd
solubihty
hydmcasbon
gas
exchange,
to
oil,
two-component
vo~atilily
of
=maining
some
four
the
no
volubility
for
This
(pressure-independent)
compositions,
applies
water,
pressure-dependent
phase.
representation
constant
model
immiscible
a simple
in the
zero
is@ennal
containing
Herrera
well
pattern
field
studks
and
1635
Hanzlik20
5-POINT
cyclic
9–POINT
and
field
---------
compare
performance
and
and
related
predict
flood
of
caustic
the
25 and
process,
to dkcem
In
recent
given
years,
difference
as
injection
of
the
C02
of
/\
used
a single,
general
N partial
difference
\
\
of
for
For
as
for
is usefuf
and
to
process
has
been
used
compare
recoveries
from
a
enhanced-recovery
thermal
methods
combustion),
and
with
;’
QRJD
in simulation
model.
and
severaJ
some
the
substance
or
coefficients
an
of
adsorption
or
isotherms,
is
of
of
conservation
of
may
be
pment
to K-values
from
or
corre]atiO”~
aflowance
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1636
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TECHNOLOGY
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36 first
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In
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atiner
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S@le-well
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mtio
agiventime
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product
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all
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can
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This
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falsely
in black-oil,
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pteserve
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wrote
tiyt
resulting
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papers.’3J’~
The
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Implementation
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black-oil
ills
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large
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in
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studies
odels3943,4547
formulations.
or
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case.
updating
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with
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et al., 31 and
for black-Oil
pressure
explicit
witbin
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today
option
black-oil
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coning,
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with
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petmeabilities
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etlicient.
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black-oil
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implicit
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1637
TABLE
l–CALCULATED
STEAM
(days)
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117
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grids
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JOURNAL
amiveat
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~
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1 show
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it reaches
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steam
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describe
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simulation
in simulation
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thegas
unstable
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Remedies
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in black-oil
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Todd
.“
on
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80%quality
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m3/d)of
effect
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MPa)
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viscosity
(260”C).
produced
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Od
Specified
thmr
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homogeneous
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study,
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grid-orientation
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Fig.
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DAYS
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black-oil
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The
inost
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permeability
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ll,OOO-grid-block
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.. \
-—
\
3,000
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undoubtedly
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INJECTOR
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40.
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I
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In
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9-POINT
TIME=SO
allow
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increasesin
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in the
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DIFFERENCE-SCHEME
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m3tiI
sharp
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simulator
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used
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117
1,000
900
of
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machines
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Diagonal
204
87.7
100,OflOwordion
Recently
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TIMES
PATTERN
2
Diagonal
Scheme
BREAKTHROUGH
NINE-SPOT
ai
gas
papem
of
TECHNOLOGY
‘
consistency
in that
obtained
from
in smooth
phase
and
densities
‘and
based
densities
also
compositions
a correlation55
converge
of
point.
to
The
separste
no
values
as
value
at
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most
calculations
today
Robinsonsg
EOS’S
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be
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In
our
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parsmetem
Table
to
2 compares
Iaboratoty
PVT
mixtums
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(54 °C)..
data
Simcm
analysis
e-t
through
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the
‘
al.
pteserited
with
C02)
(lumping
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components.
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four
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results
Baker
and
saturation
Luks
with
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without
match
57,
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these
data
regression,
using
Unit.
indicating
higher
to
to
as
study
of
of
in Alberta.
coning
formations
rate
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and
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at
for
subsequent
work
for
miscibility.
to study
as
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rate.
rste
adverse
and
Ref.
67
was
3D
to
and
calculations
to
types
restricted
displacements
ryoderate
describes
in different
study
waterloil
rangirr~
MPa)
sensitiiiy
This
indicating
(12.4
oil
C02,
level.
injection
void:ge
of
the
tests
‘sensitivity”
ultimate
a simulation
included
similar
into
is employed
resemoir
indicated
pressures.
vaporization
necessary
rste
injection,
match,
C02
reports
define
pressure-maintained,
used
psia
pressures
between
reservoirs
C02
pressure
for
1,800
poin$,
pressures,
at all
flood
a
All
dewpoints.
of
design-stage
discuss
frequently
or
two
components
Kane66
We
production
EOS.
in
severe
heterogeneity.
good
using
low
Simulation
correspond
results
as
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EOS
miscibility
relationship
cmde
6s
1 MPa).
ace
pronounced
oil
increasing
al.
sensitivity.
(C I
the
with
SACROC
Sample
Peng-Robinson
an
of
130”F
C002p0nentS
results
EOS
with
63 for
regressions,
five
showed
the
calculated
last
dkplacement
intermediate
Without
(10.
are
simulation
simulations
pressures
and
bina~
bubble-
EOS
psia
discussed
+
cmde
MPa).
pressures
immiscible
et
1,469
observed
previously
and
(11.4
regression,
multiple-contact
data.
at
oil
These
M calculated
pressure
components,
crude
pseudocomponents.
obtained
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the
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with
14 components
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JW
three
through
Dicha~
sample
components)
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were
oil
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the
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after
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PVT
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a SACROC
listed,
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last
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of
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C,3
the
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the
using
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the
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Our
~f EOS
calculated
C Ls +.
data
c,3
match
reported
and
result
of
coefficients
C02/hydmcarbon
through
to match
with
Peng-
interaction
that
C,
calculated
in the
binary
the
pressure
calculated
Katz
that
test
adjustment,
while
is necessaty.
laboratory
pressure
latter
the
EOS.
found
adjustment
EOS
C02
have
to 0.1298
point
2 were
62 except
O. 10 and
cubic
a
used
et al,
were
bubble-point
Peng-Robinson
pammeters
some
necessary.
of
We
Katz
in Table
14 components
adjusted
Peng-
EOS
ffuidq
requirements
to match
found
all
to resemoir
we
time
efforts
have
that
general
,applications
the
on .EOR
prohibitive
generally
tim”gb
of
work,
regression
Frequently,
shows
EOS
applications
and
a single,
61” describes
compositional
nonlinear
using
fmm
Redlich-Kwopg
al. 62 give
in resemoir
Martin60
obtained
Yarborough
modified
used
Redlich-Kwong56”5s
equations.
can
form.
widely
using
EOS.
by
values
EOS
values
regression
given
a single
EOS.
predicted
Rohinson
Phase
using
smoothly
Redlich-Kwong
are
y resuk.s
to identical
a critical
on
K-values
consistence
point.
The
use
and
This
convergence
appnmch
viscosities
et
densities.
source.
differentiable
computations
critical
phase
a single
The
39
TABLE
concision
simple
a modfied
2—SACROC
OIL/CO
and
brief
~ PVT
of
that
rather
Water/oil
lengthy
displacements
reference
are
is
rste-
DATA
Calculated
Observed”’
1982
regression)
Predicted
.1,660
1,660
1,660
ps~a
1,920
1,870
1,792
pressure,
psia
2,160
2,079
1,947
Saturation
pressure,
psia
2,420
2,344
2,118
Saturation
pre3sure,
psia
2.570.
2,589
2,215
Saturation
pressure,
psia
3,000
3,000.
2,352
Saturation
pressure,
psia
3.740
3724
2,534
Saturation
pressure,
psia
SaturaUOn
pressure,
Saturation
Volume
ratio
1.0
1:0
Volume
ratio
1.1016
1.1123
1.2385
Volume
ratio
1.2791
1,3043
1.4336
Volume
ratio
1.5234
1.5562
1,6970
Volume
ratio
i .6443
1.6694
1.8270
Volume
%
Hquid
73
73
82
Volume
%
tiquid
59
57
68
Volume
%
fiquid
50
51
62
Volume
oA
liquid
40
39
47
Volume
oh
kouid
Volume
oh
bquid
at
AUGUST
(after
610
7
of
psia
Crude
gas,
mol
Crude
gas,,Z
ZC02
at
.Clltlcd
pm
2,000
wt
psia
7
i.0
11
crude
—
40
39
20.3
21.2
20.8
0,776
0.781
0.75s
0,38
0.38
—
1639
“’”””r-l!””
I
,,
I
I
‘o
I
1
!,
2,
I
,,
.0
%
Rccov
O(L
Fig.
sensitive
is
if
used,
of
a
an
and
definition
Figs.
5,
a fixed
oil
across
and
find
at
rock
saturation
definitiori68
dktributions
is fairIY
the
horizontal
blocks
representing
more
incIined
water/oil
x and
block
CaS&).
Where
or
to
the
viewed
depth
blocks
ln
block
rock
and
pseudo
different
offset
by
mote
grid
viewed
the
the
about
equilibrium
latter
the
should
existence
during
be
used
of
phase
dynamic
of
segregation
a trend
a’ sense,
the
dynamic
contact
use
pseudo
viscous
and
shapes
et al, 70 and
of pseudo
from
with
resuhs
blocks
Kyte
relative
comparing
detailed
using
is an
of
of
or
fewer
layen.
systems
Until
on
most
this
in three
will
continue
simulator
recovery
a
extension
or
go~
is reached,
JOURNAL
step
and
temperature.
of
behavior
mom
will
interest.
direction.
in pan
on
of
equations
phases
we
of
in that
of
of
mukicomponent
over
wide
witness
OF PETROLEUM
the
of
processes
small
depend
and
be
use
toward
capable
will
PVT
will
i.e.,
definition.
now
of
machines.
studies
studiis-
reservoir
research
the
small
larger
understanding
pressure
strongly
compositional,
large-capacity
savings
example
this
using
high-speed,
way
or
be
perhaps
general
to represent
fluid
of
will
cost
or
under
all
33
state
we
and
toward
a single,
improved
curves
irresp~tive
very
simulating
Ref.
(inclined
reservoir
would
Simulation
computing
go?
(horizontal
pressure
of
Research
if
lengths
fluid-saturation
addition,
background
which
obtained
results
on
are
initial
the
Jacks
the
black-oil,
The
capilla~
In
give
including
1 to 2 years,
definition
practice,
difference
In
distributions
from
curves
yectorized
of
is unimpotiant
thickness
not
reflect
calculations
contacts.
discuss
Future
Within.
models
The
y dire&ions.
BeW,49
The
blOcks
values
(dip).
elevation
set
a
are
not
fluid-
pseudocurve
the grid
as
1,’7
undemunning).
cross-sectional
@
Ru”
contacts.
the
in dkto~ing
authors,
permeability
used
gasloil
cumes
act
(overrides,
will
‘equilibrium
condhion
,.O,!
..60
if pseudocurves
shut-in,
to level
Sevetal
pseudo
initialize
if
grid
time)
forces
Success
significantly
distributions,
as
ultimate
be
transition-zone
grid
ovemll
ratio
and
pressure
gravity
pool,
distributions
were
(in
equilibrium
higher
find
of
The’
the
yield
capilhy
reading
should
definition
gas/oil
exceed
case)
arguments
staggered
pressure
and
block
am
not
D-S
speaking,
waterloil
reservoir
I
m
RECOVERED
Lake
initialized
horizontal
=“d
curves
as
Selecting
mcoveiy
concept
structure
in both
capillary
significantly
the
wh!ch
complex
in the
Strictly
the
if the
rate.
correctly.
at
the
limits
we
stmightfor,vard
reservoir
becomes
pseudo
higher
resewoir
used,
of
on
water/oil
figure,
laboratory
depletion.
existence
and
oil
a fixed
discuss
cut
limit
1
40
6-Sturgeon
corresponding
limit
the
the
the
depends
conclusion.
ukimate
curves,
or
representing
1640
economic
et al. 6s69
of
vertical
an
economic
adopted.
this
we
across
pressure
place
limit
Selecting
reading
lower
Coats
give
as
1
30
m
Fig.
water
an
economic
two
7 illustmte
rate.
and
capillary
the
case
figure,
recove~
as
Thus,
economic
a higher
limit
if
is used.
6,
seciion.67
maximum
particular
of
mte
the
of
those
If
I
1
,0
,
60
cross
rate-sensitive
given
!
EnEO
rate”
weights
,:
% 0!,
in any-
oil
1
,,
pool,
B
limit
not
sensitivity
relative
River
economic
are
minimum
rate
at
5—Belly
1
ranges
a
TECHNOLOGY
,,,0,,
continued
development
variety
of
types
and
of
increasing
simulation
application
models
for
of
1
a
1
1
1
1
,..
1
1~=1
different
processes.
Conclusions
A reservoir
simulation
difference
block,
one
model
an
the
is described
used.
IMPES
stability
for
here
provided
by
of
recent
each
in terms
sequential
of
of
and
grid
or
description.
tbe
various
generally
options
tinite-
each
component
fluid
models
with
partial,
For
reseivoir
Current
formulation
of
equations.
is written
comprising
formulations
is a set
balance
equation
substance
The
model
material
employ
incrsased
—
,,,,,.
..,,
k.
implicit
formulations.
Examples
significant
advances
include
(1)
,00
a nine-point
difference
orientmion
effects;
promises
formulation
(2)
and
may
(3)
and
vectotization
fi?asibility
Cutmnt
larger,
single,
of
may
a generalized
model
generalized
processes
of
tield
away
to the
studies.
from
different
the
present
processes
applicable
toward
to all
or
%,!,
a
Fig.
most
G,W,
relating
to
Paul’s
chemical
provision
flooding
and
of
iifimnation
its
simulation.
1s.
M.,
Media,
Co.
Katz,
D. L.:
Trons.
, AIME
Buckley,
6.
Welge,
York
‘“MC
,, J.
‘A
Recoveries
by
of
16,
Producing
19.
Gas-Dtive
Oil
M. C.:
and
Gas
Odeh,
A. S.:
.’Rese~oir
(Nov.
1969)
1383-88.
s.
Hahn;
L. W.:
Recovew
Methods,,
9.
Oqaq,
W.B,.:
Pet.
10.
Tech.
AIME
(1942)
Drive,,,
Trans.,
of
146,
for
Johnsan,
Per.
11.
C;E.
Td
9 J,
Tech:
of
S.rfactam
1976)
93-102.
.’Status
zmd
Mad.els-An
and
Pd.
1976)
H.M,
C02
‘.sml.s
Jr.;
(Jan.
Stiggs,
of
1s It?”
Hydnxwbon
(Jan.
20,
107-17.
Oil
(1952)
J.
Per.
21.
Tech.
.011
76-84.
Micellar
Mcthodi.’,
J.
22.
md
Emulsion
Floods,”
K. H.:
P,!.
Tech.
and
23.
85-92.
E, F,:
.. Resewoir
Ovmview,.,
Htgb
Reservoi&
Relief
(Nov.
Nwn,~ical
15.
Harpale.
J,
Pet.
8irmdatian
Tech.
(D.c.
]97
t)
K.!.
voir,,,
paper
tion
md
SPE
J. E.,
1982
J. R.,
Rainbow
24.
2.5.
and
Spivak,
F!e[d,
A.:
Alberta,
%imu!?,ticm
Canada,”
of
J.
Reprint
Hewn,
Series,
C. L.:
[0022
Role
of a West
presented
Symposimn,
Pav&w,
.’The
SPE,
E,J,
M the
BeijinE,
Jr.,
Martin,
Dallas
(1973)
of Numerical
T.=
Cmbonme
[.11,
Petml.urn
March
19-22,
C.,
Doughty,
cmd
11,
Moranvi[k,
the
in
1312-18.
M. B.:
,of
at the
.%
,S
and
Flood
1981)
Effects
Exhibido”,
and
for
SPE
McCaner,
the
.. Misci-
dp
SPE
W!”dkdl
56th
Antonio,
E. D.:
Cornell
10292
Cm fereme
Hencra,
J.Q.
of Multivmll
Unit,
presented
tid
at
Exhibition,
Hmzlik,
a“d
Amual
5-7,
Oct.
“C02
Flood
Wasso”
S.”
SPE
56th
the
S.”
R. L.:
Dipping
Rismvoir,,,
mal
Techk4
5-7,
19s1.
Aotcmio,
Per-
Andm”s
AmI.al
Oct.
5-7,
of
Repoi
Fayem,
F.J.,
28.
Histmy
Cat
Field,,,
for
Steeply
at tbe
S.m
56th
K. H.:
S 3.
Am
Amcmio,
Coats,
Wells,,
R%iOna[
z Massive,
presented
md
HeavyOU
Cmyon
~lifomia
Exhibition,
Hawe$,
R.L,
E.F.,
Theory
(April
Pec.
Ott:
.’Cyclic
Tech.
(O@.
J.’ (Dec.
K, H.,
Mic.llm
.ictants
Pe’t.
E. R.,
Limar
Flooding,,,
f., . ‘Some
.,.J. .—.
o,
Tech.
CO ~ m
(Sept.
Rubin,
Alkafim
First
1980).
E,,
1981)
and
As.,,,,
EOR
of
‘%&;;;
;;
1617-27.
Radke,
Flcading,’.
C.1.’:
S...
Pet
‘<A
Eng.
245-5S.
K. H,,
and
?erfonnance,”
Am!..]
Accwacy
for
Cwas,
Flcad
M. R.,
J,
Vis]ocky,
19S2)
J, T.,
44th
!.
(Dec.
and.Mathews.
of Sufi
R=rvoirs,’.,
Chemical
Palm”,
Amenable
DOE/BC/03iM8-20
dezabala,
Coats,
Design
R. G.,
Reservoirs
Abdication
%
Eng.
19S2.
1979
10321
and
of
Sdrndatim
i990-98.
..seitiicm
creased
Exhibi-
SPE
Shipley,
Stimulation
tbc
Pilot
paper
..Steam
S ! -B Zoo.,
p==!t,d
at
April
18-20,
RF.,
Annual
Tcdd,
i“ the
C.mfermce
Meldau,,
SPE
27.
E, J.:
Pattern
.’Steamflood
Williams,
pOIYmer
3im.1a-
R. K.:
M.,
Eval.atio”
Match
J.
Per.
Reser-
Cobb,
R,,
PaPer
No&
Models,,,
26,
Mm.gmnent
Technical
KiRo.gh,
AUGUST
md
Sim.Mio”
1399-1408.
Simufo,km,
in Reservoir
of Reservoir
1391-98.
Langtcm,
1969)
tirm
Mcsuse
1969j
(Nov.
R. C.,
14.
16,
. The
McC.llach,
Tech.
M,
Potemial
Coats,
J.
13.
Todd,
1981)
J.
1428-36,
12.
and
and
presemed
10274
and
C02.
(July
Tech.
K. L,,
Rcsemoir,
Exhibition
1982.
of a Possible
Per.
Recovery
SPE
paper
paper
SpE
7969
Meeting,
Vemura,
195,
Miscible
1976)
m
Caustic
Herbeck,
Engineering
”
0,1
Conference
Gas/Steam
of
..Study
a Cmnplti
1981.
Fluid
Compu[ing
AIME
S~mulation—What
<status
(Jan.
2.W
Petroleum
19-22,
the
J.
Fuller,
Enhanced
Tax,
E. T.:
of
InO.
March
at
Colorado,,,
C. W.,
Gas
Field,”
Reserves,”
“Mechanism
Method
m Water
Blobmqtiist,
formance
147.
91-98.
7,
Run
Simulation
Beijhg,
Zana,
Field,
T.$ch”ical
TrarIs.,
Fiekk
p~senred
a“d
Technical
McGraw-Hill
Bay
1~23
D.J.
Profit
([946).
18-32.
Simplified
0,s
pool,
19S1.
( 1945)
Lcverett.
in Sends,,,
H.I.:
D-3
Syrnpmi.m,
Gcwe,
bk
Porous
(1949).
Estimating
118,
and
Ml
Through
Produciiotz,
Oil
Histories
of
(1936)
Displacement
City
Phys.
.’fvfethods
Fluids
Arbor,
of
Production
App&l
SE.
Ann
Pmpmim
New
M.:
ksewoks,
5.
l.c.,
Phxlmd
Inc.,
Muskat..
of Homogeneous
Flow
Edwards
M.:
Bcwk
4.
Thv
1.W.
fvfuskat,
3.
Prudhoe
spE
Technical
17.
References
2.
‘The
PaPer
Ra@y
1, hfu;kat,
RCcovmm
7—Simonette
interest.
Acknowledgment.
I appreciate
,./.
capacities,
contribute
detailed
of
which
3,.,
simulator;
storage
which
lead
models
---
grid-
simulation
speeds,
more
research
prolifefafion
fecovery
of
computer
capabilities,
of
usage,
in compositional
aid development
increased
reduces
equation-of-state
improvements
and
which
Meeting,
O, Dell,
Denver,
P. M.,
and
i“ Numerical
1972)
George,
Colemvve,
paer
SPE
Sept.
Hira-mki,
Reservoir
G. T.:
2546
.’Predicticm
.28-Ott.
G.J.:
kf
prese.t~
1,
at the
1969.
“Methods
Simulators,,
for
S SOC.
lo.
Pt-z.
515-30.
W.
D.,
Chu,
Chich,
and
Mmcum,
B. E.,
1641
‘.Thcee-Dine.sional
E.g.
29.
J,
Sim.kxion
(Dec,
Yanmik,
1974)
J, L.,
Difference
a“d
Ratio
Stcamfloodin&7,
So..
Flood
Pet.
52.
McCracken,
Rexwoir
Mobility
of
573-92.
T. A,:
Simulator
CA
Nine-Point,
for Realistic
Displacemems,,,
SOc.
F(nite-
Prediction
Per.
Ettg.
of Adverse
J,
(Aug.
Sheldon,
J. W,,
Gmmal
Paper
SPE
De”ve,,
31.
Harris,
Resewoir
1521-G
Oct.
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H.L,
32.
1960.
and
Gwder,
Drive
Trans.,
Fagi”,
R.G,
a“d
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tion
34,
and
Methods,
J.J.H,
MacDonald,
8imUi,ii0”
1910)
35.
~PE
Vegas,
36.
Problems
37,
md
i969)
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(June
55,
or
to
56.
Coats,
K. H.:
of
Dublin
Exh,bhio”,
39.
Coats.
40,
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S1...,
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E.g.
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1978)
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Annual
‘Solution
of
A
Sim.latia
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Las
IJirncnsicud,
at the
hibitio”,
41.
Las
Pat,..,
SPE
EIW.
Numerical
418-24;
VeZas,
J.T,
and
9-12,
1977.
Huf-n-P.f
Process,>’
Technical
Con
”
Technical
Con
a“d
Coats,
43.
Coats,
K. H.:
62,
paper
SPE
and
Sot.
S...
Per,
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44,
Implicit,
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J.
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9228
ptcsen[ed
E.xhibitiori,
f-as
1980)
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Three-Dkncnsional,
Per.
E.g.
Wei”stei”,
SPE
fmence
8329
a“d
Ex.
Smdy
of
at the
54th
Ve8as,
the
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J.
for
A. E.:
1981)
Wheeler,
Thermal
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X-26,
Model,,,
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Strongly
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Fully
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Model
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for
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G. K,:
Combustion
md
W. E.,
Tbmrnal
37-5S:
Co”i”g
Woods,
E. G.;
P./.
and
EIIZ.
Che”,
Recovery
Trans.,
. .Developmmt
Rc.servoir
69.
Made],,,
(Feb.
1977)
Sx.
J. A,:
49.
at
J.R,
Kyte,
Kovd,
PeY.
51.
Todd,
and
1642
!b~
SpE
Berry,
Dispersion,
E. J.:
Unstable
‘A
Miscible
E.g.
J.
M.R.
Application
New
Stabilized
R=woir
and
Numerical
50.
‘LA
Numeric.[
~9~~ted
(be
and
J.
and
(Feb.
Per.
of
Ew.
.?
s.
49th
Ann..l
for
1980)
.< New
1, S.,.
Per.
Me~had
for
Displacement
La”@iff,
J.
Functions
R, M.,
Iiom
and
Da$i8n
Unit,
Kelly
Predicting
the
W,J:
T,..,.,
, AsME,
Kane.
A. V.:
.$The
simulator
Solu-
Ptcdimio”
Eqnation
1197.
New
Two-Comta”t
Fund.
(1976)
15,
of
SIate-Which?”
Equa-
59.
Ind.
Eq.aticm
mwemed
Engi&ti~g
and
ScpI.
A.:
.< Predicting
Using
1978)
Swn-
Research,
IW15,,
l~6th
1978.
Phase
Methane
the
Behavior
Imeractio”
of
Coeffi-
1649-55.
Zma.
E.:
‘, Pha=-Behwior
“Systems,,,
So.c.
Per.
Pmwr-
E.g.
J...f &b.
Penynm.,
of
Tech.
of
Canada
Lid.
Sot.
Pet.
J, D.:
.EwIu.
Project-SACROC
(Nov.
1973)
1309-13;
of
of Oil
K. H.,
m and
Board,
Pmc.
Smith,
J.
and
and
Reservoir
Use
of
1973)
(Feb.
and
1974).
Weber,
Flow
J.‘. H.:
S...
and
Per.
C. C.:
Enx,
.. The
Pseudo
Use
of
3.
of
Thrce(March
Moddin8
a Two-Dinwmicmal
Dynamic
0,1
.. The
Simularicm
Mattax,
A, G.;
i.
1967>
Henderson,
With
1
Energy
,, .‘777-RR
. ..
(Dec.
Pm fam.ce.,,
O. E.,
knmsiona[
Ens
,as Schedule
Albeti
7511
M. H.,
Two.oimemioml
Reservoir
Rate,,z
Two-Phas+
J. R.,
j.
to Productim
the
No,
Terh.”e,
Per.
DemPwY,
-WAG
Snyder
submitted
to
Three-Dimemicmal,
Equilibrium
(1,”.
Recovery
submission
R, L.,
SOC
CO,
Unit—Kdly
19791217-31.
>s
Neilseri,
Reservoir,,,
J.
Saturation’
”
of a LarEe-ScAe
atmche$
Comervatim
K. H.,
H. H.,
Fkmd
SACROC
(Feb.
Semitivity
Jacks.
Ronquille,
Tech.
Review
Calgaty,
63-71.
and
Pet.
Project,
Ltd.,
1971)
3.
.. Pm fonnmce
of lhe
Coats,
and
Systems,
~ Miscible
Field,,>
‘CA Study
Coats,
Point
255.
Pet.
Shell
T, L.,
a CO
Recovery
J.
.<Critical
Multicomponmt
of a
Rwswoir
Fu.cticms
,’, S...
PCL
175-85.
S1 Metric
Conversion
Factors
bbl
X
1.589
873
psi
x
6.894757
.E–01
E–03
=
m3/d
=
MPa
6-9,
JPT
269-76.
of
s Sot.
Dlsti.gulshed
mmmlari,e
~e.elopments
i.dviduds
228.
b
mme
Author
series
s,.(,
of !he
the
for re.ders
rwcqnized
deflnitiw
Testing,
Purpc.ss
To inform
for
Miscible
petm[eum
..$...,;.9,
aides
are genera,
desuiptrve
presentations
ah in w area of {ethnology
by describng
who me
not specialists
as experts
work
Devdopme”t,
Predicting
%
of State
.1
to Comrol
Media,.
of
15-24.
I@’comp
53A7
Performance
AIME,
of
Ge.seous
and
Pacer
K. D.:
for
Snyder
Trans.
IMPES
Oct.
1975)
(Aug.
i“ Heteroge”eo”s
145-54,
of a Numerical
Pseudo
E.g.
in
SPE
Houston,
of
In-.Sit.
(Feb.
Use
wpec
MC.tin8,
D. W.,
1963)
Method
Scmuhm%’z
Luks,
1980)
J3khrmy.
Ew.
Application
S...
27,
Beach,
md
Oil
Celculatiom
8im”lator-The
Per,
267,
.. . .
Me@i”k,
-Reservoir
Thumodynamics
of a Gmerdized
(Nov.
A..
(Occ.
!9.
“A
Fluids,,,
Tech.
Tech.
81.
Systems
Per.
L.E.
Three-D
.. Nunl,rica[
Processes,S,
AIME,
and
Simulator,>,
W. H.:
18,
Fimoz~badi,
Rosrrmn.
Dimemional
.. Nummiml
J,
,.-,,
TWC
1979)
Viscmify
Pet.
Red[ich-Kwong
(1972)
_wzions
1979)
J.
[h.
112-
Chem.
Miami
C02
Verlical
S.,.
Eng.
Meeting,
R..
of
Gas
454-58.
Process,,
H. B.,
Simulation
En<.
48.
68.
70.
Crooksto”,
for
(Aug.
.$ Cdc.kding
:. Correlation
the
16,
.$Application
and
Resources
Model
Three-Pbuse
(Aug.
J.
Fh83CiCi~S
D. B.:
of St&in
J.
Simon.
Field,,.
Annual
65-78.
47,
D.L.
Enhanced
363-76.
McDonald,
H. G.,
Model
46.
Katz.
SC-i.
Equations
‘<Simulation
and
Tech”iq.e
&g.
233.
with
Reservoir
on
Nat].
W,
Joseph
Enz.
‘. CUNC.
‘<On
State,
Joffe,
Robinson,
L.:
ACS
E.g.
533-53.
R.H.
Tech.
----20.>6.. .
Three.
Cornpositiorial
Ccxnb.sdo”
Trindde,
Iterative
Per.
C. R.:
(1949)
1970)
(May
Pemole.m
Bsker,
66.
Parametric
Equati6”-of-S&ttc
.’ln-Sit”
1980)
S0.,
45,
8.$.
K, H,:
of
Pa.
1978)
64
Pet.
1979.
.’A
SPE
a“d
1.1.:
Fund.
cients,,,
63.
fcnznce
paper
Technical
23-26,
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Fully
Simulator,,,
Annual
K, H.,
“An
.,, J.
231.
of
(Jam
hf.
Y.arborough,
to
65.
Sept.
State,,,
. !@!w,
61.
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J.
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42.
of
.+x.
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‘A.
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AIChE
of
and
Equation
David
press”F
Steamflood
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Modeling,
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H. W.:
S...
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A
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52nd
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‘AppliczUio”
Eq.atio”s,’,
Comp”mr
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An
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P.L
and
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Soil
Fmm
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tim
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Implicit
‘A
Lampe,
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(Dc..
369-S3
,7[.:
874-82.
Jr.:
DiffcFnce
a Vector
Fussdl,
Bray,
V.
posi.rn
Reservoir
Hi~hly
and
o“
Trans.,
0,
State.,,
Asymptodc
to Resewoir
481h
AIME,
J.
Oct.
J. Y.,
Reservoir
Zudkevitch,
Instabifhy,,,
for
Per,
S7.
FommIa-
63.
Difference
SPE
and
1171-76
tions,,,,
Model
S“,.
SPE
Ridi”&,
at the
Ftnire
M,J.
447-53,
1981)
Simulator
J.,
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1973,
‘aGeothemmI
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1972)
(July
Kasic,
2253-64.
Sol.tio”s.
ties
6892
Tech.
@
SOL..
Wong,
L.T.
Lohr.oz,
Pet.
249.
38.
field
of Resmvoir
the
S...
., Methods
Ammach
at tk~
EtIS
(Aw.
a LarEe
F“s@,
1961)
Approach
and
and
C. F,:
and
to
Cornpasitional
249.
Tram.,,
Per.
54.
237.
Press,
J. G,,
Irnpficit
so,.
New
Sources
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K. H,:
3,
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ErIg,
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do”
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!-etkeman,
A
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P.M.
Pm.
R&ewoir
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~542
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E,,,q.
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A; G,,
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351h
Physiml/N.merical
Water
Method
Computers,,
,. Analysis
?,imulatiox
Miller
42S-36,
Spilletre,
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C.H.
Itztc+or
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at
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the
in tie
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7he
areas.
,wdfk
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ar!ic(as
.3”IY ,.
of recent
is e project
OF
thess
details
readership
series
in !he topics
.f
prmide
;1(”s!,,,,
ad.amas
the Technical
PETROLEUM
tisc.ssed,
kq
$M
recent
Wrillen
by
reterem~s
!he techndog~,
io VW!O.S
Ccwerage
areas
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.f
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K. H. COATS
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—
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119
65. Martin, J.J., “Cubic Equations of State
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SPE 10020
K. H, COATS
70 ●
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——
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76*
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7s1
TABLE
1
CALCULATED STEAM BREAKTHROUGIiTIMi3s(DAYS)
..FOR A NINE-SPOTPATTERN
WELL 2
DIFFERENCE
SCHEME
5-POINT
9-POINT
DIAGONAL
WELL 3
PARALLEL
47.8
87.7
DIAGONAL
204
1400
900
75.5
/
.
PARALLEL
117
1000
\
/
\
/
\~
2
<
PARALLEL~
GRID
/
\
/
\
~DIAGONAL
GRID
\’
●
D
1
0 INJECTION
●
PRODUCTION
“WELL
WELL
TABLE2
—.
SACROC01L-C02PVT
—— D.4TA
CALCULATED
6E
(~F’rER
Regression) PREDICTED
OBSERVED
—.—
.=
.——.
QUANTITY
SATURATIONPRESSURE,PSIA
SaturationPRESSURE,PSIA
SATURATIONPRESS’!RE,
PSIA
SATURATIONPRESSURE,PSIA
SATURATIONPRESSURE;PSIA
SATURATIONPRESSURE,PSIA
SATURATIONPRESSURE,PSIA
VOLUMERATIO
VOLUME RATIO
VOLUME RATIO
VOLUME RATIO
VOLUME RATIO
VOLUME % LIQUID
VOLUME % LIQUID
VOLUME % LIQUID
voL~ % LIQUID
VOLUME % LIQUID
VOLI.!!% LIQUID OF CRUDE
AT 610 PSIA
1660
1920
2160
2420
2570*
3000
3740
1.0
1.1016
1.2791
1.5234
1.6443
73
59
50
40
7
1660
1870
2079
2344
2589*
3000
3724
100
1.1123
1.3043
1.5562
1.6694
73
57
51
39
7
40
20.3
.776
.38
39
21.2
.781
.38
CRUDE GAS M.W.
CRUDE GAS Z
ZC02 AT 2000 PsIA
1660
1792
1947
2118
2215
2352
2534
1.0
1.2385
1.4336
1.6970
1.8270
82
68
:;
11
20.9
.758
* CRITICAL POINT
TABLE 3
ILLUSTRATIVE RELATIVE PERMEABILITY AND
CAPILLARYPRESSUREDATA
WATER-OILTABLE
s“
●2
.22
.3
.4
.6
.7
1.0
Pcwo
PCwo1
PCW07
GAS-OIL TABLE
sL
Sw + so
krw
krow
0.
.8
.2
.05
o*
0.
●3
●4
.6
.8
.95
1.0
0.
.03
.45
1.0
7s3
Pcgo
‘rog
Pcgol
o*
0.
.05
pcgo7
.8
krg
.7
●O2
0.
0.
TASLE 4
INITIAL VALUES OF PNASE PRESSURES MD
SATURATIONS
MOBILE
CASE
1
2
3
PCwo
PCgo < l’cwo7
3
Pcwol > l’cwo> PCW07
Pcwl > Pcwo > P~wo7
4
Pcm
5
6
Pcw > P~wol
Pcwl > Pcwo > PCW07
> Pcml
PHASES
PCgo
Sw
SATURATION S
so
%
PRESSURES
Pw
Po
PO
Pw + PCW07
Po + ~cgo7
< l’cgo7
w
1.0
0
0
Eq(lb)
< pcgo7
W,o
s“
so
o
(lb)
(la)
Pcgol > Pcgo > pcgo7
W, O, G
s“
so
%
(lb)
(laj
(Lc)
Pcgol
0,
G
sWc
so
(la)
G
W, G
sWc
s or
%
(lC)
(lC)
Sw
sor
%
Pcgo
Pcgo
Pcgo
> Pcgo
> ~cgo7
> Pcgol
Pcgol > Pcgo ‘ pcgo7
* SEE DISCUSSION
%
PC)- Pcwol
Po - Pcwol pg - Pcgol
*
(lb)
Po + pcgo7
(It)
~
—.—
---–
GRID
DIFFERENCE-SCHEME
PARALLEL
DIAGONAL
EITHER
5-POINT
5-POINT
9-POINT
\
I/
i
TIME =80
DAYS
O
INJECTOR
●
PRODUCER
FIGURE 1
CALCULATED
SHAPE OF STEAMFLOOD
FRONT IN A NINE-SPOT
PATTERN
1000
I
I
I
I
I
I
100
/
100
10
.
f
OIL
RATE
ST B/D
BE
\
/
\
\
/
/- /
10
\
I
1.0
\
/
\
/
I
/
/I
I
\
—400RB/D
---100
I
I
o
INJECT, RATE
RB/D
INJECT, RATE
I
I
i
I
I
I
10
20
30
40
50
60
% OIL
RECOVERED
FIGURE 2
BELLY RIVER B POOL-CROSS SECTION
(Figure 39 of Reference 7’2)
1
7s$
0.1
70
Ic:ooo
I
I
I
I
100
1
I
E
1000
i
10
/
/
———
———
— \ //
1
L\
,\
/
Y
/
~i
OIL
RATE
ST B/D
I 00
/1 \
‘ ‘\
L\
I
I
I
I
o
10
20
30
1500
---
10
W(
BBLI
RB/0
/
375 RB/D
1.0
\
\
/
/
/
1
/
//
“/o OIL
I
40
1
I
50
60
RECOVERED
FIGURE 3
STURGEON LAKE D-3 POOL, RUN 1
(Figure 34 of Reference 72)
~oo.l
lo,ooo~
I
I
1
I
I
I
t
II
100
II
I
——— ——.— —,
~-
1000 —
10
OIL
RATE
STB/D
B[
15,000
I 00 “
10
o
---
RE/D
1.0
3000 RB/D
I
!0
20
30
‘/o OIL
40
50
RECOVERED
FIGURE 4
SIIMONETTE D-3 POOL, RUN 2
(Figure 28 of Reference 72)
60
70
0.I