sc re chap9 permeability variations
TRANSCRIPT
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Permeability - Its variationsPermeability - Its variations
Adrian C Todd
Heriot-Watt UniversityHeriot-Watt University
DEPARTMENT OF PETROLEUM ENGINEERING
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Introduction
Seldom is a homoeneous roc! encountered"
Reser#oir o$ten contains distinct units or
la%ers o$ #ar%in roc! &ro&erties"
Permea'ilit% is not necessaril% the same in alldirections"
Permea'ilit% is anisotropic"
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Introduction
In sedimentar% roc!s #ertical &ermea'ilit% is less than
hori(ontal &ermea'ilit%
)ori(ontal &ermea'ilit% in the &rinci&al directions ma%
also 'e di$$erent On reser#oir scale* thin strea!s o$ lo+ &ermea'ilit%
material can reduce #ertical &ermea'ilit% to a lo+er #alue
than roc! measurements miht indicate"
Core anal%sis re&resents a microsco&ic scale +hereas
+ell testin re&resents a macroscale 'eha#iour
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,ariation in
Permea'ilit%
Measurements $rom
Mini-&ermeameter on
sam&le $rom Leman
Gas Field .U/0
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,ariation in Permea'ilit%
,ariation in a core can 'e
considera'le The local &ro&erties re$lect the
de&ositional &rocess o$ a
considera'le &eriod
Con#entional core anal%sis
sam&le at 1 core &er $oot"
A +ell test can re$lect
&ermea'ilit% o#er tens o$ $eet"
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A#erae Permea'ilit%
Pro'a'le a#erae o$ a heteroeneous s%stemtends to+ards eometric mean"
( )navg 1 2 3 nk k k k ....k =
( )navg 1 2 3 nk k k k ....k =
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A#erae Permea'ilit% - 2eds in Parallel-
)ori(ontal s%stem re$lects sedimentar% nature o$
roc!s
Reason $or a#erae &ermea'ilit% is to rationalisesmall core sam&les +ith those measured at +ell test
le#el"
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2eds in Parallel-
Linear $lo+A#erae &ermea'ilit% $romDarc%3s La+
T 1 2 3Q Q Q Q= + +
( )1 1 1 21
k A P PQ
L
=
( )i 1 2T
A P PQ k
L
=
( ) ( ) ( )1 1 1 2 2 2 1 2 3 3 1 2T
k A P P k A P P k A P PQ
L L L
= + +
i i
i
k AkA
=
i i
A
i
k hk
h
=
Commonl% used to a#erae
core anal%sis &ermea'ilities"
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2eds in Parallel-Radial Circular $lo+
Case o$ se#eral la%ers$lo+in simultaneousl% in a+ell
( )i i e wi
e
w
2 h k P PQ
r
ln r
=
( ) ( )( )T e w e w
i 1 1 2 2 3 3e e
w w
2 h k P P 2 P PQ Q k h k h k h
r rln lnr r
= = = + +
i i
T
h kk
h
= The #alue to 'e com&ared
throuh +ell $lo+ tests
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2eds in Series-
Linear $lo+ Reser#oir ma% ha#e 'een$olded or $aulted"
)ori(ontal la%ers no+#ertical"
A#erae &ermea'ilit%o'tained '% addin&ressure dro& across each'ed"
( ) ( ) ( ) ( )1 4 1 2 2 3 3 4P P P P P P P P = + +
( ) 31 2 11 41 1 2 2 3 3 1
Q LQ L Q L Q LP P
k A k A k A kA
= + + =
i
i
Lk
L
k
=
This is the harmonic average
permeability
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2eds in Series-Radial
$lo+ Natural #ariations in
&ermea'ilit%" 4ell 'ore damae"
Cleanin techni5ues"
In6ection &rocesses
( )2 e 12
e
1
2 k h P PQ
rln
r
=
( )1 1 w1
1
w
2 k h P PQ
rln
r
=
( )avg e wT
e
w
2 k h P PTotal flow: Q
rln
r
=
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2eds in Series-Radial $lo+
( ) ( ) ( )e w e 1 1 w
Total pressure drop: P P P P P P = +
e 1eT 12
w w1
avg 2 1
r rrQ ln Q lnQ ln
r rr
2 k h 2 k h 2 k h
= +
T 1 2At steady state flow: Q Q Q= =
e 1e
w w1
avg 2 1
r rrln lnlnr rr
k k k= +
e
wavg
1 e
w 1
1 2
rln
rkr r
ln lnr r
k k
=
+
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Modellin )eteroeneous S%stems
Permea'ilit% #ariations can o$ten 'e traced $rom +ell
to +ell"
These #ariations ena'le a la%ered reser#oir s%stem to
'e de#elo&ed
Man% $ield demonstrate this la%erin"
,er% lare &ermea'ilit% #ariations
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E7am&le o$ North Sea Field
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Modellin )eteroeneous S%stems
In some cases not &ossi'le to correlate &ermea'ilities $rom +ell
to +ell"
More di$$icult to &ut toether a reser#oir model "
Modellin reser#oirs +ith a#erae &ro&erties can onl% 'e #alid i$8
Reser#oir sands are homoeneous
Random #ariations occur across sands
Ordered distri'utions in one +ell do not correlate +ith other
+ells"
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Modellin
)eteroeneous
S%stems Permea'ilit% #ersus
de&th used to 'e
&resented on a lo-
&ermea'ilit% de&th scale"
Such a re&resentation
can lead to misleadin
#alues $or a#erae
&ermea'ilit%
Average permeability ?
True permeability
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Modellin4ater$loods
-homoeneous
#ersus la%ered"
Process8
4ater in6ected intoreser#oir to maintain
&ressure"
Good mo'ilit% ratio
Piston li!e
dis&lacement
rw w
ro o
k !
"o#ility $atio% " 1k !
=
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Modellin 4ater$loods -homoeneous s%stem
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Modellin4ater$loods
-homoeneous
s%stem
4ater 'rea!thouh
Oil &roduction until
'rea!throuh
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Modellin 4ater$loods -la%ered s%stem
La%ered &ermea'ilit% #ariations included in the model"
Reservoir model includes thickness
and rock properties of each layer
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Modellin 4ater$loods -la%ered s%stem
Water moving through high permeability layer
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Modellin 4ater$loods -la%ered s%stem
Water breakthrough after 1!! days
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Modellin4ater$loods
-la%ered
s%stem
Impact of gravity drainage
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Modellin
4ater$loods-la%ered s%stem
"ottom of reservoir
being s#ept by #ater
due to gravity drainage
Top of reservoir still
contains oil at
original saturation$
Termed %attic oil&
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Modellin 4ater$loods
-la%ered s%stem' pro(ect not as attractive as1' simulation
Water breakthrough in half the
time$
)eed for #ater treatment
earlier
*il recovery at
breakthrough much less
+uch longer times to reach
lo#ere recoveries
,o#er vertical permeabilies
make the case #orse
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Modellin 4ater$loods -la%ered s%stem
arly breakthrough
Need to im&act hih &ermea'ilit% some distance into
$ormation"
Time settin &ol%mers are a serious consideration"
Technical challenes and ris!s in their a&&lication"
Attic oil?
Gra#it% sereation"
Use o$ lo+ densit% $luid" E"" Nitroen
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La%ered Rese#oirs
La%ered reser#oirs result $rom the de&ositional
&rocess"
Understandin the de&ositional &rocess can i#e
insiht to the reser#oir enineerin im&lications"
No+ more acti#it% o$ the interation o$ eoliicalscenarios and the de#elo&ment o$ realistic reser#oir
simulation models"
U&scalin* is no+ an interal &art o$ realistic model
de#elo&ment
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Im&act o$ Permea'ilit% Distri'ution on
Dis&lacement Processk
'
.uper-homogeneous
k
'
Worst case
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Im&act o$ Permea'ilit% Distri'ution on
Dis&lacement Processk
'Tunnel
k
'Random
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Characteristics o$ Reser#oirs +ith )ih
Permea'ilit% Contrast 4ater $lo+s &re$erentiall% do+n hih &ermea'ilit% sections" Premature +ater 'rea!throuh"
De$erment o$ oil &roduction"
Ca&illar% &ressure e$$ects onl% enhance #ertical s+ee& e$$icienc%
slihtl%"
Not &er$oratin hih &ermea'ilit% sections has little success due to
ra#it% $orces etc" 4ater $inds its +a% into hih &ermea'ilit% areas"
Li$e o$ $ield loner than oriinal estimates on homoeneous
&ro&erties"
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