SC RE Chap9 Permeability Variations

7/21/2019 SC RE Chap9 Permeability Variations

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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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Water moving through high permeability layer


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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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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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SC RE Chap9 Permeability Variations

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