Geo Mechanics Yn 3

8/9/2019 Geo Mechanics Yn 3

http://slidepdf.com/reader/full/geo-mechanics-yn-3 1/32

1

Effects Of Reservoir CompactionIn Deep Water Environment

N. Yusuf

Harold Vance Department

of Petroleum Engineering.Texas A&M University



2

• Objectives

• Linear Elastic properties of a solid material

• Elastic properties applied to reservoir rock

• Revie of !"E papers

Outline



3

• #nderstand Reservoir compaction

• Determination of parameters affectin$ δk δφ δ%

• Revie industr& orks to obtain'δ

k'δφ δ

%

• Develop a criteria ( selection tool

Objectives



4

•Linear Elastic properties of a solid material

Outline



5

Youn$)s modulus' E

zz

zz

zz

zz

εσ E

z

Δz ε

A

F σ

=

=

=

ModulusYoung

strainvertical

stressvertical*

+

δz

Z

psi x

psi x

valuesTypical

5

7

103

103

=

=

rock

steel

E

E



6

"oisson Ratio'

δz

δx

*

+

zz

yy

zz

xx

yy

xx

zz

zz

ε

ε

ε

ε

Y

Δy ε

X

Δx ε

z

Δz ε

A

F

σ

−=

−=

−=

−=

=

=

ratioPoisson

strainnormal

strainnormal

strainvertical

stressvertical

Z

X

3.0

3.0

=

=

rock

steel

v

v

valuesTypical



7

,ulk modulus' !

ΔV/V

σ K

V

ΔV

εb

=

=

ulusmod bulk

strain bulk *

*

*

2v)-3(1

EK =

psi x

psi x

valuesTypical

5

7

105.2

105.2

=

=

rock

steel

K

K



8

#nia-ial modulus'

zz

zz

zz

ε

σ

ε

=ulusmodUniaxial

for exceptalloed!strain"movement #o

Constrained

Constrained Constrained

*

psi x

psi x

valuesTypical

5

7

100$.$

100$.$

=

=

rock

steel

2v)-v)(1(1

v)-E(1

+=



9

• Elastic properties applied to reservoir rock

Outline



10

!train relations%ips for "orous Rock

( )

( )

φ

φ

φ

φ φ

−+=

+−=

+

=

+=

+=

+=

1!ε!ε!ε

!ε1!ε!ε

V

V

V

!V

V

V

V

!V

V

!V

V

!V

V

!V

V

!V

!V !V !V

V V V

"b #

#"b

#

#

b

#

"

"

b

"

b

b

b

#

b

"

b

b

" #b

" #b

V b: bulk volume

V p: pore volume

V g: grain volume



11

!train relations%ips for "orous Rock

( )

g b p

g pb

g pb

C 1

C 1

C

C )1( C C

V

1

V

1

V

1

−−=

−+=

−+=

φ

φ

φ

φ φ

φ φ !#

!V 1

!#

!V

!#

!V " #b

Wit% respect to c%an$e in pressure



12

Rock compressibilit&

Elastic Compressibilities- Definitions

Volume canges: !ulk volume:

"ore Volume:

"ressure canges: #verburden "ressure:

"ore "ressure:

bV

p p

pV

c p

pc

b

ibbc p

p

V

V

1c

−=

δ

δ c

p

b

ibbp p

p

V

V

1c

=

δ

δ

#c

#

$

#c # #!

V !

V

1c

b

−= p p

c

p

ib

pc

p

%

%

1&

δ

δ−=

!ulk Volume Compressibilities

"ore Volume Compressibilities



13

Compressibilit& relations%ips for a "orous Rock

pcibp.

g pc pp

g bc pb

C C 3

C C C .2

C C C .1

φ =

=

−=

−

/immerman' 0110

!I2NI*IC+NCE3

0 psi c%an$e in Confinin$ 4or Lab5 pressure produce more strain on t%e bulk 6 porevolume t%an 0 psi c%an$e in pore pressure b& an amount e7ual to t%e matri-compressibilit&.

If matri- compressibilit& is ne$li$ible' e7ual c%an$es in eit%er pore or confinin$ 4lab5pressure produce t%e same bulk and pore volume c%an$es.

!ulk strain due to pore pressure canges

Vs bulk strain due to lab pressure canges

"ore strain due to pore pressure canges

Vs pore strain due to lab pressure canges

!$%& '()*+, due to "#)E ")E''$)Ecanges related to "#)E '()*+, due toC#,+,+,. ")E''$)E canges/



15

Compressibilit& relations%ips for a "orous Rock

bc

g

g

pc

C

C

1 K

K

1

p p p eff

−=−=

−=

α

α

Nur 6 ,&erlee' 01:03 E**EC8I;E !8RE!! L+W

!I2NI*IC+NCE3

8o simulate an e7uivalent strain in a porous rock t%e laborator&stress s%ould be less t%an t%e pore pressure depletion b& a 1- α .

α is te !iot0s constant



16

• Loadin$ conditions3•constrained strain

•#nia-ial compressibilit& Cm

#nia-ial compressibilit&

Constrained

ConstrainedConstrained

Overburden

( )

( ) bcm C

13

1C

ν

ν

−

+=



17

σ

1

δ

1

δ

3/2

l

d

σ

1

δ

1

l

d

σ

1

δ

1

δ

3/2

l

d

σ

3

Hydrostatic Test Triaxial Test Uniaxial Strain Test

8&pical Lab 8estin$

To compute C bc,C pc To compute ν C m To compute C m



18

δ

1

l

d

σ

1

Uni-axial Strain Test / Oedometer Test

!imulates t%e reservoir boundar& condition of <erolateral displacement.

"rovide direct measurement of "m' unia-ialcompaction coefficient.

Difficult&3 Re7uires si<e of core to fit E-actl& in t%ecell.

2ap in cells3 Lateral strain' disinte$ration of

sample' measurement errors.



19

Tri-axial Test

2enerall& used to determine stren$t% under various

conditions of stress3 i.e. var& σ

1

σ

3

odifications3 σ

3

−> to balance lateral effect of σ0

Calculation of ν

Difficult&3 Re7uires si<e of core to fit E-actl& in t%e cell.

δ

1

δ

3/2

l

d

σ

3

σ

1



20

Hydrostatic Test

Easiest to conduct' 9&drostatic confinin$ pressure3

easure "ore compressibilit& 3 " pc

#ul$ compressi%ility " %c

Uni'axial compressi%ility (" m ) can %e calculated

using t*e uni'axial correction factor

δ

1

δ

3/2

l

d

σ

1

!1"3

!1"1

υ

υ

−+



21

Reservoir compaction

Constrained Deformation in t%e reservoir

+-ial Compaction co=efficient Ca3

8otal reduction in reservoir %ei$%t

Ne$lectin$ variation of Cm it% pressure

( )∫ ∫ =∆ H pf

pi

m z p z pC H 0

' δ δ

( ) ( ) z p z p z C H

H

m δ δ ∆=∆ ∫ 0

p

z

Z C m

δ

δ 1= pC z mδ ε =

Constrained

Constrained

Overburden

Constrained



22

Reservoir compaction

*actors leadin$ to Reservoir compaction

• Lar$e reduction in pore pressure

• Lar$e vertical e-tent of t%e <one of pressure reduction

• Lar$e order of ma$nitude of Cm

Controllin$ ma$nitude of compaction

• "ressure maintenance' Limitin$ "erf interval

• !tud& of Cm



23

•Revie of !"E papers

Outline



24

• Earl& ork to understand t%e subject

•Causes of compaction ( subsidence

•"rediction met%od

• +pproac%3

•Observations from field data

•at%ematical derivation

•Compaction ( !ubsidence prediction

"aper Revie 0

!"E >:>?3 Land !ubsidence +bove Compactin$ Oil and 2as Reservoirs @ A 2eeertsma



25

"aper Revie 0


•!usceptible reservoirs from observed field Data

•Loose ( eakl& cemented formation

•Lo dept% of reservoir burial 4ave3 0???m5

•!i$nificant δp 4e.$ depletion t&pe reservoir5

δ

p over lar$e interval

•Consolidated reservoirs it% lar$e δp 6 9

•*actors affectin$ Cm

•Rock t&pe 4%ard' consolidated' friable' loose5

•De$ree of cementation

•"orosit& 4%i$%φ

=B %i$% Cm5

Dept% of burial



26

"rediction tool3 Calculation of Cm• !andstone3

• > rock t&pes' dept%s

•Input variables3•Rock t&pe

•"orosit& ( !tress level

•Dept%

"aper Revie 0


Interpretation3

Lo Cm3 0=> 0?=

9i$% Cm3 B 0? 0?=



27

"aper Revie 0


Limestone3 rock t&pes' 0

dept%

"rediction tool3

Limited variables



29

• Results3 ;ar&in$ responses it% e-treme cases•Case +3

•2eolo$icall& &oun$er 3softer sands

•E-%ibitin$ %i$%er "; compressibilit& 45

•Compr increases to a ma- value 40?5

• Case D3

•2eolo$icall& older sands3 %arder

•E-%ibitin$ loer initial "; Compr 405

•!li$%t decrease40?5

"aper Revie

!"E GGF:13 Compaction Effects on "orosit& and "ermeabilit& in Deepater 2ulf of e-ico=R.. Ostermeier



30

• "orosit& 6 "ermeabilit& variations3 Case +

•Loadin$ Conditions3

•!tep increases of pressure to :'??? psi

•8ime period of 0'?? da&s

•Results3

•"orosit&3 ?.> @ ?.F 4H5'

•"ermeabilit&3 0.> @ ?. D 4F.GH5

"aper Revie


5.(

ook

k

φφ

=



31

• "orosit& 6 "ermeabilit& variations3 Case D

•Loadin$ Conditions3

•!tep increases of pressure to '??? psi

•8ime period of >?? da&s

•Results3

•"orosit&3 ?.G = ?.? 4.:H5'

•"ermeabilit&3 ?.G = ?.F: D 4G.1H5

"aper Revie


3.5

ook

k

φφ

=



32

• "ermeabilit& model

•Limitations

•9i$% error ran$e3 J(= >?H

•Re7uires !tress ;s φ as input

"aper Revie


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