compressibility - webs · azman ikhsan/skm2313 3 reservoir rock properties a material under initial...

AZMAN IKHSAN/SKM2313

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RESERVOIR ROCK PROPERTIES

Compressibility• Theory

• define rock compressibility, pore volume compressibility, bulk volume

compressibility and matrix compressibility

• use equations for rock compressibility

• describe experimental method to evaluate rock compressibility

• explain the effect of compressibility on rock properties (porosity,

permeability)

Topics


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In general, the isothermal coefficient of compressibility of a material is

defined as

TP

V

Vc

1-=

A measure of the relative volume change of a fluid or solid as

a response to a presure (or mean stress) change.

Compressibility is the ability of a soil or rock to reduce in volume

with applied pressure.


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A material under initial confining pressure of P1 has volume V. When the

pressure increases to P2, the volume reduce by V.

c (compressibility) is given by;

c = -1

V

V

P2 P

1

= -1

V

V

P

The negative sign will give positive value for compressibility.

The unit for compressibility is pressure to the power of -1.

Psi-1, kPa-1, (Nm-2)-1, bar-1 dll



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3 types of porous rock compressibility’

1. Rock matrix compressibility

2. Rock bulk compressibility

3. Pore compressibility

The fraction of change in volume of the solid rock material (grains) with a

unit change in pressure.

The fraction change in volume of the bulk volume of the rock with a unit

change in pressure

The fractional change in pore volume of the rock with a unit change in

pressure.

cr = -V

r

Vr

1

P

cb = -V

b

Vb

1

P

cp = -Vp

Vp

1

P

• Jenis Ketermampatan

Compressibility


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Reservoir rock is under stress.

Internal stress by fluid in the pore

(hydrostatic)

External stresses by may have

different values in different

directions.

• Theory

Compressibility


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Production of fluid from the

pore will change the internal

stress causes the resultant

stress to change.

The change in resultant

stress will change the

volumes of matrix, pore and

bulk.

In reservoir engineering the

pore volume compressibility

is more important.

Reduction in

pore pressure

• Types of compressibility

Compressibility


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Compressibility measurement

The rock matrix will uniformly deform

under hydrostatic pressure. The bulk

deformation of the rock can be stated as

matrix compressibility, cr

Measurement of matrix compressibility, cr

cr = -V

r

Vr

1

PSaturate rock with liquid

Apply hydrostatic pressure to the

saturated rock.

• Compressibility measurement

Compressibility


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Measurement of bulk and pore compressibility, cb & cp

Copper-jacked fluid

saturated rock

Apply hydrostatic pressure on the

copper-jacked rock.

Compressibility




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p*

p, constant

luarann tekanan peningkata semasa

terasdari terkeluarygair isipadu dari

diukur liangisipadu perubahan

vs grafkecerunan

1

p

b

p

p

pp

b

p

pp

p

p

pp

p

p

pp

p

p

pb

V

pV

Vc

pcV

V

pcV

V

pcV

V

pV

Vc

VV

Carpenter & Spencer (only change the external

pressure, p*)

Pore compressibility, cp,

component of the total rock

compressibility.

Compressibility




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p*

p, constant


Carpenter & Spencer (only change the external

pressure, p*)

.increament

pressure external during water produced the

from measured volumeporein change

vsgraph of slope

1

p

b

p

p

pp

b

p

pp

p

p

pp

p

p

pp

p

p

pb

V

pV

Vc

pcV

V

pcV

V

pcV

V

pV

Vc

VV

Compressibility




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Hall : similar to experiment by Carpenter & Spencer

1

p

p

p p

V

V

Formation

compressibility

Compressibility



the total rock

compressibility=


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Hall : (constant overburden pressure), p*

1

p

p

p p

V

V

Effective compressibility

Compressibility




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Theory by Geertsma

1

*

p

b

b

bp

V

Vc

p*

p,

constant

Compressibility



cb was determined by

measuring the change in bulk

volume of saturated jacketed

core due to external hydraulic

pressure change and constant

internal pressure.


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Theory by Geertsma

cb was determined by

measuring the change in bulk

volume of saturated jacketed

core due to external hydraulic

pressure change and constant

internal pressure.

p*

p, constant

bp

bp

b

b

p

p

br

b

p

p

b

b

b

dVdV

VV

V

dV

V

dV

cc

dpdp c

V

dV

and

dpdp cV

dV

therefore, Since

1

for

shale and sandstoneFor

This showed that the change in bulk

volume is the same as the change in pore

volume.

Compressibility




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Theory by Geertsma

p*

constantp

ilitycompressib volumepore as defined

1-atau

and 0

then,directions all from equal are theIf

pb

bp

p

b

p

p

cc

c

dp

dV

Vdp

c

V

dV

dp

p

Compressibility




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Theory by Geertsma

pbp

p

cc

dp

dV

V 2

1

2

11-

Geertsma has stated that in a reservoir only the vertical

component of hydraulic stress is constant and that the

stress components in horizontal plane are characterized

by the boundary condition that there is no bulk deformation

in those directions.

Thus, the effective pore compressibility for

reservoir rocks on the depletion of internal

pressure is only one-half of that determined

by this method.

Compressibility




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Typical values for formation compressibility range from

3x10-6 to 20x10-6 psi-1 (Tarek Ahmed)

Compressibility• Compressibility measurement

In summary, it can be stated that pore volume compressibility of

consolidated sandstones are of the order of 5x10-6 to 10x10-6 psi-1

(ABW)


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Compressibility


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