Compressibility measurement - Webs

• Theory 

Topics 

RESERVOIR ROCK PROPERTIES 

Compressibility 

• 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) 

AZMAN IKHSAN/SKM2313 

1

• Theory 



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

defined as 

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

with applied pressure. 

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

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

1 V 

 

c = - 

V P 

 

T 


2

• Theory 

A material under initial confining pressure of P 1 has volume V. When the 

pressure increases to P 2, the volume reduce by V. 

c (compressibility) is given by; 



c = - 1 

V 

V 

P 2 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 


3

• Theory 




4

• Jenis Ketermampatan 

3 types of porous rock compressibility’ 

1. Rock matrix compressibility 

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

unit change in pressure. 

cr = - 

2. Rock bulk compressibility 

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

change in pressure 

Vr Vr 1 

P 

cb = - Vb Vb 1 

P 

3. Pore compressibility 

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

pressure. 

cp = - Vp 1 

Vp P 




5

• Theory 



Reservoir rock is under stress. 

Internal stress by fluid in the pore 

(hydrostatic) 

External stresses by may have 

different values in different 

directions. 


6

• Types of compressibility 

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 


7

Compressibility measurement 

Measurement of matrix compressibility, c r 

Saturate rock with liquid 



• Compressibility measurement 

Apply hydrostatic pressure to the 

saturated rock. 

The rock matrix will uniformly deform 

under hydrostatic pressure. The bulk 

deformation of the rock can be stated as 

matrix compressibility, c r 

c r = - V r 

V r 

1 

P 


8

Measurement of bulk and pore compressibility, c b & c p 

Copper-jacked fluid 

saturated rock 





Apply hydrostatic pressure on the 

copper-jacked rock. 


9


Carpenter & Spencer (only change the external 

pressure, p*) 

Pore compressibility, c p , 

component of the total rock 

compressibility. 

p, constant 





p* 

c 

p 

V 

V 

kecerunan 

p 

b 

V 

V 

V 

b 

c 

p 

V 

 

V 

p 

dari isipadu air 

p 

p 

p 

c 

p 

V 

 

V 

c 

p 

Vp 

c 

V 

p 

p 

p 

p 

graf 

1 

 

p 

Vp 

vs 

V 

perubahan isipadu liang 

ygterkeluar 

semasa peningkata n tekanan 

p 

p 

p 

p 

p 

p 

b 

 

 

 

 

p 

p 

diukur 

dari teras 

luaran 


 

10

c 

p 

V 

b 

V 

Measurement p of 1 bulk 

c 

and pore compressibility, cb & c 

p 

p 

V 

 

p p 

 

 

p 

Carpenter 

V & Spencer (only change the external 

p 

 

pressure, c 

p p*) p p 

V 

V 

b 

p 

V 

p 

p 

c 

slope of 

p 

p 

V 

p change in pore volume measured from 

the produced water during external p, constant pressure 

increament . 

 


V 

measurement 

p 

V 

p 

c 

V 

 

p 

p 

p 

V 

p 

graph vs 

V 

p 

b 


p 

 



p* 


11


Hall : similar to experiment by Carpenter & Spencer 

Formation 

compressibility 

1 

V 

p 

V 

 

 

p 

p 

 


 

 

 

p 




= 

the total rock 



12


Hall : (constant overburden pressure), p* 

1 

V 

p 

V 

 

 

p 


p 

 

 

 

 

Effective compressibility 

p 

 





13


Theory by Geertsma 

1 Vb 

cb * 

Vb 

p 

 

 

 





c b 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 

p* 


14



For sandstoneand 

dV 

V 

b 

p 

b 

and 

dV 

V 

p 

for c 

r 

dV 

 

V 

p 

Since 

 

p 

V 

dV 

c 

p 

p 

b 

cb 

 

 

c 

 

dp dp 

dp dp 

b 

1 dV 

V 

V 

dV 


b 

b 

b 

b 

shale 

, therefore 




c b was determined by 

measuring the change in bulk 

volume of saturated jacketed 

core due to external hydraulic 

pressure change and constant 

internal pressure. 

p, constant 

This showed that the change in bulk 

volume is the same as the change in pore 

volume. 

p* 


15



If the p 

dp 

dV 

V 

 

p 

p 

cb 

c 

 

0 and 

p 

are equal from all directions, 

cb 

dp 

 

atau 

1 

- 

V 


 




p 

dV 

dp 

then 

defined as porevolume 


p 

 

c 

b 

 

p 


16 

p* 

constant



1 dVp 

1 cb 

1 

- c 

V dp 2 2 

p 





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. 

p 

Thus, the effective pore compressibility for 

reservoir rocks on the depletion of internal 

pressure is only one-half of that determined 

by this method. 


17




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) 

Typical values for formation compressibility range from 

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


18




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Compressibility measurement - Webs

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