Rock Compressibility

Reservoir Rock Compressibility


Learning Outcomes

Introduction

Reservoir rocks are subjected to the internal stress exerted by fluids contained in the pores, and to external stress which is in part exerted by the overlying rocks.

The depletion of fluids from the reservoir rocks results in a change in the internal (hydrostatic) stress in the formation, thus causing the rock to be subjected to an increased and variable due to an increased and variable overburden load, and the result is the compaction of the rock structure due to an increased in the effective stress.

Compressibility of Porous Rocks

DefinitionCompressibility ： is the fractional change in pore

volume of per unit bulk volume with a unit change in pressure.

1/MPa reciprocal megapascal

Compressibility c, given by:

P

V

VPP

V

Vc b

b

b

bf

1=

1 =

12

Compressibility of Porous Rocks

The depletion of fluids from the pore space of a reservoir rock results in a change in the internal stress in the rock, thus causing the rock to be subjected to a different resultant stress. This change in stress results in changes in the grain, pore, and bulk volume of the rock.

Psi

Pf

Pf

Psi

Before developmentAfter development

A substance is initially with P pressure, V volume. When the pressure increases to P2, the volume decreased is DV.

Porosity is a function of compaction. It is generally reduced by increase in compaction

Compaction is a function of depth of burial. Sediments such as shales which have been deeply buried exhibit lower porosity

Three types of compressibility Rock- matrix (grain) compressibility, Cs

Rock-bulk compressibility, Cb

Pore-volume compressibility, Cp


Types of Compressibility

Rock-matrix (grain) compressibility

Rock-matrix compressibility is the fractional change in pore volume of the solid rock material (grains) per unit change in pressure .

P

v

Vc p

ss

1=

Rock-bulk compressibility:

It’s the fractional change in the total or bulk-volume of the formation per unit change in the reservoir pressure.

P

v

Vc b

bb

1=

Types of Compressibility

Pore-volume compressibility

Pore compressibility is the fractional change in pore volume per unit change in pressure.

P

v

Vc p

pp

1=

Total compressibility

Total compressibility is the fractional change in pore and liquid volume of the bulk-volume rock with a unit change in pressure.

The application of total reservoir compressibility, denoted by Ct, is

expressed as:

Where Sg, So, and Sw are the gas, oil, and water saturations, respectively; Cg, Co, and Cw the gas, oil and water compressibility, in Psi-1

P

v

Vc

bt

01=

Lvv p0 v =

Ct=Cf + Φ(SoCo+SwCw+SgCg)

Compressibility for Reservoir Rocks Saturated with Fluids

Compressibility of homogeneous matter like the rock materials (Cr) and the contained saturations of fluids, e.g oil, water, and / gas, are defined by Eqn.:

………………………..(1)

A discrete version of this definition, where the pressure drop ∆p is sufficiently small, gives;

………………….(2)


The compressibility of the fluids (Cf) contained in the pore volume is defined by the compressibility of the different phases; Cw +Co + Cg.

Since the pore volume is expanded by the fluid phase volumes:

Vf = Vw +Vo + Vg, a change in the pore pressure will cause the fluid volume to change.

The fluid compressibility is written as;

……………………….(3)


Where S is the fluid phase saturation (Sw + So + Sg = 1).

Of interest in relation to the production of oil and gas, is the total compressibility of the rock-fluid system. This compressibility accounts for the expansion of fluid, given by the fluid compressibility (Cf) and the reduction of the pore volume when the pore pressure is reduced, given by Cp in Eqtn.;

………………………….(4)

i.e.,

…………………..(5)


The effective HC compressibility is a useful term, related to the pore space occupied by the hydrocarbons;

………………………..(6)

An equally important term is the effective compressibility responsible for the expansion of initial water and reduction of the pore volume, when pressure is released as a result of HC production.This term, a non-HC compressibility is defined as;

…………………..(7)

Effect of Compressibility on Reservoir Rock Properties

Formation Compressibility, cf - also called pore volume compressibility

Important to reservoir engineers:1) depletion of fluid from pore spaces2) internal rock stress changes3) change in stress results in change inVp, Vm, Vb

As fluid is produced from a reservoir, the fluid pressure, Pf will usually decrease:

the force on the matrix increases causing a decrease in bulk volume and a decrease in pore volume

Formation compaction component of total rock compressibility

Compressibility measurement of bulk and pore, Cb & Cp

Hall, experiment was similar to Carpenter & Spencer

1

p

p

p p

V

V

Experimental equipment used for measuring pore volume compaction and compressibility

Effective reservoir rock compressibility

• Hall’s Correlation

Compressibility Correlations

000,000,1

392.13

c438.0

f

cf = formation compressibility, 1/psi

f = porosity, %

Compressibility Correlations

12f12

ppc12

ppc1or

e 12f

Change in porosity due to a change in pressure:

• Newman’s Correlations

f2 = porosity at pressure p2

f1 = porosity at pressure p1

cf = formation compressibility, 1/psi

42859.1

6

f872.551

)10(3200.97c

92990.06)10(47664.21

853531.0

fc

for consolidated sandstone, 79 samplesporosity range: 0.02 to 0.23, error 2.6%for limestoneporosity range: 0.02 to 0.33, error 11.8%

Rock Compressibility

Engineering

Transcript of Rock Compressibility