417

Chapter 9

COMPRESSIBILITY

GEORGE V . CHILINGARIAN, JALAL TOR kIEKE, and S.J. MAZZULLO

BZADEH, JO IN 0. ROBE TSON, HERMA I H.

INTRODUCTION

In general, compressibility ccan be defined as the rate of change of volume Vwith respect to the applied stress u per unit of volume:

c = - ( l / V ) (aV/au) (9- 1 )

The total external stress u is the sum of pore pressure p , and intergranular stress u’ . The latter stress is also termed the effective pressure pe; thus:

0 = p e = u - p p (9-2)

Several different definitions of compressibility are used in the literature depen- ding on the method of its determination (Gomaa, 1970; Rieke and Chilingarian, 1974):

(1) bulk compressibility, (2) pore compressibility, (3) formation compressibility, (4) rock solids compressibility, and ( 5 ) pseudo-bulk compressibility. (1) Bulk compressibility is commonly defined as the change in bulk volume Vb)

per unit of bulk volume, per unit change in external stress, while keeping the pore pressure p , and temperature T constant:

Bulk compressibility can also be defined as the change in bulk volume, per unit of bulk volume, per unit change in effective pressure pe, while keeping the total ex- ternal stress u and temperature constant:

The latter definition is preferred by the writers. (2) Pore compressibility is the change in pore volume V,,, per unit of pore

volume, per unit change of external stress u, while keeping the pore pressure and temperature constant:

418

Hall (1953, p. 3 10) called pore compressibility “formation compaction”, whereas the present authors prefer the following definition for pore compressibility deter- mined at a constant external stress u:

where pe is effective pressure ( = u - p p ) .

( 3 ) Formation compressibility can be defined as the change in pore volume, per unit of pore volume, per unit change of pore pressure, while keeping the external stress and temperature constant:

Hall (1953, p. 3 10) called this compressibility “effective” compressibility. (4) Rock solids compressibility is equal to the change in rock solids volume V,,

per unit of rock solids volume, per unit of external pressure at a constant temperature. If a rock sample is tested without a jacket or drainage ports, then ex- ternal stress will be equal to the pore pressure. Thus:

( 5 ) Pseudo-bulk compressibility as defined by Fatt (1958b) is the change in bulk volume, per unit change in pore pressure, per unit of bulk volume, at constant exter- nal stress and temperature:

(9-9)

In the field of soil mechanics, the term “coefficient of compressibility” a, is widely used:

a, = - (adap) (9-10)

where e is the void ratio, which is equal to the volume of voids Vp divided by the volume of solids V, : e = Vp/ V, [also, e = (Vp/ V,) = 4 ( 1 - $), where 4 = fractional porosity], a n d p is the net overburden pressure. On assuming that volume of solids V, does not change on compaction (A V, = 0), one can derive an equation relating void ratio e to bulk compressibility as follows:

Cb = - [ I / V b ) (dVb/dp) - [ l / (Vp + V,)] (avp/dp) (9-1 1)

Multiplying numerator and denominator by V, and rearranging:

cb = - l / [ V p / Vs + Vs / v,]) (dV,/ v,ap) (9-12)

419

and inasmuch as:

ae = AV,/ V, (9-13)

Eq. 9-12 becomes:

c b = - [l/(e + l)] (ae/dp) (9-14)

In terms of sample thickness, h, the bulk compressibility can be expressed as:

cb = - ( l / h ) (dh/dp) (9-15)

In many compaction experiments in which the pore pressure is kept atmospheric, the effective pressure and the applied external stress are equal.

VARIOUS LOADING CONDITIONS IN ROCK COMPRESSIBILITY MEASUREMENTS

It is very difficult to duplicate actual reservoir conditions in the laboratory because of the various loading conditions that may exist in the reservoir. Possible loading conditions on a hypothetical sediment cube are presented in Fig. 9-1. The first condition presented (Fig. 9-1A) is polyaxial loading, in which none of the three principal stresses is equal. Some investigators prefer to call this stress condition triaxial loading. Although this stress condition may represent the subsurface condi- tions, it is extremely difficult to duplicate in the laboratory, especially at high pressures.

A C

D E

Fig. 9-1. Compaction loading classification. A. Polyaxial loading (PI #p2 #p3) . B. Hydrostatic loading (PI = p2 = p3). C. Triaxial loading (PI = p2 #p,) . D. Uniaxial loading. E. Biaxial loading. (After Sawabini et al., 1974, fig. I ; courtesy of the SPE of AIME.)

420

The second possible loading condition (Fig. 9-lB) is hydrostatic, in which the three principal stresses applied are equal. This type of loading probably exists during the initial stages of deposition and compaction. The third type of loading (Fig. 9-1C) is triaxial, in which two of the three principal stresses are equal. Although some in- vestigators justifiably refer to it as biaxial stress, the term triaxial is strongly im- bedded in the civil engineering and earth sciences literature.

In the uniaxial loading condition (Fig. 9-1D), the applied force acts in one direc- tion only and is perpendicular to one surface of the sample material. The four faces of the cube that are parallel to the direction of the stress remain stationary. This arrangement can be achieved by placing a sample in a thick-walled, cylindrical chamber, the sides of which are stationary. The pressure can be applied with either one or two pistons, and the change in the volume of the sample is reflected by the change in its length. In the field of soil mechanics this method is sometimes referred to as triaxial testing.

This type of loading is possibly approached in an oil reservoir as the reservoir pressure is depleted as a result of production. It should be mentioned also that some investigators reserve the term uniaxial for cases when there is a vertical stress but no lateral strain. In biaxial loading (Fig. 9-1E), the two principal stresses are equal, while two faces of the cube are held stationary.

The best method of obtaining accurate compressibility data is to test core samples in both hydrostatic and uniaxial compaction apparatuses. These tests should be per- formed at temperatures and pressures existing in the reservoir. Before using available compressibility data, however, one should consult the following checklist:

(1) What formula was used in the calculations? As shown previously, various authors use different formulae.

(2) What was the method of calculation, e.g., was initial bulk or pore volume used in all cases, or were the volumes used those at a particular pressure at which com- pressibility was determined?

(3) What loading condition exists in the reservoir? (4) What set of compressibility data (hydrostatic or uniaxial compression) must

be used at various stages of production? Compressibility values for sands obtained in a hydrostatic apparatus, for example, are about twice as high as those obtained in the uniaxial compaction apparatus.

(5) Were tested samples dry or did they contain interstitial fluids?

COMPRESSIBILITY DATA FOR DIFFERENT POROUS MEDIA

Many investigators have presented compressibility data on consolidated rocks and unconsolidated sediments, as well as on shales and various clay minerals. These data relate compressibility to either porosity (or void ratio) or applied pressure.

Hall (1953) presented a correlation between effective rock compressibility ci and porosity as shown in Fig. 9-2. His correlation, although widely distributed and used for both sandstones and limestones, is not applicable to either unconsolidated sands or highly fractured formations. In such cases, laboratory data obtained at simulated reservoir conditions should instead be used. In the opinion of the principal author,

42 1

however, Hall's data should not be used at all. Some data on compressibility of consolidated rocks and unconsolidated

sediments have been presented by Fatt (1958a, b), Van der Knaap and van der Vlis (1967), Sawabini (1971), Newman (1973), Zimmerman et a]. (1986), and others. A comparison of the relationship between compressibility and applied pressure for un- consolidated sands, illite clay, limestone (curve number 8), sandstones, and shale is presented in Fig. 9-3.

Newman (1973) presented pore volume compressibility as a function of porosity for consolidated, friable, and unconsolidated reservoirs under hydrostatic loading conditions. He compared laboratory-measured data on 256 rock samples from 40 reservoirs (197 sandstones samples from 29 reservoirs, and 59 samples of carbonate rocks from 1 1 reservoirs) with the published data. Porosities of the samples ranged from less than 1% to as high as 35%. He used Eq. 9-16 to determine the pore volume compressibility cp (also see Eq. 9-6):

where:

Vp = pore volume of the sample at a given net (effective) pressure;

10

D

0 X

8 t t J m u) u) w 6 K a I 2 Y

0 e W

8-

Lc (L W

0 4

I E 2

(9- 16)

0

POROSITY. Ye

Fig. 9-2. Relationship between porosity in percent and effective rock compressibility in psi- ' [(change in pore volume/unit pore volume)/psi]. (After Hall, 1953; courtesy of AIME.)

422

102 103 PRESSURE, psi 104 I o5 Fig. 9-3. Relationship between compres5ibility (psi ~ ' ) and applied pressure (psi) for unconsolidated \ands, illite day , limestone. $andstones, and shale. For details of 1 ~ 18, 5ee p. 423.

d Vp = incremental change in pore volume resulting from an incremental change in net pressure; and dpe = incremental change in net pressure.

The above equation assumes that most of the pore volume change results from the net pressure difference. A common pressure base of 75% of the lithostatic pressure was used for comparison. The lithostatic pressure gradient was assumed to be equal to 1 psi/ft of depth.

Newman (1973) showed that pore volume compressibilities for a given initial porosity can vary widely, depending on the rock type. He found major differences between consolidated sands (Fig. 9-4), friable sands (Fig. 9 - 9 , and unconsolidated sands (Fig. 9-6). The relationship between pore volume compressibility and initial porosity for carbonate rocks is presented in Fig. 9-7. In the opinion of the writers, more useful correlation can be obtained if samples of similar lithologies, exposed to similar overburden pressures, and of similar initial porosities, are used. In Newman's experiments, 81 To of the samples were measured at 74"F, whereas the remaining 19% were tested at temperatures ranging from 130 to 275°F. Newman did not observe any temperature effect on compressibility. His experiments un- doubtedly represent a major effort at understanding compaction processes, and it would be rewarding to see them presented as graphs of compressibility versus pressure or void ratio versus pressure. (Also see Allen and Chilingarian, 1975.)

The following concIusions can be reached on examining the laboratory ex- perimental results obtained by several investigators (see Chilingarian and Wolf, 1975, 1976). Unconsolidated sands are readily cornpactable on applying overburden loads of 200 psi or higher. The degree to which they can be compacted is dependent upon the (a) original packing and/or bridging, (b) original void ratio, (c) shape of the grains, (d) roundness of grains, (e) sphericity of grains, (f) composition of the sand, and (8) size grading. At least up to 140°F and an overburden load of about

~ No.

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

~ 18

~

Inve

stig

ator

Saw

abin

i et

al.

(197

4)

Koh

lhaa

s an

d M

iller

(19

69)

Saw

abin

i et

al.

(197

4)

Koh

lhaa

s an

d M

iller

(19

69)

Chi

linga

rian

and

Rie

ke

(1 96

8)

Chi

linga

rian

and

Rie

ke

(1 96

8)

Knu

tson

and

Boh

or (

1963

) K

nuts

on a

nd B

ohor

(19

63)

Car

pent

er a

nd S

penc

er

( 194

0)

Fatt

(19

58b)

Fatt

(19

5813

) Fa

tt (

1958

b)

Fatt

(19

58b)

Fa

tt (

1958

b)

Podi

o et

al.

(196

8)

Podi

o et

al.

(196

8)

Chi

linga

rian

et

al.

(197

3)

Chi

linga

rian

et

al.

(197

3)

~

a Sa

tura

ted

with

for

mat

ion

wat

er.

Satu

rate

d w

ith d

istil

led

wat

er.

' Sat

urat

ed w

ith k

eros

ene.

Roc

k ty

pe

Typ

e of

app

lied

pres

sure

C

ompr

essi

bilit

y

Cal

ifor

nia

unco

nsol

idat

ed a

rkos

ic

Cal

ifor

nia

unco

nsol

idat

ed s

ands

C

alif

orni

a un

cons

olid

ated

ark

osic

Cal

ifor

nia

unco

nsol

idat

ed s

ands

~

it

e

clay

(A

PI N

O. 3

5) (

wet

),

Illite

cla

y (A

PI N

o. 3

5) (

dry)

Rep

etto

Fm

. (G

rubb

Zon

e) (

wet

)=

Lan

sing

- K

ansa

s C

ity L

imes

tone

Woo

dbin

e Sa

ndst

one

(wet

)

Feld

spat

hic

gray

wac

ke (

No.

10)

Gra

ywac

ke (

No.

7) (

wet

)' Fe

ldsp

athi

c gr

ayw

acke

(N

o. 1

1)

Lith

ic g

rayw

acke

(N

o. 1

2) (

wet

)' Fe

ldsp

athi

c qu

artz

ite

(No.

20)

Gre

en R

iver

sha

le (

dry)

G

reen

Riv

er s

hale

(w

et)b

M

ontm

orill

onite

cla

y sa

tura

ted

in

sand

sa

sand

sa

(wet

)a

(wet

)'

(wet

)'

(wet

)'

seaw

ater

Mon

tmor

illon

ite c

lay

satu

rate

d in

se

awat

er

Hyd

rost

atic

Uni

axia

l H

ydro

stat

ic

Uni

axia

l U

niax

ial

Uni

axia

l

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ngd

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ng

Net

con

fini

ng

Hyd

rost

atic

Uni

axia

l

Pore

Po

re

Bul

k

Bul

k B

ulk

Bul

k B

ulk

Bul

k B

ulk

Bul

k

Bul

k

P

Net

con

fini

ng p

ress

ure

=

exte

rnal

hyd

rost

atic

pre

ssur

e on

a j

acke

ted

spec

imen

= p

, =

(u

-

0.85

q,), w

here

u is

the

tot

al o

verb

urde

n st

ress

and

p,

is th

e po

re p

ress

ure.

Str

esse

s in

the

tria

xial

app

arat

us o

f Sa

wab

ini e

t al.

(197

4) a

ppro

ache

d hy

dros

tatic

; i.e

., th

ree

prin

cipa

l st

ress

es in

x-, y-

and

z-d

irec

tions

ar

e eq

ual;

sen

ior

auth

or b

elie

ves

that

0.8

5 sh

ould

be

equa

l to

1.

424

3000 psi, compressibility does not seem to be dependent to any large degree upon temperature or pore fluid type (Allen and Chilingarian, 1975).

Well-sorted, rounded, well-packed, clean quartz sands do not compact readily ex- cept when the applied loads are sufficient to break the sand grains. The load necessary to crush or fracture grains is not as high as one might expect, because pressures upon grain-contact points may be considerably amplified above the average load pressure by mechanical advantage. Loosely packed, irregularly shaped grains, particularly those composed of comparatively brittle materials (or those with

100 I 1 I I I I

CONSOLIDATED SANDSTONES

COFRC DATA 0 HALL'S DATA 8

0

0 0 'I\ X 0

O@

c

r'

w l 0 0 0

~ o o o o

I 0

0

u - 0 1 .a INITIAL POROSITY AT ZERO NET PRESSURE

Fig. 9-4. Relationship between pore volume compressibility at 75% lithostatic pressure and initial sample porosity at zero net pressure for consolidated sandstones. (After Newman, 1973, fig. 4; courtesy of the SPE of AIME.)

425

100 - - I 1 I I I I - - - - - FRIABLE SANDSTONES -

COFRC DATA 0 W H I L L S D A T A 0 - -

0 0 0 -

0 0 0 8 O8 O

i - a

!! I 0 0 0

P - 0 o o o o 0 0 O -

00 Q O o - k - 2

0 f * 0

k B 0

X 0 0 0 0

G 0 c

- 0 0 - 0

-

0 o o 0

- 0 -

CORRELATION

- 0

0 0 0 -

0 0 0

0 0 P

W 0

8 - 0

f 0 . I I I 0 I I I 0 5 10 15 to 25 30

cleavage) such as feldspar, compact readily by grain rearrangement and shattering of sharp grain points. When present in the pore spaces, micas, clays, and other fine- grained materials appear to act somewhat like a dry lubricant and increase sand compressibility. From available test data of the four major types of sands, arkosic sands exhibit the greatest compactibility because of composition, and, possibly, grain angularity. Volcanic tuffs, which are commonly composed largely of glass-like shards with a high bridging tendency, might be highly susceptible to compaction (Allen and Chilingarian, 1975).

3s

426

COMPRESSIBILITY OF CLAYS

Data on the compressibility of clays have been presented by Chilingar et al. (1963, 1969), Rieke et al. (1964, 1969), and Chilingarian and Rieke (1968) (Tables 9-1 and 9-11).

0 8 0

0 0 UNCONSOLIDATED SANDSTONES

0 0

MALL'S DATA 0

COFRC DATA 0 0

0 0 0

0

0 @o 0"

0

O 0 0 6 0

0 00 0

5 10 I5 m 25 M 35 INITIAL POROSITY AT ZERO NET PRESSURE

Fig. 9-6. Relationship between pore volume compressibility at 7 5 % lithostatic pressure and initial sample porosity a t zero net pressure for tinconsolidated sandstones. (After Newman, 1973, fig. 6; courtesy of the SPE of AIM€.)

427

COMPRESSIBILITIES OF FRACTURED -CAVERNOUS CARBONATES

An excellent discussion on compressibility of cavernous- and fractured rocks has been presented by Tkhostov et al. (1970). According to them, at low effective pressures (up to 200- 300 kg/cm2), the compressibility of fractures is on the order of cm2/kg, whereas that of the caverns and vugs is on the order of l o p 5 cm2/kg (cm2/kg = 7.031 x l o p 2 psi-').

The compressibility of carbonate rock crc is equal to:

i@ . 5 \ @ \

VAN OER

., K N A A I S CORRELATION

@ @

(9- 17)

-0-0-

INITIAL POROSITY AT ZERO NET PRESSURE

Fig. 9-7. Relationship between pore volume compressibility at 75% lithostatic pressure and initial sample porosity at zero net pressure for carbonate rocks. (After Newman, 1973, fig. 3; courtesy of the SPE of AIME.)

TABLE 9-1

Compressibility equations [eb = - ( I / h ) (dhldp)] of various clays calculated from thickness (h) versus overburden pressure (p) measurement5 (from Langnec et al., 1972; data from Rieke et al., 1969 and Chilingar et al., 1969)

Type of clay Condition: dry or saturated

~ ~~

Dickite Dry Halloysite Dry Hectorite (containing 60% CaCO,) Dry Illite Dry Kaolinite Drq Montmorillonite Dry

Compressibility equations obtained using different varieties of same clay

~

- 3.96 10-2 p-( l .8Y25 b -

eb = 2.27 x 10 2 p - 0 .733

4.15 10-2 p-"Y8"?"

e - 3.4 10-2 p-o.Y8?

e - 3.58 10 2 p - o . Y o Y i

b -

b -

b -

b - e - 3.29 10 2 ,y 0.9338

Dickite Distilled water eb = 3.86 10 2 0.YzJ; eh = 3 10-2 p - ( ) 7 x 8

eb 4.24 10-2 0.848. - 4.7 10-2 p - O X h 3 Halloysite Distilled water 7 h - Cb = 3 . 3 8 x 10 2 0.787. - 4.42 x 10-2 p-" .x 'o

10 2 p - " . x 2 5 9 b - Hectorite (containing 62% CaCO,)

Illite ( (different varieties) Illite

Distilled water - 3.48 x 10-2 p - " 8 i 5 ; eh = 3.73 Distilled water b -

Distilled water CL = 3.8 x 10-2 D - " y 3

Kaolinite Montmorillonitea

Distilled water Distilled water

- 3.94 10-2 p-" .Yo2 Montmorillonite Seawater b -

_ _ _ ~ _ _ _ _ ~ - ~ - ~ ~ - - - ~- ~ -. - ~ -. .-

a For the best straight line drawn through the experimental points ( p > 1000 psi). Actually the curve is concave upwards.

TABLE 9-11

Void ratio and compressibility equations icb = - [ l / (e + I)] ( d d d p ) ] for various clays saturated in water (after Langnes et al., 1972; data from Chilingar et al., 1963, Chilingarian and Rieke, 1968, and Rieke et al., 1964, 1969).

~- Type of clay Assumed density Relationship between void ratio and Compressibility equation (calculated)

(g/cm3) effective pressure

Montmorillonite 2.60 e = 2.69 - 0.467 (logp) ch = 3.25 10-2p-0874

Illite Kaolinite Dickite I-lalloysite l-lectorite (with

56% CaCO,)

2.61 2.63 2.60 2.55 2.66

1’-95 dry lake 2.53 clay (Buckhorn Lake, CA)

stone terrain (Louisville, KY)

Soil from lime- 2.67

e = 1.335 - 0.23 (logp) e = 0.885 - 0.153 (logp) e = 0.682 - 0.128 (logp) e = 1.01 - 0.165 (logp) e = 0.718 - 0.123 (logp)

e = 0.7 - 0.116 (logp)

e = 0.5 - 0.0816 (logp)

(above 1000 psi) Cb = 3.9 x 10-2 p-0 .926

cb = 3.5 x 10-2p-0.946

cb = 3.3 x p-0.y46

cb = 3.05 x p-o.y80

cb = 2.85 x p-0.954

cb = 2.8 x p-0y4h

cb = 2.25 x p-0.’52

430

where:

djfr cfr = compressibility of fractures; djcL c,, c, = compressibility of matrix. For Solnhofen Limestone, em = 0.03 x cm2/kg; whereas the com-

pressibility of caverns and fractures e,, was estimated by Tkhostov et al. (1970) to be equal to:

= fractional porosity of fractures;

= fractional porosity of caverns and vugs; = compressibility of caverns and vugs; and

cCv = 3 x em = 3 x 0.03 x l o p 4 = 0.09 x l o p 4 cm2/kg

The following simplified equation for determining the secondary pore com- pressibility was derived by Tkhostov et a]. (1970):

cps 6 [(djfr/djts) x [1350/@, - pp)] - 0.091 x lop4 (9- 18)

where:

cps

djrs

= compressibility of secondary pores (fractures + vugs and caverns),

= total fractional porosity of secondary pores; cm2/kg;

Fig. 9-8. Relationship between the pore Compressibility of carbonates and effective pressure @,. = 11, -/I,). A . Theoretical curve5 for fractured ~ cavernous reservoirs calculated using Eq. 9-18; numbers on c:rvcs designare the bfr /b , , ratios. B. Evperimental curves 01, = 0) for ( 1 ) limestone with d = 2.01%1; (2) marl with d = 2.63vo; and (3) limestone with d = 1 1 . d I D b . (After Tkhostov et al., 1970.)

43 1

pt p , = pore pressure, kg/cm2.

The relationship between the pore compressibility of carbonate rocks and effec-

= total overburden pressure, kg/cm; and

tive overburden pressure is presented in Fig. 9-8.

COMPACTION OF CARBONATE ROCKS

The significance of compaction and its role in pore space reduction in carbonate rocks have long been a matter of debate. An excellent discussion of this problem appears in a paper by Bathurst (1980). Originally, it was thought that the onset of cementation in carbonates is so early that compaction is either low or absent (Pray, 1960; Steinen, 1978). Extensive presence of deformed fossiIs, compactional drap- ings, etc., however, demonstrate moderate to high degrees of compaction in some calcareous rocks (Carozzi, 1961; Kahle, 1966; Wolfe, 1968; Brown, 1969; Zankl, 1969; Baldwin, 1971; Allen, 1974; Rieke and Chilingarian, 1974; Chilingarian and Wolf, 1975; Kendall, 1975; Wolf and Chilingarian, 1976; Chilingar et al., 1979; Bathurst, 1983; Meyers and Hill, 1983; Gaillard and Jautee, 1985). Porosity reduc- tion data in pelagic carbonate ooze recovered by the Deep Sea and Ocean Drilling Projects support the occurrence of compaction (Matter, 1974; Schlanger and Douglas, 1974; Garrison, 1981). Findings by Ricken (1986) and Bathurst (1987) sug- gest that carbonate compaction seems spatially concentrated in relatively narrow zones in bedded carbonate rocks from various environments, characterized by fabrics of mechanical compaction and pressure dissolution.

Packing and resistance to compaction of shell beds

Allen (1974) experimentally investigated three packing models of organic sea shells in the laboratory. The aim of his investigation was to establish the loosest and densest practical packing arrangements for conical, cylindrical, and spherical shells. The application of this study is to provide laboratory-determined values for shell packs and to see how packing concentration values compare with theoretically calculated ranges for the packing arrangements of equal spheres (Graton and Fraser, 1935). Knowledge of shell packing is of importance to lithification problems in carbonate sediments (see Bathurst, 1971).

Allen’s (1974) experiments involved testing the ability of shell packs to withstand an increasing compaction load. The ability of shell packs to retain large original porosities is a function of the pack’s intrinsic resistance to crushing. The overburden load was increased in the laboratory until the shells broke. The results indicated that the selected shells could be buried and withstand loads ranging from 500 to 4000 kg/m2 before breakage begins. This means that in depositional environments with low rates of sediment accumulation the cementation process probably has time to help preserve the natural shell packs before the critical overburden load could be reached. If cementation has proceeded to a sufficient extent then a critical over- burden thickness could be permanently delayed. This resistance to compaction by

432

the shell packs indicates that the high porosities and permeabilities of naturally oc- curring shell beds have an excellent chance of being preserved - i f buried.

Low packing concentrations, comparable with 0.1 - 0.2 at infinite sample size (equal sphere packings have concentrations between approximately 0.60 and 0.64)’ as calculated using the three shell shape models, were confirmed by Allen’s ex- periments. These values show that there is 5 - 10 times more space that is empty than is occupied by solids. This amount of pore space available to fluids or to mineral cements almost equals the total space occupied by the packing (Allen, 1974, p. 83). By comparison, sands and gravels at best can provide about 40% of the total space as voids. (Packing concentration = proportion of space occupied by solids relative to total space.)

Derivation of Ricken’s carbonate compaction equation

The carbonate compaction equation of Ricken (1986, 1987) is a basic and theoretically founded relationship among the following three sediment or rock parameters: content, compaction, and porosity. This relationship can be derived by considering a sediment to rock transformation of calcareous sediment containing various proportions of pore space, and carbonate and non-carbonate contents (Fig. 9-9). The non-carbonate fraction is usually composed of clay minerals, quartz, and organic matter (Wedepohl, 1970). During the sediment to rock transformation, the pore volume is reduced because of compaction or cementation and the initial car- bonate content is changed because of cementation or carbonate dissolution. Only the non-carbonate fraction remains essentially unaffected (Fig. 9-9). The non- carbonate fraction (NCd, in volume To), however, is the only constant factor in car- bonate diagenesis, when it is standardized to the primary, or uncompacted, sedi- ment bulk volume:

NCd = (100 - K ) (100 - n ) (100 -C)/10,000 (9- 19)

S E D I M E N T R O C K

Fig. 9-9. Principles of volume changes during rediment-to-sedimentary rock transformation for car- bonates. Left: uncompacted sediment with original porosity (n,J and original carbonatc content (C,). Right: compacted and lithified calcareous rock volume (compaction = K ) with diminished porosity (n) and altered carbonate content /C). The non-carbonate fraction ( N C d ) remains coilstant when i t is ex- pressed as percentage of the original sediment volume. (Alter Rickcn, 1986, fig. 5 , p. 13.)

43 3

where:

sediment (bulk) volume; C = volume of solid carbonates, expressed as the percentage of the compacted

n = porosity, percent of bulk volume; K = degree of compaction, expressed as the percentage of the original volume

of the sediment; and NCd = solid non-carbonate fraction, expressed as a percentage of the original

sediment volume. This NCd value is standardized to the original sediment volume and, therefore,

was referred to simply as the “standardized noncarbonate content”. Equation 9-19 was termed the “carbonate compaction law” by Ricken (1986, 1987), because in most rocks with low porosity, it essentially relates the carbonate volume to the degree of compaction. In so far as the specific grain densities for the carbonate and non-carbonate fractions are similar, the volume percent of carbonate in Eq. 9-19 is essentially equivalent to the weight percent content of carbonate. The compaction law is valid regardless of whether the diagenetic system is closed or open.

Carbonate compaction equation for rocks with low porosities

In many lithified calcareous rocks and marls, porosities are generally below 15070, whereas limestones commonly have porosities below 5% (Bathurst, 1980). Thus, for these low-porosity rocks, the compaction equation (Eq. 9-9) can be simplified to the following:

NC,j = (100 - K,) (100 -C)/lOO (9-20)

where the percentage of compaction (K,) in low-porosity calcareous rocks is equal to:

K , = 100 -[(1OONCd)/(lOO - C ) ] (9-21)

Thus, compaction can be calculated for porous and partially lithified sediments, and essentially non-porous rocks with various standardized non-carbonate fractions (i.e., Ned) and carbonate contents, by using Eqs. 9-19 and 9-21, respectively. As follows from Eq. 9-21, the degree of compaction in non-porous rocks is non-linearly related to the carbonate content (Fig. 9-10). For a constant value of the standardized non-carbonate content (Ned), compaction is low at high carbonate contents, large at medium carbonate contents, and very large at low carbonate contents. Such non- linear carbonate content versus degree of compaction relationships can be explained by compacting a nonporous carbonate rock through pressure dissolution as in- dicated in Fig. 9-10.

For most calcareous rocks, however, this curved relationship between the car- bonate content and degree of compaction reflects the presence of both less compacted - cemented, and more compacted - dissolution-affected rock portions. For sites at low degrees of compaction and high carbonate content, the sediment was cemented early in its diagenetic history (after some mechanical compaction) by the

434

precipitation of additional cement in the original pore space, thus inhibiting further compaction. On the other hand, low carbonate contents and a higher degree of com- paction are usually associated with pressure-dissolution of carbonate (chemical compaction). As a consequence, the degree of compaction and the carbonate con- tent in calcareous rocks can be viewed to reflect the diagenetic history, related to mechanical compaction, cementation, and pressure-dissolution of the rocks.

Testing of Ricken 's compaction equation by compaction measurements

In order to test whether the theoretically derived carbonate compaction equation is, in fact, documented in the rock record, compaction, carbonate content, and porosity were measured in the interbedded marl - limestone alternations. These

Fig. 9-10, Simplified illustration of the carbonate compaction equation, depicting how the initial car- bonate content of 9 0 5 in a non-porous limestone sample will change by constantly increasing the degree of compaction ( K , in ob) and removing carbonate by dissolution. The percentage of carbonate fraction (C) ic indicated by small numbers ivithin columns, with a scale on the right-hand side. It should be noted that the Tame values for carbonate content and compaction will be obtained when a porous sediment with the same standardized percentage of non-carbonate fraction undergoes first mechanical compaction and then cementation. Lower diagram shows the theoretical relationship between degree of compaction (40)

for samples with various .VCd contents and porosities ranging from O o b to lSro (solid and dashed curves). (After Ricken, 1986, 1987.)

435

values were then compared with the theoretical curves for carbonate content versus degree of compaction. Among these parameters, compaction is the most difficult to determine. Many authors have addressed compaction measurement by using various methods, including grain orientation and deformation (e.g., Wolf and Chil- ingarian, 1976; Bathurst, 1987), deformation of primary sedimentary structures (e.g., Baldwin, 1971), deformation of vertically emplaced sedimentary dikes (e.g., Beaudoin et al., 1984), compactional draping relative to early concretions (e.g., Einsele and Mosebach, 1955; Chanda et al., 1977), density of bioturbated patterns (Gaillard and Jautee, 1985), and experimental studies (Chilingarian and Rieke, 1976; Shinn et al., 1977). Inasmuch as most of these methods can be considered relative and only semi-quantitative, the deformation of originally circular bioturba- tion tubes (oriented parallel to bedding) was used, because these sedimentary struc- tures deform with the sediment and, therefore, their degree of compaction can be reliably determined (Plessman, 1966).

Bioturbation tubes are usually formed within the upper meter of the sediment, but below the mixed uppermost sediment layer (Ekdale et al., 1984). Bioturbation struc- tures undergo the same amount of compaction as the surrounding sediment, except burrows with early diagenetic cements (Fig. 9-1 la). Burrows suitable for direct com- paction measurement must have originally circular tubes, such as Thalassinoides, Teichichnus, Chondrites, and Planolites (Hantzschel, 1975); this can be confirmed on examining the cross-sections of vertically emplaced burrows. Such burrows are abundant in shelf and pelagic sediments (Kennedy, 1975; Ekdale and Bromley, 1984). The burrows must be parallel to the bedding and only cross-sections perpen- dicular to the burrow tubes must be used for measuring the burrow axes. Measurements can be performed in the field utilizing suitable rock samples with bur- rows. During compaction, only the vertical axis (b) is reduced and, thus, the degree of compaction (K) can be expressed as a percentage of the undeformed, horizontal axis (a) (Fig. 9-l lb):

K = [(a - b)/a] 100 = 100 - [(100b)/a] (9-22)

a C G 2 b

Fig. 9-1 I. Compaction measurement using the deformation (D) of an originally circular burrow tube (a). Normally, burrow deformation equals the actual sediment or rock compaction (b: D = K = 60%). In early cemented burrows, compaction (K) is higher than the burrow deformation (c: D = 40%). (From Ricken, 1986, 1987; courtesy of Springer-Verlag.)

436

Burrows with early cements can be recognized by their significantly higher car- bonate content and lower degree of compaction than the surrounding rock (Fig. 9- 1 lc). Despite this, compaction can be indirectly determined by using the content of the burrow fill and that of the surrounding rock. From the partial compaction and carbonate content of the burrow, a standardized non-carbonate fraction content can be calculated (Eq. 9-19), which is assumed to be the same for the burrow and the host rock. This will finally allow a calculation of actual rock compaction by using the calculated N C d value of the burrow and the carbonate content of the host rock. The degree of compaction is obtained either by solving Eq. 9-19 for K or by using Eq. 9-21. Repeated direct and indirect determinations of compaction using burrow deformation show an accuracy of f 10%. Consequently, only the means of several measurements allow a correct determination of compaction. The following practical example demonstrates this.

One wants to know the degree of compaction in a lithified marl containing cemented burrows (75% CaC03) with a significantly higher carbonate content than in the surrounding rock (50% CaC03). From the degree of shortening of the ver- tical burrow axes, compaction of the cemented burrow is calculated to be 60% (Eq. 9-22). Because porosities are low enough to be ignored, the NCd value can be calculated according to Eq. 9-20, using the burrow tube carbonate content and the degree of compaction, which results in a N C d of 10%. Under the assumption that this value (i.e., the non-carbonate fraction of the original bulk sediment volume) is the same for the cemented burrows and the surrounding sediment, the actual degree of compaction can be calculated using the carbonate content of the surrounding rock (Soyo CaC03) and the N e d value of the burrow (Eq. 9-21). Thus, the degree of rock compaction in the rock matrix is calculated to be 8O%, which is substantially higher than that indicated by the degree of compaction (60%) determined in the cemented burrows.

REFERENCES

Allen, D.R. and Chilingarian, G.V., 1975. Mechanics of sand compaction. In: G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments, Vol. I . Elsevier Amsterdam, pp. 43 - 77.

Allen, J.R.L., 1974. Packing and resistance to compaction of shells. Sedimentology, 21: 71 -86. Baldwin, B., 1971. Ways of deciphering compacted sediments. J . Sedim. Petrol., 41: 293-301. Bathurst, R.G.C., 1971. Carbonate Sediments and their Diagenesis. Elsevier, Amsterdam, 620 pp. Bathurst, R.G.C., 1980. Deep crustal diagenesis in limestones. Revista Inst. Investigaciones Geol., 34:

Bathurst, R.G.C., 1983. Neomorphic spar versus cement in some Jurassic grainstones: significance for evaluation of porosity evolution and compaction. J . Geol. Soc. London, 140: 229 - 237.

Bathurst, R.G.C., 1987. Diagenetically enhanced bedding in argillaceous platform limestones: stratified cementation and selective compaction. Sedimentology, 34: 749 ~ 778.

Beaudoin, B., Fries, G. and Pinoteau, B., 1984. Calcul des coefficients de decompaction et estimation des paleorecouvrements. Doc. B.R.G.M., Programme “Geologie Profonde de la France”, 11 : 77 ~ 89.

Brown, P.R., 1969. Compaction of fine-grained terrigenous and carbonate sediments - a review. Bull. Can. Petrol. Geol., 17: 486-495.

Carozzi, A.V., 1961. Distorted oolites and pseudo-oolites. J . Sedim. Petrol., 31: 262 -274. Carpenter, C.B. and Spencer, G.B., 1940. Measurements of compressibility of consolidated oil-bearing

89- 100.

sandstones. Rep. Invest. U.S . Bur. Mines, 3540: 20 pp.

437

Chanda, S.K., Bhattacharyya, A. and Sarkar, S., 1977. Deformation of ooids by compaction in the Precambrian Bhander Limestone, India: implications for lithification. Bull. Geol. SOC. Am. , 88:

Chilingar, G.V., Rieke, H.H. and Robertson, J.O., Jr., 1963. Relationship between high overburden pressure and moisture content of halloysite and dickite clays. Bull. Geol. SOC. Am. , 74: 1041 - 1048.

Chilingar, G.V., Rieke, H.H. and Sawabini, C.T., 1969. Compressibilities of clays and some means of predicting and preventing subsidence. In: Land Subsidence, IASH- UNESCO Publ., 89(2): 377 - 397.

Chilingar, G.V., Bissell, H.J. and Wolf, K.H., 1979. Diagenesis of carbonate sediments and epigenesis (or catagenesis) of limestones. In: G. Larsen and G.V. Chilingar (Editors), Diagenesis in Sediments and Sedimentary Rocks. Developments in Sedimentology, 25A. Elsevier, Amsterdam, pp. 247 - 422.

Chilingarian, G.V. and Rieke, H.H., I l l , 1968. Data on consolidation of fine-grained sediments. J. Sedim. Petrol., 33: 811 -816.

Chilingarian, G.V. and Rieke, H.H., 1976. Compaction of argillaceous sediments. In: W.H. Fertl (Editor), Abnormal Formation Pressures. Developments in Petroleum Science, 2. Elsevier, Amster- dam, pp. 49- 100.

Chilingarian, G.V. and Wolf, K.H., 1975. Compaction of Coarse-Grained Sediments, I . Developments in Sedimentology, I8A,. Elsevier, Amsterdam, 552 pp.

Chilingarian, G.V. and Wolf, K.H., 1976. Compaction of Coarse-Grained Sediments, I I . Developments in Sedimentology, 18B. Elsevier, Amsterdam, 808 pp.

Chilingarian, G.V., Sawabini, C.T. and Rieke, H.H. , 1973. Comparison between compressibilities of sands and clays. J. Sedim. Petrol., 43: 529-536.

Einsele, G., 1982. Limestone- marl cycles: diagnosis, significance, causes - a review. In: G. Einsele and A. Seilacher (Editors), Cyclic and Event Stratification. Springer-Verlag. Berlin, pp. 8 - 53.

Einsele, G. and Mosebach, R., 1955. Zur Petrographie, Fossilerhaltung und Entstehung der Gesteine des Posidonienschiefers im Schwabischen Jura. Neues Jahrb. Geol. Paluonlol.. Abh. 101 : 319 - 430.

Ekdale, A.A. and Bromley, R.G., 1984. Comparative ichnology of shelf-sea and deep-sea chalk. J . Sedim. Petrol., 58: 322- 332.

Ekdale, A.A., Muller, L.N. and Novak, M.T., 1984. Quantitative ichnology of modern pelagic deposits in the abyssal Atlantic. Palaeogeog. Palaeoclim. Palaeoecol., 45: 189 - 223.

Fatt, I., 1958a. Pore volume compressibility of sandstone reservoir rocks. J . Petrol. Tech., lO(3):

Fatt, I . , 1958b. Compressibility of sandstones at low to moderate pressures. Bull. Am. Assoc. Petrol. Geologists, 42: 1924- 1957.

Gaillard, C. and Jautee, E., 1985. Compaction et deformation des structures de bioturbation. Abstract, A.S.F., Paris.

Garrison, R.E., 1981. Diagenesis of oceanic sediments: a review of the DSDP perspective. In: J.E. Warme, R.G. Douglas and E.L. Winterer (Editors), The Deep Sea Drilling Project: A Decade of Pro- gress, SOC. Econ. Paleont. Min., Spec. Publ., 32: 181 -207.

Geertsma, J . , 1973. Land subsidence above compacting oil and gas reservoirs. J . Petrol. Tech., 25(6): 734 - 744.

Gomaa, E.M., 1970. Compressibility of Rocks and Factors Affecting them. Am. Inst. Min. Metall., Pet. Eng. Ann. Student Contest Meet., Univ. California Berkeley, presented paper, 58 pp.

Graton, L.C. and Fraser, H.J., 1935. Systematic packing of spheres - with particular reference to porosity and permeability. J. Geol., 43: 785 - 909.

Hall, H.N., 1953. Compressibility of reservoir rocks. Trans. Am. Inst. Min. Metall. Pet. Eng., 198:

Hantzschel, W., 1975. Trace fossils and problematica. In: R.C. Moore and C. Teichert (Editors),

Kahle, C.F., 1966. Some observations on compaction and consolidation in ancient oolites. Compass, 44:

Kendall, A.C., 1975. Post-compactional calcitization of molluscan aragonite in a Jurassic limestone

Kennedy, W.J., 1975. Trace fossils in carbonate rocks. In: R.W. Frey (Editor), The Study of Trace

Knutson, C.F. and Bohor, B.F. , 1963. Reservoir rock behavior under moderate confining pressure. In :

1577- 1585.

64 - 66.

309 - 31 1 .

Treatise on Invertebrate Paleontology, Part W. University Kansas Print. Serv., 269 pp.

19-29.

from Saskatchewan, Canada. J. Sedim. Petrol., 45: 399-404.

Fossils. Springer-Verlag, Berlin, pp. 377 - 397.

C. Fairhurst (Editor), Rock Mechanics. Pergamon, New York, pp. 627-658.

43 8

Kohlhaas, C .A. and Xliller, F.G., 1969. Rock compaction and pressure tranfient analy5is with pressure- dependent rock properties. SPE paper 2563, presented at SPE 44th Ann. Fall Meet., Denver, CO, 7 PP .

Langnes, G.L., Robertson, J .O. and Chilingar, G.V., 1972. Secondary Rmiver.v and Carbhonate Keser- ivirs. Elsevier, Amsterdam, 303 pp.

hlatter, A , , 1974. Burial diagenesis of pelitic and carbonate deep-sea sediments from the Arabian Sea. Unit. Rep. DSDP, 23: 421 - 470.

Sleyers, n’.J. and Hill, B . E . , 1983. Quantitative studies of compaciion in Missi5sippian skeletal limestones, Nem Mexico. J . Seditn. Petrol., 53: 231 -242.

Newman, G.H. , 1973. Pore-volume compressibility of consolidated, friable, and unconsolidated reser- voir rocks under hydrostatic loading. J . Petrol. Tech., 25(2): 129- 134.

Podio, A.L., Gregory, A.R. and Gray, K.E., 1968. Dynamic properties of dry and water-saturated Green River shale under stress. J. Soc. Petrol. Eng., 8(4): 389 - 403.

Plessman, W. , 1966. Diagenetische und kompressive Verformung in der Oberkreide des Hart- Nordrande5 sowie im Flysch von San Remo. Neues Johrh. Geol. Palaontol., Mh. 8 : 480-493.

Pray, L.C., 1960. Compaction in calcilutites. Bull. Geol. Soc. Am., 71: 1946. Rieke, H . H . and Chilingarian, G.V., 1974. Cornpaction of Argillaceous Sediments. Developnients in

Sedirnentology, 16. Elsevier, Amsterdam, 424 pp. Rieke, H.H. , Chilingar, G.V. and Robertson, J.O., Jr . , 1964. High-pressure (up to 500,000 psi) compac-

tion rtudies on various clays. In t . Geol. Congr., 22nd Session, New Delhi, Section IS, pp. 22 - 38. Rieke, H.H. , Ghose, S., Fahhad, S. and Chilingar, G.V., 1969. Some data on compressibility of various

clays. Proc. In t . Clay Cony. , I : 817-828. Ricken, W., 1986. Diagenelic Bedding: A Model for Marl- Limestone Alternations. Lecture Notes in

Earth Sciences, 6. Springer-Verlag, Berlin, 210 pp. Ricken, W . , 1987. The carbonate compaction law: a neu. tool. Sedirirentology, 34: 571 - 584. Sawabini, C.T. , 197 1 . Trraxial Conipacrion of Unconsolidated Sandstone Core Sarriples under Produc-

ing Conditions at a Constant Overburden Pressure qf 3000 psi uncl Constant Trrnperatrrre of 140 ‘F. Ph.D. Dissertation, University of Southern California, Los Angcles, CA.

Sanabini, C.T. , Chilingar, G.V. and Allen, D.R., 1974. Compressibility of unconsolidated, arhosic oil sands. Soc. Petrol. Eng. J . , 14: 132- 138.

Schlanger, S.O. and Douglas, R.G., 1974. Pelagic ooze-chalk - limestone transition and its implica- tions for marine stratigraphy. In: K.J . Hsu and C. Jenkyns (Editors), Pelagic Sedir?7ents. In/ . Assoc. Sedrrnentologists, Spec. PuDI., 1: 117 - 148.

Shinn, E . A . , Halley, R.B., Hudson, J .H. and LidL, B.H., 1977. Limestone compaction - an enigma.

Steinen, R.P. , 1978. On the diagenesis of lime mud: scanning electron inicroxopic observarion5 on sub- surface material from Barbados, W.I . J. Sedrrn. Petrol., 38: 1139- 1147.

Tkhostov, B.A., Vezirova, A.D., Vendel’shteyn, B. Y u and Dobrynin, V.M., 1970. Oi l in Fractured Reservoirs. lzd. “Nedra”, Leningrad, pp. 173 - 197.

Van der Knaap, W. and van der Vlis, A.C., 1967. On the cause of subsidence in oil-producing area. Sevenrh Ct‘orld Petrol. Congr., Mexico City, Vol. 3 . Elsevier, Amsterdam, pp. 85 -95.

Wedepohl, K.H., 1970. Geochemische Daren von sedimentaren Karbonaten und Karbonatgesteincn in ihrem faziellen und petrographischen Aussagewert. Verh. Grol. Bundesanstalt Wien, 4: 692 - 705.

U’olf, K.H. and Chilingarian, G.V., 1976. Compactional diagenesis of carbonate sediments and rocks. In: G.V. Chilingarian and K.H. Wolf (Editors), Compaction of Coarse-Grained Sediments. Dewloprnents in Sedirrrentology. 188. Elsevier Amrterdam, pp. 7 19 - 768.

n‘olfe, M.J., 1968. Lithification of a carbonate mud: Senonian chalk in Northern Ireland. Sedrrii. Geol.,

Zankl, H. , 1969. Structural textural evidence of early lithification in fine-grained carbonate rocks.

Zimmerman, R.W., Sonierton, W.H. and King, M . S . , 1986. Compres5ibility of porous rocks. J .

Geolog-v, 5 : 21 -24.

2: 263 - 290.

Sedrrnentologv, 12: 241 - 256.

G e o p h ~ . ~ . RPS.. 91: 12. 765 - 12, 777.