Middleton G.V. (Ed.) Encyclopedia of Sediments and Sedimentary Rocks

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DIFFUSION,

CHEMICAL

225

Todd.

J.E.. 1913. More about seplarian struclure.

Geologieal

Maga-

zine. 10: 361-364.

Ulmer-Scholle. D.S.. and SchoJle. P.A., 1994. Replacement of

evaporites within the Permian Park City Eormation, Bighorn

Basin.

Wyotning. fSA.

.Seclmwniology.

41: 1203-1222,

Ulmer-Schollc. D.S'. Scholle. P.A,, and Brady. P.V.. 1993. Silicifica-

tion of evaporites in Permian (Guadalupian) back-reef carbonates

of the Delaware basin, wesl Tc.\iis and New Mexico. Journal if

Sedimeniary

Petrology.

63: 955 965.

Van

Tuyl.

E.M.. 1916. The geodes of the Keokuk beds.

.Ameriean

Journal if

Science.

42: 34 42.

Weyl.

P.K., 1959. Pressure-solution and the force of crystallization—a

phenomenological theory. Journal of

Geophysical

Researeh.

64:

200!

2025,

Wong,

P.K.. and Otdershaw. A.. 1981. Btirial cementation in the

Devonian,

Kaybob reef comple.x. Alberla. Canada.

.Imirnal

Se-

dimentary

Petrology,

51: 507-520.

Cross-references

Carbonate Mmeralogy and Geochemistry

ements and Cementation

Diagenesis

Cieodes

Pressure Solution

,Septarian Concretions

Styloliies

DIFFUSION,

CHEMICAL

Difftision of chemicals is one of the three tnain processes of

solute movement in sedimentary porewaters. that is, diffusion,

advection (flow) and biologically indticed exchange near the

sediment water interfaee (mainly irrigation). Chetnical

diffu-

sion is the net transport that is caused by thermally generated

random motions of particles in "solution'", may they be ions,

moiecttlcs or colloids. The net result of this phenomenon is the

transfer of a solute, that is, a flux. IVom regions of high

concentration to those of low concentration. In a closed

system,

this flux leads to an eventual homogenization of the

solute concentration, if no other processes act to maintain the

gradients (Figure D23).

Pure

Water

t=0

Figure D23 Illustratitin of diffusion is a tube containing pure water and

water with dissolved dye particles (black circlesi.

The diffusive flux is governed by Pick's

P'irst

Law of

Diffusion,

which in 1-dimension has the form

(Eq. I)

where

(F,-,),

is the diffusive flux of solute /, D, is its diffusion

coefficient, C, is its concentration and

('CJcx

is its vertical

gradient. Values of D, for various solutes of interest to

diagenesis can be found in Boudreau (1997, chapter 4), and

these typically fall in the range of 0.3-1.25 x 10"' cni"s~'.

Diffusion in aqueous sediments is slower than in an

equivalent volume of water because ofthe convoluted path(s)

the diffusing particles tnust follow to eireumvent the solid

sediment particles (Figure D24); therefore, the effective solute

difTuslvity, D/, in sediments is smaller ihan I), and given by

(Eq, 2)

where 0 is the tortuosity (dimensionless). In diagenetic studies,

0 is defined as the ratio of the average incremental distance,

d/-,

that a diffusing particle must travel to eover a direct

(vertical) distance, d.v, that is, d/-/d.v (Berner, 1980),

The tortuosity can be related to a measured quantity called

the "formation factor", //, which is obtained from electrical

resistivity measurements.

bulk sediment specific cleetrical resistivity

resistivity of porewater alone

(Eq. 3)

The relationship between tortuosity and resistivity is

assumed to be ofthe form (Berner, 1980)

O'=(pf (Fq. 4)

where tp is the sediment porosity, lhat is, porewater volntne

fraction.

When measurements of /' are lacking, 0 can be

estimated by Archie's law in sands, that is,

II-^tp

- (Eq. 5)

and,

in tine-grained sediments (Boudreau, 1997, chapter 4),

(Eq. 6)

Figure D24 A particle trying to diffuse from point A to point B cannot

pass tbrougb solid sediment particles (filled shapes); it must travel

around tbese panicles and so traverses Ihe

tortuous

dotted

path,

rather

tban the direct solid-line

path.

226

DIFFUSION,

TURBLIIENT

Molecular/ionic diffusion can be an elTective transport

process over '"small"" distances in sediments. Small in this

context is defined by the so-called Peclel number

Pe =

(pvL

(Eq. 7)

where L is the distance of interest and v Is the porewater flow

speed. If Pe»l, flow is the dominant transport proeess;

conversely, if Pe«l. diffusion is dominant, while both

contribute significantly if Pe^; 1.

An example of

situation where solute transport is strongly

dominated by chemical diffusion is the penetration of oxygen

into muddy organic-rich sediments. The scale of penetration is

only a few tens of eentimeters, at most, for example. Figure D25

where the Peclet number is of the order of 10 " for v<0.1 em

per year, D,

•=

10"cm' per year, and L =

em. In such

situations, the oxygen mass balance is between the reaction

that consumes it (deeay) and the supply by diffusion. Because

such oxygen profiles are essentially time invariant when

observed from the sediment-waler interfaee. that is. steady

state,

the mathematical statement of mass balance is given by

the diagenelic equation (Berner. 1980; Boudreau, 1997)

t'.Y

a.Y,

= 0

(Eq. 8)

Chitnge of the

Uiffu\ivi' \']u\

with depth

Rate of oxvgen

consiimpiion

where R,, is generally assumed to be a eonstant. The solution

to equation S with constant D/ is of the form

C, = C'li + C]\

Gv- (Eq. 9)

where

Cf),

Ci. C2 are constants. The e.\cellent fit of equation 9

to data is also illustrated in Figure D25.

Outside of areas affected by groundwater flow, porewater

velocities in recently deposited sediments are ofthe same order

of magnitude as the accumulation velocity of the sediment.

Emerald Basin

Nova Scotia, Canada

Data from N. Silverberg

Cfiisq

Value

204.1

-465.35

260.8

470.56

0.99364

Error

3.9254

17.039

50 100 150 200

Dissolved Oxygen {pMolar)

250

Figure D25 Dissolved oxygen profile (squaresi from ^i muddy

sediment, l.iken oft the codsl ot" Nov.3 Scotia, Canada. The line through

Ihe data is equation 'i.

that is. tVom about 10 ' em per year in the nearshore to

10 ' cm per year in abyssal clays. With solute diffusion co-

effieients typically of the order of lO' cm per year, the Peelet

number for these porewaters will be less than unity for

L ranging from tens to hundreds of meters. Thus, diffusion

continues to act as a significant transport mechanism during

latter diagenesis and even over fairly large distanees. as

illustrated by the modeling of Deep Sea Drilling Project data

(Lerman. 1979; Berner. 1980).

Other chemical transport processes that ean occur in

sediments are often modeled in analogy to ehemical diffusion.

Thus,

dispersion of solutes that accompanies strong hydro-

logical flow of porewater {Pe>l) is almost universally

represented in models as equation 1 with a new etnpirical

diffusion coefficient, known as the dispersion coefficient.

Likewise, mixing of porewaters by wave-induced water

motions or by infaunal movement (not irrigation) is also

conveniently represented as ditlusion. An important point to

remember in this respeet is that molecular diffusion is always

present, while these other "diffusions'" may or may not occur

in a given situation.

Bernard P. Boudreau

Bibliography

Berner. R.A-. I^SO. Early

Diagenesis:

ATheoretivitl Approiich. Princeton

L'nivcrsity Press.

Boudreau. B.P.. 1997. Diageticllc Models and Their Inipkiuciildiiotu

Springcr-Vcrlag.

Lerman, A.. 1979. GeochemicalProce.\sts: WuierandSedimcut Einiroit-

ments. John Wiley & Sons.

DIFFUSION,

TURBULENT

A key feature of turbulent flows is that they are diffusive, so

that the mean separation between initially adjacent tluiti

particles progressively increases in time. Sedimentary partieles.

suspended in a turbulent flow, move in response to fluid

motions in addition to settling under gravity. The ratio ofthe

settling velocity of the particles. H\, to the magnitude of the

turbulent fluid fluctuations, u.. is therefore an important ratio

tor characterizing the motion and distribution o'i sediment.

(This ratio, wju^. sometimes known as the Rouse parameter, is

further diseussed below.) In this artiele we present models for

the diffusive motion of particles. We begin by re\iewing the

forees acting on individual particles and developing an

equation of motion. We then consider how to model the

evolution of a suspension of relatively heavy particles within a

fluid by introducing a volumetric concentration, which varies

both spatially and temporally. Even in a nonturbulent flow,

suspended particles are subject to random fluid motion due to

moleeular movements (Brownian motion). This leads to a

molecular dilTusivity and we demonstrate how to develop a

mathematical model of this process. In a turbulent flow, there

are random fluid motions associated with unsteady eddies. We

show how to form a mathematieal deseription for the

evolution of the average eoneentration and how, in analogy

with moleeular diffusive proeesses. it is possible to describe

DIFFUSIO.N,

TURBULENT 227

these turbulent processes using a ditTiision model. Tliis model

is empiriciil and we indicate some of ihe limits of its validity.

We show how it can be used to model the vertical distribution

oi"

relatively heavy sediment suspended in a horizontal

turbulent flow.

Particles suspended in fluids are subject to a number of

forees, which means that they are not passively adveeted by the

fluid motions. If the eoneentration of particles is high then

these torees may arise from interactions between the suspended

material (e.g.. Bagnold, 1954), but even when the suspension is

dilute, there arc a range of possible etfeets. Maxey and Riley

(1983) have tbrmulated an expression for the forees on a single

spherical partiele in an unbounded fluid. These inelude the

buoyancy force, whieh arises due to the density difference

between ihe solid and fluid phases; the drag foree, which is the

force exerted by the lluid on the surface ofthe partiele and is a

function ofthe relative veloeity between the phases: the added

mass term, which is due to the displacement and acceleration

o\'

fluid surrounding the particle; the pressure gradient term

which arises due to a nonuniform distribution of pressure

within the fluid; and the Basset history term, whieh is

assoeiated with the acceleration of fluid surrounding the

particle in response to the unsteady particle motion. In

addition forces may arise due to the rotation of the particle,

vorticity in the baekground fluid motion and the interaction

with boundaries (see Clift eial., 1978; Auton eial.. 1988).

Thus,

ihe calculation o\' the trajectory of a single particle is

complicated even in an idealized, simple flow. However, the

buoyancy and drag forees dominate the motion of most

natural partieles, with particle inertia playing a small role in

some circumstances. Denoting the particle and fluid velocity

by V and u, respeetively. we find that when the drag force is

linearly proportional to the relative velocity between the two

phases, the equation ol'motion is then given by

r,,

(Eq. 1)

where ii; is the Stoices settling veloeity, r,, = wjg is the particle

relaxation time and Z is a unit veetor aligned with the vertical

axis.

Ciiven the complexity of this equation of motion, it is

infeasible to calculate the trajectory of eaeh constituent

particle within a suspension. Rather, it is usual to mtroduee

a volumetric concentration, C{x.r), which measures the

volume of particles relative to the total volume of the

suspension and which is a scalar funetion of time and space.

(Some investigators employ a mass eoneentration which is the

mass of particulate relative to the total mass of the

suspension.) The dispersed particles are treated as a continuum

and the evolution of the concentration field is ealculated.

Whenever a quantity, sueh as temperature, salinity or the

conccnti"ation of suspended particles, is non uniformly dis-

tributed, random motions give rise to diffusion, whereby it is

gradually spread throughout space. At a mieroseopie level,

diffusive spreading is caused by the progressive increase ofthe

mean separation between adjaeent molecules, which is a

consequence of Brownian motion. The botanist Robert Brown

observed the motion of small pollen grains suspended in a

fluid. Even though the system had come close to ecjuili-

brium and the pollen grains were uniformly distributed, he

observed individual grains undergoing seemingly irregular

motion which we now term Brownian motion. For a thorough

discussion of mathematical models of moleeular interactions

and the kinetic theory of gases see Chapman and Cowling

(1970).

The etTects of diffusive spreading may be illustrated by

considering a concentration distribution. Clz.t). within a

randomly moving fluid. Here, for simplieity. only one spatial

dimension is considered although the analysis ean be general-

ized to three dimensions. The random motion ofthe fluid may

be modeled probabilistically so that Piy.dt) denotes the

probability that concentration field at position r is displaced

to a new position r ^ v atter a time <)/. T'he probability

distribution has the following features: first, the probability

of making a displaeement is unity; and displacements are in

either direetion with equal probability, so that the first

moment of the distribution vanishes. These properties may

be written as

/'(,•,,v]dv = 1 and / yP(y.<>t)dy = 0. (Eq. 2}

- ~f.

Also the seeond moment is given by

•-/'(r.(V)dv = lDb\. (Eq. 3)

Thus the mean square displacement grows linearly in time

with rate 2D. The concentration Ctr./^iV), can be expressed

as tbilows

(Eq. 4)

Forming a Taylor series expansion for the concentration field,

which is valid if the displacements are not large, yields

(Eq. 5}

Finally multiplying by the probability of a displacement and

integrating gives an expression for the change in the

concentration field during a time St

(Eq. 6)

In this expression D is termed the diffusivity and is the rate at

whieh the random fluid motion leads to the increase of the

mean-square separation of initially adjacent fluid particles.

Diffusion leads to particle movement from regions of high to

low concentration ("transport down the concentration gradi-

ent") and the diffusive flux is given by

-D

(Eq. 7)

Note that individual particles are moving randomly and

independently of the concentration gradient. However collec-

tively their motion is such that there is net migration.

For small particles it is possible to estimate the diffusion

coefficient due to Brownian motion, using arguments first

presented by Langevin (I9U8) and Einstein (1905). Both of

228

t^lFFUSION, TURBULENT

these yield

£>

(Eq.8)

where T is the temperature, k the Boltzman coeffieicnt

(A = 1.38 X

10"--'

JK '), such that ^T is a measure of the

energy of the molecular vibrations. /; is the dynamic viscosity

and (/ the partiele radius.

We are now able to formulate the eoneentration transport

equation on the assumption that the partieles are adveeted

with the fluid flow, have settling velocity u*,, and are diffused

by random processes associated with Brownian motion. For a

concentration field that is dependent on r and /, and a fluid

flow denoted ir, this gives

(Eq.9)

The relative magnitude of the diffusion to the adveetion terms

is UL/D. where U and L are the velocity and length scales of

the flow, respectively, and this ratio is termed the

Pcelel

num-

ber. For most naturally occurring flows with sediment, the

Peclet number is much larger than unity, indieating that the

diffusive transport of partieles by Brownian motion is mueh

smaller than advection with the fluid. Thus we may

approximate the sediment motion to be advection with the

fluid flow and settling under the aetion of gravity.

Many natural flows are turbulent and an essential ehar-

aeteristie of them is that the velocity fields are irregular and

fluetuating. These apparently random fluid motions are able to

induce diffusive migration, in an analogous manner to that

generated by the random molecular motion described above

(Hinze. 1959). A mathematical model of this turbulent

diffusion is most simply developed by making the Reynolds

decomposition in which the velocity and concentration fields

are decomposed into mean and fluctuating parts. In what

follows we treat only one-dimensional fields, which depend

only on r and t. Thus we write

C{=. t] = C(.-) +

£•'(_-.

/] and w{:. t) - (_-) + ir'(r, t).

(Eq. 10)

where an overbar denotes the mean quantity and the means of

the fluetuating eomponents vanish. In passing we note that this

deeomposition requires some eare if the state around which the

fluetuations are occurring is itself evolving in time. In sueh a

situation it is still possible to make a Reynolds decomposition

provided a typical timescale ofthe fltictuations is much shorter

than the timescale over whieh the flow is evolving. In a similar

vane,

the Reynolds decomposition of flows which have a

periodic variation requires the period of the oseillation to be

much longer than the timeseale of the fluetuations (Dyer and

Soulsby, 1988). The mean evolution equation in the absenee of

molecular diffusion, is given by

ac ,.,-_- ,

(Eq. 11)

The terms on the RHS of this equation are the mean settling

flux,

n\C,

the mean advective flux. TrC, and the turbulent flux.

we' (which is known as the Reynoldsflux). If the fluctuations in

the velocity and concentration fields are completely de-

correlated then the Reynolds flux vanishes. However if the

distribution of eoneentration is nonuniform, the correlation

between these fluctuating iickis provides a mechanism for the

transport of particles. A model of the Reynolds flux as a

function of the flow field and the property of the particles

awaits a complete deseription of two-phase turbulent flows.

However a simple closure assumption is to draw an analogy

between molecular diffusion and these turbulent motions and

write the diffusive migration in terms of the gradient of the

mean field.

--—,

(Eq. 12)

where A'^ is the eddy diffit.sivity (sometimes known as the

sediment diffusivity). This relationship between the Reynolds

flux and the eddy diffusivity is empirical and is justified by

the apparently diffusive nature of turbulent flows in many

situations. Here we reiterate that this diffusion is not

associated with molecular fluctuations but is entirely due to

the seemingly random turbulent fluid motion. One ofthe key

weaknesses in the analogy between moleeular and turbulent

processes in some situations the scale ofthe turbulent eddies

excursions, which comprise the "random"" flow, can be quite

large. In some boundary layer flows it is possible for the seale

of these eddies to be comparable with the length scale over

which there is signifieant variation within the eoneentration

field. Thus the Taylor series approximation used to derive the

dependence of the diffusive flux on the gradient of the

concentration field may not be valid. However in many

circumstances this eddy diffusion model has led to a good

model of the distribution of sediment within a naturally

occurring How.

In addition to transporting particles, turbulent eddies also

transport lluid and thus provide a means for interchanging

fluid elements with different momenta. Their action, therefore,

leads to an effective stress. By forming a Reynolds deeom-

position of the momentum equations it is possible to identify

Reynolds stresses whieh are eorrelations between fluctuating

velocity fields. These ean then be related empirically to

gradients of the mean velocity through the use of an eddy

viscosity. For example for the two-dimensional, horizontally-

aligned, shear flow u-(L'(r),0) with fluetuating velocity field

u' =(f/.ir'), the Reynolds stress can be written

-^-^ 677

inv

=-K^-,

(Eq. 13)

where A' is the eddy viscosity (Hinze, 1959).

In this context the Schmidt nutnber.

= KJK, is the ratio

between the sediment diffusivity and the eddy viscosity. Sinee

both processes depend on the same turbulent eddies, it is

natural to investigate whether the diffusion of sediment is

more rapid than the diffusion of momentum or viee versa.

Since a complete model of particle motion within a turbulent

flow remains elusive, it is difficult to estimate the magnitude of

ji. This led Dyer and Soulsby (1988) to suggest that in most

practical problems it is sufficient to set /? equal to unity. There

are,

however, some physical proeesses in these flows which

mean that the motion of the particles and the fluid are not

identieal and so ji should be dilTerent from unity. This

discussion is aided by identifying three timeseales within the

flow. The tirst is the partiele relaxation timescaic. r,,, which is

the time over which the relative velocity between the fluid and

particle diminishes. This timeseale is assoeiated with the inertia

of the partiele. The other two timeseales are associated with

the turbulent flow and are the integral timescale of the

i.)ll-rUSION,

TURBULENT

229

turbulenee, T) and a time scale L/wo, where L and Ut, are

length and veloeity scales of the flow. Note that the ratio T/uJ

L is not neeessarily of order unity (Hunt

i-tal..

1994).

We noted above that the gravitational force and the drag

govern the motion of individual particles, which is a function

ofthe relative velocity between the two phases. If the timescale

over which the partiele aeeelerates. r,,, is much smaller than the

limescale of the flow (either of the turbulent timeseales) then

ihe particle moves with the fluid motion and sediments under

the aetion of gravity. However within a turbulent flow there

are irregular motions with very rapid variations. Thus there

will be periods in which the particle acceleration is non-

negligible and thus the particle lags behind the fluid motion.

Henee the particulate phase is not dispersed as widely as the

fluid phase and the sediment diffusivity should be expected to

be smaller than the eddy viscosity. Csanady (1963) discusses

this phenomenon and proposes that ji is a decreasing function

TiJT;.

However, for suspensions of dust in the atmosphere,

this reduction is very small.

A second mechanism is the effect of crossing trajectories.

Heavy particles, suspended in fluid, continuously change their

fluid particle neighbors. Thus the velocity history of the

particle is different from the surrounding fluid. I-'or example, a

heavy particle will sediment out of the eddy in which it is

initially located. Thus the spatial decay of the eorrelation of

the velocity field around it is more rapid than the decay ofthe

coherent eddies. Henee the diffusivity ofthe particles should be

expected to be smaller than the diffusivity of the fluid

(Csanady, 1963; Hunt etal., 1994).

One of the most fundamental problems in sediment

transport is to establish the vertical distribution of suspended

sediment within a turbulent flow over a horizontal, rigid

boundary, such as a turbulent pipe flow or a free-surface flow

such as a river, in these flows there ean exist steady vertical

distributions of sediment in which the weight ofthe suspended

sediment is supported by the turbulent motions. (See the

experimental data reported by Coleman, 1970; Vanoni, 1946).

In terms of the diffusion equation, this balanee is expressed by

equating the settling flux and the vertical Reynolds flux. This

balance is given by

(Eq. 14)

In this expression the eddy diilusivity varies spatially which

reflects the non-isotropic nature ofthe turbulent eddies. Close

to the boundaries the size ofthe largest eddy is limited. Since

these dominate the eddy-induced transport of sediment, it is to

be expeeted that the eddy diffusiivity should inerease with

distance from the boundary. Vanoni (1946) suggests that

K.iz)

fiKurJ.\

-zjH)

(Eq. 15)

where // is the Schmidt number (assumed constant). ^-0.4 is

Von Karman's constant, // is the How depth and the boundary

shear stress

—pur. Thus the vertical profile of sediment is

given by

H -6

(Eq. 16)

where the concentration is known at a height (>. The key

parameter in this distribution is the ratio of the settling

veloeity to a measure of magnitude of the turbulent velocity

fluetuations {wju,) and this determines the shape of the

profile.

Some relativity reeent observations of turbulent, boundary-

layer flow have indieated that the notion of purely random

fluid movement is inappropriate; rather there are coherent

fluid motions which may dominate the dynamics close to the

boundary (Kline etal.. 1967; Grass, 1971). Typically there is an

inrush of relatively fast moving fluid toward the boundary and

an ejection of slowly moving fluid away from the boundary.

Collectively these are termed the turbulent bursting phenom-

enon. These types of fluid motion may have important

consequences for the suspension of sediment, sinee the ejection

events are a coherent means for lifting relatively heavy

sediment upward from the boundary (Grass et at.. 1991).

f-urthermore since these events are coherent over relatively

long length scales, it is doubtful whether a gradient-diffusion

model is an appropriate framework for analyzing the effect of

the turbulent motion. Further research is required to under-

stand the dynamics of these coherent structures and to analyze

their effeets on the mo\enient of particles

Andrew J. Hogg

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Cross-references

Autosuspension

DitTusion.

Chemical

230 DISH STRUCTURr

Grain Plow

Griivilv-DrivL-n Mass Flows

Hindered Sellling

Ntimetical Models iind Simukition of Sediment

Transport and Deposition

Physics of .Sediment Tmnsporl

Sediment Transpori by Tides

Sedimenl Ininspotl by Unidirectional Water Flows

Settling

DISH STRUCTURE

Dish structures are thin, roughly horizontal, ustially dark, fiat

to concave-upward laminations in sandsione and coarse

siltstone beds (Figure D26). The dark color usually results

from a local enrichment in mud. organic matter, micas, and

other hydraulically tine or low-density grains. Dish structures

were first described and named by Wentworth (1967) and

Stauffer (1967) from thick-bedded deep-water sandstones of

western California. Initially they were interpreted to be

primary sedimentary structures related lo the growth and

breaking of antidunes during deposilion from turbidity

currents (Wentworth. 1967) or to inhomogencous shearing

within grain Hows (Stauffer. 1967). Lowe and LoPiccolo (1974)

provided evidence that they are post-depositional struetures

formed during liquefaction and dewatering of rapidly depos-

ited sediments. Fxperiments designed to reproduce dish

structures reinforce this interpretation (Tsuji and Miyata.

1987:

Nichols t'/(//.. 1994).

Dish structures are most common in thick sandstone beds

that are usually interpreted as deposits of high-density

turbidity currents, although they have also been reported

from alluvial sandstones. In general, each concHve-up lamina-

tion or dish is underlain by a zone up to a few millimeters thick

of lighter-colored sand representing the primary water flow

path from which elays. organic particles, micas, and other

hydraulically line grains have been elutriated (Figure D27).

Many dishes have upturned enJs that define vertical water

escape conduits called pillars or pillar structures (Figure D27).

The width of individual dish structures ranges from about

to over 50cm and their vertical spacing from ().5cni lo over

30 cm. The bases of dish structures are sharp, whereas the tops

tend to be gradational. The dishes range from relatively fiat,

continuous larninae with widely spaced interruptions (Figure

D26) lo more strongly curved dishes with frequent breaks

(Figure D27). Rare bedding-plane views of dish-slructures

show a polygonal pattern of ridges separating shallow

concave-upward depressions (Lowe and LoPiccolo, 1974),

Figure D26 Contdve-upward disb structures cross-cut primary cross-

lamidcUions. The upturned ends of the dishes form peaks or pilLir

structures. Scale at top in millimeters. Turhidite Irom the

Pennsylvanian |tH kibrk Group, Oklahoma.

Figure D27 Dish structures showing well-developed underlying

light-colored water-flow palhs from which dark clay^, micas, and

organic particles have heen remove<J. Scale on right in millimeters.

Turliirlilc from the Pennsylvanian lackfork Group, Oklahoma.

DOLfiMITETEXTl.iRES

231

Dish slruclurcs

are

inlcrprclcd

form through dewatcring

oi' rapidly deposiled. cohesionless sand

and

silt. Rapid

deposition resLilis

loose packing

grains. Such sediments

often undergo partial liqtiefaction

response

shoeks

associated with tectonic

sedimentologieal proeesses.

The

escaping water entrains hydraulically mobile grains, such

clays,

organic materials,

and

tnieas. Semi-permeable lamina-

tions

act as

partial barriers

to the

upward flow

water within

the liquelied sedmieiit, forcing

ii to

move laterally toward

points where continued vertical escape

possible. Slow

seepage through

the

bounding semi-permeable laminations

results

filtering

and

concentration

the dark, hydraulieally

mobile grains

form

the

dark dish struetures. Subsidence

the central parts

of the

dishes

as the

underlying water

and

sediment escape increases dish eurvature. Primary semi-

permeable laminae

are not

always present

dish-structured

beds

and

might

not be

necessary

for

dish formation.

Minor inhomogeneities

permeability, whieh

are

likely

be present even

apparently structureless beds,

well

as the

inhomogeneous development

flow paths

due to

hydro-

dynamie instabilities,

can

probably initiate dish-structure

formation.

Allen (1982:

373 374)

proposed that some

most dish

structures

ean

form through

process ofstoping

at the

tops

water-lillcd cavities during dewatering

of a

loosely-packed,

slightly eohesi\e waier-saturated sediments. Tsuji

and

Miyata

(1987) observed formation

dish structures

line-grained

sediment

water-filled eavities settled

to the

bottom, followed

the

collapse

the

roof.

Some cavities

had

slowly subsiding

roofs,

and the

water

was

filtered through

the

subsiding,

relatively coherent sand mass.

It is

probable that dishes

can

form through both filtration along permeability barriers

liquefied sedimenis

and

stoping within water-filled eavities.

The latter process

like!}'

result

dishes with more

irregular shapes.

DOLOMITE TEXTURES

Zoltan Svlvester

and

Donald

Lowe

Bibliography

Alli^ti. J.R.L.. iy!^2. Si'cliim-uliiry SDucritres; Tlii-ir Clutrtulcr

and

Phy.sicalBasis. Volume

II.

Atnsterdatii: Elsevier.

Lowe.

D.R.. and

LoPiccolo.

R.D.. 1974.

Tlie cliaraclcrislics iind

origins

o'i

dish

and

pillar slrucltjrcs. .liiiinnil

Seiliiiieiihtiv

Perro/ogv.

44: 484 501.

Nichols.

R.J..

Sparks. R.SJ..

and

Wilson. C.J.N..

1994.

Hxpmtnental

siiidies

tlie lluidization

layered sediments iind tlic formation

oflluid escape strticltires. Si-iliincniolii^y. 41:

2^^ 253.

SlauffLT.

P.H..

1967. Grain-How deposits

and

their itnplications. Santa

Ynez Mountains. California.

Jiitirmil

Sfiliniciilaiv

PL'fi(ilui:\.

37:

487

508.

Tsuji.

T.. and

Miyata.

Y.. 1987.

Fluidization

and

liquct'action

sand

beds experimental study

and

exiimples from Nichinan Group.

./(luntiih'f

llw

Gailofiiral

.Siicii'iy oJ

Jiiihiii.

93: 791-808.

Weniwortli.

CM. Jr., 1967.

Dish struclure.

primary scdinicntiiry

siriiclurc

coarse turbidites.

.•iiiu'riicin .-issotictlioii

Pdrii/ftiiu

(iciilo^i.sls

Biillvliii. 51:

485.

Cross-references

Fluid Fscapc Structures

Graviiy-Dnvcn Mass Flows

Liquefaction iind Fluidi/iition

Pillar Structure

Tuibidiles

Rock texture

is a

composite characteristic determined

by the

si/e,

shape, distribution

and

orientation

erystals. grains

and

pores.

Texture carries genetic implieations about kinetics

nueleation

and

growth

erystals

and

directly relates

porosity

and

pcrnicahility. Therefore, elassification based

textural characteristics

appropriate when researchers

are

interested

in the

origin

dolomite

or its

petrophysieal

pro-

perties.

The

most useftil textural eharaeteristies

for

elassifying

dolomites

are

crystal shape (planar

and

nonplanar)

and the

degree

whieh textures

replaeed alloehcms

and

cements

are

preserved (mimetic versus nonmimetic replacement).

Planar and nonplanar dolomite

Crystal shape

is the

most commonly used te\tural feature

for

elassifying dolomite. Crystal shape

may be

categorized

planar

nonplanar (Sibley

and

Gregg, 1987). Planar dolomite

crystals (Figure D2S(A)) have straight dolomite-dolomite

crystal boundaries. Nonplanar dolomites (Figure D28(B))

Figure

D28 iAi

Planar dolomite. Arrows point

straight fnfacial

junctions

a tomprdmise growth boundary between adjacent

cryslals. Seroe Domi Fni., Pliocene, Bonaire,

N.A.

Cenozoic, Scale

bar

0.1

mm.

iB)

Nonplanar dolomites have both straight

and

irregular compromise boundaries (arrows). Trenton Fm., Ordovician.

Ml basin. Also notice the irregular extinclion pattern

the dark crystal

the

center and left-center

of the

lield

view. Scale bar

0.5 mm.

232

DOLOMITE

TEXTURES

have curved, lobate oi" otherwise iiTcguUir dolomite-doloinite

bounciaries. Most pctrographers use the terms planar and

nonplanar to describe dolomite crystal shape, but the terms

anhcdral. euhedral, xenotopic and idiotopic arc still commonly

used {see Classification of

Sedimeni.s

ami Sedimentary Racks).

Euhedral crystals are bounded by their faces, anhedral crystals

are not. Idiotopic refers to a texture in which the majority of

crystals are euhedral and xenotopic refers to a texture in which

the majority of crystals arc anhedral. Anhedral. euhedral.

xenotopic and idiotopic are not appropriate descriptors of

interlocking arrays of crystals observed in thin section because

one cannot determine whether or not crystal-crystal bound-

aries represent crystal faces without using a universal stage.

The terms planar and nonplanar are also flawed. These terms

refer to three dimensions when, of course, thin section

observations are two-dimensional. However, most dolomite

crystal shapes are isotropic and. therefore, planar and

nonplanar shapes are adequately represented in two dimen-

sions.

More importantly, segments of nonplanar dolomite-

dolomite boundaries may be straight and straight boundaries

may appear curved due to overlapping grains. As a result,

qualitative distinction between planar and nonplanar dolo-

mites may be very difficult even for e.xperienced petrographers.

Arbitrary criteria allow a quantitative distinction between

planar and nonplanar (Gregg and Sibley. 1984) but the vast

majority of published descriptions are based on qualitative

analysis. Fortunately, it is usually easy to distinguish planar

from nonplanar dolomite based on extinction characteristics.

Planar dolomite has straight extinction and nonplanar

dolomite usually has sweeping or segmented extinetion

(Figure D28).

Nonplanar dolomite cement, commonly referred to as

saddle dolomite (Radke and Mathis. 1980) or baroque

dolomite (Folk and Asserto. 1974). is volumetrically very

minor but common. The distinguishing features are eurved.

saddle-shaped crystal faces (Figure D29) in open pore space

and sweeping extinction. Dolomite-dolomite boundaries

between saddle dolomite crystals are nonplanar. Saddle dolo-

mite is a textural term that is commonly applied to dolomite

CaMg(COi);>, ferroan dolomite (<10 mole percent

and ankerite Ca(Fe. MgHCO.,):.

Mimetic and nonmimefic replacement

Most dolomites are composed of equant rhombs tens to

hundreds of micrometers in diameter. In these, it is generally

impossible to determine whether the dolomite replaced a

precursor calcium carbonate phase or precipitated directly

from solution. When evidence of a precursor allochem

(composite carbonate grain) or carbonate cement is present,

the replacement dolomite is referred to as mimetic or non-

mimetic (Kaldi and Gidman. 1982). Mimetic replacement of

carbonate precursors occurs when micrometer to submierom-

eter-size dolomite crystals replace the carbonate in such a

manner as to preserve the shape and internal texture of

cements or allochems (Figure D30(A)). Poor preservation of

allochems or cement texture is referred to as nonmimetic

replacement. Nonmimetic textures often include "gbosts"

which are inclusions of non-carbonate material which outline

or show internal structure of pre-dolomitization allochems or

cements (Figure D30 (B)).

Dolomite tends to nucleate epitaxially on calcite. Therefore,

mimetie replacement may preserve the crystailographic or-

ientation of calcite cements and allochems. When the host

material is aragonite. dolomite tends to nucleate non-

epitaxially. Therefore, mimetic replacement of aragonite will

Figure D29 Synthetic saddle dolomite wiih t haracterislic curved faces

produreri ma hydrothermal bomb at 250' C (see Gregg, 1983). Field of

view is 0.1 mm across.

Figure D30 MimetiL lAi ami

IHHIIIIIIIH'IK

iBi repkReriteni ol ooids.

The mimelically replaced dolomite preserves tbe radial structure

common in ooids. Nonmimetically replaced ooids are "ghosts"made

visible by inclusions of organic material. Both samples from the Praire

du Chien Cp, Ordovician, Ml Basin. Scale bdr5 =

DOLOMITE TEXTIRES

233

preserve the structure of allochems or cements but not the

original crystailographic orientation of aragonite crystals.

Crystal habit

Dolomites are not generally classified according to crystal

habit because the only common form o\' dolomite crystals is

the 110

1 I

rhombohedron. although complex polyhedra occur

(Naiman

c-tal..

1983; Gregg eial.. 1992). Spheroidal dolomites

have been found associated with submarine hydrothermal

vents (Pichler and Humphrey. 2001), hydrocarbons seeps

(Gunatilaka. 1989) and possibly bacteria (Nielsen cial.. 1997).

Crystal size distribution

Dolomites crystal size distributions are lognormal to normal

coarse skewed regardless of age or mean size (Gregg ci al..

1992;

Sibley cuil., 1993). Similar crystal size distributions are

found in other diagenetic minerals, as well as minerals in

igneotis and metamorphic rocks (Eberl eial.. 1998). Nonplanar

dolomite tends to be coarser crystalline and more lognormal

than planar dolomite (Sibley cial.,

199.3;

Woody ctciL 1996).

Trends in crystal size and characterization of crystal size

distributions have been of limited use in understanding

dolomite petrogenesis because size distributions have not been

directly linked to nueleation and grovvih theory.

Dolomite rock textures

Dolomite selectivity

Dolomite selectively replaces tbe fine crystalline portions of

limestone. Therefore, the distribution of dolomite in a rock

may reflect the original limestone te.\ture rather than the

chemistry or flow paths of dolomitizing solutions.

Fossil moldic porosity

Because dolomite selectively replaces tine crystalline compo-

nents of a rock, coarse crystalline aliochems such as

brachiopod fragments often resist dolomitization. These

resistant aliochems may be subsequently leached. Fossil moldic

porosity is also common in limestones but the fossils whicb

make up the molds in limestones are typically not braehiopods

or other coarse crystalline low Mg-calcite allocbems.

Sucrosic dolomite

Porous, planar dolomites are generally equigranular giving the

rock a sugary texture. The sugary texture is noticeable in hand

specimen as light reflects off dolomite crystal faces. These

rocks have attracted attention because they have relatively

high permeability making them valuable hydrocarbon

reservoir rocks.

Interpretations of dolomite textures

Interpretation o\' planar and nonplanar dolomite texture

(Gregg and Sibley. 1984) is based on theoretical relationships

between growth rate, supersaturation and/or temperature and

crystal morphology (Sunagawa. 1984). Planar dolomite forms

a smooth interface due to dislocation or 2-dimensional

nueleation growth (Figure D3I(A)). Nonplanar dolomite

forms a rough interface by 2-dimensional nueleation and/or

(A)

(B)

PLANAR

SPHEROIDAL

^ NONPLANAR

2D nucleation

controlled

Supersaturalion and/or temperature

Figure D31 Models for crystal growth (A) and the associated geometry

of crystal surface (B).Figure Dll(B)

modified after Sunagawa n9(H).

adhesive growth. Boundaries between dolomite types and

crystal growth mechanism overlap because 2D nueleation can

forms plane erystal surfaees at relatively low temperature and/

or degrees of supersaturation and irregular surfaces at higher

temperature and/or supersaturation (Figure D31(B)).

Spheroidal crystals are direct evidence thai low temperature

dolomites may form by adhesive growth bui the majority of

nonplanar dolomites have been attributed to growth at >50 C

based on stable isotope and fluid inclusions (Spotl and Pitman,

1998).

Mimetic and nonmimetic textures reflect the density of

nucieation sites present on the substrate being dolomitized.

Mimetic texture requires a relatively high density of nucieation

sites whereas nonmimetic texture reflects a low density of

nucieation sites. The density of nucieation sites on a substrate

is determined by the crystal size and mineralogy of the

substrate as well as the degree of supersaturation and

temperature of the solution. Mitnetic replacement is favored

in cryptocrystalline allochems. Coarse crystalline, low Mg-

calcite allochems such as braehiopods are not mimetically

replaced (Bullen and Sibley. 1984). Because the texture and

234

DOLOMITHS AND DOLOMITIZATION

mineralogy of allochems can change during diagenesis. pre-

dolomitization diagenesis can determine whether or not

allochems are mimetically replaced.

In Paleozoic rocks, echinoderm fragments are commonly

mimetically replaced whereas braehiopods are never mimeti-

cally replaced. In Cenozoic rocks, coralline algae and

eehinoderms are commonly mimetically replaced and generally

the first allochems to be replaced (Sibley. 1982). Allochems

that are normally mimetically replaced may be nonmimetically

replaced if pre-dolomitization neomorphism results in sig-

nificant crystal coarsening.

Lucia (1995) has shown correlations between porosity and

permeability of dolomites, particularly when samples are

grouped according to crystal size. Woody eial. (1996) have

shown a correlation between porosity and permeability in

planar and a lack of correlation in nonplanar dolomites.

Therefore, improved correlations between porosity and

permeability should be found if both crystal size and shape

were considered.

Duncan Sibley

Bibliography

Bullen. .SB., and Sibley. D.F,. 1984. Dolomite selectivity and mimic

replacement, d-ologv. 12: 655 65J<.

Eberl. D.D.. Drits. V.A.. and Srodon. L.. 1998. Deducing growlli

mt;i.'li;inisms lor minerals from the shapes of crystal size distribu-

tion, Aineriaiii Jdtiriialof Sciciuc. 298: 499-533.

Folk. R.L.. and A.sserto. R.. 1974. Giant aragonite rays and baroques

dolomite in tepee-fillings, Triassic of Lombardy. Italy (abstract).

American As.wciuiian of Petroleiini Geologisis. Abstracts With

Program. Antinal Meeting. San Antonio, pp. 34 35.

Gregg. J.M.. 1983. On (he formation and occurri^nee of saddle

doiomite-discussion. Joitrnti! of Sedimenlarv Petrology. 53: 1025-

1026.

Gregg. J.M.. and Sibley. D.F.. 1984. Fpigenctic dolomitization and the

origin of xenotopic dolomite lexUire. JoiiriialofSeiliiiienUirvPcrnil-

(j^?.i.

54:

908-931.

Gregg. J.M., Scott. H-. and Mazyullo. S.J.. 1992, Fariy diagenetic

rccrystallization of Holocene (<3(H) years old) perlidal dolomites.

Ambcrgis Cay. Belize.

Sc<liiiieii!olo,gy.

39: 143 160.

Guiiatilaku, A.. 1989. Spheroidal dolomites—origin by hydrociirbon

seepage? SetUmcnwIofiy. 36: 701 710.

Kaldi. J.. und Gidman. J.. 1982. F,arly diagenetic dolomite cements:

examples from ihe Permian lower magnesian Limestone of

England nnd the Pleistocene carbonates of the Bahamas. Jouriuil

ofSetlimenkiiyPL-lrology. 52: 1073 1085.

Lucia. F.J.. 1995. Rock-fabric/petrophysical classification of carbonate

pore space for reservoir characterization. Anwriteiii

.As.soc iitiioij

iij

Pfirolciiiii

G\'oloi^is!.'<

Build ill. 79: 1275-1300.

Naiman, F.R.. Bein. A,, and Folk, R.L.. 1983. Complex polyhedral

crystals of limpid dolomite associated with halite, Permian upper

Clear Fork and Gloriela formations. Texas. Journal of Seilimenttiry

Pflrolof-y. 53: 549-555.

Nielsen. P.. Swennen. R., Dickson, J.A.D., Fallick, A.E., and

Keppens. F.. 1997. Spheroidal dolomites in a Vi^^ean karst

system—bacterial induced origin. Sediineiuology 44: 177 195.

Pichler. T.. and Humphrey. J.D.. 200L Formation of dolomite in

recent island-arc sediments due to gas-seawater-sediment interac-

tion. JouiruilofSednnvnkirvRe.seiinli. 71: 394 399.

Radke. B.M.. and Mathis. R.L.. 1980. On the formation and

occurrence of saddle dolomite, .lournal of SedinienUirv

Peliolo<>v.

50:

1149-1168.

Sibley. D.F.. 1982. The oriein of common dolomite fabries. Journal

Seclm]ciilaryPeiyolof>y.

52: 1087-1100.

Sibley. D.F.. and Gregg. J.M.. 1987. Classification of dolomite rock

texture. Journal of SedimeiUarr

Pvrrologw

57: 967-975.

Sibley, D.F.. Gregg. J.M.. Broun. R.G.," and Laudon. P.R-. 1993,

Dolomile crystal size distribution. In Rczak. R.. and Lavoie. D.

(eds.).

CarhonaW Microfahrics. New York: Sprincer-Verlag.

pp.

195 204.

Spiitl. C and Pitman. J.K.. 1998. Saddle (baroque) dolomile in

carbonates and sandstones: a reappraisal of a biu-ial-diagenctic

concept. In Morad. S. (ed.). Carhonale Cemenlation in

Sanei.slones.

Special Publieations of Association of Sedimenlologists 26:

pp.

437 460.

Sunagawa. L. 1984. Growth oi" crystals in nature. In Sunagawa. I.

(ed.).

MalcritilSiieiivciniheEuylh'sInterior. Tokyo: Terra Scientific

Publishing Co.. pp. 63-1205.

Woody. R.E-. Gregg. J-M.. and Koederitz. L.F.. 1996. Effect of

texture on petrophysieal properties of dolomite: Evidence from the

Cambro-Ordovician of Southeastern Missouri. Anicriatn As.weia-

lionof Pclroleuin Geologi.sis Bidlelin. 80: 119 132.

Cross-references

Carbonate Mineralogy and Geochemistry

Cements and Cemenlation

Classiiieation of Sediments and Sedimentary Rocks

Diagenesis

Dolomites and Dolomiti/ation

Fabrie, Porosity, and Permeability

Grain Size and Shape

Surface Textures

DOLOMITES AND DOLOMITIZATION

The mineral dolomite is widely distributed in the Earth's crust,

especially in sedimentary/diagenetic settings, in rocks that

range in age from the Precambrian to the Recent. Ideal,

ordered dolomite has a formula of CaMg (CO.i): and consists

of alternating layers of Ca""^-CO^~-Mg'^'-CO^'-Ca""^ etc.

perpendicular to the crystailographic c-axis. Most natural

dolomite has np to a few percent Ca-surplus (and correspond-

ing Mg-delicit). as well as less than ideal ordering. Froiodolo-

miie has about 55 percent to 60 percent Ca and is partly to

completely disordered, thai is, the alternating layer structure is

poorly developed to non-e.\isting. Protodolotnite or partially

ordered dolomite with a few percent Ca-surplus arc common

as metastable precursors of well-ordered, nearly stoichiometrie

dolomite. Dolo.stone is a rock that consist of >75 percent

dolomite. Dolostones arc alsocalled dolomih's. especially in the

literature prior to about 1990. but the term dolomites should

be used only for different types of dolomite.

Two types of dolomite formation are common, that is.

dolomilization. which is the replacement of CaCO> by

CaMg(CO3)i, and dolomite cementation, which is the precipita-

tion of dolomite from aqueous solution in primary or

secondary pore spaces. The term dolomitization is also, yet

incorrectly, applied to dolomite cementation. A tbird type of

dolomite formation, where dolomite precipitates from aqueous

solution to form sedimentary deposits ("primary dolomite"),

appears to be rare and is restricted to some evaporitic lagoonal

and/or lacustrine settings.

Despite intensive research for several decades, the origin of

dolomites and dolostones is subject to considerable contro-

versy. This is because some of the chemical and/or the

hydrological conditions of dolomite formation are poorly

understood, and because the available data permit more than

one viable genetic interpretation in many case studies. One key