thermal conductivity and permeability assessment by electrical resistivity measurements in marine...

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Thermal conductivity and permeability assessmentby electrical resistivity measurements in marinesedimentsMichael Anthony Lovell a ba Department of Physical Oceanography, Marine Science Laboratories, University College ofNorth Wales, Menai Bridge, Gwynedd, United Kingdomb Department of Geology, University of Nottingham, Nottingham, United KingdomPublished online: 23 Dec 2008.

To cite this article: Michael Anthony Lovell (1985): Thermal conductivity and permeability assessment by electrical resistivitymeasurements in marine sediments, Marine Geotechnology, 6:2, 205-240

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Thermal Conductivityand Permeability Assessmentby Electrical ResistivityMeasurements inMarine Sediments

Michael Anthony LovellDepartment of Physical OceanographyMarine Science LaboratoriesUniversity College of North WalesMenai BridgeGwynedd, United Kingdom

Abstract The problem of radioactive waste containment,the modeling of hydrocarbon formation processes, and the pro-posed laying of fiber-optic communication cables on the seafloorhave recently focused attention on the thermal and fluid flow prop-erties of porous media. Both properties are difficult to determineaccurately for large volumes of material, particularly where dis-turbance is inevitable either on sampling or penetration of themeasuring device. Both properties, however, have been tentativelyidentified as bearing some form of analogy with electrical flow,and evaluation of these relationships with electrical measurementsmay provide practical means of obtaining rapid coverage of thesediment from a semi-remote position. Using a variety of labora-tory cells, an attempt has been made to evaluate useful relation-ships between electrical formation factor and thermal conductivityand/or permeability for both sands and clays. Formation factorexhibits a close relationship with permeability, and the capability

Present address: Department of Geology, University of Nottingham, Nottingham, UnitedKingdom.

Received February 23, 1984; accepted September 7, 1984.

Marine Geotechnology, Volume 6, Number 20360-8867/85/020205-00$02.00/0Copyright © 1985 Crane, Russak & Company, Inc.

205

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206 Michael Anthony Lovell

of predicting permeability to within an order of magnitude isshown providing the grade of sediment is identified (e.g., sand orclay). Formation factor is related to porosity and while any onesample is best represented by Archie's (sands) or Winsauer's (clays)empirical law, the overall trend is a third-degree polynomial; par-ticle shape appears to dominate both porosity and permeabilityrelationships with electrical formation factor. Thermal conduc-tivity shows a clear dependence on the porosity of a saturatedsediment. The successful prediction of thermal conductivity usinga geometrical model requiring volume and thermal conductivityvalues for the components has been demonstrated for a variety ofparticle shapes and sizes. Thermal conductivity may be relatedto formation factor through the porosity of the sample for bothsands and clays.

Introduction

The search for a suitable repository in which high level radioactivewaste can be safely confined over long periods of time has led torenewed interest in the geotechnical properties of the deep oceanfloor. Similarly, attention has focused on continental shelf sedimentsand porous media generally with the proposed laying of thermallysensitive fiber-optic communication cables and the attempts to in-crease the extraction efficiency of hydrocarbons and to model theirformation processes.

Two aspects of the geotechnical state of the sediment mass are ofspecial importance in all of these areas of investigation, the thermalconductivity and permeability. Both parameters are also problem-atical and expensive to determine accurately for large volumes ofmaterial, and permeability measurements suffer from additionalcontroversy, particularly regarding the magnitude of the hydraulicgradient used.

As electrical flow in marine sediments takes place through thefluid-filled pore space, and since electrical flow has long been con-sidered analogous to fluid flow (Archie, 1942; Schopper, 1966; Wor-thington, 1973; Brown, 1980) and thermal transfer (Rayleigh, 1892;Bruggeman, 1935), it would appear useful to try to define any prac-tical interrelationships such that the two parameters may be esti-mated from in-situ electrical measurements (e.g., Jackson, 1975).

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Electrical Resistivity Measurements 207

Permeable Porous Media

A simple, though effective, approach to a marine sediment is to con-sider the medium as an assemblage of grains, the pore spaces be-tween which are interconnected and filled with a pore fluid. Theporosity, n (the proportion of space taken up by the pores), definesin simple terms a facet of the physical state of the material and isof prime importance in many geotechnical and geophysical analyses.

Electrical conduction in marine sediments generally occursthrough the pore fluid, the mineral structure being an insulator incomparison with the saline water (Brace et al., 1965; Taylor Smith,1971; Jackson, 1975). The measured electrical resistivity is thus afunction of the nature and distribution of the pore fluid; for marinesands this dependence on pore shape (dictated by particle shape) hasbeen clearly demonstrated (Jackson et al, 1978). In order to removethe effect of the pore fluid nature on the measurement, such thatthe determination is effected solely by the structure of the sedi-ment, an electrical formation factor (FF) may be defined:

resistivity of the porous mediumresistivity of the pore fluid

This quantity has been used ubiquitously in the oil industry to eval-uate the porosity of a reservoir rock (Archie, 1942; Winsauer et al.,1952), while for marine sediments Boyce (1968,1980) and Kerma-bon et al. (1969) have extended such predictions to deep sea clays,and Jackson (1975) and Jackson et al. (1978) to clean sands.

Permeability refers to the ease with which a fluid flows througha medium. For sands this may be assessed in the laboratory by aconstant head permeameter test (Akroyd, 1964; British StandardInstitution, 1961), while for clays a value may be derived from theuniaxial consolidation test either directly by measurement of fluidflow across the sample or indirectly from consolidation theory (Ter-zaghi, 1943). Generally the consolidometer-derived permeabilityvalues are between one and two orders of magnitude less than thosemeasured directly (Nickerson, 1978; Bryant et al., 1981; Hamdi,1981), and while there is no definitive explanation of this phenom-enon, various experimenters have pointed to the difference in the

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state of the samples being tested, particularly the strain imposedin the consolidometer. Mitchell and Younger (1967) also query theuse of consolidation-derived permeability values where the devel-oped gradients are very high, though they query the general appli-cability of laboratory results using excessively high gradients; innature, gradients are low and deviations from Darcy's law are mostsevere.

Although discrepancies do exist between the direct and consoli-dometer-derived permeabilities, both sets of data relate in somemanner to fluid flow in the test sample. It would seem likely there-fore that there is some as yet undefined relationship between thetwo sets of data, even if that relationship involves defining a dif-ference in the nature of the fluid flow. A relationship with one setof data therefore may be taken as indicating the likelihood of asimilar, though not necessarily the same, relationship with an alter-native data set.

Bullard et al. (1956) and Ratcliffe (1960) have shown a clear de-pendence of thermal conductivity on water content, while Sass et al.(1971) provide a simple geometrical relationship which allows thecomputation of the bulk thermal conductivity of a system from thevarious volumes and conductivities of the constituents. Thermalconductivity measurements on laboratory samples of marine sedi-ments are readily accomplished using the transient needle probetechnique (Von Herzen and Maxwell, 1959).

Laboratory Measurements

Marine sediments are considered here as two separate systems,sands and clays, since their intrinsic nature necessitates differenthandling techniques. Sands are composed primarily of cohesionlessparticles and may therefore be repeatedly redeposited in the labora-tory under a variety of conditions. Clays, however, are composedof fine cohesive particles and are deposited in situ over long timeperiods; consequently, they develop intricate structures and com-plex lattice arrangements, with bonding between the particles. Thissediment fabric is easily disturbed and distortions once effected arelargely irreversible; clays are not therefore easily redeposited in thelaboratory.

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, M, = 0-90

f« = 0 21

• 3 ,2 .1 0Grain Size. 0

-1 -2

100

75

50

*25

M,

a=-0-29

: 0 13

• 3 .2

Grain•Í 0Size 0

-3

M,= 1 075 O r * . = 0 50

v.50[ ""

• 3 «2 «1 0 -1 -2Grain Size, 0

25

M, = 0-97o . = 0 51

«3 »2 »1 0Grain Size, 0

-1 -2

10075

50

25

u

100

75

50

*25f\U

M*

•

M,

. °#

i

= 0= 0

3

: 1- 0

3

7527

r—

• 2Grain

72

•35

r

—

•2Grain

• 1Size

—\—,

00

0Size t

f I m

-1 -2

9

-1 -2

M. = 1 10

50,

.2 -1 0Grain Size, 9

H. = 2 74

°, : 0 K

. 2 «1 0Grain Size.«.

-1 -2

100

75

50

25

0

M» = 0-33a , = 0 26

• 3 «2 «1 0 -1 - 2Grain Size. t.

FIGURE 1. Grain size histograms for major components of artificial sands.

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The sand samples are a suite of 12 artificially prepared sands,representative of a range of particle shapes, mean grain sizes, andgrain size distributions (Figure 1). They are studied using two de-positional cells, a porosity cell and a permeameter.

The surficial deep sea sediments are from 4-m-long Kastenlotgravity cores taken in the northeast Atlantic; they are described inTable 1 and are examined using a modified consolidometer cell.

Jackson's Porosity Cell

Jackson (1975) designed a novel porosity cell which enabled con-current formation factor and porosity values to be obtained for asand sample redeposited in the laboratory. The cell is describedin detail in that earlier publication and is shown schematically inFigure 2. By depositing a sample under water, using a technique

Table 1Deep Sea Clay Samples

SampleNo.

1

2

3

4

5

6

7

8

9

SedimentType

pelagic ooze

turbidite

turbidite

pelagic ooze

pelagic ooze

nanofossil turbidite

nanofossil turbidite

calcareous pelagicclay

calcareous pelagicclay

Mean GrainSize, 4>

8.9

9.4

9.3

8.9

10.3

9.7

8.9

9.2

10.0

Location

32 34.7'N22 27.5'W

32 34.7'N22 27.5'W

32 34.7'N22 27.5'W

32 34.7'N22 27.5'W

32 34.7'N22 27.5'W

31 33.2'N24 50.5'W

31 33.2'N24 50.5'W

30 22.0'N23 35.0'W

30 22.0'N23 35.0'W

SampleCode

D10406/1

D10406/3

D10406/7

D10406/11

D10406/20

S126/2-1

S126/2-4

S126/15-4

S126/15-11

Depth,cm

20

36

104

185

304

' 44

70

81

179

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Electrical Resistivity Measurements

40mm-51-

211

Water

Graduated cylinder

Sediment

70mm

Needle probe

— Electrode plate

FIGURE 2. Jackson's porosity cell.

shown by Kolbuszewski (1948) to produce a very loose packingstructure, and then gradually vibrating the cell to produce increas-ingly dense packings, Jackson found it was possible to produce agraph of formation factor against porosity for any one sample.

The electrical formation factor is determined using a four-elec-trode array mounted in two electrode plates, located on oppositesides of the cell chamber. Each plate contains a potential electrode.The plates are composed of a matrix of stainless steel screws (Figure3), each electrode constituting the alternate series of screws which

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Voltage electrode4mm. día. S.S. screw

65mm.

Current electrode6-5mm. dia. S.S.screw.

FIGURE 3. Electrode plate (porosity cell).

are wired in series to form a plate electrode; the pairs of opposingcurrent and potential electrodes are in turn connected in paralleland the complete arrangement is thus equivalent to a standardfour-electrode array.

The cell is slightly modified to accommodate a thermal conduc-tivity needle probe. In the present series of measurements the probewas inserted vertically through the base of the cell, although inser-tion horizontally through the wall allows for an analysis of thethermal anisotropy of a sample (Lovell, 1983, 1985).

Square Permeameter Cell

The square constant head permeameter effectively constitutes ahybrid of the porosity cell and a standard laboratory permeameter;the electrical resistivity is again measured horizontally using a sim-ilar style of electrode arrangement, while the permeability is mea-sured vertically. Both measurements relate to approximately thesame volume of material. Additionally, it is possible to introduce athermal conductivity needle probe into the cell horizontally. Figure4 shows the cell schematically, while Figure 5 shows a plan of an

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InletBreather valve

Outlet

Perforated plateGravel filter

Outlet tomanometer tube

•Electrode plate

Not to scale

FIGURE 4. Schematic section through square permeameter.

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Current electrode:face of plate coated withmetallic paint.

m

m

m

m

m

I7

m

m

m

m

m

m

m

m

m

m

— 75 mm.

/

<s> m

m m

• ^

m m

m mj

/

-Voltage electrode:2 mm. dia. SS screw.

FIGURE 5. Electrode plate (square permeameter).

electrode plate. The plates are similar in operation to the matrixelectrodes of the porosity cell; the potential electrode still consistsof a number of screws wired in series across the face of the plate,although the current electrode is the background surface throughwhich the potential screws protrude. This surface is electrically con-ducting silver paint and is insulated from the potential electrode.This modified design follows that used by Jackson in a triaxial cell(Schultheiss, 1982).

The Modified Consolidometer Cell

The choice of the consolidometer cell allows a clay sample to ex-hibit a range of decreasing porosities corresponding to increasesin applied vertical stress. The stress condition at a particular stage

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may in turn be equated to an effective depth in the sediment col-umn, while the consolidation results provide a measurement of thepermeability of the sample.

The main novelty of the modified cell (Figures 6 and 7) is itsconstruction, being manufactured almost entirely from polyvinylchloride (PVC), which effectively removes the conducting effect ofthe cell during electrical resistivity measurements on the sample.Within this basic design are contained piezoelectric transducers toenable measurement of the compressional wave velocity (1 MHz)and piezoelectric bimorph elements for measuring the shear wavevelocity of the sample. Each pair of transducers, one transmitterand one receiver, is located in a Perspex plate, which itself is locatedadjacent to the exterior faces of the porous discs, with respect tothe sample. An additional pair of piezoelectric compressional wavetransducers (1 MHz) is introduced into the cell wall, giving a hori-zontal propagation path. These transducers enable more accuratemonitoring of velocity variations over a fixed separation and allow

AXIAL LOAD

Face of disc painted withsilver metallic paint:current electrode

S.S. wire ring:potential electrode

Backing

Temperature probe

FIGURE 6. The modified consolidometer cell.

S wave bimorphcrystal

P wave crystals

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PVC. CUP.

S wavecrystal

POROUS DISC

P wavecrystal

S.S. wire ring:potential electrode

FACE OF TOP CAP

FIGURE 7. Plan view: top cap and base of modified consolidometer cell.

a simple assessment of any sound speed anisotropy. The inclusionof the piezoelectric crystals enables an assessment of the role ofpermeability and electrical formation factor in defining the com-pressional wave velocity; this is a separate part of the study and isreported elsewhere (Lovell and Ogden, 1983).

The inner surfaces of each of the Perspex plates is coated withelectrically conducting silver paint to form two current electrodes.Two potential electrodes, each in the form of a single circular stain-less steel wire, are located on the inner surfaces of the porous discs,the whole comprising a standard four-electrode resistivity measur-ing system.

The sample ring itself is also constructed of PVC. A hole in theside wall of the sample ring (approximately 0.8 mm diameter) en-ables the introduction of a thermal conductivity measuring needleprobe. The cell base is constructed with a slot cut away in the sidewall to enable the introduction with ease; a single thermistor probemay be inserted, if no needle is to be present, to enable the tem-perature of the sample to be monitored throughout the test.

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Suitable tests using conventional and modified cells show thereto be negligible effect on the consolidation behavior due to thepresence of the geophysical elements and no appreciable loss ofmaterial due to the introduction of the needle probe.

Electrical Resistivity Measurements

Each of the cells incorporates a four-electrode arrangement com-prising two current and two potential electrodes. An alternatingcurrent at a nominal frequency of 0.4 Hz (4 Hz) is supplied by anABEM SAS300 Terrameter (ABEM AC Terrameter), the voltageacross the sample being measured at the potential electrodes by apotentiometer integral to the instrument. The measurement is de-signed to give the resistance of the sample, which may in turn beused to compute the resistivity (or formation factor) through ageometrical constant which relates to the geometry of the electrodearrangement. Electrical resistivity measurements are, however, verysensitive to temperature. It is therefore important that the tempera-ture be monitored in each of the cells to enable corrections to bemade in computing the electrical resistivity or formation factor.

In defining the electrical formation factor of the surficial clayspecimens, the resistivity of the pore fluid is taken to be that of thebottom water at the location where the core was taken (KuUenberg,1952; Siever et al., 1965). Additionally, the electrical formation fac-tor values quoted are for a high conductivity pore fluid; in thepresence of such a fluid the particle surface conduction due to clayminerals will be minimal. This surface conduction effect, however,will become increasingly important if the pore fluid is less saline,and hence the results quoted here may not be validly extended tosuch low conductivity pore fluid materials.

Thermal Conductivity Measurements

Thermal conductivity measurements are made using the needleprobe technique whereby the temperature-log time slope for anunknown sample is compared with that for a calibrated standardof known thermal conductivity (Bloomer and Ward, 1979). Severe

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7 r

5 -

o

3 -

o. 2 -

Quartzsand

Increasing spread of sizes

FF=n

f Similar spread of sizes;g different meansh

i 100 V. shellj 70 V. »k 50 V. ••I 3 0 V. <•

m 0 V. ••

20 40

Porosity , '/..

60 80 100

FIGURE 8. Best fit Archie lines for artificially constructed range of quartz andshell sands.

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time restrictions are imposed on the needle probe used in the con-solidometer cell by the sample size, particularly at high axial loads.However, the results are considered to be accurate to within 7%.

Results

Electrical Formation Factor-Porosity

A detailed study of the formation factor-porosity relationship forclean marine sands using the porosity cell has been reported else-where (Jackson et al., 1978). The essence ofthat work showed thatsands obey Archie's law to a reasonable degree, with the exponentm decreasing with increasing sphericity of the particles. The valueof m varies from close to 2 for shelly sands to 1.5 for natural quartzsands. The results of this study confirm the earlier work (Figure 8)and while each individual sample is best represented by a separateequation, an expression describing all of the data in the form of athird-degree polynomial may be obtained:

n = 1.4154 - 0.4799(FF) + 0.067(FF)2 - 0.0033(FF)3

Measurements in the modified consolidometer on a suite of ninesurficial clays from the northeast Atlantic show each sample exhibitsan increase in formation factor with decreasing porosity (corre-sponding to increasing vertical stress). The nature of this relation-ship is linear for each particular sample when plotted on a log-logscale (Figure 9) and is best described after Winsauer et al. (1952):

FF = Cn~m

where m varies between 1.36 and 3.50 and C varies between 0.95 and1.25.

Plotting all of the individual linear relationships on one graphproduces the effect seen in Figure 10. However, examination of thedata points underlying these interpretations suggests the overalltrend is not linear (Figure 11) but is better expressed as a third-degree polynomial:

n = 1.3861 - 0.4626(FF) + 0.0833(FF)2 - 0.0073(FF)3

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3-5r

Sample No. 9.

3 0

20

55 60 65 70 75

Porosity. */•.

FIGURE 9. Electrical formation factor plotted against porosity for a single deepsea sample during a consolidation test.

This fit is similar to that of Kermabon et al. (1969). Boyce (1968)produced a linear fit along the lines proposed by Winsauer et al.(1952) for a small number (<50) of measurements on recent sedi-ments from the Bering Sea:

FF= 1.30H-1-45

A similar type of fit to the present data gives

FF= 1.29H-1-42

and the similarity between the two is remarkable.More recently, Boyce (1980) has published data for samples from

the Deep Sea Drilling Project (DSDP), and it is interesting to com-

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60 70 80

Porosity, */..

90 100

FIGURE 10. Electrical formation factor-porosity data for nine deep sea sedi-ment samples; each interpreted individually as FF = Cn~m.

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3 0

2-5

2 0

V5

10

-(Boyce. 1968.)

-(Taylor Smith. 1971.)

"3rd. degree polynomial

( Kermabon , 1969.)

60 70 80

Porosity. */..

90 100

FIGURE 11. Electrical formation factor plotted against porosity for all nine sedi-ments, interpreted as a single function.

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o

Formation factor.1 2 3 4 5

80

120

o160

200

240

280

. • * x Boyce 1980 (DSDP)

• «f • Sample Nos. 1-9.

• •x

x

f. - •• xX

X

X

X

X

X

X

X

X

X

X

FIGURE 12. Electrical formation factor plotted against consolidometer effectivedepth for the deep sea sediment samples. Also plotted are DSDP data (Boyce,1980).

pare the results for natural sediments from depth in the sedimentcolumn with those of this study, where variations in depth arecrudely reproduced in the consolidometer. Figure 12 shows theresults for both sets of measurements plotted against depth, whileFigure 13 shows the functions describing both sets of data in termsof their porosity relationships. At high porosities the data agreereasonably well with published values for recent sediments. For the

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= n-2-o

30

Boyce, 1980 (OSDP data)

Surficiat sediment suite

(Equation 4.21.)

50 60

Porosity.

70 80 90 100

FIGURE 13. Electrical formation factor plotted against porosity for the deep seasediments. Also plotted are DSDP data (Boyce, 1980).

low porosity measurements, however, where the consolidometer at-tempts to artificially create the conditions at depth, the formationfactor values fall on the low side for similar in-situ porosities; i.e.,the electrical resistivity of the in-situ sample is greater than that

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of the equivalent laboratory-consolidated sample. The differencemay be explained in terms of the comparatively open structure ofthe laboratory sample and the lack of any bonding or cementationwhich may occur in situ. Additionally, if the sediment is anisotropic,then this difference may exceed that shown here since the DSDPformation factors relate to the horizontal direction while the mea-surements for this study relate to the vertical direction. In a singlevertically anisotropic sample the horizontal formation factor wouldbe expected to be less than the vertical.

Electrical Formation Factor-Permeability

An analogy between electrical flow and fluid flow has been con-sidered plausible by numerous authors, although the precise natureof any interrelationship between the two has proved elusive.

Plotting formation factor-permeability as a log-log relationshipfor the sand samples shows a linear trend for each sand sample(Figure 14), suggesting there exists a relationship between the twosimilar to that of Brace (1977),

$ = C{FF)~X

where

C = h2/kh = hydraulic radiusk = shape factor (2-3)$ = permeability

The results for such plots are tabulated in Table 2 and show thatboth C and x increase with decreasing sphericity of the particleshape. For an increasing spread of sizes C decreases and x increases.The coefficient C appears to be a function of the pore size, both interms of the equation of Brace (1977) (and, earlier, Wyllie andSpangler, 1952) and these results; with increasing spread of sizes,C decreases as the pore space volume decreases (decreasing n, in-creasing FF), while a decrease in sphericity of the particles towardsplate-like grains opens out the structure (increasing n, decreasing

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5 0

1 0

0 5

0 1

005

0 01

0005

Y

Data corrected to 20*C.

Quartzsand

4 a

a bIncreasing spread of sizes

Ddo e* f Similar spread of sizes;og different means»h

• i 100 V. shellSand/ ,shell J ' i 70 •'•

mixtures] * ' 3 0 '<'I • m 0 V.

o ^

V

\ . . . .

; A

x^

\8

\

\ X

2 t*

Apparent Formation Factor

8 10

FIGURE 14. Permeability plotted against formation factor for artificially con-structed range of quartz and shell sands.

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Table 2Permeability (<f>)-Formation Factor (FF)

Regression Lines for Sand Samples(<f> = C(FF)-*).

SampleNo.abcdef, mghijk1

C0.10690.08510.08920.06950.83470.05520.04570.00560.84830.0966

—0.2743

X

2.96322.98603.24233.29473.21602.23443.23412.81416.37463.5308

—3.9109

R0.980.990.990.980.980.970.980.990.940.95—

0.99

FF) and hence C increases. The exponent x, meanwhile, increaseswith both decreasing sphericity and increasing spread of sizes. Indeveloping his model from that of Wyllie and Spangler (1952)through Archie's law, Brace (1977) attaches a dependence of x onthe exponent in Archie's law. This would suppose a certain depen-dence on the shape of the particles, x increasing with decreasingsphericity: this is upheld by the results presented here.

The results for the surficial deep sea sediments again providelinear plots on a log-log scale (Figure 15). The results for leastsquare regression lines for each sample are presented in Table 3and segregate the samples according to each of three cores. Unfor-tunately no particle shape or mineralogical data are available forthe samples.

The dominant effect may not be associated with the initial phys-ical state of the sample (void ratio, e0, values being ungroupedby these divisions), but may rather be connected with the particlearrangements. Such particle shape effects are supported by the sandsdata and also by the physical descriptions of each core being dif-ferent, and may be due to mineralogical variations.

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3-5r

3 0

2 5

»i

20

1-5

10

59 4 8

S

8 5

89

\ \

6 74

3 6 1 ,I

3

3

10-10 10-9 10-8

Permeability, m/s

FIGURE 15. Electrical formation factor plotted against permeability for the deepsea sediments.

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Table 3Permeability ((j>)-Formation Factor (FF)

Regression Lines for Deep SeaClay Samples (<j> =

SampleNo.

13456789

C(10~6)

3.51411.50013.71399.45690.56093.78280.02540.1123

X

9.54439.68139.33839.2878

10.842412.34946.39037.5583

R0.980.990.990.980.990.990.960.98

Thermal Conductivity-Porosity

Measurements of thermal conductivity in the sands are made withthe needle oriented vertically in the porosity cell, while measure-ments in the permeameter are for the needle oriented horizontally.Figure 16 shows a log-arithmetic plot of thermal conductivityagainst porosity. This shows a general adherence of the data to thegeometric equation (Sass et al., 1971) relating the total or bulk ther-mal conductivity kb to the thermal conductivities of the components:

where

ks = thermal conductivity of solid particleskw = thermal conductivity of pore fluid

The majority of the data relate to quartz sands and are adequatelydescribed by the equation (least-squares fit):

/c2, = 8.58(1-|"0.64(n)

where fcquartz = 8.58 W/mK and fewater = 0.64 W/mK. The value ofquartz compares very well with the range of values quoted by Clark(1966), although the value for water represents a 7% error at most.

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230

50

40

^ 30

Michael Anthony Lovell

2 0

10

0-9

100 V. quartzKo- 8-58 W/mK

10 20 30 50 60 70Porosity , '/..

FIGURE 16. Thermal conductivity plotted against porosity for sands of differentparticle shapes and sizes.

The pure shell sand data is fitted by this two-component modelusing a value for the solid's thermal conductivity of 3.32 W/mK,the quartz/shell mixtures falling between the two, though closer tothe data for quartz sands.

Measurements on the surficial deep sea clays are for pre-andpost-loading conditions, although where it was possible to insertthe needle probe under load conditions measurements were alsoattempted. Figure 17 is a plot of log thermal conductivity-porosity,

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1-4

1-2

• 0-8

T3COu

0-6

£ 04

+ Seawater

0 20 40 60 80 100Porosity, •/..

FIGURE 17. Measured thermal conductivity plotted against porosity for thedeep sea sediments.

the linear trend suggesting adherence to the geometric model again.A least squares regression analysis provides conductivity values of2.01 W/mK for the solids and 0.63 W/mK for the pore fluid. Thevalue for the solids compares with 2.9 W/mK for minerals otherthan quartz, and 0.25 W/mK for organic matter (Hillel, 1980), whilethe value for water represents a maximum consistent error of 5%.

Any analysis of the data with effective depth is made difficult bythe small number of data points at pressure. From the data avail-able it is feasible, however, to suggest that there is no measurableeffect beyond the reduction in void ratio (porosity) and hence watercontent.

Bullard and Day (1961) found the thermal resistivity R (the re-ciprocal of the thermal conductivity) to be linearly related to thewater content:

R = l/fc = (161 ± 14) + (651 ± 30)w

This equation has been used to compute the thermal conductivitiescorresponding to the porosities at which measurements were made

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o

1-2r

1-1

g

¡vi1

con

du

ct

"oE

the

ite

da

lcu

lc

1 0

09

0-8

0-7

0-60 6 07 0-8 09 10 VI

Measured thermal conductivity, W/mK.

1-2

FIGURE 18. Predicted thermal conductivity plotted against measured thermalconductivity for the deep sea sediments. (Prediction from Bullard and Day, 1961.)Slope of line is 1.

for the clays; Figure 18 is a plot of computed against measuredconductivities with a line of slope = 1 also drawn. The agreementis reasonably good considering the errors in both the measuredand computed values.

Thermal Conductivity-Electrical Formation Factor

The electrical formation factor has been shown to exhibit an ap-parently unique relationship with porosity for each of the sandsand clays studied (Figures 8 and 10), while a general equation may

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• Needle horizontalx Needle vertical

50

4-5

40

3 5

3 0

1

2 0

1-5

1 0 -

K w - 0 61 W/mK.100*/. quartz

KQ- 8-58 W/mK.

3 4Formation (actor

100V. carbonateKc-3-32 W/mK.

FIGURE 19. Thermal conductivity plotted against formation factor for the arti-ficial sand samples.

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describe each suite of samples together. By combining an equationrelating formation factor with porosity and the geometric equationrelating thermal conductivity to porosity, it is possible to achievean equation relating thermal conductivity to electrical formationfactor; this analysis is similar to that of Hutt and Berg (1968) whounsuccessfully attempted to relate electrical measurements using atwo-electrode array to thermal conductivity for marine sediments.

Figure 19 is a plot of formation factor-thermal conductivity forthe sand samples. Two features are apparent; first, there is a rela-tionship between the two parameters and second, there is a cleartendency for the measurements with the needle oriented horizon-tally and vertically to separate out. The model fit is obtained bytaking the two extremes of Archie's law for sands and combiningthem with the two extremes of the geometric model (pure quartzand pure shell sand). The evident anisotropy exhibited by the mea-surements with the needle probe oriented in two mutually per-pendicular directions suggests a directional dependence exists forthermal conductivity in sands; this is discussed in detail elsewhere(Lovell, 1983, 1985).

POLYNOMIALe - GEOMETRICt

l -2r

E

* 10

>

| 0-8

5

0-6

10 1-5 20 2-5 30 3-5

Formation factor.

FIGURE 20. Measured thermal conductivity plotted against electrical formationfactor for the deep sea sediments. The model is based on combining the geometric(k) and polynomial (FF) equations with porosity.

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For the surficial clays Figure 20 is a plot of thermal conductivityagainst electrical formation factor with a model fit based on apolynomial formation factor-porosity fit combined with the two-component geometric model. Figure 21 is a plot of measured ther-mal conductivity against predicted thermal conductivity based onthis model.

Conclusions

Thermal conductivity in both clean saturated sands and deep seaclays is dependent on the water content of the sample. For a fully

1-2r

£

10

u

f 0-985

£ 0 8

0 7

0 606 07 08 0-9 10 1-1

Measured thermal conductivity, W/mK.

1-2

FIGURE 21. Predicted thermal conductivity (polynomial-geometric,) plottedagainst measured thermal conductivity for the deep sea sediments. Slope of lineis 1.

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saturated sediment this dependence may be expressed in terms ofthe porosity of the sample. In deep sea clays the conductivity maybe adequately described by the empirical equation of Bullard andDay (1961), while the geometric equation (Sass et al., 1971) predictsthe conductivity for both sands and clays on the basis of porosity.The successful use of the latter equation for porous systems ofspherical and lamellae particles has been demonstrated.

Thermal conductivity may be predicted using electrical (resistiv-ity) formation factor measurements through the common relation,porosity (see below). For deep sea clays the use of the third-degreepolynomial describing the electrical relationship with porosity to-gether with the geometric thermal equation provides an acceptableprediction, while for clean sands individual Archie-type fits (electric)combined with the geometric (thermal) equation are best.

For deep sea clays, each sample produces a linear trend on alog-log plot of formation factor-porosity, representing the changein formation factor with mechanical loading (producing decreasingporosity values). Each of these trends may be described by an em-pirical equation (Winsauer et al., 1952):

FF = Cn~m

where m varies between 1.36 and 3.50 and C varies between 0.95and 1.25.

A plot of all the data points, however, suggests the overall rela-tionship between formation factor and porosity is not linear but isbetter represented by a third-degree polynomial:

n = 1.3861 - 0.4626^) + 0.0833(KF)2 - 0.0073(i=T)3

For clean saturated sands, porosity exhibits a linear relationshipto electrical formation factor when plotted on a log-log scale. Eachsample may be described by Archie's empirical law:

FF = n~m

where m varies between 1.9 for lamellae-shaped particles to 1.4 forequidimensional quartz grains. The range of quartz and shell sands

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studied may also be expressed, though not as well, in terms of athird-degree polynomial:

n = 1.4154 - 0.4799(FF) + 0.0687(FF)2 - 0.0033(FF)3

Permeability shows a linear relationship with electrical forma-tion factor for clean saturated sands when plotted on a log-logbasis:

<|> = C(FF)-X

This empirical equation allows permeability to be predicted towithin an order of magnitude. Both C and x increase with de-creasing sphericity of the particles, while for increasing spread ofsizes C decreases and x increases. The coefficient C would seem tobe a function of the pore size, while x can be shown to exhibit acertain dependence on the exponent m in Archie's empirical lawrelating formation factor to porosity. The coefficient would thusbecome a function of the particle shape, or, indirectly, pore shape.

Permeability-electrical formation factor measurements on cleansands show a clear repeatability which suggests that the relation-ship between the two is single-valued for any one sample depositedin the same manner.

Consolidometer-derived permeability values for deep sea claysexhibit a linear relationship on a log-log basis with electrical for-mation factor. Individual least square fits produce similar equa-tions for each member of a core sequence. It is suggested that thedominant effect may be particle shape, influenced by mineralogythrough the adsorption properties of the particle structure. Em-pirically, the equations allow permeability to be predicted to withinan order of magnitude.

Acknowledgments

An examination of this nature inevitably calls on the resources of a largenumber of colleagues and support staff. The many contributions to theproject are innumerable and varied in extent, but the total help affordedis considerable and is gratefully acknowledged by the author. I am par-ticularly indebted to Mr. D. Taylor Smith for his guidance and support

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throughout the project and for critically appraising the original manu-script. I am also grateful to Dr. R. Penny for help with preliminary workon the sand samples, to Dr. J. Bloomer who introduced me to the geo-metric equation, to Dr. P. Schultheiss for providing the deep sea samples,and to both him and Dr. P. Jackson for informative discussions. Mr. P.Ogden designed the electronics for the modified consolidometer, whileMr. F. Dewes drafted the illustrations. This work has been supported bya NERC studentship, a grant from British Petroleum, and a joint researchcontract from the European Atomic Energy Community and the Depart-ment of the Environment.

References

Akroyd, T. N. W. 1964. Laboratory testing in soil engineering, geotechnical mono-graph No. 1. Bracknell: Soil Mechanics Ltd.

Archie, G. E. 1942. The electrical resistivity log as an aid in determining somereservoir characteristics. Transactions of the American Institute of Mining andMetallurgical Engineers 146:54-62.

Bloomer, J. R., and J. Ward. 1979. A semi-automatic field apparatus for the mea-surement of thermal conductivities of sedimentary rocks. Journal of Physics,Section E, 12:1033-35.

Boyce, R. E. 1968. Electrical resistivity of modern marine sediments. Journal ofGeophysical Research 73:4759-66.

Boyce, R. E. 1980. Determination of the relationships of electrical resistivity, soundvelocity, and density/porosity of sediment and rock by laboratory techniquesand well logs from DSDP sites 415 & 416 off the coast of Morocco. InitialReports of the Deep Sea Drilling Project, 50:305-18.

Brace, W. F. 1977. Permeability from resistivity and pore shape. Journal of Geo-physical Research 82:3343-49.

Brace, W. F., A. S. Orange, and T. R. Madden. 1965. The effect of pressure on theelectrical resistivity of water saturated crystalline rocks. Journal of Geophysi-cal Research 70:5669-78.

British Standards Institution. 1961. Methods of testing for civil engineering pur-poses, B.S. 1377. London: Her Majesty's Stationery Office.

Brown, R. J. S. 1980. Connection between formation factor for electrical resistivityand fluid-solid coupling factor in Biot's equations for acoustic waves in fluid-filled porous media. Geophysics 45(8): 1269-75.

Bruggeman, D. A. G. 1935. Berechnung verschiedener physikalircher Konstantenvon heterogenen Substanzen. Annalen der Physik (Leipzig) 24:636-79.

Bryant, W. R., R. H. Bennett, and C. E. Katherman. 1981. Shear strength, con-solidation, porosity, & permeability of oceanic sediments. In The Sea. Vol.7.The Lithosphere, 1555-616. New York: John Wiley and Sons.

Bullard, E. C., A. E. Maxwell, and R. Revelle. 1956. Heat flow through the deepsea floor. Advances in Geophysics 3:153-81.

Bullard, E. C., and A. A. Day. 1961. The flow of heat through the floor of the

Dow

nloa

ded

by [

Tex

as S

tate

Uni

vers

ity -

San

Mar

cos]

at 0

7:31

30

Apr

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Atlantic Ocean. Geophysical Journal of the Royal Astronomical Society (TheEarth Today) 4:282-92.

Clark, S. P. (ed.) 1966. Handbook of Physical Constants. Memoir 97. New York:The Geological Society of America, Inc.

Hamdi, F. A. I. 1981. Variations of seismic velocity with depth in near surfacemarine sediments and their engineering significance. Ph.D. thesis, Universityof Wales, U.K.

Hillel, D. 1980. Fundamentals of Soil Physics. London: Academic Press.Hutt, J. R., and J. W. Berg. 1968. Thermal and electrical conductivities of sand-

stone rocks and ocean sediments. Geophysics 33:489-500.Jackson, P. D. 1975. An electrical resistivity method for evaluating the in-situ

porosity of clean marine sands. Marine Geotechnology 1(2):91-115.Jackson, P. D., D. Taylor Smith, and P. N. Stanford. 1978. Resistivity-porosity-

particle shape relationships for marine sands. Geophysics 43:1250-68.Kermabon, A., C. Gethin, and P. Blavier. 1969. A deep-sea electrical resistivity

probe for measuring porosity and density of unconsolidated sediments. Geo-physics 34:554-71.

Kolbuszewski, J. J. 1948. An experimental study of the maximum and minimumporosities of sands. In Vol. 1 of Proceedings of the 2nd International Con-ference on Soil Mechanics and Foundation Engineering, 158-65. Rotterdam,Delft: Secretary to the Conference.

Kullenberg, B. 1952. On the salinity of the water contained in marine sediments.Paper 21. Goteborg, Sweden: Meddelanded fran Oceanographiska Institut iGoteborg.

Lovell, M. A. 1983. Resistivity-thermal conductivity-porosity relationships formarine sediments. Ph.D. thesis, University of Wales, U.K.

Lovell, M. A. 1985. Thermal conductivities of marine sediments. Submitted toQuarterly Journal of Engineering Geology 18(3) (London) (May 1984).

Lovell, M. A., and P. Ogden. 1983. Remote assessment of permeability/thermaldiffusivity of consolidated clay sediments. Report to the European AtomicEnergy Community. Brussels: EUR- series, Report no. EN 9206, 1984.

Mitchell, J. K., and J. S. Younger. 1967. Abnormalities in hydraulic flow throughfine-grained soils. In Permeability and Capillarity of Soils, Special TechnicalPublication 417, 106-39. Philadelphia: American Society for Testing andMaterials.

Nickerson, C. R. 1978. Consolidation and permeability characteristics of deep seasediments: North Central Pacific Ocean. M.Sc. thesis, Worcester PolytechnicInstitute, Worcester, Mass.

Ratclifle, E. H. 1960. The thermal conductivity of ocean sediments. Journal ofGeophysical Research 65:1535-41.

Rayleigh, J. W. S. 1982. On the influence of obstacles arranged in a rectangularorder upon the properties of a medium. Philosophical Magazine IV, Series 5.34:481-502.

Sass, J. H., A. H. Lachenbruch, and R. J. Munroe. 1971. Thermal conductivity ofrocks from measurements on fragments and its application to heat-flow de-terminations. Journal of Geophysical Research 76:3391-401.

Dow

nloa

ded

by [

Tex

as S

tate

Uni

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ity -

San

Mar

cos]

at 0

7:31

30

Apr

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Schopper, J. R. 1966. A theoretical investigation of the formation factor/perme-ability/porosity relationship using a network model. Geophysical Prospecting14:301-41.

Schultheiss, P. J. 1982. The influence of packing structure on seismic wave ve-locities in sediments. Ph.D. thesis, University of Wales, U.K.

Siever, R., K. Beck, and R. A. Berner. 1965. Composition of interstitial waters ofmodern sediments. Journal of Geology 73:39-73.

Taylor Smith, D. 1971. Acoustic and electric techniques for sea floor sedimentidentification: In Proceedings of International Symposium on EngineeringProperties of Sea Floor Soils and Their Geophysical Identification, 235-67.Seattle.

Terzaghi, K. 1943. Theoretical Soil Mechanics. New York: John Wiley and Sons.Von Herzen, R. P., and A. E. Maxwell. 1959. The measurement of thermal con-

ductivity of deep-sea sediments by a needle probe method. Journal of Geo-physical Research 64:1557.

Winsauer, W. O., A. M. Shearin, P. H. Masson, and M. Williams. 1952. Resistivi-ties of brine saturated sands in relation to pore geometry. Bulletin, AmericanAssociation of Petroleum Geologists 36:253.

Worthington, P. F. 1973. Estimation of the permeability of a Bunter sandstoneaquifer from laboratory investigations and borehole resistivity measurements.Water and Water Engineering July: 251-57.

Wyllie, M. R. J., and M. B. Spangler. 1952. Application of electrical resistivitymeasurements to the problem of fluid flow in porous media. Bulletin of theAmerican Association of Petroleum Geologists 36:359-403.

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thermal conductivity and permeability assessment by electrical resistivity measurements in marine...

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