An electrical resistivity method for evaluating the in‐situ porosity of clean marine sands

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An electrical resistivity method for evaluating the in‐situporosity of clean marine sandsPeter Douglas Jackson aa Dept. of Physical Oceanography, Marine Science Laboratories, University College of NorthWales, Menai Bridge, Gwynedd, U.K.Published online: 23 Dec 2008.

To cite this article: Peter Douglas Jackson (1975): An electrical resistivity method for evaluating the in‐situ porosity of cleanmarine sands, Marine Geotechnology, 1:2, 91-115

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An Electrical Resistivity Methodfor Evaluating the In-Situ Porosityof Clean Marine SandsPETER DOUGLAS JACKSON*

Abstract A well-known parameter in electrical bore-hole loggingis the formation factor (formation resistivity/pore-water resistivity)and its relationship to formation porosity (or void ratio). This inturn can be used to give an assessment of the foundation character-istics of a saturated sand. To use this relationship in marine sedimentinvestigation's, a device has been constructed which measures theresistivity of a seafloor sand by passing a focused current into thesediment from a superior position, rather than by physically pene-trating the sediment with an electrode array which would inevitablyproduce a mechanical disturbance. At present, the investigated depth(which is a function of the size of the electrode array) relates to azone within 0.5 m of the water-sediment interface. Knowing thesediment resistivity, the formation factor can be determined from aseparate assessment of the pore-water resistivity. The formationfactor is empirically related to the porosity of the sand by means ofa graph prepared from measurements made in a formation factor-porosity cell, which allows both parameters to be determined simul-taneously throughout a range of packing conditions. From thedetermination of in-situ porosity the relative density of the sand canbe subsequently calculated.

IntroductionThe present-day projection of hydrocarbon reserves shows that by the last

decade of this century half of the world's total oil and natural gas, produced bynoncommunist countries, will be obtained from wells in offshore areas; and thatproduction will be considered in water depths approaching 3000 m. If theseprojections are to be realized, a revolution in seafloor technology is an urgentnecessity; of particular importance is the establishment of techniques of geotech-

*Dept. of Physical Oceanography, Marine Science Laboratories, University College of NorthWales, Menai Bridge, Gwynedd, U.K.(Received March 3, 1975; Revised May 27, 1975.)Marine Geotechnology, Volume 1, Number 2Copyright © 1975 Crane, Russak & Company, Inc.

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9 2 PETER DOUGLAS JACKSON

nical site investigation for the emplacement of civil engineering structures on theseafloor.

In an area such as the North Sea, a whole range of sediment grades, fromgravels to muds and clays, exists as the foundation material. Undisturbed sam-pling, particularly with the coarser grades of sediment, is almost impossible. Thepresent-day procedure with sands, in the absence of any exploration platform, isto collect as good a sample as possible and to use a cone penetrometer from aremotely operated in-situ device (Taylor Smith, 1975). Cone penetrometers,however, suffer from the fact that the ground has to be displaced ahead and tothe side of the cone-head to accommodate it; this casts some doubt on thereliability of the results.

As the electrical resistivity of a sand is affected by its state of compaction,and as it should be theoretically possible to measure the depth variation of thisquantity without penetrating the sediment, a device could be constructed toovercome the objections to penetration testing. This paper describes in-situ andlaboratory experiments, with one such device, to measure the in-situ porosity (orvoid ratio) of a clean sand (i.e., less than 1% silt-clay fraction), and to subse-quently assess its relative density.

Electrical Resistivity of Porous MediaWhen an electric current passes through a porous medium, such as a quartz

sand, most of the conduction is via the pore fluid, for the mineral grainsthemselves are insulators. As resistivity is defined as the resistance of a cube ofmaterial, with the current flowing normally to one face, the resistivity of aporous medium is dependent on the percentage of the cube that is pore space,and the way that these spaces are interconnected. Thus it is to be expected thatporosity and permeability can be correlated in some way to electrical resistivity.The measurement of the electrical resistivity of the porous medium should bemade in a manner that eliminates the value of the resistivity of the pore fluid(since it is the structure of the medium that is of interest and not the pore fluid);to this end the resistivities are converted to a parameter called Formation Factor(FF), where

_ resistivity of the porous mediumresistivity of the pore fluid

The literature is extensive on the use of this quantity in the assessment of theporosity of oil-bearing rocks (Archie, 1942; Winsauer et al., 1952) and hasrecently been used to examine the in-situ porosity of marine sediments (Boyce,1968; Kermabon et al., 1969; Taylor Smith, 1971 ; Erchul and Nacci, 1972).

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EVALUATING THE IN-SITU POROSITY OF CLEAN MARINE SANDS 93

A problem does exist in the assessment of the resistivity of the pore fluid. Insurficial marine sediments it has been shown that the salinity of the pore watersvaries little from that of the overlying seawater (Kullenberg, 1952;Siever et al.,1965). Thus the resistivity of the pore fluid can be assumed to be equal to thatof the seawater above. However, the effective resistivity of the pore fluid can bealtered by ion-exchange phenomena in clay-rich sediments, and also by a processcalled surface conduction, where water molecules are absorbed onto the surfaceof individual grains, making them conductive (Brace et al., 1965; Keller andFrischknecht, 1966). Brace et al. (1965) have shown that surface conduction,which is pronounced in fine-grained rocks of low porosity, is negligible when thepore fluid resistivity has a magnitude similar to that of seawater. Thus, for cleansands, the formation factor can in theory be measured in situ.

As stated earlier the relationship between formation factor and porosity hasbeen extensively studied and most authors end up with an empirical equation ofthe form (Winsauer et al., 1952):

where a and m characterize the rock, and n is the porosity (volume of porespace/total volume). It is important to note that this equation was obtainedusing data on porous rocks, where undisturbed sampling is possible, allowingboth the formation factor and porosity to be measured exactly. The aboveequation cannot be applied with the same success to sands because the in-situformation factor and porosity are almost certainly altered during the samplingprocess. Empirical relationships between F F and porosity have been producedfor marine sands (Kermabon et al., 1969; Taylor Smith, 1971); however, thespread in their results was rather large, commensurate with the uncertainty inthe measurement of FF and n.

For assessments of relative density it is essential that the in-situ porosity (orvoid ratio, see Appendixl.p. 115) is known precisely. This can only be achieved bycollecting a representative sample of the sediment, and assessing the variations offormation factor with packing in the laboratory, allowing an FF/n curve to beplotted for the sample concerned. Knowing the in-situ formation factor thein-situ porosity (and void ratio) can be read off the FF/n curve, from which therelative density may be calculated.

In-Situ Measurements of Electrical ResistivityMost methods used to study the electrical resistivity of marine sediments are

based on the standard techniques which have been used for decades in geophysi-cal prospecting on land, and on later modifications that have been used in the

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9 4 PETER DOUGLAS JACKSON

electrical logging of bore holes. The basic principles behind these methods arewell known and many good reviews exist in the geophysical literature, such asthose by Kunetz (1966), Keller and Frischknecht (1966), and Parasnis (1972).In essence, the technique consists of a four-electrode array which passes a director low-frequency alternating current of known intensity through two electrodesinto the ground, while measuring a potential difference between the other twoelectrodes. Separate potential electrodes are necessary to overcome the effects ofcontact impedances at the current electrodes, and to ensure that the potentialdifference variations are as representative of the ground resistivity variations aspossible.

Using such a system, the resistivity of the medium is calculated from the ratioof the potential difference to the current passing, and from a proportionalityfactor which depends on the geometrical arrangement of the four electrodes. Inone widely used configuration, the Wenner array, the electrodes are in-line andequispaced at a distance a apart; if the two outer electrodes pass a current / andthe two inner ones measure a potential difference AV, the resistivity of themedium is given by

p = 2 na-AV/I.

This expression represents a true resistivity only when the medium is homoge-neous, isotropic, and semi-infinite. For all other cases it represents an apparentresistivity being an average assessment of a heterogeneous sediment possiblycontaining many layers. For a two-layer case, when a is small most of the currentpenetration is shallow and the resistivity measured is that of the surface layer;while at larger electrode separations the effective penetration of the current isdeeper and the measured value tends towards the resistivity of the lowermedium.

To determine the formation factor a separate measurement of the pore-waterresistivity is required. In investigations of a seafloor sediment, using a Wennerarray which is arranged to pass constant current, for reasons given earlier it isassumed to be sufficient to measure the potential difference (Vw) when theelectrodes are surrounded by water, and again when they are in contact with thesediment (Vs); the ratio of the two, VJVW> gives the formation factor of thesediment. It is an "apparent formation factor" as its value can be altered byvertical and lateral changes in composition of the medium beneath the elec-trodes; these changes can be of diagnostic value.

The Effects ofSeawater on Resistivity MeasurementsIn land observations, the measurements are usually made with the electrodes

at the surface of the ground, which is overlain by an insulator (i.e., air). Seafloor

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EVALUATING THE IN-SITU POROSITY OF CLEAN MARINE SANDS 9 5

investigations, in contrast, suffer from the fact that the overlying medium is agood conductor (seawater). However, even with this considerable disadvantage,resistivity measurements have been made using a simple four-electrode array, thisbeing towed either at the sea surface or dragged along the seabed (Schlumbergeret al., 1934; Bogoslovsky and Ogilvy, 1974). The effect of conducting seawateris to give an apparent resistivity (of the seabed) much less than the true value.For example a Wenner array with an electrode separation of 100 m (i.e., a = 100m) towed at the surface of a 50 m depth sea (resistivity 0.25 S2-m) wouldregister only a relatively small change when passing over sediments of contrastingresistivities. In this example, the measured change in resistivity would be from0.37 to 0.47 i2-m while, passing from clay of true resistivity 0.5 S2-m to sand ofresistivity 1.25 i2-m. In addition, the low value of the resistivity of seawaterwould make it necessary to pass a very high current (over 100 A) to produce apotential difference greater than 500 mV between the potential electrodes.

Usually, in common with normal geophysical prospecting an alternatingcurrent is used, the frequency of which is a compromise between two conflictingeffects: the skin depth phenomenon, and polarization of the current electrodes.The skin depth is defined (Kunetz, 1966) as the depth at which the currentdensity is reduced to about one third of its expected DC value, and is inverselyproportional to the square root of both the frequency of alternation and theconductivity of the medium. For example, in seawater (resistivity 0.25 £2-m)passing a current alternating at 1000 Hz, the skin depth would be 7 m; a muchlower frequency would be required to increase the current penetration. Polariza-tion is caused l>y the movement of charged particles (ions) through the porefluid towards the current electrodes, eventually producing a cloud of chargedparticles around them. This cloud of charge tends to inhibit any further flow ofions, and in the present context is regarded as a contact impedance. For a DCcurrent, the polarization increases with time, the final result being electrolysis.The use of an alternating current stops electrolysis and limits polarization. Thefrequencies used in practice are usually in the range 4 to 40 Hz, which minimizesthe detrimental effects of the skin depth phenomenon and polarization of thecurrent electrodes.

Previous In-Situ ProbesSome of the first measurements of electrical resistivity of marine sediments

were made, in the laboratory, on cores taken from soft clays (Boyce, 1968).Kermabon et al. (1969) described a free-falling probe that.penetrated unconsoli-dated sediments, with a Wenner array in the nose. The probe was designed topenetrate up to 10 m and to measure the apparent resistivity, as it was extracted,by pushing the electrodes outwards against the sediment to ensure good contact.Bouma et al. (1971) and Kermabon (1972) have described penetrating probes

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96 PETER DOUGLAS JACKSON

that employed a focusing system based on the Laterolog 3 (Doll, 1951). Thebasic principle employed in this focusing system (which is common to the othersystems discussed) is best illustrated by referring to Figure 1. The electrodes aredepicted in a vertical Une, as in the case of electrical bore hole logging. Thecurrents from the outer guard electrodes (7lf l¡ and I2, h in Figure 1) arecontrolled in such a manner that there is zero potential difference between theirrespective potential (balancing) electrodes (XY, X'Y', and CD, CTZ-see Figure1). The current 70 is forced to flow in a direction normal to the electrode pad by

OSCILLATOR LOGICCONSTANTCURRENTSOURCE

VOLTAGE

MEASUREMENT

DIGITAL

VOLTMETER

INDEPENDENT CURRENT CONTROLLER,used in focussing.

rIo

HJSonim

The last quarter cycle is sampled.

Figure 1. The electronic system showing the mode of operation and themethod of measurement together with the principle of the focusing technique.

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EVALUATING THE IN-SITU POROSITY OF CLEAN MARINE SANDS 9 7

the guard ring currents (J l t Is and 72, 76), this being indicated by the zeropotential difference existing between the balancing electrodes. This currentfocusing forces Io directly into the sediment, minimizing the effects of a thinconductive layer next to the electrodes. For the Laterolog 3, voltage measure-ments are made at current electrodes, and therefore any contact impedances(which are shown later to be large in marine investigations) will be included inthe results. Other focusing systems such as the Laterolog 7 or the microlaterolog(Doll, 1951 and 1953) have separate potential electrodes and do not suffer fromthese effects. Erchul and Nacci (1972) described a resistivity probe based on aconventional corer with a Wenner array inside the core barrel, and a focusingelectrode array identical to the microlaterolog on the outside of the barrel. Thefocusing was designed to limit the volume into which the current flowed, theauthors claiming that this was necessary to reduce the error in the apparentformation factor. It is not clear how satisfactorily this was achieved sincesampling a small volume increases the effects of small, local changes in thecomposition of the sediment which may be caused by disturbance duringpenetration.

The above probes are penetrating, and can only be used in very soft sedimentssuch as clays. Coarser sediments such as sands and gravels are impossible topenetrate using conventional corers or probes. Williams (1970) described a probethat lay directly on the sediment. The electrodes were embedded in a rigidinsulator and they consisted of a ring electrode, and a hemispherical one, thehemisphere being at the center of the ring. However, there was no method ofeliminating the effects of a water layer between the electrodes and the sediment.

A Flexible In-Situ Resistivity ProbeA flexible, focused, in-situ resistivity probe has been designed to lie on the

seafloor without penetrating the sediments. Its function is to measure theapparent formation factor of the surficial sediments without disturbing them.The probe consists of a large, thin, insulator with an electrode array embeddedin its.underside. The insulator is flexible in order to minimize the thickness ofthe water layer between the electrodes and the sediment; the current is focusedin an attempt to minimize the effect of conduction in this water layer.

The electrodes have been fabricated using stainless steel rings partly em-bedded in two grooved plexiglas disks; these disks have been machined in such away that when they are attached to the rubber insulator, the electrodes,plexiglas, and rubber are flush with one another (Figure 2). The rubber sheet isvery much larger than the electrode separation ensuring that the electrodes arebacked, to all intents and purposes, by an infinite insulator. Laboratory measure-ments using a model probe indicated that the insulator must be at least 2.3 times

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the length of the electrode separation to keep the error inherent in the assump-tion of an infinite insulator below 2%.

The electrode configuration (Figures 2 and 3) contains a focusing devicebased, in principle, on the microlaterolog (Doll, 1953); it is similar to twomicrolaterologs placed side by side with current flowing from one to the other.A constant current 70 of value 5 mA (Figure 3) is passed between the twocentral electrodes. The current 7i is automatically controlled to produce zeropotential difference between electrodes X and Y;I2 is controlled in a similar butindependent manner, producing zero potential difference between electrodes Cand D. The current 70 is switched in direction at a rate of 40 Hz which is lowenough to be regarded as switched DC but high enough to minimize polarization.When initially tested in situ, both focused and unfocused measurements weremade, the unfocused ones being made with the two currents 7i and/ 2 constantin intensity, and equal and opposite in value (in phase with/0) .

The potential difference used to calculate the apparent formation factor isthat between electrodes X and D (Vxd) or Y and C (Vyc, see Figure 3). Thesepotential electrodes are unaffected by contact impedances because they pass acurrent of only 10"s mA. The current 70 is constant and therefore Vyc is ameasure of the resistivity of the medium concerned. As stated previously theapparent formation factor can be calculated knowing the potential difference

Figure 2. A schematic diagram of the flexible in-situ probe showing the relativeposition and size of the electrodes compared to the insulating pad. X, Y, C, Dare potential electrodes, while 70, 7 t , and I2 are current electrodes. Thé currentspassed are 5 mA for 70 and 50 mA for 7i and 72. All dimensions in mm.

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Figure 3. The current field (theoretical) for a double microlaterolog (Doll,1953). X, Y and C,D are the two pairs of electrodes at which the potentialgradient is adjusted to be zero.

Vyc, when the pad is on the seafloor, and when it is surrounded by the overlyingseawater.

For in-situ measurements the pad is attached to a framework of galvanizedscaffolding tube, which is heavy enough to maintain its position on the seafloor.The framework is designed to allow the pad to be raised or lowered on its own,enabling more than one reading to be made exactly at the same location. Aconsistency in the readings was assumed to be an indication that good contacthad been made with the sediment. The flexible pad was weighted to make itconform to the bottom topography, thus minimizing the thickness of the waterlayer between it and the sediment.

The effect of such a water layer has been studied using model experimentswhich have shown that a layer of seawater, of thickness 1/1 OOth of the electrodeseparation, between the electrode pad and the sediment will reduce the unfo-cused apparent formation factor by 16%. Further experiments using the in-situprobe indicated that substantial weighting of the plexiglas disks was necessary to

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reduce this effect. Results of repeated measurements on a sand produced anunfocused apparent formation factor of 4.6 ± 2%, this consistency suggestingthat the water layer was probably very thin, with thickness variations of lessthan 1 mm (calculated on the basis of the 2% error function). It has beendemonstrated experimentally that the effective sediment depth examined is afunction of the electrode separation; in this particular case the electrode separa-tion is 750 mm giving an effective penetration depth of about 0.5 m.

In-situ results taken from measurements made on a variety of sedimentsdemonstrated that the focusing technique could not compensate for a waterlayer in between the electrodes and the sédiment, but it did give an indication ofthe thickness and variability of the layer. For example, a set of readings, taken insitu on a bed of gravel and large pebbles, produced an unfocused apparentformation factor of 4.25 ± 0.25, and a focused one ranging from 10.6 to 4.2.The cause of the large variation in focused values was attributed to the unevenwater layer that undoubtedly existed next to the electrodes. It was deducedfrom these results that the focusing device, although crude, was able to detectthe presence of a rough seabed, where the consistent unfocused values, if takenby themselves, indicated a good contact with a smooth seabed.

A typical set of results obtained on a sandy seafloor is shown in Figure 4. Thelow initial values were probably caused by ripples; the readings increased withsuccessive drops of the pad suggesting that any ripples had been smoothed outthus reducing the thickness of the water layer. The first drop (Figure 4) showsthe unfocused values to be greater than the focused ones, suggesting that theweighted electrodes must have made intimate contact with the sand, but thatripples probably still existed beneath the insulator. If there were ripples beneaththe electrodes, the focused values would fluctuate wildly, as in the case of apebbly seafloor. The apparent formation factor eventually reached avalué of 4.1± 0.1, which is nearly as high as the maximum value produced in the laboratoryusing a sample from the in-situ location; this makes it almost certain that thewater layer beneath the electrodes was thin enough to be neglected. From this itfollows that the initial focusing system could not compensate for a water layerbeneath the insulating pad and the sediment. While comparisons betweenfocused and unfocused values indicate the reliability of the collected data, it isnecessary to examine the electric field problems presented to establish designcriteria for a reliable focusing device.

Electronics and FocusingThe essential features of the basic electronics are shown in Figure 1. A

constant current of 5 mA is switched in direction using four electronic switcheswhich are triggered by the oscillator. This produces a square wave of current

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5.2

4.8

2 4.4

I 4.0

3.6

3.2

Sample :-Very line sand and shells

Station No > RW2

Freq * 40 Hz— • Fccussed— « Unfocussed

0 4 8 12 16Number of Drops

Figure 4. A typical set of in-situ results using a simple focusing system, showingrepeated drops onto a shallow marine sand.

which is passed through the two electrodes 70 (Figure 2). The potential differ-ence, used in the measurements, is that between X and D (Vxd, Figure 2). Inshape, Vxä is a square wave, and its amplitude is measured because there is a DCoffset (probably caused by electrochemical reaction at the metal electrodes).The current controllers (A in Figure 1) are used to focus the current in themanner described earlier.

The in-situ probe (already described) has two controllers, and a recentlyconstructed laboratory probe (described below) has six. The number of control-lers was increased because subsequent experiments showed that two controllerscould only focus part of the current. The principle of operation, using manycontrollers, is illustrated in Figure 1 where four are shown. Each controlleris independent of the others; a current, say Ix (Figure 1), is automaticallyadjusted until the potential difference across the relevant voltage electrodes (Xand Y) is substantially equal to zero. The basis of the technique is to maintainthe shape of the 70 current field by fixing the position of the zero of potentialgradient. The shape of the Io current field is important (Figure 3), because if itchanges, the geometrical factor (the proportionality factor relating the currentand potential difference to the resistivity of the medium) will also change, thusproducing an error in the measured value of apparent formation factor.

Laboratory experiments were carried out using the in-situ probe prior togoing to sea. The probe was secured, upside down, in a large tank partially filled

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with seawater. The level of water was such that there was a 100 mm layer ofwater above the electrodes, thus producing a layered case analogous to thatexpected on the seabed. When two controllers were used in conjunction withtwo circular potential electrodes (Figure 5) it was impossible to make the voltagebetween these electrodes equal to zero (i.e., the automatic system was inopera-tive), indicating that the shape of the Io current field had varied. In a secondexperiment, the automatic controllers were removed and the intensities, of / jand 72 were made equal and opposite, but variable. The locus of the zero ofpotential gradient was obtained, and is shown qualitatively in Figure 5. Thesalient point is that increasing the intensity of the current made the locus of thezero of potential gradient less concentric than before; it is thus impossible tomaintain the shape of the 70 current field by simply increasing the intensity of aring current source. Automatic focusing was achieved using two controllers whenthe voltage electrodes were reduced to segments.

Subsequent laboratory experiments' have been carried out using a rigid probewhich has three current sources in each ring (Figure 6). The ring electrodes (of

(a)

Figure 5. (a) An electrode configuration using circular rings to focus a constantcurrent 70; the configuration proved unsatisfactory, (b) Variation in the shape ofthe locus of the zero of potential gradient for a two-layer system as the ringcurrent is increased, while the central current remains constant.

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Current electrode

\ Potential electrodes

510 mm

150mmJjS0mm J J50mm J~fTT ^

Figure 6. A laboratory probe with segmented electrodes; each segment has twopotential electrodes and one current electrode. The zero of potential gradient isconstrained to lie between the potential electrodes by automatic controllers(current sources). One controller is connected (independently) to each currentelectrode.

Figure 5) have been segmented; each segment has two potential electrodes andone current electrode to which one current controller is connected. The seg-ments labeled 73 and 74 (Figure 6) each consist of two symmetric segmentswhich have been electrically connected. With such an arrangement it waspossible to constrain the zero of potential gradient to lie between the potentialelectrodes, thus maintaining the shape of the 70 current field. The results ofrepeated drops onto the same piece of sediment are shown in Figure 7. Theyindicate that by the use of multisources it is possible to compensate for theeffects of a substantial water layer between the electrodes and the sediment;further experiments have shown that the thickness of this layer can be as muchas l/20th of the electrode separation, without reducing the apparent formationfactor. The focused readings (using multisources) were more consistent than theunfocused ones; the focused values of apparent formation factor were all within4.8 to 5.0, whereas the unfocused ones increased gradually from 3.3 to 5.1.Focusing using two controllers produced results that were only slightly greaterthan the unfocused ones, showing that two controllers could not compensatesatisfactorily for the water-layer effect.

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4.8

4.4

4.0

3.6

3.2

A

^ - - . . . . . . . . . <

. - • . - • • •

0 4 S 12 16 20 24Number of Drops

Figure 7. Results of laboratory experiments comparing the influence of 6 and 2controllers with unfocused values ÇA, B, C, respectively).

It was concluded that focusing with a multisource system is better than witha single source. The in-situ probe is being modified accordingly. It should thenbe practicable to take measurements where it is impossible to get good contact(i.e., on very uneven deposits, or in locations with relatively high water velocitieswhich tend to lift the pad off the seabed).

Laboratory Measurements of the Formation Factor of Clean SandsA sand can have a considerable range of porosity values. Kolbuszewski (1948)

has shown that, for one sand, the porosity can vary from 38 to 50%; thus for asand, it is advisable to measure the porosity (or void ratio) concurrently withany property such as formation factor. A few measurements have been made onsands reconstituted in the laboratory (Taylor Smith, 1971; Erchul and Nacci,1972) using a four electrode array usually fixed inside an insulating core tube.Erchul and Nacci (1972) have produced data for both loosely and denselypacked sand in which they predict the porosity to within 2% (i.e., about 38 to42%) on the basis of formation factor and porosity measurements made in thelaboratory.

The laboratory cell described below is used to produce a graph of formationfactor vs porosity for each particular sand sample, rather than the use of anempirical relationship which applies to all sediments. Using such a graph it ispossible to estimate the in-situ porosity from a determination of the in-situformation factor, and then to predict the in-situ relative density (and hence thestate of compaction of a sandy seabed).

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The Laboratory CellThe essential features of the cell are shown in Figure 8. The body is

machined out of solid plexiglas. Each of the two electrode plates (Figure 9)consist of a matrix of stainless steel screws, half of which comprises one voltageelectrode, while the other half makes up one current electrode. This is afour-electrode system where the voltage and current electrodes are arranged toproduce two "plate" electrodes. With these electrode plates it is possible toproduce an almost uniform current density in a large volume of sediment, whilealso obtaining an average value of the potential difference across the sediment(and hence an average resistivity). Changes in level of electrolyte (or sediment)do not affect the readings so long as the level remains at least 60 mm above theneck (Figure 8). The graduated cylinder acts both as a sediment reservoir and asa volume measuring device, allowing the formation factor and porosity to be

L 35mm .1

Sediment level —at a known volume.

= = Z - ^

Water

^Graduated cylinder actingas a reservoir and porositymeasurement. .

Sediment

70 mm

Electrodes, voltageand current.

Thermistor

Figure 8. The resistivity cell showing the bypass system, and the volumemeasuring device. The electrodes pass a constant cunent (70) of 45 m A.

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, 65mm

1

65mm

Figure 9. An electrode plate containing two electrodes in the same plane. Thelarge circles pass current and are all connected in parallel, while the small circles,which are also connected in parallel, comprise one potential electrode.

calculated concurrently. The porosity is calculated, knowing the volume of thesediment, using the method described in Appendix I, p. 115.

The sample container is 80 mm in diameter. Kolbuszewski (1948) has shownthat the loosest state of packing is affected by the size of the container, and thatthe value of maximum porosity can be increased by up to 10% (i.e., from n = 40to 44%) when using containers smaller than 76 mm in diameter.

Preliminary Tests Using the Laboratory CellA series of experiments was carried out in order to test the operation of the

cell and its associated electronics.

1. The constant current source (which provides the current to the elec-trodes) was tested using a purely resistive load. The current source andthe leads to the potential electrodes were connected to the same resis-tance box. The load presented by the box was varied and a graph wasdrawn of resistance vs the amplitude of the voltage waveform. The resultsplotted out as a straight Une proving that the current output is indepen-dent of the load. The waveform at the potential electrodes was "square"and equal to that at the current electrodes.

2. The cell was filled with seawater, and the frequency of the constantcurrent source was varied. The potential differences between the two

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pain of electrodes were very different, especially at low frequencies(Figure 10). The waveform at the potential electrodes was square, as incase 1 above, but that at the current electrodes was not: it increased inamplitude during each half-cycle as shown in Figure 10. As the frequencyincreased the waveform at the current electrodes decreased in amplitudeand became almost identical to the waveform at the potential electrodes.It was concluded that there was a considerable contact impedance at thecurrent electrodes at low frequencies which was probably caused bypolarization of the electrodes. The use of separate potential electrodeseliminated the effect of this phenomenon on the results.

3. Saturated sand, already washed in the electrolyte, was deposited into thecell filled with the same electrolyte. The deposition was made, withoutany entrapped air, in a manner described by Kolbuszewski (1948) toproduce the "loosest" packing. A reading of voltage across the electro-lyte was made prior to deposition; subsequent readings across the sedi-ment could then be calculated in terms of formation factor. As thesediment in the chamber compacted, pore water was expelled and forcedits way upward through the sediment in the graduated cylinder produc-ing an effect called piping (commonly observed during permeabilityexperiments), which tended to keep the sand in the cylinder looselypacked. Therefore, the porosity of the sand was not uniform, and a pointwas reached when the measured porosity of the sediment decreasedwithout any increase in formation factor. To overcome this effect asystem was incorporated to allow the pore water to bypass the neck ofthe cell.

4. The cell constant (which relates the ratio V/I to resistivity) was obtained

2.0

Two separate runs Current = 45.0 mA

k.A A: j ( | (, f Current electrodes

B: -ff-^—f Voltage electrodes

10 100Frequency, Hz

1000

Figure 10. The variation of voltage with switching frequency, measured at boththe potential and current electrodes, for a constant current (70) of 45 m A and acell constant of 7.8.

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by a direct measurement of the resistivity of an electrolyte. The resistiv-ity of the electrolyte, sampled from the lower part of the cell, wasmeasured using a universal bridge (Wayne Kerr Model No. B221) and aplatinum electrode cell (Wayne Kerr Model No. C521). The cell constantwas obtained by the equation p .= K' V/I, where p is the resistivity of theelectrolyte, K is the cell constant, V is the measured voltage across theelectrolyte, and / is the current. The experiments were made within aperiod of 3 min; it was assumed that the temperature of the electrolytehad not changed appreciably in this time. The experiment was repeatedseveral times giving K = 7.8 ± 2%.

5. To verify that the cell measured the same formation factor for a certainpacking state irrespective of the electrolyte resistivity, the chamber wasfilled many times with the same sand in its loosest packing state, eachtime varying the conductivity of the electrolyte. The potential differenceacross the sediment was plotted against the potential difference acrossthe electrolyte (for a constant current of 45.0 mA). All the data lie on astraight line with virtually no scatter (Figure 11); the gradient of the Uneequals the formation factor.

6. A series of experiments was carried out to assess the effects of tempera-ture changes on formation factor. The resistivity of a well-stirred electro-lyte was plotted as a function of temperature, the temperature beingmeasured with a quartz-crystal thermometer. As expected, the resistivity

4.0

3.0

2.0

1.0

0 0.2 0.4 0.6 0.8 1.0 1.2Voltage across Electrolyte. V

Figure 11. A plot of voltage across an electrolyte vs voltage across a sandsample in its loosest packing state saturated with the electrolyte, for/0 alternat-ing at 125 Hz and a sample temperature of 11°C. Separate depositions weremade with electrolytes of differing conductivity by altering their freshwaterseawater ratio.

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was very sensitive to temperature changes, showing a decrease of 2.6% per°C rise at 15°C. A thermistor, mounted on a pedestal, was incorporatedinto the cell which allowed the temperature of the medium in the cell tobe monitored continuously. The pedestal was necessary because the testswith a thermistor mounted in the chamber wall indicated that the readingsrelated to the temperature of the wall and not to the material inside.During all subsequent experiments, changes in temperature were mini-mized by keeping the laboratory at a nearly constant temperature, andby completing each set of readings within 15 min. The effect of anysmall changes in temperature were noted and compensated for using theresistivity/temperature graph described above.

Measurements of the Variation of Formation Factor with Porosity ChangesA sample Of marine sand, approximately 1.5 kg in weight, was deposited into

the cell, as described in test 3 of the preceding section, readings of temperatureand voltage having previously been made on the electrolyte filling the cell.

Initially the sand was very loose and unstable; this value of void ratio wasstated by Kolbuszewski (1948) to be the maximum value emax. Measurementsof voltage, temperature, and volume were made on the sediment, from which theformation factor, porosity, and void ratio were calculated knowing the densitiesof both the grains and the electrolyte.

The sample was compacted in stages using a combination of hand-twisting,tapping, and vibrating on a sieve shaker. Readings of voltage and volume weretaken at various intervals as the compaction increased, enabling a graph offormation factor vs void ratio (and porosity) to be produced. Greatest compac-tion was achieved by continuously vibrating the sieve shaker, without taking anyintermediate readings; the value of void ratio, thus obtained, was taken to be theminimum value e m ¡ n , used later in the calculation of relative density.

Figure 12 is an example of four depositions using the same sample of sand, andit is included to show the repeatability of the experiment. Figure 13 depicts theFF/n curves, obtained from graphs similar to Figure 12, for four differentsamples of sand, namely, RW2, 73/4/1, 1/8, 1/7. It should be noted thatalthough their grain-size parameters are different (Table 1) samples 1/8 and RW2produced almost identical FF/n curves. For samples RW2 and 1/7 the values offormation factor and porosity relating to maximum compaction (obtained bycontinuous vibration) did not lie on their main FF/n curves, which means thatthe samples have exhibited two different values of formation factor at the sameporosity. It appears that two different, very stable, packing structures have beenformed. The two points A and B (Figure 13) on the FF/n curve for RW2 are theminimum values of porosity (or void ratio) produced by the two methods of

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4.4

4.2

4.0

o 3.8

3.4

3.2

Sample 1/8

3.00.60

Porosity, "/.42 44

0.65 0.70 0.75 0.80Void Ratio

0.85 0.90

Figure 12. An example of four depositions of the same sample, each symbolrepresenting a different deposition. The graph illustrates both the scatter and therepeatability of the results (the grains had a specific gravity of 2.67).

compaction described above; further vibration over periods greater than 15 mindid not change the position of either of the points. Thus, as indicated earlier,formation factor cannot be uniquely defined using only porosity even for onesample. Formation factor must depend on the manner of packing and the waythe current is forced through the medium; for the worst case considered (i.e.,RW2) this effect represents an error of 1% in the porosity (i.e., 1 part in 40).

Calculation ofln-Situ Porosity and Relative DensityThe in-situ apparent formation factor of sample RW2 (Figure 4) was taken to

be 4.1 ± 0.1. The difference between the apparent formation factor and the trueformation factor, caused by a water layer between the electrodes and thesediment, is indeterminate but must be small because the in-situ values are onlyslightly below the maximum value obtained in the laboratory. Thus this sourceof error in the inferred in-situ porosity is probably insignificant.

There is an error introduced during the conversion from in-situ apparentformation factor to porosity; it is illustrated by the scatter of results in Figure12, representing an error of ± 3%. The constituent parts of this error are largelyunknown because they depend on the effects of nonuniform porosity in the cell

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4.4

4.2

4.0

3.8

E

£• 3.6

3.4

3.2

3.0

73/4/1 Coarse shelly sandRW2 Very line sand and shells

1/8 Medium sand1/7 Medium - fine sand

In-situ F F . 4 1 • 1 lor RW2F F . 4 3 iO-2 for 73/4/1

40Porosity , V.

0.6 0.7 0.8Void Ratio

0.9

SO

1.0

Figure 13. Formation factor vs porosity for four different sand samples. Eachgraph represents the average of several depositions of the same sample, as inFigure 12.

(caused by différent wall effects in the chamber and cylinder) and on the factthat the formation factor can be multivalued at a constant porosity even in onesample. To some extent this error is to be expected: Garrells et al. (1949) haveshown that diffusion of solutions through porous media is dependent on a"directional porosity"; and Klinkenberg (1951) has shown that there is ananalogy between diffusion and electrical conductivity. The error introduced bythe laboratory measurements was assumed to be equal to the scatter in resultsdescribed previously (i.e., 3%). A relationship exists where

relative density = Cmax

where e is the in-situ void ratio (volume of voids/volume of solids).The magnitude of emax is well defined by the method of deposition (Kol-

buszewski, 1948); the value of emin may be less well known (Tavenas and LaRochelle, 1974) but has been assumed to be that shown in Figure 13.

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Table 1Grain Size Characteristics

Sample73/4/1

RW2

1/8

1/7

Median DiameterMd<t>1.29

2.86

1.98

2.03

Mean DiameterM<t>1.44

2.83

1.95

2.01

Standard Deviationo<t>

0.72

0.21

0.28

0.29

For sample RW2 the in-situ apparent formation factor was assumed to be 4.1± 0.1, from which the in-situ void ratio and porosity were deduced (Figure 13),being 0.65 ± 0.04 and 39 ± 2%, respectively. The in-situ relative density wascalculated using 0.91 ± 0.02 as em a x and 0.60 ± 0.02 as emin; the errorsindicated are conservative because the extremes of packing may not have beenachieved during the experiments.

From the above values, the in-situ relative density is 0.84 ± 0.3, but if themaximum and minimum packing conditions were known precisely this errorwould be reduced to 0.13. This illustrates that the major source of enor in therelative density result arises from the errors in emax and em i n rather than fromthe uncertainty in the value of the in-situ void ratio.

Conclusions1. Measurements of the electrical resistivity of a seafloor sand using conven-

tional electrode arrays to assess its in-situ porosity are seriously disturbedby the presence of low-resistivity seawater, which tends to make theelectric current flow in the water rather than in the sediment. The waterpath acts in an analogous way to a "short circuit" giving resistivity valuesmuch smaller than the true ones even for very thin layers.

2. Experiments with a weighted flexible insulating pad, and a crude focus-ing system embedded in the insulator (to contain the electric currentboth below the pad and in the sediment), show that the presence of awater layer between the electrodes and the sediment makes precisedownward focusing impossible. The shape of the electric field is sodisturbed by the seawater layer that potential difference nulling (anindication of correct focusing) cannot be achieved.

3. Further experiments with a rigid probe where the electrodes are seg-mented and the electric field is controlled by six independent currentsources (where originally only two were used) show that focusing can be

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obtained through correct definition of the electric field. Such a system,as at present designed, can tolerate a water layer about l/20th of theelectrode separation without serious change in the measured magnitudeof the sediment resistivity. As in conventional systems, the depth of theinvestigations is related to the electrode spacing.

4. Laboratory measurements have shown that, when using an alternatingcurrent which is derived from a DC constant current source switched indirection, there is a contact impedance at the current electrodes that canbe very large compared to the resistivity of seawater. For reasons givenearlier, it was assumed that this contact impedance was caused, at least inpart, by polarization of the current electrodes, which was found todecrease with increasing switching frequency. The use of separate poten-tial electrodes ensures that the measured potentials are independent ofany contact impedances at the current electrodes. It follows that anyresistivity measurement of seafloor sediments, where the potential differ-ence is measured between the current electrodes, must be suspect.

5. In-situ resistivity (formation factor) measurements of a sand can only berelated to the in-situ porosity (or void ratio) through the establishmentof the formation factor/porosity variations for that particular sand,rather than by the use of a "best fit" curve for the whole range of sands,where the scatter in the data is large. The correct relationship can best beobtained via sediment settling in a formation factor/porosity cell, follow-ing which an in-situ porosity can be assessed to better than 5%.

6. The settling cell also allows the values of maximum and minimum voidratio to be obtained for a particular sand sample. Using these values it ispossible to calculate the relative density of a sand to an overall error of atleast 30%. This error is dependent on the errors in em a x and em i n tosuch an extent that there is some doubt as to the usefulness of therelative density result. However, the degree of compaction may beassessed by comparing the in-situ apparent formation factor with themaximum and minimum values of formation factor produced in thelaboratory; for RW2 this indicates that the seabed was close to its stateof maximum compaction.

AcknowledgmentsThis study was made possible by Contract No. F60/4/7 with the Engineering

Geology unit of the Institute of Geological Sciences. I would like to thank Mr.D. Taylor Smith for his suggestions and overall guidance. I am indebted to Mr. P.G. Simpkin for the continuous and enlightening discussions we have had over thepast two years and I wish to thank Mr. I. K. Nixon of Soil Mechanics Ltd., for a

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most informative discussion concerning sand and its packing. I am grateful toMr. R. F. Jacques for the machining of the Resistivity Cell and Mr. R. Cratchleyfor critically reading the manuscript. Finally, the encouragement and assistanceof my colleagues at the Marine Science Laboratories must not go unrecognized,especially Mr. F. Dewes who drafted the illustrations.

ReferencesArchie, G. E., 1942. The electrical resistivity log as an aid in determining some reservoir

characteristics. Transactions of the American Institute of Mining and MetallurgicalEngineers, vol. 147, pp. 54-62.

Bogoslovsky, V. A., and A. A. Ogilvy, 1974. Detailed electrometric and thermometricobservations in offshore areas. Geophysical Prospecting, vol. 22, pp. 381-392.

Bouma, A. H., W. E. Sweet, F. B. Chmelik, and G. L. Heubner, 1971. Shipboard and in-situelectrical resistivity logging of unconsolidated marine sediments. Third Offshore Tech-nology Conference Preprints, vol. 1, pp. 253-268.

Boyce, R. E., 1968. Electrical resistivity of modern marine sediments from the Bering Sea.Journal of Geophysical Research, vol. 73, pp. 4579-4766.

Brace, W. F., A. S. Orange, and T. R. Madden, 1965. The effect of pressure on the electricalresistivity of water saturated crystalline rocks. Journal of Geophysical Research, vol. 70,pp. 5669-5678.

Doll, H. G., 1951. The laterolog-A new resistivity logging method with electrodes using anautomatic focussing system. Transactions of the American Institute of Mining andMetallurgical Engineers, vol. 192, pp. 305-316.

Doll, H. G., 1953. The microlaterolog. Transactions of the American Institute of Mining andMetallurgical Engineers, vol. 198, pp. 17-32.

Erchul, R. A., and V. A. Nacci, 1972. Electrical resistivity measuring system for porositydetermination of marine sediments. Marine Technology Society Journal, vol. 6, no. 4,pp. 47-53.

Garrels, R. M., R. M. Dreyer, and A. L. Howland, 1949. Diffusion of ions throughintergranular spaces in water-saturated rocks. Geological Society of America Bulletin,vol. 60, pp. 1809-1828.

Keller, G. V., and F. C. Frischknecht, 1966. Electrical methods in geophysical prospecting.London, Pergamon Press, 519 pp.

Kermabon, A., 1972. Recent developments in deep sea electrical resistivity probings—itsapplication to the sedimentary study of the Red Sea hot brines. Oceanology Interna-tional 1972 Conference Papers, Brighton, United Kingdom, pp. 385-391.

Kermabon, A., C. Gehin, and P. Blavier, 1969. A deep-sea electrical resistivity probe formeasuring porosity and density of unconsolidated sediments. Geophysics, vol. 34, pp.554-571.

Klinkenberg, L. J., 1951. Analogy between diffusion and electrical conductivity in porousrocks. Geological Society of America Bulletin, vol. 62, pp. 559-564.

Kolbuszewski, J., 1948. An experimental study of the maximum and minimum porosities ofsands. Proceedings of the 2nd International Conference on Sou Mechanics and Founda-tion Engineering, vol. 1, Rotterdam, pp. 158-165.

Kullenberg, B., 1952. On the salinity of water contained in marine sediments. MeddelandedOceanograilska Instit i Goteborg, no. 21, 37 pp.

Kunetz, G., 1966. Principles of direct current resistivity prospecting. Geoexploration mono-graphs, series 1, no. 1, Berlin, Gerbruder Borntaeger, 103 pp.

Parasnis, D. S., 1972. Principles of applied geophysics. London, Chapman Hall, 214 pp.Schlumberger, C., M. Schlumberger, and E. G. Leonardon, 1934. Electrical exploration of

water-covered areas. Transactions of the American Institute of Mining and MetallurgicalEngineers, vol. 110, pp. 122-134.

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Siever, R., K. C. Beck, and R. A. Berner, 1965. Composition of interstitial waters of modernsediments. Journal of Geology, vol. 73, pp. 39-73.

Tavenas, F., and P. La Rochelle, 1974. Accuracy of relative density measurements. Géotech-nique, vol. 22, pp. 549-562.

Taylor Smith, D., 1971. Acoustic and electrical techniques of marine sediment identifica-tion. Proceedings of the International Symposium on Engineering Properties of Sea-Floor Soils and Their Identification, Seattle, Washington, pp. 235-267.

Taylor Smith, D., 1975. Geophysical assessment of sea-floor sediment properties. Oceanol-ogy International 1975 Conference Papers, Brighton, United Kingdom, pp. 320-328.

Williams, C. E., 1970. In-situ formation factor measurements at the water-sediment inter-face. In Interocean 1970, vol. 2, Dusseldorf, VDI Verlag, pp. 87-88.

Winsauer, W. O., H. M. Shearin, P. H. Masson, and M. Williams, 1952. Resistivity ofbrine-saturated sands in relation to pore geometry. American Society of PetroleumGeologists Bulletin, vol. 36, pp. 253-277.

Appendix I

Calculation of PorosityConsider a volume of sediment, (V), which contains both water and solids.

The total weight of the sediment, W, and the densities of the solids and water, ps

and p w , combine to give:

where Vs and Vw are the volumes of solids and water, respectively. From thesetwo equations Vw can be calculated, where the porosity (n) is Kw/Fand

Vw = (ps-V-W)l(ps-pw).

The densities of the water and solids (ps and pw ) were calculated separatelyusing a 500 ml specific gravity bottle. The volume V was obtained from thegraduated cell, and was calculated from weighings. The void ratio was calculatedfrom void ratio (e) = n\ (1— n).

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Documents

An electrical resistivity method for evaluating the in‐situ porosity of clean marine sands