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Electrical properties 285

Table 5.1. Resistivities of

Resistivity (Om)

Mineral Formula Range Average

~ Biz53 18-570 Covell ite cus 3 X 10-’-8 X lo-’ 2 X lo-’ CYS 3 X 10-5-0.6 lo-, CuFeS, 1.2 X 10-5-0.3 4 x lo-’ Cu5FeS4 2.5 X 10-5-0.5 3 x IO-~ FeS, 2.9 X 10-s-1.5 3 x 10-1 Pyrrhotite FeA 6.5 X 10-6-5 X IO-~ HgS 2 x lo7 MoS, 10- - lo6 10 PbS 3 X 10-5-3 X 10’ 2 x IO-~ Millerite NiS 3 x IO-~ CyFeSnS, 10-3-6 X lo3 Stibnite S& lo5- lo1’ 5 x 106 ZnS 1.5 - lo7 10’ ite CoAsS 3.5 x 10-~-10-~ FeAsS 2 X 10-’-15 IO-~ Niccolite NiAs 10-~-2x IO-~ 2 x IO-~ A12Q . nH20 2 x io2-6 x lo3 Cuprite CYO - 300 30 FeCr204 1-106 Specularite Fe2Q 6 X Fez03 3.5 x 10-~-10~ Limonite 2Fe2Q . 3H20 lo3-lo7 Fe304 5 X 10-’-5.7 X lo3 llmenite FeTiQ - 50 Wolframite Fe, Mn, WO, 10-10’ Mn02 5 x 10-~-10 Si 0, 4 x 1o1O-2 x 1014 Sn02 4 x 10-~-10~ 0.2 Rutile Ti02 30-1000 500 (pitchblende) uo2 1-200 Anhydrite CaSO, 1o9 Calcite CaCQ 2 x 1012 Fluorite CaF2 8 X IOl3 Siderite Fe*(C4)3 70 Rock salt NaCl 30 - 1013 Sylvite KCI 101-1012 Diamond C 10-10l4 Serpentine 2 x io2-3 x lo3 Hornblende 2 x 102-106 Mica 9 x 10~-10~~ Biotite 2 x 102-106 Bitum. coal 0.6-10’ Anthracite 10-~-2x 10’ Lignite 9-200 Fire clay 30 Meteoric waters 30-lo3 Surface waters (ign. rocks) 0.1 -3 x 10’ Surface waters (sediments) 10-100 Soil waters 100 Natural waters (ign. rocks) 0.5 - 150 9 Natural waters (sediments) 1-100 3 Sea water 0.2 Saline waters, 3% 0.1 5 Saline waters, 20% 0.05 286 Electrical properties of rocks and minerals ers or none at all. Under the influence of an external where + is the fractional pore volume (porosity), S varying electric , the atomic electrons are dis- is the fraction of the pores containing water, pw is placed slightly with respect to their nuclei; this slight the resistivity of water, n = 2, and a, rn are con- relative separation of negative and positive charges is stants, 0.5 I a I 2.5, 1.3 I rn I 2.5. For example, known as dielectric polarization of the material and suppose S = 1, a = 1.5, and rn = 2, then pJpW = it produces a current known as the displacement lS/# and for values of + = 0.01, 0.1, 0.3, 0.5, current. pe/pw becomes 1.5 X lo4, 150, 17, and 6, respec- tively. (b) Electronic conduction. The electrical resistivity Water conductivity varies considerably (see Table of a cylindrical solid of length L and cross section 5.1), depending on the amount and conductivity of A, having resistance R between the end faces, is dissolved chlorides, sulfates, and other minerals pre- given by sent. The geometrical arrangement of the interstices in p = RA/L (5.5) the rock has a less pronounced effect, but may make If A is in square meters, L in meters, and R in the resistivity anisotropic, that is, having different ohms, the resistivity unit is the ohm-meter (Qm). For magnitudes for current flow in different directions. dimensions in centimeters the unit becomes the Anisotropy is characteristic of stratified rock that is ohm-centimeter (Qcm): 1 Qm = 100 Qcm. generally more conductive in the bedding plane. The The resistance R is given in terms of the voltage anisotropy effect depends on the ratio of maximum V applied across the ends of the cylinder and the to minimum resistivity, may be as large as 2 in some resultant current Z flowing through it, by Ohm's graphitic slates, and varies from 1 to 1.2 in rocks law : such as limestone, shale, and rhyolite. As an example, consider the layered formation R = V/Z shown in Figure 5.1, having resistivities p1 and p2 where R is in ohms and the units of V and I are whose respective fractional volumes are v and 1 - U. volts and amperes. Here the resistivity in the horizontal direction - a The reciprocal of resistivity is the conductiviv u, stack of beds effectively in parallel - is where the units are siemens per meter (S/m). Then

u = l/p = L/RA = (Z/A)/( V/L) = J/E (5.6) where J is the current density (A/&) and E is the In the vertical direction, the beds are in series so that electric field (v/m).

Pu = Pl* + P2(1 - (5.9) (c) Electrolytic conduction. Because most rocks are poor conductors, their resistivities would be ex- Then the ratio is tremely large were it not for the fact that they are usually porous and the pores are filled with fluids, Pu mainly water. As a result the rocks are electrolytic - = (1 - 2u+ 22) + conductors, whose effective resistivity may be defined Ph as in Equation (5.3, where the propagation of cur- rent is by ionic conduction - by molecules having an If v 1 and p2/p1 >> 1, this simplifies to excess or deficiency of electrons. Hence the resistiv- ity varies with the mobility, concentration, and de- (5 .lo) gree of dissociation of the ions; the latter depends on the dielectric constant of the solvent. As mentioned previously, the current flow is not only slow com- If the layer of resistivity p1 is for water-saturated pared to ohmic conduction, but represents an actual beds, this ratio might be quite large. transport of material, usually resulting in chemical transformation. (d) Dielectric conduction. The mechanism of di- The conductivity of a porous rock varies with the electric conduction - the displacement current - was volume and arrangement of the pores and even more described briefly at the beginning of this section, with the conductivity and amount of contained wa- where it was pointed out that the displacement cur- ter. According to the empirical formula due to Archie rent flows only in nonconductors when the external (19421, electric field changes with time. The significant pa- rameter in dielectric conduction is the dielectric pe = a+-"S-"p, (5.7) constant k, sometimes called the specijic inductive Electrical properties 287

Figure 5.1. Anisotropic resistivity as a result of horizontal bedding.

capacity of the medium. In analogy with magnetic 5.2.3. Magnetic Permeability quantities M, H, k, B, and p (53.2.1) we have an Where EM sources are employed, the voltage in- electrostatic set: electric polarization (electric dipole duced in a subsurface conductor varies not only with mornent/unit volume) P, electric field strength the rate -of change of magnetic field, but also with E, electric susceptibility q, electric displacement the magnetic permeability of the conductor. From yl,/unit area) D, and dielectric constant k. In Maxwell’s equation, electrostatic units, the relations between these are aH P = qE D = E + 4nP = E(l + 4aq) = kE V XE= -1.1- (5.11) at

whereas in mks units, we see that currents induced in the ground are enhanced by the factor p. Practically, however, the permeability rarely is appreciably greater than unity, P=qE D=eOE+P=E(eO+q)=EE except. for a few magnetic minerals (95.4.3); conse- (5.12) quently it is of no particular significance in electrical work, except when F%03 is present in large concen- and the dielectric constant k = 1 + q/eo = e/eo. tration. In electrostatic units, P, E and D are volts per centimeter and q and k are dimensionless. In mks 5.2.4. Polarization Potentials units E, eo, and q are in farads per meter, P, D are in coulombs per square meter, E is in volts per Where a steady current is passed through an elec- meter, and k is again dimensionless and the same in trolytic conductor containing particles it is either system. possible, as described in Section 5.3.1, to determine The dielectric constant is similar to the conductiv- the effective resistivity. If a current is suddenly ity in porous formations in that it varies with the switched on or off in a circuit containing an elec- amount of water present (note that water has a very trolyte, a finite time elapses before the potential large dielectric constant; see Table 5.5). We shall see increases to a fixed value or drops to zero. The in Section 6.2.3 that displacement currents are of delayed buildup or decay of current is characteristic secondary importance in earth materials because of electrolytic conduction, and is due to accumula- electrical prospecting methods generally employ low tion of ions at interfaces between the electrolyte and frequencies. mineral particles. As a result, a potential opposing 288 Electrkal properties of rocks and minerals

Area = A. cap (.

Wjre rings

High imbdance

Figure 5.2. Simplified schematic of equipment for measuring resistivity of core samples.

the normal current flow is developed across the The power source may be dc or preferably low interface. A similar effect is observed at the contact frequency ac (400 Hz or less). The possibility of between electrolytes and clay particles. These are anisotropy can be checked by measuring the resistiv- known as polarization potentials; the process is called ity in two directions, provided the shape is suitable the induced polarization effect. Induced polarization for this. (IP) prospecting involves these interface potentials. Obviously one can make these measurements in They will be considered in more detail in Section 9.2. the field as well, on drill core, grab samples, even outcrop, if the electrode contact is reasonably good. Estimates of resistivity, made samples by using an 5.3. MEASUREMENT OF ELECTRICAL on ohmmeter and merely pressing or scraping the termi- PROPERTIES OF ROCKS AND MINERALS nals of the against the surface however, are not very trustworthy. 5.3.1. laboratory Measurement of Resistivity In order to measure directly the true resistivity of a rock, mineral, electrolyte, and so forth, it is neces- sary to shape the sample in some regular form, such 5.3.2. Measurement of Dielectric Constant as a cylinder, cube, or bar of regular cross section. An ac bridge may also be used to measure the An experimental arrangement is shown in Figure 5.2. resistivity of soils and electrolytes. At audio frequen- The main difficulty is in making good electrical cies any reactive component - normally capaci- contact, particularly for the current electrodes. For tive- must be accounted for in order to get a good this purpose tinfoil or mercury electrodes may be bridge balance. Consequently the measurement de- used and it is generally necessary to apply pressure termines the effective capacitance, as well as resistiv- to the current electrodes; sometimes the ends of the ity, of the specimen. Since capacitance varies with sample are dipped in soft solder. From Figure 5.2 the dielectric constant of the material, it is thus and Equation (5.6) the resistivity is given by possible to determine the latter by substitution. The Schering capacitance bridge is suitable for this mea- p = AV/LI surement in the laboratory (Hague, 1957). Typical values of electrical constants 289

Table 5.2. Resistivities of various

Ore Other minerals Gangue P (am)

Pyrite 18% 2% (chalco) 80% 300 60% 5% (ZnS) + 15% 20% 0.9 95 % 5% (ZnS) 1.o Pyrrhotite 41 % 59% 2.2 x lo-, 79% 21 % 1.4 x IO-~ 95 % 5% 1.4 x IO-~ SbS, in quartz 4 X lo3-3 X lo7 FeAsS 60% FeS 20% 20% SiO, 0.39 FeAsS 10-~-10-~ CusFeS, 3 x IO-~ CusFeS, 40% 60% SiO, 7 x 10-2 Fe, Mn, WO, CoAsS lo3- 10’ PbS, near massive 0.8 Fe2Q 0.1 - 300 Fe,Q, massive 2.5 x lo3 Fe30, 60% 45 75% brown iron 25 % 2 x 104-8 x los Fe304 5 x 103-8 x lo3 30% 5% PbS, 15%FeS 50% 0.75 80% 10%PbS, 10%FeS 1.7 x lo3 90% 5% PbS 5% 130 Graphitic slate 0.13 Graphite, massive 10-,-5 X MoSz 2 x io2-4 x lo3 MnO, colloidal 1.6 CYS 3 x 10-2 CuFeS, 10-,-1 CuFeS, 90% 2% FeS 8% SiO, 0.65 FeCr,O, 1o3

5.4. TYPICAL VALUES OF ELECTRICAL are characterized by ionic bonding so that the va- CONSTANTS OF ROCKS AND MINERALS lence electrons are not free to move; the charge carriers are ions that must overcome larger barrier 5.4.1. Resistivities of Rocks and Minerals potentials than exist either in the semiconductors or conductors. Of all the physical properties of rocks and minerals, A further difference between conductors and electrical resistivity shows the greatest variation. semiconductors is found in their respective variation Whereas the range in density, elastic wave velocity, with temperature. The former vary inversely with and radioactive content is quite small, in magnetic temperature and have their highest conductivities in susceptibility it may be as large as However, the lo5. the region of 0 K. The semiconductors, the other resistivity of metallic minerals may be small on as as hand, are practically insulators at low temperatures. Slm, that of dry, close-grained rocks, like gab- a looser classification, rocks and minerals are bro large lo7 Slm. The maximum possible In as as considered to be good, intermediate, and poor con- range is even greater, from native (1.6 X lop8 ductors the following ranges: Om) to pure sulfur (Wam). within A conductor is usually defined as a material of (a) Minerals of resistivity to about 1 am. resistivity less than Slm, whereas an insulator is (b) Minerals and rocks of resistivity 1 to lo7 Slm. one having a resistivity greater than lo7 Slm. Be- (c) Minerals and rocks of resistivity above lo7 Slm. tween these limits lie the semiconductors. The and graphite are all conductors; they contain a large Group (a) includes the metals, graphite, the sul- number of free electrons whose mobility is very fides except for sphalerite, cinnabar and stibnite, all great. The semiconductors also carry current by mo- the arsenides and sulfo-arsenides except SbAs,, the bile electrons but have fewer of them. The insulators antimonides except for some compounds, the 290 Electrical properties of rocks and minerals

Table 5.3. Resistivities of various rocks and sediments Table 5.4. Variation of rock resistivity with water content

Rock type Resistivity range (am) Rock % H20 P (Qm)

Granite porphyry 4.5 x lo3 (wet)-1.3 x lo6 (dry) Si ltstone 0.54 1.5 x lo4 Feldspar porphyry 4 x lo3 (wet) Siltstone 0.38 5.6 X 10' Syenite 102 - 106 Coarse grain SS 0.39 9.6 x lo5 Diorite porphyry 1.9 X lo3 (wet)-2.8 X lo4 (dry) Coarse grain SS 0.1 8 10' Porphyrite 10-5 x lo4 (wet)-3.3 x lo3 (dry) Medium grain SS 1.o 4.2 x lo3 Carbonatized Medium grain SS 0.1 1.4 X 10' porphyry 2.5 x lo3 (wet)-6 x lo4 (dry) Graywacke SS 1.16 4.7 x lo3 Quartz diorite 2 x lo4-2 x lo6 (wet) Graywacke SS 0.45 5.8 x lo4 -1.8 X lo5 (dry) Arkosic SS 1.o 1.4 x lo3 Porphyry (various) 60-lo4 Organic limestone 11 0.6 x lo3 Dacite 2 x lo4 (wet) 1.3 6 X lo3 Andesi te 4.5 X lo4 (wet)-1.7 X lo2 (dry) Dolomite 0.96 a x lo3 Diabase (various) 20-5 x lo7 Peridotite 0.1 3 x lo3 Lavas io2-5 x lo4 Peridotite 0 1.8 x lo7 Gabbro lo3- lo6 Pyrophyllite 0.76 6 X lo6 Basalt 10-1.3 X lo7 (dry) Pyrophyllite 0 1on Olivine norite lo3-6 X lo4 (wet) 0.31 4.4 x lo3 Peridotite 3 x lo3 (wet)-6.5 x lo3 (dry) Granite 0.19 1.8 X lo6 Hornfels 8 X lo3 (wet)-6 x lo7 (dry) Granite 0 10'0 Schists Diorite 0.02 5.8 x lo5 (calcareous Diorite 0 6 X lo6 and mica) 20-lo4 Basalt 0.95 4 x lo4 Tuffs 2 X lo3 (wet)-1OS (dry) Basalt 0 1.3 X 10' Graphite schist 10-102 Olivine-pyrox. 0.028 2 x lo4 Slates (various) 6 X lo2-4 X lo7 Olivine-pyrox. 0 5.6 x lo7 Gneiss (various) 6.8 X lo4 (wet)-3 X lo6 (dry) Marble 102-2.5 X 10' (dry) Skarn 2.5 X lo2 (wet)-2.5 X 10' (dry) Quartzites graphite (5 x lo-' to 10 Om range, = 10-~ Om (various) 10-2 x 10' average) and sulfur (107-10'6 Om range, = 1014 Om Consolidated shales 20-2 x lo3 average). Argillites 10.-8 X lo2 The variation in resistivity of particular minerals Conglomerates 2 x lo3-lo4 is enormous, as can be seen from Table 5.1. Among Sandstones 1-6.4 X 10' the more common minerals, pyrrhotite and graphite Limestones 50-lo7 appear to be the most consistent good conductors, Dolomite 3.5 x io2-5 x lo3 Unconsolidated whereas pyrite, galena, and magnetite are often poor wet clay 20 conductors in bulk form, although the individual Mark 3 - 70 crystals have high conductivity. Hematite and spha- Clays 1-100 lerite, in pure form, are practically insulators, but Oil sands 4-800 when combined with impurities may have resistivi- ties as low as 0.1 Om. Graphite is often the connect- ing link in mineral zones, which makes them good tellurides, and some such as magnetite, man- conductors. ganite, pyrolusite, and . Most oxides, ores, The range of resistivities of various waters is and porous rocks containing water are intermediate notably smaller than for solid minerals; the actual conductors. The common rock-forming minerals, sil- resistivities are also lower than those of a great many icates, phosphates and the carbonates, nitrates, sul- minerals. fates, borates, and so forth, are poor conductors. Table 5.2 from Parkhomenko (1967) lists resistivi- The following tables list characteristic resistivities ties for a variety of ores. In general it appears that for various minerals and rocks. The data are from pyrrhotite in massive form has the lowest resistivity, various sources, including Heiland (1940, Ch. lo), that the resistivity of zinc ores is surprisingly low Jakosky (1950, Ch. 5), Parasnis (1956, 1966, Ch. 6), (possibly due to the presence of lead and Keller (1966), and Parkhomenko (1967). fractions), and that molybdenite, chromite, and iron Resistivities of the various metals in pure form, ores have values in the range of many rocks. from antimony to zinc, vary by only about 2 orders Table 5.3 lists typical values for rocks and uncon- of magnitude. (Bi = 1.2 X Om, Ag = 1.6 X solidated sediments. The ranges are quite similar to Om). Tellurium is an exception (= Om). that for water, which is the controlling factor in Two other elements of common occurrence are many rocks.