Factors influencing resistivity or electrical conductivity in soil materials

This section provides a brief overview of the factors influencing soil resistivity (or electrical conductivity). Additional discussion regarding this subject is given in Chapter 2 and Chapter 4. The ability of a soil material to transfer electric current, as indicated by the resistivity (or electrical conductivity) of the soil, is determined by the components that make up the soil. Soil typically consists of solid, gas, and liquid phases (Figure 5.2). The solid phase of the soil includes both mineral and organic matter and, excluding the larger fragments (generally rock materials), can be divided by

FIGURE 5.1 Flow of electric current, I, through a cylinder composed of uniform material with resistivity , p, which produces a difference in an electric potential, AV, from one end of the cylinder to the other.

FIGURE 5.1 Flow of electric current, I, through a cylinder composed of uniform material with resistivity , p, which produces a difference in an electric potential, AV, from one end of the cylinder to the other.

Solid Gas Liquid

Phase Phase Phase

Solid Gas Liquid

Phase Phase Phase

FIGURE 5.2 Magnified thin section of a soil. Solid-phase quartz particles are good electric current insulators, and clay mineral and organic matter particles transmit current if surfaces are wetted. The gas phase is essentially made up of air, which does not transmit electric current. The soil solution liquid phase contains dissolved ions and therefore has the capability to deliver electric current.

particle size into sand (2.0 to 0.05 mm), silt (0.05 to 0.002 mm), and clay (less than 0.002 mm) fractions. Quartz, considered an excellent electric insulator, usually dominates a soil's sand and silt size fractions. The clay size fraction is made up primarily of clay minerals and organic matter. Given sufficiently wet conditions, clay minerals and organic matter contribute significantly to electric current flow in soil, and more information on this topic will be provided later in the section. The soil gas phase is mostly air, which is a good insulator, and like quartz, will oppose the flow of electric current. The soil liquid phase is an electrolytic aqueous solution, referred to as the "soil solution." An electrolyte is a chemical substance that will dissociate into ions within a solution. There are usually a variety of dissolved anions and cations in the soil solution, and some of the most common are SO42-, Cl-, HCO3-, NO3-, PO43-, Ca2+, Mg2+, K+, Na+, and NH4+.

Unlike a copper wire, where the electric current charge carriers are electrons, dissolved ions within the soil solution serve as the electric current charge carriers in a soil. Therefore, the electric current in soil is largely electrolytic, meaning that the flow of electric current is governed substantially by the movement of dissolved ions in the soil solution. Insight regarding the resistivity behavior of sandy and silty soils is provided by Archie's law, which is based on electrolytic current flow through a porous media. Archie's law is empirical, and it quantifies the relationship between the overall porous media resistivity, the resistivity of the electrolytic aqueous solution present in the porous media, and the amount of electrolytic solution present per unit volume of porous media. The law was developed particularly for clay-free rocks and sediment, and therefore, can also be used for soils that contain essentially no clay minerals or organic matter. The form of Archie's law most applicable to both saturated and unsaturated conditions for a sandy or silty soil is given as follows:

where p is the overall soil resistivity; pW is the resistivity of the soil solution; 9 is the porosity (volume fraction of soil not part of solid phase); S is the saturation (volume fraction of the porosity filled with soil solution); zt is a constant with a value between 0.5 and 2.5, often initially approximated by 1.0; z2 is a constant ranging from 1.3 to 2.5, but closer to 1.3 for loose sediments; and z3 is a constant with a value usually close to 2 when S is greater than 0.3 (Keller and Frischknecht, 1966; Parasnis, 1986; Reynolds, 1997). Inspection of Equation (5.3) shows that p for a sandy or silty soil depends on pW and the volumetric water content, 8, which can be defined as the volume of soil solution per unit volume of soil, equaling the product of 9 and S (8 = 9S).

It warrants pointing out that the values of pW and 8 are often, but not always, interrelated. One clear example is where higher-temperature conditions lead to evapotranspiration-associated losses of soil solution (decreased 8), resulting in the soil solution dissolved ions becoming more concentrated within the soil solution that remains. This increased ion concentration decreases pW because there are now a greater number of electric current charge carriers per unit amount of soil solution. Interestingly, the likely overall result for this soil drying scenario (decreased 8 and pW) is a rise in p, the reason for which will be discussed in more depth later in the section. Although there is an understanding that pW and 8 are often interrelated, in order to focus the discussion within the next three paragraphs strictly on pW, especially regarding potential effects on overall soil resistivity, p, it is assumed, for the sake of argument, 8 remains constant.

The pW in Equation (5.3) is itself a function not only of the dissolved ion concentrations as previously implied, but also the dissolved ion mobilities. Dissolved ion mobility is, in turn, governed by the ion type and temperature conditions. Equation (5.3) indicates that pW and p are directly related when there is no change in 8. Consider a case where there is an increase in the total dissolved ion concentration (decreased pW), while 8 remains constant. This case obviously results in a greater number of charge carriers per unit volume of soil, thereby enhancing the capacity of the sandy or silty soil to transmit electrolytic current, in turn leading to a decrease in p. One possible agricultural situation involving a scenario in which pW and p are reduced, while the beginning versus ending 8 conditions are the same, is a fertigation event where a soil initially at field capacity and having a dilute soil solution is intensely flushed with a more concentrated solution containing nutrients (NO3-, PO43-, and K+), followed by the soil then being allowed to drain back to field capacity. (Field capacity for a particular soil corresponds to the remaining 8 value that occurs when all the possible gravity drainable water has been leached from the initially saturated to near-saturated soil.)

The capacity of a sandy or silty soil to deliver electrolytic current depends not only on the total amount of ions present but also on the mobility of the various ions within the soil solution. Accordingly, the distribution of the types of dissolved ions within the soil solution potentially has a strong impact on pW, and likewise p, given constant 8. The reason for this impact is that the different dissolved ions typically found in the soil solution have different mobilities. As an example, at 25°C, given a constant electric potential difference driving electrolytic current in an aqueous solution, the mobility of SO42- is approximately twice the mobility of HCO3- (Keller and Frischknecht, 1966). Therefore, assuming all other aspects are equal, a soil solution with SO42- as the dominant anion will have a lower pW value than soil solution with HCO3- as the dominant anion.

Temperature conditions additionally influence ion mobility and, therefore, pW. Ion mobility in an aqueous solution is inversely dependent on the viscosity of the solution, which is inversely dependent on solution temperature. For instance, as temperature decreases, soil solution viscosity increases, ion mobility is reduced, and pW rises (soil solution electrical conductivity is lowered). An equation commonly used to adjust pW due to changes in temperature is where pW_ T is the soil solution resistivity at a temperature of T (°C), pW_ 25°C is the soil solution resistivity at a reference temperature of 25°C, and z4 is a temperature coefficient with a value of 0.022/°C (McNeill, 1980). Equation (5.4) reveals that a decrease in temperature from 35°C to 15°C would increase pW by 56 percent. Based on the direct relationship between pW and p in Equation (5.3), this temperature change would also cause the overall sandy or silty soil resistivity to increase by 56 percent (given negligible evapotranspiration losses and 8 remains constant). The important implication of Equation (5.4) is that seasonal and even daily temperature fluctuations can have a significant effect on near-surface soil resistivity values. (Daily temperature fluctuations in near-surface soil of 10°C are not uncommon.) As a special case, extremely cold conditions, in which the soil solution freezes, will cause the overall sandy or silty soil resistivity to become extremely high (conductivity falls to zero), due to the difficulty in transmitting electric current through ice.

Equation (5.3) indicates an inverse relationship between p for a sandy or silty soil and the volumetric water (soil solution) content, 8 (= 9S). Although this inverse relationship is usually found for most soils, instances do occur when this relationship does not hold, implying that other factors need to be taken into account. There are two fairly intuitive effects that 8 can have on p. First, given set concentrations for the dissolved ions within the soil solution (pW is now assumed to be constant), a change in 8 causes a change in the total number of charge carriers (dissolved ions) per unit volume of soil, in turn altering the soil's capacity to distribute electric current as defined by p (or o, EC). Waterlogged soil conditions produced by an irrigation event conducted to flush salts from the soil profile, followed next by complete gravity drainage, is one agricultural scenario corresponding to pW remaining constant, while 8 changes from near-saturation to field capacity. Under this scenario, p gets larger as the soil drains.

Regarding the second effect of 8 on p, as 8 varies significantly, so too does the continuity of soil solution through which electrolytic current is transferred. These changes in the soil solution continuity in turn alter the soil's ability to transfer electric current as quantified by p. To further emphasize this second 8 effect, a substantial decrease in soil wetness (lower 8) reduces the thickness of the soil solution films covering solid soil particles, thereby lengthening the electric current flow travel paths within the soil solution (increased tortuosity), and as indicted by Equation (5.2), diminishing the overall capability of the soil to convey current (higher p). Wet soils near saturation or at field capacity will exhibit good soil solution continuity for distributing current, but for extremely dry soils, soil solution films may not completely cover all the solid surfaces, thus severely reducing the connectivity of travel paths for electrolytic current flow. In an example discussed previously, soil drying reduces the amount of soil solution present (lower 8), narrowing and lengthening the soil solution conduits for electrolytic current flow, which in turn almost always results in an increased p value, even though there is a drop in pW due to evapotranspiration concentrating dissolved ions in the remaining soil solution.

Up to this point, the discussion regarding soil resistivity has focused on sandy or silty materials containing no clay minerals and organic matter. Most soils, however, have significant amounts of clay minerals (layered aluminosilicates) and organic matter. Soil organic matter can be divided into two components. The first component includes only a few percent of the total soil organic matter and includes living organisms (worms, bacteria, fungi, etc.) and nondecomposed substances such as dead plant roots. The second component, representing the large majority of soil organic matter, is the stable, decomposed residue called "humus" (Bohn et al., 1985). It is the stable, decomposed residue portion of the soil organic matter which affects the overall soil resistivity, p. Clay minerals and organic matter often coat the larger sand- and silt-sized particles, resulting in the sides of soil pores being dominantly composed of these clay mineral and organic matter materials, consequently giving these materials a much larger impact on soil processes than would be inferred based on their weight percent alone. The general manner in which the previously discussed factors influence pW and 8, and likewise p, is the same regardless of whether a soil does or does not contain clay minerals and organic matter. The major difference regarding soils containing clay minerals and organic matter is that given sufficiently wet conditions, there is an additional effect caused by the presence of clay minerals and organic matter, which tends to enhance electric current flow.

Substitution of ions different from the ones normally composing the clay mineral crystal lattice and the functional groups that are a part of the humus chemical structure typically yield large numbers of discrete negatively charged sites on the surfaces of clay mineral and organic matter particles. Cations are electrostatically attracted and become attached at the negatively charged surface sites. The quantity of the negatively charged surface sites per unit amount of dry soil is referred to as the cation exchange capacity (CEC). Given a sufficient amount of soil solution covering the clay mineral and organic matter surfaces, these attached cations are exchangeable and often displaced by other cations temporarily present in the soil solution. The displaced cations move freely within the soil solution adjacent to clay mineral and organic matter surfaces and can then displace cations at different negatively charged exchange sites. The displacement and movement of cations from exchange site to exchange site produces a mechanism by which electric current is essentially transmitted elec-trolytically through a soil along clay mineral and organic matter surfaces. As previously indicated, assuming conditions are wet enough, the presence of clay minerals and organic matter in significant amounts will increase the capability of the soil to deliver electric current, corresponding to a p value lower than what would have been obtained if the clay minerals and organic matter were absent.

The mechanism of electrolytic current transfer facilitated by clay minerals and organic matter depends on the number of negatively charged surface sites. Accordingly, if this mechanism of electric current delivery dominates, which is certainly not always the case, then a strong inverse correlation between the cation exchange capacity (CEC) and p is to be expected. However, different clay minerals exhibit different CEC values. Furthermore, pH governs part of the clay mineral CEC and all of the soil organic matter CEC. The resulting implication regarding CEC dependence on clay mineral type and pH is that an inverse relationship between p and the total amount of clay minerals and organic matter present, although anticipated, probably will not be as strong as the inverse relationship between CEC and p, again assuming this clay mineral and organic matter facilitated, surface-based, electrolytic current transport mechanism dominates.

Water molecules orient themselves within the electric field adjacent to clay mineral and organic matter surfaces. This phenomenon prevents freezing of the soil solution portion near the clay mineral and organic matter surfaces. Furthermore, as temperatures drop below 0°C, dissolved ions tend to migrate out of the soil solution portion that begins to freeze, causing the unfrozen soil solution next to clay mineral and organic matter surfaces to become much more concentrated with dissolved ions. The main consequence for soils containing significant amounts of clay minerals and organic matter is that these soils maintain their ability to deliver electric current, even when temperatures drop below 0°C for prolonged periods. Therefore, when temperatures stay at 0°C or below for an extended time, soils containing significant amounts of clay minerals and organic matter will typically have lower p values than soils having little clay mineral and organic matter material.

The following equation for soil resistivity, valid for temperatures above 0°C, was developed by Rhoades et al. (1976), and takes into account clay mineral and organic matter facilitated, surface-based, electric current:

P Pw Ps

The pS value in Equation (5.5) is the clay mineral and organic matter resistivity component, and z5 and z6 are empirically derived constants. The validity of Equation (5.5) is supported, in part, because of similarities to Equation (5.6) (Schlumberger Wireline and Testing, 1991), which is commonly used in the petroleum industry to determine the resistivity value of a shaly (clayey) sand.

P ziPw RSH

For Equation (5.6), the variables p, pW, 9, and S along with constants, Zj, z2, and z3 were previously defined, and VSH is a shale (clay) volumetric characteristic, the value of W is a function of S, and RSH is a quantity related to the shale resistivity. The first terms to the right of the equal signs in Equation (5.5) and Equation (5.6) certainly exhibit a degree of equivalence to one another, because each contains 8 in the numerator and pW in the denominator. (With respect to Equation (5.6), remember, 8 = 9S.) The quantities that make up the second term on the right side of Equation (5.6) indicate that this term is a resistivity component related to the presence of clay minerals, much the same as the second term on the right side of Equation (5.5).

Equation (5.5) and Equation (5.6) imply a soil model having two separate but continuous electric current pathways, effectively corresponding to two parallel resistors within an electric circuit, where the first of the pathways involves electrolytic current delivery strictly through the bulk soil solution, and the second pathway involves electrolytic current delivery along clay mineral and organic matter surfaces (Knight and Endres, 2005). Here, the term "bulk soil solution" is used to indicate all of the soil solution excluding the thin layers of soil solution adjacent to clay mineral and organic matter surfaces, which contain the "cloud" of cations attracted to the negatively charged surface sites. Rhoades et al. (1989) developed a soil resistivity equation based on another somewhat different model having two separate electric current pathways, where the first pathway is constrained to the larger soil pores and involves electrolytic current transfer strictly through the "mobile" portion of the bulk soil solution. The second pathway is constrained to the smaller pores and electrolytic current transfer through the "immobile" portion of the bulk soil solution alternates with electrolytic current transfer along clay mineral and organic matter surfaces. As an electric circuit, this second model again corresponds overall to two resistors in parallel, but the difference with respect to the first model is that one of these parallel resistors is in effect representative of two resistors in series. The second model considers current flow to be negligible via a "continuous" pathway involving just the electrolytic current transport along clay mineral and organic matter surfaces. More information on the soil resistivity equation derived from this second model is provided in Chapter 2 and Chapter 4. Regardless of the model, there is general agreement that the flow of electric current in soil occurs by two mechanisms; electrolytic current transmission through the bulk soil solution and electrolytic current transmission along particle surfaces composed of clay minerals and organic matter.

Discussions involving Equation (5.3), Equation (5.4), and Equation (5.5) imply that the soil resistivity, p, is influenced by complex interactions among a number of different factors. These complex interactions make it entirely possible for the correlation between one specific factor and p to be much weaker or even the inverse of what might be expected (Allred et al., 2005; Banton et al., 1997; Johnson et al., 2001). The occurrence of this type of result simply indicates that there are other factors, either individually or as a group, that have a greater impact on p than the specific factor being considered. Some factors affecting p, such as soil temperature and soil volumetric water content, are very transient, often exhibiting substantial changes over periods of a few hours or days. Other factors affecting p, if they vary temporally at all, do so at a slower rate, and in this category are soil properties including pH, organic matter content, clay content, CEC, and specific surface. Factors like nutrient level and salinity sometimes exhibit little variation over long periods, but will then change rapidly with an irrigation or fertilizer application event. Changes in soil temperature and shallow hydrologic conditions can cause the average p value within an agricultural field to increase or decrease (Allred et al., 2005). Soil resistivity spatial patterns within an agricultural field, however, have been found to remain relatively consistent over time, regardless of temperature and shallow hydrologic conditions, indicating that p spatial patterns are governed predominantly by the spatial variations in soil properties (Allred et al., 2005, 2006; Lund et al., 1999).

5.4 THEoRETICAL CURRENT FLoW IN A HoMoGENEoUS EARTH AND apparent resistivity

Resistivity methods produce three-dimensional patterns of electric current flow and electric potential within the subsurface. Figure 5.3 two-dimensionally illustrates the distributions of current flow (solid black arrowhead lines) and potential (circular dashed black lines) in a vertical plane that intersects the positions of four electrodes, C1, C2, P1, and P2 located at the ground surface. For simplicity, the lines of equal potential shown in Figure 5.3a represent only the electric field due to current applied at Cj, and the lines of equal potential shown in Figure 5.3b represent only the electric field due to current collected at C2. Figure 5.3a shows that electric current, +I, applied at the surface

FIGURE 5.3 Electric current flow (solid black arrowhead lines) and electric potential (circular dashed black lines) due to (a) an isolated electrode, C1, through which current, +I, is applied into the ground, and (b) an isolated electrode, C2, through which current, -I, is collected from the ground. The electrode locations for measurement of potential are P1 and P2.

FIGURE 5.3 Electric current flow (solid black arrowhead lines) and electric potential (circular dashed black lines) due to (a) an isolated electrode, C1, through which current, +I, is applied into the ground, and (b) an isolated electrode, C2, through which current, -I, is collected from the ground. The electrode locations for measurement of potential are P1 and P2.

through a single isolated electrode, C1, will spread out in a radial pattern away from C1 within the ground beneath it (again, solid black arrowhead lines), given that the soil or rock material through which the current travels is homogenous and isotropic. Figure 5.3b shows that for an isolated electrode, C2, that collects current, -I, from the ground, there is again a radial pattern of subsurface current flow, but in a direction toward C2. Regardless of whether electric current is being applied or collected by an isolated electrode, surfaces of equal electric potential due to a particular current electrode will have a hemispherical shape centered about the position of that current electrode, represented two-dimensionally in Figure 5.3 by dashed circular lines.

Consider the gray hemispherical shell with a wall thickness of dr that is depicted in Figure 5.3a. For illustration, the gray hemispherical shell appears thick, but for the sake of discussion, assume it is infinitesimally thin, so dr is actually extremely small. The current application electrode, Cj, is located at the shell's radial center. Let r be the radial distance from C1 to the inside surface of the gray hemispherical shell. The area of the shell's inside surface is 2nr2. The resistivity of the homogeneous and isotropic material making up the subsurface is designated as p. The total electric current flowing across this hemispherical shell equals +I, which is the electric current applied at C1. The electric potential difference from the inside to the outside surfaces of the thin hemispherical shell is dV.

A form of Ohm's law, based on the scenario just described, can be given as follows:

2 nr2

Upon integration, the electric potential at a distance r from C1 is expressed as follows:

2 n r where z7 = 0, because Vr = 0 at infinite distance from C1. If r is set to equal the distance between C1 and P1 (r = CP), then the potential at P1 due to the current applied at C1 is:

0 0

Post a comment