IMPACT OF CONDUCTIVE MINERALS ON

MEASUREMENTS OF ELECTRICAL RESISTIVITY

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF GEOPHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE

OF DOCTOR OF PHILOSOPHY

ADAM TEICHERT TEW

MARCH 2015

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/gx072rj6544

© 2015 by Adam Tew. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii

http://creativecommons.org/licenses/by-nc/3.0/us/http://creativecommons.org/licenses/by-nc/3.0/us/http://purl.stanford.edu/gx072rj6544

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Gerald Mavko, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Eric Dunham

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Jack Dvorkin

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

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iv

Abstract

The electrical properties of rocks have been used in geophysical interpretation for

decades. At low frequencies, the dominant controls on the electrical resistivity of

rocks are typically the brine resistivity and the volume fraction of brine. Sometimes

other factors become important.

The primary objective of this thesis is to identify the physical rules that govern the

impact of conductive minerals on the low frequency electrical properties of rock. This

relationship is examined primarily by measuring the complex, frequency dependent

resistivity of clean, well characterized artificial sediments in the laboratory. Important

factors which mediate the impact of conductive minerals include the volume fraction,

the dry conduction fraction and the electrochemistry occurring at the grain/brine

interface.

Chapter 1 includes a review of the history of resistivity measurements, a look at

Archie’s law and the modes of electrical conduction in rock. Unlike most rocks which

carry electric current through the ions in the pore fluid, rocks which contain

conductive minerals can sometimes pass significant amounts of current through the

free electrons in the rock matrix. If rocks of this type are interpreted using an

uncorrected Archie model, the water saturation will be overestimated, which may

result in a productive reservoir being overlooked.

In Chapters 2 and 3, the complex resistivity of a set of well-defined sediments at

frequencies from 50 Hz to 100 kHz is reported. The parameters of grain size, porosity,

v

brine salinity and saturation were varied. The resistivity of sediments and consolidated

artificial samples which contained varying fractions of conductive grains (up to 30%

by volume) is reported. In these tests reductions in resistivity were observed at higher

frequencies when the conductive fraction was increased. Large and/or abrupt changes

were not observed, likely because the dry conductive threshold was not reached.

In Chapter 4, some simple electrode/brine experiments are reported which

examined the magnitude of the electrode potential that must be overcome to drive

charge transfer across the interface between conductive grain and brine. It turned out

that the voltage threshold is relatively high for pyrite compared to the voltage

gradients typically present in geophysical measurements so this potential current

pathway can often be assumed to carry no current, at least in DC measurements.

Conductive minerals which are present in high enough volumes can form

conductive pathways through the host rock. Below the dry conduction threshold, the

fraction of conductive mineral has little impact on the DC resistivity, but at higher

frequencies reduces resistivity. Above the dry conduction threshold, the conductive

minerals can have a dramatic effect on the DC resistivity.

Chapter 5 includes a discussion of ways to predict resistivity in rocks which

contain conductive minerals both above and below the dry conduction threshold.

Determining whether or not the rock of interest is above or below the dry conduction

threshold is important as the methods of interpretation differ above and below. The

threshold can vary from a low volume fraction in rocks with conductive veins, to high

volume fraction in rocks with non-conductive grain coatings. Below the threshold,

results are comparable to the measurements reported in Chapter 3. Above the

threshold, additional measurements are needed for interpretation. A framework for

incorporating those measurements is presented. Also discussed are various details

related to testing and avenues for future research.

vi

Acknowledgements

There were many who contributed to this work and to my education at Stanford in

one way or another and I am grateful for those efforts and interactions. Here, I

highlight a few individuals who played especially important roles.

Gary Mavko and Jack Dvorkin provided advice and guidance in the latter half of

this project. They excelled at finding my incomplete ideas and unexplained data points

and asking difficult questions that helped me to improve my understanding of the

physics. Their ideas were particularly useful in building a consistent interpretation of

the data and in identifying new avenues for analysis and interpretation.

Tiziana Vanorio introduced me to the lab and gave me a lot of time and guidance

as I learned the equipment and developed a research plan. I enjoyed the time I spent

working with her on various projects. Her instruction related to lab methods and data

analysis has been invaluable.

Eric Dunham was a member of my reading, defense, and annual review

committees. Rosemary Knight was a member of my annual review committee and the

advisor of my second project.

Financial support for this work came from the SRB and its affiliates.

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Contents

Abstract .......................................................................................................................... iv

Acknowledgements ....................................................................................................... vi

Contents ........................................................................................................................ vii

List of Tables ................................................................................................................. ix

List of Figures ................................................................................................................ xi

Chapter 1 Introduction .................................................................................................... 1

Archie’s Law .............................................................................................................. 2

Units ........................................................................................................................... 8

Modes of conduction in earth materials ................................................................... 10

Low Resistivity Pay ZONES .................................................................................... 14

Research Focus and summary .................................................................................. 15

Chapter 2 Fundamental resistivity measurements ........................................................ 17

Introduction .............................................................................................................. 17

Methods .................................................................................................................... 18

Results ...................................................................................................................... 25

Discussion ................................................................................................................. 38

Chapter 3 Complex resistivity with conductive grains ................................................. 48

Introduction .............................................................................................................. 48

Methods .................................................................................................................... 53

Results ...................................................................................................................... 63

Discussion ................................................................................................................. 70

Chapter 4 Grain and brine interface ............................................................................. 73

Introduction .............................................................................................................. 73

Electrolysis Experiments .......................................................................................... 75

viii

Results ...................................................................................................................... 77

Discussion ................................................................................................................. 82

Chapter 5 Conclusions, Recommendations and Future Work ...................................... 92

A first step: Percolation thresholds .......................................................................... 92

Above the percolation Threshold ............................................................................. 96

Complex resistivity and frequency effects ............................................................... 97

Testing parameters .................................................................................................... 98

Making this useful (And how this relates to Archie’s Law) .................................. 100

Future avenues for study ........................................................................................ 104

Final Words ............................................................................................................ 105

Appendix: Data ........................................................................................................... 106

References .................................................................................................................. 127

ix

List of Tables

Table 1: Summarizes the electrode tests which have been reported, including the electrode material, the test solution, the apparent voltage threshold, and the Figure where the results are displayed. ................................................................ 81

Table 2: Variable fraction coarse and fine grain sand, brine saturated (50 g/l) ......... 106

Table 3: Variable fraction coarse and fine grain sand, brine saturated (4 g/l) ........... 107

Table 4: Variable fraction sand & powder, brine saturated ........................................ 108

Table 5: Variable salinity brine .................................................................................. 110

Table 6: Variable salinity in coarse acrylic ................................................................ 112

Table 7: Variable salinity in brine saturated sand ...................................................... 114

Table 8: Variable brine saturation in quartz sand ....................................................... 116

Table 9: Coarse sand arranged in parallel and series with fine sand and mixed sand 118

Table 10: Consolidated, brine saturated, coarse acrylic and pyrite ............................ 119

Table 11: Unconsolidated, brine (1) saturated, coarse acrylic and pyrite .................. 119

Table 12: Unconsolidated, brine (2) saturated, coarse acrylic and pyrite .................. 120

Table 13: Fine grained acrylic & steel shot ................................................................ 121

Table 14: Electrolysis, steel in H2SO4 solution .......................................................... 123

x

Table 15: Electrolysis, copper in H2SO4 solution ...................................................... 124

Table 16: Electrolysis, pyrite in H2SO4 solution ........................................................ 125

Table 17: Electrolysis, pyrite electrodes in NaCl solution ......................................... 126

xi

List of Figures

Figure 1.1: Illustration of the difference between gravitational and electric potential for brine. On the left, all molecules (charged or not) respond to the gravitational potential. On the right, only the ions experience a net force, and the direction of the force is charge dependent. .............................................................................. 11

Figure 1.2: Dark, iron bearing minerals (likely magnetite and hematite) that have separated out on a beach. Photographed area is approximately 1m wide. ........... 13

Figure 2.1: Photo of the test vessel, including upper stainless steel electrode. The vessel was built using parts from a MC Miller soil cylinder. ............................... 19

Figure 2.2: Cumulative grain size for the coarse and fine sands which were used in the sand mixing test. ................................................................................................... 23

Figure 2.3: Diagrams of the four test geometries. Current ran vertically through the cylinders. In the upper left: coarse and fine sand in series. In the upper right: coarse and mixed sand (50% coarse sand and 50% fine sand) in series. In the lower left: coarse and fine sand in parallel. In the lower right: coarse and mixed sand in parallel. ..................................................................................................... 24

Figure 2.4: Resistivity of brine as a function of salt concentration. For each salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. .................................................................................................................. 26

Figure 2.5: Reactivity of brine as a function of salt concentration. For each salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz. ...................... 26

Figure 2.6: Resistivity of brine saturated coarse acrylic as a function of salt concentration. For each salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. .......................................................... 27

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Figure 2.7: Reactivity of brine saturated coarse acrylic as a function of salt concentration. For each salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz. ...................................................................................................... 28

Figure 2.8: Resistivity of brine saturated beach sand as a function of salt concentration. For each salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. .......................................................... 29

Figure 2.9: Reactivity of brine saturated beach sand as a function of salt concentration. For each salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz........................................................................................................................ 29

Figure 2.10: Resistivity of beach sand as a function of saturation. For each saturation, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. .................................................................................................................. 30

Figure 2.11: Reactivity of beach sand as a function of saturation. For each saturation, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz ....................... 31

Figure 2.12: Resistivity of sand saturated with 4 g NaCl/L DI-water as a function of coarse fraction. For each mixture, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. .......................................................... 32

Figure 2.13: Reactivity of sand saturated with 4 g NaCl/L DI-water as a function of coarse fraction. For each mixture, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz. ................................................................................................. 32

Figure 2.14: Resistivity of sand saturated with 50 g NaCl/L DI-water as a function of coarse fraction. For each mixture, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz. ................................................................................................. 33

Figure 2.15: Reactivity of sand saturated with 50 g NaCl/L DI-water as a function of coarse fraction. For each mixture, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz. ................................................................................................. 33

Figure 2.16: Resistivity of sand as a function of frequency and geometry. Note the vertical axis does not start at 0. Unlike most figures in this and other chapters the color code does not represent the different test frequencies – it represents the specific test geometry. .......................................................................................... 34

xiii

Figure 2.17: Reactivity of sand as a function of frequency and geometry. Unlike most figures in this and other chapters the color code does not represent the different test frequencies – it represents the specific test geometry. ................................... 34

Figure 2.18: Porosity of mixed sand and powder as a function of sand fraction. The point at 0.77 sand fraction was oversaturated with brine, compared to the same dry mixture’s porosity. ......................................................................................... 35

Figure 2.19: Resistivity of mixed sand and powder as a function of sand fraction (by mass). For each mixture, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. The 0.77 sand fraction mixture was oversaturated with brine. ...................................................................................... 36

Figure 2.20: Reactivity of mixed sand and powder as a function of sand fraction (by mass). For each mixture, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz................................................................................................................. 36

Figure 2.21: Resistivity and reactivity of mixed sand and powder as a function of porosity. For each mixture, measurements were made at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted. ............................................................... 37

Figure 2.22: Resistivity of brine as a function of salinity. Schlumberger data taken from Schlumberger Log Interpertation Charts, Edition 2000, Gen-9. Data shown from this study was measured at 10 khz. .............................................................. 38

Figure 2.23: Conductivity of brine as a function of salinity. ........................................ 39

Figure 2.24: A 2D illustration of the geometry of bimodal grain size mixtures. As drawn, there is some overlap between coarse and fine grains which should not occur, however, using the relatively low grain size ratios depicted here other, more complicated, effects are introduced if the coarse and fine grains do not overlap. ................................................................................................................. 40

Figure 2.25: Resistivity of sand as a function of coarse fraction. Series and parallel resistivities have been added to Figure 2.12. Series geometry data shown with green dashes. Parallel geometry data is marked with red X’s. Blue squares are homogenous mixtures of coarse and fine sand. For each mixture, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz. ............................................. 42

Figure 2.26: Resistivity of sand as a function of coarse fraction. Figure shows 2 kHz data. Series geometry data shown with green dashes. Parallel geometry data marked with red X’s. Voigt-Reuss boundaries are shown in black between the components of both tests – the lower pair is the boundaries for combinations of

xiv

the coarse and fine sand, the upper pair is the boundaries for combinations of the coarse and mixed sand. The red dashed lines are Voigt-Reuss boundaries assuming a 2% uncertainty in the resistivities of the end members. .................... 42

Figure 2.27: Reactivity of sand as a function of coarse fraction. Series and parallel reactivities have been added to Figure 2.12. Series data shown with green dashes, parallel geometry points marked with a red X. Blue squares are homogenous mixtures of coarse and fine sand. For each mixture, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz...................................................................... 44

Figure 3.1 Close up of two consolidated samples. The sample on the left is 100% acrylic. Colored grains in the sample on the left are grains of colored acrylic. The sample matrix on the right is 30% pyrite and 70% acrylic by volume. ................ 55

Figure 3.2: Illustration of the final system configuration for measuring complex resistivity on core plugs. Colored lines represent tubing - red lines carry hydraulic fluid, purple lines carry compressed air, and blue lines carry the pore fluid. The green lines are the electrical leads, which connect the electrical meter to the core holder. X’s represent valves. ................................................................................ 59

Figure 3.3: Resistivity versus frequency for brine saturated, consolidated mixtures of pyrite and acrylic. Unlike in most figures in this and other chapters, the color code does not represent the different test frequencies. Instead, it identifies the sample. .................................................................................................................. 64

Figure 3.4: Reactivity versus frequency for consolidated mixtures of pyrite and acrylic. Unlike in most figures in this and other chapters, the color code does not represent the different test frequencies. Instead, it identifies the sample. ............ 65

Figure 3.5: Resistivity versus pyrite volume for unconsolidated mixtures of pyrite and acrylic saturated with 50 g/l brine. Resistivity was recorded at five frequencies for each pyrite fraction. ........................................................................................ 66

Figure 3.6: Reactivity versus pyrite volume for unconsolidated mixtures of pyrite and acrylic saturated with 50 g/l brine. Reactivity was recorded at five frequencies for each pyrite fraction. .............................................................................................. 66

Figure 3.7: Resistivity versus pyrite volume for unconsolidated mixtures of pyrite and acrylic saturated with 25 g/l brine. Resistivity was recorded at five frequencies for each pyrite fraction. ........................................................................................ 67

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Figure 3.8: Reactivity versus pyrite volume for unconsolidated mixtures of pyrite and acrylic saturated with 25 g/l brine. Reactivity was recorded at five frequencies for each pyrite fraction. .............................................................................................. 68

Figure 3.9: Resistivity versus steel volume for unconsolidated mixtures of steel and acrylic saturated with 25 g/l brine. 5 frequencies were tested at each steel fraction. ................................................................................................................. 69

Figure 3.10: Reactivity versus steel volume for unconsolidated mixtures of steel and acrylic saturated with 25 g/l brine. 5 frequencies were tested at each steel fraction. ................................................................................................................. 69

Figure 4.1: Test setup for electrolysis experiments. ..................................................... 76

Figure 4.2: Photo of pyrite electrodes after testing. The gridlines are approximately 5 mm apart. .............................................................................................................. 77

Figure 4.3: DC voltage vs current for two stainless steel strips suspended in a very dilute sulfuric acid solution. When the test was repeated (blue diamonds) more time was provided between voltage changes. ....................................................... 78

Figure 4.4: DC voltage vs current for two copper strips suspended in a very dilute sulfuric acid solution. ........................................................................................... 79

Figure 4.5: DC voltage vs current for two pyrite crystals suspended in a dilute sulfuric acid solution. When the test was repeated (red diamonds) the time between tests was increased. ....................................................................................................... 80

Figure 4.6: DC voltage vs current for pyrite crystals suspended in a 50 g NaCl per L DI-water solution. ................................................................................................. 81

Figure 4.7: Schematics of three slightly more complicated grain fluid systems. The blue area is brine. Yellow blocks are highly conductive grains (compared to the brine). The grey blocks represent electrodes. The red lines mark approximate equipotential lines. The small green squares mark areas of the grain through which charge is passing. The top figure shows a conductive grain blocking a pore. The middle figure shows a conductive grain blocking a pore in parallel with an unblocked pore. The bottom figure shows a conductive grain partially blocking a pore. .................................................................................................... 84

Figure 4.8: Shown are four highly conductive grains partially blocking brine filled pores, varying only in the voltage applied between the two electrodes. In the

xvi

upper left, with 8V, current flows through most of the grains surface and the grain (including the interfaces) appears more conductive than the fluid. In the upper right, with 4V, current flows only through the ends of the grain, and the grain appears to match the conductivity of the fluid. In the lower left, with 3V, current can only pass through a small portion of the surface and the grain appears less conductive than the fluid. Finally, at the lower right, with 2V, the grain carries no current and looks like an insulator. ...................................................... 85

Figure 4.9: Shown are three conductive grains partially blocking pores otherwise filled with a conductive brine. The conductivity of the grains is identical to the brine. The voltage between the electrodes varies between the illustrations, from 24V to 6V to 2V. .................................................................................................. 86

Figure 4.10: Shown are three conductive grains partially blocking pores otherwise filled with a conductive brine. The conductivity of the grains is much less than the brine. The voltage between the electrodes varies between the illustrations, from 8V to 4V to 2V............................................................................................. 87

Figure 4.11: Adapted from He and Ekere (2004). Figure shows estimates of percolation thresholds at several insulating to conducting grain diameter ratios. At 1, the insulating and conducting grain size is the same. At 6 the conductive grain diameter is one sixth the insulating grain size diameter. ............................. 89

Figure 4.12: A simple illustration of three rocks which are all above the dry conduction threshold in at least one direction. The area highlighted in yellow and covered with yellow circles is above the dry conduction threshold – so it could, for example, contain 50% pyrite. The grey areas do not contain conductive minerals. The vertical percentage of rock which contains conductive minerals varies in these three rocks from 100% on the left to 20% on the right. ............... 90

Figure 5.1: Illustrations of some possible conductive mineral geometries. The conductive mineral is shown in red. On the left is shown the baseline clean sand. The figure labeled “One grain size” illustrates a pack in which both conductive and non-conductive grains are a uniform grain size. “Two grain sizes” shows smaller conductive grains filling the pore space of the initial non-conductive pack. “Veins” illustrates conductive veins cutting through the pack. “Coordination number” shows a pack which has been compressed, thereby increasing the number of contacts each grain makes with other grains. “Grain Coatings” shows the original pack which has been coated with a thin conductive layer. The alternative is also possible, where the conductive grains are covered with a thin non-conductive layer. ......................................................................... 94

Figure 5.2: Conductivity versus conductive volume fraction for four geometries. Vertical dashed lines at 0.3 and 0.7 mark the rock porosity and solid fraction

xvii

respectively. The orange lines represent a geometry which begins conducting immediately, such as brine in a water wet rock (Archie behavior). The geometry represented by the blue lines requires a volume fraction of 26% before it begins conducting (conductive mineral behavior). Grey lines are Voigt-Reuss bounds. ............................................................................................................................ 102

1

Chapter 1

Introduction

Modern geophysicists have an overwhelming number of tools at their disposal for

characterizing rocks both in the laboratory and in the subsurface. For several decades,

work in the rock physics community has taken advantage of newly available high

resolution seismic and bore hole sonic data. As a result, an emphasis has been placed

on the characterization of the elastic properties of rocks, and much less attention has

been paid to other material properties of rocks. Some of these other properties, such as

radioactivity and density, have simple theoretical underpinnings. However, properties

related to the nature of the pore network are more difficult to understand and explain,

typically because these properties depend on the interaction of many complex physical

processes.

Electrical resistivity measurements were the first type of wireline log to be used to

assess oil and gas prospects (Ellis, 2007). Archie’s Law (published in 1942) and

related variants, combined with calibration data, are often sufficient to improve the

user’s understanding the distribution of hydrocarbons. The electrical properties of

rocks are dependent on the complex irregular pore space (Man, Jing, 1999), a fact that

makes relative simplicity of Archie’s law is a bit puzzling. The difficulty of obtaining

consistent, reliable resistivity measurements in the lab (Sprunt et al., 1990) continues

to complicate the interpretation of resistivity data.

2

Surface based resistivity surveys have been used in near surface explorations in

applications like geotechnical work, groundwater contamination, seawater intrusion

and archaeology (Daily, 2004). Deeper imaging surveys for the energy industry are

rare these days, though EMGS continues to make a business providing them. Deep

(few km) electrical surveys offer better contrast for fluids but poorer resolution than

seismic.

ARCHIE’S LAW

When discussing the electrical properties of rocks, it is necessary to include a

discussion of Archie’s law and its variants and addendums.

Electrical resistivity techniques have been used since the 1940s. The technique

was introduced in a seminal paper by Shell’s Gus Archie, which introduced and

clarified the relationship between reservoir characteristics, particularly water

saturation, and electrical resistivity (Archie, 1942). Archie based his conclusion on the

behavior of clean sandstone samples taken from the Gulf of Mexico. He found that the

resistivity of each brine-saturated rock sample, Ro, increased linearly with the brine

resistivity, Rw. He dubbed the term relating these two factors the formation factor, F,

where F = R0 / Rw . This had been proposed earlier by Sundberg (1932).

Archie found that the relationship between F and the porosity (ϕ) of brine

saturated rocks took the form F = 1 / (ϕ m ), where m was between 1.8 and 2 for his

data. For partially saturated rocks, he proposed the “resistivity index”, I, where

I=Rt / R0

and Rt is the measured resistivity of the partially brine saturated rock. Measurements

of resistivity in partially saturated rocks had been performed before (Martin, 1938;

Jakosky, 1937; Wyckoff, 1936; Leverett, 1939); Archie used the results of those

experiments to develop the relationship I=1 / Snw where Sw is the water saturation and

the constant n is approximately 2. By combining the equations for the formation factor

and resistivity index. He obtained the equation now known as Archie’s Law:

Rt = Rw / (ϕ m · Snw)

3

The simplicity of the formula and its broad usefulness have made it a staple of well

log interpretation for decades. It has been found to satisfactorily describe experimental

data for a wide range of situations and rock types. Efforts to understand and explain

the fitting exponents, n and m, have continued.

Exponent m, which relates porosity to the formation factor, was noted by Archie to

be approximately 1.3 in unconsolidated sands, but near 2 in Gulf Coast sandstones. In

sandstones, diagenesis is primarily driven by cementation of the grains; therefore, m

became known as the cementation exponent (Guyod, 1944). Even in this early paper,

it was noted that the actual relationship between cementation, resistivity and m was

more complicated and could only be determined in the laboratory. The next

breakthrough came when Wyllie and Rose (1950) attempted to relate m to textural

parameters of the rock such as tortuosity and specific surface area, as had been done

by Kozeny and Carman (1937) for permeability. Wyllie and Rose defined the

tortuosity (T) of the pore space as

T = (La / L) 2

where La is the flow path length and L is the direct length. They then computed the

formation factor as a function of tortuosity and porosity, giving

� =√(�)

�

for a fully saturated rock.

They also attempted to apply the model to partially saturated rocks, finding that n

should lie between 1.7 and 2.5. However, after additional studies by Archie, it became

apparent that pressure driven fluid flow and electrically driven ion flow do not behave

in the same way. Specifically, Archie found that while permeability depended on pore

structure and porosity, the formation factor was not impacted strongly by variations in

pore structure, instead varying with porosity alone (Archie, 1952).

The difficulties of actually measuring, or even defining, tortuosity in the pore

network of a real rock made it difficult to test the predictions of Wyllie and Rose .

Finally, in 1952, Winsauer and others from Humble Oil devised a way to measure

tortuosity by timing how long it took for ions to pass through the pore space. They

applied the new technique to a variety of sandstones from across the US and found

4

that the measured results deviated from the predictions of Wyllie and Rose. They

proposed an alternative formulation for the formation factor:

F=0.62/ ϕ 2.15.

In response, Wyllie returned to the lab and performed a number of experiments on

rocks of varying cementation, grain shape, and porosity (Wyllie, 1953). He proposed

the relationship

F=C/ ϕ k,

generalizing the formulation of the formation factor proposed by the Humble Oil

group, adding fitting parameter C, which had previously been assumed by Archie to be

1. By the 1960s it was generally recognized that the Archie parameters were best

determined empirically, despite the large number of competing theoretical models

(including Wyllie, 1950; Wyllie, 1953; Winsauer, 1953; Fatt, 1956; Owen, 1952). For

F=a / ϕ m

a and m could be derived from well log data to some degree, though a large study by

Phillips Petroleum Co. demonstrated that a and m values varied significantly across

one field, limiting the usefulness of this technique (Porter, 1970). Over the years,

several formulas were developed to predict m within specific data sets. (Neustaedter

1968, Coates 1973, Gomez-Rivero 1976, Raiga-Clemenceau 1977, Sethi 1979, Olsen

2008, Azar 2008). Wafta (1987) showed that even within a well, m will vary

throughout a carbonate reservoir. Despite these efforts,, and particularly in carbonates,

simple relationships between porosity and formation factor consistently fail due to the

complexity of the rocks and the high variability in m for the same porosity. Later

classification of carbonates into eight rock types combined with an extensive lab

survey provided a more useful predictor (Towle, 1987).

Although early attempts to use tortuosity to relate m to the formation factor didn’t

work out, modeling efforts continue. In 2008, Abousrafa et al. published a pore

geometry model and concluded that “the formation resistivity factor . . . is almost

entirely controlled by pore throat radius, whereas both pore throat and void radii affect

the cementation factor.” Revil (2014) demonstrated that, for low salinity brines, the

5

surface conductivity of the grains biases the values calculated for m. Work reported by

Dvorkin (2011) showed the potential for using 3D CT imaging to constrain m.

Theoretical work has also continued. It has been shown, for instance, that m=1.5

for spherical grain packs (Sen, 1981), and that grain size in non-shaley rocks has little

impact on the electrical properties of those rocks (Cohen, 1981). In 2012, Kennedy

and Herrick proposed a new conductivity model for rocks that were well-described

using Archie’s law. To quote Kennedy and Herrick’s paper, “The petroleum industry’s

standard porosity-resistivity model [i.e., Archie’s law], although it is fit for its

purpose, remains poorly understood after seven decades of use.” They derived a

method with similar predictive power, but instead of the rather arbitrary a, m and n,

their model’s inputs have a priori physical interpretations. As the paper points out, the

conductivity of a rock is a product of the brine conductivity, the brine fraction and a

geometric factor. In Archie’s law, geometric information in Archie’s law is convoluted

within several variables, making interpretation of the fitting parameters unclear. The

Kennedy and Herrick model overcomes this shortfall by separating the geometric

information so that each variable described one geometric attribute. The three

geometric attributes are (1) the percentage of the porosity’s cross sectional area which

is brine, (2) a term which describes the relative size of pore throats, (3) a geometrical

factor independent of porosity and (4) a term for so called excess conductivity, which

would be zero in an Archie-type rock.

Despite this progress, developing an understanding n, the saturation exponent in

Archie’s Law, has been more challenging. It has been shown that while saturation is

important, fluid distribution in the pore space also affects this exponent. The fluid

distribution in turn is a function of the wettability (Keller, 1953), the displacement

history, and the pore size distribution (Diederix, 1982; Swanson, 1985). The

difficulties of determining n in the lab have forced experimenters to preserve or re-

creating down-hole conditions in the laboratory.

One problem with Archie’s experimental work is that it relied on only four

published data sets of partially saturated rocks (Martin, 1938; Jakosky, 1937;

Wyckoff, 1936; Leverett, 1939). This paucity of data led Archie to conclude that an n

6

of 2 describes most rocks. More realistic experimental work reported by Guyod (1948)

and Dunlap (1949) showed that n ranged at least from 1 to 2.5. Dunlap also showed

that n was not strongly influenced by porosity or permeability, but was influenced by

pore fluid displacement history.

Shaley sands posed another challenge for Archie’s law. Patnode and Wyllie (1950)

noted that Archie’s law was inaccurate for shaley sands and artificial clay slurries.

They proposed that the observed decrease in resistivity with increasing clay content

could be explained by introducing a conductive solid component. The problem with

this idea is that clays are generally not conductive when dry. Observing this, in 1953

Winsauer and McCardell proposed that the observed extra conductivity arises not

directly from the conductivity of the clay minerals, but from an electrical double layer

in the brine near the grain surface. The double layer is caused by the excess bound

charge on the clay surface, which attracts moveable charge carriers (ions in this case)

from the brine, concentrating them near the mineral’s surface and separating them by

charge into two layers. In such a scenario, clay could appear conductive when wetted

with brine and also appear insulating when dry. They formulated their predictions of

rock conductivity as:

C0 = 1 / F · ( Cw + Cz )

where Cz is the double layer conductivity and Cw is the brine conductivity. Theoretical

work provided a solution built from thermodynamic principles and ion transport

theory which related the total conductivity to the mobility of the clay’s counterions

(the ions in the brine which were attracted to the surface by the unbalanced charge at

the surface of the clay minerals), their concentration, and a ratio of ion mobilities near

to and far from the surface (De Witte, 1955). A method was later developed to

approximate these parameters from the cation exchange capacity (CEC), which could

more easily be measured (Hill, 1956).

In 1967, Waxman and Smits proposed a new model for shaley sand

conduction:

C0 = (1/F) · ( B·Qv + Cw ),

7

where B is counterion equivalent conductance and Qv is counterion concentration.

These values could be estimated from core measurements. They also performed a

number of useful experiments to measure the conductivity of shaley sands in the

laboratory; their findings conformed well to their model’s predictions. Clavier, Coates

and Dumanoir (1984) built on the idea presented by Waxman & Smits to produce a

new dual-water model, which accurately described sample types that had previously

fit the model predictions poorly.

For a more detailed historical review and handy guide to the different forms and

uses of Archie’s law, see the series of publications by Schlumberger titled Archie I

(1988), Archie II (1988) and Archie III (1989). These articles show the successes of

Archie’s law and describe modifications made over the years to fit particular needs.

Archie’s law can be adapted to many situations with good success, in some measure

because with three empirical fitting parameters, there is quite a bit of wiggle room.

To a petrophysicist, Archie’s Law is tremendously useful for extracting

information from well logs as long as good calibration data is available. From a rock

physics perspective, the usefulness of Archie’s Law is limited by its empirical nature.

The underlying mechanisms which determine electrical properties are fairly well

understood, but they tend to be difficult to measure or quantify. In addition, Archie’s

law itself doesn’t tell us what about the rock makes it behave electrically in a certain

way. Computational pore scale modeling may make this kind of quantification more

feasible in the future, but it is likely that Archie’s law will continue to be reliant on

existing data for calibration.

Archie’s Law assumes that electrical measurements are made at zero frequency,

and that there are no frequency effects, or that such effects have already been

removed. For measurements recorded at or below a few thousand Hz, Archie’s Law is

often sufficient. However, at higher frequencies (MHz and higher), the fitting

parameters change substantially. It is important to be aware of this when interpreting

LWD or MWD data, as it is typically recorded at hundreds of thousands or a few

million Hz, and may not correlate well with existing laboratory measurements without

additional efforts to account for the frequency differences.

8

Through the remainder of this dissertation, Archie’s Law will see little use, as the

emphasis will be on interpretation rather than prediction. In my experiments,

saturation, porosity, and resistivity are all known so there is nothing left for Archie’s

law to predict. This avoids the uncertainties associated with the three fitting. The

saturation exponent, for example, can be predicted from the measurements reported in

Chapter 2.

UNITS

There are a number of terms that come up in discussions of electrical properties of

rocks. When dealing with electrical circuits and circuit elements, the typical terms are

resistance, reactance and impedance.

Resistance (R) is a property of a circuit element that resists current flow through

that element. The resistance is equal to the voltage (V) across the element divided by

the current passing through the element (I).

R = V/I

Resistance opposes current flow caused by both constant and alternating voltages,

and the resistance itself is not frequency dependent. Typical units of resistance are

Ohms. Conductance (G) is the reciprocal of resistance.

G = 1/R = I/V

Reactance (X) is another property of a circuit element that resists the flow of

current. Unlike resistance, reactance is frequency dependent and can be either

capacitive or inductive. Circuit elements are typically defined by a frequency

independent property, either the inductance (L) or the capacitance (C) of the element,

which is combined with the angular frequency to determine the reactance. In terms of

the inductance and capacitance, reactance can be expressed as:

X = XL - XC

XL = 2πf L

XC = 1 / (2πf C)

9

where f is the frequency in Hertz, L is in Henrys, C is in Farads and X, XL and XC are

in Ohms. Capacitive reactance reduces current at lower frequencies, while inductive

reactance reduces flow at higher frequencies.

Impedance (Z), sometimes called complex impedance, is the total resistance to

current flow through a circuit. If the current is DC, Z = R. Otherwise impedance has a

component of both resistance and reactance and Z = R + jX. The magnitude of the

impedance is:

|Z| = sqrt ( R2 + X2 )

θ describes the phase angle between the current and voltage. It is zero when there

is no inductance or capacitance.

θ = arctan ( X / R )

Resistivity (ρ, units of Ohm ⋅ meter) is similar to resistance in that they both resist

current flow and both are frequency independent. However, while resistance is a

function of the element shape and composition, resistivity is a material property. For

instance, a carbon ribbon would have a constant resistivity throughout its material, but

a measured resistance would depend on the distance between the test points, with

longer distances having higher resistance. If the geometry of the system is known, it is

possible to determine the material resistivity from a resistance measurement. As an

example, the conversion from resistance to resistivity for a wire is:

ρ = R⋅A / L

where A is the cross sectional area of the wire and L is the length.

Conductivity (σ) is the reciprocal of resistivity, and represents the ease of

movement of free charges.

Reactivity is to reactance as resistivity is to resistance – the same geometric

scaling is applied to both (for instance A/L for a wire), and the phase angle is the same.

Impeditivity (similar to impedance) is the square root of the sum of the squares of

resistivity and reactivity. The terms reactivity and impeditivity are less frequently used

and do not have as clear a physical interpretation as resistivity. They are, however,

useful when discussing bulk complex electrical properties. Further, because the

difference between the reactivity and reactance is a simple scaling factor when

10

calculated this way, conclusions drawn from trends in the reactivity are as valid as

conclusions from trends in the reactance.

Dielectric permittivity (ε, units of Farads per meter) or just permittivity is

conceptually similar to electrical conductivity. It relates charge separation, rather than

current, to the applied electric field. The permittivity represents the polarization

strength of bound charges. This property can also be expressed as a ratio between the

permittivity of the material and the permittivity of free space – that ratio is the

dielectric constant (or relative permittivity) of that material. At 1 GHz, the dielectric

constant for air is approximately 1, for oil is 3-4, for quartz is 4-4.5, and for water it is

roughly 80 (regardless of salt content).

MODES OF CONDUCTION IN EARTH MATERIALS

Electric flow is fundamentally a net movement of charge carriers in a particular

direction. The most common charge carriers in relatively shallow earth materials are

ions, such as sodium and chlorine, dissolved in the pore fluid. The conductivity of the

pore water is roughly proportional to the concentration of dissolved ions. Deeper in

the crust, molten rock is also conductive, being composed of ions which are able to

move past one another when in an electric field. In addition to ionic flow, conductive

minerals such as graphite and pyrite have free or weakly bound electrons, which can

also flow. Hydrocarbons, gasses and many common minerals lack free charge carriers

and are, as a result, excellent insulators.

The flow of ions through pore water in response to an electric field is generally the

dominant source of conductivity in a rock. In some sense, this flow is similar to bulk

fluid moving through the pore space, where the fluid permeability is analogous to the

electrical conductivity. However, ion movement in response to an electric field differs

from water flow through a pipe in response to a gravitational field. With fluid flow,

there is a zero flow velocity boundary at the sides of the channel and an increase in

velocity towards the maximum flow rate, which is found at the center of the channel.

In contrast, ion flow in response to an electric field will be in both directions. Both

positive and negatively charged ions will be present, and the opposite charges travel in

11

opposite directions (Figure 1.1). The net amount of force on the fluid is approximately

zero, so the velocity profile across the channel is relatively constant. The net water

velocity, while low, can be either positive or negative depending on the ionic species

and concentrations present. This type of flow has been modeled in several papers

(Wang, 2011; Freund, 2002; Lorenz, 2008) and demonstrated experimentally (Paul,

1998). The result is that when electrical conductivity is determined by ion flow

through relatively large pores, the size of the pores has little impact on the electrical

conductivity of the system. This is different from fluid permeability, where larger

pores result in dramatically stronger flow.

Figure 1.1: Illustration of the difference between gravitational and electric

potential for brine. On the left, all molecules (charged or not) respond to the gravitational potential. On the right, only the ions experience a net force, and the direction of the force is charge dependent.

There is another type of brine conductivity that occurs near the grain/brine

interface. At many crystal surfaces there is a net charge where the regular charge

balanced pattern of atoms is interrupted at the edge of the crystal. The permanent

unbalanced charges at the surface influence nearby material. If pore water is present, a

double layer of positively and negatively charged ions will form near the crystal

12

surface. This area of brine, in which the cations and anions have separated, is more

conductive than the bulk brine. Clay minerals, and particularly swelling clay minerals,

have a large surface area, a high surface charge and small pore diameters, which make

their surface conductance a relatively important component of the total conductance.

In clay-free sandstones and gravels, the surface charges and areas are smaller relative

to pore diameters, which are much larger. In these rocks, the effects of charge

separation at the pore walls are often negligible.

A less common, electric path is through conductive minerals in the rock matrix.

Conduction through conductive granular media is not simply proportional to the

material’s conductivity. DC current flow requires a continuous, unbroken electrical

path from one measuring electrode to the other electrode. In granular media, a discrete

number of paths may form, depending on the grain type distribution. In a randomly

sorted isotropic granular media without a conductive pore fluid, such as dry sand, with

just a few conductive grains scattered through it, there may not be any connected

pathways between those grains. In this case, essentially no current can flow through

the system. If more and more conductive grains are added, at some point the first

conductive pathway through the system will form. The percolation threshold is the

minimum concentration of conductive grains required before the first conductive paths

form. Near the percolation threshold, not every random distribution of particles will

include a conducting path, so in addition to the minimum conductive fraction, we also

need to specify a probability of getting a conductive path through the random

assortment. This probability will depend on the geometry of the test region as well as

the ratio of the sample size to the grain size. For instance, a shallow but wide box

filled with a mixture of conductive and insulating grains will more frequently contain

a vertical conductive path than it will a horizontal one.

The dry conduction threshold only sets a lower bound for the amount of

conductive material required before a DC electrical current can be observed. We need

substantially more information to predict how much flow there will actually be.

If the distribution of conductive grains is not homogenous, which is often the case

with pyrite (Cohen, 1984), then the value of the percolation threshold is harder to

13

ascertain. If, for instance, a fracture contains a vein of native copper, the amount of

conductive material required to see an impact could be almost zero. In real rocks, it

will be difficult to determine percolation thresholds without a detailed understanding

of the rock and the sources of the conducting materials. Detrital pyrite, which is

uncommon because pyrite weathers quickly at the surface, would probably have a

percolation threshold similar to those thresholds observed in random sand packs. It

may still vary from those values if the pyrite was sorted from the other sand

components due to its higher density (see Figure 1.2).

Framboidal and diagenetic pyrite forms primarily within what was the pore space

of the original mineral matrix. As a result, the dry conduction threshold for this type of

deposition may be lower than for homogenous, uniform sized sand. Again, when

conductive minerals such as pyrite and copper are deposited in fractures, the fraction

of mineral that needs to be conductive to see an effect can be very small.

In Chapter 5 I discuss percolation thresholds in greater depth.

Figure 1.2: Dark, iron bearing minerals (likely magnetite and hematite) that have

separated out on a beach. Photographed area is approximately 1m wide.

Tortuosity, path shape, contact size, grain size, the frequency of the electrical

signal (skin effect), pressure, temperature, pore fluid conductivity, and mineral

14

resistivity all affect the resistance observed through the framework of a conductive

grain pack.

For the time being, we’ll consider electric flow through the conductive minerals,

ignoring possible flow within pore fluids. Grain to grain contact areas can be very

small, resulting in high resistance at that point. As a result, most of the voltage drop as

the current flows through the conductive minerals occurs at the contact points. At

higher frequencies the voltage drops will be more homogenous because as the skin

depth on the grain decreases, the contact areas appear larger relative to the rest of the

electrical path. More electrical coupling between disconnected grains may occur at

higher frequencies. Electrons can tunnel through small gaps between grains, which in

some cases may significantly increase the apparent contact size.

As the net confining stress on a conductive grain pack is increased, intra-grain

deformation results in larger grain-to-grain contact patches, which increases the

conductivity of the pack. In addition, the contact number – the average number of

other grains touched by a particular grain – increases, which also leads to an increase

in conductivity. In grain packs with both conducting and non-conducting grains, this

increase in pressure and the resultant increase in the contact number may be enough to

change a non-conducting assemblage to a conducting one.

LOW RESISTIVITY PAY ZONES

In oil and gas exploration, hydrocarbon-bearing layers can usually be identified by

their relatively high resistivities - hydrocarbons are much less conductive than the

brines that typically saturate deep subsurface reservoirs. Despite this general trend,

hydrocarbons do occur in low resistivity zones. These zones can’t be detected using

resistivity techniques. These “low resistivity pay zones” tend to be found in laminated

shaley sands, freshwater formations, regions rich in conductive minerals, regions of

fine-grained sands, and regions of internal microporosity and superficial microporosity

(Worthington, 2000; Boyd, 1995). The high surface areas of shaley sands, regions of

high microporosity, and fine grained sand units add extra conductivity to hydrocarbon

bearing layers making them difficult to detect using resistivity techniques. Conductive

15

minerals may provide an alternative path for electric flow through reservoir, again

reducing the resistivity. Finally, fresh water formations surrounding hydrocarbon-rich

regions have comparable resistivities to oil-bearing zones, making them difficult to

differentiate using resistivity. These factors, when not identified, can result in

calculated water saturations that are too high, and may make a good prospect appear

economically infeasible.

In 2004, Kennedy published a framework for interpreting pyrite-affected logs

using the photoelectric factor. Included in that publication were several examples of

pyrite-affected well logs. Worthington (2000) noted three reservoirs with recorded low

resistivity pay zones caused by conductive minerals: the Teradomari Formation in

northern Japan, the Simpson Series in Oklahoma, and the Trimble field in Mississippi.

Resistivity in the Munsterland black shale was observed to be much lower than in

the similar Konzen shale by Duba et al. (1988). The black shale included up to 11%

globular or framboidal pyrite and 5-8% organic carbon (not graphite). The authors

attributed the difference primarily to a carbon film that bridged grain contacts, and

noted that the pyrite present would be electrically connected by the carbon.

RESEARCH FOCUS AND SUMMARY

The fundamental processes behind the electrical response of rocks are generally

understood. While Archie’s law remains a useful tool for interpretation, there are other

models that are more strongly grounded in the physical attributes of sandstones,

carbonates, and rocks with a clay component.

Within the oil and gas industry, the complications of identifying low-resistivity

pay zones have only been partially addressed. Our understanding of and ability to

predict the impact of conductive minerals in particular could benefit from additional

efforts to understand the phenomena behind these impacts. An important long-term

goal is the development of a robust interpretation system that will allow us to

understand where, and to what extent, conductive minerals will have a meaningful

effect on resistivity.

16

To improve our understanding of resistivity and particularly complex resistivity in

clean systems with and without conductive minerals, I have undertaken a number of

experiments, which are discussed in the next few chapters. Chapter 2 discusses

measurements made on clean sands and mixtures. Chapter 3 extends those

experiments into mixtures that include conductive grains. Chapter 4 narrows the focus

to the interactions that take place at the interfaces between conductive grains and brine

in the pore spaces. Finally, Chapter 5 draws on experimental work to identify the

underlying physical traits that control the resistivity and complex resistivity of earth

materials containing conductive grains.

17

Chapter 2

Fundamental resistivity measurements

INTRODUCTION

Low frequency electrical measurements of granular media are utilized in a variety

of specialties within geophysics and soil science. Electrical resistivity (or

conductivity) measurements are especially common and have been in use for decades.

With alternating current equipment the signal is best expressed as two components, the

resistance and the reactance. The electrical resistivity is the real component of the total

system impedance – it is the portion of the signal which represents energy dissipation.

The imaginary component of the measurement is a reactance, and indicates charge

storage within the system. The reactance is generally ignored in logging because the

magnitude is relatively low, and it can be difficult to isolate experimentally; however,

it does contain information about the system and may prove useful in some situations.

The goal of this portion of the project was to build a dataset that provides a

consistent set of complex resistivity measurements for a variety of common

situations found in granular media. Specifically, we test the effects of saturation,

brine salinity, various geometries of dissimilar sands, mixing different grain sizes.

Mixing of coarse and fine sand and examining the resulting electrical properties has

been examined previously (Lemaitre et. al., 1988; Wyllie and Gregory, 1953;

Nettelblad and Niklasson, 1996; Biella et. al., 1983). Numerous studies have

18

investigated the resistivity of various sand/clay mixtures (Wildenschild et al., 2000 is a

good example).

These tests were performed using various sands and sodium-chloride brines at

atmospheric pressure and room temperature. The data presented here provides a

consistent set of experimental data that share many of the same methods and

equipment. This is important when examining the reactive portion of the electrical

signal, because often the test equipment and especially the electrode contacts with the

sample cause a substantial portion of the response – and that response will vary from

one machine to another. By using one machine for all of the tests, we reduce the

variation in this systemic error. The tests also serve to validate the testing

methodology and to identify the equipment sensitivity to the tested conditions. Finally,

the data provides a reliable foundation for further experiments looking at other, more

subtle effects by defining sensitivities, finding experimental strengths and weaknesses

and potential avenues for exploration.

METHODS

The test vessel was a vertically oriented transparent non-conductive circular

cylinder, approximately 12 cm deep with a 16 cm inside diameter which

accommodated a sample volume of approximately 2.3 liters (Figure 2.1) The

geometric conversion factor from ohm to ohm-meter for this vessel was 0.167 meters.

The same conversion factor was used for both resistivity and reactivity. At the bottom

of the cylinder, a 13 cm diameter stainless steel electrode was permanently seated.

Once the cylinder was filled with sediment, a similar stainless steel electrode was

seated on the top. A 2.8 kg weight was placed on top of the removable electrode when

possible; the clay rich samples would flow around the edges of the electrode and allow

it to sink so the extra weight was not used for those materials. The purpose of the

weight was to maintain a consistent contact area between the material and the

electrode, which was a particular issue for the coarser and less ductile sand mixtures.

Adding the weight did not visibly compress the sediment, and considering the size of

the sample and the degree of uncertainty in sample length (approximately ± 1mm) it is

19

unlikely that the addition of the weight changed either the porosity or sample length

significantly.

Figure 2.1: Photo of the test vessel, including upper stainless steel electrode. The

vessel was built using parts from a MC Miller soil cylinder.

In testing, artificial brines were prepared by mixing NaCl with de-ionized water.

All sands and powders were air dry and free flowing (i.e., not cohesive or clumped)

prior to testing.

Electrical measurements were made using a Fluke PM6304, which is an RCL

circuit analyzer. The test voltage was set at 1 volt, but the operating voltage was often

lower due to the low resistances and power limits of the machine. The accuracy

specified in the user manual is +/-0.1% through most of the range of interest.

The general procedure for testing is presented here, and modifications for specific

tests are noted below. The needed material weights were calculated based on the

desired volumes and material densities. Materials were then measured out by weight

and combined in a tub outside the test vessel. Brine was measured out by weight and

added until the material was saturated. Full saturation was determined in relatively

coarse materials by a loss of cohesion and accumulation of brine on the surface when

the sediment was vibrated. In finer materials full saturation was marked by a glossy

surface and slight flow when the container was tipped (Soil Survey Field and

Laboratory Methods Manual). Once saturated, material was scooped from the tub into

the test vessel and vibrated until any visible air gaps were removed. Material was

20

added until the vessel was filled to a marked level, which was the same for all tests.

Saturation conditions were checked again using the same criteria. If the saturation was

acceptable, the upper electrode was pressed into place by hand and the vessel was

vibrated briefly to seat the electrode against the test material. Effort was made to

ensure that the upper electrode was parallel to the lower electrode and that the upper

electrode closely matched the depth guide to ensure a consistent sample length. If the

material would support the 2.8 kg weight, it was added on top of the upper electrode.

After the vessel was filled, the RCL meter was zeroed across shorted electrical

leads at 2 kHz as specified in the user manual. The electrical lines between the RCL

meter and the test vessel were connected, and measurements began. A set of

measurements consisted of recording the resistor-capacitor series circuit equivalent at

50, 120, 2000, 10,000, and 100,000 Hz and the temperature of the room (between 19.5̊

and 21.5̊ C). Sets began and ended at 2 kHz. Typically, a set of measurements was

recorded within 15 minutes of the vessel being filled and a second set was made at

least 1 hour later. If the measured resistances from the two sets were within 1%, the

test would be concluded, otherwise the vessel was left to sit for at least one additional

hour and then another set of measurements was made on the same material until the

results stabilized. Generally this was not required. Possible causes include changes in

room temperature, brines not initially at room temperature, air entrained during

sediment preparation floating up and exiting the system or compaction caused by

vibrations in the room.

When the testing of each brine/material combination was concluded, the test vessel

was washed and dried. The material was either discarded, or transferred to a tub and

adapted for re-use in a later test, generally by adding another material (salt, powder, or

contrasting sand). If the material was reused, it was stirred until it was visibly

homogenous. Then the material, or a portion of the material, was transferred back to

the test vessel and the general procedure was repeated.

21

NaCl concentration

The complex resistivity of various concentrations of NaCl brine was recorded in

three situations. First, with only brine, second with brine saturating acrylic grit (Aero-

Clean Thermoplastic Acrylic Granulated Blast Cleaning Media 12/16, roughly cubical,

12-16 mesh, with a median diameter of 1.4mm) and third with various brine

concentrations saturating an unseived, washed beach sand from Moss Landing beach

in Monterey County, California. The Moss Landing sand had a median diameter of

approximately 250 microns, with a larger spread in grain size than other sands used.

The beach sand was washed to ensure any residue of sea salt had been removed and

could not increase the salinity of the test fluid.

When performing the pure brine experiment, the test vessel was initially filled with

de-ionized water and at each successive concentration, salt was added and dissolved

within the test vessel. Concentrations of ~0, 1, 2, 4, 8, 16, 32, 64, 128, 196 and 256 g

NaCl per liter DI-water were tested.

In the second set of tests, the acrylic grit was initially saturated with brines from 0

to 275 g NaCl per liter DI-water. Salinities began at 25 g NaCl per liter DI-water and

the brine concentration was increased to 50, 75, 100, 150, 200 and 275 g NaCl per liter

DI-water. Then fresh media was saturated with DI-water and the brine concentration

was increased to 1, 2, 4, 8, 15, 25, and 50 g NaCl per liter DI-water. This allowed full

coverage of the test range, and two repeated tests (25 g and 50 g) at the beginning and

end of testing to check for consistency.

Finally, the beach sand was initially saturated with DI-water and salt was added to

increase the concentration to 1, 2, 4, 8, 16, 32, 64, 128, 196 and 256 g per liter DI-

water.

Saturation

The effect of saturation on complex resistivity was measured by adding a 4g NaCl

per liter DI-water solution to Moss Landing beach sand (the same type of sand used in

22

the NaCl concentration experiment). Saturations varied from 0 to 1 in increments of

0.1 for a total of 11 saturations.

Initially the plan was to simply pour additional brine into the top of the sand filled

test vessel and wait for it to disperse throughout the sand. This method would have

avoided grain packing changes between tests. Unfortunately, the brine did not diffuse

through the sand, and resulted in highly saturated patches in otherwise dry sand.

Adding additional fluid simply expanded the saturated patches until the brine reached

the lower electrode (resistivities were very high prior to breakthrough).

To get more homogenous saturation, brine and sand were combined in a tub

outside the test vessel where they could be stirred together until they were visibly

homogenous and then transferred to the test vessel. The same material was reused

between tests by transferring back and forth from the test vessel to the large tub where

additional brine could be stirred in. The partially saturated sands would not flow when

vibrated and had to be pressed into the vessel. The weight of the packed vessel was

recorded at each step so the bulk density and porosity of the sand packing could be

calculated.

Mixing coarse and fine sand

In this test, two types of sand, one with relatively fine grains and one with

relatively coarse grains, were combined in varying quantities and saturated with brine.

The test was done once with 50 g NaCl per liter DI-water and then again with 4 g

NaCl per liter DI-water. Approximate grain size distributions were estimated from

supplier data and are shown in Figure 2.2.

23

Figure 2.2: Cumulative grain size for the coarse and fine sands which were used

in the sand mixing test.

The two sands had a mean grain size ratio of approximately 5. The finer sand was F-

80 Ottawa sand from US Silica. The coarser sand was “16 Mesh Cleaning Sand” from

Legend, Inc. Mixtures with coarse volume fraction of 0, 0.2, 0.4, 0.6, 0.8 and 1 were

measured.

Sands in Parallel and Series

Four tests were done to test the electrical properties of differing sands in parallel

and in series arrangements. See Figure 2.3 for illustrations of the geometries tested.

Sands were saturated with 4 g NaCl per liter DI-water. In the first test, the lower half

of the vessel was filled with the same type of coarse sand used in the previous

experiment and the upper half was then filled with the same type of fine sand used in

the previous experiment. In the second test, the same types of sand were placed side

by side in the cylindrical test vessel. This was accomplished using a cardboard divider

between the two halves which was removed once the saturated sands were in place.

The third and fourth tests were identical to tests one and two except the fine sand was

replaced with a mixture of equal weight fine and coarse sand (1:1). In the fourth test,

0

20

40

60

80

100

0 0.5 1 1.5 2

Cum

ulat

ive

%

Mean diameter (mm)

24

~15% of the cardboard divider was lost in the sample, and remained at the boundary

between the coarse sand and the mixed sand throughout the measuring process.

Figure 2.3: Diagrams of the four test geometries. Current ran vertically through

the cylinders. In the upper left: coarse and fine sand in series. In the upper right: coarse and mixed sand (50% coarse sand and 50% fine sand) in series. In the lower left: coarse and fine sand in parallel. In the lower right: coarse and mixed sand in parallel.

Mixing sand and powder

CISCO No. 90 white silica sand (fine, median diameter approximately 160

microns) was mixed with a calcined kaolinite (a powder visually similar to cake flour)

from Natural Pigments LLC. They were mixed with sand fractions of 0, 0.19, 0.35,

0.47, 0.58, 0.67, 0.75, 0.77, 0.82, 0.90, 0.95 and 1 by mass. These sand fractions were

used to identify the mixtures, so as an example, mixture 0.82 was 82% sand and 18%

powder by weight. For mixtures 0.75, 0.82, 0.90 and 0.95, the sand and powder were

mixed together while dry and then brine was added until saturated. Mixture 0.77 was

only mixed after the sand, powder and brine had been added, and the powder remained

somewhat lumpy. Mixture 0.77 was also oversaturated, in the sense that the volume of

brine added was greater than dry pore volume. If the sample had been sand, the excess

water would have collected on the top and could have been removed, but due to the

powder content, the mixture remained homogenous and the test vessel was filled with

25

the material in that oversaturated state. Mixtures 0.19, 0.35, 0.47 and 0.58 were

created by adding sand to Mixture 0. An electric mixer was used to ensure thorough

mixing before the material was added to the test vessel. The weight of the filled vessel

was recorded for each mixture to allow for a porosity calculation using a density of

2.65 g/cc for the sand (dominantly quartz) and 2.4 g/cc for the powder (specified by

manufacturer).

RESULTS

Room temperatures were consistently between 19.5° and 21.5° C and the results

have not been temperature corrected. The final (stable) set of measurements for each

material combination is reported here. Measured resistances were more consistent (as

a percent difference) than were the capacitances for tests separated by 15-20 minutes.

Over several days, the RCL meter showed greater drift in the reported capacitance as

well, again as a percent difference. From hour 1 to hour 25 after the beginning of a

test, the measured resistance may vary by 1% while the capacitance may vary by 8%.

There was not a clear trend of variation between one test and the next – the resistivity

may rise over time in one test and decline in another, but all longer duration tests

showed that the sediment’s electrical properties were stable after 24 hours. Whether

this variation is the sample/apparatus interacting over time (corroding electrode;

sample settling), due to an environmental change (temperature; pressure; humidity) or

a limitation of the meter is unclear.

Reactivity was always most negative at 50 Hz and progressively closer to zero for

the higher frequencies up to 10 kHz. The results at 100 kHz were generally similar to

those at 10 kHz.

NaCl concentration

For salinities of 1 g/l and up, brine resistivities ranged from 5.5 to 0.05 Ω⋅m as

salinity rose; reactivities were lower magnitude and ranged from -0.4 to nearly 0 Ω⋅m.

Results are shown in Figure 2.4 and Figure 2.5, and recorded in Table 5 of the

26

appendix. I show later (Figure 2.22) that this agrees well with Schlumberger empirical

curves.

Figure 2.4: Resistivity of brine as a function of salt concentration. For each

salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted.

Figure 2.5: Reactivity of brine as a function of salt concentration. For each

salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz.

0

1

2

3

4

5

6

0.9 9 90

Res

istiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.9 9 90

Rea

ctiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

27

In the saturated coarse acrylic, for salinities of 1 g/l and up, resistivities ranged

from 19 to 0.15 Ω⋅m as salinity increased and reactivities were lower magnitude and

ranged from -0.5 to nearly 0 Ω⋅m. Results are shown in Figure 2.6 and Figure 2.7, and

recorded in Table 6 of the appendix.

Figure 2.6: Resistivity of brine saturated coarse acrylic as a function of salt

concentration. For each salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted.

0

5

10

15

20

25

0.9 9 90

Res

istiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

28

Figure 2.7: Reactivity of brine saturated coarse acrylic as a function of salt

concentration. For each salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz.

In the saturated beach sand, for salinities of 1g/l and up, resistivities ranged from

26 to 0.2 Ω⋅m as salinity increased and reactivities were lower magnitude and ranged

from -0.7 to nearly 0 Ω⋅m. Results are shown in Figure 2.8 and Figure 2.9, and

recorded in Table 7 of the appendix.

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.9 9 90

Rea

ctiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

29

Figure 2.8: Resistivity of brine saturated beach sand as a function of salt

concentration. For each salinity, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted.

Figure 2.9: Reactivity of brine saturated beach sand as a function of salt

concentration. For each salinity, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz.

0

5

10

15

20

25

30

0.9 9 90

Res

istiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.9 9 90

Rea

ctiv

ity (

ohm

m)

NaCl concentration (g/l brine)

100 khz

10 khz

2 khz

120 hz

50 hz

30

Saturation

The effect of saturation on complex resistivity was measured by adding a 4g NaCl

per liter DI-water solution with Moss Landing beach sand (the same type of sand used

in the NaCl salinity test). The resistivities ranged from near 140 to 0 Ω⋅m, with higher

resistivities at lower saturations. Reactivities ranged from -10 to near 0 Ω⋅m with

higher reactivities at lower saturations and frequencies. Results are shown in Figure

2.10 and Figure 2.11, and recorded in Table 8 of the appendix.

Figure 2.10: Resistivity of beach sand as a function of saturation. For each

saturation, resistivity was measured at 5 frequencies from 50 Hz to 100 kHz, all of which are plotted.

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Res

istiv

ity (

ohm

m)

Saturation

100 khz

10 khz

2 khz

120 hz

50 hz

31

Figure 2.11: Reactivity of beach sand as a function of saturation. For each

saturation, reactivity was measured at 5 frequencies from 50 Hz to 100 kHz

Mixing coarse and fine sand

When coarse and fine sands were mixed in various proportions and saturated with

4g/l NaCl brine, resistivity ranged from approximately 6.3 Ω⋅m in 100% fine sand, to

a peak of 9 Ω⋅m with 40% coarse sand and down to 5.5 Ω⋅m with 100% coarse sand.

Reactivity varied from 0 to -0.7 Ω⋅m, with most of the variation due to the frequency

of the measurement. See Figure 2.12 and Figure 2.13 for results. Results are also

recorded in Table 3 in the appendix.

-12

-10

-8

-6

-4

-2

0

0 20 40 60 80 100

Rea

ctiv

ity (

ohm

m)

Saturation

100 khz

10 khz

2 khz

120 hz

50 hz

32

Figure 2.12: Resistivity of sand saturated with 4 g NaCl/L DI-water as a function

of coarse fraction. For each mixture, resistivity was measured at 5 frequencies from 50 Hz to 1