LTU-EX-2011-33533716.pdf

MASTER'S THESIS

Sensus Aquae in Ferrum ac AirCharacterization of Electrical Properties of a Moisture Measurement System

Christian A. M. Karlsson

Master of Science in Engineering TechnologySpace Engineering

Lule University of TechnologyDepartment of Computer Science, Electrical and Space Engineering

Sensus Aquae in Ferrum ac Air Characterization of Electrical Properties of a Moisture Measurement System

Christian A.M. Karlsson

Lule University of Technology Department of Computer Science, Electrical & Space Engineering

Division of EISLAB

2011-08-24

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Cover illustration: Images from left to right

LKAB Kiruna aerial picture (2008), photo taken by LKAB

LKAB mine Kirunavaara, cross-section of mine, image produced by LKAB

Iron ore from Kirunavaara mine (2010), photo by C. Karlsson

The first CEO of Kirunavaara and Loussavaara mine, Hjalmar Lundbohm, drawing published by LKAB

A pile of magnetite concentrate (2010), photo taken by C. Karlsson (assisted by Rolf Schrter)

LKAB KK4 lightened, photo by LKAB

Pellets in a gloved hand, photo by LKAB

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ABSTRACT

Fast precise moisture measurement in mineral process plants, has long been a difficult

problem. In this master thesis a foundation for a new way of measurement using transmission

line theory, is laid out. Macroscopic electro-magnetic properties of the measured sample can

be linked to those of the individual constituents of the sample. Thus one is believed to be able

to do a precise estimate of the amount of moisture in a sample. In our case the samples are

moist magnetite concentrate.

The characterization of sample macroscopic electro-magnetic properties is done by using a

coaxial cell, performing frequency spectra measurement. In this master thesis, the electrical

behavior that links the measured data to the macroscopic electro-magnetic properties is

examined. It exists two setups, one inductive and one capacitive.

The DC resistivity of the moist magnetite concentrate is determined and some interesting

phenomena, suggested to be self potential were discovered. This phenomenon is in general

known from geochemistry of mineral rich clays. This made the measurements of resistivity

tricky to perform, some measurements were achieved and a new relation between moisture of

the moist magnetite concentrate and resistivity is presented.

Studies have been performed on the history of attempts of solving this problem, as well as

current relevant research. Reference samples have been prepared in a geotechnical laboratory.

Impedance frequency behavior of the measurement equipment is measured and presented,

with different curves for different moisture content. From these measurements it is obvious

that the moisture affects the impedance of the measurement equipment and thus it is possible

to use this method to measure moisture content, if one can determine the electrical model

which describes the measurement system.

A few equivalent circuits of transmission lines have been discussed, and one was chosen to

represent the purely coaxial part of the coaxial cell. Other parts have been modeled with other

elements of AC theory.

A new electrical model for the coaxial probe is proposed, based on LC resonances. Some

Comsol FEM simulations have been performed on the coaxial cell, as well as on electric

property sensors. Ideas to designs of electrical sensors are discussed. It is mainly the geometry

which has been investigated.

First it was proposed that a phenomenon of resonance occurs at the interface of the bottom

and coaxial part of the cell, LC resonance. The resonance effect has later been investigated

and identified as quarter wavelength resonance, due to the length of the measurement cell and

change of wave velocity due to wave propagation in MUT.

Simulations of proposed circuit equivalents in Orcad with PSpice have given some correlation

with measured data for dry and non-conducting samples.

There is still work to be done, to complete an accurate mathematical model of the system.

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PREFACE

This master thesis covers some of the first trembling steps toward the solution of measuring

moisture content in the magnetic granular media, moist magnetite concentrate, also containing

some different minerals which add further complexity to the problem of electrical

measurements. This problem has engaged engineers and scientists for a few decades.

The recipient of the result is the mining company LKAB which is interested in the technique

for the refinement of their pelletization process. Also some electronic companies have shown

some interest to future developments for a wider production of measurement units. The reason

for high precision moisture measurements at LKAB is the effect it puts on the formation of

pellets. Pellets are round balls with a certain prerequisites of roundness and diameter. When

shaping the pellets, the moisture content of the moist magnetite concentrate affect the quality

and the shaping of the pellets. Thus having the ability to easily monitor the moisture content

of moist magnetite concentrate, would increase productivity and improve quality of pellets.

The idea is to find the moisture content by using one or two electric property mixing

formulas, the Maxwell-Garnet formula and / or the Bruggeman formula. These two formulas

describe the relation between electric properties and constituent volume fractions, thus one

can deduce the different volume fractions by measuring the electric properties.

In this master thesis we will not go into calculations with mixing formulas, but focusing on

the measurements of the electric properties of the material under test (MUT). The electric

properties which describe the media are electric permittivity [F/m], magnetic permeability

[H/m] and resistivity [m]. Later these properties can be used together with the already known properties of each separate component which then allows us to extract the moisture

content from one or both of the mixing formulas.

Christian Karlsson

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ACKNOWLEDGEMENT

I would like to thank my supervisor Torbjrn Lfqvist for his support, inspiration and

devotion to the project. Again Torbjrn Lfqvist and Johan Borg for extremely important

laboratory assistance without which the project would have been far more time consuming.

Lars-Gran Westerberg (TFMM) for his discussion around Comsol Multiphysics modelling

and Sverker Fredriksson (TFMM) for refinement of my report writing technique, through a

few courses.

Many people at EISLAB LTU has brought understanding to the problem and given valuable

help in theoretical issues. The following peoples are appreciated for these contributions

Torbjrn Lfqvist, Johan Borg, ke Wisten, Johan Carlsson and Kalevi Hyypp. Mikael

Larsmark provided help by constructing electrode plates for the resistivity measurement

equipment.

Dr. Per-Erik Martinsson (Project Manager for Process IT) for his interest and support for the

project SAFA. Thanks to Dr. Bertil Plsson (TKG) for access to the geotechnical laboratory.

Magnus Westerstrand (TKG) for discussions on process water characteristics and self

potential. For test samples and introduction to the refining process by LKAB and sa

Partapuoli. Discussions of details on the process between grinding iron ore and the pellets

formation, as well as the characteristics of the magnetite concentrate and pellets by Seija

Forsmo.

Also many thanks to the people who have supported me throughout my master studies, those

who have made me determined to finish my master and my family for their support.

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TERMS, DEFINITIONS AND ABBREVIATED TERMS

AC Alternating Current

B Bruggeman

BUW Bauhaus-University Weimar

CCPL Creative Commons Public License

Concentrate Concentrated mineral powder

DC Direct Current

Dry Case Material measurement where the Rp parameter is high enough to be neglected in

the model

E Electric

EISLAB Embedded Internet System Laboratory

E-M Electro-Magnetic

GPR Ground Penetrating Radar

Green Non-Sintered Pellet

Pellet

HUT Helsinki University of Technology

LTU Lule University of Technology

M Magnetic

M-G Maxwell-Garnett

MUT Material Under Test

PEEC Partial Element Equivalent Circuit (method)

SAFA Sensus Aquae en Ferrum ac Air (project name)

SDSP Soil Dielectrics Spectroscopy Probe

TDEM Time Domain Electro Magnetic Measurement

TKG Department of Chemical Engineering and Geosciences

VNA Vector Network Analyzer

Wet Case Material measurement where the Rp parameter is low enough to be

considered a part of the circuit.

WikiUN Wiki User Name

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CONTENTS

Abstract .................................................................................................................................... IV

Preface ...................................................................................................................................... VI

Acknowledgement ................................................................................................................. VIII

Terms, Definitions and Abbreviated Terms .............................................................................. X

Contents ................................................................................................................................... XII

Figures ................................................................................................................................... XIII

1 Introduction ......................................................................................................................... 1

1.1 The Objective of the Project ........................................................................................ 1

1.2 The Objective of this Master Thesis ............................................................................ 1

2 Literature Study ................................................................................................................... 2

2.1 A Short Introduction to the LKAB Process of Interest ............................................... 2

2.2 General Properties of Magnetite Concentrate and Pellet ............................................. 3

2.3 A Short Introduction to the Measurement Environment ............................................. 4

2.4 Summary of LKABs Earlier Tested Measurement Techniques ................................. 4

2.5 Other Research Groups ................................................................................................ 6

2.6 Possible Measurement Techniques .............................................................................. 7

2.7 Suitable Setups for Magnetic and Conductive Materials ............................................ 9

2.8 Electric Equivalent Models ......................................................................................... 9

3 Lab Work and Measurements ............................................................................................ 11

3.1 Preparation of Moist Magnetite Concentrate Samples .............................................. 11

3.2 Resistivity (DC) ......................................................................................................... 12

3.3 Permittivity, Permeability and Parasitic Resistance (AC) ......................................... 15

4 Why Comsol Modeling ..................................................................................................... 20

4.1 Coaxial Cell Inductive and Capacitive Setup ......................................................... 20

4.2 Capacitive Surface Sensors ....................................................................................... 22

5 Calculations and Electric Modeling .................................................................................. 25

5.1 Evaluation of Models and Motivation for Chosen Model ......................................... 25

5.2 Improvements in Calculation after A. Saremi Work ................................................. 30

5.3 Calculations Using the Saremi Circuit Model - Inductive Setup .............................. 31

5.4 Simple Model Analyses ............................................................................................. 35

5.5 Calculation Using Electric Circuit Proposed by C. Karlsson .................................... 41

5.6 Resonance Analysis ................................................................................................... 48

6 Discussion of Results and Final Conclusions .................................................................... 50

7 Discussion of Future Work ................................................................................................ 51

8 References ......................................................................................................................... 53

Appendix A Geometric and Material Constants ................................................................... 55

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Appendix B Preparation of Moist Magnetite Concentrate .................................................... 56

Appendix C Resistivity Measurements ................................................................................. 57

Appendix D Mathematical System - Saremi Model ............................................................. 58

Appendix E Inductive Mathematical System - Karlsson Model ........................................... 59

Appendix F Capacitive Mathematical System - Karlsson Model ......................................... 61

Appendix G Matlab Functions - Cost and Zload Functions .................................................. 62

Appendix H Matlab Script Inductive Optimizer ................................................................ 63

Appendix I Matlab Script PLOT Results ........................................................................... 66

Appendix J Matlab Script Constants .................................................................................. 68

Appendix K Matlab Script Data Loader ............................................................................ 69

FIGURES

Figure 1: A flow diagram of a part of the LKAB process. ......................................................... 2

Figure 2: A picture of a sandcastle, illustrating the properties that granular material gains from

moisture. This picture has been released in to the public domain, at pdphoto.org. ................... 3

Figure 3: A pile of dry magnetite (left) and a pile of 11 % wet sample pile (right). .................. 4

Figure 4: Schematic picture of linking coaxial elements, licensed use under CCPL (CC BY-

SA 3.0) by WikiUN Qianchq [30; 31]. .................................................................................... 10

Figure 5: Industrial mixer, photo by T. Lfqvist ...................................................................... 11

Figure 6: Table of ideal moisture content and actual moisture content. .................................. 12

Figure 7: In the back there is a white bucket with moist sample of magnetite concentrate. In

the front there is a resistivity measurement setup, consisting of a plastic pipe, with outside

covered in aluminium foil. In the bottom of the pipe, there is a circular copper surface. The

surface constituting an electrode connected to a wire exiting the bottom of the setup. A similar

circular surface can be thread into the pipe from above, thus connecting through the sample

put in beforehand to the surface in the bottom and finally constitute a connected system. One

can do measurements between the two cables exiting the setup. The wooden plate in the

bottom is for stability of measurement setup. To the left, an abandoned measurement device, a

general resistance meter. .......................................................................................................... 13

Figure 8: Schematic picture illustrating the geometric dependence of the resistivity

measurement setup, licensed use under CCPL by WikiUN Omegatron [30]. ......................... 14

Figure 9: DC resistivity versus actual moisture content. The red arrow indicates that the value

at zero percent moisture, most probably can be considered infinite, as the measurement

equipment reached its limit. The actual characteristic is believed to be of the type one over

fraction, according to this diagram though, from two percent to eleven percent an almost

linear behaviour. ....................................................................................................................... 15

Figure 10: Measurement setup with coaxial cell and VNA. The coaxial cell is connected only

through one VNA port. The wooden box contains a calibration set for calibration of the VNA.

.................................................................................................................................................. 16

Figure 11: Real part impedance spectra for inductive setup translated from the measured S11

parameters. ............................................................................................................................... 18

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Figure 12: Imaginary part impedance spectra for inductive setup determined from the

measured S11 parameters. ........................................................................................................ 18

Figure 13: Real part impedance spectra for capacitive setup determined from the measured

S11 parameters. ........................................................................................................................ 19

Figure 14: Imaginary part impedance spectra for capacitive setup determined from the

measured S11 parameters. ........................................................................................................ 19

Figure 15: Cross-Section of coaxial cell. ................................................................................. 20

Figure 16: 3D Model of Inductive Coaxial Cell. ..................................................................... 21

Figure 17: 3D Model of Capacitive Coaxial Cell. ................................................................... 21

Figure 18: Geometry of Capsense1. ......................................................................................... 22

Figure 19: Graphical E-Field Representation of Capsense1. ................................................... 22




Figure 23: L-type equivalent circuit with correction equivalent. ............................................. 27

Figure 24: T-type equivalent circuit with correction equivalent. ............................................. 27

Figure 25: PI-type equivalent circuit with correction equivalent. ............................................ 28

Figure 26: Saremi equivalent circuit with correction equivalent. ............................................ 28

Figure 27: Semi-lumped semi-distributed equivalent model with split correction lid and

bottom. ...................................................................................................................................... 29

Figure 28: Karlsson proposed inductive equivalent circuit with correction equivalent. .......... 29

Figure 29: C. Karlsson proposed capacitive equivalent circuit with correction equivalent. .... 30

Figure 30: Real r provided by optimization of Saremi model for different water content. ... 33

Figure 31: Imaginary r provided by optimization of Saremi model for different water

content. ..................................................................................................................................... 33

Figure 32: Conductivity provided by optimization of Saremi model for different water

content. ..................................................................................................................................... 34

Figure 33: Error surface representing the impedance error for the optimized Saremi model

compared to the measured impedance...................................................................................... 34

Figure 34: r provided by simple inductive model for air. ...................................................... 36

Figure 35: r provided by simple inductive model for water. ................................................. 36

Figure 36: r provided by simple inductive model for dry magnetite concentrate. ................. 38

Figure 37: r provided by simple inductive model for 2% moisture. ...................................... 38





Figure 42: Measured equivalent impedance for air (theoretical value by simple model),

Matlab Calculated Impedance Using C. Karlsson Circuit. ...................................................... 42

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Figure 43: Measured equivalent impedance for de-ionized water (mQ).................................. 42

Figure 44: Measured equivalent impedance for dry magnetite concentrate. ........................... 43

Figure 45: Orcad air equivalent with constant maximum magnitude resistance. .................... 44

Figure 46: Orcad plot of equivalent impedance for air. ........................................................... 44

Figure 47: Orcad water equivalent with constant maximum magnitude resistance. ................ 45

Figure 48: Orcad plot of equivalent impedance for water........................................................ 45

Figure 49: Matlab calculation of the air case. .......................................................................... 46

Figure 50: Matlab calculation of the water case. ..................................................................... 47

Figure 51: Matlab calculation of the dry case. ......................................................................... 47

1

1 INTRODUCTION

This master thesis covers measurement of E-M properties of magnetic and conductive

granular material, moist iron ore concentrate. The reason to measure E-M properties is that it

forms the foundation for determining moisture content.

1.1 The Objective of the Project

The objective of the project is to do precise moisture measurement of moist iron ore

concentrate. Having the ability to easily monitor the moisture content of moist iron

concentrate, would increase productivity, improve the quality of iron ore pellets and make

production cheaper.

The vision of this project is to develop an in-line moisture sensor unit, capable of accurate

precise measurement of moisture down to 0.1 % precision. To achieve this, it is necessary to

know the density and temperature of the MUT, if the sample is not in a controlled

environment. Hence for characterization of measurement equipment and MUT, we stay in a

controlled environment, the laboratory. Later when field measurements are performed, the

effect of temperature and density deviations has to be incorporated.

1.2 The Objective of this Master Thesis

The objective of this master thesis is to develop models for determination of E-M properties,

which constitutes a basis for a new measurement technique for determining moisture content.

The master thesis shall also work as documentation for further research and development, as

well as describe the work performed during the master thesis period.

The E-M properties which describe the characteristics of material under test (MUT) are the

electric permittivity, r [F/m], magnetic permeability, r [H/m], and resistivity [m]. Later these properties can be used to find the moisture content of the MUT.

For the extraction of the E-M properties r and r, the intention is to use a single or two different near-field antennas / sensors. Probably one electric and one magnetic sensor, needs

to be designed, if a combination is not possible. The E-M properties can be retrieved from the

expressions of capacitance and inductance. Then the value of r and r can be determined due to the following relationship [1], in equation 1.1:

(1.1)

Where C [F] is the capacitance obtained from the equivalent models when the model has been

applied to the moisture measurement values of impedance. C0 [F], the capacitance according

to the model when air (or preferably vacuum) constitute the MUT.

The work is based on an earlier attempt to determine moisture content, from which the results

brought some doubt. It was preferable to find a better lumped electrical equivalent model for

the measurement cell and make new measurements to verify the model. This cell is supposed

to be evaluated by reflection measurements which could be related to impedance and at the

end to capacitance and inductance, through the electrical equivalent model. Further literature

studies and discussions have brought a deeper understanding and have resulted in some ideas,

which will be presented throughout this master thesis.

2

2 LITERATURE STUDY

Studies have focused on different techniques to measure moisture or E-M properties. The

analyses have covered what the physical and chemical properties are of the magnetite

concentrate used in the moist filter cake at LKAB? Other tested methods for measuring

moisture in moist magnetite concentrate for LKAB? Which other research groups exists?

Which apparatus has been used for E-M measurements on materials? Which setups can be

used for measurements on magnetic and conductive materials? Which electric models are

there? What work has earlier been performed within the project at LTU?

2.1 A Short Introduction to the LKAB Process of Interest

The LKAB process that is of interest for the understanding of the problem is the balling

process and the preparation of the moist magnetite concentrate to become a green pellet, the

wet process. Magnetite is a specific type of iron ore, below these terms will come in context.

For the balling process it is very important to control the moisture content of the moist

magnetite concentrate. First the iron ore is ground to suitable size for pelletizing, cleaned by

magnetic separation and flotation. The resulting slurry is mixed with different additives and

put through press filters to reduce water content, resulting in a moist filter cake suitable for

balling. The moist filter cake is stored in a storage silo, where it is further transported from

and mixed with a binder and again put in a storage silo. From there portioned to a balling

drum, where seeds starts the balling process and the balls slowly grows, exemplified by rolling a snowball. The described part of the process can be seen in Figure 1.

Figure 1: A flow diagram of a part of the LKAB process.

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If one wish to understand the reasons behind the interest of moisture content of the moist filter

cake (or our lab equivalent, moist magnetite concentrate) one could think of the properties of

sand castles depending of sand moisture content (Figure 2), sand being another granular

material. Also magnetic effects operate in this material, causing attraction and repulsion

between particles.

A selection is made by screening the green pellets to correct size [2]. Green pellets that has

exceeded the determined size, goes to a new grounding station and are inserted into the

balling drum as seeds again. Smaller green pellets also go back to the drum as seeds. Those

green pellets that have passed screening are loaded to the pelletizing machine for drying and

sintering, at about 250 C and 1250 C respectively.

It is of course during the wet process which LKAB would like to perform online moisture

measurements and more specifically between the filters and balling drum (red square in

Figure 1). Today these measurements are performed manually once per work shift; a sample

is taken, weighed, dried and weighed again, this will provide the amount of moisture as

percent mass [3].

2.2 General Properties of Magnetite Concentrate and Pellet

Magnetite is an iron oxide containing, FeOFe2O3 (Fe3O4). The magnetite concentrate are

finely ground iron ore. The fineness of the magnetite concentrate is roughly 80% - 45 m in

diameter (meaning that 80% of the magnetite granules are 45 m or less in diameter),

controlled by screening. Pelletizing is done using external binders, where the most common

one is bentonite clay, commonly sodium activated bentonite clay. Typical composition of

magnetite concentrate is 71 % Fe, 23 % Fe2+

and 0.6 % SiO2. Additives are about 0.5 %

bentonite binder and grounded olivine, (Mg,Fe)2SiO4. Our laboratory equivalent however

contains as close to pure dry magnetite concentrate as it ever becomes in the LKAB process.

For mathematical modeling our approach is to assume a clean matrix of magnetite based on

spherical particles.

The water mass concentration of the moist filter cakes used today is around 8 - 9 %. At this

concentration it provides a suitable base for the agglomeration process. Too low water content

Figure 2: A picture of a sandcastle, illustrating the properties that granular material gains from moisture. This picture has been released in to the public domain, at pdphoto.org.

4

will have a to slow growth or none at all, too high will either grow too fast and / or collapse

due to insufficient binding properties. In modeling the moist magnetite concentrate will be

modeled as a fixed matrix of magnetite with fixed inclusions.

The accepted green pellets have a diameter around 10 mm with some small margin.

Figure 3: A pile of dry magnetite (left) and a pile of 11 % wet sample pile (right).

2.3 A Short Introduction to the Measurement Environment

The MUT (moist magnetic concentrate) is due to its fineness and magnetic properties a dirty

material and thus tends to smear down most things in its environment. The following

characteristic phenomena occur in the moist magnetite concentrate; conduction, galvanic

corrosion, self potential and it acts abrasively. When looking at the moist filter cake, one can

add seasonal change of the salinity of the process water (as well as the moisture abundant in

the MUT.)

2.4 Summary of LKABs Earlier Tested Measurement Techniques

Throughout the years many methods of measuring moisture content have been tested [3], the

currently used measurement technique is the manual weigh-dry-weigh test, which provides an

accurate result. This process is time consuming, why LKAB would wish to have an in-line

and real-time measurement technique.

Tested methods which are not related to the measurement technique we try to introduce will

be mentioned. Methods related to our measurement technique will be deeper discussed with

emphasize on their implications for our measurement technique.

Unrelated Techniques Tested

First the weigh-dry-weigh method has been the target for development and refinement, but

still this method suffers from difference in sample collection, heating may induce chemical

reactions changing mass relations, the method is time consuming and does not allow in-line or

real-time measurements.

Different general commercial moisture measurements units have been tested without any

stable results, mainly due to the complex nature of the moist magnetite concentrate. Chemical

analysis of moisture dependence of chemical reactions resulting in a pressure proportional to

the moisture contents has been tested; the pitfall of this test seems to have been its minor

sample volume.

5

Multivariate analysis has been tested; but has been considered in minor further interest to this

project. The problems with the technique are the stability of the method when it is exerted to

external disturbance and that it is a system that needs training by estimating moisture from

pre-known moisture samples. Radiometric measurement technique has been tested where the

observation only could be done for long term variation over the period of a day. Therefore has

been considered being a non sufficient measurement technique.

Related Techniques Tested

Within the microwave area, an instrument called Hydro-Probe II has been tested, by

submersing it into the moist magnetite concentrate. The general opinion then was that the

equipment did not work as the moist magnetite concentrate was absorbing around 90 % of the

signal. The signal used was 300 MHz to 1.2 GHz, either this experiment shows that the

commercial techniques for moisture measurement does not work for moist magnetite

concentrate, due to its complex nature (if the instrument was not developed having the

complex nature in mind) or it shows that EM waves has trouble of penetrating the MUT,

especially in the microwave range.

At a seminar of moisture measurements with microwaves in subject [3] it was stated that

microwaves could not be used as a measurement technique as moist magnetite concentrate

absorbs the microwaves. Also commercial companies have stated that this is the case, that

microwaves cannot be used as measurement technique due to the major absorption of signal

power. Measurements of optical reflection have been tested. Optical techniques in general

require massive maintenance, calibration and are very sensitive to external disturbance. Only

if a method can find some frequency where all disturbances are extremely low compared to

the response of the variable representing the moisture content this method has usability.

Electric conductivity has been investigated as an interesting method, by measuring the

conductivity between two electrodes; one could determine the moisture content. In the process

industry this method is not believed to be of sufficient stability due to the many parameters

from which the moisture measurement depends on. The measurement depends on the grain

size, process water salinity, moist magnetite concentrate temperature, geometry, compression

and moisture content. Another experiment confirms that the resistivity is heavily dependent of

moisture content [4]. Resistivity is the reciprocal of conductivity.

Short on the Apparent Demands of the Measurement Equipment

When analyzing earlier evaluated measurements it is apparent that

Accuracy - The accuracy should be around 0.1%

Tolerant - The measurement should be stable towards environmental changes / process disturbance

Instant - Preferred to be real-time measurements

Independent - Should have minimal maintenance

Representative - Propose a value representing a whole batch

These are quite tough demands under the circumstances for in-line measurements. However

the method presented in this master thesis is believed to cope with them.

Untested Techniques and Our Role in the Continuation

From studies of earlier tested techniques it obvious that one will need to utilize a

multivariable solution as all methods suffer from other environmental effects. The author

6

believes that either submerged measurements with sample contact will have the most

controllable and/or measurable environment or a macro sized capacitance and/or inductance

and/or resistivity measurement module. Examples of non tested methods (2005) are heat

conduction, density, measurements with ultrasound and infrasound, pressure posed to static

obstacles, nucleus spin resonance (Proposed by the company Omicron) and other chemical or

heating related methods.

There are also many untried measurement techniques related to electromagnetic and/or

frequency spectra measurement. These methods are mentioned as radio waves (transmission),

dielectric property measurements, electromagnetic AC measurements, inductive methods,

capacitive methods; at this point it seem a bit messy as all these seems to be different parts of

the same kind of measurement technique, just that they are mathematically- and model-wise

separated.

Some short conclusions when it comes to electromagnetic measurements. One has tested

transmission of microwaves submerged, optical surface reflections of microwaves (outside

media) and electrical resistivity measurements submerged. Where the transmission and optical

reflection techniques has been discarded due to lack of quality. The resistivity has shown to

be sensitive to moisture content, but faces uncertainties due to large number of dependent

parameters.

The method proposed by T. Lfqvist and C. Karlsson is to utilize a model which measures the

AC spectra of capacitive, inductive and conductive behavior of the moist magnetite

concentrate. By large means it is reasonable to believe that a commercial product must also be

able to measure the temperature and resistivity of process water and dry magnetite or utilize

some kind of calibration at least month wise. At first the ambition would be to prove the

legality of this method. A big strength is that this method utilizes many parameters which by

themselves are moisture dependent. If one could determine these parameters, there would be

many parameters to use in moisture estimation. Only one of the parameters is sensitive for all

constituents, that is capacitance and one parameter is sensitive for the magnetite that is

inductance, the actual material dependent variables are the electric permittivity (dielectric

constant) and magnetic permeability (magnetization constant). Together these two will allow

us to determine the amount of magnetic particles (magnetite grains) from air and water, with

that as input we can determine the amount of particles with higher dielectric constant from

those that have less. That is water from air that in the end allows us to estimate the water

content. This estimation is done using a two phase mixing formula causing an input to a three

phase mixing formula, allowing the water content to be determined. Another interesting

property we might find from knowing the permeability is the dry density or mass volume of a

moist powder.

2.5 Other Research Groups

A book containing an overview of theory and techniques in the field of E-M aquametry have

been written by K. Kupfer at BUW [5]. One co-writer of the book is A. Sihvola at HUT

whose research is focused to the area of material characterization of matter with high

dielectric loss.

An Italian group involved in planetary research and sub soil measurements has performed

measurements with a toroidal probe. This was a step in the direction of building an instrument

intended for a mission to Mars to perform moisture / ice content measurements in Martian

soil. The Martian soil connects with our experiments due to its rich iron content.

7

There are also many other people around the world which has brought contributions to and

been working on the problems of moisture measurements, as well as measuring other material

properties using the electromagnetic properties.

Short information of A. Sihvolas Work and Concerning M-G and B A. Sihvola has been working with aquametry [6; 7], with the main target of building model

systems for material with high dielectric losses. In his work he has studied the geometry

effects of host and inclusions, where the host is the main constituent and inclusions are

secondary constituents. Mainly it is the formulas by M-G and B, which have resulted in more

knowledge for the effects in using mixing formulas. He is the author of the book,

Electromagnetic Mixing Formulas and Applications [7]. A. Sihvola together with L. Jylh has

also developed a differential formula for effective permittivity [8] which combines the effects

of the M-G and B [7] formulas, thus they have achieved a formula that are valid for quite high

permittivity contrasts which seems to be the case of these measurements. Initially the

ambition will be to prove the electric behavior of the measurement equipment.

Short Information on the Work Performed by the Italian Group

The group consists of many members of different disciplines; astrophysics, electronics,

geology, computer and system engineering. They have been working with several techniques

to discover the E-M parameters of the sand of Mars, as SDSP, GPR and TDEM. The reason

why they use the many techniques is that the environment at Mars is varied and they have no

knowledge of any parameter in advance. On earth one knows some parameters and can

calibrate for them in calculations.

2.6 Possible Measurement Techniques

Studies were performed on summarizing documents and articles evaluating different

instruments; Venkatesh and Raghavan (2005) [9], the NIST standard document [10] by

Baker-Jarvis et al. (2005) and the two ASTM standard documents D 7449 (2008) [11] and D

5568 (2009) [12]. The NIST document is the most valuable of the documents.

Literature studies and discussions have come up with a few different ideas to setups using

capacitance and inductance to determine the E-M constants. The different methods are based

on reflection measurements or reflection-transmission measurements. The reflection methods

will be discussed further in subchapters to identify problems or advantages of each method,

using facts from article studies.

Reflection Measurements

Open-ended coaxial measurements

Toroidal probe

Open and closed coaxial cell

Micro-strip sensor

Reflection-Transmission Measurements

2-port coaxial cell

2-port transformer

Earlier unsuccessful experiments on plate capacitors, N. rlander, and a technique developed

in an earlier report by A. Saremi, a version of reflection measurements of an inductive

8

(closed) / capacitive (open) coaxial cell. This open/closed technique will be further developed

by the author later in this master thesis.

Open-Ended Coaxial Measurements

This measurement technique is based on the change of fringing field capacitance due to

change of material measured, in example compared to air. The simplest interpretation is this

by Jaspard and Nadi [13], in equation 2.2. First the interpretation of measurement as

admittance, in equation 2.1:

(2.1)

Where Y11 [1/ or S] correspond to the admittance of the system using only one port of the VNA. Y0 [1/ or S], is the characteristic admittance of the VNA cable, in our case (1/50) S. The S11 parameter is a scattering parameter which says something of the reflection caused in

the macroscopic measurement equipment. The indexes in all cases refer to the first element of

a matrix, where the index represents a port number; in this case only port one. Thus looking at

the admittance due to the reflection of a pulse sent at port one, observed at port one.

(2.2)

G [1/ or S] is the conductance (inverted impedance) due to leak currents between the center conductor and the outer cylinder. The angular frequency [rad/s], Cfc [F] capacitance regarding the full length of coaxial cable, from the VNA cable connector to the cut surface

used as sensor and Cfm [F] being the full material dependent fringing field capacitance.

Simulations in Comsol have not been able to confirm the validity of these, which could have

been caused by bad conditions for boundary values in the simulation or that the model is

insufficient. Most probably this is due to adaptations of the model, which has not been

implemented, dependency of other geometrical factors. There is also a more advanced model

for determining the complex r, described in the book Microwave Electronics: Measurement and Materials Characterization [14]. Even though the title of the book refers to microwaves,

this is somewhat applicable for RF as well.

This technique / theory might be needed for the construction of a surface sensor for the

measurement module, but probably cannot be used to characterize the material properties in

our case, as the response of the fringing field capacitance should be quite small and it will

only measure the capacitive property within the measured volume. This was realized from

Comsol FEM simulations and reading articles.

Also from simulations and articles it seems to be most sensitive at the core, where current are

injected and there are a certain area of the flange shield which gives optimal fringing field

response. Also letting the core penetrate deeper and letting the flange stay at the surface may

have a good impact on the fringing field capacitance. Important contributions to this area

which the author has studied follows; Zheng and Smith (1991) [15], Moreau and Aziz (1993)

[16], Gasvenor (1993) [17], Baker-Jarvis (1994) [18], Aimoto and Matsumoto (1996) [19],

Folger and Tjomsland (1996) [20], Jaspard and Nadi (2001) [13], Hagl et al (2003) [21],

Cheng et al. (2006) [22], Ellison and Moreau (2006,2008) [23; 24], MacLaughlin and

Robertsson (2007) [25] and Oppel et al (2008) [26].

9

Toroidal Probe

As described above this has been tested earlier by an Italian group. The toroidal probe seems

to be a good measurement technique, but the trick is to get the material into the toroid. The

solution of the Italian group is to use an air winded toroid, which would allow the toroid to be

pressed down into the moist magnetite concentrate. Then the toroid is filled with moist

magnetite concentrate and as the inductance is only dependent of the material characteristics

of the material inside the toroid windings, it is easy to determine the measured volume.

The group used a constant volume of Martian soil and the sensitivity should be really good

due to the concentrated fields. This geometry may be a good geometry for the magnetic

sensor to be used for in-line measurements. No experiments, modeling or deeper literature

studies have been done yet, on this method.

Open and Closed Coaxial Cell

An earlier report by A. Saremi [27] has been written on the coaxial cell, but some of the

modeling is questionable. Some new measurements, analysis and simulations will bring

further light on the subject. The general overview sources contained the best written material

found for this measurement technique, as well as previous measurements performed at

EISLAB [27] and newly acquired knowledge from new measurements and modeling. See

chapter 5 for further information.

Micro-Strip Sensor

A micro-strip sensor is believed to be one of the sensors to be used for an in-line solution.

Together with the magnetic toroid / loop / transformer it would constitute a full laboratory

solution for the measurement of r and r. The drawback associated with this type of sensor is its surface sensitivity and that it will not represent a whole batch properly. To solve these

issues, one solution could be to have a lot of measurement units well distributed and

submersed in the moist magnetite concentrate. This would allow a mean value representation

of the moist magnetite concentrate moisture content and decrease the risk of moist concentrate

surface anomalies.

Interesting articles discussing this type of sensor are published by Avitabile et al. (2001) [28],

interdigital dielectrometry by Guggenberg and Zaretsky (1995) [29] and Sonnet Application

Note, SAN-206A (2006) [30], for design of RFID sensors. RFID sensors are probably useful

sensors to use for material measurements in the radio frequency spectra, even though the

measurement in itself has nothing to do with RFID.

2.7 Suitable Setups for Magnetic and Conductive Materials

When determining moisture in magnetic and conductive media, it is important to use both

inductive and capacitive technique. For the material characterization it seems to be suitable to

use the open and closed coaxial cell. This will allow measurement of a constant volume,

which will simplify the verification of the measurement. When measuring in-line, the pair of a

micro-strip sensor (mainly capacitive) and a magnetic sensor (mainly inductive) will probably

constitute the laboratory measurement setup.

2.8 Electric Equivalent Models

There are two types of electrical equivalent models which can be used to model a

transmission line [1]. It is the lumped parameter model and the distributed parameter model.

In this sense we either see the transmission line as a RLC circuit or that the element is made

10

up of infinitesimal elements of RLC circuits. The modeling which has been performed on the

coaxial cell is of the lumped parameter type.

When it comes to distributed parameters, there is a common model for the impedance of an

element of a transmission line [1] (characteristic impedance). There is a special formula to

relate the characteristic impedance to the impedance seen by a VNA, through different

segments of different lengths for lossy lines. A schematic sketch in Figure 4 describe the

different variables in equation 2.3.

(2.3)

(2.4)

Here the Zi+1 [] the complex impedance at any point on the line, looking towards the load. The Zi [] are the complex impedance at the distance li [m] towards the load. Z0,i [] the characteristic impedance of the coaxial line, linking point (i+1) with (i). i [1/m] is the propagation constant (segment i), i [dB/m] the attenuation constant (segment i) and i [rad/m] the phase constant (segment i). The expressions for matched, short and open refers to

special conditions regarding the impedance of the load, where one can see the impedance at

Z2 by using Z0 = Z0,1 and = 1. However in our case using the coaxial cell, the aluminum bottom will not be represented by the short condition as resistance and inductance exists.

Using the plastic lid we might be able to use the condition, open, provided that one consider

that the plastic lid constitute another coaxial element and the fringing field capacitance are

small enough. The fringing field capacitance is the capacitance due to the escaping field in the

open or semi-open case.

The continued work within this master thesis will be with the lumped parameter model.

Lumped parameter models for two conductor transmission lines can be modeled in three

different ways according to literature; L-type, T-type and PI-Type [1] p.477 and 533. The

variation of these makes it plausible that other combinations of the components could be used

as well.

The lumped parameter model proposed by A. Saremi is another one [27], see chapter 5.3.

Figure 4: Schematic picture of linking coaxial elements, licensed use under CCPL (CC BY-SA 3.0) by WikiUN Qianchq [30; 31].

11

3 LAB WORK AND MEASUREMENTS

3.1 Preparation of Moist Magnetite Concentrate Samples

Purpose

The sample preparation of moist magnetite concentrate was performed in the laboratory of the

TKG department. The samples will provide both a basis for calibration and test. For full

liability these measurements should be repeated a few times with newly prepared moisture

samples.

Equipment

The equipment used was 9 plastic buckets with lid, scale, an industrial mixer (depicted in

Figure 5), measuring cylinder, de-ionized water and bags with dry magnetite concentrate.

Execution

Weighing empty bucket with lid, weighing half-filled bucket with lid and calculating the

amount of dry magnetite and the amount of water that should be added to give each moistened

sample its right moisture content 0, 2, 4, 6, 7, 8, 9, 10, 11 mass percent. Due to inaccuracy of

the amount of water added to the samples (equation 3.1), also actual percentage has been

calculated (equation 3.2).

(3.1)

(3.2)

Where mm is the mass of magnetite, mw is the mass of water, fw is the mass fraction of water

and the mass fraction of magnetite are of course fm=1-fw.

Figure 5: Industrial mixer, photo by T. Lfqvist

12

Results and Conclusions

The resulting moisture contents deviates quite a bit from the intended, thus using separate

buckets measuring dry magnetite and water, will make the percentage more precise and

constitute a better testing frame. The actual moisture contents are presented in the table in

Figure 6 below.

Figure 6: Table of ideal moisture content and actual moisture content.

Moisture %m Real %m

2 2,044

4 3,054

6 6,061

7 7,278

8 8,311

9 9,373

10 10,43

11 11,44

3.2 Resistivity (DC)

Purpose

The purpose of determining resistivity was to model parasitic resistance in the model of the

impedance for calculation of permittivity / permeability dependence.

Equipment

The setup (depicted in Figure 7) consisted of a cylindrical plastic pipe with a circular plate in

the bottom and a height adjustable circular plate in the top. Both plates connected to wires.

The measurement apparatus were a regular resistance measurement unit and a fine tunable DC

voltage measurement unit with programmable current.

13

Execution

The measurement equipment was connected to the wires of the measurement apparatus. First

DC Resistance was measured with a resistance meter, it was noticed that the DC resistance

was changing rapidly, this seemed strange. Second voltage was measured with the same

equipment and no voltage source attached, still the measure equipment showed a voltage

across the plates. Decision to use constant current measurement equipment instead was made,

and then one could make measurements of voltage for positive and negative current. Followed

by calculation of resistance and taking the mean value of them to find the most accurate

resistance. For each sample measurement, also the height of the cylindrical bulk mass sample

was noted. The resistance was then converted to resistivity and conductivity by a geometric

dependence [1] p.166 using equation 3.3. A schematic picture in Figure 8 depicts the different

variables.

(3.3)

Figure 7: In the back there is a white bucket with moist sample of magnetite concentrate. In the front there is a resistivity measurement setup, consisting of a plastic pipe, with outside covered in aluminium foil. In the bottom of the pipe, there is a circular copper surface. The surface constituting an electrode connected to a wire exiting the bottom of the setup. A similar circular surface can be thread into the pipe from above, thus connecting through the sample put in beforehand to the surface in the bottom and finally constitute a connected system. One can do measurements between the two cables exiting the setup. The wooden plate in the bottom is for stability of measurement setup. To the left, an abandoned measurement device, a general resistance meter.

14

Where [m] is the resistivity, R [] the resistance measured on the sample length l [m] and using electrodes of area A [m

2].

Results and Conclusions

The measurement data and results can be found in appendix C and results in the following

figure, Figure 9. The effect of generating a voltage, suggested to be self potential, is very

interesting and will certainly affect electrical measurements on the moist magnetite

concentrate. At least for DC measurements and could be another interesting phenomenon of

study further for other reasons or maybe for measurement of moisture with DC levels. This is

a problem which mainly occurs during DC measurements, should not interfere too much in

the AC model.

Analysis of the measured data show that resistivity is approximately reversely proportional to

the moisture content expressed as a fraction, at least within the interval 0-12 % moisture. Only

doubts would be around 2-4 %, but as our area of interest is mainly around 8 % the results can

be considered sufficient. The bad results around 2-4 % could also somehow be related to the

measurements, as the voltage was fluctuating. The recording of values was done when the

fluctuations slowed down a bit. One could issue that it should be done after a certain time, but

satisfactory results could be presented with the current method.

Figure 8: Schematic picture illustrating the geometric dependence of the resistivity measurement setup, licensed use under CCPL by WikiUN Omegatron [30].

15

The measurements have been performed in a laboratory environment where the temperature

has been at room temperature and the packing density of the MUT has been as low as possible

but still so that the amount of macroscopic air pockets are at a minimum. Measuring higher

moisture percentage gets more troublesome as air pockets are unavoidable due to the

agglomeration process. Despite this effect it is obvious from the measurement data that the

conductivity is very high, around 10 % moisture. The measurement of dry magnetite

concentrate gave the same voltage value as it did when the two electrodes were in free space.

This indicates that if moisture content goes towards zero, the resistivity goes toward infinity.

This implies that there are two models needed to model each setup of equipment one with

parasitic resistance and one without, if it is not possible to use a combined model which

satisfies both cases.

3.3 Permittivity, Permeability and Parasitic Resistance (AC)

Purpose

By determining the E-M properties of the moist magnetite concentrate it is possible to

determine moisture content through the mixing formulas Maxwell-Garnett and Bruggeman.

Thus this measurement is the core of this project to accurately determine the E-M properties.

For accuracy it is also very important that we understand the effects in the MUT and the

measurement cell. Which covers the most of the time spent in this master thesis work. The

first objective is to measure the complex and frequency dependent S11 parameters. From there

one can calculate the E-M properties.

Figure 9: DC resistivity versus actual moisture content. The red arrow indicates that

the value at zero percent moisture, most probably can be considered infinite, as the

measurement equipment reached its limit. The actual characteristic is believed to be of

the type one over fraction, according to this diagram though, from two percent to

eleven percent an almost linear behaviour.

16

Equipment

Equipment used was a VNA and the measurements cell, depicted in Figure 10. The

measurement cell drawing, dimensions and more pictures are to be found in appendix A. The

measurement cell can be used in two setups, inductive (for magnetic properties) using

metallic bottom and capacitive (for electric properties) using plastic bottom. Thus we end up

with two equations and two unknowns for each measurement. The cables to the VNA were 50

cables.

Execution

Scripts for GPIB communication were used to make ten measurements for each sample, and a

statistical analysis is possible to determine the variance and other statistical measures, when a

satisfactory model has been found. The script acquires the frequency used and the complex

S11 parameters from the VNA as a matrix of the size of frequency times ten. The matrices are

stored in Matlab files (.mat). The S11 parameter could be translated to the impedance seen at

the connection between 50 VNA cable and the connector-lid system of the measurement cell. According to equation 3.4 below:

(3.4)

Zeq is the impedance seen by the VNA and correspondingly the impedance matched with the

equivalent circuit discussed in chapter 5, at the time of publishing believed to be best

described by the model proposed by C. Karlsson. represents the reflection coefficient [1]

Figure 10: Measurement setup with coaxial cell and VNA. The coaxial cell is connected only through one VNA port. The wooden box contains a calibration set for calibration of the VNA.

17

p.442. In our case Z0 is 50 (characteristic impedance of VNA cable) and reflection is equal to the S11 scattering parameter (one VNA port measurement).

Measurements were done on various moisture contents 0 %, 2 %, 6 %, 7 %, 8 %, 9 %, 10 %

and 11 %. Where the intervals are shorter around 8 % to give better accuracy at the interval

where it is intended to determine the moisture content in the end. Data from moistening

process could be found in appendix B. Some measurements have been done on regular water,

de-ionized water and air.

Results, Modifications and Conclusions

The values from initial measurements on air had a low correlation with model values; this was

believed to be caused by the VNA, that it measures impedance best around 50 . Then air measurements are supposed to be badly represented by measurement data. By physical means,

this was believed to be caused by lack of parasitic current (associated to the parasitic

resistance). For example, air has very low conductivity, as well as it causes a rather low

inductance, compared to water of a factor of approximately 80.

These conditions would result in a loss of the parasitic resistance in the model by A. Saremi

as the resistance gets very high and thereby can be neglected. This case also occurs when

measuring de-ionized water or dry magnetite concentrate, which also has a high resistivity

(low conductivity). Later analysis has disproved this idea, the bad correlation were probably

caused by bad data treatment and/or insufficient modeling. For further analysis, see chapter

5.5.

Some modifications to the measurement device have been done. The connection between

connector and center rod was first a coiled spring, as it was feared that this spring somehow

would affect the impedance behavior of the circuit, it was replaced by a needle-hole

connection, where the needle has a bow of feather material to tighten the connection

(commercial component). It seem like the effects on the impedance was minor, but the

connection between the conductors was greatly enhanced, which allows measurements to be

performed with ease. Also the center rod has been polished.

Measurements on samples of moist magnetite concentrate clearly show that the system cannot

only be modeled by an inductance or a capacitance alone. In the case with metal bottom

(inductive), first we will assume that all current goes through the conductor and therefore the

capacitance is not part of the model. Then if there is no capacitance behavior, it is clear that

the interaction between the leak current associated with the parasitic resistance and the current

that passes through the material dependent inductor interact to form a non-linear inductive

behavior. This will be discussed further in the discussion of chapter 5, Calculation and

Electrical Modeling. New model proposes that there should be capacitance in the inductive

model as well.

The first peak of the curves is probably the peak of the quarter wave resonance, which has a

decreasing frequency and magnitude, for increasing moisture content. In the imaginary

inductive case (Figure 12) the quarter wave resonance is more dominant than the other effects

and hence the nice asymptote. There is some confusion of the curve corresponding to 6 and 7

% in all graphs. The effects in the capacitive setup are still not identified, but are believed to

follow the theory as strictly as the inductive case.

18

Figure 11: Real part impedance spectra for inductive setup translated from the measured S11 parameters.

Figure 12: Imaginary part impedance spectra for inductive setup determined from the measured S11 parameters.

19

Figure 13: Real part impedance spectra for capacitive setup determined from the measured S11 parameters.

Figure 14: Imaginary part impedance spectra for capacitive setup

determined from the measured S11 parameters.

20

4 WHY COMSOL MODELING

To get a greater understanding of capacitance and inductance contributions, as well as having

a geometrical view of the fields allows us to develop better instruments or make our

equivalent models better. The equivalent models might need correction from fringing field

effects resonance phenomenon or similar.

Several Comsol models have been developed, some models of the inductive and capacitive

setup. A few versions of microstrip capacitive sensors have been evaluated. There has been no

breakthrough with any sensor so far, but one can see that the fringing field capacitance of the

capacitive coaxial set up should be negligible, if the surrounding media are air. This depends

on the length of the coaxial cell, combined with the spread and extended field in the media air

(outside the coaxial cell), which has a fairly lower permittivity than does the magnetite

concentrate and water. If one would immerse it into the moist magnetite concentrate this

would probably not be the case, concerning open ended probing.

4.1 Coaxial Cell Inductive and Capacitive Setup

A graphical representation of the coaxial cell presented in Figure 15 below:

For the inductive cell in Figure 16, we can see that the electric field is strongest along the

strictly coaxial part; the measurement cell excluded the lid and bottom. The electric field

weakens when approaching the edges of the coaxial cell. The edges in this case are the

inductive short (metal bottom) and the lid with connection to coaxial cable and eventually the

VNA. Especially magneto static or quasi static simulation of this setup could be of further

value to understand such things as end effects.

The end effects observed, means that the capacitance calculated in the inductive case

according to the latest equivalent model would be slightly larger than the actual one. For the

capacitive setup in Figure 17 the capacitance of the last part, the coaxial segment where the

plastic lid constitute dielectric will have an increased capacitance in reality. First due to the

fringing field effects and second due to the plastic layer attached outside the cylinder (part of

the plastic bottom) which further will increase effects of the fringing field. Due to the length

Figure 15: Cross-Section of coaxial cell.

21

of the coaxial part we will assume that the irregularities are negligible. Thus we will neglect

fringing field effects and loss of capacitance due to the inductive short. Later these effects

might need more study, when one considers more accuracy and sensitivity for measurements.

Figure 16: 3D Model of Inductive Coaxial Cell.

Figure 17: 3D Model of Capacitive Coaxial Cell.

22

In Figure 17 the outer discs (blue), tell that there is no electric potential outside the

measurement cell (as expected). The dotted lines (red) show the electric field and the arrows,

pointy structure (red), show the orientation of the field inside the cylinder. The internal disk,

rainbow colored, shows the magnitude of the electric potential.

At this point the models does not offer more than further geometrical understanding of the

problem, the models must be more sophisticated to give more information. The further need

off modeling will rather be towards the in-line measuring sensors, than on the coaxial probe.

4.2 Capacitive Surface Sensors

Some different surface sensor geometries have been simulated, offering some insight to the

distribution of electric field and electric energy density. The geometries simulated are of a 2D

symmetrical one, that means that the view should be rotated 360 around the left edge or r=0.

After this the sensor becomes somewhat of a circular disc.

During these simulations it was discovered that long grounding planes will enhance the

sensitivity of the sensor, an approximate of twice the diameter of the centre electrode seems to

be a good dimension. In the picture above there are two smaller rings as grounding plane, this

is not efficient. Instead if one could use the second ring as a guard, meaning putting the same

voltage as to the centre electrode, but without direct connection. Thus the electric fields that

generate the capacitance will not bulge at the ends. This will give a more centre aligned field.

Figure 18: Geometry of Capsense1.

Figure 19: Graphical E-Field Representation of Capsense1.

23

Another thing to address could be the length of the electric field lines; it is generally known

that capacitance is proportional to electrode area and reversely proportional to the distance

between the electrode areas. What this really means is that the distance between the electrode

areas causes the field lines to travel a further distance before decoupling in ground. Thus short

field lines are field lines with a great impact on capacitance. If one sticks with the surface

sensor, one would like to have a maximal area of the centre electrode, because this is where

the sensitivity is at its highest. A maximal area would be achieved by a sphere, where one

could experiment with different radius. When area are increased one will need higher power

to maintain the energy density, as the current are more spread out on the surface.

The authors recommendation is to use some kind of parallel or semi parallel electrode

solution, this to maximize the capacitance measurability and thereby accuracy of

measurements. One possibility would be to use geometry similar to an old thread roll or time-

glass with an extended waist, thus one might avoid problems with the moist magnetite

concentrate not entering the cavity of measurements. This kind of geometry would belong

with the parallel plate type, be of cylindrical symmetry and possibly have conical plates. The

plates would also have a hole in the middle to allow cables to the outer electrode.


24

Another interesting thing was discovered, maybe not too surprising, when using multiple

circles with increasing radius. Fed with the same feed (voltage), it has a superposition effect

(Figure 22). This means it has a very good electric energy density; however the capacitive

system also becomes very complex. If one would utilize this system one would need some

advanced algorithm calculating the capacitance seen by each electrode ring, thus using the

different capacitances for as good value as possible.



25

5 CALCULATIONS AND ELECTRIC MODELING

5.1 Evaluation of Models and Motivation for Chosen Model

The first electrically equivalent models investigated consist of two parts, the first part are the

correction part for correction between the coaxial theory (the material dependent part) and the

VNA.

The second and most important part is the coaxial theory determined part [1]. The coaxial part

is the part which allows extraction of the E-M material characteristics. The first part of the

circuit analysis has been inspired by A. Saremis work.

The latest models consist of the material dependent part and the modeling of the bottom part;

it seems that any resistance or inductance of the lid causes no larger effects of overall

impedance. In the end it could off course affect the accuracy of the E-M parameters; this is a

question for the accuracy analysis once the method has been verified in general.

The behavior of these E-M characteristics is not known, thus to generally validate the model it

is necessary to first of all well know the different characteristics and the models counterpart,

the parameters. If modeling is not fully correct these extracted E-M parameters will be wrong.

This however does not imply that the moisture content from mixing formulas would be

wrong, as the E-M properties are determined the same way for all measurements, the relation

between composite parameter (containing different properties) still could cause accurate

results for moisture. The formulas are valid for different parameters, why not a composite

parameter, but this would require further investigation. However the main idea still is to try to

find the actual E-M parameters, as these might also be useful for other purposes.

First of all, one can analyze the impedance of the whole setup, to see which characteristics

there are. It is also important to keep correct physical measures of the device in equations;

even though one might have better equation correlation with slight offset, otherwise the model

may compensate for formula errors and thereby give wrong answers. This when considering

accurate determination of the individual E-M parameters.

To characterize the connector-lid system (VNA-coaxial cell) we can measure the short

circuited simple system, namely lid and bottom connected. However this cannot directly be

used as a modeling correction for the connector-lid system as there are also the characteristics

of the bottom included. Here we need to separate the effects of the connector-lid and bottom

system. Also it is important to notice that the areas of these surface current spread on the

bottom will be different connecting directly to the lid instead of through the coaxial

cylindrical part, the area is bigger for the latter. Due to area dependence of the surface current,

the parameters Rc and Lc cannot be directly split into lid and bottom, without knowing

anything about the area dependence.

Theoretical studies of the bottom phenomena was not been successful using the Saremi

circuit, it is also suggested that this bottom dependence as part of the single-loop coil would

be material dependent. If so, this would cause a dependence of frequency and moisture. It

would certainly be good to find such a theoretical dependence; probably one can see the

effects of the surface current stream of this connection between the middle conductor and the

bottom as end effects when a conducting rod is connected to a circular disc.

26

The newest idea is to determine the geometrical dependence from measurements on water and

air, then modeling the inductance as rLG. If that is valid our problem simplifies. Similar

calibrations have been done by others for similar setups.

When choosing an equivalent circuit for moisture determination; it is necessary to combine

the behavior of leakage (G or Rp) with the material dependent inductive behavior. Later it has

been understood that also the capacitance of the coaxial part must be a part of the circuit as

well as the bottom impedance.

The Parameters of Equivalent Circuits for Coaxial Cell

For any two conductor transmission line one can represent the impedance by a lumped

parameter model where the parameters are calculated according to equations 5.1 to 5.4.

Where skin resistance, Rs [], inductance, L [H] (most models) / LM [H] (latest models), conductance, G [S or 1/], and capacitance C [F] (most models) / CM [F] (latest models). These parameters however are dependent of the transmission line geometry; hence for coaxial

elements they are as follows [1] (geometrical properties can be found in appendix A):

(5.1)

(5.2)

(5.3)

(5.4)

These parameters were also derived by A. Saremi in [27].

[F/m] is the permittivity, [H/m] is the permeability, [1/(m)] is the conductivity, a [m] is the core conductor radius, b [m] the inner radius of the cylinder wall, [rad/s] the angular frequency and l [m] is the length of the cylindrical symmetric coaxial segment. The subscripts

c and d stands for conductor and dielectric respectively.

Other parameters are described along with the corresponding models and their development.

In the latest model the bottom resistance, R [], is calculated using the skin-depth, [m], by:

(5.5)

(5.6)

27

Where [Hz] is the frequency and the other variables are the same as described for the equation above.

If one uses LC resonance theory to model the bottom impedance, the theoretical skin-

resistance of the bottom needs an adjustment multiplying with a coefficient to get the right

magnitude for the damping of resonances. The bottom inductance might be modeled as

follows in equation 5.7:

(5.7)

Where [H] is the geometrically dependent inductance and can be

determined for the case when the coaxial cell is empty, containing air or preferably vacuum,

we can find the parameter inductance of the bottom based on multiplying with the magnetic permeability.

L-type Circuit

Figure 23: L-type equivalent circuit with correction equivalent.

In the L-type equivalent circuit in Figure 23 it is easy to see that if we short-circuit the

capacitor the leakage would be short-circuited as well, thus we would get a purely inductive

behavior. One should be aware that the characteristics of the material properties also might

interfere with our model, why it is important to model by care and keep addressing the pit-

falls of this problem. Minding this, this model does not seem to be the one we are looking for.

T-type Circuit

Figure 24: T-type equivalent circuit with correction equivalent.

If the capacitor is shorted here in Figure 24, the same happen, except the skin resistance and

inductance will be halved. Again this will result in a circuit with only resistance and

inductance. Another way of seeing this case would be to accept C here and realize that the

impedance could also be affected by a capacitance along the coaxial even if it is shorted by

the end. However as the model does not take the opening capacitance into account, so that

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something can be short-circuited, after all it seems to be a bad model. Keeping these ideas in

mind, continue with the next type of model PI-type circuit in Figure 25.

PI-type Circuit

Figure 25: PI-type equivalent circuit with correction equivalent.

Here the leakage and capacitance divided in two halves, and then if the right capacitor is

short-circuited the effect of half of the capacitance and leakage (G or Rp) will stay in the

model. When starting this analysis one should be aware that this is a step in the direction of

making a semi-lumped semi-distributed model. Because if one appreciate the fact that

capacitance is split in two, it could as well be split in more parts. A distributed model is built

by infinitesimal elements of these equivalent circuits, preferably by the L-type.

Somewhere between the two models we will have a number of lumped models where each

parameter value is divided by the number of the lumped models used, and then we can only

short circuit the last capacitor. The parameters otherwise has the same properties as when only

one lumped model is used. This type of modeling maybe would better reflect the behavior of

the measurement cell. When this interpretation is used, the mathematical system will become

large and bring time consuming analysis.

Thus it is a good idea to analyze the system where we completely can ignore the capacitance,

but still keep the effects of leakage (G or Rp). Thus we will continue working with the Saremi

model when considering optimization, discussed below. If it considered being insufficient for

modeling purpose, we will continue with building a semi-lumped semi-distributed equivalent

circuit. For ease we will build this system by matrices, so that the increase of the number of

lumped models is practically simple.

Saremi Circuit

Figure 26: Saremi equivalent circuit with correction equivalent.

This is the model used in the optimization calculation with somewhat of a success (Figure

26). By previous analysis, this model seemed to be the best model to predict the behavior of

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the measurement cell. If the analysis is not enhanced using a chain of lumped models by

matrices. Further analysis and earlier knowledge of model simplification suggest that this

model should be replaced by another model.

Thus we will make a jump in the modeling and continue working with an expanded L-type

model. The semi-lumped semi-distributed model are still of interest, maybe for future

analyses.

Semi-Lumped Semi-Distributed Circuit System

Analysis of such a rather complex system is very time consuming, to simplify the work with

the equations and the modeling; it is convenient to choose a matrix approach to the problem.

It exist several sets of parameters to relate the output to the input of a two-port circuit system,

not to be mixed with the ports of the VNA. In this case we would have seen our system as a

two-port system and it will be illustrated in figure 27 below, this if correction parameters for

the lid would be used.

Figure 27: Semi-lumped semi-distributed equivalent model with split correction lid and bottom.

For microwaves the S parameters are good as voltage and current values are not well defined.

One can transform one two port matrix to another for other parameter such as Z, T or G [31].

New Electrical Model Proposed by Karlsson

Figure 28: Karlsson proposed inductive equivalent circuit with correction equivalent.

When analyzing the complex impedance regarding the effects of the correction parameters Rc

and Lc, one could see that subtracting the modeled impedance of the combination of the lid

and bottom from any measured impedance did not change the magnitude of impedance by

much, thus we neglect these effects at the lid position (first) and instead modeling only the

bottom resistance and impedance (last). The bottom skin-resistance is very small, but

according to the LC resonance theory it would affect the impedance much, due to damping

effects of the LC resonance peak which would occur as a result of the parallel connection

between bottom inductance and coaxial capacitance of the coaxial part.

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In general when considering AC current one would model a conductor as a serially coupled

resistance and inductance. Simple analyses done for dry systems, eg no conduction; air, de-

ionized water and dry magnetite concentrate, resulted in the choice of this model, as by theory

one could build the actual impedance curves and this was done in Orcad with PSpice. The

bottom resistance causes a resonance peak at the real part of impedance as well, more about

this analysis in chapter 5.5.

New in this model are also that the whole material dependent capacitance is kept, this is the

effect of a non ideal system, the inductance and along the coaxial part as well as that of the

lid. Also the capacitance is distributed throughout the system and cannot be short-circuited;

by an ideal coaxial cell it could neither be short-circuited due to the resistance and inductance

of the bottom. Only for a completely ideal conductor case one could totally short the

capacitance, but in such a case probably none of the material parameters we are interested in

would be present.

For the capacitive measurement setup one probably just connects a new segment of coaxial

cell to the inductive version without bottom (in model without bottom inductance). Initially

the plastic bottom effects will be neglected and left for later analysis of model quality.

Figure 29: C. Karlsson proposed capacitive equivalent circuit with correction equivalent.

General for the two models are that the parasitic resistance vanish for the dry case,

corresponding to a case where there are no conduc

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