The dielectric properties of solid biofuels

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Mälardalen University Press Dissertations No. 90

THE DIELECTRIC PROPERTIES OF SOLID BIOFUELS

Ana Marta Paz 2010

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ISSN 1651-4238

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Mälardalen University Press Dissertations No. 90

THE DIELECTRIC PROPERTIES OF SOLID BIOFUELS

Ana Marta Paz

Akademisk avhandling

som för avläggande av teknologie doktorsexamen i energi- och miljöteknik vid Akademin för hållbar samhälls- och teknikutveckling kommer att offentligen försvaras

fredagen 26 november 2010, 10.00 i Lambda, Mälardalens högskola, Västerås. Fakultetsopponent: Dr Ebbe Nyfors, Roxar, Norway

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Abstract

The use of bioenergy has been increasing due to efforts in fossil fuels replacement. Modern bioenergy technologies aim for high efficiency and low pollution levels, which increases the need for methods for the on-line characterization of biofuels.

Dielectric methods have been identified as useful for the sensing of solid biofuels because they allow for rapid, nonhazardous, nondestructive, and bulk determination of material properties. The dielectric properties describe the interaction between the material and the electromagnetic waves. Dielectric properties are intrinsic of the materials and can therefore be used for the development of prediction models that can be applied regardless of the measurement technique. The study of the dielectric properties is also important as it improves the understanding of the dielectric behavior of the materials. This thesis focuses on the dielectric properties of solid biofuels and their use in the characterization of these materials. The work presented includes the development of new methods permitting the determination of the dielectric properties of solid biofuels with large particle size (waveguide method), broadband measurement of the dielectric properties (coaxial-line probe), and the use of a previously developed method for the accurate determination of the dielectric properties (free-space method). The results includes the dielectric properties of solid biofuels and their dependence on parameters such as frequency, moisture, density, and temperature.

This thesis also presents semi-theoretical models for the determination of moisture content, which obtained a RMSEP of 4% for moisture contents between 34 and 67%, and an empirical model that resulted in a RMSEC of 0.3% for moisture contents between 4 and 13%.

Finally, this thesis includes measurements of the influence of salt content on the dielectric properties and a discussion of its use for estimation of the ash content of solid biofuels.

ISBN 978-91-86135-94-2 ISSN 1651-4238

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Acknowledgments

I would like to express my gratitude to all those who gave me support during my research studies and made this thesis possible:

- My main supervisor and school research director Professor Erik Dahlquist for giving me the opportunity to become a research student at Mälardalen University, and for his support and conﬁdence during these years.

- Dr. Eva Thorin for supervision, guidance and tireless support, and for being co-author in several papers.

- Dr. Jenny Nyström for supervision, for being co-author in several papers, and for her warm friendship.

- Dr. Samir Trabelsi with special gratitude for the enthusiasm, ideas, co-authoring in several papers, and inspiring discussions during my intense internship in his research group.

- Dr. Stuart Nelson for the ideas, inspiring research life, and for his dedicated work as co-author of several papers.

- Dr. Clarke Topp for interesting discussions, ideas, and for his work as co-author.

- Värmeforsk for ﬁnancing projects included in my research studies, and the heat and power plants Eskilstuna Energi och Miljö and Mälarenergi for the support with the measurements and biofuel samples.

- The colleagues at the Russell Research Center, and the Nelson and Trabelsi families for welcoming me and making me feel at home in Athens (GA). - My colleagues at Mälardalen University for the companionship, help with

experiments, and other things such as the ping-pong games. - My friends and family for their affectionate support.

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Abstract

The use of bioenergy has been increasing due to efforts in fossil fuels re-placement. Modern bioenergy technologies aim for high efﬁciency and low pollution levels, which increases the need for methods for the on-line charac-terization of biofuels.

Dielectric methods have been identiﬁed as useful for the sensing of solid biofuels because they allow for rapid, nonhazardous, nondestructive, and bulk determination of material properties. The dielectric properties describe the interaction between the material and the electromagnetic waves. Dielectric properties are intrinsic of the materials and can therefore be used for the de-velopment of prediction models that can be applied regardless of the measure-ment technique. The study of the dielectric properties is also important as it improves the understanding of the dielectric behavior of the materials.

This thesis focuses on the dielectric properties of solid biofuels and their use in the characterization of these materials. The work presented includes the development of new methods permitting the determination of the dielec-tric properties of solid biofuels with large particle size (waveguide method), broadband measurement of the dielectric properties (coaxial-line probe), and the use of a previously developed method for the accurate determination of the dielectric properties (free-space method). The results includes the dielec-tric properties of solid biofuels and their dependence on parameters such as frequency, moisture, density, and temperature.

This thesis also presents semi-theoretical models for the determination of moisture content, which obtained a RMSEP of 4% for moisture contents be-tween 34 and 67%, and an empirical model that resulted in a RMSEC of 0.3% for moisture contents between 4 and 13%.

Finally, this thesis includes measurements of the inﬂuence of salt content on the dielectric properties and a discussion of its use for estimation of the ash content of solid biofuels.

The results presented in this thesis contribute to the development and im-provement of methods for determination of important characteristics in solid biofuels such as moisture content, density, and salt content using dielectric measurement techniques.

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Sammanfattning

Bioenergianvändningen har ökat tack vare insatser för att byta ut fossila bränslen. Modern bioenergiteknik strävar efter hög effektivitet och låga emis-sioner. Detta har lett till ett behov av metoder för online-karakteriseringen av biobränslen.

Dielektriska metoder har identiﬁerats som fördelaktiga for mätning av biobränslen, eftersom de kan ge en snabb, ofarlig och icke-förstörande bestämnig av stora volym av material. De dielektriska egenskaperna beskriver samverkan mellan material och elektromagnetiska vågor. Dielektriska egenskaper är speciﬁka egenskap hos ett material och kan användas för utvecklingen av prediktionsmodeller som kan tillämpas oavsett mätteknik. Undersäkningen av dielektriska egenskaper är också viktiga för att de förbättrar förståelsen av materialen.

Denna avhandling fokuserar på dielektriska egenskaper hos fasta biobränslen och deras användning för karakteriseringen av dessa material. Det arbete som presenteras här innefattar utvecklingen av nya metoder som tillåter bestämningen av dielektriska egenskaper hos fasta biobränslen med stor partikelstorlek, bredbandmätning och användning av en tidigare utvecklad metod för noggrann bestämning av dielektriska egenskaper. Resultaten inkluderar de dielektriska egenskaperna för fasta biobränslen och deras beroende av parametrar som frekvens, densitet, temperatur och fukt.

Denna avhandling presenterar även semiteoretiska modeller för bestämnin-gen av fukthalten, som gav en RMSEP på 4% för fukthalter mellan 34 och 67%, och en empirisk modell som gav en RMSEC på 0.3% för fukthalter mellan 4 och 13%.

I avhandlingen ingår också mätningar av påverkan av salthalten på dielek-triska egenskaper och en diskussion om deras användning för skattningen av askinnehållet i fasta biobränslen.

De resultat som presenteras bidrar till utveckling och förbättring av dielek-triska metoder för bestämning av viktiga egenskaper hos fasta biobränslen som fukthalt, densitet och salhalt.

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List of Papers

This thesis is a comprehensive summary of the following papers, numbered in reverse chronological order of their writing. In the thesis, the papers are refered to by Roman numerals.

I Ana Paz, Samir Trabelsi, Stuart Nelson, and Eva Thorin. Measurement of the 0.5- to 15-GHz dielectric properties of sawdust, submitted to

IEEE Transactions on Instrumentation and Measurement, 2010.

II Ana Paz, Samir Trabelsi, Stuart Nelson, and Eva Thorin. Inﬂuence of sodium chloride on sawdust dielectric properties, submitted to IEEE

Transactions on Instrumentation and Measurement, 2010.

III Samir Trabelsi, Ana Paz, and Stuart Nelson. Dielectric-based method for determining moisture content and bulk density of peanut-hull pellets, IMPI2010, International Microwave Power Symposium

Conference Proceedings, pages 190-195, Denver (CO), USA, 2010.

IV Ana Paz, Samir Trabelsi, and Stuart Nelson. Dielectric properties of peanut-hull pellets, IMTC2010 Instrumentation and Measurement

Conference Proceeding, pages 62-66, Austin (TX), USA, 2010.

V Ana Paz, Eva Thorin, Jenny Nyström, and Erik Dahlquist. Complex Permittivity of woody biomass at radio frequencies, submitted to

Measurement Science and Technology, 2009.

VI Ana Paz, Eva Thorin, and Clarke Topp. Dielectric mixing formulas for water content measurement in woody biomass, Wood Science and

Tech-nology, DOI 10.1007/s00226-010-0316-8, 2010.

Ana Paz contributed with idea, method, and experimental work to all papers except the following:

Paper I: initial idea by Samir Trabelsi and Stuart Nelson. Paper III: idea and method by Samir Trabelsi and Stuart Nelson. Paper VI: initial idea by Clarke Topp.

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Other papers by the author

Ana Paz. Moisture content determination from dielectric properties of solid biofuels, Aquametry 2010, First European Conference on Moisture

Measurement Conference Proceedings, pages 318-325, Weimar, Germany,

2010.

Ana Paz, Eva Thorin, and Jenny Nyström. Dielectric properties of woody biomass at radio frequencies, ISEMA 09, Electromagnetic Wave

Interaction with Water and Moist Substances Conference Proceedings,

pages 249-268, Helsinki, Finland, 2009.

Ana Paz, Jenny Nyström, Eva Thorin, and Erik Dahlquist. Measuring water content in woody biomass directly in transport containers, submitted to journal 2009.

Ana Paz, Eva Thorin, and Erik Dahlquist. A new method for bulk measurement of water content in woody biomass, Ecowood 2008, Third

Conference on Environmental Compatible Forest Materials Proceedings,

Porto, Portugal, 2008.

Ana Paz, Jenny Nyström, and Eva Thorin. Inﬂuence of temperature in moisture content measurement of biofuel, IMTC2006, Instrumentation and

Measurement Technology Conference Proceedings, pages 175-179,

Sor-rento, Italy, 2006.

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Symbols

ε relative complex permittivity ε′ the dielectric constant

ε′′ the dielectric loss factor

ε0 permittivity of the free space (F·m−1)

ε′∞ permittivity at inﬁnite hight frequencies

εe permittivity of the host phase in a mixture

εi relative dielectric constant of the component i in a mixture

ε_′st static permittivity ε′′

rd loss factor due to dielectric losses

θi volumetric content of the component i of a mixture (vol·vol−1)

θ volumetric moisture content (vol·vol−1)

µ permeability (H·m−1)

ρw water density

ρ density (or bulk density) ρd dry bulk density

σ conductivity (S·m−1)

τ relaxation time (s)

ω angular frequency (rad·s−1)

ψ density-independent function

B magnetic ﬂux density (T)

D electrical ﬂux density (C·m−1)

Di depolarization factor for the component i in a mixture

E electrical ﬁeld strength (V·m−1)

J current density (A·m−2)

H magnetic ﬁeld strength (A·m−1)

j square root of -1

ms mass of dry phase

mt total mass

mw mass of total water phase

MC gravimetric moisture content (% mass·mass−1)

v total volume

vs volume of the solids

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Abbreviations

CEN European committee for standardization GPR ground penetrating radar

MG Maxwell-Garnett dielectric mixing model RMSEC root mean square error of calibration RMSEP root mean square error of prediction RF radio frequency

TDR time domain reﬂectometry VNA vector network analyzer

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List of Figures

2.1 The dielectric properties of free water at 0, 20 and 60°C. . . 26

2.2 The dielectric properties of wood cell wall substance. . . 28

3.1 From biomass to bioenergy. . . 29

3.2 Sawdust. . . 30

3.3 Tops and needles. . . 30

3.4 Residual woodchips. . . 31

3.5 Shelled peanuts and peanut-hull pellets. . . 31

3.6 Classiﬁcation of the biofuels included in this thesis. . . 32

4.1 Waveguide method . . . 36

4.2 Free-space method. . . 37

4.3 Coaxial-line probe. . . 38

6.1 The permittivity of sawdust versus frequency. . . 43

6.2 The permittivity of sawdust versus density. . . 44

6.3 The permittivity of sawdust versus temperature. . . 45

6.4 The permittivity of sawdust versus MC. . . 46

6.5 The permittivity of sawdust versus θ. . . 47

6.6 The complex MG mixing model. . . 48

6.7 Prediction results with the complex MG model. . . 48

6.8 The Argand-diagram of the permittivity divided by density. . . 49

6.9 The density-independent function versus MC. . . 49

6.10 The inﬂuence of salt content on the dielectric properties. . . 51

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Part I:

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1. Introduction

Humans have for a long time used biomass as a fuel, but about 150 years ago, it was fossil fuels that propelled the industrial revolution. Today, a major part of energy, chemicals, and materials has fossil origins. Fossil fuels have higher energy density than biofuels (about 30 MJ·kg−1for coal and about 19 MJ·kg−1

for dry woodchips), but fossil fuels have important drawbacks such as nega-tive environmental consequences, the uneven distribution of reserves, and the foreseeable exhaustion of those reserves. While the estimates on how long the fossil reserves will last are not consensual, it is known that the as yet unexplored reserves will require higher exploration costs, increasing the fuel price [1]. The current interest in renewable energy is related to attempts to secure energy supply and reduce the emission of greenhouse gases. The In-tergovernmental Panel on Climate Change estimates that 56.6% of the global warming capacity derived from anthropogenic emissions has its origin in the use of fossil fuels [2].

The European Union has set a goal of 20% of the energy use to be from renewable sources by 2020 [3]. Bioenergy is responsible for two thirds of the renewable energy in the European Union and was identiﬁed as having the largest growth potential among renewable sources because of relatively low costs, low life cycle emissions, less dependence on short-term weather changes, and development of the agro-forestry sector [4].

Solid biofuels are products and by-products of agriculture, forestry, and their associated processing industries. Some examples of solid biofuels are woodchips, sawdust, and straw. Direct combustion of solid biofuels at com-bined heat and power plants is a mature and highly efﬁcient conversion tech-nique. This technique has been implemented in Sweden on a large scale, where bioenergy accounted for 20% of the total energy supply in 2008 [5], and is un-dergoing worldwide expansion.

1.1 Characterization of solid biofuels

Unlike those of fossil fuels, the properties of biofuels vary widely. These vari-ations are due to different factors such as the origin of the biomass, the time of harvest and collection, storage, and handling procedures [6]. The use of solid biofuels at an industrial level increased the need for the rapid and non-destructive sensing of their properties. Moisture content is the parameter with 17

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the largest variation in solid biofuels. The typical moisture content for non-processed solid biofuels varies between 20% and 60%, while for pelletized biofuels the moisture content can vary between about 5% and 12% [7].

The determination of the moisture content of solid biofuels is important for pricing, quality control, and the control of the conversion process. The price of biofuel is dependent on its moisture content because it directly affects the heating value. The possibility of correct pricing is one of the largest economic benefits of rapid moisture sensors [8]. The moisture content can also be deci-sive for the quality of a biofuel, for instance before a densification process [9], or at plants where moisture content determines the acceptance or rejection of biofuels. Moisture can also decrease the overall process efficiency and in-crease the emission of pollutants due to incomplete combustion [7]. When the moisture content is known, biofuels can be mixed in order to achieve a certain average moisture content (a common practice at heat and power plants), and process parameters such as input flows can be controlled.

Presently, the moisture content of solid biofuels used in heat and power plants is determined with the standard oven method, which consists of dry-ing samples in an oven and registerdry-ing the mass difference before and after drying [10]. This method is very accurate for solid biofuels [11], but it is labor-consuming and requires a long waiting time for drying. Furthermore, it demands sampling of the solid biomass material, delivered to power plants in large truck containers. Samples are taken from surface layers of the biofuel in the containers, leading to a moisture value that is not representative of entire the biofuel load.

Due to the increasing interest in the rapid measurement of moisture con-tent of solid biofuels, some methods have recently been developed for that purpose. A comparative study of commercially available methods was per-formed by Jensen et al. [12], who studied dielectric methods for at-line de-termination of moisture content in solid biofuels, either by placing biofuel in a sample holder or by using a probe. There are also instruments using near infrared spectroscopy, with a penetration depth in a range of a few the mil-limeters, which are suitable for on-line measurements of biofuels in conveyor belts [13].

Nyström [8] reviewed the methods that could be used for measuring mois-ture content of biofuel for power plants. The study compared methods such as the dual X-ray, the indirect plant efﬁciency method, near-infrared spec-troscopy, radio and microwave methods, and nuclear magnetic resonance. Di-electric methods using radio frequency were considered the only ones suitable for measuring a representative bulk of material, due to the large penetration depth of radio waves. Nyström [14] developed a reﬂection method using radio frequencies, with the vision of its further development into an application for on-line moisture measurement of the biofuel directly in the truck containers.

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1.2 Dielectric measurements

The expression ”dielectric measurements” is used to describe the measure-ment of the interaction between dielectric materials and electromagnetic ﬁelds at radio and microwave frequencies. The phenomena occurring during the in-teraction between electromagnetic waves and materials are brieﬂly presented in chapter 2.

Dielectric measurements have multiple advantages when compared with other measurement methods. Besides permitting the rapid and nondestructive determination of the properties of materials, dielectric measurements are non-hazardous, due to the use of low power levels, and have large penetration depth which provides subsurface sensing [15,16].

Electromagnetic fields can be coupled to the materials under test using structures such as coaxial lines, hollow waveguides, and air-coupled antennas, measuring transmitted and/or reflected waves [16]. The parameters measured can be attenuation, phase shift, and scattering coefficients, from which the dielectric properties, characterized by the complex permittivity, can be calcu-lated.

Some applications determine the properties of interest in the material di-rectly from the parameters measured. An example is the method presented by Kraszewski [17] for the determination of moisture using attenuation and phase-shift. Also Nyström [14] used multivariate data analysis to determine the moisture content in biofuels using a range of reﬂection coefﬁcients in the time domain.

It is also possible to retrieve the dielectric properties from measured pa-rameters and thereafter determine the physical properties of the material. The dielectric properties are intrinsic of the material and therefore independent of the measurement method and setup. The study of dielectric properties allows for the development of prediction models that can be applied regardless of the measurement method, as was also noted by Trabelsi et al [18]. Studying the dielectric properties also contributes to the understanding of the dielectric behavior of the material, which can lead to improved sensing technology.

Many applications make use of the dielectric properties for the characteriza-tion of materials. An example is time-domain reﬂectometry (TDR), in which the dielectric constant is obtained from the travel time measured. The volumet-ric moisture content is determined from the dielectvolumet-ric constant using empiri-cal polynomials or dielectric mixing formulas [19, 20]. The method has been widely used for soils but also for other porous materials such as snow [21,22]. Topp’s calibration polynomial found application in a variety of soils and also with measurement techniques such as ground penetration radar (GPR) [23].

Another interesting example is the work by Trabelsi et al [24] who devel-oped a model for the determination of density and moisture from the dielectric properties and which showed very good results in a variety of particulate ma-terials such as grain, seeds, shelled and unshelled peanuts, and pellets [18,25]. 19

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Multivariate analysis was also used by Kent [26] for the determination of the composition and quality of foodstuffs from frequency spectra of dielectric properties.

There are several applications of dielectric measurements for the on-line characterization of materials, as reviewed and compiled in different works [15,16,27–29]. Some examples of on-line applications are the free-space mea-surements for moisture determination in green tea in conveyor belts [27], and the resonant sensors for measuring the compositions of materials under ﬂow in pipelines [15].

Solid biofuels are mixtures of woody and herbaceous materials. There are several studies on the dielectric properties of wood [30–32], but studies on the dielectric properties of solid biofuels have not been previously published. As resumed by Kraszewski [33], the development of new sensors requires not only adequate technology but also speciﬁc knowledge concerning the material of interest. Therefore, the focus of the work presented in this thesis was on the study of the dielectric properties of solid biofuels.

1.3 Problem description and research questions

As previously mentioned, knowledge of dielectric properties is very important for the development of new applications for material characterization. The study of the dielectric properties of materials such as wood, soil, and grain allows us to get an indication of the dielectric behavior of solid biofuels and to analyze the possibility of measuring such properties with dielectric mea-surements. However, the dielectric properties of solid biofuels are unknown. This is the problem underlying the work in this thesis, and from which the following three main questions are drawn:

1. What is the dielectric behavior of solid biofuels and what is the inﬂuence of parameters such as wave frequency, density, temperature, and moisture content?

2. How can moisture content be determined from the dielectric properties? 3. Which other characteristics of biofuels can be determined from the

dielec-tric properties?

1.4 Contributions of this thesis

The main contributions of the present thesis can be summarized as follows: - The determination of the dielectric properties of solid biofuels (sawdust,

tops and needles, residual woodchips, and peanut-hull pellets), and their dependence on frequency, temperature, density, and moisture.

- The development of new methods for the determination of the dielectric properties of solid biofuels with large particle size (waveguide-reﬂection 20

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method), broadband measurements (coaxial-line probe), and the applica-tion of a previously developed method for accurate measurements (free-space reﬂection method).

- The development and application of semi-theoretical and empirical models for moisture and density determination from the dielectric properties of solid biofuels.

- The study of the inﬂuence of salt content on the dielectric properties and a discussion on their use for the estimation of the ash content of solid biofu-els.

The main contributions of the papers included in this thesis can be summed up according to the research questions they are most related to:

Question 1 - The dielectric behavior of solid biofuels and the inﬂuence of wave frequency, density, temperature, and moisture

Paper VI presents the apparent dielectric constant determined from measure-ments with the waveguide reﬂection method, for different types of solid biofuels (sawdust, tops and needles, and residual woodchips) for a sin-gle frequency of 0.5 GHz. It is the ﬁrst published estimate of a dielectric property of solid biofuels.

Paper V describes a method for the determination of the complex permittivity from measurements performed with the waveguide reﬂection method. The complex permittivity is presented for different types of solid biofuels (sawdust, tops and needles, and residual woodchips) for a single frequency of 0.5 GHz. The fraction of loss factor due to conductivity is also estimated using a dielectric mixing formula.

Paper IV presents the complex permittivity of peanut-hull pellets at microwaves (5 to 15 GHz) and its variation with frequency, moisture, temperature, and density.

Paper I presents the complex permittivity of sawdust over a wide frequency range (0.5 - 15 GHz) for different moisture contents. The papers also presents a method for the determination of actual sample density in measurements with the coaxial-line method.

Question 2 - The determination of moisture content determination from the dielectric properties

Paper VI models the dielectric constant with dielectric mixing models and evaluates their use for the determination of moisture content.

Paper V models the complex permittivity with a dielectric mixing model and veriﬁes its use for the determination of moisture content.

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Paper III uses a density-independent function for determination of moisture content from the complex permittivity.

Question 3 - The determination of other properties than moisture content Paper II presents a study on the inﬂuence of salt content on the broadband

dielectric properties of sawdust.

Paper III uses a density-independent function for the determination of the density of peanut-hull pellets.

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2. The interaction of electromagnetic

waves with materials

James Maxwell worked out a theory of electromagnetism in 1864, supported by twenty equations describing the behavior of electric and magnetic fields [34]. These equations were later combined and simplified into four elegant equations, known as Maxwell’s equations. Three constitutive equations (2.1), (2.2), and (2.3) describing the relationship between electromagnetic fields and materials, can be derived from Maxwell’s equations:

D = εE (2.1)

B = µH (2.2)

J = σE (2.3)

where E is the electrical field strength, D the electrical flux density, H the magnetic field strength, B the magnetic flux density, and J the current density. Permittivity ε, permeability µ, and conductivity σ are the electromagnetic constitutive parameters of materials. The constitutive parameters are intrin-sic properties of the materials and are also called the electromagnetic proper-ties [35,36].

Permittivity describes the interaction of a material with an electric field and is a measure of how much the electric charge distribution in the material is changed by the application of an electric field. Permeability describes the in-teraction of a material with a magnetic field. It is a measure of the magnetiza-tion or occurrence of magnetic moments in a material under the influence of a magnetic field. All materials respond to magnetic fields to a certain degree, but it is only for ferromagnetic materials that the permeability varies significantly from the permeability of free space. Other materials are therefore generally assumed to be non-magnetic [36].

Conductivity is a measure of how easily electrons can travel through the ma-terial under the influence of an external electric field. Depending on their ductivity, materials can be classified as insulators, semi-conductors, and con-ductors. Conductors have a large number of loose electrons that migrate from one atom to another when an electrical field is applied. In semi-conductors, there is smaller number of free charges. Insulators have very low conductiv-ity, usually in the range 10 to 20 σ·m−1[36].

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2.1 Dielectric properties

In works on the electromagnetic characterization of materials, the term "di-electric" is used to describe materials with high polarizability. The perme-ability of dielectrics is comparable to that of free space and is therefore not considered in dielectric measurements. The conductivity of dielectrics is low, but its effects can be present the measurement of the complex permittivity. In other words, the electromagnetic properties of dielectrics are characterized by the complex permittivity, whose components are the dielectric properties.

Permittivity is expressed as a complex number, as shown in (2.4), in order to represent the energy storage and energy dissipation phenomena that occur in the material under the inﬂuence of an electric ﬁeld. The real part of permittiv-ity, ε′, is called the dielectric constant and describes the energy storage. The

imaginary part, ε′′, is the dielectric loss factor and describes energy losses.

The permittivity of a material is expressed in relation to the permittivity of free space, which is why it is a relative parameter with no units.

ε = ε′_{− jε}′′ (2.4)

Power loss occurs due to differences between the alignment of the charges and the electric ﬁeld (dielectric losses) and due to conductivity. Permittivity can therefore be expressed as in (2.5), where ε′′

rd, is the loss factor due to

dielectric losses, ε0 is the permittivity of free space, and ω is the angular

frequency.

ε = ε′_{− j(ε}′′

rd+_ωεσ

0) (2.5)

The dielectric constant, ε′, affects the speed of propagation and the

wave-length of electromagnetic waves. The loss factor, ε′′represents the power that

is absorbed by the material, and, has only minor inﬂuence on the velocity of a propagating wave [28].

2.2 Polarization phenomena

Permittivity can be understood as measure of the polarization that occurs in a medium when submitted to an electric field. Polarization is a process of distortion of the electric charges in a material, which tend to align with the electric field. The period required for the charges to align with the electric field, is the relaxation time, τ. The frequency corresponding to the relaxation time is called the relaxation frequency, and is calculated according to (2.6):

frelaxation= 1

2πτ (2.6)

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At frequencies under the relaxation frequency, the charges in the material are able to align with the ﬁeld, but as the frequency approaches the relaxation frequency, a phase lag between the charges and the ﬁeld arises, resulting in energy dissipation [37].

The different phenomena contributing to polarization are discussed in the next sections.

Electronic and atomic polarization

Electronic polarization occurs in neutral atoms when the electron cloud is distorted by an external electric ﬁeld. Atomic polarization occurs due to dis-tortion in the molecules without a permanent dipole but with regions that have positive and negative charges. For many dry solids these are the dominant polarization mechanisms, which determine their permittivity at radio and mi-crowave frequencies. Because electronic and atomic inertia are small, the re-laxation time is very small, and the resonant frequency is above the microwave region. If only these polarization mechanisms are present in a material, its di-electric constant is rather low and it is nearly lossless [35].

Orientation or dipole polarization

Dipole polarization occurs in molecules with a permanent dipole. Because the inertia of the molecule is higher than that of an electron or an atom, this type of polarization requires longer periods to develop and the relaxation frequency is lower than for electronic and atomic polarization. Materials with permanent dipole moments are characterized by high dielectric constants at frequencies below the resonant frequency of the molecules, as well as a peak in the loss factor at the relaxation frequency [28,35].

Ionic conductivity and the Maxwell-Wagner effect

Conductivity is the movement of unbound charge carriers under an electro-magnetic ﬁeld. In moist materials, dissolved ions may contribute to conduc-tivity, which dominates the loss factor, ε′′, at low frequencies, according to

(2.5).

In heterogeneous dielectrics, ionic conduction can also affect the dielectric constant, ε′. As the ions move under the inﬂuence of the electric ﬁeld, they

accumulate in interfaces, creating regions in the material with higher con-ductivity. This results in space-charges with a relatively long relaxation time, which contribute both to conduction and polarization. This type of polariza-tion, called the Maxwell-Wagner effect, was noted in moist wood [31, 32].

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2.3 The dielectric properties of water

The arrangement of the H2O molecule is responsible for the unusual

proper-ties of water and its multiple functions in nature. The electric charges are not uniformly distributed over the water molecule, which results in a permanent electric dipole moment [38]. Apart from the polarizability due to electronic and atomic displacement, the water molecule can develop dipole polarization. Figure 2.1 shows the complex permittivity of water at radio and microwave frequencies. Figure 2.1 was obtained with relaxation times, τ, for water at different temperatures, published by Kaatze [38] and with the Debye equation for polar substances, according to (2.7),

ε = ε′∞+ ε′st− ε′∞

1 + jωτ (2.7)

where ε′∞ is the permittivity at inﬁnitely high frequencies for which dipole

polarization has no time to develop, ε_′st is the static permittivity correspond-ing to the permittivity at low frequencies, where dipole polarization develops fully, and ω is the angular frequency.

108 109 1010 1011 10 20 30 40 50 60 70 80 Frequency (Hz) Permittivity, ε ε’ 0°C ε’’ 0°C ε’ 20°C ε’’ 20°C ε’ 60°C ε’’ 60°C

Figure 2.1: The dielectric properties of free water at 0, 20 and 60 °C as a function of frequency. The complex permittivity was calculated using the Debye equation with parameter values published by [38].

Looking at the behavior of water at 20°C, it can be noted that the relaxation frequency is at about 17 GHz. At frequencies below the relaxation frequency, ε′ is high due to the alignment of the water molecules with the ﬁeld; as the

frequency approaches the relaxation frequency, the ability of the molecules to align with the ﬁeld decreases, a lag between the phase of the ﬁeld and that of the molecules grows and peaks at the relaxation frequency, where ε′′is

maxi-mal. At frequencies higher than the relaxation frequency of water molecules, both ε′and ε′are very low.

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Figure 2.1 also shows that the complex permittivity varies not only with frequency but also with temperature. The relaxation frequency decreases with temperature. This is because the relaxation time, τ, is inversely proportional to temperature, as molecular movement is faster at higher temperatures [28], and according to equation (2.6), the relaxation frequency decreases when τ in-creases. Temperature also inﬂuences ε_′st, which decreases with rising temper-ature. This is because a higher temperature leads to an increase in molecular disorder and makes dipole polarization difﬁcult even at lower frequency [28]. Ice

The molecular structure of ice differs from that of liquid water, which inﬂu-ences its dielectric properties. Water molecules form hydrogen bonds with the oxygen atom of neighboring molecules. In their regular structure, ice molecules form three hydrogen bonds, which makes them unable to rotate in the direction of an external electric ﬁeld at microwave frequencies [39]. The relaxation frequency is shifted far down to the kHz region, and at microwave frequencies the ε′of ice is about 3.5 and losses are very low [28].

2.4 The dielectric properties of wood

Wood is the dry constituent of many solid biofuels. The dielectric properties of wood can also exemplify how the characteristics of dry materials differ from those of water.

Figure 2.2 shows the complex permittivity of wood cell wall substance as a function of frequency. The ﬁgure was obtained with data from Torgovnikov [31] for an electric ﬁeld oriented perpendicularly to the tubular cells of the wood. The dielectric behavior of the wood cell wall substance is typical of a polar substance, with ε′ decreasing with frequency, and a small peak in ε′′.

This behavior indicates the presence of some polar molecules in wood cell wall substance, but the importance of dipole polarization in dry wood is very small compared with its effect in water. Electronic and atomic polarization are dominant phenomena, which also implies a minimal inﬂuence of temperature [31].

Figure 2.2 refers to the complex permittivity of wood cell wall substance that has a density of 1.53 g·cm−3. Dry wood is a mixture of wood cell wall

substance and air, with typical densities between 0.4 and 0.8 g·cm−3, and

con-sequently a lower permittivity than wood cell wall substance. Moist wood and bound water

With the addition of water, the dielectric properties of wood change dras-tically. Because of the polar nature of water, its dielectric properties at radio and microwave frequencies dominate those of the materials where it is present. 27

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102 104 106 108 1010 0 1 2 3 4 5 6 7 Frequency (Hz) Permittivity, ε ε’ ε’’

Figure 2.2: The ε of the wood cell wall substance at temperatures of 20-25 °C as a function of frequency. Values are for an electric ﬁeld perpendicular to the tubular cells of the wood and as published by Torgovnikov [31].

However, the resultant dielectric properties of the moist material are not a sim-ple combination of the dielectric properties of the dry matter and water.

Water in solid materials has different thermodynamic properties than free water. Water in wood is primarily held by chemical bonds. These are hydrogen bonds formed by the hydroxyl groups in the wood cell walls. As moisture increases, water occupies the cell cavities and pores, held only by mechanical forces. The chemically bound water is generally called bound water, and the fraction up to which water is chemically bound in wood is called the ﬁber saturation point. This point can generally be assumed to be 30% of the mass of dry material [40].

The properties of bound water are complex and inseparable from those of the dry phase. There can be different degrees of binding, and different ﬁber saturation points, depending on the constitution of the dry phase. Therefore a phase known as solid solution, composed of the dry-matter and bound-water fractions in wood, is often used in studies [40].

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3. Solid biofuels

Biofuels are solid, liquid, or gaseous products derived from organic raw ma-terials [6]. Some biofuels are obtained directly from biomass without any pro-cessing or conversion, as is the case with some logging residues. In other cases, biomass undergoes some form of processing such as chopping in order to obtain woodchips, or drying and densiﬁcation to produce pellets and bri-quettes. Some biofuels are obtained through a conversion process, as is the case with ethanol, biogas, and bio-oil. Ultimately, all fuels are combusted for the production of electricity, heat, or mechanical work. Figure 3.1 illustrates the relationships between biomass, biofuels and bioenergy services.

Biomass Non-fuels Biofuel Solid biofuels Liquid and gaseous biofuels Bioenergy (Electricity Heat Work)

Figure 3.1: From biomass to bioenergy. Adapted from CEN [41].

The biofuels studied in this thesis were:

Sawdust: residue from sawmills, rather homogeneous with particle size smaller than 5 mm, mainly from spruce and pine.

Tops and needles: residue from forest operations such as cleaning and prun-ing, a mixture of small woody parts and more or less green tops, mainly from spruce and pine.

Residual woodchips: residue from the demolition of objects made of un-treated wood, such as pallets, with large and rather heterogeneous par-ticle size that can vary between 10 and 150 mm.

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Peanut-hull pellets: residues from the peanut processing industry that un-dergo a pelletization process for increasing their density, homogeneous cylindrical particles with a diameter of about 8 mm and a length of 9 mm.

Figures 3.2 to 3 show examples of sawdust, tops and needles, residual woodchips, and peanut-hull pellets.

Figure 3.2: Sawdust.

Figure 3.3: Tops and needles.

Biofuels can be classiﬁed according to different criteria such as biomass production system (energy crops, by-products), economic sector (forest biomass, agricultural biomass, municipal waste), and class of material (woody biomass, herbaceous biomass, fruit biomass). The European 30

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Figure 3.4: Residual woodchips.

Figure 3.5: Shelled peanuts and peanut-hull pellets.

Committee for Standardization (CEN), defines solid biofuels as products and wastes from forestry and agriculture, and wastes from their associated transformation industries. The CEN also presented a classification for solid biofuels according to origin and source, with the aim of facilitating the communication between sellers, buyers, equipment manufacturers, and authorities [41]. Figure 3.6 shows the classification of the solid biofuels studied in this thesis according to CEN.

3.1 Deﬁnitions of solid biofuels properties

As mentioned in section 1.1, the properties of biofuels are highly variable. They vary primarily with the type of biomass and growing conditions such as soil type and climate. Harvest, handling, and storage procedures, as well 31

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Woody biomass Fruit biomass Forest plantation wood Wood processing industry by-products and residues Used wood Fruit processing industry by-products and residues Chemically untreated

fruit residues Nuts Peanut-hull pellets Logging residues Chemically untreated wood residues Chemically untreated wood Bleands and mixtures Without bark Withour bark Tops and needles Sawdust Residual woodchips

Figure 3.6: The solid biofuels in this thesis according to the CEN classiﬁcation of origin and sources [41].

as treatment such as drying, grading, and densification, will also affect the final characteristics of the biofuels. Important physical characteristics of bio-fuels are moisture content, bulk density, and ash content [14,42]. The moisture content is important for pricing and quality control, and also for controlling the conversion process. The bulk density affects the flow dynamics of mate-rials and can also be important for the determination of quality. Ash content affects the heating value, and may contribute to increased concentrations of pollutants in the flue gases, as well as to several equipment-related problems such as slagging, fouling, and corrosion, thus causing a decrease in the over-all efficiency of the plant, equipment wear and failure, and unscheduled and costly shut-downs [43, 44]. Chlorine has been mentioned as the most impor-tant element causing ash-related problems, since it is responsible for making alkali available in a corrosive form [42, 43,45].

Density

The density, also termed bulk density, of a material is deﬁned as the total mass of the material, which is the mass of water mw and the mass of solids ms,

divided by the total volume, v, according to equation (3.1):

ρ =mw+_v ms (3.1)

Other deﬁnitions of density are also mentioned in this thesis. The dry bulk density, ρd, is used in Paper VI, deﬁned as the mass of solids divided by the

total volume, according to equation (3.2):

ρd=m_vs (3.2)

Paper VI also used the deﬁnition of density of dry solids, ρs, which is

de-ﬁned as the mass of solids divided by the volume of the solids, vs, according

to equation (3.3). In the case of wood the density of the dry solids is that of the wood cell wall, which properties are shown in ﬁgure 2.2.

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ρs=ms

vs (3.3)

Moisture content

The gravimetric moisture content, MC, is the quotient between the mass of water mwand the total mass of the sample mt, according to (3.4).

MC = mw

mt · 100 (%mass·mass

−1₎ (3.4)

Moisture content can also be deﬁned on a volumetric basis. The volumetric moisture content, θ, is the quotient between the volume of water, vwand the

total volume of the sample, v, according to (3.5). The volumetric moisture content, θ, refers to the water volume fraction, independent of the material density. In materials with high moisture content, whose dielectric properties are dominated by those of water, the permittivity shows a better correlation with θ than with MC [46].

θ =v_vw (vol·vol−1₎ (3.5)

The reference moisture content of the biofuels considered in this work was determined with the gravimetric oven method, which meant weighing the bio-fuel samples before and after drying at 105°C for at least 12 hours. The ref-erence method for moisture determination yields results in gravimetric units, and it is possible to calculate θ from MC using (3.6), where ρw is the water

density.

θ =MC₁₀₀_ρρ

w (vol·vol

−1₎ (3.6)

Ash content

The ash content of a biofuel is the amount of inorganic matter in the fuel that is left unburned after combustion. Ashes can be present in the ﬂue gas phase or be left in the bottom part of the furnace.

Ash content is deﬁned on a gravimetric dry basis, as the mass of ash, mash,

divided by the mass of solids, ms, according to equation 3.7.

Ash = mash

ms · 100 (%mass·mass

−1₎ (3.7)

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4. Measurement of the dielectric

properties

As discussed in section 1.2, there are different methods for measuring dielec-tric phenomena. In this thesis, three different measurement systems were used: the waveguide method, the free-space method, and the coaxial-line method. The measurement methods are useful in different measurement situations and have different characteristics such as measurement frequency, setup, and vol-ume of the sample. Table 4.1 gives an overview of some characteristics and principal advantages of each of the three measurement methods. They are fur-ther described in the next sections.

Table 4.1: Overview of some characteristics of the methods for measurement of the dielectric properties used in this thesis.

Measurement system Waveguide Free-space Coaxial-line

Frequency (GHz) 0.56 5 - 15 0.5 - 15

Sample volume (m3₎ ₁ _0.01 _0.001

Particle size (mm) <150 <9 <1.2

Principal advantages measurement of large

vol-ume; reﬂection concept that can be applied on-line

accurate measurement of

low-loss materials broadbandmeasurements

Used in papers _{V and VI} _{I, III, and IV} _{I and II}

4.1 Waveguide method

The method was developed by Nyström [14] for measuring the moisture con-tent of biofuels. It was developed as a laboratory-scale system, using an ap-proach meant to be further developed to measure an entire depth of biofuel di-rectly in lorries where only one side of the biofuel is accessible, requiring the use of a reﬂection method. Nyström achieved good results with the waveguide reﬂection system using multivariate data analysis to correlate time-domain data with moisture content [14].

Figure 4.1 shows a diagram of the method. The system consists of two steel drums; the upper drum shields the antenna and the other drum contains the 35

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sample. The two drums are connected during the measurements, and act as a cylindrical waveguide. The lower drum is the sample holder and the antenna hangs in the upper drum. The antenna is connected to a vector network an-alyzer (VNA). The measured complex reflection coefficient is corrected for systematic errors due to directivity, source matching, and reflection tracking in the coaxial cables and in the waveguide. This calibration uses three stan-dard measurements: short, offset short, and load. Afterwards, a Kaiser win-dow is applied to the frequency-domain data, resulting in a dominant centre frequency of 555 MHz. The windowed frequency-domain data is transformed into the time domain with the inverse Fourier transform and, from the time-domain data, the surface and bottom reflection peaks are identified.

Figure 4.1: The waveguide measurement system. The upper drum shields the antenna, which is connected to a VNA, and the other drum contains the sample. Figure from Nyström and Franzon [47].

This measurement system was used in studies presented in Paper V and Paper VI for measurements of sawdust, tops and needles, and residual wood-chips. In Paper VI, the apparent dielectric constant was calculated using the velocity of the electromagnetic waves, obtained from the travel times between surface and bottom reﬂection peaks, and the depth of the material. In Paper V, a more complete method was applied for the extraction of the complex di-electric permittivity from measurements with this system. The method used the velocity of the electromagnetic waves and the attenuation of the waves at the bottom of the sample holder.

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4.2 Free-space method

This measurement system was developed by Trabelsi et al. [25] and has been shown to provide very accurate determination of the bulk dielectric properties of low-loss materials. It consists of a free-space transmission measurement method, as shown in Figure 4.2. Two linearly polarized horn-lens antennas are connected to a VNA. The system is calibrated in the frequency range from 2 to 18 GHz, but the frequency range for the measurements depends on whether the attenuation obtained is within the dynamic range of the system [25]. The sample holder was a box with a rectangular cross section, made of Styrofoam, a material with a dielectric constant close to that of air. The dielectric prop-erties, ε′ and ε′′, are determined from measurements of the attenuation and

phase shift of waves traversing a layer of material, according to a procedure described in Paper IV.

This method was used in studies presented in Paper III, Paper I and Paper IV for the measurement of sawdust and peanut-hull pellets.

Figure 4.2: Diagram of the free-space system. The transmitter and receiver horn an-tennas on each side of the sample holder are connected to a VNA. Figure from Trabelsi and Nelson [18]

4.3 Coaxial-line method

This is a commercial system for measuring the dielectric properties of liquids, solids with a ﬂat surface, and ﬁne granular materials. It consists of an Agilent Technologies 85070E open-ended coaxial-line probe and a Hewlett-Packard 8510C network analyzer with associated software. The probe used for the measurements was the high-temperature probe with 3 mm-diameter coaxial line and a 19 mm-diameter ground-plane. Measurement calibration was done 37

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with the inbuilt calibration correction using a short, open air, and distilled water at 25°C as standards. An Agilent Technologies Ecal module was also used with the probe providing automatic correction for possible displacements of the coaxial cable connecting the probe to the network analyzer. A stainless-steel cup with an inside diameter of 19 mm and a depth of 19 mm, designed for use with the high-temperature probe [48], was used as the sample holder. Figure 4.3 shows the coaxial-line probe and the sample holder.

Figure 4.3: The sample holder and the high-temperature dielectric probe.

The coaxial-line probe is a very advantageous instrument in dielectric char-acterization because it allows measurements within a wide frequency range, but its utilization in granular materials is challenging due to the difﬁculty of controlling the density of the measured samples. The repeatability of the mea-surements of granular materials with the dielectric probe is dependent on the contact between the probe and the sample, and the density of the sample in the region around the open end of the coaxial line. The effective density of the measured samples is likely to differ from the average density of the total sam-ple [48]. A method for determining the effective density of sawdust samsam-ples measured with this probe was presented in Paper I.

This measurement system was used in studies presented in Paper I and Pa-per II for the measurement of sawdust.

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5. Determination of moisture content

In order to determine the moisture content from the dielectric properties, a model is necessary describing the relationships between those parameters. Models relating the dielectric properties to the physical properties can have a theoretical, semi-theoretical, or empirical basis. The advantage of theoret-ical models is their contribution to improved understanding of the dielectric behavior of the materials and of water binding modes [49]. Empirical param-eters are often included in theoretical models in order to improve their ability to ﬁt empirical data. Empirical models are useful in practical applications as they are often simpler than theoretical models and can provide good prediction results.

In this thesis semi-theoretical approaches using dielectric mixing models and an empirical approach based on a density-independent function were used. A general presentation of these approaches is given in the next sections.

5.1 Dielectric mixing models

Dielectric mixing models relate the permittivity of a mixture to the permittiv-ity of all the individual components of the mixture, their fractional volumes, and the polarization effects, which are dependent on the shape of the compo-nents.

Dielectric mixing models can have a pure theoretical basis, or can incor-porate empirical parameters. The parameter describing the shape of the con-stituents is often obtained empirically in order to improve the performance of mixing models in practical applications, but also because it is very difﬁcult to deﬁne the shape of the constituents on a theoretic basis.

Mixing models have been used to describe the dielectric behavior of differ-ent materials such as soil [50], granular materials [51], as well as snow and ice [52]. Practical applications privilege the use of simple mixing equations such as the power law model, shown in equation (5.1):

εβ =

n

∑

i=1

(ε_iβ· θi) (5.1)

where εiand θiare the permittivity and the volumetric content, respectively,

of the constituent i, and β is the geometric factor.

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The power law model does not account for interactions between the dif-ferent constituents in the mixture. This interaction is accounted for in other mixing models, with expressions derived from the Maxwell equations (2.1)-(2.3) and based on different mixing assumptions. An example is the Maxwell-Garnett model (MG). This model is most adequate for sparse mixtures with in-clusions of a determined geometry distributed in a host phase [52]. The model is shown in equation (5.2): ε = εe+εe n

∑

i=1 γ 1 − γ (5.2) where γ =θi 3 _k=x,y,z

∑

εi− εe εe+D_i,k(εi− εe) (5.3) εe is the permittivity of the host phase, which in this case is air. Di,k is the

depolarization factor of the inclusion i in the direction k, being the geometry of the inclusions deﬁned by the semi-axes in the orthogonal directions x, y, and z. The depolarization factor can be calculated according to equations presented in [52].

The determination of the moisture content from dielectric mixing models may not be applicable in many practical cases because values have to be as-signed to several parameters such as permittivity of the dry solids and bulk density.

The Maxwell-Garnett model was used to predict the volumetric moisture content of solid biofuels in Paper V and Paper VI.

5.2 Density-independent functions

Studies have also been developed in order to determine the gravimetric mois-ture content, MC, from the dielectric properties. An approach that has been used by some authors consists of developing a function of the dielectric prop-erties that, for a determined temperature, is only dependent on the moisture content.

Trabelsi and Nelson [53] developed such a density-independent function which has been tested with good results in several types of grains and seeds [18]. The function is based on the Argand-diagram of the complex permittivity divided by the density of the materials. From this diagram, obtained from data at a given frequency and temperature, a linear regression equation is obtained, according to equation (5.4): ε′′ ρ =af[ε ′ ρ −k] (5.4) 40

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where af is the slope and k is the x-axis intercept of the regression line.

Equation (5.4) can also be used for the determination of density. af is a

cal-ibration parameter used in the density-independent function, ψ, according to equation (5.5):

ψ =

ε′′

ε′₍a_fε′_{− ε}′′₎ (5.5)

The relation between ψ and MC is linear, and from the linear regression equation, the slope a and the x-intercept b are obtained, and MC is determined according to equation (5.6):

MC = ψ − b_a (5.6)

5.3 Statistics for the performance of the models

The analysis of the methods for moisture content determination was made using the root mean square error, according to (5.7):

RMSE =

(ymeas− ycalc)2

n − 1 (5.7)

where ymeas is the empirical moisture content, ycalcis the moisture content

calculated with the model, and n is the number of samples.

In experiments with large data sets, the data was divided into a calibration and a validation set. The calibration set was used to develop the calibration model and the validation set to measure the prediction performance by using the root mean square error of prediction (RMSEP). When the data set did not allow a validation with an independent set, the performance was analyzed using the root mean square error of calibration (RMSEC), also referred to as SEC in Paper III.

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6. Results and discussion

6.1 Dielectric behavior

Frequency dependence

Figure 6.1 shows the variation of ε′and ε′′with frequency for sawdust at ﬁve

moisture levels. These results were obtained with the coaxial-line probe and were published in Paper I. Figure 6.1 (a) shows that ε′ decreases with

fre-quency for all moisture levels, but samples with MC larger than 27% have an inﬂection point at about 9 GHz after which the decrease of ε′with frequency

is steeper. Figure 6.1 (b) shows a peak in ε′′for the high moisture samples at

the same frequency. The inﬂection point in ε′and the peak in ε′′evidence the

relaxation of the free water molecules in the sawdust samples. The relaxation of free water at 20°C occurs at 17 GHz, as shown in ﬁgure 2.1, but it is known that a shift of the relaxation to lower frequencies occurs when the water is bound [38]. Even in samples with water above the ﬁber saturation point, the total water-phase has a lower energy level than free water, which explains the lower relaxation frequency. The fact that ε′of sawdust decreases also before

the relaxation at 9 GHz can be attributed to the presence of bound water in the sample with a relaxation frequency occuring under the measured frequency range. 109 1010 1 2 3 4 5 6 Frequency (Hz) (a) Dielectric constant, ε´ 109 1010 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Frequency (Hz) (b) Loss factor, ε´´ MC=45% 21% 13% 27% 13% MC=45% 37% 27% 21% 37%

Figure 6.1: The complex permittivity of sawdust with MC between 13 and 45% and temperature of 20°C in the frequency range 0.5 − 15 GHz.

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Density dependence

The study presented in Paper IV is here used to show the effects of density and temperature on the dielectric properties. The measurements were performed with the free-space method which provides very accurate estimates for low-loss materials. All measurements refer to the dielectric properties of peanut-hull pellets, at a frequency of 5 GHz.

Figure 6.2 shows how ε′ and ε′′ vary with density for peanut-hull pellets

at four moisture levels and a temperature of 20°C . Figure 6.2 (a) shows that the dielectric constant, ε′, increases linearly with density for the entire MC

range. The inﬂuence of density on the loss factor, ε′′, shown in ﬁgure 6.2 (b)

is smaller than for ε′, and is visible only at higher moisture contents. The

increase of the dielectric properties with density was to be expected, because an increase in ρ with constant MC and volume, means an increase of both dry matter and water in the sample, according to equations (3.1) and (3.4).

0.5 0.55 0.6 0.65 0.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 Dielectric constant, ε´ Density, ρ (g ⋅ cm−3) (a) 0.5 0.55 0.6 0.65 0.7 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Loss factor, ε´´ Density, ρ (g ⋅ cm−3) (b) MC= 4% MC= 6% MC= 10% MC= 13%

Figure 6.2: The complex permittivity as a function of density for peanut-hull pellets at 20°C and 5 GHz.

Temperature dependence

In order to analyze the variation of the dielectric properties with temperature, the effect of density was minimized by dividing the dielectric properties by the density [18]. Figure 6.3 shows how the dielectric properties divided by den-sity vary with temperature varying between -20°C and 40°C. Both ε′_/ρ and

ε′′/ρ increase linearly with temperature, which contrasts with the behavior of

free water. As discussed in section 2.3, ε′and ε′′ of free water decrease with

temperature (see Figure 2.1). But part of the water in the sawdust samples is bound to the solid phase. Jones and Or [54] studied the effects of temperature 44

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on the dielectric properties of granular material, concluding that an increase in temperature is accompanied by two concurrent phenomena: the release of some of the bound water, which increases the overall permittivity of the ma-terial, and a decrease in the permittivity of the free water. The authors suggest that one of the phenomena dominates the changes of the overall permittivity of the mixture until a certain point where both phenomena would have equal inﬂuence. In the case of the peanut-hull pellets in ﬁgure 6.3, the increase in permittivity resulting from the release of bound water dominates the variation of the permittivity of the mixture.

Figure 6.3 also shows that the effect of temperature is greater for higher moisture contents. This is to be expected because temperature mainly affects the phenomena of dipole polarization, which occurs in water.

The linear behavior of the dielectric properties within the temperature range shown in figure 6.3 indicates that the water in the sample is unfrozen. This nonfreezing condition can be explained because the water is bound to the dry matter and requires lower temperatures to break those bounds and freeze. In grain the freezing point has been identified at -20°C, where an inflection in the relation bewteen the dielectric properties and temperature occurs [55].

−20 0 20 40 2.5 3 3.5 4 4.5 ε´/ ρ Temperature, (°C) (a) −200 0 20 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ε´´/ ρ Temperature, (°C) (b) MC=4% MC=6% MC=10% MC=13%

Figure 6.3: The complex permittivity divided by density as a function of temperature for peanut-hull pellets at 5 GHz.

Moisture content dependence

According to the theory discussed in sections 2.3 and 2.4, moisture content is expected to strongly inﬂuence the dielectric properties of biofuels. In this section, the variation of the dielectric properties of both peanut-hull pellets 45

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and sawdust is presented. The results are based on the studies published in Paper I and Paper IV, and were obtained with the free-space method.

Figure 6.4 shows how ε′and ε′′vary with the gravimetric moisture content,

MC. The dielectric properties increase with MC for both biofuel types, but

are much higher for the peanut-hull pellets than for sawdust at a given MC. This is due to the higher density of the peanut-hull pellets. For a MC of about 13%, ρ is 0.6 g·cm−3for peanut-hull pellets and 0.2 g·cm−3for sawdust. This

difference means that the sample of peanut-hull pellets has both more dry-matter and more water per volume than the sawdust samples.

0 20 40 60 1 1.5 2 2.5 3 3.5 Dielectric constant, ε´

Gravimetric moisture content, MC (%) (a) 0 20 40 60 0 0.1 0.2 0.3 0.4 0.5 0.6 Loss factor, ε´´

Gravimetric moisture content, MC (%) (b)

sawdust

peanut−hull pellets

Figure 6.4: The dielectric properties as a function of the gravimetric moisture content for sawdust and peanut-hull pellets at 20°C and 5 GHz.

The volumetric water content, θ, can be used to analyze the dielectric prop-erties of both biofuel types for similar water volumes. Samples with similar θ have a similar volumetric fraction of water, and density inﬂuences only the rel-ative fractions of solids and air. Because the dielectric properties of water are higher than those of dry-matter, the dielectric properties of moist substances are expected to be mostly inﬂuenced by the water fraction. Figure 6.5 shows the variation of ε′ and ε′′ with θ for sawdust and peanut-hull pellets.

Fig-ure 6.5 (a) shows that ε′ of peanut-hull pellets is higher than that of sawdust,

but the difference decreases as θ increases. On the other hand, ﬁgure 6.5 (b) shows that ε′′of peanut-hull pellets is smaller than that of sawdust for lower

θ levels, while both tend to converge for θ of about 0.1.

The difference in the dielectric properties of both biofuel types may be due to differences in the dry bulk density of the samples, which represents the fraction of dry-matter, to differences in the water-binding forces of the bio-fuel types, and to differences in the granular structure of the particles in the mixtures, which affects the depolarization of the waves. The dry bulk density, 46

The dielectric properties of solid biofuels