Scholarly article on topic 'Dielectric properties of coals in the low-terahertz frequency region'

Dielectric properties of coals in the low-terahertz frequency region Academic research paper on "Earth and related environmental sciences"

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Coal / Dielectric property / THz / Free space method

Abstract of research paper on Earth and related environmental sciences, author of scientific article — Wei Fan, Chengyan Jia, Wei Hu, Chuanfa Yang, Lingyu Liu, et al.

Abstract The dielectric properties of Shanxi anthracite and Shandong bituminous coals in China are investigated in the low-terahertz (THz), W-band of frequency from 75GHz to 110GHz for the first time. In this frequency range, the complex dielectric constant of coal samples is obtained using the free space method. It is found that both the real parts of the dielectric constant for bituminous and anthracite decrease considerably with increasing frequency from 75GHz to 110GHz. The anthracite coals exhibit higher real and imaginary part values than bituminous coals. The imaginary part of the coal samples exhibits a more significantly decreasing trend in the frequency range from 90GHz to 110GHz compared with frequencies below 90GHz. The dielectric properties of all the coal samples are strongly dependent on the moisture content of the coals. Increasing moisture content leads to higher complex dielectric constant values. The effect of moisture on the dielectric properties of coals depends substantially on the influence of moisture content on the transmission and reflection of THz wave in the coals. The results show that the transmission coefficient of anthracite and bituminous exhibits an exponentially decreasing trend with increasing moisture content (from 0% to 10%). However, the reflection coefficient seems to follow a Gaussian-like changing trend with increasing moisture content, reaching a maximum around 4.5%.

Academic research paper on topic "Dielectric properties of coals in the low-terahertz frequency region"

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Dielectric properties of coals in the low-terahertz frequency region CrossMar

Wei Fana, Chengyan Jia a, Wei Hua, Chuanfa Yangb, Lingyu Liub, Xiansheng Zhangb, Tianying Chang a,b'*, Hong-Liang Cuia,b

a School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun, Jilin 130061, China b Institute of Automation, Shandong Academy of Sciences, Jinan, Shandong 250103, China

ARTICLE INFO

ABSTRACT

Article history:

Received 27 April 2015

Received in revised form 12 September 2015

Accepted 12 September 2015

Available online 25 September 2015

Keywords: Coal

Dielectric property THz

Free space method

The dielectric properties of Shanxi anthracite and Shandong bituminous coals in China are investigated in the low-terahertz (THz), W-band of frequency from 75 GHz to 110 GHz for the first time. In this frequency range, the complex dielectric constant of coal samples is obtained using the free space method. It is found that both the real parts of the dielectric constant for bituminous and anthracite decrease considerably with increasing frequency from 75 GHz to 110 GHz. The anthracite coals exhibit higher real and imaginary part values than bituminous coals. The imaginary part of the coal samples exhibits a more significantly decreasing trend in the frequency range from 90 GHz to 110 GHz compared with frequencies below 90 GHz. The dielectric properties of all the coal samples are strongly dependent on the moisture content of the coals. Increasing moisture content leads to higher complex dielectric constant values. The effect of moisture on the dielectric properties of coals depends substantially on the influence of moisture content on the transmission and reflection of THz wave in the coals. The results show that the transmission coefficient of anthracite and bituminous exhibits an exponentially decreasing trend with increasing moisture content (from 0% to 10%). However, the reflection coefficient seems to follow a Gaussian-like changing trend with increasing moisture content, reaching a maximum around 4.5%. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://

creativecommons.org/licenses/by/4.0/).

1. Introduction

Coal as one of the major fossil fuels plays an important role in the development of commerce and industry, and as such, it impacts man's daily life profoundly. It has been estimated that nearly 42% of the world's electricity is generated by the burning of coal [1]. Coal-related research has received sustained and wide-spread attention in the past, and in recent years it has witnessed a resurgence with the diminishing reserves as well as the ever-increasing demand. However, large-scale extraction of coal remains for the most part a hazardous undertaking. Along with cave-ins and coal dust fire and explosion, methane gas explosion and water in-rush represent the ultimate hazards in today's coalmines [2], which threaten life and property on a daily basis. While a slow accumulation of methane and water can be detected and safety measures taken in time, sudden appearance of methane and water due to inadvertent drilling in coalmine tunnels have claimed thousands of lives and disrupted production worldwide

* Corresponding author at: School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun, Jilin 130061, China. Tel.: +86 18612519976.

E-mail address: tchang@jlu.edu.cn (T. Chang).

in the last few years alone. To prevent such accident from occurring, a look-ahead device that can penetrate rocks, soil, and coal and forewarn the presence of water and methane gas in large quantity is needed. At present, such a device does not exist. While technologies have advanced enormously, and several candidates for such a purpose look promising, such as ground penetrating radar, transient electromagnetic method, electrical conductivity/ resistivity measurement, and ultrasonic wave devices, a reliable working device is still years away [3]. Recently, our laboratory has been engaged in the research and development of a low-terahertz (THz), i.e., W-band electromagnetic wave imaging Radar which measures resonances in the absorption of the THz radiation by water molecules and CH4 molecules in order to detect the presence of pockets of water and/or methane gas up to several meters through rock, soil, and coal, from the radar receiving antenna. The design of such a THz device requires the fundamental grasp of physical properties of coal, especially its complex dielectric permittivity (including real and imaginary parts of it, corresponding to the index of refraction, and loss/attenuation, respectively). It is therefore of great importance to study dielectric characteristics of electromagnetic waves propagating in coal. While such studies have been carried out to some extent in the RF and microwave frequency bands, in conjunction with work on ground penetrating

http://dx.doi.org/10.1016/j.fuel.2015.09.027 0016-2361/© 2015 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

radar and transient electromagnetic methods [4-7], to date no work has been done in the required W-band and beyond. In fact, with the development of microelectronics technology, more sophisticated apparatus and instruments became available for measurement of the dielectric properties of coal in the last decade. Some factors affecting the permittivity of coal such as rank, aniso-tropy, pyrite concentration and distribution, moisture content, temperature and mineral matter concentration were investigated in the past few years [8-19]. However, the electrical complex permittivity measurements of coals in THz band are not yet available. The present study is undertaken to attempt to fill this void.

THz wave is an electromagnetic wave that occupies a middle spectral region between microwaves and infrared light waves (wavelength ranges from 0.03 mm to 3 mm). The research of THz has received a great deal of attention in recent years [20-25]. THz technology has been widely applied in a number of areas such as molecular recognition (many vibration modes of complex and biological molecules lie in the THz range) [21], security screening and non-destructive analysis of materials. As the transmitted frequency of radar reaches millimeter wave and THz band, numerous physical, chemical and biological systems have clear absorption spectral features in the THz region. In addition, water is strongly absorptive of THz radiation. Therefore, utilizing these characteristics to study the dielectric properties of coals in the THz band can help solve some problems for design of penetrating ground radar in different frequency band. In this paper, we investigate the effects of THz radiation in the frequency range from 75 GHz to 110 GHz and the moisture content on the dielectric permittivity of anthracite and bituminous coals commonly found in China by using the free space method.

As one of the non-resonant methods, and unlike the open-ended probe [18,19] and resonant cavity methods, the free space method has been widely used for many years [26-35]. It has many advantages over other resonant methods and open-ended probes methods: (1) it is particularly attractive for nondestructive test in some construction industry for its noncontact modality [26]; (2) it only requires moderate sample preparation since the sample can be sufficiently large to reduce edge diffraction effects and thin sample may induce sagging effect; (3) in order to improve accuracy of measurements, its calibration method is simple compared with other methods; (4) it is very convenient to test the relationship of coal permittivity with temperature since resonant method and open-ended probes are limited in waveguide and require more complex system structure for temperature determination. Last but not least, using the free space method together with the new millimeter/submillimeter wave Agilent measurement technology and the Virginia Diode Inc (VDI) extension modules [36], it is possible to extend the measuring frequency of the coal dielectric properties to the terahertz (THz) band.

2. Methodology

2.1. Dielectric measurement theory using the free space method

The dielectric property of an isotropic material is subsumed in the complex permittivity in the form [33]

where s represents the real part, and s" the imaginary part of the complex dielectric permittivity. The two parts in Eq. (1) are used to describe the dielectric response of materials in an electromagnetic field. The real part is associated with the capacity of the medium to store electromagnetic energy and the imaginary part relates to the dissipation of the stored energy into heat. The loss tangent is

another important parameter that indicates how well a material dissipates stored energy into heat.

tan h = £"/£'

When an electromagnetic wave propagates in a lossy dielectric material, its magnitude decreases because of the absorption of power by the material. The penetration depth PD, can be used to express the rate of decay of the stored energy, which can be expressed as a function of both the real part and the loss tangent by [37]:

2ft/V2ë7[v/l + tan2 e - l]

The quantity PD is used to describe the distance from the material surface where the intensity of the electromagnetic radiation falls to 1/e of its value at the surface.

In general, measured magnitudes of the real and imaginary part in Eq. (1) are relatively low, and the two parts in Eq. (1) are usually re-scaled by dividing them with the permittivity of free space (s0 = 8.85 / 10~12 F/m), the resultant quantities are termed the real and imaginary parts of the relative complex permittivity.

It is assumed that the planar coal sample has a transverse (relative to the direction of propagation of the electromagnetic wave) dimension that is large enough compared with the wavelength of the impinging radiation, such that diffraction effects can be neglected. A plane electromagnetic wave of frequency m travels from the transmitting antenna to the receiving antenna through air and the coal sample of thickness d. The transmission scattering parameter (S21) and reflection scattering parameter (S11) are measured in free space. By applying appropriate boundary conditions at the air-sample interfaces, S21 and S11 can be expressed in terms of r and T as follows [34]:

C(! - T2) l - T2 C2 '

T(! - C2)

1 - T2 C2 '

where C is the reflection coefficient at the air-sample interface, T is given by

T = e-cd,

C = ZSn - l

Zsn+ l '

In Eqs. (6) and (7), Zsn and y are normalized characteristic impedance and propagation constant of the sample. They are related to s by the following equations:

C = Co Ve'

ZSn = A -

where y0 = j2n/X0 is the propagation constant of free space, k0 is the free-space wavelength.

From Eqs. (7)-(9), it follows that

£ = —

Co + C

2.2. Experimental setup

Fig. 1a shows a schematic of the dielectric measurement system setup in the THz band by using the free space method. The THz signal is generated by the extension modulel and transmitted by a

e = e - je"

' Transmit part Coaxial Horn i

Extension Module1(VDI Corp.)

' Receive part Coaxial Horn

Extention Module2(VDI I Corp.)

Vector Network Analyzer (E5247A,Agilent Technology)

Portl V y Port2

Transmit part

Sample Holder Receive part

Guide rail

Fig. 1. Experimental setup of the THz dielectric property measurement system. (a) Block diagram of the THz dielectric measurement system using the free space method. (b) The guide rail and the sample holder for the measurement system. (c) Schematic of TRL calibration for free space.

conical horn antenna, and received by a matching conical horn antenna and the extension module2. A pair of spot-focusing lens with diameter 25.4 mm is used to spot-focus the THz transmitting signal on the coal sample, with a focal length of 25 mm. Available extension modules cover the frequency range from 75 GHz to 500 GHz in a number of frequency bands, with matching conical horn antennas for each frequency band, i.e. 75-110 GHz, 140-220 GHz, 220-330 GHz, and 325-500 GHz. Both the transmitted and received signals are connected with a Vector Network

Analyzer (VNA). The scattering parameters (Sn and S21) can be calculated using software provided with the VNA (Agilent 85071E). Here we utilize the frequency band from 75 to 110 GHz as the measurement frequency for the time being, and will extend into higher-frequency bands in the near future.

The sample holder is mounted on a guide rail to adjust the distance of coal sample from the transmitting conical horn antenna, which is shown in Fig. 1b. The variable position of the coal sample holder is controlled by a step motor in 1 im increment.

The distance between the left horn and the surface of the sample, L, should satisfy the far-field condition, L > 2D2/kc, where D is the diameter of conical horn (16.3 mm) and kc is the central wavelength (3 mm) in the entire swept frequency. The maximum coal sample transverse size should satisfy Ds > 2L tan(1/2Bw) where Bw is the full 3 dB beamwidth (here is 13 deg). According to the parameters provided by the manufacturer, we set L > 18 cm and DS > 40 mm.

Before the actual measurement is undertaken, a calibration based on the "Thru", "Reflect" and "Line" (TRL) standard is performed to reduce measurement error that might be caused by multiple reflections, other noise and diffraction. Fig. 1c shows the schematic of the TRL calibration for free space. The calibration steps are all automated and divided into three. Firstly, set a distance between the two coaxial horns and measure the thru using the VNA. To measure the reflect, the two horn antennas must be moved back by the thickness of the standard metal plate. The separation distance between the antennas is set as 0.75 mm (quarter wavelength at 100 GHz). The line standard is then realized by precisely moving the two horn antennas back again. Finally, the antenna needs to be precisely moved back to the original position. Another application of the reflect standard is to only move a metal plate to the calibration planes for reflection measurements. In addition, a time-domain gating technique is used to eliminate the multiple reflections of antennas and ambient reflections.

2.3. Sample preparation and experimental procedure

A variety of coal samples were selected from Shandong bituminous and Shanxi anthracite coals, and their proximate and ultimate analyses [38] are shown in Table 1 and Table 2, respectively. All the bulk coal samples were obtained from large blocks of coals taken directly from their native mines. Using a cleaver and a saw, along with sandpapers, all the samples were fashioned into cubic shape with 70 mm in length. The assessment of composition of the bulk coals is complicated due to the complexity of natural coal samples and the difficulties of measuring the moisture content, for example. During the experiment each sample was put on a shelf and placed in a baking furnace. The baking furnace has the capability of operating at the maximum of 300 °C. The residual content of moisture in the coal samples was measured periodically by taking out the shelf after being held at the temperature 250 °C for 90 min and weighing on a digital balance (BSM5200, with a precision of 0.001 g).

All measurements are carried out at room temperature, the sweep frequency ranges from 75 to 110 GHz and the maximum power output from the radiating antenna is 2 dBm in continuous wave (cw) mode. During the process of investigating the effect of THz radiation on the complex permittivity of coals, each sample

Table 1

Properties of Shandong bituminous and Shanxi anthracite (as-received basis proximate analysis).

Table 2

Ultimate analyses of samples based on a dry basis (%).

Sample No. Thickness Mt A VM FC

(mm) (%) (%) (%) (%)

Shandong A 7.97 6.91 7.09 18.35 67.65

bituminous B 10.23 3.42 5.72 15.43 75.43

C 11.54 2.47 2.45 18.85 76.23

D 12.51 7.97 9.65 12.17 70.21

E 13.75 9.45 5.74 15.47 69.34

Shanxi anthracite F 16.24 2.53 1.31 4.05 92.11

G 20.60 1.42 2.47 4.68 91.43

H 23.57 2.17 2.84 4.52 90.47

I 28.71 2.41 3.16 1.66 92.77

J 34.62 4.35 2.13 5.96 87.56

Sample No. Carbon Hydrogen Oxygen Nitrogen Sulfur

A 80.23 2.02 5.17 1.53 1.79

B 78.54 2.79 4.04 1.74 2.13

C 81.04 3.02 5.20 1.21 2.34

D 77.51 3.12 3.18 1.22 2.12

E 79.33 2.61 5.57 1.37 1.14

F 82.45 1.23 2.17 1.44 0.78

G 81.21 2.47 2.05 1.48 0.65

H 84.54 2.33 1.83 1.34 0.97

I 83.44 1.45 3.79 1.56 0.88

J 82.71 1.37 1.84 1.62 0.78

is tested for six times and arithmetic average values are recorded. In order to investigate the effect of moisture content on the dielectric properties of coals, accurate determination of the different moisture content of the selected coals is an important prerequisite, which involves the following steps: (1) measure the initial weight M1 of the coal sample using the digital balance; (2) Bake-dry the coal sample completely with a baking furnace under 200 °C for a long time to obtain the dry weight M2. The relative deviation of the two is therefore:

M1 - M2

Repeat steps (1) and (2) until RD falls below 0.1%; (3) Put the coal sample into a humidifier to get the required moisture content. It should be noted that humidifying the coal sample requires several days. In addition, the measurement must be carried out immediately after the completion of step (3) to avoid the environmental effects on the measurement results.

3. Results and discussion

3.1. Measured THz dielectric properties of coals

The magnitude of the measured S11 with time-domain gating is shown in Fig. 2 after the TRL calibration. We considered the magnitude of S11 when there is coal sample and without, respectively. From the measured data, the magnitude of S11 is less than -40 dB, which is in agreement with previously obtained result [34]. The result demonstrated that the TRL calibration has a high accuracy for determining the complex s-parameters of coal.

Mt: moisture content; A: ash; VM: volatile matter content; FC: fixed carbon.

Fig. 2. The magnitude of measured Sn after TRL calibration with and without coal A.

After the TRL calibration and time domain gating measurement of the sample, we assess the accuracy and uncertainty of the freespace s-parameters measurement. In such a measurement, the errors are mainly of two kinds. The first to be considered is associated with the instrument setup. Because of the high quality and sensitivity of the VNA (Agilent 85071E), with ±0.045 dB and ±2° accuracy in amplitude and phase of S11 (or S22), instrument errors such as the THz wave frequency instability, power variation, etc. are negligible. For the S21 (or S12) measurement, the error of the amplitude and phase is ±0.025 dB and ±2°, respectively. The second source of errors to be considered is the connection between the cables and the extension modules. In the calibration, a slight offset movement of the metal plate position led to s-parameters measurement errors. These errors can be avoided by several repeated measurements. In addition, possible mismatch between the source and the load is removed by taking the inverse Fourier transform of the frequency-domain data to time-domain [34], as we have seen in the amplitude of the measured S11 without a coal sample in Fig. 2. It should be pointed out that the multiple reflections inside the coal sample cannot be removed completely, although their impact on the measurement accuracy is tolerable, as we found clearly that such peaks in the swept frequency band have an average amplitude of (e.g. in Sn) less than -35 dB.

The dielectric properties of bituminous and anthracite coals plotted as functions of THz frequencies are shown in Fig. 3. From the measured results, one can observe that both the real and imaginary part of Shandong bituminous coal exhibited a sharp decrease with increasing frequency. In Fig. 3a, the real part of Shandong bituminous coal range from 2.37 to 2.9 depending on frequency. In Fig. 3b, the relevant imaginary part range from 0.17 to 0.38. For Shandong bituminous coals, the imaginary part in general exhibits a different trend from the real part. For example, the imaginary part in the frequency range 90 6 f 6 110 shows a more significant decrease than the frequencies <90 GHz. Meanwhile, the real part of Shanxi anthracite coals vary from 3.45 to 4.15 (Fig. 3c) and the imaginary part from 0.37 to 0.58 (Fig. 3d).

Both the measured real and imaginary part of bituminous coals exhibits lower values than those of the anthracite coals. The decreasing trend of the dielectric constant of Shanxi anthracite coals is more precipitous compared with that of the Shandong bituminous coals. The probable reason is the effect of different volatile matter or ash component content on the dielectric property of coals from anthracite to bituminous coals. The variation for anthracite and bituminous coals are coincidence with previous investigation from [17].

It can be seen from above results that lower rank coals have higher dielectric constant values than higher rank coals in the measured frequency band. The decreasing trend of relative dielectric constant coincides with previous work in the lower frequency band [15].

We note also that the frequency dependence of selected coal samples with different moisture content is different. For instance, in Fig. 3a, at the frequency from 75 to 110 GHz, the real part of sample E is much higher than that of sample C because the moisture content of sample E (9.45%) is higher than of sample C (2.47%). However, the variation for three other bituminous samples is not obvious due to the approximate equality of moisture content. These results show that moisture content has a great impact on the dielectric properties of anthracite and bituminous coals in the frequency range studied. Since the higher moisture content under the condition with the same measurement frequency means the higher energy (mainly heating energy) dissipation of THz wave in the coal, which leads to the increase of dielectric loss of coals as shown in Fig. 3b and d. The detailed measurement of the effect of moisture content on dielectric properties of coals is shown later. Based on the ±0.045 dB and ±2° accuracy figures of amplitude and phase measurements in S11 and ±0.025 dB and ±2° in S21, we estimated that the dielectric constant of coals can be determined with an accuracy of better than 7%.

Since the complex permittivity characterizes the interaction between the electromagnetic wave and the microscopic constituents of the material, and the macroscopic frequency response

Fig. 3. Variations of the dielectric permittivity with frequency for coals: (a) real part, (b) imaginary part of bituminous coal samples, (c) real part and (d) imaginary part of anthracite coal samples.

of the material as represented by its dielectric permittivity depends on the polarizability of the material [39,40]. The relation between the polarizability and dielectric constant is given as:

e = 1 + 4pv (12)

The contributions to the polarizability are from four basic mechanisms of polarization, i.e., space-charge relaxation, dipolar relaxation, ionic resonance, and electronic resonance:

V = Vs + Vd + Vi + Ve (13)

It is clear that there will not be significant contributions from the terms vi and ve because the frequencies involved in the present measurement are far below the resonant frequencies of the ionic and electronic processes. In addition, coal samples treated in the frequency range excite very little space-charge contributions. With increasing frequency especially when 90 6 f 6 110 GHz (Fig. 3b), the dipolar polarizations involving the bound charges in the coal sample will be enhanced with increasing external electric field. Under such conditions, the strengthened dipolar term vd, representing the dissipation of energy with the relaxation of it, is

considered as the dominant term in determining the decreasing trend of complex permittivity of coal with variation of frequency as shown in Fig. 3, rather than vs.

We next consider the variation of dielectric properties of coal samples with frequency measured using the free space method, with the resulting amplitudes of reflection (|R|) and transmission coefficient (|T|) for the bituminous and anthracite coals shown in Figs. 4 and 5, respectively. According to the discussion from the previous section, assuming the attenuation of an electromagnetic wave from transmitting antenna into the coal samples is large enough that the multi-reflection between the two surfaces of the coals can be neglected. For non-magnetic materials, i ? 1. Under such conditions we can obtain the following simplified expression from Eqs. (4)-(10):

s - (ln(1 7f-'"(T))' (14)

The formulas show that there is a simple relationship between dielectric properties of coals and frequency f, |R|, |T| and the thickness of the sample.

Frequencv(GHz)

Fig. 4. Amplitude of (a) reflection coefficient (R) and (b) transmission coefficient (T) for the bituminous coals.

icy(GHz)

Fig. 5. Amplitude of (a) reflection coefficient (R) and (b) transmission coefficient (T) for the anthracite coals.

|R| of both bituminous and anthracite coals exhibits a dramatically decreasing trend with increasing frequency, while |T| shows a first slightly decreasing and then increasing trend as a function of increasing frequency. The bituminous coals have lower |R| (0.21 6 | R 6 0.26) than anthracite coals (0.31 6 |R| 6 0.34), while |T| is about ten times that of the anthracite coals. With regards to |T|, as expected, the value depends on the thickness of the coal for the same coal type. The lower |T| shows that only little electromagnetic wave propagate through the whole sample.

The variation of |R| for both anthracite and bituminous coals is predicated mainly on the variation of the real part of the complex permittivity. On the other hand, the variation of |T| can be explained as follows: when frequency increases, the dissipation

of the electromagnetic energy in coals increases as expected, leading to the decrease of |T|. In this process, we note that the variation of |R| is monotonic (decreasing gradually with frequency). And with the continuously increasing frequency, the absorbed electromagnetic energy in the samples increases. Therefore, the decrease of reflection coefficient and the increase of absorbed energy in coal lead to the slight increase of the |T| when f > 90GHz (Figs. 4b and 5b). Here we invoke the relation that the sum of the reflected, transmitted, and absorbed power equal to unity when scaled with the input power.

Using Eq. (3), the penetration depth of coals with frequency variation is calculated and shown in Fig. 6. The penetration depth of anthracite ranges from about 1.8 mm to 2.35 mm and of

- (a) {..... • F —G A H ▼ 1 ♦ J _ t i

(b) — A-.-B a C ▼ D ■X ♦ E a : : 1 t II : A ^ ^ i T T ♦ ♦.....H lit,.........................................ml' ♦ ♦........ ♦♦ ♦!!!! MM IMJ; ...............................................: .. ♦ ♦ ♦♦♦ ♦ ........;................................. <1<1<1<1<1<1<

105 110

Frequency(GHz)

Fig. 6. The penetration depth of (a) anthracite and (b) bituminous coals as functions of frequency from 75 to 110 GHz.

Fig. 7. Dielectric permittivity of selected bituminous (a and b) and anthracite (c and d) coal samples vs. moisture content, at 110 GHz.

bituminous from 2.4 mm to 4 mm, respectively. From the measured results, we can see that there is strong absorption of THz wave power in the coals, which can also be seen from

Pa = 2pf e"|E2

where E is electric field of THz wave in the coal. The decrease of both s" and E together with the increase of frequency leads to the variation of penetration depth shown in Fig. 6.

3.2. Effects of moisture content on the complex permittivity of coal in the THz band

The dielectric properties of selected bituminous and anthracite coal samples vs. moisture content are shown in Fig. 7. It is obvious that the real part increases significantly with increasing moisture content for both the bituminous and anthracite coals. The imaginary part of selected coal samples has a similar tendency with moisture content variation (Fig. 7b and d). Fig. 7a shows that the real part values of selected bituminous sampling coals increase from 2.33 to 2.78 with moisture content increasing from 0% to 10%. Similar results are also obtained with anthracite coals of which the real part varies from 3.39 to 3.88 with the same moisture content variation (shown in Fig. 7c). A comparison of Fig. 7a and c reveals that anthracite coals have relatively higher real part values than bituminous coals with moisture content variation in the 110 GHz band. However, the real part values of selected coal samples within the same coal type exhibits certain degree of overlap and cross-over. For instance, coal F has a higher real part value than coal I with moisture content below 2.5%, and a lower value for moisture content beyond 2.5%. These observations show that the moisture of the coal samples plays an important role in the dielectric properties of anthracite and bituminous coals in the low THz band. The ultimate explanation is attributed to the strong effect of water on THz wave propagation. The moisture-frequency dependence of the complex dielectric permittivity derives mainly from the frequency characteristics of molecular interaction of water with the THz radiation, and the latter is well documented [41].

The transmission and reflection coefficients of selected coals vs. moisture content are shown in Figs. 8 and 9, respectively. It is seen that, in Fig. 8, when the moisture content of coals increases, the transmission coefficient decreased significantly (as expected, since water, being strongly absorptive, plays a decisive role in THz transmission). Both the transmission coefficients of selected bituminous and anthracite coals exhibit an exponentially decreasing trend with moisture content variation. From Fig. 8a and b, transmission coefficient of selected bituminous and anthracite coals decreases roughly from 40% to 80% and from 21% to 76% with moisture content increasing from 0% to 10%, respectively. The measured data of transmission coefficient of the coal samples were fitted by using a mathematical curve fitting model given as:

T (x) =

where x is the moisture content. It is reasonal to assume that there is an exponential relationship between the transmission coefficient and moisture content of the coal samples, which is determined by the fitting parameters A, t and y0 jointly. The detailed fitness and statistic parameters for each coal sample are shown in Table 3. The parameter Adjusted Residual Square (Adj. R-square) is a measure of how close the fitting curve is from the actual data points and the closer it is to one the better the fitting result. The Adj. R-square value showed that the proposed model relation describes very well the measured data. It is observed from Table 3 that, although the same fitness functional form seems to work for all

the tested coals, the parameters A, t and y0 of each coal type showed obvious differences. For instance, the same parameters A1 = A2 = A3 and t1 = t2 = t3 for coal C and F are ascertained, while y0 is different. The observation showed that moisture content has a great impact on the transmission coefficient for THz propagation in coal. The significant differences among those fitness parameters showed that the transmission coefficient can reflect the internal structural and compositional complexities of coal.

However, the variation of reflection coefficient against moisture content seems more complicated than that of the transmission coefficient. In Fig. 9, for selected bituminous and anthracite coal samples, the reflection coefficient exhibits a first increasing and then decreasing trend with increasing moisture content. It is such that a Gaussian fit can be used to describe the variation trend in the moisture content range from 0% to 10%. The maximum reflection coefficient of bituminous and anthracite coals reach about 46% when the moisture content is about 5% while the minimum value is about 27%, which obtains for completely dried coal samples, as well as for those samples having nearly 10% moisture content. Such a Gaussian-like trend might be analytically modeled by the following expression for the reflection coefficient as a function of the moisture content x from 0% to 10%

R(x) = Ke-(x-xc)2/2w2 + C0

The detailed fitness parameters are given in Table 4. There is no substantial difference for those parameters between the bituminous coals and the anthracite coals. In other words, the reflection

Fig. 8. Transmission coefficient of (a) bituminous and (b) anthracite coal samples as a function of moisture content, at 110 GHz.

coefficients depend primarily on the surface characteristics of the coal samples, and only secondarily on the internal structure and composition of the coals.

Using Eq. (3), the penetration depth of coals with increasing moisture content is calculated at 110 GHz, and the results are shown in Fig. 10. As expected, when the moisture content increases, the penetration depth decreased dramatically.

The behavior of the reflection coefficient as a function of sample moisture content bespeaks the influence of two competing factors. As we have seen so far that the real part and imaginary part of the dielectric constant both increase as moisture content increases. The former is related to the index of refraction and the latter to absorption, as demonstrated by Tanno et al. [42] who estimated water content in coal and obtained THz transmittance spectra of raw and dried coal. The index of refraction enters consideration through the Fresnel reflection at the air-sample interface, which should account for the initial increase of the reflection. However, as moisture content increases further, absorption by the sample becomes dominant, which exponentially increases as moisture content increases. This indirectly suppresses reflection as well as transmission, which should be the dominant factor for moisture content beyond about 5%, irrespective of the types of coal samples, as seen in Fig. 8.

The fundamental reason for the differences between the variation of transmission and reflection coefficient with water content is attributed to the state of the water in the coal. It is well known that several forms of water exist in coals, which are classified into five types [43]: surface adsorption water, adhesion water, interior adsorbed water, capillary water, and interparticle water. With the increase of moisture content, there exist a great number of free water molecules at the surface of the coal sample. The free water can readily respond to the external THz wave, so we can see the drastic decrease of the transmission coefficient with increasing moisture content in Fig. 8. In addition, the bituminous coals have relatively higher transmission coefficient than the anthracite coals with the same moisture content, since there exists much porosity [44] in bituminous coals than in anthracite coals. Such pore

Parameters Уо A1 t1 A2 t2 A3 t3 Statistics

Chi-square Adj. R-square

A 23.7785 3.4996 0.0195 23.9855 12.9119 25.7376 5.2861 0.6338 0.9946

B 29.0896 15.5712 6.9196 15.5713 6.9197 15.5713 6.9196 0.8589 0.9926

C 0.5156 24.9953 15.7956 24.9953 15.7956 24.9953 15.7956 0.3697 0.9967

D -2856.04 101.583 25.838 1414.67 214.147 1414.69 2.0358 0.3352 0.9965

E -167.112 114.937 97.7412 7.9541 1.4907 124.058 98.69 0.2189 0.9971

F 1.5157 24.995 15.7956 23.1384 15.7956 24.9953 15.7956 0.3697 0.9967

G 14.2568 18.3011 4.9516 18.3011 4.9516 18.3011 4.9516 1.0704 0.9947

H 19.4588 14.0543 9.6609 14.0543 9.6609 14.0543 9.6609 0.6091 0.991

I -212.2187 140.7465 87.1544 140.7465 88.5456 2.6349 1.5515 0.7951 0.9915

J -2856.04 101.5835 25.8387 1414.67 2.9725 1414.69 2.0358 0.3352 0.9965

Table 4

Fitness parameters for reflection coefficient fitting of coal samples.

Parameters C0 xc w K Statistics

Chi-square Adj. R-square

A 25.9763 4.9013 2.6816 15.8088 0.2367 0.9875

B 27.7227 4.282 2.4013 15.3441 0.2543 0.987

C 28.5429 4.4336 2.4843 15.1346 0.3989 0.9805

D 29.7746 4.8827 2.5217 14.1805 0.3546 0.9793

E 24.8064 5.0135 2.4867 15.7504 0.6674 0.9694

F 27.7227 4.282 2.4012 14.3441 0.2543 0.987

G 24.1961 4.1353 2.7571 18.2742 0.9376 0.9651

H 30.1871 4.5493 2.6773 14.6427 0.496 0.9706

I 29.7746 4.8827 2.5217 14.1805 0.3547 0.9793

J 26.6329 3.7783 2.6033 15.1825 0.5159 0.9764

Fig. 9. Reflection coefficient of (a) bituminous and (b) anthracite coal samples as a function of moisture content, at 110 GHz.

Table 3

Fitness parameters for transmission coefficient fitting of the tested coal samples.

1-6 . I . ¡ . I , I . i . ¡ . I , I . i

0123456789 10 Moisture Content(%)

Fig. 10. The penetration depth of (a) anthracite and (b) bituminous coals as a function of moisture content, at 110 GHz.

structures can be considered as air cavity whose permittivity is almost one. This means THz wave can penetrate the bituminous coals more easily than the anthracite coals. Therefore, the transmission coefficient of the bituminous coals is much greater than the anthracite coals (Figs. 4b and 5b). For the reflection coefficient variation of coals shown in Fig. 9, the bound water in the coal plays a major role in the increasing part of R with moisture content below 4.5%. This is because the bound water cannot respond to the THz radiation. Next we consider the free water, with continuous increase of moisture content, the associated increase of free water leads to the decrease of reflection coefficient due to the increase of THz wave attenuation in the samples. On the other hand, we have concluded that the real and imaginary part of the complex dielectric permittivity of both anthracite and bituminous coals increase with the increase of free water, as shown in Fig. 7.

4. Conclusions

THz dielectric properties of Shandong bituminous and Shanxi anthracite coals, from two of the major coal producing regions of China, were studied for the first time, employing a free space THz measurement system. Effects of moisture content on the dielectric properties of selected coals in the THz frequency range from 75 GHz to 110 GHz have been investigated experimentally.

The experimental results show that the complex dielectric constant of selected anthracite and bituminous coals decreases considerably with increasing frequency from 75 GHz to 110 GHz. In this frequency range, the anthracite coals exhibit higher values of real and imaginary part than the bituminous coals. The imaginary part of the coal samples exhibits a more significantly decreasing trend in the frequency range from 90 GHz to 110 GHz than that in the frequency region below 90 GHz. In addition, the decreasing trend of the real and imaginary part of the samples is coal-type dependent. It is also observed, for the same coal type at the same frequency, the higher the moisture content, the higher the real and imaginary part values.

The variation trend of dielectric properties of selected coal samples with moisture content is also investigated. The real part and imaginary part of bituminite and anthracite coals increase sharply with increasing moisture content from 0% to 10% at the frequency 110 GHz, as expected. The effect of moisture on the dielectric properties of coals in turn affects substantially the transmission and reflection of THz wave propagation in the coal samples. The results

show that the transmission coefficient of anthracite and bituminous seems to exhibit an exponentially decreasing trend with increasing moisture content from 0% to 10%. On the other hand, the reflection coefficient of coals exhibits a Gaussian-like trend with increasing moisture content, reaching a peak value around 5% moisture content, irrespective of the coal types. Such a behavior can be understood in terms of the different roles played by the bound and free water in interaction with the THz radiation, and the interplay between the Fresnel reflection of the THz wave at the air-coal interface, and the propagation loss through the coal samples.

Acknowledgements

This work has been financially supported by the Ministry of Science and Technology of China (Project No. 2012BAK04B03), and the Strategic Priority Research Program of the Shandong Academy of Sciences.

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