Temperature Effect on the Thermal Conductivity of Black Coal

Apr 4, 2018 - ... (λ) of the wet and dry coal samples increases with temperature passes through a ... from 0.341 to 0.497 W·m–1·K–1 for wet coa...
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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Temperature Effect on the Thermal Conductivity of Black Coal Ada E. Ramazanova,† Ilmutdin M. Abdulagatov,*,§ and Pathegama G. Ranjith‡ †

Thermophysical Properties Division, Geothermal Research Institute of the Russian Academy of Sciences, Makhachkala, Dagestan 119991, Russia Federation § Physical Chemistry Department, Dagestan State University, Makhachkala, Dagestan 3670000, Russia Federation ‡ Deep Earth Energy Lab, Department of Civil Engineering, Monash University, Melbourne, VIC 3800, Australia ABSTRACT: The guarded parallel-plate technique was employed on a black coal sample for an accurate measurement of the thermal conductivity over the temperature range from 298 to 496 K. The combined expanded uncertainties of the temperature (T) and thermal-conductivity (λ) measurements at the 95% confidence level with a coverage factor of k = 2 are estimated to be 20 mK and 5%, respectively. It was experimentally observed that the measured thermal conductivity (λ) of the wet and dry coal samples increases with temperature passes through a maximum around 390 K, and then it decreases gradually at higher temperatures. We attribute this maximum to the evolution of the volatile matter (VM) (devolatilazation) and aromatization of the carbon (pyrolysis), which is known to occur under heat treatment, and therefore, tends to increase the thermal conductivity. Over the experimental temperature range, the measured thermal-conductivity varied from 0.341 to 0.497 W·m−1·K−1 for wet coal samples before thermal treatment and from 0.272 to 0.316 W·m−1·K−1 for dry samples after thermal treatment. A considerable difference in thermal conductivity behavior was observed for the primary (originally nonthermally treated) and the second (thermally treated) repeated run. No temperature maximum or minimum (regular behavior) was observed in the thermal conductivity behavior for the thermally treated coal sample. The observed temperature behavior of the black coal’s thermal conductivity (λ) is a result of the complexity of the temperature behaviors of a, CP, and ρ, i.e., is the superposition of various temperature behaviors of a, CP, and ρ, and it reflects the temperature behavior of the heat capacity. This means that the temperature behavior of CP dominates the thermal diffusivity in λ = ρaCP. This means that the temperature behavior of λ and CP is strongly correlated.

1. INTRODUCTION Accurate knowledge of the effect of temperature on the thermal conductivity and heat capacity of coal is necessary to develop mathematical models of thermal processing of coal, such as drying, briquette making, low-temperature carbonization, fuel conversion, coking, etc. The effect of coal pyrolysis and the devolatilization process on its thermophysical characteristics is important for understanding coal technology in its different stages: from the mining of coal to its end-uses in industrial furnaces, high-intensity combustors, or utility boilers. Coal is a complex substance, which undergoes structural changes during heating at high temperatures due to various types of reactions (pyrolysis, for example).1−5 The reliability and predictive capability of the mathematical models of coal pyrolysis processes strongly depend on the accuracy of the coal properties used for this purpose, which vary strongly with temperature. Coal decomposition involves many coupled physical and chemical phenomena, and it is difficult to isolate one phenomenon in order to study it separately. The design of solid fuel combustion to enhance the efficiency of coal combustion and conversion processes to protect the environment, using new technology of coal gasification and liquefaction and coal-related processes, required knowledge of the thermophysical characteristics of solid fuels as a function of temperature.6−12 On the basis of thermophysical property data, © XXXX American Chemical Society

the study of the expansion of the burned-out areas, thermal conduction, and temperature field distribution of the surrounding rocks in the process of underground coal gasification is possible.13 The heat transfer process from coal fires is a complex phenomenon.14 The fire systems involve transient mass and heat transfer, reaction kinetics, and fluid dynamics.15 The study of the thermal conductivity (λ), thermal diffusivity (a), and specific heat capacity (CP) of coal during spontaneous combustion is very important for understanding and controlling the development of coal fires. Four key thermodynamic properties (ρ, CP, λ, and a) are required for mathematical modeling (solving a set of differential equations) of underground coal fires (heat and mass flow through coal).15−18 In addition, the thermophysical properties of coal, such as ρ, CP, λ, and a, also play a fundamental role in the mass and heat transfer in the Earth’s interior, i.e., to understand the thermal state and evaluation of the Earth’s interior, for the determination of the temperature gradients in the interior of the Earth (underground temperature distribution in a coal seam).19−22 Since thermal gradients are inversely proportional to thermal conductivity, Received: December 12, 2017 Accepted: March 30, 2018

A

DOI: 10.1021/acs.jced.7b01079 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Turian et al.27 reported thermophysical property (thermal conductivity, heat capacity, and density) data for various types of coals (Illinois Ziegler mine no. 5 coal and Pittsburgh seam no.8 coal) at room temperature. The derived values of the λ thermal diffusivity data a = ρC , from the measured values of λ,

conductivities lowered by a factor of 10 imply thermal gradients that are 10 times higher than those in more common rock types. The limited data available show that the thermal conductivity of coal is as much as an order of magnitude lower than that of most other rocks (see below). The thermal diffusivity and thermal conductivity data of coal available in the research literature are usually based upon a limited number of samples or sample locations (see below, Section 2). Since the number of different types of coal is very large, detailed measurements on all of them are impractical. Therefore, the ability to predict the properties of various types of coal from theoretical models (generalized relationships between λ and composition), based on a few key characteristics (proximate analysis, VM, ash, C, H, N, O, and S contents) at any given temperature, is essential for the technological development of energy resources. The purpose of this work is to study the effect of temperature on the thermal conductivity of black coal and various other factors (VM, moisture, porylys, and decomposition, for example) affecting these properties. Temperature is one of the most important factors affecting the thermal properties of materials. Temperature exerts a considerable influence on the transmission of heat through materials. For example, the temperature dependence of the thermal conductivity of coal gives us a clue to the mechanism of heat transfer within coal. Therefore, the main objectives of this study are to provide accurate experimental thermal conductivity data for a black coal sample at temperatures from 298 to 466 K using a guarded parallel-plate technique. This work is part of our studies on the thermodynamic and transport properties of rock and coal materials under high temperatures and high pressures.23,24

P

ρ, and CP, for the coal samples were between 0.174 and 0.142 mm2·s−1, respectively. The measurements of the suspension in water coal particles with different size were made using two horizontal parallel cooper plates. The upper plate was heated at a constant heat flux, and the lower plate was maintained at a constant low temperature. The temperature difference between the plates was below 5 K. The solid coal thermal conductivities were estimated using the measured relation between the λ and coal particle size φ by extrapolating into φ→1 or using the dilute limit slope of λ versus the φ curve. The thermal conductivity of USA coals was studied by Herrin and Deming.28 The samples represented 55 locations from throughout the USA and included 6 light, 10 subbituminous coals, 36 bituminous coals, and 3 anthracite samples. The measurements were performed using a dividedbar apparatus. They found that the thermal conductivity of coals is controlled by their composition and can be predicted by a three-component geometrical mean model. The measurements were made at 295 K. The authors reported the results of the thermal conductivity measurements and explored how the thermal conductivity of USA coals is correlated with rank, composition, and density. 2.2. Indirect Method of Thermal-Conductivity Measurements of Coal (Contact-Free Laser-Flash Method). Usually, in an indirect method of thermal conductivity determination, measured thermal diffusivity data, together with the heat capacity and density data, are converted to thermal conductivity using a well-known theoretical relation, λ = aρCP. Most authors are employing contact-free laser-flash methods to simultaneously measureme the thermal diffusivity and heat capacity of the same specimen, and then these data are converted to thermal conductivity. The details of the laser-flash method (accuracy, physical bases, advantages and disadvantages) and its application for the measurement of the thermal diffusivity and heat capacity were reported by many authors, see, for example, Bozlar et al. 29 and our previous publications.23,30 Wen et al.31 used a contact-free laser-flash method (LFA 457 apparatus) to measure thermal diffusivity of bituminous coal from the Wuda coalfield over a temperature range of 298−573 K. The measured values of thermal diffusivity, together with the density and heat capacity data, were used to calculate the thermal conductivity of coal samples. The same technique was used by Deng et al.32 to measure thermal-diffusivity of coals from different provinces of China during pyrolysis, oxidation, and reoxidation over a temperature range of 303−573 K. The measured values of thermal diffusivity were used to calculate the thermal conductivity of the same coal samples. Thermogravimetric (TG) experiments were conducted to analyze the variation of the coal mass. The authors found that as temperature increased, the thermal diffusivity decreased first and then increased (passing through minimum); the specific heat capacity increased first and then performed steadily; the thermal conductivity was presented a slow increment first and then rapidly grew. The authors provide a detailed discussion of the temperature dependence of the three key thermophysical parameters of various types of coals and the correlations between them. Gu33 employed the laser-pulse

2. REVIEW OF PREVIOUS THERMAL CONDUCTIVITY MEASUREMENTS FOR DIFFERENT TYPES OF COAL All previous thermal conductivity studies of coal can be divided into two groups: (1) Direct measurements of the thermal conductivity using contact methods, and (2) indirect determination of the thermal conductivity based on other measured properties (thermal diffusivity, heat capacity, and density) using contact-free methods. 2.1. Direct Thermal-Conductivity Measurements of Coal. Dindi et al.25 measured the thermal conductivity and thermal diffusivity of wet and dry solid coal (Illinois Basin bituminous coal) samples as a function of temperature using the transient-hot-wire and transient-hot-plate methods (steadystate). The data for the thermal conductivity and thermal diffusivity were fitted to polynomial functions for convenient use. The same technique was employed by Badziochet al.26 to measure of the thermal diffusivity and thermal conductivity data of 12 kinds of coal. They found that the thermal conductivity of coal samples slightly changes with temperature in the range of 373−573 K (an average value is about 0.23 W·m−1·K−1). Above this temperature range, thermal conductivity and diffusivity increase rapidly. Tang et al.13 reported the heat capacity and thermal conductivity data as a function of temperature from 373 to 1273 K for six types of rock samples from the coal measure strata, and the measured data were compared with theoretical predictions. The authors used the hot-wire method (transient-state) to measure of the thermal conductivity of coal. The uncertainty of the thermal conductivity measurement was 3%. They found that the thermal conductivity and heat capacity are decreasing with the temperature increasing just below 723 K. B

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method to simultaneously measure the thermal diffusivity and heat capacity of several types of Chinese coals over a temperature range from room temperature to 700 K. These data, together with the density of the coal sample under study, were used to calculate the thermal conductivity. Il’chenko and Revenko34 studied the thermophysical properties (enthalpy, heat capacity, and thermal conductivity) of different types of Ukrainian coals from various locations over the temperature range of 373−1173 K. The measured values of heat capacity and thermal conductivity were used to calculate λ the thermal diffusivity coefficient of the coals as a = ρC .

thermal conductivity, thermal diffusivity, heat capacity, and density measurements was studied for previously reported data. As a rule, the directly independently measured thermal conductivity data for coals are not consistent with the data derived from measured thermal diffusivity, heat capacity, and density data. Therefore, one of the purposes of the present work is to study the thermodynamic consistence between independent direct thermal conductivity, thermal diffusivity, heat capacity, and density data for the same coal sample.

3. EXPERIMENTAL SECTION 3.1. Sample Description and Characteristics. The coal sample was provided by the Deep Earth Energy Laboratory, Department of Civil Engineering, Monash University (Melbourne, Australia). The sample came from the Appin coalmine in the Sydney Basin. Coal can be separated into the following substances which define the temperature dependence of it thermal conductivity and other properties: fixed carbon, primary VM (released at lower temperatures), secondary VM (released at higher temperatures), ash, and moisture. Ultimate and proximate analyses of the coal sample are given in Table 1.The density, ρ, of the coal sample at 298.15 K is 1600 kg·m−3,

P

Zhumagulov35 studied the temperature dependence of the thermal conductivity and heat capacity of Shubarkol coal using the quasi-steady thermal-state method. He found that at temperatures between 573 and 673 K, the thermal conductivity of coal increases with the rate of 0.014 W·m−1·K−2. Further heating the coal sample leads to rapid changes in the rate of the thermal conductivity increase. This can be explained by the predominance of exothermal reactions and the ordering of the structure of the coal. The observed thermal conductivity behavior of Shubarkol coal has been compared with similar data for bituminous coals by Agroskin and Lovetskii.36 The thermal conductivity data reported by Zhumagulov35 for Shubarkol coal were systematically lower than those reported by Agroskin and Lovetskii36 over the entire experimental temperature range. The heat effects that accompany pyrolysis exert a significant influence on the heat-transfer coefficients of the entire charge when heated to high temperatures. As a result, the effective heat capacity and thermal conductivity of the coking mass may vary at different rates in the various stages of the process. Therefore, differences in the temperature dependencies of the thermal conductivity and heat capacity around 573−673 K lead to a temperature minimum of thermal diffusivity at these temperatures. The thermal conductivity of the Huainan-Huaibei coalfields was measured by Peng et al.37 The measured values of the thermal conductivity of coal measure strata (127 samples) ranged from 0.37 to 4.36 W·m−1·K−1, the average value being 2.54 W·m−1·K−1. Reported thermal conductivity data of coal measure strata were used to study its influence on a geothermal field in the Huainan-Huaibei coalfield. Rezaei et al.38 used the one-dimensional heat-transfer method to determine the thermal conductivity of a series of coal ash and synthetic ash samples at elevated temperatures. The effects of the parameters, such as temperature, porosity, and sintering time, were studied. The thermal conductivity of the samples was generally observed to increase with increasing temperature.39 Mills40 reviewed experimental methods of thermal conductivity measurements for coal slags and provided an evaluation of the reported thermal conductivity data. The different contributions from (1) the thermal (“phonon”) conductivity; (2) radiation conductivity; and (3) electronic conductivity were interpreted. Thus, as one can see, most reported thermal conductivity data for various types of coals were performed using various techniques, conventional contact and contact-free laser-flash methods. Most authors are not provided detailed uncertainty assessments of the measured thermal conductivity data that does not allow to estimate their reliability. Most cases with no verification of the reliability of the measured and derived (calculated from thermal diffusivity and heat capacity data) thermal conductivity data were provided by the authors. Also no thermodynamic consistency between the independent

Table 1. Coal Analysis, Chemical Composition of the Black Coal Sample ρ/kg·m−3

1600

moisture/wt % ash/wt % VM/wt % C/% O/% H/% N/% S/% Si/% Al/% Fe/% K/% Mn/%

3.000 10.00 35.00 79.65 9.350 5.130 1.470 0.347 2.475 1.043 0.295 0.229 0.011

porosity 5%, moisture content 3 wt %, and ash yield 10 wt %. As Table 1 shows, the main components of the black coal sample are carbon, 79.65%; oxygen, 9.35%; hydrogen, 5.13%; nitrogen, 1.47%; sulfur, 0.347%; silicon, 2.475%; and aluminum, 1.043%, accompanied by small amounts of Fe, K, and Mn, etc. The Raman spectrum was used in the characterization of the coal sample. Figure 1 shows the Raman spectrum of the black coal sample, with two main bands at 1590 and 1360 cm−1 and some weak bands at 3350, 3250, 2800, 2600, and 2000 cm−1 from different types of impurity crystals. This is similar to the Raman spectra of some types of disordered carbons, and the origin of these bands is best discussed in relation to those found in graphite and carbons.41 The band at 1590 cm−1 is related to a band of graphite which has been assigned to the E2G vibrations (vibrations of carbon atoms in the basal plane along the crystallographic direction a).41 The D-band at 1360 cm−1 was attributed to defects (structural imperfections, defects of graphite planes, the presence of hetero atoms, etc.) present in structural units and disorder. The cylindrical coal sample with a L/D ratio of 2−2.5 has been used, 123 mm long with a diameter of 50 mm. The two C

DOI: 10.1021/acs.jced.7b01079 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 1. Raman spectrum of coal sample (under 298 K).

Figure 2. Schematic diagram of the experimental high-pressure and high-temperature thermal conductivity apparatus. (1) Vacuummeter; (2) vacuum pump; (3) pressure transducer STS ATM; (4) valves; (5) gas cylinder; (6) compressor; (7) thermostate; (8) high-pressure chamber; (9) thermoregulator TPM10; (10) switch; (11) potentiometer P363−2; (12) multimeter KEITHLY 2000; (13) power supply TEC-23; and (14) reference resistance coil P321.

ends of the specimen were ground flat and parallel to each other at a level of accuracy of about 0.05 mm. 3.2. Experimentation. The effective thermal conductivity (ETC) of dry and wet black coal samples has been measured by a guarded parallel-plate apparatus. This technique was widely and successfully used previously by many researchers to make accurate measurements of the thermal conductivity of

rocks.42−47 It is an absolute, steady-state measurement device with an operational temperature range of 270−600 K and hydrostatic pressures up to 1000 MPa. The method (apparatus, procedure of measurements, and detailed uncertainty assessment) has been fully described in our previous publications.23,24,48−51 A schematic diagram of the construction of the thermal conductivity cell and the compensation heater is shown D

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Figure 3. High-pressure thermal conductivity measuring cell (A) and construction of the heater (B). (A) (1) Leading capillary; (2) sealing nuts; (3) chamber body; (4) sealing ring; (5) spring; (6) cooler; (7) sample; (8) thermocouples; (9) heater; and (10) output wires. (B) (1) Thermocouples; (2) bronze disk; and (3) spiral made of nichrome wire.

Figure 4. Detailed view of the thermal conductivity measuring cell.

soldered to the body of the heater. The temperature difference (temperature gradient) and temperature of the chamber were measured with four copper-constant thermocouples. The detailed view of the measuring cell is shown in Figure 4. The thermal conductivity, λ, of the specimen in this method was deduced from the relation

in Figure 2. The thermal conductivity apparatus consists of a high-pressure chamber, a thermal conductivity measuring cell (see also Figure 3A), an air thermostat, a high precision temperature regulator, and a high-pressure liquid and gas compressor. The temperature in the air thermostat was controlled automatically to within ±5 mK. In this method, thermal conductivity is obtained from simultaneous measurements of the steady-state heat flux Q and temperature gradient in the sample placed between the heating and cooling plates. The good thermal contact between the heater and the sample was assured using thermal interface materials (wetting agent, such as vaseline or glycerin). To reduce the effect of the contact resistance (imperfect thermal contact between the sample and the adjacent bronze disk), the sample and heater surfaces were polished flat to within 0.05 mm and smooth. The spring (see Figure 3A) was also used to create contact pressure (pressure of 1−2 MPa was applied axially) to improve the thermal contact between the sample and heater. Two thermocouples were embedded in the center of the inner surface of the bronze disk (see Figure 3B). The heater (Figure 3B) was located between these thermocouples. The other two thermocouples were

λ=

Q − Q los S1 ΔT1 h1

+

S2 ΔT2 h2

(1)

where Q = Q1 + Q2 is the total heat flow transferred from the heater to the upper and lower specimens; Q1 and Q2 are the heat flows transferred by conduction through the lower and upper specimens, respectively; Qlos is the heat lost through the lateral surface of the samples; S1 and S2 are the cross-sectional areas of the specimens that heat flows through; h1 and h2 are the height of the samples; and ΔT1and ΔT2 are the temperature differences across the samples thickness. The thermal conductivity was obtained from the measured quantities, Q, Qlos, ΔT1, ΔT2, S1, S2, h1, and h2. The heat flow Q from the heater was distributed between the two E

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samples Q1 and Q2. The values of Q were corrected by a specimens lateral loss factor Qlos. The lateral heat-losses were measured by using samples of pyrex glass of well-known 2π h conductivity, Q los = λpyr ΔT ln(d / D) . From the uncertainty of

Table 2. Measured Values of the Thermal Conductivity (λ) of Wet and Dry Black Coal Samples before and after Thermal Treatment Using the Guarded Parallel-Plate Techniquesa

the measured quantities (Q, Qlos, ΔT1, ΔT2, S1, S2, h1, and h2) and the corrections, the total combined expanded uncertainty in the thermal conductivity measurement at the 95% confidence level with a coverage factor of k = 2 less than 5%. The reproducibility of the measurement is about 2.0%. This value of the uncertainty (5%) is not including the uncertainty due to contact resistance and radiative heat transfer. Therefore, the uncertainty of the ETC data obtained with the method is probably higher than 5%. According to Hofmeister et al.,52 contact resistance with heaters and thermocouples, and possibly among constituent grains, leads to a systematic and substantial underestimation of lattice thermal conductivity of 20%. To check and confirm the validity of the method and procedure of the measurements, the thermal conductivity measurements were made with standard (reference) material (fused quartz) using the present apparatus. Fused quartz has been recommended as a standard material for the test and calibration of the thermal conductivity apparatus (see, for example, Devyatkov et al.53). The thermal conductivity of fused quartz has been used previously to calibrate the apparatus for measuring the ETC of rock specimens by many authors using various versions of the contact methods. Excellent agreement within 1.0 to 2.5% was found between the present data and the majority of the reported values for the reference sample (fused quartz) by other authors (see, for example, refs 48−51). The measured thermal conductivity data for fused quartz using the present contact method were compared with the data obtained using the LFA 457 methods. The discrepancy was acceptable (within 3 to 5%). This good agreement for fused quartz demonstrates the reliability and accuracy of the present measurements for the coal sample and corrects the operation of the instrument.

wet coal sample before thermal treatment

a

dry coal sample before thermal treatment

coal sample after thermal treatment (second run)

T/K

λ/W·m−1·K−1

T/K

λ/W·m−1·K−1

T/K

λ/W·m−1·K−1

298.15 299.02 322.13 340.02 352.10 371.07 372.01 390.03 410.08 422.21 435.15 450.04 462.06 480.14 495.15

0.340 0.339 0.379 0.419 0.457 0.491 0.491 0.502 0.488 0.471 0.445 0.412 0.392 0.381 0.380

298.2 299.4 300.0 325.8 342.6 359.0 377.8 377.0 383.3 399.4 437.4 463.0 473.5 486.1 -

0.321 0.320 0.314 0.351 0.367 0.380 0.390 0.391 0.390 0.385 0.357 0.333 0.328 0.333 -

298.2 299.7 300.0 320.0 330.4 342.2 355.7 374.0 404.0 436.4 466.1 466.2 480.2 496.1 -

0.269 0.269 0.270 0.275 0.279 0.285 0.289 0.292 0.297 0.309 0.317 0.316 0.322 0.326 -

Standard uncertainties, u, are u(T) = 10 mK and ur(λ) = 2.5%.

the thermal conductivity of the coal sample slightly changes with the temperature increasing from 0.267 to 0.326 W·m−1· K−1, i.e., gradually increasing with the temperature without a maximum or minimum. The thermophysical properties of coal depend on many factors, such as composition, structure, VM, rank, and temperature, and can be determined only by experiment. All of the previously reported data for various types of coals (see above, Section 2) show a rise in thermal conductivity while temperature increases, which has been attributed to (a) radiant heat transfer across pores and cracks; (b) changes in the conductivity of the coal due to pyrolysis; and (c) changes in intrinsic conductivity with temperature. At low temperatures (below 873 K), the effect of the radiant heat transfer across the pores is relatively small and can be neglected. The temperature dependence of the thermal conductivity of coal is consistent with values reported for pure amorphous carbon. The thermal conductivity of minerals is much higher than those of organic materials; therefore, if the amount of coal ash increases, the thermal conductivity coefficient increases. The structure of the organic matter in coal gradually becomes more compact and regular at high temperatures (around 973 K); therefore, the thermal conductivity gradually increases, approaching that of graphite. Our previously measured values of the thermal diffusivity (a)30 and heat capacity (CP)30 of black coal (see Figures 7 and 8) together with the density data (ρ) were used to calculate the thermal conductivity by applying the well-known thermodynamic relation, λ = aρCP. Measurements of the thermal diffusivity (a)30 of the same black coal were performed using the LFA 457 apparatus over the temperature range of 301−823 K with a combined expanded uncertainty of 3%. This technique was widely used for the study of the thermal diffusivity of solid materials (see, for example, Bozlar et al.29). The isobaric heat capacities (CP) of the same sample were measured30 over the temperature range of 308−763 K using DSC 204 F1 with a combined expanded uncertainty of 1%. Some selected values of

4. RESULTS AND DISCUSSION Measurements of the thermal conductivity of the black coal sample were made in the temperature range of 298−496 K. The experimental results for the wet and dry samples before (primarily) and after the thermal treatment (second run) are presented in Table 2 and are shown in Figure 5 as a function of temperature. As Figure 5 shows, the measured thermal conductivity of the wet coal sample (before thermal treatment) increases as the temperature passes through a maximum near 390 K, and then it decreases at higher temperatures. This temperature behavior of the measured thermal conductivity is in good agreement with the values calculated from a well-know thermodynamic relation, λ = aρCP (see Figure 5), using previously measured thermal diffusivity (a, contact-free laserflash LFA 457 method),30 heat capacity (CP, DSC 204 F1),30 and density (ρ, using the constant value of density, 1600 kg· m−3) data for the same coal sample. As Figure 5 shows, the present directly experimentally observed temperature behavior of the thermal conductivity of black coal is qualitatively and quantitatively consistent with the values derived from the independent indirect measurements of the thermal diffusivity, heat capacity, and density data reported in our previous works.30 The temperature behavior of the thermal conductivity of coal considerably changes after the heat treatment (see Figure 6 and Table 2). After the heat treatment (second run), F

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Figure 5. Comparison of the measured thermal conductivities of black coal and derived values of (λ = ρCPa) of untreated wet (full circles) and dry (open circles) black coal samples. ●, calculated from measured values of ρ, CP, and a30 for a wet coal sample; ○, calculated from measured values of ρ, CP, and a30 for a dry coal sample; △, (this work) direct measurements of the λ for a wet coal sample; and ▲, (this work) direct measurements of the λ for a dry coal sample.

Figure 6. Comparison of the measured thermal conductivities of black coal and derived values of (λ = ρCPa) of thermal-treated (second run) wet (full circles) and dry (open circles) black coal samples. ●, calculated from measured values of ρ, CP, and a30 for a wet coal sample (after being thermal treated); ○, calculated from measured values of ρ, CP, and a30 for a dry coal sample (after being thermal treated); △, direct measurements of the λ for a wet coal sample in this work (after thermal treatment, second run).

mm2·s−1; CP = 1.27 kJ·kg−1·K−1 (for a wet and nonthermal treated sample), 1.175 kJ·kg−1·K−1 (for a dry and nonthermal treated sample), and 1.0 kJ·kg−1·K−1 (for a thermally treated sample); and ρ = 1600 kg·m−3. The derived values of the thermal conductivity of coal at room temperature of 298.15 K for wet (nonthermal treated), dry (nonthermal treated), and thermally treated samples are λ = aρCP = 0.354, 0.327, and 0.278 W·m−1·K−1, respectively. These derived values of thermal conductivity at room temperature are in good agreement with

the experimental thermal diffusivity and heat capacity data for the black coal are presented in Tables 3 and 4 and are depicted in Figures 7 and 8. Unfortunately, there are no temperaturedependent density data for the black coal sample under study. The measured value of density of the black coal at room temperature provided by the supplier was 1600 kg·m−3. Therefore, we applied the relation, λ = aρCP, to calculate the value of the thermal conductivity of black coal at room temperature (298.15 K) using the measured values of a = 0.174 G

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Figure 7. Measured thermal diffusivity of black coal as a function of temperature from laser-flash FLA method.30 Solid lines are calculated from the correlation.30

Figure 8. Comparison of the measured heat capacities of black coal samples for wet and dry coal samples (before thermal treatment, left) and second repeat runs (thermally treated, right) as a function of temperature.30 (Left) ●, wet coal sample (before being thermally treated) and ○, dry coal sample (before being thermally treated). (Right) After being thermally treated (second run).

experimental temperature range of a and CP using the constant value of density, 1600 kg·m−3, at 298 K. The derived values of λ = aρCPare presented in Table 5 and are shown in Figures 5 and 6 for wet and dry samples before and after thermal treatment together with the present direct measured values of the thermal conductivity. The uncertainty of the derived values of the thermal conductivity due to the fixed values of the density is negligible, because the temperature variation of the density is small. The maximum uncertainty of the derived values of thermal conductivity is about 5−6%. The values of thermal conductivity for the thermally treated coal sample (see Figure

the present direct measurements of the thermal conductivities of 0.340, 0.321, and 0.269 W·m−1·K−1, respectively. The discrepancies (3.8, 1.8, and 3.3%, respectively) are within their experimental uncertainties. This is additional confirmation of the reliability, accuracy, and thermodynamic consistence of the measured values of the thermodynamic (heat capacity and density) and transport (thermal diffusivity and thermal conductivity) properties of the black coal sample. Also, this is confirming the correct operation of the present thermal conductivity apparatus and its correct calibration. We calculated the thermal conductivity of the coal sample in the whole H

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Table 3. Measured Values of the Thermal Diffusivity (a) of Black Coal Samples Using the Laser-Flash Technique30 (Selected Data)a

a

T/K

a/mm2·s−1

301.75 371.45 422.45 473.25 523.15 572.95 623.45 673.65 723.45 773.25 823.15

0.173 0.160 0.155 0.152 0.155 0.160 0.168 0.180 0.193 0.214 0.235

Table 5. Derived Values of the Thermal Conductivity (λ = aρCP) of Dry Black Coal Samples from Measured Values of the Thermal Diffusivity (a) and Heat Capacity (CP) after Thermal Treatmenta

a

Standard uncertainties, u, are u(T) = 15 mK and ur(a) = 1.5%.

T/K

λ/W·m−1·K−1

313.15 373.15 433.15 493.15 553.15 613.15 673.15 733.15 758.15 771.15

0.264 0.292 0.306 0.329 0.359 0.404 0.459 0.519 0.556 0.526

Standard uncertainties, u, are u(T) = 10 mK and ur(λ) = 2.5%.

thermodynamically consistence with the present thermal conductivity measurements. According to Herrin and Deming,28 who summarized thermal conductivity data for 55 coal samples, the values of the thermal conductivity of different types of coal under ambient conditions (at room temperature of 295 K) ranged from 0.22 to 0.55 W·m−1·K−1 (almost 10 times lower than that for most rocks). The present results for the nonthermally treated dry sample (0.321 W·m−1·K−1) and for the thermally treated sample (0.269 W·m−1·K−1) fall into this range. Gu33 reported thermal conductivities for Chinese coals. The value of the thermal conductivity of coal at 295 K, 0.260−0.267 W·m−1· K−1, reported by Turian et al.,27 is in good agreement with the present result of 0.269 W·m−1·K−1. The values of thermal conductivity (0.23, 0.22, 0.25, 0.23, 0.24, and 0.26 W·m−1·K−1) for coals from the Yimachagcun, Tangshagou, Dafong, Aping, Dadong Wucun, and Yongdingzhuang areas, respectively, at room temperature are also in good consistent with the present result. Thermal conductivity data reported by Badzioch et al.26 for 12 types of coal in the temperature range from room temperature to 1173 K showed that the thermal conductivity of the coal samples changes slightly (an average value is about 0.23 W·m−1·K−1) with a temperature in the range of 373−573 K. Dindi et al.25 also reported thermal conductivity data for coal using the hot-wire method at temperatures up to 693 K. Figure 9 shows the comparison of the present thermal conductivity data for dry and wet black coal samples with the reported data25,33 for other types of coal. It can be noted that, the

6) slightly increase with temperatures between 373 and 433 K, while above 473 K, sharp changes were observed. At low temperatures (below 433 K), the residual water evaporation increases the empty space in the pores. This is one of the possible reasons why the thermal conductivity decreases at low temperatures. At high temperatures, the pyrolysis (chemical reaction) process changes the coal’s microstructure and contents, leading to rapid increases in thermal conductivity. As we can note, the derived values of the thermal conductivity of black coal for wet and dried samples before annealing differ considerably in the low temperature range (below 503−513 K), where vaporization of water was observed. Above 513 K, the difference is small. For annealed wet and dried samples (second runs), the difference in the thermal conductivity is very small (within experimental uncertainty). We also observed that the temperature behavior of the derived values of the thermal conductivity for the untreated sample was just like the heat capacity behavior. This means that the contribution of the temperature behavior of the heat capacity dominates the temperature behavior of thermal diffusivity in λ = aρCP. However, we did not take into account the temperature dependence of the density, especially in the a low temperature range, where CP shows a maximum, and density shows rapid changes due to mass losses. The two controversy effects, CP increases and ρ decreases, compensate each other, and the derived values of λ exhibit regular behavior. This confirms the accuracy and reliability of our previous measurements of thermal diffusivity and heat capacity for black coal, and they are

Table 4. Measured Values of the Heat Capacity (CP) of Black Coal Samples Using the DSC Technique (Selected Data)30,a wet coal sample before thermal treatment

a

dry coal sample before thermal treatment

coal sample after thermal treatment (second run)

T/K

CP/kJ·kg−1·K−1

T/K

CP/kJ·kg−1·K−1

T/K

CP/kJ·kg−1·K−1

304.15 364.15 424.15 484.15 544.15 604.15 664.15 724.15 749.15 769.15

1.267 1.822 1.855 1.517 1.539 1.666 1.800 1.800 1.958 1.948

307.15 363.15 423.15 483.15 543.15 603.15 663.15 723.15 743.15 771.15

1.175 1.458 1.507 1.347 1.513 1.640 1.767 1.815 1.957 2.023

313.15 373.15 433.15 493.15 553.15 613.15 673.15 733.15 758.15 771.15

0.916 1.141 1.242 1.344 1.430 1.524 1.596 1.639 1.677 1.709

Standard uncertainties, u, are u(T) = 10 mK and ur(CP) = 0.5%. I

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Figure 9. Comparison of the present measured thermal conductivity of dry black coal samples (before thermal treatment, full circles) and second repeat runs (thermally treated, open circles) as a function of temperature together with the reported data25,33 for other type coals. Dashed lines were calculated from the correlations.25,33

5. CONCLUSIONS

magnitude of the present and reported thermal conductivity data for various types of coals are very close. The distinct behavior of the thermal conductivity (λ) for different temperature regions results from combining a, CP (see Figures 7 and 8), and ρ in relation to λ = ρaCP, which are complex functions of temperature. The observed temperature behavior of the black coal’s thermal conductivity (λ) is the result of the complexity of the temperature behaviors of a, CP, and ρ, i.e., it is the superposition of various temperature behaviors of a, CP, and ρ, and it reflects the temperature behavior of the heat capacity (see Figures 5 and 8). This means that the temperature behavior of CP dominates the thermal diffusivity (λ = ρaCP), i.e., the temperature behavior of λ and CP are strongly correlated. Independent measurements of all of these thermophysical parameters (a, CP, λ, and ρ) allow to estimate their internal thermodynamic consistency through the thermodynamic relation, λ = ρaCP. The experimentally observed temperature behavior of thermal diffusivity (Figure 7) demonstrates that in the initial (low) temperature range, where a slightly decreases with a rising temperature, the contribution to the thermal conductivity is less than the heat capacity, ρCP, i.e., ρCP increases with temperature faster than λ. For the present coal sample, the ratio λ/a changes from 1.64 to 2.73 × 106 J·K−1·m−3 for the dry thermally treated sample and from 1.41 to 2.44 × 106 J·K−1·m−3 for the wet coal. For most rock materials (sandstones, for example), the reported value of ρCP = λ/a changes within 1.9−2.3 × 106 J·K−1·m−3. Our result is close to that range. The reported thermal conductivity data (see also Singer et al.,54 Stanger et al.,55 and KosowskaGolachowska et al.6) for various types of coals are basically increasing with temperature. However, the rate of the temperature variation of the thermal conductivity is very small at temperatures up to 773 K, and rapid changes were observed above 873 K due to devolatilization, the combustion of char, and other structural changes.

(1) The guarded parallel-plate technique was employed on a black coal sample for an accurate measurement of the thermal conductivity in the temperature range of 298− 496 K. (2) We have experimentally observed that the measured thermal conductivity (λ) of the wet and dry coal samples increases with temperatures passing through a maximum around 390 K, and then it decreases gradually at higher temperatures. We attribute this maximum to the evolution of the volatile matter (VM) (devolatilazation) and the aromatization of the carbon (pyrolysis), which is known to occur under heat treatment, and therefore tends to increase the thermal conductivity. (3) The decomposition of the complex disordered macromolecular structure (individual functional groups) of the coal is the result of the complexity thermal conductivity behavior in distinct temperature ranges. (4) The results of the present study showed that the temperature behavior of the thermal conductivity for the primary coal sample (wet and dry) and the second repeated run is considerably different, while the difference between the thermal-treated wet and dry samples (second runs) is very small (within experimental uncertainty). (5) The thermal conductivity of the thermal-treated sample exhibited a monotonic temperature increase without any anomalies (without a maximum or minimum in the difference of the primary coal sample). This means that heating changes the structure of the coal, i.e., the structure of the organic matter in coal gradually becomes more compact. (6) Directly measured thermal conductivities of the black coal sample were compared with the values derived from the independent thermal diffusivity, heat capacity, and J

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density measurements using a well-known thermodynamic relation, λ = ρCPa. Good agreement within 5−6% was found between the directly measured results and the derived (indirect measurements) values of the thermal conductivity. This is additional confirmation of the reliability and correctness of the measured values of the heat capacity and thermal diffusivity and their thermodynamic consistency. (7) The observed temperature behavior of the black coal’s thermal conductivity (λ) is the result of the complexity of the temperature behaviors of a, CP, and ρ, i.e., it is the superposition of various temperature behaviors of a, CP, and ρ, and it reflects the temperature behavior of the heat capacity. This means that temperature behavior of CP dominates the thermal diffusivity (λ = ρaCP), i.e., the temperature behavior of λ and CP is strongly correlated.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ilmutdin M. Abdulagatov: 0000-0002-6299-5280 Pathegama G. Ranjith: 0000-0003-0094-7141 Notes

The authors declare no competing financial interest.

■

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