Thermo-physical properties of coal under transient conditions

Fuel Processing Technology, 8 (1984) 241--252

241

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

THERMO-PHYSICAL PROPERTIES OF COAL UNDER TRANSIENT CONDITIONS

O.J. HAHN

Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506 (U.S.A.) M.W. A K H T A R

Technology for Energy Corporation, Knoxville, TN 37922 (U.S.A.) and R.C. BIRKEBAK

Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506 (U.S.A.) (Received July 26th, 1982; accepted July 13th, 1983)

ABSTRACT Coal samples were obtained along the vertical axis in an eight-inch diameter experimental moving bed coal gasifier. This system had a throughput of half a tonne o f sized (6 x 20 mm) coal per day. The specific heat and thermal conductivity were measured using the line heat-source method with a transient sample temperature. The coal sample was heated at a rate of 4 K/rain during the property measurement. The heat capacity and thermal conductivity were obtained from an iterative fit of the experimental data to the heat conduction equation taking due account of the probe size and contact resistance. The apparatus was tested with samples of known properties such as alumina powder and glass micro-beads. The measurements reported here cover the range from 300--700 K. Effects of surface moisture and pyrolysis reactions can be identified. The results are compared with data in the literature measured at constant sample temperatures. The line source technique is well suited to transient property measurements.

INTRODUCTION

Thermo-physical properties of coal are continuously changing during gasification. Detailed knowledge o f these properties such as thermal conductivity and specific heat as a function of heat-up rate, temperature and past gasification conditions will aid in the computer modeling of these systems. In general, methods for measurement of thermal conductivity can be classified as steady state and transient methods. The steady state methods are time consuming, b u t have been known in the past for the more accurate results. The transient methods are gaining popularity due to the advent of computerized data acquisition and control systems. Amongst the hightemperature testing methods the choices are: the linear heat-flow and the

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© 1984 Elsevier Science Publishers B.V.

242 radial heat-flow method. A detailed description of these methods is given by Touloukian [ 1 ]. Laubitz [ 2] emphasizes the importance of determination of power input into the heater, and accuracy of thermocouple positioning which govern the choice between these two methods. Power input is more accurately measured in radial methods, whereas the linear heat-flow methods have an advantage in thermocouple placement. Recent instrumentation, and experimental set-ups, that satisfy the idealizations incorporated in defining the mathematics of the situation have reduced the spread of the thermophysical data on many materials. To account for any remaining corrections that are still thought necessary in these set-ups, the authors either correct their results, or show these deviations from ideal to be negligible as found in Healy et al. [3], Kestin and Wakeham [4], Horrocks and McLaughlin [5], and McLaughlin and Pittman [6]. Healy, deGroot and Kestin [3] presented the theory of the transient hotwire method for measuring thermal conductivity, and used the general perturbation method to ascertain the required corrections. Principle corrections discussed were: wire finite dimensions, radiation, compressibility, convection, variable fluid properties, heating over a finite length, and Knudsen effects. Ziebland [ 7] compared typical thermal conductivity methods; the guarded hot plate (a linear heat-flow method), concentric cylinders, and the steady state hot-wire cells, with regards to their susceptibility to stray conduction paths. He concluded that the errors were smallest in the hot-wire cell (that is, the radial heat-flow method). It should, therefore, be expected that the transient version would be even less affected because of the fine wires and larger cell-to-wire diameter ratios. Horrock and McLaughlin [ 5] have recommended the transient hot-wire method to be "intrinsically capable of accuracies comparable to those of the best steady state methods". In a later paper, McLaughlin with Pittman [6] reviewed and extended the theory of the radial heat-flow method, establishing design criteria to minimize experimental errors, and provided for corrections due to residual losses. They pointed out that the primary factor which limited the precision of measurement by this method, had been the difficulty in the recording of transient voltages sufficiently accurately. These two papers [5,6] with the works by Kestin and Wakeham [4] and Healy et al. [3], have paved the way for the use of the transient line heat-source method, effectively by improving the understanding and correction of unavoidable errors in the experimental set-up and by using the most suitable mathematical or numerical procedure. One area of concern in the line heat-source method though has been the problem of contact resistance between heater wire and medium. Watkins [8] and Watkins and Birkebak [9] handled this problem mathematically, for substances in powder form, and determined it by an iterative procedure. To measure the thermal properties of solids that cannot be molded around the central heating wire, Gustafsson, Karawacki and Khan [10] have given the theory and experimental results for solids: fused quartz, glycerine and

243 Araldite, using a hot-strip method. The method employs a heater in the form of a strip, instead of a wire as in the line heat-source method. The metal strip is pressed between two slabs of the material whose properties are being measured. Attempts also have been made to measure simultaneously all the thermal properties: heat capacity, thermal diffusivity, thermal conductivity; and the thermal penetration property -- product of density, specific heat and thermal conductivity -- by Filipov [11] and Abdel--Wahed et al. [12]. Wechsler and Glaser [ 13 ] have concluded that the line heat-source method, a form of radial heat-flow method, is a reliable and versatile apparatus for measurement of thermal conductivity from vacuum to atmospheric pressures and temperatures from 77 to 800 K for rocks and minerals in vesicular and powder form. The m e t h o d is particularly useful for studying small samples when the "short-time" analytical solution is used. Similar experiments have been run on liquids, gases, and powdered samples by Trump et al. [14], DeGroot et al. [15], and Cremers [16]. They describe the transient hot-wire m e t h o d as an "absolute" and high precision method. The concept of a "quasi-steady state" which prevails in transient methods, is considered useful where moisture migration, and other such effects persist during steady state

J l _ 2 = : Steadily Rising Sample Temperature 2 ' - 3 ' : Rise Due to Line Heat Source Exp. 2'-4'= Profile in Absence of Line Heat , ~ Source

~

¢u o

5'

~t -~ ,

I' b l T r a n s i e n t - S o m p l e Temperature Method

E

oj I-

I - 2 : S a m p l e at Constant Temperature 2 - 3 ; R i s e Due to Line Heat Source Exp. 2 - 4 : P r o f i l e in Absence Line Heat Source

I

2

3

4

a) Steady-Sample Temperature Method

Time

Fig. 1. C o n c e p t o f line heat-source m e t h o d for d e t e r m i n a t i o n o f thermo-physical properties o f substances.

244

conditions. This is discussed by Abdel--Wahed, Pfender and Eckert [12]. The line heat-source method appears to be a reliable way of determining the thermo-physica/properties of substances in powdered or granular form. If the sample temperature is steadily increased at a fixed rate, the line heatsource m e t h o d can be used to measure the thermal properties o f the sample, using the temperature rise with respect to the sample temperatures that "would have been" observed if the "fine-source" was not turned on. The concept is defined more clearly in Fig. 1. THEORY

The basic experimental set-up is shown in Fig. 2. A heated wire with thermal properties ~p and kp passes through the center of the medium of thermal properties am and kp. The wire has heat generation A per unit volume and time. The initial temperature in both the wire and the medium is constant. The differential equations for the heater wire and medium are a2Tp ar:

+-

1 aTp r

ar

3:Tin 1 OTm ~ + - ar 2 r ar

1 OTp C~p at 1 aT m

ap

at

-

A

kp

- 0

for 0 < r < R

(1)

for r > t t

(2)

=~ >>=jGuord Heater

Voltage Thermocouple

Leads

Sample Cylinder

ine Source Wire i ~_2 R

'ig. 2. Schematic sketch of line heat-source apparatus.

245

The initial conditions are Tp = T m = 0 for t = 0. For the case of no contact resistance between the wire and the media the solution to the above equation is given in Carslaw and Jaeger [19]. The equation for the contact resistance between the wire and the medium is given as H(Tp -

Tin)

=

aTp ~Tm = -kp ~r ~r

-km

for r = R

(3)

Watkins [8] and Watkins and Birkebak [9] solved the above three equations simultaneously. Their method is as follows: Assuming constant properties over limited temperature ranges of a b o u t 10 K and letting 0m = T m / ( A R 2 / 4 k m ) Op = T p / ( A R 2 / 4 k m )

= (~m/~) In (~

= km/k p

~?

= kp/RH

4)

=

7

= am t/R 2

r/R

The above equations reduce to ~20p

~20 m

+

+

a~¢

1 aOp

f12 aOp

1

~0 m

a0 m

¢

a¢

a7

=

-77 0~

~0 m Op - 0 m

for 0 < ¢ < 1

(4)

- 0

for ~ > 1

(5)

¢

(6)

~

-

a¢

- -4a

~Op

a¢

for

= 1

The solution of these equations using Laplace transforms and above boundary conditions is: 8m = Ei(¢2/4T) + y

e x p ( - U 2 r ) G(U) d U

(7)

0

and

[8G(U)

1

~(u) { U Yo(¢U)} + 2 U s {Jo(¢U)} [U~(U) 2 + U'[¢(U)/U] 2

U

246

4/3~U J2([3U) (~U)~

2J0 (¢U)~(U)] Uq,(U)

(8)

[U¢(U)] 2 + U*[¢(u)/u] ~

where:

~(U)

[3 J, ([3U)Yo (U) - Jo(~U)

Y,(U) +

+~[3UJ,([~U)Y,(U)

(9a)

(U) = ~ J~ ([3U)Jo (U) - Jo(~U) J, (U) + ~?[3UJ, ([3U) J, (U)

(9b)

@(U) = [3 J, ([~U)Yo (U) - Jo([3U) Y,(U) + ~?~UJ, (~U) Y, (U)

(9c)

The basic approach was to solve the above equations numerically and fit the temperature to the experimental data. Initial guesses of the unknown parameters, the specific heat and thermal conductivity of the medium and the contact resistance were inserted into the solution of the heat conduction and contact resistance equations. The calculated temperatures for a specific set of parameters were compared with the experimental results. A pattern search with gradient corrections was initiated for the minimum least-squares difference between the experimental and calculated temperatures. The integration of the previous equation was done by using the trapezoidal rule with Romberg's extrapolation. The integration terminated after the difference between two successive calculations became "less than a given tolerance, or if the interval has been subdivided a specified maximum number of times". The three parameters to be determined were the values of medium heat capacity, PmCPm, medium thermal conductivity, kin, and the contact resistance parameter, ,~. The wire properties, ppCpp and kp, line source wire radius, R, the parameter r/R (where r is the distance of the thermocouple from the center of the cell), the power-input per unit length of the line source, A, the number of data points {temperature rise versus time lapse), the initial guess of the required parameters, and step sizes were input parameters. The actual program used in the analysis was a modified version of the program given by Watkins [8] and was run on a HP-1000 F-Series Computer System using HP FORTRAN FTN4. EXPERIMENTS AND RESULTS

The line heat-source apparatus, Fig. 2, consists of a central Ni--Cr heating wire, a thermocouple, and environment heaters. The cell was 26 mm in diameter and 180 mm long. Three sectional heaters surrounded the cell for rapid temperature control. Further details of the experiment setup are given in Ref. [19].

247

A "~ 0 . 4

x

= Touloukian

( Porous Bubbles of A l u m i n a ) I

O

= Touloukian

(Highly

A

= Present

Porous Reagent Grade A l u m i n a ) I

Work(Reagent

Grade Alumina Powder)

E ~

0.3

._~ ~ 0.2 o

o E

13.1

I.I 200

I 500

I 600

Temperature ( K )

Fig. 3. Thermal conductivity of ignited alumina powder.

The test method and apparatus were checked out using glass beads and powder alumina samples. Our results for alumina are compared in Fig. 3 with those in Ref. [1], and there is satisfactory agreement. The glass beads results also agree with previous investigators. The test samples were obtained from the moving bed gasifierat the University of Kentucky that was operated using high volatile bituminous coal, Eastern Kentucky Elkhorn No. 3. The coal analysis is given in Table 1. TABLE 1 Summary o f analysis o f Kentucky Elkhorn No. 3 coal Proximate analysis (dry) a

Ultimate analysis

Initial coal Ash Volatile matter Fixed carbon Sulfur Heating value

3.0% 37.6% 59.3% 0.7% 14,669 Btu/lb (34,122 kJ/kg)

Carbon Hydrogen Nitrogen Chlorine Oxygen Free swelling index

81.2% 5.7% 1.6% 0.0% 7.8% 4.0

Carbon Hydrogen Nitrogen Chlorine Oxygen

95.8% 1.2% 1.4% 0.0% 1.6%

Carbonized sample from U.K. gasifier Ash Volatile matter Fixed carbon Sulfur

6.0% 5.8% 88.2% 0.5%

aCoal contained 3.42% moisture.

248 TABLE 2 Size distribution of coal sample Range (~ m)

Top layer (wt. %)

Bottom layer (wt. %)

0--30 30--40 40--53 53--75 >75

12.69 13.63 42.23 18.28 9.17

12.69 5.95 24.04 6.83 50.49

% %

9 7

x

5

>,

3

0 = Experiment With E l k h o r n 4 # 3 Coal, ,0 = Virgin C o a l [ S i n g e r 8t Tye z l ] r-1 = Coal Carbonized At 8 5 0 C [Singer a Tye" ]

Q.

o "1"

I

I

I

I

400

500

600

700

Temperature ( K )

3E

E

1.0 J

-

0.8

u

"o 0.6 (3

-~ 0.4 E

~ 0.2 I

400

I

500 Temperature ( K )

I

I

600

700

Fig. 4. Properties of gasifier coal from the 8-inch (0.2 m) layer above the ash zone out of a 45-inch (1.1 m) total bed.

249 0 = Average Properties of 5 Runs = Virgin Cool, Singer I~ Tye2', [ 1 9 7 9 ] r'l = Coal Carbonized At 850C, Singer S T y e 2 1 , [ 1 9 7 9 ]

Y

to

o X o.

% u

I

0

"~ I 400

o a~ "1-

I 500 Temperature ( K )

(Elkhorn -~3 Coal) I 600

I 700

V

E

+.L3

1.0 0.8

o ..........~-

>

-o 0.6 c

8 -~ 0 . 4 E 0.2

I 400

I 500 Temperature ( K )

I

I

600

700

Fig. 5. Properties of gasifier coal from the t o p 8-inch (0.2 m) layer out of a 45-inch (1.1 m) total bed.

The small gasifier was operated at steady state with a bed height between 40 to 48 inches (1.0--1.2 m). Due to refractory walls the temperature profile in the gasifier approximated that found in larger moving bed gasifiers such as those in a 10-foot (3.5 m) Wellman--Galusha [20]. Samples were taken out of an eight-inch (0.2 m) layer from the top and bottom of the gasifier. The top layer was exposed to exit gas with a composition of 24% CO, 6% CO2, 14% H2, 2.2% CH4 and 53.8% N2. The bottom layer was exposed to heated air with 10% steam composition. The gasifier was quenched with liquid nitrogen to stop the gasification reaction. The coal or char samples from these layers were ground in a hammer mill and sifted through a Tyler No. 40 mesh screen. The size distribution of the samples is given in Table 2. The samples were inserted in the sample cell and tamped uniformly. Figures 4 and 5 present the results of the heat capacity and thermal conductivity measurements from the two layers under transient heating conditions

250

of 4 K/min. The results of these measurements are compared with those reported by Singer and Tye [21] for Pittsburgh Steam coals under steady state conditions over a similar temperature range. The transient method shows the anticipated effect of surface moisture on the samples around 350--375 K and the rise in both thermal conductivity and specific heat above 600 K for the upper layer in the gasifier. The properties of the bottom layer, except for the surface moisture effect, are essentially independent of temperature as would be anticipated for the remaining carbon. The results shown in Figs. 4 and 5 are an average based on five samples with a spread of +10%. The mean value of the wire--coal contact heat transfer coefficient, H, was approximately 3.5 × 104 W/m 2 K. This did not change significantly over the temperature range. The values of the thermal conductivity and specific heat of the coal were not very sensitive to changes in the wire--coal contact heat transfer coefficient. CONCLUSIONS

The line heat-source technique for thermal property measurements is well suited to transient measurements of coal. The heat-up rate of the sample was limited to 4 K/min for these measurements owing to the heater design. Future work will explore the thermal properties at higher heat-up rates more in the range of those found in moving bed gasifiers, that is 10--20 K/min. ACKNOWLEDGEMENT

The work in this paper was in part supported by the Institute for Mining and Minerals Research, University of Kentucky, Lexington, KY. NOMENCLATURE

A

Cpx Ei(x) H J0,J1, Y0, YI k

R r T t

U

heat generation (W/m 3) specific heat (W s/kg K) exponential integral contact heat transfer coefficient (W/m 2 K) Bessel functions thermal conductivity (W/m K) radius of heater wire (rn) radius (m) temperature (K) time (s) dummy variable of integration thermal diffusivity (m2/s) diffusivity ratio, kp/R H

¢

non-dimensional space variable, r/R

251

7" Om Pm Cpm pp Cpm o~

non-dimensional time variable, a m t/R 2 medium t e m p e r a t u r e dimensionless, Tm/(AR2/4 k i n ) kin/otto

kp/~p km/kp

Subscripts m p

m edi um pr obe or wire

REFERENCES 1 Touloukian, Y.S., 1970. Thermophysical Properties of Matter. The TPRC Data Series, Vol. 2 and Vol. 10 (Thermal Conductivity -- Nonmetallic Solids). 2 Laubitz, M.J., 1969. Measurement of the thermal conductivity of solids at high temperatures by using steady-state linear and quasi-linear heat flow. In: R.P. Tye (Ed.), Thermal Conductivity, Vol. 1, pp. 111--183. 3 Healy, J.J., DeGroot, J.J. and Kestin, J., 1976. The theory of the transient hot-wire method for measuring thermal conductivity. Physics, 82C: 392--408. 4 Kestin, J. and Wakeham, W.A., 1978. A contribution to the theory of the transient hotwire technique for thermal conductivity measurements. Physica, 92A: 102--116. 5 Horrocks, J.K. and McLaughlin, E., 1963. Non-steady-state measurements of the thermal conductivities of liquid polyphenyls. Proc. Roy. Soc. London, A273: 259--274. 6 McLaughlin, E. and Pittman, J.F., 1971. Determination of the thermal conductivity of toluene (Parts I and II). Trans. Roy. Soc. London, A270: 557--602. 7 Ziebland, H., 1969. Experimental determination of the thermal conductivity of fluids. In: R.P. Tye (Ed.), Thermal Conductivity, Vol. 2, pp. 65--148. 8 Watkins, J.A., 1970. A general method of determining the thermophysical properties of insulating materials using an extension of the line heat source technique. Master's Thesis, University of Kentucky, Lexington. 9 Birkebak, R.C. and Watkins, J.M., 1971. A general method for determining the thermophysical properties o f insulating materials using an extension of the line heat source technique. Second International Conference on Thermal Conductivity, Albuquerque, NM, September. 10 Gustafsson, S.E., Karawacki, E. and Khan, M.N., 1979. Transient hot-strip method for simultaneously measuring thermal conductivity and thermal diffusivity of solids and fluids. J. Phys. D, Appl. Phys., 12: 1411--1421. 11 Filipov, L.P., 1966. Methods o f simultaneous measurement of heat conductivity, heat capacity and thermal diffusivity of solid and liquid metals at high temperatures. Int. J. Heat Mass Transfer, 9 : 681--691. 12 Abdel--Wahed, R.M., Bligh, T.P. and Eckert, E.R.G., 1978. An instrument for measuring the thermal penetration property 'cppk'. Int. J. Heat Mass Transfer, 21 : 967--973. 13 Wechaler, A.E. and Glaser, P.E., 1965. Pressure effects on postulated lunar materials. Icarus, 4: 335--352. 14 Trump, W.M., Leubke, H.W., Fowler, L. and Emery, E.M., 1977. Rapid measurement of liquid thermal conductivity by the transient hot-wire method. Rev. Sci. Instrum., 48(1): 47--51. 15 DeGroot, J.J., Kestin, T. and Sookiazian, H., 1974. Instrument to measure the thermal conductivity of gases. Physica, 75: 454--582.

252 16 Cremers, C.J., 1971. A thermal conductivity cell for powdered samples. Rev. Sci. Instrum., 42 : 1694--1696. 17 Crane, R.A. and Vachon, R.I., 1977. A prediction of the bounds on the effective thermal conductivity of granular materials. Int. J. Heat Mass Transfer, 20: 711--723. 18 Debbas, S. and Rumph, H., 1966. On the randomness of beds packed with spheres or irregular shaped particles. Chem. Eng. Sci., 21 : 582--607. 19 Akhtar, M.W., 1981. Thermo-physical properties of coal using line heat source method. Master's Thesis, University of Kentucky, Lexington, KY. 20 Hahn, O.J., Wesley, D.P., Swisshelm, B.A., Maples, S. and Withrow, J., 1979. A mass and energy balance of a Wellman--Galusha gasifier. Fuel Processing Technology, 2 : 1--16. 21 Singer, J.M. and Tye, R.P., 1979. Thermal, mechanical, and physical properties of selected bituminous coal and cokes. U.S. Bur. Min., Rep. Invest., R.I. 8364.