Influence of pressure on the combustion rate of carbon

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 3085–3094

INFLUENCE OF PRESSURE ON THE COMBUSTION RATE OF CARBON ROBERT H. ESSENHIGH Department of Mechanical Engineering The Ohio State University Columbus, OH 43210, USA ANN M. MESCHER Assistant Professor of Mechanical Engineering Department of Mechanical Engineering University of Washington Seattle, WA 98195, USA

The influence of pressure on the combustion rates of carbon (or coal) particles is shown, by comparison of prediction with experiment, to be zero to minor in the temperature range studied. This result is contrary to the empirical (nth order) assumption widely adopted in much of the literature that predicts a substantial pressure dependence at all temperatures. Two models were used in the comparison, and the results were compared with three independent experimental sets of data. These experiments were measurements of burning times of single coal particles by Tidona [19] at 1, 1.5, and 2 atm; reaction rates of char particles by Monson et al. [15] at 1, 5, 10, and 15 atm; and (noncritical) ignition temperatures of coal particles in the pressure range 0.4–1.7 atm [20]. The first model was based on the fundamental Langmuir–Nusselt– Thiele suite of theoretical equations in the form of the extended resistance equation (ERE) [35]. The second model combined the Nusselt BLD analysis with the empirical nth order assumption that the reaction rate at all temperatures is proportional to the nth power of the partial pressure of the oxygen concentration (pnox) [2,3]. The ERE model was able to predict the structural form of the experimental results with adequate prediction of numerical values, particularly of the reaction rates measured by Monson et al. In particular, the ERE predictions and experiments jointly showed small to no dependency of the rates on pressure, contrary to the predictions of the empirical model. We conclude that the empirical model has no experimental support for the assumptions made and that fundamentally based equations can be developed or already exist that can be used to predict carbon combustion reaction rates at elevated or reduced pressure with acceptable confidence.

Introduction The influence of pressure on the combustion rates of carbons and coals is a significant fundamental and practical problem that has been a subject of analysis and investigation for several decades. The history of carbon reaction studies [1–3], however, shows a clear dichotomy with regard to the reaction rate equations used and, specifically, their representation of the dependence on pressure, which is the central issue in this paper. The dichotomy turns, particularly, on whether the reaction mechanism is a two-step or one-step process where the two-step model has been developed from fundamental concepts but the onestep assumption is empirical. We set these positions in context by a brief summary of the key elements of the alternate models available. Fundamental studies originating with Rhead and Wheeler [4] and Langmuir [5] focused initially on experimentally based [4] two-step phenomenologi-

cal models [5] and, specifically, an adsorption-desorption process on presumed active sites. Only the adsorption step is identified as pressure-dependent so that the pressure dependence of the overall reaction is a function of the relative magnitudes of the two steps and, thus, of temperature. In a 1981 review [1] of then-available experimental sources on effect of pressure, including combustion of coal in diesel engines, gas turbines, and shock tubes, the balance of the evidence essentially supported a marginal pressure dependence, if any, indicating on this model the dominance of the desorption step for the relevant range of experimental conditions. We show substantially the same result in this paper. In support of the phenomenological assumptions, mechanistic (ab initio) models [6,7,8] likewise imply or use this two-step process, generally stated in terms of pressure-dependent molecular orbital analyses for the chemisorption process and pressure-independent electron binding-transfer processes for

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COAL AND CHAR COMBUSTION TABLE 1 Summary (comparison) of experimental conditions and objectives

Ref. No.

Author(s)

[19]

Tidona

[15]

Monson et al.

[20]

(this work)

Experimental objective measurement of particle burning times measurement of specific reaction rates measurement of ignition temperatures

the desorption or film decomposition step; the last has been given particular study in connection with catalytic behavior [9]. Statistical models of the poretree, random pore, or fractal type [10–13] generally can use any statement of a rate expression or equation considered appropriate but do not directly address the problem at issue here. In recent studies [2,3,14,15], however, the most commonly used approach to describe the reaction rate has been use of a single-term empirical equation, implicitly representing a one-step mechanism, although this has long been known to be at variance with experiment. Pressure is included explicitly in this equation as a power index of the oxygen partial pressure, pnox (the nth order rate expression). As such, it predicts a primary dependence on pressure at all temperatures. The source for this expression most usually cited is Frank-Kamenetskii [16], and a recent review by Smoot [3] identifies nearly a score of flame models using the expression. As an empirical equation, the nth order expression can only curve fit. Nevertheless, the coefficients obtained are generally represented as rate parameters, although typically such parameters have been shown to vary from one experimental condition to another [14,17] so that their value in prediction and extrapolation is well-known to be problematic. Smoot and Fletcher [18] make the point with particular emphasis, stating that the nth order expression is “coal specific, and inappropriate for extrapolative use.” This clearly defines the problem at issue. Likewise, Monson et al. [15] specifically question “whether a more fundamental rate expression . . . (can) better describe the total pressure effects.” This observation alone provides a prime reason for examination of the theoretical position to provide a fundamental basis in place of the acknowledged empiricism. Thus, our objective in this paper is to examine options for theoretical prediction, based on available fundamental developments, with experimental verification from three different sources in support. Two of those sources are data published by others [15,19]; the third is data we reported in conference recently [20] and now present here in publication.

Temperature range: 8C

diameter lm

pressure range: atm

2200–3000

100–300

1, 1.5, 2

1300–2200

70

400–600

350–600

1–15 0.4–1.7

These three suites of experiments, as shown in Table 1, differ markedly in method of experiment, particle size, temperature range, and experimental objective. However, as we will show, they all support the position advanced here, developed from the fundamental theory that the pressure dependence of the reaction rate can be formulated in fundamental terms. This shows a variation from independence of the absolute pressure at lower temperatures to a minor dependence for small particles at high temperature. Experimental Tidona Experiments Tidona [19] measured burning times of particles as a function of diameter at three different pressures. Using the same techniques and procedures employed by Ubhayakar and Williams [21], selected particles of coal were injected into quiescent oxygen environments at room temperature and ignited with a ruby laser (consequently, they were burning in cold surroundings). Both absolute pressure and oxygen mass fractions were varied, with experimental data values reported for oxygen partial pressures of 1, 1.5, and 2 atm and oxygen mass fractions of 0.7–1. Particle sizes ranged from 100 to 300 lm. Combustion times were determined by high-speed cinemicrography and two-color optical pyrometry. The temperature records showed that after an initial temperature jump to stable combustion, the temperatures then remained substantially constant until extinction or final burnout with values in the range 2500–3300 K. The photographic records also indicated swelling of the particles by factors up to 2 at about the moment of ignition; this is consistent with other results [22]. In analysis of the data, Tidona reported that the combustion was controlled by boundary-layer diffusion (BLD) and that, as shown in Fig. 1, the burnout times varied, as expected, with the square of the initial diameter, in accordance with the standard

CARBON COMBUSTION UNDER PRESSURE

Fig. 1. Tidona Data [19]. Variation of burning time (tb) with square of initial diameter (d2o ), as predicted by Eq. [10] (Nusselt equation) for coal particles burning at 1, 1.5, and 2 atm; and showing independence of burning constant (slope of line, KD) with pressure as predicted by Eq. (10). Experimental and predicted values of KD are in agreement at 200 s/cm2 (for values of standard deviations, see text).

Fig. 2. Monson et al. Data [15]. Arrhenius plot of specific reaction rate (variation of log [rate] versus reciprocal temperature) for 70-lm char particles reacting at pressures of 1, 5, 10, and 15 atm compared with predictions (lines) from Eq. (10). Measurements and predictions show minor influence of pressure on reaction rate at the higher temperatures, partially modified by decreasing reaction penetration factor (e) with increasing pressure.

Nusselt theory [23] as summarized later. Figure 1 is constructed from the reported [19] results; they show no significant influence on the burning times caused by change in pressure. Monson et al. Experiments Monson et al. [15] measured combustion rates of coal chars in an electrically heated drop tube reactor of generally standard design inside a pressure container. The capabilities included operation at pres-

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sures of 1–15 atm, temperatures of 700–14008C, and particle residence times of 30–1000 ms. A modified Sandia particle imaging system [24] was used to obtain simultaneous measurements of particle velocity, temperature, and diameter. Partially reacted char residue was collected by sampling and used to determine burn off (from tracer analysis). A substantial body of results is reported in the paper; the results of relevance to our purpose here were those for data on the variation of specific reactivity (in g/cm2 • s) with temperature, as shown in Fig. 2, and change in density with burn off. Figure 2 is a replot of their rate data with our independently calculated prediction lines included, using the theoretical procedure described later. This Work Ignition temperatures of captive coal particles in a size range similar to that of Tidona were measured by attaching the particles to thermocouples and burning them between two small electrically heated coils. Earlier work at normal pressures using this method of experiment concentrated on the study of burning times, mostly for coal particles at normal, vitiated, and elevated oxygen concentrations [25,26] and for CWF drops [27]. Unique to these experiments was the enclosure of the equipment in the pressure container and the focus on measurement of ignition temperatures by measuring the temperature variation with time (T-t signal) under noncritical ignition conditions and determining the ignition temperature as the point of inflection (POI) of the T-t curve during heat up [28,29]. The POI was obtained by differentiation of a fourth-order curve fit to the experimental T-t curves. The general procedure is outlined in Ref. 28 and has been most completely developed and described by Fu and Zeng [29]. The experimental system used is illustrated in Fig. 3. The heating system consists of two plane, horizontal wire resistance coils of 1 inch diameter spaced 1/2 inch apart and heated electrically. The particles are cemented to fine thermocouples and positioned between the two coils. The carrying fibers are attached to a rotor so that up to four particles can be rotated into position sequentially after successive burnout. The whole device is enclosed in a sealed container that allows a fourfold variation in pressure (from 0.4 to 1.7 atm) and is pierced by the electrical leads to heat the coils and by the TC leads for the T-t signal. As the particles heat up and ignite, the time-dependent TC output passes through an A/D converter and is recorded in PC (Lotus) files. The temperature range in the experiments was determined by the range of ignition temperatures (Tig) found experimentally from the POIs of the T-t curves, as illustrated in Fig. 4. As can be seen from this plot, there is no evident influence of pressure.

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COAL AND CHAR COMBUSTION

chemical reaction of the oxygen at the external or internal surface of the particle; as identified in the Introduction, this can be represented as either a two-step or one-step process. Regarding the prediction of the different rate processes, there is a substantial amount of common quantitative agreement regarding the BLD process. There is also qualitative agreement that there can be joint external surface and/or internal reaction, with agreement further that the quantitative basis for determining the (physical) in-diffusion to the interior is provided by the Thiele analysis [30]. This is true even though in many boiler model programs the internal burning is stated [3,18] to be accounted for only implicitly and nonmechanistically. Fig. 3. This Work. Schematic (plan view) of particleignition device showing heating coils and hub carrying four particles on TCs and indicating connections for power supply to coils and for data acquisition (passed to A/D converter and into Lotus files).

BLD Equation For the diffusion of oxygen in nitrogen through the boundary layer of a reacting carbon particle to form a mixture of CO and CO2 at the particle surface, the standard form DE for the transport of the oxygen is [31] gox 4 1(qDox) • (dyox/dr) ` vyox

(1)

and the solution for the oxygen supply rate to the surface of a spherical particle, 1gsox, is 1gsox 4 k*D(y`ox 1 ysox) ` 4 (1 ` f) • C • (qDox/a) • (yox 1 ysox)

(2)

Diffusion Rate Kinetics

Fig. 4. This Work. Variation of (noncritical) ignition temperature (Tig) with pressure showing lack of dependence of ignition temperature on pressure in agreement with Eq. (14). Bars are 1 SD on 8 measurements per point.

Translation of the oxygen molar diffusion rate to the carbon surface, (1gsox ), into mass of carbon removed per unit area transforms Eq. (2) into the specific reaction rate, Rs [32,33]: ` Rs 4 kD • (yox 1 ysox) 4 1r • (da/dt)

(3)

Theory

kD 4 (1 ` f ) • C • (q0 • Doox/a) • (T/T0)0.7

(4)

The equations of concern for this study are those governing the combustion of a spherical particle of carbon or coal in oxygen-enriched or vitiated air with variation of absolute pressure. The standard primary description of the behavior is a two-stage physicalchemical process. Stage 1 is the physical in-diffusion of reacting oxygen to the particle surface through any inert component and against out-diffusing reaction products (the Nusselt boundary layer or BLD diffusion process), sometimes with continuing diffusion to the interior of the particle. Stage 2 is the

The influence of pressure (P) on the diffusion rate depends only on the group (q0Doox). Since Doox (molar basis) is inversely proportional to pressure [31,34] and density is proportional to pressure, the product, (qD), is then independent of total pressure over the pressure range involved in these experiments. Consequently, in BLD-controlled reactions such as Tidona’s experiments, no influence of pressure is predicted. This BLD analysis is essentially common to all approaches. The differences in viewpoint with regard to the dependence of the rate equations on pressure thus focus on the treatment of the gas–solid rate kinetics.

Choice of Model

with

CARBON COMBUSTION UNDER PRESSURE

Gas–Solid Rate Kinetics The alternatives for the gas–solid chemical rate kinetics differ principally in the use of: (1) a two-step reaction based on fundamental considerations, and (2) the one-step reaction adopted on an empirical basis. 1. The two-step fundamental rate expression most fully developed, and best supported experimentally, is the Langmuir [5] adsorption-desorption model (for discussion of alternatives, see Refs. 1 and 33). For nondissociative adsorption with internal reaction governed by Thiele kinetics, the modified Langmuir is obtained [33,35,36]: 1/Rs 4 (1/eka • yox) ` (1/ekd)

(5)

where e 4 1 ` a/3 and a is the power index for the variation of density with diameter during reaction (r/ro) 4 (d/do)a [35]. It is also potentially predictable by a range of expressions depending on the zone in which the reaction takes place [36]. 2. The one-step nth order reaction rate expression most consistently used by the empiricists, as cited by Monson et al. and others [2,3,14,15,17] has the form Rs 4 k • pnox 4 k • Pn • ynox

(6)

where k is a proportionality constant commonly identified as a (single-step) velocity constant. The power index, n, is an empirical parameter that is either specified arbitrarily or obtained from the experimental results under analysis. The effect of internal reaction is not included in this expression (see Eq. [5]); it is evidently introduced by inspection [18].

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Pressure Dependencies The dependencies for the specified velocity constants are as follows: 1. No dependencies. (a) The diffusion velocity constant, kD, given by Eq. (4), is pressure independent, as shown previously by equation development. (b) The desorption velocity constant, kd, is pressure independent by specification. 2. Dependency. The adsorption velocity constant, ka, is given by the following [33]: ka 4 (3/8)(qoPo/2 • p)1/2 • (P/Po) (9) • (T/To)1/2 • exp(1Ea/RT) showing a first-order dependency. 3. Unspecified. The pressure dependency of the empirical velocity constant, k, in Eq. (8) cannot be specified ab initio. It is arbitrarily specified, as noted, by formulation as the nth-order expression, as given in the Introduction and in Eq. (8). Numerical values of the pressure dependency (index n) have to be assumed or determined by experiment. Results and Data Evaluation Tidona Data A summary evaluation of Tidona’s data is provided in his original paper [19]. What we add here in summary is the equation derivation used (not given in his paper). Accepting Tidona’s position that the particles were burning at the diffusion limit, the relevant rate equation is Eq. (3) with ysox 4 0. The solution is standard [25,32] and is most commonly written in the Nusselt square-law form [23] for the variation of time as a function of diameter, d. In the burnout limit, tb, for an initial diameter, do, this gives: tb 4 KD • do2

(10)

Combined Kinetics

where

The complete rate equations obtained after combination of diffusion and reaction have the alternate forms:

(11) KD 4 ro/[8 • (1 ` f ) • C • (qD) • y`ox] Figure 1 is a replot of Tidona’s data according to Eq. (10). The three lines are least-squares regressions through the origin for the three pressures (respectively 1, 1.5, and 2 atm), after data check using small-number-statistics considerations [37], with corresponding KD values 217, 226, and 192 (s/cm2) with SDs of 16, 10, and 12. The mean KD value is 212, which is within 1 or 2 SDs of the individual values and is within 1 SD of the (mean) value of 206 given by Tidona. It is also within 1 SD of the (approximate) value of 200 calculated from Eq. (11). For the calculation, parameter values used were ro 4 1.43 g/cm3, qo 4 1.29 2 1013 g/cm3; Do 4 0.18 cm2/s; f 4 1; C 4 1; y`ox 4 0.21; and the calculation included corrections for density reduction by volatiles loss (for VM 4 39%); swelling (by a factor up to 2); temperature correction in the boundary layer to allow for cold ambient in the determination of qD;

a. The extended resistance equation [35] based on the fundamental derivations 1/Rs 4 (1/kD • yox) ` (1/e • ka • yox) ` (1/e • kd)

(7)

b. The empirical formulation [1,2,15,16] Rs 4 k • [pox • (1 1 Rs/Rs,m)]n

(8)

In this expression, it may be noted that the value of Rs requires solution of a (1/n)th-order expression. Frank-Kamenetskii [16] describes a graphical method for this. Many investigators using this expression do not appear to use a root extraction procedure.

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COAL AND CHAR COMBUSTION TABLE 2 Rate Coefficients for Figure 2

This work: Two-step (Langmuir-type) reaction: All curves: Common parameters at all pressures

Second Thiele Factor Values

koa 4 0.435 g/cm2 • s kod 4 4.5 g/cm2 • s Ea 4 7500 cal/mol Ed 4 24,000 cal/mol

P(atm) e

1 3.6

5 2.5

10 2.0

15 1.8

Monson et al.[15]: One-step (empirical basis) reaction: “Rate” parameters change with pressure P(atm) 1 ko (g/cm2 • s) E(cal/mol)

1.78 14,800

and correction for very high ambient oxygen concentration (0.7–1 mass fraction), which requires use of 1ln(1 1 y`ox) in place of y`ox [26]. The value of KD calculated before correction was about 100 (s/ cm2) and, with the corrections, was approximately doubled in essential agreement with the experimental value. In evaluating the corrections, the density reduction by VM loss (reducing ro and hence KD by approximately 2) and swelling (increasing KD by about 4) were the two largest and accounted, overall, for a doubling (approximately) in the initially calculated value. Therefore, what these results show is that the functional form of the diameter-squared relation is supported by experiment; the numerical value of the burning constant obtained experimentally is in agreement, within expected error, with the calculated value; and the experimental values of KD are substantially independent of absolute pressure, in agreement with prediction. Ignition Data (this work) Determination of ignition temperatures under noncritical conditions depends on determining the point of inflection (POI) in the temperature–time (T-t) curve (at [d2T/dt2] 4 0) rather than the (nominal) plateau (at [dT/dt] 4 0). This is a variant of the Semenov TET analysis applied to ignition of particles as reviewed elsewhere [38]. The noncritical criterion was proposed in an earlier paper [28] and studied in detail by Fu and Zeng [29]. For a particle of mass m, specific heat c, and temperature T, the net rate of heat supply Q, to the particle as it heats up is the difference between the rate of heat released by the reaction, QG, and the rate of loss to the ambient, QL, thus m • c • (dT/dt) 4 Q 4 QG 1 QL

(12)

5

10

15

0.0382 3400

0.0227 3800

0.0098 4900

Solution of this equation yields a sigmoid T-t curve; and, in noncritical ignition theory, ignition occurs at the point of inflection, corresponding to the Taffanel and le Floch condition that dQ/dT 4 0. However, the van’t Hoff condition (Q 4 0) does not hold (see Ref. 38). Using Eq. (6) as a diagnostic approximation to Eq. (5), Eq. (12), after differentiation to obtain the point of inflection, becomes, in dimensionless form [38,29], d2h/ds2 4 df/ds 4 [[exp(11/h)]/h2i 1 1/Kd] • f 4 0

(13)

Using the Cassel and Liebmann [39] power approximation for the Arrhenius group, exp(11/h) 4 B • hb; Eq. (13) becomes, after substitution and expansion, 2 4 1/BKd 4 (2/Bd) • (k/k h yn ) hb1 i o c ox

(14)

Eq. (14) shows dependence of ignition temperature (hi) on diameter and oxygen mole fraction [yox] but not on pressure; the prediction of lack of dependence on pressure is supported by the experimental results shown in Fig. 4. Monson et al. Data Evaluation of these data requires the use of a complete rate equation, either Eq. (7) or Eq. (8). Evaluation in terms of Eq. (8) was performed by Monson et al. with the indicative result that the fairly compact data band shown in Fig. 2 was “exploded,” with a data range of more than an order of magnitude at any given temperature, and requiring markedly different values of ko and E (listed in Table 2), for the same chars for curve-fitting lines at the four different pressures. This clearly shows the inadequacy of the empirical nth-order curve fit and the need for an alternate approach.

CARBON COMBUSTION UNDER PRESSURE

Fig. 5. Monson et al. Data [15]. Comparison of experimental (Monson data points) with calculated (this work, lines) reaction rates for the 70-lm char particles reacting at pressures of 1, 5, 10, and 15 atm.

The alternative advanced here, of the use of Eq. (7), is illustrated in the predictions shown in Fig. 2. In this figure, the same values for the reactivity parameters, koa, Ea, kod, and Ed, based essentially on literature values [1,33,35,40] and listed in Table 2, were used for all the curves. There is a small dependence on pressure that is due to the adsorption term (Eq. [9]), modified, as we will examine, by the reaction penetration factor e. The values used for e were obtained from the experimental density/diameter data reported by Monson et al. [5] for the four pressures (Table 2). The values used for the BLD parameters were in general those used in the Tidona calculations, but the BLD influence is minor to trivial in any event for the Monson experimental conditions. The accuracy of the calculations was also checked by plotting the experimental values against the calculated values, as shown in Fig. 5. The line shown as the regression for all the data values, with omission of four outliners from the calculation based on Ref. 37, has a slope of 1.00 (exactly the theoretical value) with a SD of 0.03. The lines for the four pressure sets (1, 5, 10, and 15 atm), calculated individually, had slopes of 0.93 5 0.04, 1.04 5 0.08, 1.07 5 0.06, and 1.12 5 0.05. Adjacent lines are within 1 SD of each other, and are within 1 to 2 SDs of the theoretical value of unity. Any residual trend caused by pressure is considered marginal. Within the noise of the measurements, Fig. 2 shows no evident trend in the experimental data with pressure. The computed lines apparently show some minor influence, but with the trends strongly influenced at a second order of magnitude by the reaction penetration factor e, as noted previously. The three higher pressures show marginal differences that are well within the noise of the experimental data. At the lower temperatures, the lowest (1 atm) pressure line is seen to predict rates greater than at

3091

the higher pressures, with a reversal upon moving to the higher temperatures. This crossing of the lines is due to the differences in the values of e. If the same value of e is used, all the lines converge to a common trend line at the lowest temperatures, governed almost totally by the desorption term. As the temperature increases, the concave downward trend develops, and the lines diverge (at a second order of significance for this particle size) because of the differences in pressure. We reemphasize, however, the second-order level of any pressure influence in the experimental range of concern. With increasing temperature, extrapolation shows that the influence of pressure becomes more marked but remains substantially secondary. Conclusions The conclusions to be drawn from evaluation of these three suites of experiments would thus seem to be clear-cut. Where reaction is controlled by diffusion, as in Tidona’s experiments, or by desorption, as in our ignition experiments, the prediction that reaction is independent of pressure is clearly supported. In the case of Monson’s experiments, the situation is a little more complex but in accordance with the predictive equations and still showing relatively little influence of pressure. For those experiments, the prediction is that for a common degree of reaction penetration—value of e—a degree of pressure sensitivity is to be expected. As seen in Fig. 2, the experimental results show little or no pressure sensitivity caused by the differences in reaction penetration, e, as measured experimentally. The further, more general conclusions, are that for temperatures below about 10008C, the reaction is controlled mainly by the chemical desorption parameter and a linear fit on the Arrhenius plot is possible. However, for temperatures above 10008C, the Arrhenius line is clearly curved as a result of the increasing importance of the adsorption term with increasing temperature; thus, the rate data on an Arrhenius plot cannot be represented adequately or accurately by a linear fit to the data, contrary to the implications of Eq. (8). Additionally, the commonality of the data as shown by Fig. 2 is partly a consequence of the differences in reaction penetration (e) at different pressures. These results show that the equations developed from the available fundamental theories of reaction are evidently adequate for accurate interpretation and/or prediction of carbon reaction rates. Accordingly, we see no further reason to continue the use of the empirical relations such as the nth-order expression other than for diagnostic purposes. It would appear appropriate, instead, to give proper critical attention to the fundamental theoretical developments that are already available on this point in the relevant literature.

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COAL AND CHAR COMBUSTION

Nomenclature a d Dox Ea Ed f gox hc k*D kD ka kd k n pox P QG QL r Rs t T Ts Tg v yox a e r q k

particle radius particle diameter oxygen diffusion coefficient adsorption activation energy desorption activation energy reaction mechanism factor (f 4 1 for CO2 formation; f 4 2 for CO formation) mass rate of flux of oxygen through boundary layer enthalpy of reaction diffusion velocity constant for oxygen supply to surface diffusion velocity constant in term of mass removal rate of carbon from surface adsorption velocity constant: 4 koa, exp(1Ea/ RT) desorption velocity constant: 4 kod, exp(1Ed/ RT) empirical velocity constant: 4 ko • exp(1E/ RT) empirical reaction order oxygen particle pressure total pressure heat released by reaction in TET analysis heat lost from reaction system in TET analysis radius specific reaction rate at particle surface (mass removal rate of carbon per unit area) time temperature surface (particle) temperature ambient gas temperature Stefan flow velocity oxygen mole fraction concentration power index in density/diameter relation: (r/ ro) 4 (d/do)a reaction penetration factor: 4 (1 ` a/3) solid (particle) density ambient gas density thermal conductivity Acknowledgments

It is with great pleasure that we acknowledge provision by Dr. Monson of a disk containing complete data records reported in his paper (Ref. 15).

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CARBON COMBUSTION UNDER PRESSURE

22. 23. 24.

25. 26. 27.

28.

29. 30.

Soc. 123:747–756 (1974); Combust. Flame 26:23–34 (1976). Essenhigh, R. H. and Yorke, G. C., Fuel 44:177–186 (1965). Nusselt, W., V.D.I. 68:124 (1924). Tichenor, D. A., Mitchell, R. E., Henken, K. R., and Niksa, S., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, pp. 1213–1221. Essenhigh, R. H., J. Engineering Power, 85:183–188 (1965). Beeston, G. and Essenhigh, R. H., J. Phys. Chem. 67:1349–1355 (1963). Zghoul, A. M. and Essenhigh, R. H., Proc. 2nd Annual Pittsburgh Coal Conference, University Pittsburgh and DOE-PETC, September 1985, pp. 658–665. Chen, M. R., Fan, I. S., and Essenhigh, R. H., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, pp. 1925– 1932. Fu, W. B. and Zeng, T. F., Combust. Flame 88:413–424 (1992). Thiele, E. W., Ind. Eng. Chem. 31:916–920 (1939).

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31. Bird, R. W., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena, Wiley, New York, 1960. 32. Field, M. A., Gill, D. W., Morgan, B. B., and Hawksley, P. G. W: Combustion of Pulverised Coal, The British Coal Utilization Research Association, Leatherhead, 1967. 33. Essenhigh, R. H., Energy Fuels 5:41–46 (1991). 34. Reid, R. C., Prausnitz, J. M., and Poling, B. E., The Properties of Gases and Liquids, McGraw Hill, New York, 1987. 35. Essenhigh, R. H., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 89–96. 36. Essenhigh, R. H., Combust. Flame 99:269–279 (1994). 37. Dean, R. B. and Dixon, W. J., “Simplified Statistics for Small Numbers of Observations,” Anal. Chem. 23(4):636–638 (1951). 38. Essenhigh, R. H., Misra, M. K., and Shaw, D. W., Combust. Flame 77:3–30 (1989). 39. Cassel, H. M. and Liebmann, I., Combust. Flame 3:167 (1959). 40. Essenhigh, R. H. and Misra, M. K., Energy Fuels 4:171–177 (1990).

COMMENTS Thomas H. Fletcher, Brigham Young University, USA. You mentioned that rate coefficients were taken from the literature. How did you deal with effects of coal type? Was it only in the “second” effectiveness factor, or were the A and E values adjusted? Author’s Reply. No coal type factor was involved since the rate coefficients were only required for the Monson et al. [1] data and in that paper there was only one char. For the A and E values used in the predictions, our basis for selection was the auto-correlation plot given elsewhere [2] between ln(A) and E. This reduces the two variables, A and E, to substantively one for a given reaction. There was some adjustment of the paired values, but within the limits defined by auto-correlation plots. At this time, there would appear to be no evident coal type (rank) effect on the E (or A) values, that is to say, on the chemical components of reactivity, at least at the level of engineering measurement or use. Burn-out can be faster if the char formed is more open and there is easier access to the particle interior—determined by the Second Effectiveness factor. The apparent influence of coal rank would appear to depend less on chemical properties and more on physical conditions such as heating rate. This is not to say that some influence of coal type may not be determined in the future but this will require in our view more complete/reliable experimental measurements (such as joint measurements of both rates and density changes, as in the Monson experiments) coupled with more complete analysis of the experimental results. This will have to be repeated for a range of coals under different

char forming conditions to create a reliable data pool to determine the influence of coal type. To our knowledge, this data base does not yet exist, and the best evidence at this time is that coal rank is of minor importance.

REFERENCES 1. Monson, C. R., Germane, G. J., Blackbam, A. U., and Smoot, L. D., Combust. Flame 100:669–683 (1995). 2. Essenhigh, R. H. and Misra, M. K., Energy Fuels 4:171–177 (1990). ● L. Douglas Smoot, Brigham Young University, USA. This analysis shows declining influence of adsorption with rising pressure with little influence of pressure dependent adsorption. Results of the previous paper in this session [1] that adsorption was the dominant suggested kinetic rate control with desorption being negligible. Is there a straightforward explanation for this observe difference?

REFERENCE 1. Croiset, E., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 3095–3102.

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Author’s Reply. The observation that the pressure-dependent adsorption has small influence on the overall reaction rate is essentially true except at the lowest (1 atm) pressure (where the influence is between first and second order). The conditions of the previous paper [1] that the reaction was adsorption dominated suggests a conclusion that could be dependent on sufficient differences in the experimental method. One critical difference in the relative velocity between sample particle and gas stream where the particles in the Monson’s [2] experiments were essentially travelling with the gas stream, but in [1] paper there was a relative velocity of 0.2 m/sec (20 cm/sec). If the boundary layer is sufficiently reduced by this then it seems to me that the conclusions of that paper must follow, if the Langmuir is, indeed, applicable. If Dr. Smoot is drawing attention to the need to start a comparative critical review of both potential rate equations and the relevant contents involved, I would totally agree and I would support such an initiative. I believe it is long overdue. REFERENCES 1. Croiset, E., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 3095–3102. 2. Monson, C. R., Germane, G. J., Blackham, A. U., and Smoot, L. D., Combust. Flame 100:669–683 (1995). ● Eric Suuberg, Brown University, USA. The literature on intrinsic carbon oxidation kinetics shows very few examples of simple integer O2 reaction order (e.g., Ref. 1 of this paper, or Suuberg et al. [1]). Few results support zero order. There is little doubt, as concluded in this paper, that observed orders are determined by complicated reaction sequences. It was earlier observed [1] that gasification of a

char at 623 K gave an order with respect to O2 of 2/3, whereas O2 chemisorption (on the same char) at lower temperature was first order. Moreover, the 2/3 order observed during gasification was constant over 3 orders of magnitude O2 pressure, apparently ruling out use of the simple Langmuir model proposed here (since it cannot predict a constant fractional order over this wide a pressure range). Thus it appears that there is still an unresolved question as to a suitable explanation for the empirical nthorder rate expression. REFERENCE 1. Suuberg, E. M., Wojtuwicz, M., and Calo, J. W., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 79–87. Author’s Reply. This does raise a point that needs much more experimental attention. The original literature following Langmuir does provide some data. A recent examination/test of the Langmuir is given in Ref. 33 of the paper but more tests are badly needed. Regarding Dr. Suuberg’s observation [1] that he reported a Pox 2/3 this also supports the need for more careful direct investigation of the Langmuir—and of the other rate expressions that are available in the literature (Temkui, etc.) In particular, the dissociative Langmuir could be the better description of Dr. Suuberg data, and I think this should be explored, along with the other possible candidates. My basic position is that: data I have examined do generally support the Langmuir, where this can be tested; the Langmuir has a theoretical basic: the nth order (power Frendlich) does not. If then the Langmuir is found the most generally supported, then we still should focus on development of an alternative equation, but based on fundamentals, rather than revert to unsound empiricism.