Experiments and Computational Modeling of Pulverized-Coal Ignition SEMI-ANNUAL. Reporting Period Start Date: 04/01/1998 End Date: 09/30/1998

Transcription

1 Exeriments and Comutational Modeling of Pulverized-Coal Ignition SEMI-ANNUAL Reorting Period Start Date: 04/01/1998 End Date: 09/30/1998 Authors: John C. Chen Samuel Owusu-Ofori" Reort Issue Date: 10/31/1998 DE-FG22-96PC North Carolina A&T State University Deartment of Mechanical Engineering 1601 East Market Street Greensboro, NC 27411

2 Disclaimer This reort was reared as an account of work sonsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their emloyees, makes any warranty, exressed or imlied, or assumes any legal liability or resonsibility for the accuracy, comleteness, or usefulness of any information, aaratus, roduct, or rocess disclosed, or reresents that its use would not infringe rivately owned rights. Reference herein to any secific commercial roduct, rocess, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imly its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and oinions of authors exressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 1

3 Abstract Under tyical conditions of ulverized-coal combustion, which is characterized by fine articles heated at very high rates, there is currently a lack of certainty regarding the ignition mechanism of bituminous and lower rank coals. It is unclear whether ignition occurs first at the article-oxygen interface (heterogeneous ignition) or if it occurs in the gas hase due to ignition of the devolatilization roducts (homogeneous ignition). Furthermore, there have been no revious studies aimed at determining the deendence of the ignition mechanism on variations in exerimental conditions, such as article size, oxygen concentration, and heating rate. Finally, there is a need to imrove current mathematical models of ignition to realistically and accurately deict the article-to-article variations that exist within a coal samle. Such a model is needed to extract useful reaction arameters from ignition studies, and to interret ignition data in a more meaningful way. We roose to examine fundamental asects of coal ignition through (1) exeriments to determine the ignition mechanism of various coals by direct observation, and (2) modeling of the ignition rocess to derive rate constants and to rovide a more insightful interretation of data from ignition exeriments. We roose to use a novel laser-based ignition exeriment to achieve our objectives. The heating source will be a ulsed, carbon-dioxide (CO 2 ) laser in which both the ulse energy and ulse duration are indeendently variable, allowing for a wide range of heating rates and article temeratures both of which are decouled from each other and from the article size. This level of control over the exerimental conditions is truly novel in ignition and combustion exeriments. Laser-ignition exeriments also offer the distinct advantage of easy otical access to the articles because of the absence of a furnace or radiating walls, and thus ermit direct observation and article temerature measurement. The ignition mechanism of different coals under various exerimental conditions can therefore be easily determined by direct observation with high-seed hotograhy. The ignition rate-constants, when the ignition occurs heterogeneously, and the article heating rates will both be determined from analyses based on direct, article-temerature measurements using two-color yrometry. For the modeling ortion of this study we will comlete the develoment of the Distributed Activation Energy Model of Ignition (DAEMI), which simulates the conventional dro-tube furnace ignition exeriment. The DAEMI accounts for article-to-article variations in reactivity 2

4 by having a single reexonential factor and a Gaussian distribution of activation energies among the articles. Previous results show that the model catures the key exerimental observations, and that adjustments to the model arameters ermit a good fit to exerimental data. We will comlete the model by (1) examining the effects of other variations in hysical arameters on the model, (2) alying the model to ublished results in order to extract reaction arameters, and (3) extending the model for alication to laser-based ignition studies, such as our own. Table of Contents Disclaimer...1 Abstract...2 Table of Contents...3 Executive Summary...3 Introduction...4 Objectives...4 Results from This Reorting Period and Discussion...5 Personnel...5 Comutational Model...5 Exeriment...6 Meetings and Conferences...6 Goals for Next Quarter...6 Aendix A...7 Executive Summary During the ast reorting eriod, modifications to the DAEMI were comleted. The changes were imlemented to examine two asects of ignition modeling: (1) the effect of varying the number of articles chosen to interact with the laser, and (2) the size distribution for article sizes. We have also comleted making initial measurements of the ignition temeratures of a suite of coals at three oxygen concentrations, and for three article size ranges. The reduction of this data from raw signals to temeratures has begun, and we exect it to be comleted during the next reorting eriod. 3

5 Introduction The ignition of ulverized coal has been the subject of research for nearly 150 years, with the initial motivation being the avoidance of coal-dust exlosions in mines. In more recent times, due to the world s increased reliance on coal for ower generation and the need to maximize energyconversion efficiency, research has shifted to understanding the fundamental mechanism of coal ignition and measuring its kinetic rates. The imortance of ignition to coal-flame stability is obvious the more easily a articular coal ignites after injection into a boiler furnace, the better its flamestability characteristics. A less obvious ramification of the ignition rocess is its role in establishing extended, fuel-rich zones in coal flames which are resonsible for the destruction of NOx and its conversion to benign N 2. Certainly, the ignition rocess is inextricably linked to the formation of this NOx-reduction zone, and the ignition behavior of coals and coal blends will strongly affect the ease and extent of formation of this zone. This connection is deserving of further study and its understanding is the goal toward which we hoe to aly the results of this roosed study. Secifically, we roose to examine fundamental asects of coal ignition through (1) exeriments to elucidate the ignition behavior of coals, and (2) modeling of the rocess to derive accurate and useful rate constants, and to rovide a more insightful interretation of data from ignition exeriments. Objectives Our objectives for this roject are to: 1. develo a novel exerimental facility with extensive otical-diagnostic caabilities to study coal ignition; 2. determine the ignition mechanism of coals under simulated combustion conditions by direct observation with high-seed hotograhy; 3. examine the effects of various exerimental conditions, including coal rank, article size, oxygen concentration and heating rate, on the ignition mechanism; and 4. measure the ignition rate constants of various coals. 5. modify our existing ignition model to examine the effect of article-size distribution on the ignition behavior; 6. incororate, if necessary, a size distribution into the model; 7. aly the model to extract ignition rate constants from reviously ublished data from conventional exeriments; 4

6 8. modify the model and aly it to our laser-based ignition studies for determination of ignition rate constants. Results from This Reorting Period and Discussion During the ast reorting eriod, we have made excellent rogress on model develoment for this roject. We are nearing comletion of two manuscrits for submission and ossible ublication. The first, The Ignition Behavior of Pulverized Coals, concerns mainly the exerimental measurements that we have obtained, and interrets these measurements in terms of the model in its current form. The second manuscrit, Modeling the Ignition of Pulverized Coals, will focus on the current modifications to the Distributed Activation Energy Model of Ignition (DAEMI) which we are in the rocess of imlementing, along with some suorting exerimental measurements. Personnel The MS-candidate student working on the exeriment ortion of this roject, Ms. Vida Agyeman, has taken maternity leave as of late Setember. She has recovered and is back to attend classes. We exect that she will return to full time work on this roject by the end of this calendar year. The MS-candidate working on the modeling ortion of this roject, Ms. Jianing Zheng, has comleted her thesis and will be defending it on November 13, A ortion of her draft thesis, comleted on October 22, 1998, is included as an aendix to this reort, and forms the bulk of the work comleted during the ast reorting eriod. Finally, Professor John Chen, the Project Director for this roject, has resigned his osition at North Carolina A&T State University, and is currently an Associate Professor of Mechanical Engineering at Rowan University, effective August Professor Chen will continue to consult on this roject, which has been transferred to Dr. Samuel Owusu-Ofori, Professor of Mechanical Engineering at North Carolina A&T State University. Comutational Model A ortion of Ms. Jianing Zheng s MS thesis, titled Modeling the Ignition Behavior of Pulverized Coals, is included as Aendix A of this reort. The two sections included are Model Analysis and Results, and Discussion. 5

7 Exeriment During the ast reorting eriod we have comleted the measurement of ignition temeratures for a suite of four coals (Pittsburgh #8 high-volatile bituminous, Pocahontas lowvolatile bituminous, Wyodak subbituminous, and Pust lignite) at three oxygen concentrations, and for two or three article size ranges. The data reduction is currently underway to convert the raw signal measurements to temeratures. We exect this to be comleted during the next reorting eriod. The comlete set of data will be used as inuts to the modified Distributed Activation Energy Model of Ignition (DAEMI). Meetings and Conferences A aer describing the results contained in this reort was reared and submitted to the 1999 Combustion Institute Joint US National Meeting, to be held in March 1999 in Washington, DC. At the Sring 1998 American Chemical Society National Meeting, we resented a aer describing our research. This aer, co-authored by John Chen, Maurice Richardson, and Jianing Zheng, won the Richard A. Glenn Award, the Fuel Chemistry Division s Best Paer Award. Goals for Next Quarter During the next reorting eriod, we will comlete the data reduction for the temerature measurements made during this summer. The data will form the basis for further model develoment using the DAEMI. 6

8 Aendix A MODEL ANALYSIS AND RESULTS 3.1 Introduction Exeriment Laser Ignition Exeriment The exerimental setu consists of a wind tunnel, gas flow system, coal feeder, detector, laser gate, ulse generators laser and Otical system. Figure 3.1 shows a schematic of the laser ignition exeriment. Sieve-sized coal articles are droed batch-wise into a laminar uward-flow wind tunnel with quartz test section (5cm square cross-section). The gas is not reheated, The gas flow rate was set so that the articles emerged from the feeder tube, fell aroximately 5 cm, then turned and traveled uward out of the tunnel. This ensured that the articles were moving slowly downward at the ignition oint, chosen to be 2 cm below the feeder-tube exit. A single ulse from a Nd:YAG laser was focused through the rest section, then defocused after exiting the test section, and two sides in this manner achieved more satial uniformity and allowed for higher energy inut than a single laser ass. For nearly every case, one to three articles were articles were contained in the volume formed by the two intersecting beams, as determined by revious observation with high-seed video. The laser oerated at 10 Hz and emitted a nearly collimated beam (6 mm diameter) in the near-infrared (1.06 µm wavelength). The laser ulse duration was 100 µs and the ulse energy was fixed at 830 mj er ulse, with ulse-to-ulse energy fluctuations of less than 3%. The laser ulse energy delivered to the test section was varied by a olarizer laced outside of the laser head, variation from 150 to 750 mj was achieved by rotating 7

9 the olarizer. Increases in the laser ulse energy result in heating of the coal articles to higher temeratures. At the ignition oint the beam diameter normal to its roagation direction was 3 mm on each ass of the beam. An air-iston-driven laser gate (see Fig. 3.1) ermitted the assage of a single ulse to the test section. The system allowed for control of the delay time between the firing of feeder and he assage of the laser ulse. Finally, ignition or non-ignition was determined by examining the signal generated by a highseed silicon hotodiode connected to a digital oscilloscoe. Figure 3.2 resents tyical signal traces from the hotodetector for both ignition and non-ignition events. Features of the trace for the ignition case is similar to that described reviously. Particle temerature was measured by two-wavelength yrometry. A simle lens couled to an otical fiber bundle collected light emitted by the igniting articles. The outut from the fiber bundle is collimated and searated into two beams via a dichroic filter. Light of wavelengths below 0.75 µm (the dichroic filter s cut-off wavelength) was assed through a bandass interference filtered centered at 0.7 µm with a otical bandwidth of 40 nm. The remaining light was assed through an interference filter centered at 0.9 µm with an otical bandwidth of 10 nm. Searate high-seed silicon hotodiodes detected each beam following the otical filters. The yrometer was calibrated using a 2-mm diameter blackbody source at 990 o C. 8

10 laser beam laser gate focusing lens rism beam dum quartz test section lens otical fiber detector / amlifier O 2 /N 2 defocusing oscilloscoe flow conditioning section O 2 /N 2 Figure 3.1 Schematic of the laser ignition exeriment 0.08 (b) Detector Signal, V Time, ms 9

11 (b) Detector Signal, V Time, ms Figure 3.2 Signal traces from hotodetectors showing (a) non-ignition and (b) ignition events for the Pittsburgh #8 bituminous coal. Particle size was µm, and oxygen concentration was 100%. The short-lived sike in both traces result from laser heating of the coal surface and subsequent cooling. Ignition and combustion of the coals causes the long-lived emission of (b). 10

12 Figure 3.3 Tyical data from a conventional ignition exeriment showing the relation between ignition frequency (or robability) and gas temerature for a bituminous coal. Data extracted from Ref Ignition frequency (%) Laser energy (mj) Figure 3.4 Tyical data from our laser ignition exeriment showing the relation between ignition frequency and laser energy for bituminous coal. 11

13 Figure 3.5 Distribution of Activation Energy as a Gaussian Distribution Figure 3.6 Distribution of coal article size as a To-Hat Distribution 12

14 3.1.2 Dro-Tube Exeriment by T. F. Wall s Grou [4] The ignition exeriments were carried out using a ulse ignition technique. Metered flows of O 2 and N 2 were assed through an electrically heated tubular furnace at a rate of 500ml/min (s.t..). A small quantity of samle was contained in a glass funnel with a caillary stem. By gently taing the funnel with an electric vibrator, a ulse of fuel ( mg or 1170 article for 75-90µm size coal) was droed into the furnace through a water-cooled robe. A hotomultilier was used to detect the occurrence of ignition, which was indicated by the visual flash of an igniting article. The furnace was maintained at a fixed temerature. Ten to twenty ulses of fuel were injected, and the number of ulses for which ignition resonses were detected was noted on a chart recorder. Figure 3.3 give tyical results of ignition resonse versus furnace gas temerature and indicate a temerature range over which the ercentage of ulses resulting in observed ignition flashes increases from 0 to Model Formulation Figure 3.4 show tyical data obtained from our ignition exeriment conducted by varying the laser energy while holding oxygen concentration, article size and tye of coal. Fig. 3.4 and Fig. 3.3 show that ignition frequency increases aroximately linearly with lus laser energy or gas temerature, and these are inconsistent with the heterogeneous ignition theory reviously described. If all articles of a coal samle used in an exeriment have the same reactivity, that is if they are described by a common Arrhenius rate constant as in Eq. (2.7), then the data would show an ignition frequency of 0% until the critical laser energy corresonding to that at the critical ignition condition is reached. At any laser energy or gas temerature above critical ignition condition, the ignition frequency would be

15 One of the reasons why ignition frequency increases gradually with increasing laser energy or gas temerature is obvious: Within any coal samle, there exists a distribution of reactivity among the articles. Thus, in the laser ignition exeriment, in which a batch of erhas articles of a samle is droed into the furnace, there is the robability (or frequency) that at least one article has a reactivity that meets or exceeds the critical ignition condition set forth in equations (2.1) and (2.2) as the laser energy is increased. This is the ideal of DAEMI [10]. Of course, there exist other variations among the articles within a samle, such as article size and secific heat. Variation in size alone could account for the observed increase in ignition frequency with the laser energy ulse (or gas temerature) [1,4,5,8]. It cannot account for other exerimental observation, namely, the variation in the sloe of the ignition frequency with oxygen concentration. A distribution in secific heat would only affect the rate at which a article attains its equilibrium temerature, but would not change the value or the reactivity. Perhas other variations could cause the observed behavior of ignition frequency. It is our remise that the distribution in reactivity and article size dominates all other variations. We roose to add the distribution of article size into the DAEMI. 3.3 Simulation Procedure Fig.3.5 shows the distribution of activation energy versus frequency for a samle for which E 0 =58 kj mol -1 and σ=5.5 kj mol -1. The intervals of activated energy is 1kJ mol -1 ( E=1kJ mol -1 ). The Distributed Activated Energy Model of Ignition (DAEMI) simulates our laser ignite and dro-tube exeriment by allowing for the articles within the coal samle to have a distribution of reactivity (Chater 2.3). We first calculate the robability of articles for being in each of the intervals. 14

16 The distributed of article size model of ignition assumes that in a small range of article size, the distribution of article size is To-Hat distribution (Fig 3.6). The interval of article size is 1µm ( D= m). Particle sizes are groued into three. These are to 125.0µm, 125 to 150µm, to 180.0µm resectively Base Case Now, the heat generated by a sherical carbon article undergoing oxidation on its external surface is given by the kinetic exression: Q gen S = H x c n o2 E A 0 ex RT (3.1) Similarly, the heat loss from the surface of a article at temerature T is the sum of losses due to convection and radiation. Thus, heat loss from the surface is given as: Q S loss 4 4 ( T T ) = hs( T Tg ) + εσ bs g (3.2) For the convection-loss term, we assume that the Nusselt number equals 2, as is aroriate for very small articles, which leads to h = 2k g / d. Q S loss 2k g 4 4 = S( T Tg ) + εσ bs( T Tg ) (3.3) d At the critical ignition condition, Q = Q, we obtain gen loss E = RT 2k d ln g 4 4 ( T T ) + εσ ( T T ) H g c x n o2 A 0 b g (3.4) where the required arameters for this equation were calculated as follows: 15

17 For base case of the model, we assumed that T was obtained from the equilibrated temerature calculations by use of a linear regression to regress T as a function of laser energy (see aendix 1). For examle, for 70µm.116µm and 165µm coal article the temerature are given as functions of laser energy as [19] T = Elaser (116 µ m) (3.5) T µ E (3.6) ( 70 m) = laser + T µ E (3.7) ( 165 m) = laser + For variable article size, we use interalation mathematics method define: ( T T )( d 116e 6) (70µ m) (116 µ m) T + T(116 µ m) = d <116µm (3.8) (70 116) 1 e 6 ( T T )( d 116e 6) (165 µ m) (116 µ m) T + T(116 µ m) = d >116µm (3.9) ( ) 1 e 6 k g the gas thermal conductivity in the boundary layer around a heated article was given by a linear fit to the conductivity of air [11]. T + 5 Tg k = g (3.10) 2 H c is defined by the equation [16] H c y 1 = H ' C, CO + H ' C, CO (3.11) 2 y + 1 y + 1 It is well known that the roduct of carbon oxidation is both CO and CO 2, H C, CO ' and H ' C, CO2 are the heats of combustion corresonding to the following oxidation reaction [11]. 16

18 1 C + O 2 C + O 2 2 CO; H ' CO ; H ' 2 C, CO C, CO2 = 9,210 = 32,790 kj kgc kj kgc (3.12) Where y = molco molco = 59.95ex T (3.13) ε, the emissivity of coal articles was taken as 0.8. n, the reaction order was taken as 1. χ o2 was chosen to be 1.0 corresonding to a 100% oxygen concentration. For each laser energy, twenty runs were made to obtain ignition-frequency distributions laser Ignition Exeriment When we were using this version of DAEMI to fit the laser ignition exeriment. The exeriment data of T was reading directly from data files (see aendix 3). Then to calculate average temerature (T avg ) and standard deviation (T σ ), base on Normal Distribution, T avg T = (N is the number of T ) (3.14) N 2 ( T Tavg ) Tσ = (3.15) N 1 to obtain the range of temerature, namely, T avg -2T σ < T < T avg +2T σ, by randomly choosing article temerature from the range to obtain critical energy at each condition. In this exeriment, in which a batch with several hundred articles are droed in to the test section, and only a few are heated by the laser ulse. There is an increasing robability (or frequency) as the laser energy is increased that at least one of the heated articles is reactive 17

19 enough to ignition under the given conditions. For nearly every case, one to three articles are hit in the test section by two intersecting laser beams. This is determined by observations with highseed video. For simulation, thirteen hundred articles are then selected randomly as they feed into the test section and two articles are further selected randomly from these 1300 to be hit by the laser ulse, keeing in mind that no article can be selected twice. For randomly selected two articles with article size and activation energy. Substituting reexonential factor (A 0 ), mean of Gaussian distribution of activation energy (E 0 ), standard deviation of Gaussian distribution (σ) and reaction order (n) in Eq. (3.4), E can be calculated as the critical (or threshold) activation energy that a article may have and still ignite under the given conditions. The result (E) is comared with the activation energy. If the result (E) is greater than the activation energy among the articles that were hit, then the article is considered ignited. At each set of oerating conditions (coal tye and size, oxygen concentration, and laser energy), 20 attemts at ignition are made in order to get the ignition frequency, or robability, which is the arameter sought from these studies. We comare this simulated ignition frequency with the exerimental results over a range of laser ulse energy Dro-Tube Exeriment In simulating the dro-tube ignition exeriment, we assumed that 10 6 article are in the initial batch. A batch of 1170 articles of a samle is droed into the furnace in each simulation of an exerimental run. No article can be selected more than once. Whether or not ignition occurs for a run is determined by the article in the batch of 1170 with the lowest activation energy. Now, using Eq. (3.1) and Eq. (3.3) we can obtain the heat generated Q gen and Q loss. In order to determine the critical ignition temerature of the article, T, and critical activation 18

20 energy, E, the critical ignition condition, Q gen = Q loss, and dq gen dq = loss are solved dt dt simultaneously. Q gen and Q loss are given in Eqs. (3.1) and (3.3), and lead to the following derivatives with resect to temerature: dq dt gen ex E E A0 RT RT n = SH c xo2 2 (3.16) dq dt loss 2k g 3 = S + 4εσ bst (3.17) d Note that the neglection of the T deendence in k g introduces a small error in Eq. (3.15). Following dq gen dq = loss, we set Eq. (3.14) equal to Eq. (3.15) and solve for the dt dt quantity E/RT : E RT = 2k H d c g x n o2 T + 4εσ T b 4 E A0 ex RT (3.18) The denominator is recognized to be Q gen /S Eq. (3.1), which by Q gen = Q loss is also Q loss /S Eq. (3.2). Thus Eq. (3.16) can be rewritten as: E RT = 2k d g ( T 2k d g T + 4εσ T g T ) + εσ b b ( T 4 4 T 4 g ) (3.19) This relation for E/RT is substituted into the exression Q gen -Q loss = 0 to obtain a function, F, which is a function of T only: 19

21 F( T = H x c ) = Q gen Q loss ex 2k d 2k 2k d g 4 T 4εσ bt d n g o A 2 0 g b g = g 4 4 ( T Tg ) + εσ b ( T Tg ) 4 4 ( T T ) εσ ( T T ) 0 (3.20) The reasonable root of F (T ) corresonds to the critical ignition temerature of the article, and substitution of this value into Eq. (3.19) roduces the critical activation energy at the critical ignition condition. k g, the gas thermal conductivity in the boundary layer around a heated article was given by Eq. (3.10). χ o2 was chosen to be 0.5 corresonding to a 50% oxygen concentration. ε, the emissivity of coal article was taken as 0.8. H c was defined by the equation from (3.11) to (3.13). Substituting all the required values in Eq. (3.4), E obtain the result as the critical (or maximum) activation energy that a article may have and still ignite under the given conditions. By randomly choosing each article with activation energy for a run, then get the article in the batch of 1170 with the lowest activation energy. we comared the result (E) with the lowest activation energy. If the result (E) is greater than the lowest activation energy among the article that was heated in a run, The article was ignited. 3.3 Modeling Results Results of the Base Case of the Model 20

22 Figure 3.7 and Fig. 3.8 shows the effect of oxygen concentration and number of article (M) on ignition frequency for article size range of µm and µm, resectively. It can be seen that at each oxygen concentration, ignition frequency increases monotonically over the range of laser ulse energy. Below this range, the ignition frequency is zero, and above this range the result is 100% ignition frequency. As the number of article (M) is increased from 1 to 300, the frequency distribution shifts to lower laser energy values. This behavior is due to the fact that, within any coal samle, there exists a distribution of reactivity among the articles. As the oxygen concentration is decreased from 100% to 67%, the frequency distribution shifts to higher laser energies or equivalently, higher article temeratures, as exected. This is consistent with the ignition theory since at decreased oxygen concentration, higher temeratures are necessary for heat generation by the articles (due to chemical reactions) to exceed heat loss from the articles and lead to ignition. The shift in distribution can be viewed in two ways: for a fixed laser ulse energy, a decrease in oxygen concentration leads to a decrease in the ignition frequency, all else being equal; Second, a decrease in oxygen concentration imlies that a higher laser ulse energy is needed, in order to achieve the same ignition frequency. Figure 3.9 and Fig show the same effect of Distribution Particle Size in µm and average article size (165µm) on ignition frequency for oxygen concentration of 100% and 67%. Fig.3.11 and Fig.3.12 also show that the same effect of distribution article size in µm and average article size (115µm) on ignition frequency for 100% and 67% of O 2. 21

23 Ignition frequency (%) M=300, 67% oxygen M=50, 67% oxygen M=10, 67% oxygen M=3, 67% oxygen M=1, 67% oxygen M=300, 100% oxygen M=50, 100% oxygen M=10, 100% oxygen M=3, 100% oxygen M=1, 100% oxygen Linear (M=300, 67% Laser energy (mj) Figure 3.7 Modeling results showing the effect of M (numbers of articles were ignited at one dro time) and oxygen concentration on ignition frequency. (a) Solid-line exress 67% oxygen concentration (x o2 =67%); (b) Dash-line exress 100% oxygen concentration (x o2 =100%). Particle size is µm, and all other arameters are as listed in Table

24 M=300, 67% oxygen M=50, 67% oxygen M=10, 67% oxygen M=3, 67% oxygen Ignition frequency (%) M=1, 67% oxygen M=300, 100% oxygen M=50, 100% oxygen M=10, 100% oxygen M=3, 100% oxygen M=1, 100% oxygen Linear (M=300, 67% oxygen) Laser energy (mj) Figure 3.8 Modeling results showing the effect of M (numbers of articles were ignited at one dro time) on ignition frequency. (a) Solid-line exress 67% oxygen concentration (x o2 =67%); (b) Dash-line exress 100% oxygen concentration (x o2 =100%). Particle size is µm, and all other arameters are as listed in Table

25 Table 3.1 Parameters Used in the Base Case of the Model of Laser Ignition Exeriment Variable Value E 0 A 0 σ n ε 58 kj/mol 250 kg/m 2 s 5.5 KJ/mol

26 Particle size: 165 and um, oxygen concentration: 100% Ignition frequency (%) M=3,d=165um M=10,d=165um M=10, d= um M=3,d= um Linear (M=3,d=165um) Linear (M=10,d=165um) Linear (M=10, d= um Linear (M=3,d= um) Laser energy (mj) Figure 3.9 Modeling results showing the effect of average article size 165µm and the range of article size µm in ignition frequency. Oxygen concentration is 100%. All other arameters are as listed in Table 3.1. (a) Solid-line exress article size d =165µm; (b) Dash-line exress distribution article size D in µm. 27

27 Praticle size:165 and (um), Oxygen concentration: 67% Ignition frequency (%) M=10,d=165um M=3,d=165um M=10,d= um M=3,d= um Linear (M=10,d=165um) Linear (M=3,d=165um) Linear (M=10,d= um) Linear (M=3,d= um) laser energy (mj) Figure 3.10 Modeling results showing the effect of the average article size 165µm and the range of article size µm on ignition frequency. Oxygen concentration is 67%. All other arameters are as listed in Table 3.1. (a) Solid-line exress article size d =165µm; (b) Dash-line exress distribution article size d in µm. 28

28 Particle size: 116 and um, Oxygen concentration: 100% Ignition frequency (%) M=3,d=116um M=10,d= um M=3,d= um M=10,d=116um Linear (M=3,d=116um) Linear (M=10,d= um) Linear (M=3,d= um) Linear (M=10,d=116um) Laser energy (mj) 29

29 Figure 3.11 Modeling results showing the effect of average article size 116 µm and the range of article size µm in ignition frequency. Oxygen concentration is 100%. All other arameters are as listed in Table 3.1. (a) Solid-line exress article size d =116µm; (b) Dash-line exress the distribution of article size d in µm. 30

30 Praticle size : 116 and um, Oxygen concentration: 67% Ignition frequency (%) M=3,d=116um M=10,d=116um M=3,d= um M=10,d= um Linear (M=3,d=116um) Linear (M=10,d=116um) Linear (M=3,d= um) Linear (M=10,d= um) Laser energy (mj) Figure 3.12 Modeling results showing the effect of the average article size 116 µm and the range of article size µm on ignition frequency. Oxygen concentration is 67%. All other arameters are as listed in Table 3.1. (a) Solid-line exress article size d =116µm; (b) Dash-line exress distribution article size d in µm. 31

31 3.3.2 Results of Simulation Laser Ignition Exeriment The simulations for the exeriments were erformed via a FORTRAN code (Aendix 3). The code was designed to roduce frequency distribution data for a given article size (diameter, d) range, oxygen concentration and, temerature of article and laser ulse energy. As discussed earlier, for each run two articles are selected randomly from 1300 articles. The article size and activation energy are determined whether or not ignition occurred for the run. For each tye coal, the arameters required as inut are the average activation energy (E 0 ), standard deviation for the Gaussian distribution (σ), and re-exonential factor (A 0 ). Figure show the exeriment data for the Pittsburgh #8 coal with modeling results using anther method, that calculate average temerature and standard deviation to obtain the range of article temerature at each condition. Figure show the exeriment data for the Pust coal with the modeling results using the range of article temerature. Figure 3.18 shows the exeriment data for the Wyodak coal with the modeling results using the range of article temerature. The behavior of the model with resect to changes in each of the arameters was first observed. The arameters are then modified to obtain a final set of values to imrove the model. The final arameters that fit our laser ignition exerimental data of each tye coal are given the following table. Table 3.2 shows all Pittsburgh#8 coal s arameters of Figure There are all Pust coal s arameters of Figure in Table 3.3. There are all Wyodak coal s arameters of Figure 3.18 in Table

32 Pittisburgh#8 coal, Particle size: um Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxygen Data ex. of 75% oxygen Modeling result of 75% oxygen Linear (Data ex. of 100% oxygen Linear (Data ex. of 75% oxygen) Figure 3.13 Simulation results of our laser exeriment for article size (d 35 ) µm Pittiburgh#8 coal, using the range of the article Laser energy (mj)

33 Pittsburgh#8 coal, Particle size: um 100 Figure temeratures. All other arameters are as listed in Table 3.2 Simulation results of our laser exeriment for article size (d ) µm Pittiburgh#8 coal, using the range of the article temeratures. All other arameters are as listed in Table Ignition frequency (%) Data ex. 0f 100% oxygen Modeling result of 100% oxygen Data ex. of 67% oxygen Modeling result of 67% oxygen Linear (Data ex. 0f 100% oxygen Linear (Data ex. of 67% oxygen) Laser energy (mj)

34 Pittsburgh#8 coal, Partical size: um Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxygen Data ex. of 75% oxygen Modeling result of 75% oxygen Linear (Data ex. of 100% oxygen) Linear (Data ex. of 75% oxygen) Laser energy (mj) Figure 3.15 Simulation results of our laser exeriment for article size (d ) µm Pittiburgh#8 coal, using the range of the article temeratures. All other arameters are as listed in Table

35 Table 3.2 Parameters Simulate Pittsburgh#8 Coal in Laser Ignition Exeriment using the range of measured article temerature Variable Value E 0 A 0 σ n ε 135 kj/mol 250 kg/m 2 s 12 KJ/mol

36 ust coal, Particle size: um Ignition frequency (%) Data ex. of 67% oxygen Modeling result of 76% oxygen Data ex. of 100% oxygen Modeling result of 100% oxygen Linear (Data ex. of 67% oxygen) Linear (Data ex. of 100% oxygen) Laser energy (mj) Figure 3.16 Simulation results of the laser Exeriment for article size (d ) µm Pust coal, using the range of the article temeratures. All other arameters are as listed in table

37 Pust coal, Particle size: um Ignition frequency (%) Data ex. of 67% oxygen Modeling result of 67% oxygen Data ex. of 100% oxygen Modeling result of 100% oxygen Linear (Data ex. of 67% oxygen) Linear (Data ex. of 100% oxygen) Laser energy (mj) Figure 3.17 Simulation results of the laser Exeriment for article size (d ) µm Pust coal, using the range of article temeratures. All other arameters are as listed in table

38 Wyodak coal, Particle size: um Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxygen Data ex. of 67% oxygen Modeling result of 67% oxygen Linear (Data ex. of 67% oxygen) Linear (Data ex. of 100% oxygen) Laser energy (mj) Figure3.18 Simulation results of the laser exeriment for article size µm Wyodak coal, using the range of article temeratures. All other arameters are as listed in table

39 Table 3.3 Parameters Simulate Pust Coal in Laser Ignition Exeriment Variable Value E 0 A 0 σ n ε 120 (kj/mol) 200 (kg/m 2 s) 40 (KJ/mol) Table 3.4 Parameters Simulate Wyodak Coal in Laser Ignition Exeriment Variable Value E 0 A 0 σ n ε 115 (kj/mol) 100 (kg/m 2 s) 40 (KJ/mol) Dro-Tube Exeriment 45

40 The required simulations for dro-tube exeriments have erformed by a FORTRAN code (Aendix 2). The code was designed to roduce frequency distribution data for a given average article size (diameter d) or the maximum diameter (dmax) and minimum diameter (dmin) of article size range, oxygen concentration and, temerature of gas. The article with the lowest activation energy determines whether or not ignition occurred for a run. The arameters required to be inut were average activation energy (E 0 ), standard deviation for the Gaussian distribution (σ), reexonential factor (A 0 ) and reaction order (n). Resectively, Figure show the exeriment data for coal#1 and coal#2 with the modeling results using distribution of article size. There are all arameters of coal#1 and coal#2 for Figure in Table 3.5 and Table 3.6. Figure show the exeriment data for coal#1 and coal#2 with the modeling results by average article size. These arameters of coal#1 and coal#2 for Figure are listed in Table 3.7 and Table

41 Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxygen Data ex. of 50% oxygen Modeling result of 50% oxygen Data ex. of 21% oxygen Modeling result of 21% oxygen Data ex. of 10% oxygen Modeling result of 10% oxygen Laser energy (mj) Figure3.19 Simulate result of dro-tube exeriment [4] for article size 75-90µm coal #1, using distribution article size is incororated into the DAEMI. All other arameters are as listed in Table

42 Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxygen Data ex. of 50% oxygen Modeling result of 50% oxygen Data ex. of 21% oxygen Modeling result of 21% oxygen Data ex. of 10% oxygen Modeling result of 10% oxygen Laser energy (mj) Figure 3.20 Simulation results of dro-tube exeriment [1] for article size µm coal#2, using distribution article size is incororated into the DAEMI. All other arameters are as listed in Table

43 Table 3.5 Parameters Simulate cola#1 in Dro-Tube Exeriment [4] (Using distribution of article size in DAEMI) Variable Value E 0 A 0 σ n ε 70.0 (kj/mol) (kg/m 2 s) 1.0 (KJ/mol) Table 3.6 Parameters Simulate cola#2 in Dro-Tube Exeriment [4] (Using distribution of article size in DAEMI) Variable Value E 0 A 0 σ n ε 71.0 (kj/mol) (kg/m 2 s) 1.0 (KJ/mol)

44 Ignition frequency (%) Data ex. of 21% oxygen Modeling result of 21% oxygen Data ex. of 10% oxygen Modeling result of 10% oxygen Data ex. of 50% oxygen Modeling result of 50% oxygen Data ex. of 100% oxygen Modeling result of 100% oxygen Laser energy (mj) Figure 3.21 Simulation results of dro-tube exeriment [4] for article size 83 µm coal #1. All other arameters are as listed in Table

45 Ignition frequency (%) Data ex. of 100% oxygen Modeling result of 100% oxyge Modeling result of 50% oxygen Data ex. 21% of oxygen Modeling result of 21% oxygen Data ex. of 10% oxygen Modeling result of 10% oxygen Data ex. of 50% oxygen Laser energy (mj) Figure 3.22 Simulation results of dro-tube exeriment [4] for article size 83 µm coal #2. All other arameters are as listed in Table

46 Table 3.7 Parameters Simulate cola#1 in Dro-Tube Exeriment [4], using the average article size. Variable Value E 0 A 0 σ n ε 92 (kj/mol) 110 (kg/m 2 s) 10 (KJ/mol) Table 3.8 Parameters Simulate cola#2 in Dro-Tube Exeriment [4], using average article size. Variable Value E 0 A 0 σ n ε 98.6 (kj/mol) 111 (kg/m 2 s) 12 (KJ/mol)

47 DISCUSSION OF RESULTS 4.1 Comarison with Dro-Tube Exeriment Either the range of article size (75-90µm) or the average article size (83µm) can be used in the current version of DAEMI. The DAEMI can be fitted to the exerimental data [4] shown in Figures Figures also shown the almost same effect of Distribution Particle Size in µm and average article size 83 µm on ignition frequency for oxygen concentration from 10% to 100%. The small standard deviation, σ (1.0 kj/mol) is used to obtain the results from the current version of DAEMI using the distribution of article size and the average article size. The narrow distribution (small standard deviation) leads to a small energy range since most articles have similar activation energies. This behavior is due to the fact that a distribution of reactivity exists among the articles. The article diameters are randomly selected from the range of article size to calculate the critical activation energy. Different article diameters corresond to the different critical activation energies. When the different critical activation energy is larger than the activation energy that a article has, that article is considered ignition. The larger σ ( kj/mol) is used to obtain the modeling results from the old version of DAEMI using the average article size. Since the subsidiary simulation condition is that the article own the lowest activation energy in the batch could be ignited. According to the exeriment henomenon, it is not always true that only the article own the lowest activation energy can be ignited. In Tables , these arameters that were obtain by consider the article in the batch of 1170 articles could has the lowest activation 54

48 energy was ignited, are different with E 0 =84.0 kj/ml, σ=4.0 kj/mol and n=0.4 that Dr. Chen got from the batch of 100 articles before. So the different simulation rocess and exeriment value obtain the different simulation arameter. Figures show the effect of oxygen concentration for both the modeling results and exeriment data: As oxygen level is decreased from 100% to 10%, the frequency distribution shifts to higher laser energies or, equivalently, higher article temeratures. This is consistent with ignition theory since at decreased oxygen levels, higher temeratures are necessary for heat generations (due to chemical reactions) that exceed the heat loss from the articles and leads to ignition. As shown in Tables , whether we used the distribution of article size or the average article size, the modeling result that is obtained by one set of arameters only fits the exeriment data of one tye of coal. The results show clearly that ignition reactivity is strongly deendent on the coal tye. Particle-to-article variation in hysical and/or chemical roerty of the fuel can be accounted for in order to model the ignition data correctly, and to accurately describe the ignition reactivity. In the future research, statistical test should be used to calculate the confidence intervals, according to a secified significance level to decide on the best set of ignition reactivity arameters. According to the exerimental data, for same coal tye, oxygen concentration and article size, ignition frequency increases with increasing gas temerature. This case is similar to the base case, namely, ignition frequency increases with article or gas temerature. So the modeling results fit the Dro-Tube exeriment data [4] of one article size. The simulation gave the best results for the µm coal#1 article using E 0 =

49 kj/mol, σ=1.0 kj/mol, A 0 =300 kg/m 2 s, n=0.5. The model also was found to give the best fit to the µm coal#2 article for E 0 =71.0 kj/mol, σ=1.0 kj/mol, A 0 =320 kg/m 2 s, n=0.5. It is also found that using n=1.0 difficult to fit to the exeriment data [4]. 4.2 Comarison with Laser Exeriment For the laser exeriment, the DAEMI incororated the distribution of article size. The modeling results and the exerimental data are shown in Figures These figures all show the effect of oxygen concentration for both the modeling results and exerimental data at the same article size. As the oxygen level is decreased from 100% to 67%, the frequency distribution shifts to higher laser energies, this henomenon is same as the Dro-Tube exeriment. Using those different exerimental techniques, we could imrove the ignition theory. Figures and Tables indicate that the model could account for article-to-article variations in reactivity by having a single re-exonential factor and a Gaussian distribution of activation energies among the articles within a tye coal (a samle). The simulation gives final result for the Pust coal all over the laser energies considered, the oxygen concentration and article size using E 0 =120.0 kj/mol, σ=40.0 kj/mol, A 0 =200 kg/m 2 s, n=1.0. The modeling results fit the Wyodak coal all over the laser energies, the oxygen concentration and the article size using E 0 =115.0 kj/mol, σ=40.0 kj/mol, A 0 =100 kg/m 2 s, n=1.0. The modeling results also fit the Pittsburgh#8 all over the laser energy, the oxygen concentration and the article size using E 0 =135.0 kj/mol, σ=12.0 kj/mol, A 0 =250 kg/m 2 s, n=

50 The measured article temeratures of Pust and Wyodak coal are lower than the Pittsburgh#8. The simulation result of Pust and Wyodak are better than that of the Pittsburgh#8. The heat generated by a sherical carbon article undergoing oxidation on its external surface, it is determined by the kinetic exression and the oxidant diffusion exression. At the lower range of article temerature, the heat is mainly generated by the kinetic exression; at the higher range of article temerature, the heat is mainly generated by the oxidant diffusion exression. In the current version of DAEMI, the generated heat is considered to be by the kinetic exression. So the simulation result of coal at the lower article temerature is better than that at the higher article temerature. Figure 4.1 shows the measured article temerature of the laser exeriment. According to the DAEMI, the ignition frequency increases with increasing laser energy. The reason could be effect of the distribution of activation energies among the articles within a samle. When the higher laser energy is used, the ignition could haen between the higher and lower activation energy levels, so the ignition frequency at higher laser energy is higher than that at the lower laser energy. For each activation energy, we can calculate the article temerature by the ignition theory, the higher range of article temerature is obtained by the higher laser energy. But the measured article temeratures of the laser exeriment are not like this shown in Figure 4.1. For the base case, Figures also show the same effect of Distribution Particle Size in µm, µm and average article size 116 µm, 165 µm on ignition frequency for oxygen concentration 67% and 100%. For the heterogeneous coal ignition, it is well known that the roduct of carbon oxidation is both CO and CO 2, and the reaction order n is deended on the carbon 57

51 oxidation. The roortion of the roduct CO and CO 2 could assume is different using the different ignition exerimental mechanism. Since the different article temerature was obtained by the different ignition exerimental mechanism [3]. So the reaction order n=0.5 obtained from simulating the Dro-Tube exeriment, n=1.0 obtained from simulating the laser ignition exeriment. 58

52 temerature (a) (b) laser energy laser energy (mj) (c) (d) temerature laser energy laser energy temerature (K) (e) laser energy (mj) Particle temerature (K) (f) laser energy (mj) Figure 4.1 Temerature distribution versus laser energy for Pittsburgh#8 coal. (a) Particle size: µm, O 2 : 100%; (b) Particle size: µm, O 2 : 75%; (c) Particle size: µm, O 2 : 100%; (d) Particle size: µm, O 2 : 67%; (e) Particle size: µm, O 2 : 75%; (f) Particle size: µm, O 2 : 100%. 59

53 Disclaimer This reort was reared as an account of work sonsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their emloyees, makes any warranty, exressed or imlied, or assumes any legal liability or resonsibility for the accuracy, comleteness, or usefulness of any information, aaratus, roduct, or rocess disclosed, or reresents that its use would not infringe rivately owned rights. Reference herein to any secific commercial roduct, rocess, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imly its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and oinions of authors exressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 1