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Some aspects of measurement, interpretation and practical use of results from solid fuel reactivity studies
Energy 26 (2001) 1185–1195 www.elsevier.com/locate/energy
Some aspects of measurement, interpretation and practical use of results from solid fuel reactivity studies Jacek Z˙elkowski
*
Institut fu¨r Energieverfahrenstechnik und Brennstofftechnik, Technische Universita¨t Clausthal, Erzstraße 18, D38678 Clausthal-Zellerfeld, Germany
Abstract The reactivity of solid fuels i.e. fossil fuels, waste fuels and coal processing products is a feature decisive for the reaction rate under various burning conditions and affects both the burn-up factor of the fuel in the furnace and hence also the combustion efficiency, which further influences the usability of the so-called furnace wastes (too high content of underburnts excludes further utilisation), the ability of fuels to create NOx, temperature distribution in the furnace etc. The reactivity of solid fuels is not actually tested on the standardised basis because of the lack of unified definitions of terms, deficiency of a fairly simple laboratory method for the reactivity determination and of a practical method for the interpretation of the test results. A step towards standardisation of the methodology of reactivity tests can be made by using such terms as combustion intensity u [kg/s], surface combustion rate q [kg/m2/s] and chemical reaction rate constant Kkin [kg(C)/m2/s/Pa0,5] together with kinetic constants k and E determining the fuel reactivity. 2001 Published by Elsevier Science Ltd.
1. Introduction One of the characteristics of solid fuel is its ability to react with oxygen under various burning conditions. This feature generally described as “reactivity” affects both the burn-up factor of the fuel in the furnace and thus the further usability of the so-called furnace wastes (too high content of underburnts in ash makes further utilisation impossible), the fuel’s ability to produce NOx, temperature distribution in the furnace, etc. Although very important, the reactivity itself is not a feature of the fuel that is tested in a standardized way as is the case with the net calorific value, moisture content, chemical composition, etc., mostly because of:
* Tel. +49-5323-722526. E-mail address: [email protected] (J. Z˙elkowski).
0360-5442/01/$ - see front matter 2001 Published by Elsevier Science Ltd. PII: S 0 3 6 0 - 5 4 4 2 ( 0 1 ) 0 0 0 7 9 - 2
J. Z˙elkowski / Energy 26 (2001) 1185–1195
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Nomenclature A ash d E f1, f2 K kD ko m mC PD PO2 q qdiff S t T u X a, ß ⌬ r
reaction surface (m2) ash content (kg/kg) grain diameter (m) activation energy (J/mol/K) coefficients chemical reaction rate constant (kg/(m2*s*Pa0,5)) diffusion coefficient (kg(O2)/m2/s/Pa) coefficient of chemical reaction rate constant (kg/(m2*s*Pa0,5)) mass (kg) pure coal mass (kg) passivation parameter partial pressure of oxygen (Pa) surface combustion rate (kg/m2/s) pure coal loss rate as result of diffusion intensity of oxygen to the reaction surface (kg(C)/m2/s) apparent specific reaction surface (m2/kgC) time (s) temperature (K) pure coal mass loss rate (kg(C)/s) burn-up factor (kg/kg) exponentials difference density (kg/m3)
Indexes A C D gas kin o rest roh s
surface pure coal diffusion gas surrounding the reacting surface chemical reaction kinetics initial value burn-up residue initial state (before combustion) apparent value in relation to pure combustible mass
1. lack of explicit definition of terms, 2. lack of fairly simple laboratory method for the determination of the reactivity, 3. lack of practical method for the interpretation of study results.
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This paper is a contribution to the interpretation and the practical use of the research results obtained from the study of solid fuel reactivity.
2. Definitions of terms Close co-operation between the University of Clausthal and the International Foundation for Combustion Research in Ijmuiden (IFRF) has shown, that the comparison of results obtained during reactivity measurements of coals when using various methods [1–6] is only possible when identically defined terms are used as follows: Combustion intensity u [kg(C)/s] is a mass decrement rate of pure coal at any time in the course of combustion process. It depends both on the surface combustion rate “q” and directly on surface size “At” for the surface where the combustion reaction of the element C takes place.
冋册
dmC kg u⫽ ⫽At∗q dt s
(1)
Surface combustion rate “q” [kg/m2/s] is the measure of the decrement of the combustible fuel mass on the unit reaction surface and depends both on chemical reaction rate “qkin” (i.e. on fuel reactivity and combustion conditions and hence on oxygen concentration PO2 [Pa] and temperature T [K] in the combustion space) and on the rate of oxygen diffusion to the reaction surface “qdiff”. From the fact that the surface combustion rate q at any time must be equal to the diffusion rate of the oxygen to the reaction surface “qdyf” and to the chemical reaction rate “qkin” mC qdyf⫽kD∗(PO2(gas)⫺PO2(A))∗ and qkin⫽冑PO2(A)∗Kkin mO2
(2)
the following relationship results
冉
q⫽Kkin∗ PO2(gas)⫺
冊 冋 册
q kD
0,5
kg(C) m2∗s
(3)
Chemical reaction rate constant Kkin is known as the Arhenius equation:
冉 冊冋
E Kkin⫽ko∗exp ⫺ R∗T
kg m ∗s∗Pa0,5 2
册
(4)
that contains two kinetic constants, known as — pre-exponential coefficient ko and — activation energy E Kinetic constants ko and E calculated experimentally define the reactivity of the fuel in question.
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3. Some methods of measurement of solid fuel reactivity There are many methods of measurement of solid fuel reactivity. The most widely used apparatus is the so-called Field’s drop tube. Recently in the University of Clausthal a fixed bed reactor has been developed and tested. The Field’s drop tube (Fig. 1a) consists of an electrically heated, vertically oriented tubular combustion chamber fed with gas. The gas contains an exactly determined concentration of oxygen and is heated up to the chamber temperature. A continuous stream of coal grains (coke) of
Fig. 1.
Drop tube and exemplary measurement results.
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determined size (generally 63–125 µm) is supplied into the chamber. While burning, the coal grains fall down to the bottom of the chamber where they are sucked off and undergo analysis. The burn-up factor is calculated from the ash content in initial grains and partially burn-up grains as
冉 冊
1−ashrest ⌬m C⫽X⫽1⫺ mo 1−ashroh
(5)
While changing the staying time (burn-up path) a burn-up characteristic can be obtained as shown in Fig. 1b. The advantage of this method exists in the clarity of experimental conditions, while its shortcomings are a great degree of laboriousness (separate measurement runs must be carried out for each combustion temperature and each concentration of oxygen), high costs of apparatus, limited grain size and possible measurement error, especially in the case of low ash content of the tested fuel. The fixed bed reactor is shown in Fig. 2. A tested sample of exactly determined mass and granularity (ca. 2 g and d=1.4–2 mm) is put into the container through which a gas at a temperature of ca. 800°C is conveyed. The sample ignites and incinerates under the influence of the gas. The
Fig. 2. Fixed bed reactor — comparison of its size with the drop tube.
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temperature of the sample is measured with three thermocouples. The concentration of oxygen in the sample is determined through mixing the air with nitrogen. A three-way valve installed downwards in the container makes it possible to feed the gas through the sample or to exhaust it into the atmosphere. The reaction in the container can be terminated at any time by freezing the sample with the stream of cold nitrogen. The temperature of the reacting sample is measured in 10 ms intervals and recorded on line. The temperature vs. time curve and the data from the sample analysis are the basis for the calculation of the mass and energy balances for any recorded time interval and thus for the calculation of the mass of the burn-up coal. After termination of the experiment the sample residue is weighed, and the result is compared with the mass calculated from the balances. If the difference is greater than 5% the measurement must be repeated. The advantage of this method is a relatively simple apparatus (Fig. 2b), ability to determine the reactivity of fuel with very small ash content, and the fact, that each measurement takes into account — so to speak automatically — the influence of temperature and oxygen concentration on the burn-up rate. 4. Some methods of practical interpretation of measurement results 4.1. Principle Results of the solid fuel reactivity measurement carried out in Field’s drop tube (constant temperature and constant oxygen concentration) are represented mostly as a change in the burnup factor X,
冋册
mo−m(t) ⌬m kg X⫽ ⫽ mo mo kg
(6)
or a change in combustible mass residue U=1⫺X vs. time. A change of burn-up factor dX/d(depends on the surface combustion rate q and an instantaneous reaction surface A in relation to the initial mass of the sample moC A dX ⫽q∗ ⫽q∗S dt moC
(7)
and thus also on the so-called apparent specific reaction surface S interpreted as an outer surface of the grain in relation to the initial content of elemental C in the grain: S⫽
冋册
A p∗d 2 m2 ⫽ 3 moC p∗d o kg ∗rS 6
(8)
where S [kgC/m3] is the apparent density of combustible mass in the grain. The difficulty related to the exact determination of the surface A where the chemical combustion reaction takes place has two consequences: 앫 First, the reactivity (kinetic constants) of solid fuels is estimated from the combustion characteristics in the first stage of combustion, when the grain surface is nearly equal to the initial surface
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앫 Second, during the interpretation of results, especially when projecting the results onto the further combustion stages, an assumption is generally made, that the reaction takes place on the outer surface of the grains. The determination of the reaction surface A [m2] is a very complex issue because in reality in the initial combustion stages the reaction takes place on the outer surface of the grains and also in grain pores, whereas these surfaces can be partially covered with the ash. Under the influence of temperature the coal grain (coke) can expand, and thus increase the potential reaction surface. As the combustion proceeds the grain surface is covered with ash to an increasing extent, which decreases the effectiveness of the reaction surface. It cannot also be excluded, that the grain “breaks into pieces” in the course of combustion, thus increasing the reaction surface. Generally, there are two approaches to the mathematical description of reaction surface during combustion, namely: 1. the so-called “pseudochemical models” of the combustion process, that assume that the combustion reactions take place on the surface of spherical grains and the surface can change during the combustion, and 2. models of combustion on the porous surface, where the surface is exposed to the combustion, depending on the instantaneous structure of pores, condition of oxygen diffusion etc. The pseudochemical models are generally used in the technical calculations. These models can be differentiated into 앫 pseudochemical model with constant reaction surface, 앫 model with reaction surface decreasing linearly with burn-up factor (IFRF model), and 앫 models with a non-linear change of reaction surface (Smith’s models and (Haas-model). The main principles of these models are described below: 4.1.1. Pseudochemical model with constant surface of reaction This model assumes that the reaction surface is maintained constant within the whole range of combustion: dX ⫽q∗So and X⫽q∗So∗t dt
(9)
This leads to the conclusion that the burn-up factor should increase linearly with time (Fig. 3 curve A). The results of experiments have shown that such a characteristic appears only in the first stage of combustion and the times of full burn-up of grains calculated on the basis of reactivity, i.e. with the pre-exponential coefficient ko and activation energy E as measured in the first stage of combustion do not correspond to the actual combustion times (Fig. 3 curve D). The reason for such a behaviour can be seen in a too simplified model of the reaction surface assumed.
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Fig. 3.
Burn-up factor of coke calculated from various models of reaction surface changes [6].
4.1.2. Model with reaction surface decreasing linearly with the burn-up factor (model IFRF) This approach was proposed by the International Foundation for Combustion Research in Ijmuiden, Holland. This model assumes that the reaction surface A [m2] decreases linearly with the burn-up factor X [kg/kg] dX S(X) ⫽1⫺X that is ⫽q∗So∗(1⫺X) therefore X(t)⫽1⫺exp(⫺q∗So∗t) So dt
(10)
The exponential function reflects much better the change of burn-up factor vs. time (Fig. 3 curve B). Nevertheless this approach adheres to the simplification which says that the specific reaction surface is described by the linear function independent of coke properties and combustion conditions. When calculating the burn-up time according to this model it is very often the case that higher values are obtained than those measured. The differences are especially evident in the middle and last stages of combustion (Fig. 3). 4.1.3. Smith’s models Already in 1972 and later [7,8] Smith proposed to describe the instantaneous change of reaction surface in terms of separately defined change in grain diameter and change of apparent density of combustible mass d⫽d0∗(1⫺X)a and rS(C)⫽rS(C)0∗(1⫺X)b
(11)
From the law of conservation of mass m r∗d 3 ⫽ ⫽(1⫺X)⫽(1⫺X)3∗a∗(1⫺X)b⫽(1⫺X)3a+b mo ro∗d 3o results, that at any moment a relationship exists:
(12)
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1⫺b⫹3∗a or b⫽1⫺3∗a
1193
(13)
and thus: S⫽
6 6 S(X) ⫽ ⇒ ⫽(1⫺X)(2∗a−1) 1−2a d∗rS(C) d0∗rS(C)0∗(1−X) So
(14)
which means in effect, that d(X) ⫽q∗S0∗(1⫺X)2∗a−1 dt
(15)
or: 1
X⫽1⫺[1⫺2∗(a⫺1)∗qo∗So∗t]2∗(1−a)
(16)
It is worth mentioning (Eq. (14)), that the assumption a=0,5 means, that the specific surface stays constant during the whole combustion process (S=So=const.). Smith has further extended his model by assumption, that in the course of combustion only the centrospherical outer part of the grain is activated douter C d⫽ dinn
(17)
and has proved, that the change in the grain diameter and change in density can be described as 1−X d⫽d0∗(1⫺X⫹X∗C3d)0,333i rS⫽rS(0)∗ 1−X+X∗C3d
(18)
4.1.4. Hass model (extended IFFR model) [6] Assuming that the clearly visible decrease of combustion intensity in the last stage of combustion of solid fuels with ash content — as observed during experiments — results from 앫 production of the ash layer on the reacting surface 앫 the change of the reaction surface because of burn-up Haas [6] proposes to include the influence of these factors by introduction of two coefficients to the linear relationship according to IFRF, namely:
冉 冊
1−A S(X) ⫽(1⫺X)∗f1∗f2 where f1⫽ S(0) 1−A0
PD
(19)
The first of these (f1) takes into account, that in the course of combustion the ash content in the grain increases and as a result the active reaction surface is even smaller than So*(1⫺X) (1st model IFRF). The reaction surface decrease factor depends on the fuel “structure” and on the “structure” of the ash layer produced. This last influence incorporates the so-called “neutralisation”
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Fig. 4.
Reaction surface changes calculated from various models.
factor (PD — passivation factor). The second coefficient (f2) represents the differences between the actual reaction surface and the reaction surface assumed as So*(1⫺X). It allows for the influence of the combustion characteristic on the specific reaction surface and takes into account that — at low temperatures the combustion reaction takes place both on the outer surface of the grain and on the pore surface within the grain, whereas — at high temperatures the oxygen concentration on the outer grain surface is so small, that it is hardly sufficient for the combustion on the outer grain surface that decreases as the burnup factor grows. Fig. 4 shows the possible surface changes for the various models. Shots of various cokes under an electronic microscope have shown (Fig. 5), that in the course of combustion the smooth coke grains gain a developed porous surface lying under the outer surface. When — in the surroundings of the grain — there is sufficient quantity of oxygen it can
Fig. 5. Structure and size of grains of the same coke with various burn-up factors (Haas [6]). (A) coke burn-up 0%; (B) coke burn-up 33%, (C) coke burn-up 89%.
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penetrate the porous structure and react with a much greater surface than the outer surface of the grain. While burning, the pores open widely and at some point the grain breaks into pieces und burns afresh while its surface diminishes in size. 5. Summary 1. Determination of solid fuel reactivity should consist of the measurement of the burn-up factor X vs. time and calculation of kinetic constants based on the first phase of burning while taking into account the influence of the temperature and the oxygen concentration in combustion space, oxygen diffusion to the reaction surface and instantaneous size of the reaction surface on the instantaneous surface combustion rate “q”. 2. During the determination of the kinetic constants defining the reactivity of the fuel in question it is always necessary to specify the method of description of the surface changes during combustion. As shown in this paper, a generally recommended way is to use the so called “pseudochemical model” of combustion characteristics, that takes into account, that the combustion reaction occurs on the spherical grain surface changing in the course of combustion progress. 3. Practical experience gathered by the author [4] have shown, that the burn-up calculations for the polydispersive coal dust in big power plant boilers made on the basis of laboratory results from reactivity measurements carried out for a given coal, coincide substantially well with operational results. So the results of fuel reactivity studies carried out for solid fuels and their mixtures are used today as an indicator for initial assessment of coals bound to be burnt in specific furnace equipment.
References [1] Field MA, Gill DW, Morgan BB, Hawskley PGW. Combustion of pulversed coal. Leatherhead: British Coal Utilisation Research Association, 1967. [2] Zelkowski J et al. Kohlecharakterisierung im hinblick auf die verbrennung mahlbarkeit, zundwilligkeit, reaktivitat, verschlackung. 8. DVV-Kolloquium “Kohlenstaub-Aufbereitung: ein Beitrag zur NOx-Minderung” Essen, 8.12.92 VGB-Kraftwerkstechnik 72, 1992. Heft 12; S.1130. ¨ zdemir M, Zelkowski J. New application of the fixed bed reactor to the measurement of coal reactivity under [3] O dynamic combustion conditions. In: Flowers ’97; Florence World Energy Research Symposium. “Clean energy for the new Century”, 30.07–01.08.1997, Florenz. [4] Zehner P, Zelkowski J. Dzialania dle rozzerzenia bazy paliwowej na przykladzie wielkich elektrowni neimieckich heyden i staudinger (Preussenelektra AG). In: VIII Konferencja Kotlowa “Aktualne problemy budowy i eksploatacji kotlo´ w”. Szczyrk, 24–26 listopada 1998r. [5] Haas J. Char Burnot model for atmospheric coal combustion. IFRF Doc. No. 961010, 1996. [6] Haas J. Experimentelle untersuchungen der reaktivitat von kohlenkoks zur modellierung seines verbrennungsverhaltens in staubfeuerunggen. Dissertation TU Clausthal, April 1999. [7] Smith IW, Tyler RJ. Fuel 1972;51:312. [8] Smith IW. The combustion rate of coal char: a review. In: Int. 19th Symp. on Combustion. Pittsburgh: The Comb. Institute, 1978:1045–1065.
Some aspects of measurement, interpretation and practical use of results from solid fuel reactivity studies Jacek Z˙elkowski
*
Institut fu¨r Energieverfahrenstechnik und Brennstofftechnik, Technische Universita¨t Clausthal, Erzstraße 18, D38678 Clausthal-Zellerfeld, Germany
Abstract The reactivity of solid fuels i.e. fossil fuels, waste fuels and coal processing products is a feature decisive for the reaction rate under various burning conditions and affects both the burn-up factor of the fuel in the furnace and hence also the combustion efficiency, which further influences the usability of the so-called furnace wastes (too high content of underburnts excludes further utilisation), the ability of fuels to create NOx, temperature distribution in the furnace etc. The reactivity of solid fuels is not actually tested on the standardised basis because of the lack of unified definitions of terms, deficiency of a fairly simple laboratory method for the reactivity determination and of a practical method for the interpretation of the test results. A step towards standardisation of the methodology of reactivity tests can be made by using such terms as combustion intensity u [kg/s], surface combustion rate q [kg/m2/s] and chemical reaction rate constant Kkin [kg(C)/m2/s/Pa0,5] together with kinetic constants k and E determining the fuel reactivity. 2001 Published by Elsevier Science Ltd.
1. Introduction One of the characteristics of solid fuel is its ability to react with oxygen under various burning conditions. This feature generally described as “reactivity” affects both the burn-up factor of the fuel in the furnace and thus the further usability of the so-called furnace wastes (too high content of underburnts in ash makes further utilisation impossible), the fuel’s ability to produce NOx, temperature distribution in the furnace, etc. Although very important, the reactivity itself is not a feature of the fuel that is tested in a standardized way as is the case with the net calorific value, moisture content, chemical composition, etc., mostly because of:
* Tel. +49-5323-722526. E-mail address: [email protected] (J. Z˙elkowski).
0360-5442/01/$ - see front matter 2001 Published by Elsevier Science Ltd. PII: S 0 3 6 0 - 5 4 4 2 ( 0 1 ) 0 0 0 7 9 - 2
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Nomenclature A ash d E f1, f2 K kD ko m mC PD PO2 q qdiff S t T u X a, ß ⌬ r
reaction surface (m2) ash content (kg/kg) grain diameter (m) activation energy (J/mol/K) coefficients chemical reaction rate constant (kg/(m2*s*Pa0,5)) diffusion coefficient (kg(O2)/m2/s/Pa) coefficient of chemical reaction rate constant (kg/(m2*s*Pa0,5)) mass (kg) pure coal mass (kg) passivation parameter partial pressure of oxygen (Pa) surface combustion rate (kg/m2/s) pure coal loss rate as result of diffusion intensity of oxygen to the reaction surface (kg(C)/m2/s) apparent specific reaction surface (m2/kgC) time (s) temperature (K) pure coal mass loss rate (kg(C)/s) burn-up factor (kg/kg) exponentials difference density (kg/m3)
Indexes A C D gas kin o rest roh s
surface pure coal diffusion gas surrounding the reacting surface chemical reaction kinetics initial value burn-up residue initial state (before combustion) apparent value in relation to pure combustible mass
1. lack of explicit definition of terms, 2. lack of fairly simple laboratory method for the determination of the reactivity, 3. lack of practical method for the interpretation of study results.
J. Z˙ elkowski / Energy 26 (2001) 1185–1195
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This paper is a contribution to the interpretation and the practical use of the research results obtained from the study of solid fuel reactivity.
2. Definitions of terms Close co-operation between the University of Clausthal and the International Foundation for Combustion Research in Ijmuiden (IFRF) has shown, that the comparison of results obtained during reactivity measurements of coals when using various methods [1–6] is only possible when identically defined terms are used as follows: Combustion intensity u [kg(C)/s] is a mass decrement rate of pure coal at any time in the course of combustion process. It depends both on the surface combustion rate “q” and directly on surface size “At” for the surface where the combustion reaction of the element C takes place.
冋册
dmC kg u⫽ ⫽At∗q dt s
(1)
Surface combustion rate “q” [kg/m2/s] is the measure of the decrement of the combustible fuel mass on the unit reaction surface and depends both on chemical reaction rate “qkin” (i.e. on fuel reactivity and combustion conditions and hence on oxygen concentration PO2 [Pa] and temperature T [K] in the combustion space) and on the rate of oxygen diffusion to the reaction surface “qdiff”. From the fact that the surface combustion rate q at any time must be equal to the diffusion rate of the oxygen to the reaction surface “qdyf” and to the chemical reaction rate “qkin” mC qdyf⫽kD∗(PO2(gas)⫺PO2(A))∗ and qkin⫽冑PO2(A)∗Kkin mO2
(2)
the following relationship results
冉
q⫽Kkin∗ PO2(gas)⫺
冊 冋 册
q kD
0,5
kg(C) m2∗s
(3)
Chemical reaction rate constant Kkin is known as the Arhenius equation:
冉 冊冋
E Kkin⫽ko∗exp ⫺ R∗T
kg m ∗s∗Pa0,5 2
册
(4)
that contains two kinetic constants, known as — pre-exponential coefficient ko and — activation energy E Kinetic constants ko and E calculated experimentally define the reactivity of the fuel in question.
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3. Some methods of measurement of solid fuel reactivity There are many methods of measurement of solid fuel reactivity. The most widely used apparatus is the so-called Field’s drop tube. Recently in the University of Clausthal a fixed bed reactor has been developed and tested. The Field’s drop tube (Fig. 1a) consists of an electrically heated, vertically oriented tubular combustion chamber fed with gas. The gas contains an exactly determined concentration of oxygen and is heated up to the chamber temperature. A continuous stream of coal grains (coke) of
Fig. 1.
Drop tube and exemplary measurement results.
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determined size (generally 63–125 µm) is supplied into the chamber. While burning, the coal grains fall down to the bottom of the chamber where they are sucked off and undergo analysis. The burn-up factor is calculated from the ash content in initial grains and partially burn-up grains as
冉 冊
1−ashrest ⌬m C⫽X⫽1⫺ mo 1−ashroh
(5)
While changing the staying time (burn-up path) a burn-up characteristic can be obtained as shown in Fig. 1b. The advantage of this method exists in the clarity of experimental conditions, while its shortcomings are a great degree of laboriousness (separate measurement runs must be carried out for each combustion temperature and each concentration of oxygen), high costs of apparatus, limited grain size and possible measurement error, especially in the case of low ash content of the tested fuel. The fixed bed reactor is shown in Fig. 2. A tested sample of exactly determined mass and granularity (ca. 2 g and d=1.4–2 mm) is put into the container through which a gas at a temperature of ca. 800°C is conveyed. The sample ignites and incinerates under the influence of the gas. The
Fig. 2. Fixed bed reactor — comparison of its size with the drop tube.
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temperature of the sample is measured with three thermocouples. The concentration of oxygen in the sample is determined through mixing the air with nitrogen. A three-way valve installed downwards in the container makes it possible to feed the gas through the sample or to exhaust it into the atmosphere. The reaction in the container can be terminated at any time by freezing the sample with the stream of cold nitrogen. The temperature of the reacting sample is measured in 10 ms intervals and recorded on line. The temperature vs. time curve and the data from the sample analysis are the basis for the calculation of the mass and energy balances for any recorded time interval and thus for the calculation of the mass of the burn-up coal. After termination of the experiment the sample residue is weighed, and the result is compared with the mass calculated from the balances. If the difference is greater than 5% the measurement must be repeated. The advantage of this method is a relatively simple apparatus (Fig. 2b), ability to determine the reactivity of fuel with very small ash content, and the fact, that each measurement takes into account — so to speak automatically — the influence of temperature and oxygen concentration on the burn-up rate. 4. Some methods of practical interpretation of measurement results 4.1. Principle Results of the solid fuel reactivity measurement carried out in Field’s drop tube (constant temperature and constant oxygen concentration) are represented mostly as a change in the burnup factor X,
冋册
mo−m(t) ⌬m kg X⫽ ⫽ mo mo kg
(6)
or a change in combustible mass residue U=1⫺X vs. time. A change of burn-up factor dX/d(depends on the surface combustion rate q and an instantaneous reaction surface A in relation to the initial mass of the sample moC A dX ⫽q∗ ⫽q∗S dt moC
(7)
and thus also on the so-called apparent specific reaction surface S interpreted as an outer surface of the grain in relation to the initial content of elemental C in the grain: S⫽
冋册
A p∗d 2 m2 ⫽ 3 moC p∗d o kg ∗rS 6
(8)
where S [kgC/m3] is the apparent density of combustible mass in the grain. The difficulty related to the exact determination of the surface A where the chemical combustion reaction takes place has two consequences: 앫 First, the reactivity (kinetic constants) of solid fuels is estimated from the combustion characteristics in the first stage of combustion, when the grain surface is nearly equal to the initial surface
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앫 Second, during the interpretation of results, especially when projecting the results onto the further combustion stages, an assumption is generally made, that the reaction takes place on the outer surface of the grains. The determination of the reaction surface A [m2] is a very complex issue because in reality in the initial combustion stages the reaction takes place on the outer surface of the grains and also in grain pores, whereas these surfaces can be partially covered with the ash. Under the influence of temperature the coal grain (coke) can expand, and thus increase the potential reaction surface. As the combustion proceeds the grain surface is covered with ash to an increasing extent, which decreases the effectiveness of the reaction surface. It cannot also be excluded, that the grain “breaks into pieces” in the course of combustion, thus increasing the reaction surface. Generally, there are two approaches to the mathematical description of reaction surface during combustion, namely: 1. the so-called “pseudochemical models” of the combustion process, that assume that the combustion reactions take place on the surface of spherical grains and the surface can change during the combustion, and 2. models of combustion on the porous surface, where the surface is exposed to the combustion, depending on the instantaneous structure of pores, condition of oxygen diffusion etc. The pseudochemical models are generally used in the technical calculations. These models can be differentiated into 앫 pseudochemical model with constant reaction surface, 앫 model with reaction surface decreasing linearly with burn-up factor (IFRF model), and 앫 models with a non-linear change of reaction surface (Smith’s models and (Haas-model). The main principles of these models are described below: 4.1.1. Pseudochemical model with constant surface of reaction This model assumes that the reaction surface is maintained constant within the whole range of combustion: dX ⫽q∗So and X⫽q∗So∗t dt
(9)
This leads to the conclusion that the burn-up factor should increase linearly with time (Fig. 3 curve A). The results of experiments have shown that such a characteristic appears only in the first stage of combustion and the times of full burn-up of grains calculated on the basis of reactivity, i.e. with the pre-exponential coefficient ko and activation energy E as measured in the first stage of combustion do not correspond to the actual combustion times (Fig. 3 curve D). The reason for such a behaviour can be seen in a too simplified model of the reaction surface assumed.
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Fig. 3.
Burn-up factor of coke calculated from various models of reaction surface changes [6].
4.1.2. Model with reaction surface decreasing linearly with the burn-up factor (model IFRF) This approach was proposed by the International Foundation for Combustion Research in Ijmuiden, Holland. This model assumes that the reaction surface A [m2] decreases linearly with the burn-up factor X [kg/kg] dX S(X) ⫽1⫺X that is ⫽q∗So∗(1⫺X) therefore X(t)⫽1⫺exp(⫺q∗So∗t) So dt
(10)
The exponential function reflects much better the change of burn-up factor vs. time (Fig. 3 curve B). Nevertheless this approach adheres to the simplification which says that the specific reaction surface is described by the linear function independent of coke properties and combustion conditions. When calculating the burn-up time according to this model it is very often the case that higher values are obtained than those measured. The differences are especially evident in the middle and last stages of combustion (Fig. 3). 4.1.3. Smith’s models Already in 1972 and later [7,8] Smith proposed to describe the instantaneous change of reaction surface in terms of separately defined change in grain diameter and change of apparent density of combustible mass d⫽d0∗(1⫺X)a and rS(C)⫽rS(C)0∗(1⫺X)b
(11)
From the law of conservation of mass m r∗d 3 ⫽ ⫽(1⫺X)⫽(1⫺X)3∗a∗(1⫺X)b⫽(1⫺X)3a+b mo ro∗d 3o results, that at any moment a relationship exists:
(12)
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1⫺b⫹3∗a or b⫽1⫺3∗a
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(13)
and thus: S⫽
6 6 S(X) ⫽ ⇒ ⫽(1⫺X)(2∗a−1) 1−2a d∗rS(C) d0∗rS(C)0∗(1−X) So
(14)
which means in effect, that d(X) ⫽q∗S0∗(1⫺X)2∗a−1 dt
(15)
or: 1
X⫽1⫺[1⫺2∗(a⫺1)∗qo∗So∗t]2∗(1−a)
(16)
It is worth mentioning (Eq. (14)), that the assumption a=0,5 means, that the specific surface stays constant during the whole combustion process (S=So=const.). Smith has further extended his model by assumption, that in the course of combustion only the centrospherical outer part of the grain is activated douter C d⫽ dinn
(17)
and has proved, that the change in the grain diameter and change in density can be described as 1−X d⫽d0∗(1⫺X⫹X∗C3d)0,333i rS⫽rS(0)∗ 1−X+X∗C3d
(18)
4.1.4. Hass model (extended IFFR model) [6] Assuming that the clearly visible decrease of combustion intensity in the last stage of combustion of solid fuels with ash content — as observed during experiments — results from 앫 production of the ash layer on the reacting surface 앫 the change of the reaction surface because of burn-up Haas [6] proposes to include the influence of these factors by introduction of two coefficients to the linear relationship according to IFRF, namely:
冉 冊
1−A S(X) ⫽(1⫺X)∗f1∗f2 where f1⫽ S(0) 1−A0
PD
(19)
The first of these (f1) takes into account, that in the course of combustion the ash content in the grain increases and as a result the active reaction surface is even smaller than So*(1⫺X) (1st model IFRF). The reaction surface decrease factor depends on the fuel “structure” and on the “structure” of the ash layer produced. This last influence incorporates the so-called “neutralisation”
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Fig. 4.
Reaction surface changes calculated from various models.
factor (PD — passivation factor). The second coefficient (f2) represents the differences between the actual reaction surface and the reaction surface assumed as So*(1⫺X). It allows for the influence of the combustion characteristic on the specific reaction surface and takes into account that — at low temperatures the combustion reaction takes place both on the outer surface of the grain and on the pore surface within the grain, whereas — at high temperatures the oxygen concentration on the outer grain surface is so small, that it is hardly sufficient for the combustion on the outer grain surface that decreases as the burnup factor grows. Fig. 4 shows the possible surface changes for the various models. Shots of various cokes under an electronic microscope have shown (Fig. 5), that in the course of combustion the smooth coke grains gain a developed porous surface lying under the outer surface. When — in the surroundings of the grain — there is sufficient quantity of oxygen it can
Fig. 5. Structure and size of grains of the same coke with various burn-up factors (Haas [6]). (A) coke burn-up 0%; (B) coke burn-up 33%, (C) coke burn-up 89%.
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penetrate the porous structure and react with a much greater surface than the outer surface of the grain. While burning, the pores open widely and at some point the grain breaks into pieces und burns afresh while its surface diminishes in size. 5. Summary 1. Determination of solid fuel reactivity should consist of the measurement of the burn-up factor X vs. time and calculation of kinetic constants based on the first phase of burning while taking into account the influence of the temperature and the oxygen concentration in combustion space, oxygen diffusion to the reaction surface and instantaneous size of the reaction surface on the instantaneous surface combustion rate “q”. 2. During the determination of the kinetic constants defining the reactivity of the fuel in question it is always necessary to specify the method of description of the surface changes during combustion. As shown in this paper, a generally recommended way is to use the so called “pseudochemical model” of combustion characteristics, that takes into account, that the combustion reaction occurs on the spherical grain surface changing in the course of combustion progress. 3. Practical experience gathered by the author [4] have shown, that the burn-up calculations for the polydispersive coal dust in big power plant boilers made on the basis of laboratory results from reactivity measurements carried out for a given coal, coincide substantially well with operational results. So the results of fuel reactivity studies carried out for solid fuels and their mixtures are used today as an indicator for initial assessment of coals bound to be burnt in specific furnace equipment.
References [1] Field MA, Gill DW, Morgan BB, Hawskley PGW. Combustion of pulversed coal. Leatherhead: British Coal Utilisation Research Association, 1967. [2] Zelkowski J et al. Kohlecharakterisierung im hinblick auf die verbrennung mahlbarkeit, zundwilligkeit, reaktivitat, verschlackung. 8. DVV-Kolloquium “Kohlenstaub-Aufbereitung: ein Beitrag zur NOx-Minderung” Essen, 8.12.92 VGB-Kraftwerkstechnik 72, 1992. Heft 12; S.1130. ¨ zdemir M, Zelkowski J. New application of the fixed bed reactor to the measurement of coal reactivity under [3] O dynamic combustion conditions. In: Flowers ’97; Florence World Energy Research Symposium. “Clean energy for the new Century”, 30.07–01.08.1997, Florenz. [4] Zehner P, Zelkowski J. Dzialania dle rozzerzenia bazy paliwowej na przykladzie wielkich elektrowni neimieckich heyden i staudinger (Preussenelektra AG). In: VIII Konferencja Kotlowa “Aktualne problemy budowy i eksploatacji kotlo´ w”. Szczyrk, 24–26 listopada 1998r. [5] Haas J. Char Burnot model for atmospheric coal combustion. IFRF Doc. No. 961010, 1996. [6] Haas J. Experimentelle untersuchungen der reaktivitat von kohlenkoks zur modellierung seines verbrennungsverhaltens in staubfeuerunggen. Dissertation TU Clausthal, April 1999. [7] Smith IW, Tyler RJ. Fuel 1972;51:312. [8] Smith IW. The combustion rate of coal char: a review. In: Int. 19th Symp. on Combustion. Pittsburgh: The Comb. Institute, 1978:1045–1065.