A M O D H L FOR
T H H S P O N T A N E O U S H K A T I N C i
O F S T O R E D C O A L
I). SCI I M M
'W
» Vm
'-AJ*!"JW I I »*.>!*Jm
■#ci<
«Sfe
¥Sd
Mft.<
■.sac
fe^
^ a
a..-» i ^
1
A MODEL FOR THE SPONTANEOUS HEATING
OF STORED COAL
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Delft, op gezag van de
Rector Magnificus prof. dr. J.M. Dirken, in het
openbaar te verdedigen ten overstaan van een
commissie door het College van Dekanen daartoe
aangewezen op donderdag 11 juni 1987 te 16.00 uur
door
DIRK SCHMAL
geboren te Wassenaar,
natuurkundig ingenieur.
Dit proefschrift is goedgekeurd door de promotor
PROF. IR. J.A. WESSELINGH
Aan Son ja
Mirande
Bernadine
CONTENTS Page
SUMMARY 1 SAMENVATTING 5 1. INTRODUCTION 9 2. THE PROCESS OF SPONTANEOUS HEATING 14
2.1 Qualitative description 14 2.2 Variables involved 14
2.2.1 General 14 2.2.2 Coal 15 2.2.3 Internal variables 17
2.2.3.1 The oxidation of coal by molecular
oxygen 17 2.2.3.2 Adsorption and desorption of water 21
2.2.3.3 The oxidation of pyrite 23
2.2.4 External variables 24 2.2.4.1 Transport of reactants
(oxygen and water) 24 2.2.4.2 Transport of heat 25
2.3 Mathematical description 26 2.3.1 General equations 26 2.3.2 Literature on models 28 3. THE MODEL FOR SPONTANEOUS HEATING 32
3.1 Items used in the formulation of the model 32
3.2 The mathematical model 35 3.3 Initial and boundary conditions 37
4. METHODS OF SOLUTION 39 4.1 Analytical solutions 39 4.2 Numerical solutions 40 5. INPUT DATA USED IN CALCULATIONS WITH THE MODEL 43
5.1 Introduction 43 5.2 Internal variables 45
5.2.1.1 General 45 5.2.1.2 Isothermal storage test 45
5.2.1.3 Adiabatic storage test 47 5.2.1.4 Heat of adsorption of water 49 5.2.2 Data for the internal variables 50
5.2.2.1 Coal oxidation rates and the influence
of variables involved 50 5.2.2.2 Heat of reaction 56 5-2.2.3 Adsorption and desorption of coal
moisture 56 5.2.2.4 Heat of adsorption/desorption 58
5.2.2.5 Oxidation of pyrite 59
5.3 External variables 59 5.3.1 Experimental method to measure gas flow
velocities in coal piles 59 5.3.2 Data for the external variables 62
5.3.2.1 Pile porosities 62 5.3.2.2 Gas flow velocities and flow patterns 62
5.3.2.3 Diffusion coefficient 63 5.3.2.4 Thermal conductivity of coal piles 63
5.3.2.5 Other external variables 64
RESULTS OF MODEL CALCULATIONS 65
6.1 Introduction 65 6.2 Analytical solutions for some simple situations 68
6.2.1 Maximum heating rate due to oxidation 68 6.2.2 Maximum temperature rise and heating rate
due to the wetting of coal 68 6.2.3 Oxygen transfer by diffusion,
heat transfer by conduction 69 6.2.4 Oxygen transfer by convection,
heat transfer by conduction 70 6.2.5 Oxygen and heat transfer by convection 70
6.3 Numerical solutions 71 6.3.1 Results for the dry coal model 71
6.3.1.1 Standard conditions 71 6.3.1.2 Influence of the flow velocity 75
6.3.1.3 Influence of the thermal conductivity
of the coal pile 76 6.3.1.4 Influence of the porosity of the
coal pile 77 6.3.1.5 Influence of the reactivity of the
coal 78 6.3.1.6 Influence of the reduction of the
reactivity of the coal 79 6.3.1.7 Influence of the initial coal
6.3.2 Results for the moist coal model 81 6.3.2.1 Standard conditions 81 6.3.2.2 Influence of the flow velocity ' 83
6.3.2.3 Influence of the initial coal
temperature 85 6.3.2.4 Influence of the moisture content
of the coal 86
7. VERIFICATION OF THE MODEL 87 7.1 Design of the test piles 87 7.2 Predictive calculations 92
7.2.1 Input data for the internal parameters 92 7.2.2 Input data for the external parameters 93
7.2.3 Results 95 7.2.3.1 Peclet numbers 95
7.2.3.2 Temperatures calculated in the
test piles 96 7.2.3.3 Oxygen concentrations in the
gas phase 100 7.2.3.4 Losses in calorific value 102
7.3 Results of field measurements 103 7.3.1 Coal temperatures 103 7.3.2 Gas phase oxygen concentrations 107
7.3.3 Losses in calorific value 107 7.3.4 Gas flow velocities 111 7.4 Comparison of the model with practice 114
7.4.1 General remarks 114 7.4.2 Coal temperature 115
7.4.2.1 Maximum temperature 115 7.4.2.2 Site of maximum temperature 116
7.4.3 Oxygen concentrations 117 7.4.4 Losses in calorific value 117 7.4.5 Gas flow velocities 118
7.5 Model improvement 119 7.5.1 Changes in the model 119
7.5.2 Results 121
8. PRACTICAL IMPLICATIONS 125 8.1 Prevention and restriction of spontaneous heating 125
8.3 Suppression of spontaneous heating 127 8.4 Influence of pile size and shape on the spontaneous
heating process 128 8.5 Calorific losses 130 8.6 General remarks 131
9. CONCLUSIONS 133
APPENDIX A : The term for mass transfer due to evaporation
and condensation 138
APPENDIX B : Influence of diffusion, gas injection and gas
sampling on the velocity measured 140
APPENDIX C : Location and sizes of the three test piles 144
APPENDIX D : Summary of TNO/KEMA contribution to ESTS study
on walled-in storage (Van Cappelle, 1986) 148
REFERENCES 149
NOMENCLATURE 158
ACKNOWLEDGEMENTS 161
SUMMARY
As part of an investigation into the spontaneous heating of coal piles, a one-dimensional model has been developed to describe the spontaneous heating process in stored coal at relatively low tem-peratures (below 100°C). The ultimate unsteady state model takes into account: depletion of oxygen and generation of heat by chemi-sorption of oxygen in the coal, evaporation and condensation of coal moisture and their heat effects, transport of oxygen and water vapour by diffusion and convection and transport of heat by conduc-tion and convecconduc-tion. The model consists of five simultaneous dif-ferential equations: three for the conservation of oxygen mass, of moisture and of heat, respectively, one for the rate of reaction of oxygen with coal and one for the rate of evaporation and condensa-tion of water.
The equations were solved numerically, using the method of Gear. To obtain the necessary input data for the calculations with the model, laboratory measurements were conducted on the heat generating prop-erties and the variables influencing them of various steam coals. Field experiments using tracer gases were made to obtain an insight into the magnitude of gas flow velocities in stored coal and the mechanisms involved.
Calculations with the computerized model give as a result the pro-files for: oxygen concentration both in gas phase and' adsorbed on the coal, the temperature, the coal moisture content and the loss in calorific value, both as a function of time and place (along a stream line of the flowing air).
From a sensitivity analysis the most important parameters in the process of spontaneous heating at temperatures up to about 100°C were determined. They are: the porosity of the pile (degree of com-paction), the initial coal temperature, the evaporation/condensation of moisture and, of course, the reactivity of the coal towards oxygen in the air.
The validity of the model (e.g. in predicting safe storage times) was checked on three 2500-ton piles of one and the same Australian steam coal. The piles were of the the same shape, but of different porosities: loosely stored, slightly compacted with a bulldozer and
densely compacted with a vibrating roller. A comparison of the re-sults of calculations with those of measurements in these three test piles shows that in its ultimate form the model provides a good description of the spontaneous heating process and therefore it can be used for predictive purposes.
From the calculations with the model and the experiments made, un-derstanding has been gained about a number of phenomena occurring in stored coal. The most important results are summarized below:
It was found that three situations can exist in a coal pile: 1 A situation in which porosity is so low that only
diffu-sion and conduction are responsible for the transport of the reactants (oxygen and water) and heat, respectively. Even in very reactive coal the rate of temperature rise in this case is limited because the quantity of oxygen trans-ported into the pile is very low.
2 An intermediate situation where mass transport is mainly dictated by convection, while for heat transport convec-tion still plays a minor role. This situaconvec-tion is often found in loosely stored or slightly compacted steam coal. 3 A situation in which porosity is so high that convection
is the most important transport mechanism, both for mass and heat. In this case dangerous situations are not reach-ed, because the heat generated by coal oxidation is re-moved by flowing air.
It can be concluded that the spontaneous heating behaviour of the same coal at different storage conditions can be very dif-ferent due to the large influence of pile porosity. Also due to this effect small local differences in porosity can lead to great differences in local spontaneous heating behaviour in the same coal pile.
- Evaporation and condensation play an important role in the spontaneous heating of coal at somewhat higher temperatures (above 50 - 60°C). Evaporation leads to a decrease in rate of spontaneous heating because it removes heat efficiently. At temperatures of about 80 - 90°C the temperature levels off,
because all heat generated by the oxidation of the coal is removed by evaporation of coal moisture. The constant tempera-ture level is maintained until the coal becomes dry locally. At that spot a steep temperature rise occurs leading to local self-ignition in a relatively short time.
The Arrhenius dependence of the coal oxidation rate on the temperature leads to a large influence of initial coal tem-perature on the warming-up time of coal. Therefore coal cooling before storage might be used as a measure to extend safe stor-age time.
The large contribution of natural convection to flow in a coal pile as was found in the field tests, can lead to a situation where coal temperatures in the winter can get higher than in the summer.
Natural convection not only plays a role in heated piles, but very often also in 'cold' piles, because in practice the coal temperature after the transport in a sea ship is generally higher than the day and night averaged temperature of the am-bient air.
Spontaneous heating is a very slow process; it can take years to reach a steady state. Therefore solutions for the steady-state equations have only a limited applicability, i.e. when even in the steady state no dangerous temperatures are reached.
The slow rates of the process lead also to time lags of months between, for example, the seasonal variations in ambient tem-perature and their occurrence somewhat deeper in the pile. When compaction or other measures to prevent oxygen from flow-ing into the pile are not taken well, in certain situations this can lead to an increased rate of spontaneous heating in-stead of the expected decrease.
In order to get an insight into the losses in capital when storing steam coal and the cost effectiveness of measures, the losses in calorific value were estimated for a number of situations. As long
as temperature remains low (below 50°C), the losses for steam coal in normal piles will usually be below 1% a year. At higher tempera-tures (80 - 90°C) they may be as high as 3 - 5% a year on an aver-age. Local losses can be much higher, especially at sites where the coal runs dry.
The model and the insight obtained with it were used for the quan-titative judgment of the effectivity of measures applied in practice to prevent or restrict spontaneous heating (e.g. by compaction) and for the proposal and judgement of new types of measures on their merits (e.g. lowering of the initial coal temperature, use of walled-in storage). The results of the calculations were further applied to the estimation of safe storage times for steam coals at various conditions of storage.
The model can also be used to get an insight into other types of processes (e.g. chemical reactions involving heat effects in packed bed reactors).
SAMENVATTING
EEN MODEL VOOR DE BROEI VAN OPGESLAGEN STEENKOOL
Als onderdeel van een onderzoek naar de broei in steenkoolbergen, is een ééndimensionaal model ontwikkeld dat het broeiproces in opgesla-gen steenkool beschrijft bij temperaturen onder de 100°C. In het uiteindelijke model zijn de volgende factoren in rekening gebracht: verwijdering van zuurstof uit de gasfase en warmte-ontwikkeling ten gevolge van chemisorptie aan de kool, verdamping en condensatie van steenkoolvocht en de daardoor veroorzaakte warmte-effecten, port van zuurstof en waterdamp door diffusie en convectie en trans-port van warmte door geleiding en convectie. Het model bestaat uit vijf differentiaalvergelijkingen: twee stofbalansen (zuurstof en waterdamp), een energiebalans, een vergelijking voor de zuurstof-reactiesnelheid en een vergelijking voor verdamping en condensatie van water.
Voor het oplossen van de vergelijkingen is een door Gear ontwikkelde numerieke methode gebruikt. Om de voor de berekeningen met het model benodigde invoergegevens te verkrijgen zijn laboratoriummetingen uitgevoerd aan de warmte-ontwikkeling van diverse soorten ketelkool en de invloed daarop van diverse variabelen. Om inzicht te krijgen in de grootte van de gassnelheden in steenkoolbergen zijn praktijk-metingen uitgevoerd waarbij gebruik is gemaakt van trace'rtechnieken. De berekeningen met het model geven als resultaat de profielen voor de zuurstofconcentratie in de gasfase en geadsorbeerd aan de kool, voor de temperatuur, voor het vochtgehalte van de steenkool en voor het calorisch verlies, alle als functie van tijd en plaats (langs een stroomlijn van de door de berg stromende lucht).
Uit een gevoeligheidsanalyse volgen de belangrijkste parameters die een rol spelen in het lage temperatuur broeiproces. Dit zijn: de porositeit van de berg (bepaald door de mate van verdichten), de begintemperatuur van de steenkool, de verdamping en condensatie van vocht en, uiteraard, de reactiviteit van de steenkool ten opzichte van de luchtzuurstof.
De waarde van het model (bijv. voor het voorspellen van veilige op-slagtijden) is getoetst met behulp van drie 2500-tons bergen van één
soort Australische ketelkool. Deze bergen hadden dezelfde vorm en afmeting, maar verschillende porositeit: losgestort, aangereden met een bulldozer en ingetrild met een trilwals. Uit een vergelijking van de resultaten van de berekeningen met die van metingen aan de drie proefbergen volgt, dat het uiteindelijke model een goede be-schrijving geeft van het broeiproces in opgeslagen steenkool en dus bruikbaar is voor het doen van voorspellende berekeningen.
De uitgevoerde berekeningen en de proeven hebben geleid tot een verbeterd inzicht in het broeiproces in opgeslagen steenkool. Het onderstaande geeft een samenvatting van de belangrijkste resultaten.
In opgeslagen steenkool kunnen zich drie situaties voordoen: 1. Een situatie waarin de porositeit zo laag is dat het
transport van de reactanten (zuurstof en water) en warmte wordt bepaald door diffusie respectievelijk geleiding. Zelfs bij opslag van zeer reactieve kool is de snelheid waarmee de temperatuur stijgt beperkt, omdat de hoeveel-heid zuurstof die de berg instroomt klein is.
2. Een overgangssituatie waarbij convectie bepalend is voor het zuurstoftransport, terwijl bij de afvoer van warmte de convectie nog nauwelijks meedoet. In deze situatie kan, ten gevolge van de slechte warmte-afvoer, in korte tijd een hoge temperatuur optreden. Deze situatie wordt in de praktijk vaak aangetroffen in opgeslagen ketelkool, die niet goed is verdicht en/of in losgestorte ketelkool. 3. Een situatie waarbij de porositeit zo hoog is (losgestorte
kool), dat naast geleiding ook convectie zorg draagt voor afvoer van de opgewekte warmte. De temperatuur blijft, evenals in situatie 1, laag. In dit geval wordt dit echter veroorzaakt door het feit dat alle opgewekte warmte kan worden afgevoerd via de door de berg stromende lucht. Uit het bovenstaande blijkt dat het broeigedrag van steenkool sterk afhangt van de opslagcondities. Vooral de porositeit (mate van verdichting) speelt hierbij een zeer grote rol. Hier-uit volgt direct dat kleine lokale verschillen in porositeit (inhomogeniteiten) tot grote lokale verschillen in broeigedrag in een berg kunnen leiden.
Verdamping en condensatie spelen een belangrijke rol bij steen-koolbroei, vooral bij wat hogere temperaturen (boven de 50 tot 60°C): er treedt een vertraging in de zelfopwarming op vanwege het efficiënte transport van warmte als gevolg van verdamping van steenkoolvocht. Dit leidt uiteindelijk tot een constante temperatuur van 80 tot 90°C, omdat daarbij alle door kooloxida-tie opgewekte warmte wordt afgevoerd via verdamping. De con-stante temperatuur blijft gehandhaafd tot er lokale uitdroging van de steenkool plaatsvindt. Op de desbetreffende plaats treedt daarna een sterke temperatuurstijging op, omdat het oxidatieproces doorgaat, maar de opgewekte warmte niet meer wordt afgevoerd. Na relatief korte tijd treedt dan zelfont-branding op.
Omdat het verband tussen oxidatiesnelheid en temperatuur wordt gegeven door een e-macht (de Arrhenius vergelijking) heeft de begintemperatuur van de steenkool een zeer grote invloed op de opwarmtijd. Om die reden kan koeling van steenkool vóór het opslaan (bijvoorbeeld met de buitenlucht) een zeer effectieve methode zijn om de veilige opslagtijd te verlengen.
De grote invloed van vrije convectie op de stroming door een berg kan leiden tot situaties waarbij de steenkooltemperatuur in de winter hoger wordt dan in de zomer.
Vrije convectie speelt niet alleen een rol in broedende bergen, maar is ook van groot belang voor het broeigedrag van "koude" bergen, omdat bij import van steenkool via zeetransport de kooltemperatuur vaak hoger is dan de over dag en nacht gemid-delde buitenluchttemperatuur.
Broei is een zeer langzaam proces; het kan jaren duren voordat een stationaire situatie wordt bereikt. Om die reden zullen oplossingen van de stationaire vergelijkingen die het broei-proces beschrijven slechts een beperkte toepasbaarheid hebben (alleen voor situaties waarbij zelfs in stationaire toestand geen gevaarlijk hoge temperatuur wordt bereikt).
De traagheid van het broeiproces is verder de oorzaak van vertragingstijden van de orde van enkele maanden. De seizoens-variaties in buitenluchttemperatuur bijvoorbeeld zijn daardoor
pas maanden later merkbaar op enige afstand van het bergopper-vlak.
- Als verdichting of andere maatregelen, die tot doel hebben te voorkomen dat er luchtzuurstof in de berg stroomt, niet goed worden uitgevoerd, dan kan dit onder bepaalde omstandigheden leiden tot een averechts effect: in plaats van onderdrukking van broei treedt een versnelling van het proces op.
Om een inzicht te krijgen in de grootte van de financiële verliezen bij opslag van steenkool ten gevolge van achteruitgang van de calo-rische waarde en de effectiviteit van maatregelen ter voorkoming ervan, zijn de calorische verliezen voor een aantal situaties met het model berekend. Zolang de temperatuur laag blijft (onder de 50 °C) zullen deze verliezen in "normale" ketelkool onder de 1% per jaar blijven. Bij hogere temperatuur (bijvoorbeeld 80 tot 90°C) kun-nen de gemiddelde verliezen al oplopen tot 3 a 5 procent per jaar. De lokale verliezen kunnen uiteraard veel hoger zijn, zeker als er lokaal uitdroging en zelfontbranding optreedt.
Het model en het inzicht dat daarmee is verkregen in het broeiproces zijn gebruikt voor een beoordeling van de effectiviteit van in de praktijk toegepaste maatregelen ter voorkoming of beperking van broei (bijvoorbeeld aanrijden en intrillen) en voor het voorstellen en beoordelen van nieuwe maatregelen (verlagen van de kooltempera-tuur voor het storten, opslag tussen muren). De resultaten van de berekeningen zijn verder gebruikt voor het aangeven van veilige opslagtijden voor verschillende situaties.
Het model heeft een wijder toepassingsgebied dan steenkoolbroei. Behalve voor andere soorten broeiprocessen (hooi, turf) kan het ook worden toegepast voor geheel andere processen, zoals bijvoorbeeld voor chemische reacties in een gepakt bed waarbij warmte-effecten optreden.
1. INTRODUCTION
Spontaneous heating of coal is a well-known problem in mining, transport and storage of coal. It leads to losses in calorific value, to uncontrolled and mostly undesired changes in coking and thermal properties of the coal and, under unfavourable conditions, to spontaneous combustion, which in turn can result in injury of persons and damage of property. In all these cases financial losses are a result.
In the last ten years the number of spontaneous heating problems has increased considerably. It is not expected that this will change drastically in the near future. The causes are:
Due to the energy crises in the seventies the quantities of coal mined, transported and stored have shown a considerable growth. Especially countries which are largely dependent on im-port for their energy demand (e.g. Japan, the Netherlands etc.) are converting to coal as one of their main energy vectors. More and more coals of lower rank are being mined, transported and stored. Generally these coals give more problems because they have a higher susceptibility towards spontaneous heating than coals of higher rank. When in the future coal gasification should become economically viable, the use of low rank coal will grow even more.
It is expected that central processing of coal (separation, blending, mixing etc.) will take place more and more in the future. The manipulations in these processes will mostly lead to a higher susceptibility of the coal towards spontaneous heating.
Despite the long-time experience with spontaneous heating and ex-tensive investigations made on the subject, the nature of the fac-tors influencing this process are not yet completely understood. An-other important item from an economical point of view is that infor-mation about losses in calorific value is hardly available, neither
from measurements nor from estimations or calculations. The main reasons for this lack of knowledge are that spontaneous heating is a very complex process in which many variables are involved and that
properties of the various coals found in the world show large dif-ferences .
Earlier attempts to quantify and predict the spontaneous heating process in stored coal were mostly based on laboratory measurements on one or more of the properties related to the spontaneous heating behaviour of the coals. At best they give information about the relative susceptibility towards spontaneous heating of the coal sam-ples investigated. Even with much experience it remains difficult to predict spontaneous heating behaviour for instance for coal quali-ties or conditions of storage differing from usual.
Full-scale investigations on coal have been performed a few times. Although they give valuable information, such experiments have not been made often because of the high cost and long times involved and the problems in translation of the results to other coal types and storage conditions.
Therefore some time ago the need was felt for developing mathe-matical models which should give a more quantitative description of the process of spontaneous heating, taking not only into account the spontaneous heating properties of the coal itself, but also the 'ex-ternal' factors such as the transport of the reactants responsible for spontaneous heating and transport of heat away from the loca-tions where it is generated. When such a model gives a realistic description of the process of spontaneous heating, various applica-tions can be envisaged:
Sensitivity analyses, giving an insight into the relative in-fluence of the variables in the process of spontaneous heating for the various storage conditions and coal types used in prac-tice. Such insight is necessary for the selection of the appro-priate measures to prevent or restrict spontaneous heating. - Prediction of safe storage times at various conditions when
coal properties are known. Comparison with expected storage times provides information about the need of preventive mea-sures.
- Estimation of losses in calorific value under various condi-tions. This makes it possible to weigh the cost of measures against the financial losses to be expected.
Stellingen bij het proefschrift van D. Schroal, Technische Universiteit Delft, 11 juni 1987.
1. Het voorspellen van het broeigedrag van opgeslagen steenkool door middel van laboratoriummetingen is niet mogelijk zonder rekening te houden met de opslagcondities.
Dit proefschrift, hoofdstuk 6.
2. In de winter kan broei ernstiger vormen aannemen dan in de zomer.
Dit proefschrift, hoofdstuk 7.
3. Het gebruik van broeimodellen voor het aangeven van maatregelen ter voorkoming of beperking van broei, wint sterk aan waarde als met het model ook calorische verliezen kunnen worden ge-schat.
Dit proefschrift, hoofdstuk 8.
4. Als, ter voorkoming of beperking van broei, maatregelen welke betrekking hebben op vermindering van de zuurstoftoevoer, niet goed worden uitgevoerd kunnen zij een averechts effect hebben. Dit proefschrift, hoofdstuk 7.
5. De bewering dat een temperatuurdaling in opgeslagen steenkool, na een aanvankelijke stijging, alleen een gevolg kan zijn van achteruitgang in reactiviteit is niet juist.
P. Nordon, Fuel 58 (1979). K.S. Brooks, Ph.D. Thesis 1985,
University of the Witwatersrand, Johannesburg.
6. De conclusie, dat er geen vrije convectie in steenkoolbergen kan optreden wanneer er lokaal evenwicht is tussen steenkool-en luchttemperatuur, is niet juist.
P. Nordon, Fuel 58 (1979).
7. Gezien het feit dat zelfs door veel personen die middelbaar, hoger of universitair technisch onderwijs hebben gevolgd, ver-mogen, energie en (elektrische) lading veelvuldig met elkaar worden verward, verdient het aanbeveling om hieraan in de op-leiding enige extra aandacht te besteden.
8. Het lijkt niet onredelijk dat universiteiten aan promovendi, met een werkkring buiten de universiteit, een gedeelte van de voor hun academische promotie gemaakte kosten in rekening bren-gen.
9. Het oplossen van milieuproblemen wordt vertraagd door het op-nemen van verbindingen in het stoffen- en processenbesluit horend bij de Wet chemische afvalstoffen als het stoffen be-treft die met succes worden toegepast in de milieutechnologie en geen zwaarwegende schadelijke eigenschappen hebben.
10. De eventuele opheffing van de leerstoel elektrochemische tech-nologie aan de Technische Universiteit Eindhoven zou een ver-arming betekenen van de universitaire opleiding in de Schei-kundige Technologie in Nederland.
11. Het broeikas-effect leidt tot verminderde kooldioxyde-produktie en tot energiebesparing.
12. De relatief sterke verontwaardiging bij grensoverschrijdende milieuvervuiling vergeleken bij die afkomstig uit eigen land wekt sterk de indruk dat er politieke motieven in het spel zijn.
13. Het gebruik van de contradictio in terminus "door-en-door zinkt" als reclameslogan getuigt van weinig begrip van het ver-zinkproces.
Reconstruction of spontaneous heating incidents, e.g. for in-surance purposes.
Assistance in the design of coal yards, with respect to a mini-misation of calorific losses.
Only in the last ten years the modelling of spontaneous heating has come into a stage that makes a realistic description viable. This is a consequence of both the renewed interest in coal science and the developments of computers in the last two decades which makes it possible to do calculations with the complex mathematical equa-tions describing the process of spontaneous heating.
Although some models for spontaneous heating have been described in literature, the need was felt to make a new model (using of course the information given in literature) because of the following rea-sons :
The gaining of a better understanding of the process of sponta-neous heating, which is necessary for a solution of the spon-taneous heating problems occurring in practice.
The more sophisticated, realistic models were especially de-veloped and used for lignite and char. For the Netherlands and also most other coal importing countries, at the moment there is not much interest in these types of fuel. The situation which has to be dealt with is the import and the storage of large quantities of mostly bituminous coals used for the gen-eration of steam (for electricity or industrial purposes). The influence of moisture, although known to be important, was not incorporated in the calculations with the models described in literature because of the 'prohibiting computing effort', using the methods of solution chosen.
Calculation or estimation of losses in calorific value was not incorporated in the models described.
On the basis of these arguments a one-dimensional mathematical model describing the process of spontaneous heating at low temperatures (< 80 to 100°C) has been developed. In this thesis this model and representative results of calculations are given and compared with results of large-scale field experiments.
This study has been performed in the framework of the Dutch National Research Programme on Coal (NOK), which was started because of re-introduction of coal in the Netherlands as one of the main sources of energy. The spontaneous heating part of this programme consisted of three portions:
1. Laboratory measurements on the influence of a number of vari-ables on the heat generating properties of various (sub-) bituminous steam coals, giving among other things as a result the input data for the model.
2. Development of the model and the related computer programme describing the spontaneous heating process in stored coal. 3. Field measurements of temperature, gas composition, losses in
calorific value and gas flow rates in the pores between the coal particles, one of the objectives being comparison between theory and practice.
The laboratory measurements and the development of the model were carried out at TNO, the Dutch Organization for Applied Scientific Research. Field measurements were conducted by KEMA, the Central Research Institute of the Power Plants in the Netherlands.
The spontaneous heating research programme was started in 1981 and terminated in 1986, the last two years mainly being devoted to large-scale field experiments with three 2500 tons of coal piles, one of the purposes being the verification of the model. This thesis has partly been compiled from previous reports and publications (Van Heuven et al. (1982), Schmal et al. (1984a, b, c ) , Schmal et al.
(1985), Schmal (1985, 1986, 1987)). Many of the data used in the calculations and the verification of the model were taken from the reports on the laboratory experiments (Heemskerk (1982, 1983, 1984) and Van Liempt (1985)) and the field tests (Kok (1981, 1983, 1984 1986a, b, 1987)).
In Chapter 2, a qualitative description, mainly based on literature, is given of the spontaneous heating process and the variables play-ing a role in this process. Also the general equations for the spontaneous heating process in stored coal are given in a one-dimensional form and compared with the models developed by others.
In Chapter 3, a description of the model we used, including its restrictions and assumptions, is given. In Chapter 4, the methods of solution are presented. Chapter 5 gives the experimental methods used to obtain the input data for calculations with the model which were not available from literature. Further, results of these measu-rements are given. Chapter 6 gives the results of a sensitivity analysis showing the relative influence of some of the more impor-tant variables. Chapter 7 deals with the verification of the model. The large-scale field experiments are described and results of mea-surements are compared with those of calculations.
The practical aspects of coal storage (e.g. measures to prevent or restrict spontaneous heating) emanating from the study are the sub-ject of Chapter 8. In Chapter 9, the final conclusions of the study are given.
2. THE PROCESS OF SPONTANEOUS HEATING
2.1 QUALITATIVE DESCRIPTION
In the spontaneous heating of coal the following types of processes play a role (see e.g. the reviews of Wilke (1966), Kim (1977), Daw
(1982) and Rigby (1982)):
a. Processes causing a heat effect. The most important are: oxidation of coal by oxygen from the air and the possible catalytic effects on it by other compounds (e.g. water, pyrite etc.);
adsorption and desorption of water due to the differences between real and equilibrium moisture concentrations of
coal and air. Both heat of condensation (evaporation) and heat of wetting are involved.
Under special conditions other heat generating reactions might play a role, the one mostly mentioned in literature being the oxidation of pyrite.
b. Transport of the reactants. The most important reactants, taking part in the heat generating process, are oxygen and water. They are transported by diffusion and convection. Con-vection in coal piles may be caused by differences in wind pressure at the surface of the pile (forced convection) and differences in temperature between the pile and the surrounding air (free or natural convection).
c. Transport of heat. Heat is transported away from the sites where it is generated due to temperature gradients. Conduction and convection are the mechanisms responsible.
2.2 VARIABLES INVOLVED
2.2.1 General
Two types of variables can be distinguished in the process of spon-taneous heating. They will be called internal and external variables.
Internal variables are those which are related to the heat generat-ing properties of the coal itself as given under a. in § 2.1. The external variables are the variables which are mainly assessed by storage conditions and physical properties of coal and air. They determine the transport processes of the reactants and heat (see b. and c. in § 2.1).
In the next paragraphs, firstly a short description of the material coal and the methods used to classify it are given. Then the vari-ables influencing spontaneous heating will be described on the basis of information from literature.
2.2.2 Coal
Coal is the carbonaceous remains of vegetable matter. The decay of this matter leading to the formation of coal is caused both by bio-logical and chemical processes. A large influence on the coalifica-tion process is exercised by the pressure and temperature increases caused by the sediment layers formed above the coal in the course of time.
The age of coal varies from about 1 million to 500 million years. Various classification methods have been proposed for the ranking of coal. Most used classification parameters are calorific value, proximate analysis, ultimate analysis and petrographic analysis. The proximate analysis gives the percentages of volatile matter, fixed carbon, moisture and ash (or mineral matter). The ultimate analysis gives the percentages of the most important elements (C, H, 0, N, S ) , mostly given on dry and ash free basis (shortly written as daf of dmmf).
In Table 1 the generally used ASTM classification by rank is given. This classification is based on calorific value and proximate anal-ysis (Rigby, 1982).
In petrographic classifications a difference is made between macro-scopic rock types and the more or less homogeneous micromacro-scopic con-stituents, which are called macerals by analogy with the minerals occurring in inorganic rocks (Van Krevelen and Schuyer, 1957). Gen-erally four rock types are distinguished: vitrain, clarain, durain and fusain.
Table 1 Simplified classification of coals by rank
(ASTM D-388, 1980)
Class and group
Fixed carbon limits Volatile matter limits Calorific value limits (per cent)
Dry mineral matter free basis Equal or greater Less
than than
(per cent) Dry mineral matter
free basis
Greater Equal or
(Btu per lb) Moist mineral matter
free basis Equal or greater Less Anthracite 1. M e t a - a n t h r a c i t e 2. A n t h r a c i t e 3 . Semi-anthracite 98 92 86
-98 92 Bituminous1. Low volatile bituminous coal
2. Medium volatile bituminous coal 3. High volatile A bituminous coal
4. High volatile B bituminous coal
5. High volatile C bituminous coal
Sub-bituminous 1. Sub-bituminous A coal 2. Sub-bituminous B coal 3. Sub-bituminous C coal Lignitic 1. Lignite A 2. Lignite B 78 69
-86 78 69 -14 22 31 -22 31 -14000 13000 11500 -14000 13000 10500 11500 9500 10500 8300 9500 6300 8300 6300The macerals can be distinguished in the following types:
a. Macerals having t h e i r origin in woody and cortical t i s s u e s :
v i t r i n i t e , f u s i n i t e , and semi-fusinite.
b. Macerals having t h e i r origin in plant material other than woody
t i s s u e s : e x i n i t e , r e s i n i t e , s c l e r o t i n i t e and a l g i n i t e .
c. A maceral the origin of which has not been traced: tnicrinite.
Sometimes, other classifications are also used. For a much more
com-plete description of coal, i t s origin and properties reference i s
made to the book of Van Krevelen and Schuyer (1957).
2.2.3 Internal variables
2.2.3.1 The oxidation_of_coal_by_molecular_oxYgeri
The chemistry of low temperature oxidation of coal by oxygen from air has been studied by numerous investigators. Despite this the phenomenon of oxidation is not yet completely understood. In the following the most important items relating to spontaneous heating are discussed. More information can be found in the reviews of Kreulen (1948), Van Krevelen and Schuyer (1957), Sevenster (1958, 1959), Beier (1962), Wilke (1966) and Itay (1983). It is generally accepted that three types of processes occur:
physical adsorption e.g. by Van der Waals forces,
chemical adsorption (chemisorption) leading to the formation of coal-oxygen complexes and
chemical reactions leading to the break down of the less stable coal-oxygen complexes, often resulting in the formation of gaseous products as CO, C0„ and H„0.
Physical adsorption is a reversible process. Sevenster (1958) has shown that physical adsorption only plays a major role below 0°C. At higher temperatures the non-reversible chemisorption is the dominant process. At temperatures above 70 - 80°C the chemisorption process merges into or is superimposed on chemical reactions leading to the formation of the gaseous products mentioned before.
The types of chemical reactions taking place will not be discussed here, because the matter is rather complicated and not used in the model. For the literature on it reference is made to the reviews mentioned above.
For the purpose of modelling the two most important overall chemical reactions for bituminous coal in a simplified form are (Kok, 1981): C1 0 0H? 401 1 + 113 02 -> 100 C 02 + 37 H20 (+ 4.2 x 108 J/kmol 02) (1)
for the complete oxidation and
C100H74°11 + 1 7-5 °2 * C100H74°46 ( + 2"5 x l0& J / k m o 1 °2) ( 2 )
Both oxidation reactions are exothermic, the complete oxidation giv-ing off more energy in the form of heat than the chemisorption reac-tion. The reaction enthalpies found by various investigators mostly are in between those of the reactions (1) and (2).
The rate of oxidation of coal depends on numerous factors, the most important being temperature, E^t^aJ^j>re_ssure of oxygen in the gas, surface area available for the reaction, oxidation history and coal composition^structure (see reviews above).
The_ JJifjjuejice__of .temperature is generally presented by an Arrhenius type of equation:
r = A exp (-E/RT) (3)
in which r is the reaction rate (for instance in kg 0„/(kg coal s ) ) , A the pre-exponential factor, E the activation energy, R the gas constant and T the absolute temperature. In this equation A is determined by the other factors mentioned. For many coals it has been found that a useful approximation is that the rate doubles every 10°C rise in temperature (Sevenster, 1959).
Activation energies found by various investigators vary from 10 -110 kJ/mol 0„ adsorbed, the value depending on temperature, coal type and last but not least the method of investigation.
The influence of oxygen pressure found in the literature is mostly given in the form of a power law relation:
r *
Po
W
2
where pn is the oxygen partial pressure and n the power. Values 2
found for n vary between 0.5 and 1 (Ono et al., 1982a).
Itay (1983) found that n is 1 starting with freshly mined or crushed coal (chemical reaction is rate determining) and decreases to 0.5 in the course of time (diffusion through a product layer of 'oxy coal' is rate determining). He modelled the oxidation rate using the shrinking core model.
The influence of surface_area is not always clear, often due to the fact that the surface area available for the oxidation reaction is
mostly unknown. Of course particle size, which determines the ex-ternal surface is an important factor. Generally the rate increases with decreasing particles size. This follows directly from the fact that low-temperature oxidation of coal is a reaction taking place at the surface and in the larger pores of the coal particles, as was clearly shown by Van Krevelen and Schuyer (1957). For small parti-cles the rate found is not very much dependent on particle size; for larger particles it decreases more or less proportionally to the inverse of the particle diameter. The particle size range at which transition between the extremes occurs depends on coal com-position and structure. It is mostly found to be in the range of particle size between 1 and 10 mm (Miinzner and Peters (1966), Sondreal and Ellman (1974)).
T^Ë_2xi^2tï2ïï_{}iS£2ïY n a s a v e rY large influence on the rate of oxi-dation. Coal particles freshly exposed to air (freshly mined or crushed coal) show much higher rates of oxidation than coal which has been in contact with air for some time (weathered coal). The differences in rate can be orders of magnitude for a given coal. Van Doornum (1954) found an exponential decay in rate as a function of exposure times. Also an Elovich type of dependence (hyperbolic decay, Sevenster (1959), Nordon (1979)) and a power law (Miinzner (1966)) have been found.
The figures available all refer to fresh coal. Figures about the decrease in oxidation rate for weathered coal (for example coal stored after sea transport) were not found.
The_influence_of coal composition and_structure is very complex; many contradictory opinions on the role of various factors can be found in literature. One of the main complicating factors is that the oxidation rate is not only determined by the chemical compounds in the coal (e.g. because of differences in oxidation rates of the various organic/petrographic constituents). Also the structural properties (surface area etc.) of the various constituents and the presence of compounds catalyzing the oxidation reaction or forming intermediates play a role.
At the moment it is not yet possible to give a clear picture of the influence of the various compounds in coal on the oxidation rate, for example in the form of relations between oxidation rates and
compositional parameters. The matter is too complex. Probably the only general rule applicable is that the oxidation rate rises with rising oxygen content (or diminishing carbon content, Beier (1962), Wilke (1966), Itay (1983)). In other words (see Table 1 ) : the higher the rank, the lower the oxidation rate. It is not sure whether the chemical composition itself is only responsible for this difference. It could be argumented as well that differences in structure between the various coals are responsible (the lower the rank, the higher the friability, the pore volume and the internal surface area). Also in the case of petrographic composition the differences in oxi-dation rate can be caused both by differences in chemical composi-tion and structure. Vitrinite for example shows a relatively high oxidation rate (Wilke, 1966) and is relatively friable (Berry and Goscinski, 1982).
Catalytic effects are generally attributed to sulphur-containing compounds such as pyrite and mercaptans, the mechanism being that the oxidation product (sulphuric acid) accelerates the rate of dation of organic compounds in the coal (Beier, 1962). Pyrite oxi-dation also leads to the formation of Fe(III) compounds, which oxidize coal under the formation of Fe(II) compounds. These on their turn will be oxidized to Fe(III) by oxygen in air (redox reaction, see Beier (1962)). Further it has been found that the oxidation of pyrite leads to swelling, which in turn can cause breakage of the coal particles leading to an enlarged surface area available for the oxidation reaction (Wilke (1966), Mowrer and Dungan (1982)). The influence of water is also manifold. At very low and very high moisture contents of the coal oxidation rates are generally low. The highest oxidation rates are mostly found at or near the equilibrium moisture content of the coal under normal conditions (the so-called bed moisture, see Wilke (1966), Mowrer and Dungan (1982)). Most in-vestigators conclude that a minimum amount of water is necessary for the oxidation to occur at a measurable rate (Beier, 1962). This is probably because of the role of water as a constituent or inter-mediate in the oxidation reactions. For example: the oxidation of pyrite only occurs when water is available. This is also the case in the formation of peroxides which are important intermediates in the oxidation reactions (Beier, 1962). At too high moisture contents the
oxidation reaction is inhibited because the oxygen has to diffuse through the layer of free water formed on the surface and in the pores of the coal particles (Wilke, 1966). An extreme situation occurs when coal is stored under water, which is a very effective method to stop the oxidation reaction completely.
Adsorption of moisture and oxidation of pyrite can lead to increased temperatures and therefore indirectly accelerate the oxidation re-action (see equation 3 ) . This is due to the exothermal character of these reactions. This will be discussed in the next paragraph.
The main conclusion from the literature on the influence of coal composition on oxidation rate is that generally applicable relations between composition and oxidation rate can hardly expected to be found in the near future. For the time being, when the reactivity of a certain coal has to be known, e.g. for prediction of its sponta-neous heating behaviour in storage, it will have to be measured with suitable laboratory methods on representative samples of the coal.
2.2.3.2 Adsorption and desorgtion of water
The heat released at the adsorption of water from the atmosphere consists of two components, viz. the heat of wetting and the heat of condensation. When water is supplied in liquid form, only the heat of wetting is liberated.
A number of investigators have done experiments on the wetting and drying of coal and its heat effects, mostly in combination with the oxidation reaction (see e.g. Berkowitz and Schein (1951), Hodges and Hinsley (1964), Hodges and Acherjee (1964), Güney (1971) and Bhat-tacharyya (1971, 1972)). In most cases extreme situations were in-vestigated occurring in practice only in special cases (e.g. moist coal in dry air or dry coal in moist air). The highest heat output, which is the sum of the heat of wetting, the heat of condensation and the heat of oxidation, is generally obtained when dry coal is brought into contact with air saturated with moisture. For coal and air both saturated with moisture and for dry coal and air the heat outputs are much lower, but still positive. In this case, when equilibrium exists between coal and air the heat effects are caused by oxidation only. When moist coal is brought into contact with dry
air the heat output is generally negative, i.e. the heat necessary for desorption (evaporation) is higher than the heat generated by oxidation. As an example the ratios of the heat outputs in those four situations as found by Hodges and Acherjee (1964) are given. They are about 5 : 2 : 1 : -2 for dry coal/wet air, moist coal/wet air, dry coal/dry air, moist coal/dry air. The low oxidation rate for dry coal/dry air compared to the rate for moist coal/wet air is probably due to a catalytic effect of water (see § 2.2.3.1). The ratios given clearly illustrate that adsorption/desorption of water under extreme conditions can have a large influence on the sponta-neous heating behaviour and should be taken into account when study-ing or modellstudy-ing spontaneous heatstudy-ing.
Data on the heat of wetting show that coal rank has an important influence on the heat of wetting. For high rank coal (anthracite) Bhattacharyya (1972) finds that the total heat of adsorption is equal to the heat of condensation (~ 2.4 x 10 J/kg H . 0 ) . In this case the heat of wetting can be neglected. For sub-bituminous coals the maximum heats of wetting estimated from the heat outputs mea-sured by Bhattacharyya (1972) were about 10 J/kg H_0, which is about 40% of the heat of condensation. For lignite the heat of wett-ing found by Sondreal and Ellman (1974) was 10 J/kg H„0. Nordon and Bainbridge (1983) have directly measured the heat of wetting for a bituminous coal and found a value for the wetting of completely dry coal of 0.2 x 10 J/kg H20 , which is about 10% of the heat of con-densation. For the heat of immersion they found the same value. Further they found that the higher the moisture content, the lower the heat of wetting; near the equilibrium moisture content it ap-proaches zero.
Some practical situations in which adsorption or desorption of water can be important are:
- When air with a low relative humidity flows through stored coal, desorption will occur. An example is the flow of ambient air through a pile where temperature is not far away from the boil-ing point of water. In this case water will have a retardboil-ing effect on the temperature rise (Bhattacharyya, 1972).
When coal has been dried for some reason and is stored in air having a high relative humidity, heat generation due to ad-sorption can give a substantial contribution to the temperature rise. This will accelerate spontaneous heating by oxidation (see equation 3 ) .
When fires in stored coal are extinguished using water, the heat of wetting is liberated. This effect will generally be restricted. Nordon and Bainbridge (1983) calculated a maximum temperature rise of about 16°C when dry bituminous coal is wetted. When excess water is used the temperature rise will be less. Problems due to this effect might be expected in low rank coals, because of the relatively high heat of wetting.
Concluding it can be said that under conditions that can occur in practice adsorption or desorption of water can have an important influence on the process of spontaneous heating, the main effect being caused by the latent heat of condensation of water.
2.2.3.3 The_oxidation_of_£Yrite
When pyrite is oxidized by molecular oxygen the following exothermal reaction occurs (Wilke, 1966):
2 F e S2 + 7 02 + 2 H20 ^ 2 H2S 04 + 2 F e S 04 (+ 0.37 x 108J'/kmol 02) (5) or when Fe(II) at the same time is oxidized to Fe(III) (Doddema, 1982):
4 F e S2 + 15 02 + 2 H20 ^ 2 H2S 04 + 2 F e2( S 04)3 (+ 0.56xl08J/kmol 0 ) (6) The heat of reaction, based on the quantity of oxygen adsorbed, is only about 10% of the heat of reaction for the oxidation of coal by oxygen.
The pyrite content of normally used coals is less than 1%. It should therefore be expected that, under normal conditions, for most coals the contribution from the pyrite oxidation to the spontaneous heating can be neglected. This has been confirmed by practical
experience (Wilke, 1966).
The much more important role of pyrite and its oxidation products on the oxidation rate of coal was discussed before (Chapter 2.2.3.1).
2.2.4 External variables
2.2.4.1 Transgort_of_reactants_£oxygen_and_water)
The transport of the gaseous reactants (and products) is determined by the processes of molecular diffusion and convection.
The variables in the case of diffusion are the diffusion coefficient and the pile porosity. As a first approximation the product of both variables forms the effective diffusity of the pile. Values for pile porosities are scarce in literature. From compaction experiments with lignite performed by Sondreal and Ellman (1974) it follows that porosity can be in the range of 0.05 to 0.4, depending on the degree of compaction.
The most important types of convection which can occur are:
forced convection due to externally generated pressure differ-ences across a pile' (e.g. because of wind in open storage or because of forced ventilation in mines);
natural convection due to temperature differences in the coal or between the coal and the ambient air.
Very little information on the magnitude of the gas flow velocities found in stored coal and pile porosities is available from litera-ture.
For rough estimations the Ergun relation for laminar flow in packed beds might be used, if pressure differences Ap and porosities e are known (Beek and Muttzall, 1975):
A
P= 170
n^ 0_i<o!
( 7 )d eJ
where r| is the dynamic viscosity of air, v the superficial velocity, L the 'length' of the pile and d the diameter of the coal particles. More realistic values can probably be calculated from relations be-tween pressure differences and velocities which were determined by
Sondreal and Ellman (1974) for lignite-filled columns at various packing densities (porosities). Transferred to SI units they found:
Ap = 1 0( 1 2-1 2- 7-8 £ ) n v(0-806 + 2.48 e) L ( g )
In practical situations forced convection in open piles can be caused by pressure differences Ap due to wind flow. These are of the order of magnitude of the dynamic pressure:
Ap = % pavw 2 (9)
where p is the density of air and v the wind velocity. For wind
Ka ' w
velocities of 3 - 10 m/s the pressure difference varies from 5 to 50 Pa.
For natural convection the pressure difference depends on the tem-perature differences. It is approximately given by:
Ap = pa g L AT/T (10)
where g is the gravitational acceleration and AT the difference be-tween pile and ambient temperature. For temperature differences of
10 - 100 K and typical pile dimensions of 10 m, the pressure dif-ferences are comparable to those due to wind.
With the porosities found at various degrees of compaction by Son-dreal and Ellman (1974) it can be calculated, combining equation 7 or 8 with equation 9 or 10, that air flow velocities in open piles
-2 -8
will be in the range of about 10 - 10 m/s. The value depends very much on porosity: in equation 7 for example a difference of a factor 2 in porosity gives a difference of about a factor 10 in velocity.
2.2.4.2 Transgort_of_heat
The transport of heat can be caused by conduction and convection. Conduction occurs mainly via the coal particles. Conduction via air can be neglected because of the relatively low thermal conductivity of air.
The e f f e c t i v e thermal c o n d u c t i v i t y A for a bed of coal i s much c
lower than that of the coal itself. Wilke (1966) gives a table of values found by him in literature. They are mostly in the range of 0.1 - 0.2 W/(m K ) , depending on pile porosity and coal composition. Values found for lignite by Sondreal and Ellman (1974) are in the same range at not too high moisture contents. The values increase with increasing moisture content.
Heat is also transported away from the site where it is generated by convection, due to the heat capacity of air. The mechanisms for the air flow are the same as described in § 2.2.4.1.
2.3 MATHEMATICAL DESCRIPTION
2.3.1 General equations
The spontaneous heating of coal is a process in which (see § 2.1): oxygen and water are transported into the pile via convection and diffusion,
oxygen and water are adsorbed on the coal particles (water can also be desorbed),
heat is generated (or withdrawn) due to adsorption (desorption) of water and
heat is transported via conduction and convection.
The general equations describing this process are those often used to model processes in chemical engineering. They are the coupled equations of conservation of heat and mass (both including produc-tion terms) which can be found in most chemical engineering hand-books. They are given below in a one-dimensional form using Cartesi-an coordinates. The same equations cCartesi-an be written in two- Cartesi-and three-dimensional form and also in cylindrical or spherical coordinates. The one-dimensional equation of conservation of mass of oxygen reads:
3c 3 ( v c J 32c. 3 c ,
e — - + — - e D i + (l - e) — = 0 (11) 3t 3x 3x 3t
in which the successive terms represent:
I the local accumulation of oxygen (e is the pile porosity, c. the oxygen concentration in the gas phase, and t the time), II the convective transport of oxygen in the gas phase (v is the
superficial gas flow velocity and x the distance),
III the diffusive transport of oxygen in the gas phase (D is the diffusion coefficient of oxygen) and
IV the depletion of oxygen due to chemisorption at the coal (c„ is the concentration of adsorbed oxygen).
The same general equation can be used for water (vapour): 2
3c, 3(vc_) 3 c. 3c,
e — - + — - e D — ^ + (1 - e) — = 0 (12) 3t dx 3x 3t
in which the terms have the same meaning as above (c„ is the water concentration in the vapour phase and c, in the coal phase).
The general equation for conservation of heat reads:
, . , 3 T± 3T _,_ 3(vT) . 32T p c ( 1 e ) — + p c e — + p c — — A —^ -c p-c
at
a paat
a paax
ca
x 2 V VI VII VIII 3c 3c4 - AH (1 - e) g ^ - AHw (1 - e) g ^ = 0 (13) IX X in which the successive terms represent:V the local accumulation of heat in the coal (p is the coal den-sity, c the heat capacity or specific heat of the coal and T the absolute temperature),
VI the local accumulation of heat in the air between the coal particles
the air),
VII the convective transport of heat,
VIII the conductive transport of heat (\ is the thermal conductivi-ty of the coal bed),
IX the heat generated on adsorption of oxygen (AH is the heat of adsorption of oxygen) and
X the heat generated (or withdrawn) on adsorption (desorption) of water (AH is the heat of adsorption of water).
2.3.2 Literature on models
An important step in the modelling of spontaneous heating was done by Van Doornum (1954). He gives a heat balance for the spontaneous heating process. The main restrictions are:
The assumption of a constant oxygen concentration in the pile, giving rise to higher oxidation rates than occur in practice. The assumption that heat transfer occurs only by conduction. At higher velocities, however, convection will also play a role. The neglection of the influence of adsorption and desorption of water.
He used his model to predict the maximum temperature in a pile for one-dimensional Cartesian and cylindrical coordinates. The results of laboratory measurements on oxidation rate, taking into account the influence of temperature and time on this rate, were used as input data.
A more or less comparable model was formulated by Niesert (1969), who also takes into account the diffusion of oxygen into the pile. He gives solutions for a cylindrical geometry only. Convection, both of oxygen and heat, and the influence of water are not incorporated in this model.
Debreczeni (1972) gives the complete differential equations for con-servation of mass and heat (excluding the influence of water). He only uses them for a qualitative description of the spontaneous heating process and does not give any solution.
A more extended model was given in a report by Sondreal and Ellman (1974). In the following aspects their work is comparable with the
model of Van Doornum (1954): heat tranfer only by conduction, con-stant oxygen concentration (for most calculations) and heat genera-tion dependent on temperature and previous oxidagenera-tion time. An impor-tant difference with the calculations of Van Doornum is that not only the maximum temperature is calculated as a function of time, but also the temperature profiles. To make this possible a numerical method of solution (the finite difference method) had to be used and calculations were carried out by a computer. Some results of calcu-lations are given in which transport of oxygen by convection is in-corporated. Oxygen diffusion has been neglected. The influence of adsorption and desorption of water has also been neglected. Sondreal and Ellman (1974) have done many measurements on the variables play-ing a role in spontaneous heatplay-ing. However, because all of the mea-surements have been done with North Dakota lignite, most data are not directly applicable to steam coals. An exception is probably formed by data on porosity and gas flow velocities, which will not depend very much on coal properties.
The most complete model is that of Nordon (1979) giving the complete differential equations for conservation of oxygen, water and energy and for the reaction rate of oxygen with coal. For mass transport both convection and diffusion are included and for heat transport both convection and conduction.
To solve the (one-dimensional) equations Nordon used also the finite difference method. The influence of moisture was not incorporated in the calculations because of the 'prohibitive computational efforts'. Just as with Sondreal and Ellman (1974), direct application of the results to bituminous coals is restricted, because all measurements and calculations were performed for char of a pyrolysis process, with properties which differ very much from those of bituminous coals.
A model of Baum (1981) is comparable with that of Van Doornum (1954) in that it only takes into account conduction of heat and that the oxygen concentrations are kept constant. Using the finite difference method of solution he gives solutions of the equations of conserva-tion of heat for various geometries. Computerized calculaconserva-tions of critical conditions for the occurrence of spontaneous combustion were performed for beds of pulverized coal.
In none of the models mentioned attempts were made to calculate the losses in calorific value due to the oxidation reaction.
After the development and most of the calculations with our model five more papers about mathematical modelling of spontaneous heating have been published.
Handa et al. (1983) presented a two-dimensional model for spontane-ous heating, also using the finite difference method of solution. With this model they calculate temperature and velocity profiles for the case of natural convection. Forced convection and adsorption/ desorption of water are not incorporated.
Edwards (1983) presents a one-dimensional model comparable with that of Nordon (1979), including, as an extra, terms for thermal diffu-sion within the particles and a separate calculation of particle and air temperature. Using the finite difference method of solution he has performed a parametric analysis (sensitivity analysis). The main results are:
particle and air temperature are equal due to the relatively low rates of oxidation/heat generation,
buoyancy can be neglected at the conditions investigated, ventilation rate and inlet air temperature mainly determine whether or not combustion can occur and
porosity (compaction) is a more important parameter than part-icle size.
Calculations are restricted to relatively high ambient temperatures (65°C) because of the very long computational times needed at lower temperatures. The role of water is not incorporated in the model. A more recent model is that of Brooks (1985) (see also Brooks and Glasser (1986)), who uses a model comparable with that of Nordon (1979). For solving the one-dimensional unsteady state equations he used a method different from those used by the other authors. It is the so-called technique of lines involving the use of a ninth-order Legendre polynomal to fit the temperature profile at any given time. Although this method differs from that discussed in the next chap-ter, it has the same advantage, viz. reducing the partial differen-tial equations to a set of ordinary differendifferen-tial equations having
only derivatives in time. This leads to amenable savings in cal-culation times.
Brooks (1985) also made calculations on the mechanisms causing the flow of air in a coal pile. He came to the conclusion that only natural convection and forced convection due to wind pressure play a role. To calculate flow velocity he combines equations 7 with 9 (forced convection) and 10 (natural convection). In the case of natural convection for T in equation 10 he uses the average pile temperature T and for AT the difference between T and the
r av av
ambient temperature T , . Other effects namely diffusion, barometric 'breathing' (flow due to changes in ambient pressure) and thermal 'breathing' (flow due to the daily changes in ambient temperature) can be neglected.
Brooks (1985) compares the results of calculations with the model with measurements in a one-dimensional analogue of a coal pile for the case of forced convection. It consists of a pipe filled with coal particles. It has a diameter of about 8 cm and a height of 24 cm. The walls are insulated and bottom and top ends are open. Gener-ally there is good agreement between measurements (using dry coal) and calculations.
Also dating from 1985 is a model of Chauvin et al. (1985) who devel-oped a one- and two-dimensional version based on the equations of heat and mass conservation and reaction rate. This model describes the spontaneous heating process for pulverized coal stored in a con-tainer (hopper). The equations are numerically solved using the finite difference method. Using the model they find three regimes of air flow. For the lowest flow rates heating is very slow and con-trolled by oxygen supply. At medium flow rates the oxidation leads to spontaneous combustion. At very high flow rates another stable regime is found whereby cooling by convection is sufficient to dissipate the heat produced.
Also in those four more recent models, neither the influence of moisture, nor losses in calorific value were incorporated.
3. THE MODEL FOR SPONTANEOUS HEATING
3.1 ITEMS USE IN THE FORMULATION OF THE MODEL
To obtain a workable model it is necessary to make assumptions which of course take into account the experience gained by other investi-gators and the models described in literature at the moment of for-mulation of the model. These assumptions should be checked; their value will often depend on coal properties. Experiments are needed to obtain input data for calculations with the model which are not available from literature (e.g. the oxidation rates of the coals involved).
The items used in the formulation of the model are presented below. In those cases where measurements were thought to be necessary or should give useful additional data, this is indicated.
1. For the time being a one-dimensional presentation of the spon-taneous heating process has been chosen (using Cartesian co-ordinates). For the case of diffusion/conduction it will give an approximate description along a line perpendicular to the pile surface assuming that pile dimensions are larger than the depth to which the oxygen diffusion occurs. When convection is involved the equations give an approximate description of the process along a streamline of the air flow. In Figure 1 this is illustrated by some examples.
Some examples of streamlines in a coal pile Some examples of diffusion in a pile (no convection)
Fig. 1 Simplified flow and diffusion situations occurring in stored coal.
With more information about air flow in stored coals one or more 'representative' streamlines can be chosen. Because this information is not available in the literature, it has to be obtained in field experiments.
2. The model gives a description of the spontaneous heating pro-cess up to about 80 - 100°C. At higher temperatures the chemi-cal reactions and also their modelling becomes very complicat-ed. Further it is known from experience that at temperature above 80 - 100°C spontaneous heating leads to combustion in relatively short times. This should be checked experimentally.
3. From the results of measurements and calculations described in literature it was clear that the period of time needed to reach a steady state can be very long (up to years). It was therefore decided to incorporate the time-dependent terms in the model.
4. The following remarks are made on the chemisorption (oxidation) reaction:
a. The influence of temperature is described by means of the Arrhenius equation 3.
b. The influence of oxygen concentration (partial pressure) is described by a power law with an (unknown) power n (equation 4) .
c. It is expected that time has very little or no influence on oxidation rate, because imported coal has been contact with air for a long time before being stored. This influ-ence of the oxidation history will more generally be de-scribed by a function f(c_), which is expected to be equal to one in the case of weathered coal.
d. It is assumed that the heat of reaction is independent of temperature. This is not really true because at high tem-perature (70 to 80°C or more) the complete oxidation reac-tion also plays a role. As menreac-tioned in Chapter 2.2.3.1 the heat of reaction in this case is higher than for chemisorption only.
