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388  Dust Explosions in the Process Industries


             the upper stable flame propagation branch. On cooling, that is, increasing U, n, or both
             in equation (5.lo), the rate of reaction is reduced. However, the reaction continues right
              down to (5) in Figure 5.2, from which the system temperature drops to a stable condi-
              tion in the extinguished regime.
               The scheme illustrated in Figures 5.1 and 5.2 is quite general and applicable to dif-
              ferent types of systems. More extensive treatments of the general ignitiodcombustion-
              stability theory were given, for example,by Gray and Lee (1967), Gray and Sherrington
              (1977), and Bowes (1981). The classical basis for this type of analysis was established
              by Semenov(1959) and Frank-Kamenetzkii (1969). The book by Bowes (1984) provides
              a unique, comprehensiveoverview of the field of self-heating and ignition, not the least
              in solid materials, including dust layers and heaps.
                Although the basic considerationsimplied in Figures 5.1 and 5.2 to some extent pro-
              vide a satisfactory general definition of  ignition, the precise theoretical definition has
              remained a topic of scientific discussion. One example is the dialoguebetween Lermant
              and Yip (1984, 1986) and Essenhigh (1986).



              5.2
              SELF-HEATINGAND SELF-IGNITION
              IN POWDER DEPOSITS

              5.2.1
              OVERVIEWS

              Bowes (1984) reported the state of the art of experimentalevidence and theory up to the
              beginning of the 1980s.Considerableinformationwas available,and theory for predicting
              self-heatingproperties of powders and dustsunder various conditions of storage had been
              developed.
                There were nevertheless some gaps in the quantitativeknowledge, one of which is bio-
              logical heating. In vegetable and animal materials such as feedstuffs and natural fibers,
              self-heating may be initiated by biological activity, in particular if the volume of mate-
              rial is large, its moisture content high, and the period of storage long. However, because
              the microorganisms responsible for the biological activity cannot surviveat temperatures
              above about 75"C,biological heating terminates at this temperature level. Further heat-
              ing to ignition, therefore, must be due to nonbiologicalexothermic oxidation, for which
              theory exists. It is possible, however, that the long-term biological activity in a real
              industrial situation may generate chemically different starting conditions for further
              self-heatingthan the conditions establishedin laboratory test samples heated artificially
              to 75°C by heat from the outside. Further research seems required in this area.
                Starting with the extensive account by Bowes (1984), Beever (1988) highlighted the
              theoretical developments that she considered most useful for assessing the self-heating
              and ignition hazards in industrial situations. In spite of many simplifying assumptions,
              the models available appeared to agree well with experimental evidence. However,
              extrapolating over orders of magnitude, from laboratory scale data to industrial scale,
              was not recommended. Biologicalactivity was not involved in the self-heatingprocesses
              considered. See also Sections 9.2.3.3 and 9.3.5.2 in Chapter 9 for further references.
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