Mathematical and information models of a grain elevator as a potentially explosive control object are developed. These models create the base for software of a decision support system for explosion safety of grain elevators. Mathematical model is based on combination of the fuzzy logic and classical mathematical methods from the mathematical theory of combustions and explosions. Information model of the grain elevator as a complex potentially explosive object is also developed. Grain elevator is considered from the point of view of system analysis as the complex hierarchical system. This system is structurized, elementary potentially explosive objects are indicated. All kinds of these objects are described with their attributes and relationships, information structure diagrams are also built Appropriate software has been developed and some calculations have been done. These calculations are useful from the point of view of the grain elevator designing. It is proved that monolithic reinforced concrete silos are noticeably less explosive than prefabricated reinforced concrete silos and metal silos are much more explosive than reinforced concrete ones. It is also proved that increasing the height of the silo increases its explosion hazard. But the most interesting result is that a low degree of fire hazard does not always corresponds to a low degree of its explosiveness.
There are lots of explosions at the grain processing enterprises and grain storages all over the world every year. Grain elevators are among the most explosive grain enterprises.
There were 15 grain dust explosions reported
for the U.S. in 1994 [
A grain elevator is a facility for stockpiling and storing large quantities of grain and for bringing and keeping the grain in good conditions. Any grain elevator contains a tower with a bucket elevator (noria) or a pneumatic conveyor, which picks up grain from a lower level and deposits it in a silo (or, sometimes, in other storage). The construction of silo buildings, tied to the working building of the grain elevator, is widespread.
If there is a sufficient concentration of flammable flour or grain dust in the air anywhere in the elevator, an explosion may occur.
The distribution of the dust-air mixture
explosions at grain enterprises at the place of
origin is such that silos and bunkers account for
almost half of the total number of explosions [
Thus, the most explosive elements in the system of grain enterprises are silos and bunkers, as well as bucket elevators and conveyors.
One of the reasons for the large number of
explosions at grain elevators is that the automated
control systems of these elevators have certain
disadvantages [
The development of an appropriate mathematical and information models of a grain elevator as a potentially explosive object (PEO) is the aim of this research.
As shown earlier [
Thus for the constructing of DSS for
explosion safety it is preferable to use the model
of decision-making under uncertainty, that is
based on the fuzzy-set theory and fuzzy logic [
But fuzzy logic should be used in combination
with the exact mathematical theory of
combustions and explosions [
Mathematical modeling of the grain elevator
as complex PEO consists of the following steps:
Each separate object of the grain elevator
(bucket elevator, silo, over-silo floor, sub-silo
floor, working building, etc.) is considered as
an elementary potentially explosive object
(EPEO). Such EPEO is geometrically modeled
as flat channel (unlocked, closed at one end or
closed at both ends) or round cylindrical tube
(also unlocked, closed at one end or closed at
both ends).
For each EPEO, the concentration limits
of ignition and explosion are determined
separately, as well as the explosion induction
distance Xs [
Thus mathematical model for the decisionmaking on hazards of grain elevator explosions is constructed.
Information modeling of the grain elevator as
a complex PEO is developed in accordance with
the principles, which are set out in the scientific
works [
Grain elevator (complex PEO) is considered
from the point of view of the system analysis as
the complex hierarchical system. This system is
structurized, EPEO are indicated. All kinds of
these objects are described with their attributes
and relationships [
On the base of mathematical and information models in the decision-making on hazards of grain elevator explosions the corresponding software has been developed. The program is Russified, so all the captions in the program are made in Russian.
The following example shows how the corresponding subroutine («SilosOtdelniy») evaluates the explosion hazard of an individual silo. The silo is chosen as an example as it is the most explosive part of the elevator.
A user can choose one of the standard reinforced concrete silos or they may independently set the shape and dimensions of the silo (reinforced concrete silo or metal silo) (Figure 1).
It is assumed that each silo has a circular, square or rectangular cross-section.
More complicated cross-sectional shapes of a grain elevator silo are possible in principle, but in practice they are extremely rare. In addition, using the factor of application of fuzzy logic, the complex shape of the silo section can usually be replaced with a simpler one (one of the three above).
Further calculations require specifying the type of dust-air mixture or grain product, dust concentration, humidity, temperature and dust dispersion (i.e. average size of dust particles) (Figure 2). All these values can be measured using standard metrological devices in the operating mode of a grain elevator and the software in this case should to be a part of the software of the corresponding automated control system. In some cases, the corresponding values can be set in the program by the operator or the decision-maker.
The current values of temperature and dust concentration are compared with the ignition temperature and the lower concentration limit of ignition.
The ignition temperature and the lower
concentration limit of ignition are obtained as a
result of the approximation of the known
empirical data [
The result of evaluation of the possibility of ignition and fire occurrence is depicted on the monitor screen as shown in Figure 3.
As it can be seen from Figure 3, the
decisionmaker is not dealing with the numerical values of
fuzzy logical variables, but with linguistic
variables.
Evaluations for the possibility of a
fire-toexplosion transition, the explosion induction
distance and the time of the fire-to-explosion
transition are carried out according to [
For a monolithic reinforced concrete silo [
For a prefabricated reinforced concrete silo [
For a metal silo made by rolling or winding, the explosion induction distance is reduced in the program by 50 times, since the inner wall surface of such silo resemble the Shchelkin spiral.
All the above estimates of the explosion induction distance are approximate (especially for prefabricated reinforced concrete and metal silos), therefore, the estimates of the explosiveness of the silo given below are “fuzzy”. Therefore, the corresponding fuzzy variables are introduced into consideration, over which logical operations are performed according to the laws of fuzzy logic.
The computer program (subroutine «SilosOtdelniy») displays various kinds of messages on the monitor screen as a result of the calculations.
Messages about the explosion induction distance and the time of the possible fire-toexplosion transition (Figure 4) represent the necessary information for decision-making on ensuring explosion safety and/or explosion protection.
It is obvious that if the time of the possible transition of combustion into an explosion is long enough, then it is possible to make a wide variety of decisions (organizational, technical, technological).
If this time, on the contrary, is short, then the only possible solution is to stop immediately the technological process with the simultaneous evacuation of personnel.
In the latter case, it is possible to replace the automated control with an automatic one.
Calculations show that the time of the possible fire-to-explosion transition in organic dust-air mixtures is hundreds and thousands of times longer than the development time of an explosion in combustible gas mixtures.
The type of message with a fuzzy evaluation of the explosiveness is shown in Figure 5.
An important point is that all the above estimates are made without the participation of experts (evaluators).
The complications of experts' interaction with
each other are well known [
Therefore, it is advisable to avoid the
participation of experts in solving such
decisionmaking tasks [
Mathematical and information models of a grain elevator as a potentially explosive object are developed. These models create the base for software of DSS for explosion safety of grain elevators.
Appropriate software has been developed and some calculations have been performed.
These calculations are useful not only from the point of view of testing the proposed method of mathematical modeling of a grain elevator as a potentially explosive object or testing the software itself, but also from the point of view of the grain elevator designing (i.e. appropriate decisions on the explosion safety and explosion protection can be made already at the stage of the elevator design).
The results of the calculations are summarized in the following conclusions (some of which are quite obvious in themselves): If the humidity rises, then both the explosion hazard and the fire hazard of the grain elevator decrease. Temperature fluctuations within a few tens of degrees have little effect on the fire hazard and explosion hazard of the grain elevator. A decrease in the average size of dust particles in the dust-air mixture leads to the increase of the explosion hazard of this mixture. Fine dust is much more explosive than coarse dust (this conclusion is theoretically quite obvious). Monolithic reinforced concrete silos are noticeably less explosive than prefabricated reinforced concrete silos. Metal silos are much more explosive than reinforced concrete ones. Increasing of the height of the silo increases its explosion hazard. A low degree of fire hazard does not always corresponds to a low degree of its explosiveness (in this case, the explosiveness is understood as the possibility of an explosion in case of ignition).