Prof. Dr. Nagiev A.G.

Sumgait state university,Sumgait, Azerbaijan

E-mail: nashfn@hotbox.ru

ABOUT AN INCORRECTNESS OF THE USED FORMULA

FOR RESIDENCE TIME DISTRIBUTION IN CHEMICAL REACTORS OF IDEAL MIXING

In engineering of chemical processes the formula which expresses function of distribution of time of stay of particles in the device with a continuous stream is often used. For a long time in engineering of chemical processes this distribution for reactors of ideal mixture express the following formula:

. (1)

However the given formula not correctly reflects statistical essence of chaotic process of wandering of a particle in the device. From this formula the particle which has entered into the device follows, that, the greatest chance instantly has to leave it as экспоненциальным the law defines a maximum of function (1) in the initial moment when .

Obviously, dominating factor here should be, as well as in the formula (1), average account time, but a maximum of this distribution it should be equaled to size, instead of . Here; volume; объемный the substance expense.

This important argument allows to accept a hypothesis about normal distribution with a population mean equal on . Really, those reasons, which cause premature (concerning size ) an exit of a particle from the device, in the statistical relation with the same intensity can cause its delay in the device (a sign of symmetry of chaos). The particle which has entered into the device, can instantly leave it or be in it infinitely long, but, the maximum probability should fall to size of average account time of stay in the device. Obviously, function does not reflect (1) this property.

The function offered alternatively, has the following appearance:

. (2)

On fig. 1 schedules of both functions, when are shown: - standard (1) (a continuous curve) and offered (2) (dotted).

Fig. 1. Schedules of standard and offered functions RTD at .

Apparently, it is unique, that can pull together these functions, is an identical size of characteristic time. It is known, that in the theory of linear systems this parameter is designated as constant time of a dynamic link.

In it the erroneous identification of characteristic parameter (RTD) with size of constant time of transient of a dynamic link is covered. From it the correct idea of experimental definition ФРВП originates not. It is considered [1,2], that the experimental fact, An exponential changes of concentration in time after indicator input (a portion of particles of dye) in flowing system in the form of instantly operating impulse can be considered as model of probability of time of stay of particles in flowing system. This position essentially is not true. Introduction of a portion of the indicator in flowing system will form some concentration of these particles which decreases eventually. Spending such experience, it is possible to investigate only the pulse transitive characteristic of a dynamic link on concentration of the indicator. This experience cannot define - «what probability of an exit меченой a particle from flowing system in a time interval (, )?» . During the initial moment, i.e. at , concentration in a target stream is maximum not because indicator particles have the maximum probability instantly to leave volume that is why, that the number of particles of the indicator is maximum in the beginning.

An exponential the law of change of weight of the indicator, or its concentration that is the decision of differential equation , says only that number of particles of the indicator (concentration) in volume decreases in due course also it finds the exact reflex ion in a target stream as in system all particles ideally mix up.

In work the mathematical conclusion of the correct formula (2) is resulted.

By the present day the formula (2) is given to attention of experts, having received publication in 2003 in «the Azerbaijan chemical magazine» [3] which is reviewed in many bibliographic editions, and in 2005 it is published in Izv. VUZ - ov «Chimiya i chimicheskaya technoloqiya» [4]. Unfortunately, this amendment is met by a number of experts sceptically [5] and became a point of issue on pages of the scientific press. It has entailed the author of the present report again to come back to a conclusion of the same formula, but with application of other methodology of the proof.

It is necessary to notice, that the importance of updating of this formula is indisputable not only for area of processes and devices of chemical technology, this formula is widely claimed in many areas of engineering researches - in continuously carried out processes of crystallization, granulation, crushing of loose materials, etc.

REFERENCES

1. O.Levenspiel. Chemical Reaction Engineering, John Wiley & Sons.1999, 3rd ed.

2. Romankov P.G.,Frolov V.F. Massoobmennie processi chimixeskoy technoloqii./L.,Chimiya, 1990, P.76.

3. Nagiev A.G. K voprosu opredeleniya funkcii raspredeleniya vremeni prebivaniya veshestva v reaktore idealnoqo peremeshivaniya// Azerbayjanskiy chimicheskiy jurnal, 2003, No.2, P.46 – 49.

4. Nagiev A.G. Kriticeskaya zametka k voprosu opredeleniya funkcii raspredeleniya vremeni prebivaniya veshestva v apparate idealnoqo peremeshivaniya.//Izv.VUZ-ov “Chimiya I chimicheskaya technoloqiya”V.48, 2005, No.11, P.102-104.

5. Muratov O.V.,Frolov V.F. K voprosu o raspredelenii vremeni prebivaniya veshestva v apparate neprerivnoqo deystviya.// Izv.VUZ-ov “Chimiya I chimicheskaya technoloqiya”V.50,No.11, 2007, 34-39.