CS209307B1 - Method of material analysis by model - Google Patents

Abstract

The method of analyzing materials using a model according to the invention simultaneously enables quantitative determination of all important material parameters by finding identical courses of transient characteristics of the reacting system with the analyzed material and transient characteristics of the model of the reacting system, where the unknown parameters of the reacting system with the analyzed material are equal in their magnitude to the values of the parameters of the reacting system set on the model for this case.

Description

(54) Method of material analysis by model

The method of analyzing materials using a model according to the invention simultaneously enables quantitative determination of all important material parameters by finding identical courses of transient characteristics of the reacting system with the analyzed material and transient characteristics of the model of the reacting system, where the unknown parameters of the reacting system with the analyzed material are equal in their magnitude to the values of the reacting system parameters set on the model for this case.

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The invention relates to a method of analyzing materials using a model, which consists in using knowledge

I measured transient characteristics of reacting systems with analyzed materials to determine their physical constants and chemical composition.

Existing methods of material analysis either do not use the transition characteristic at all, for example acidimetric titrators, radiometric method and the like, or use the transition characteristic only for the relative determination of the reaction properties of materials, without the possibility of quantitative determination of the values of their physical constants and chemical composition, i.e. parameters that influence the course of the respective transition characteristic. It is understandable that the values of the parameters of materials that were determined by different methods may differ significantly from each other.

A parameter can be considered any constant quantity that has an influence on the course of the transient characteristics of the reacting system with the analyzed material. In the case of a physical process, these are physical parameters, in the case of a chemical reaction, these are physical and chemical parameters, since a chemical reaction always takes place in some apparatus with physical parameters.

The above disadvantages are eliminated by the method of material analysis by a model according to the invention, the essence of which is that a reacting system is created from the analyzed material, suitable additional materials or energies and apparatus, which, for a given vector of input quantities, a vector of unknown values of the parameters of the reacting system and a given vector of state quantities of the reacting system, has a measurable vector of transient characteristics of the reacting system, after which a model of the reacting system is created which, for the same values of the vector of input quantities, a vector of selected values of the parameters of the reacting system and a vector of selected values of the initial conditions of the state quantities of the reacting system, and a vector of transient characteristics of the reacting system model, has a vector of transient characteristics of the reacting system model, then a quantitative determination of the unknown values of the vector of parameters of the reacting system is performed by finding the values of the vector of these parameters for _the corresponding courses of the vectors of measured transient characteristics of the reacting system and transient characteristics /

of the model of the responding system, determined repeatedly on the model of the responding system at variously chosen values of the vector of parameters of the responding system, until it is true that both vectors of the transient characteristics of the responding system and its model differ from each other less than permitted by a pre-specified criterion, when the unknown values of the vector of parameters of the responding system are equal in size to the values of the vector of parameters of the responding system set on the model for this case.

The method of analyzing materials using a model according to the invention enables simultaneous quantitative determination of all important material parameters and their connection to the course of their transient characteristics, regardless of the apparatus used in which the transient characteristics were measured and the device used to implement the model, thereby eliminating the influence of the apparatus design, heat losses to the environment, thermotaxation, and the like.

The invention is further described and explained in more detail with the aid of a drawing showing a model of a reacting system and examples.

The drawing shows a model M _g of a reacting system S, which has: a vector of time-dependent input quantities ;t B(t) = B ₂ (t), ... , B _k (t 0 ; a vector of parameters of the reacting system, which are time-independent quantities C = f ^C l' ^C 2' ·· » ^C nJ ia and a vector of transient characteristics of the reacting system model P(t), which are functions of time t, the vector of input quantities B(t), the vector of parameters C, the vector of state quantities of the reacting system X(t) and the model Mg : ^M P(t) = £ ^Μ Ρχ( t) , ^Mp 2( t) , . . . , ^M P^,( t)J = M _g ^B( t) , C, X(t)Jwhere x(t) =[x _i (t), x ₂ (t),..., x _R (t)J.

The model of the reacting system M _g can be implemented, for example, by a suitable physical device - the result is a physical model, or by a computer - the result is a computer model.

Each model of a reacting system M _g has its own block structure, which defines the causal dependencies between the vectors of quantities B(t), C, X(t), ^P(t) and thus allows the calculation of the vector of transient characteristics ^P(t).

The reacting system S exhibits, for given vectors of input quantities B(t) and initial conditions X _p (t) = [x _lp (t), x _2p (t),..., X _Rp (t )], a completely unique vector of transient characteristics ®p/^) ®P ₂ (t),..., $p^( t)|, which can be determined by measurement.

The block structure for the model of the reacting system M _g can be constructed using the laws of physics and chemistry for mass conversion during a reaction, reaction kinetics, heat exchange during a reaction, or other laws according to the specific case of the reacting system S.

If we set X _p (t) = x(t) for the same B(t), then for the block structure of the model

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M reacting system M _tt there is a set of vectors of transient characteristics P( t) , which are functions of the vector of parameters C. For each selected combination of values of components Tc^, C ₂ ,.:.,C^j of the vector of parameters C, the vector of transient characteristics ^P(t) is found (for example, in the case of a computer model by calculating the block structure on a computer) and compared with the vector of transient characteristics $P(t). The strategy of changing the values of the components of the parameter f ^c i' ^c 2'···' ^c nJ is guided by the deviations of ^P(t) from ^P(t). The procedure is repeated until the consistent course of both vectors of transient characteristics ^Mp (t) and ^S P(t) is achieved, which will be better than required by the previously specified criterion. Here the procedure ends and the values [c*, C*, .... C*J , at which the condition of consistent course of vectors ^Mp (t) and ®P(t) is met, give the values of the parameters of the analyzed reacting system.

The construction and implementation of the model of the reacting system M _g can be considered as the calibration part;

X 46 I ^C l' ^C 2'··' ^C N | ^za Part of the method of analyzing materials by the model according to the invention.

The following provides several examples of different responding systems, their transient characteristic vectors, and measured parameters.

Example 1

Heating, evaporation and cooling of water.

A purely physical reacting system, where an electric immersion heater, thermometer and stirrer are immersed in a glass beaker filled with water. The beaker is placed on a scale. At a certain time, the switch of the immersion heater is turned on and the water is heated to a predetermined temperature, e.g. 80 °C, by the constant electrical power supplied. When this temperature is reached, the switch is turned off, the time of switching off is recorded and the water begins to cool. The reaction ends when the water reaches approximately the ambient temperature again. During this process, the electrical power is converted into heat in the immersion heater, which heats the water. Heat losses are represented by the transfer of heat from the water to the apparatus and from the apparatus to the surroundings. Further losses of heat and water are caused by the evaporation of water to the surroundings. The apparatus here consists of a glass beaker, thermometer, stirrer and immersion heater. The model of this reacting system should quantify the following vectors: (see figure):

Vector of input quantities B(t), K = 7:

B^(t).- ambient atmosphere temperature

Bg(t) - initial temperature of the apparatus

B^(t) - initial mass of water

B^(t) - initial water temperature

B-ít) - relative humidity of the surrounding atmosphere

Bg(t) - effective surface area for water evaporation

B?(t) - heat supplied by the immersion heater

Parameter vector of unknown values C, N = 5:

- constant of heat loss from the apparatus to the surrounding atmosphere Cg - constant of heat loss from water to the apparatus

C^ - specific evaporation of water at 30 °C

- specific evaporation of water at 80 °C

- thermal capacity of the apparatus

Vector of state variables X(t), R = 4: ,

Xj^t) - total heat loss from the apparatus to the surrounding atmosphere

Xg(t) - total heat loss from water to the apparatus

X^(t) - total mass of evaporated water

X/|(t) - total heat loss for water evaporation

Vector of transient characteristics ^{S * *} P(t), M = 2;

with

P^(t) — measured water temperature

S ' Pg(t) - measured weight of water

For a specific implementation of a reacting system, the following values of the parameters of the given reacting system in SI units have been determined:

C* = l,l4

C* = 4.20

C* = 4.80 . io” ⁸

C* with 6.20 . io ⁸

C* = 400

Example 2

Hydrataoe of powdered lime.

This is a physico-chemical reaction system, where water is poured into a glass beaker equipped with a cork stopper, a stirrer and a thermometer. After pouring powdered lime into the water

hydrate with the release of heat, which heats the reacting mixture. After the hydration is complete, when all the free calcium oxide has reacted, heat loss to the surroundings causes the reacted mixture to cool. The reaction ends when the reacted mixture reaches approximately ambient temperature again. The apparatus here consists of a glass beaker, a thermometer, a stopper and a cork.

The model of this reacting system has the following vectors of quantities (see figure):

Vector of input quantities B(t), K = 6:

BjjC t) - weight of dosed powdered lime

Bg(t) ” initial temperature of lime

Β^(ΐ) - initial temperature of the dosed water

B^(t) - mass of dosed water

B^(t) - initial temperature of the apparatus

Bg(t) - ambient atmospheric temperature

Parameter vector of unknown values C, N = 7:

- the proportion of the mass of free calcium oxide in lime

Cg - exponent of the differential equation for the hydration kinetics from the interval of values 0.5 to 2

- hydration constant of lime

- the power base in the exponential function for the dependence of the lime hydration rate on the temperature of the reacting mixture from the value interval 1.01 to 1.04

- constant of heat loss from the hydrating mixture to the apparatus Cg - constant of heat loss from the apparatus to the surrounding atmosphere C? - heat capacity of the apparatus

The parameters C^ to depend, among other things, on the location and method of calcination of the limestone. There is no other measuring method for determining free calcium oxide (pai-ainetr C^). The parameters C? to depend on the apparatus used.

Vector of state variables X(t), R = 3: ¹ '

X^(t) - total heat loss from the apparatus to the surrounding atmosphere

Xg(t) - total heat loss from the reacting mixture to the apparatus

Xj(t) - total mass of reacted free calcium oxide

Vector of transient characteristics ^P(t), M = 1:

ρ,ίt) - measured temperature of the reacting mixture

For a specific design of the reacting system and the lime used, the following values of the parameters of the given reacting system were determined - in SI units:

C* = 5.86 C* = l64o

C* = 0.65 10“ ⁶ c* = 1.03 c* = 23.02

3· example

Dissolution of aluminum in an alkaline environment.

This is a physical-chemical reacting system, where lime hydrate is poured into a metal container equipped with a stopper and a thermometer. After pouring aluminum, in the form of flakes or paste, into the lime hydrate, the dissolution of aluminum begins, forming hydrogen and releasing heat, which in turn heats up the reacting mixture. The components of the vector of input quantities B( t) include the masses and initial temperatures of the dosed masses, the initial temperature of the apparatus and the ambient temperature i

atmosphere. The components of the vector of parameters of unknown values C include the proportion of the mass of free aluminum in the dosed aluminum, the dissolution constant of aluminum, and the parameters of the apparatus used.

with

The transient response vector P(t) can be given by these two components:

with

P^(t) - measured temperature of the reacting mixture Sp^t) - measured pressure of hydrogen and water vapor.

Example 4

Hydration of cement paste.

This is a physical-chemical reacting system, where a mold is inserted into a container equipped with a stopper, a thermometer and an environment with saturated water vapor, into which cement paste is dosed, that is, water, + clinker + gypsum. Cement paste hydrates with the release of heat, while simultaneously hardening. The components of the vector of input quantities B(t) include the masses and initial temperatures of the dosed masses, the initial temperature of the apparatus and the temperature of the surrounding atmosphere. The components of the vector of parameters of unknown values C include the relative masses of minerals in the clinker, the phase composition, the hydration constants of individual minerals, the relative content of sulfite SO^ in gypsum, and the parameters of the apparatus used.

with

The transient response vector P(t) can be given by these two components:

with

Pj(t) - measured temperature of the reacting mass ^Pgít) - measured strength of the reacting mass

The method of analyzing materials using a model according to the invention is applicable in physics, chemistry, construction, or other areas where the analyzed material and any additional materials or energy create a system that reacts with the apparatus, on which the vector of transition characteristics can be measured.

The invention is particularly suitable for continuous input quality control of raw materials for production technologies that depend on the course of transient characteristics during the reactions of these raw materials, for example in the production of aerated concrete.

Claims (1)

SUBJECT OF THE INVENTION Method for analyzing materials by a model, characterized in that the analyzed material, suitable additional materials or energies, and the apparatus are formed responsively. a system which for a given vector of input quantities, a vector of unknown values of the parameters of the reactive system and a given vector of the quantities of the reactive system, has a measurable vector of the transient characteristics of the reactive system. parameters of the reactive system and the vector of selected values of the initial conditions of the reactive system state variables, has a vector of transient characteristics of the model of the reactive system, then quantify unknown values of the vector of the reactive system parameters the model of the reactive system ascertained repeatedly on the model of the reactive system at different the system until the two vectors of the transition characteristics of the reactive system and its model differ less from each other than allowed by a predetermined criterion, where the unknown values of the vector of the parameters of the reactive system are equal in size set to the values of the parameter vector responsive. system.