WO2004050920A1

WO2004050920A1 - Reaction vessel operation control method, device, computer program, and computer-readable record medium

Info

Publication number: WO2004050920A1
Application number: PCT/JP2003/012997
Authority: WO
Inventors: Hiroyuki Yoshino; Yasushi Kurita; Masatoshi Miyawaki; Hiroyuki Furuta; Junichi Nakagawa; Masahiro Yamamoto
Original assignee: Nippon Steel Corporation
Priority date: 2002-11-29
Filing date: 2003-10-09
Publication date: 2004-06-17
Also published as: TW200415343A

Abstract

A reaction vessel operation control device comprises an input unit (101) to which inputted is data on temperature measured by thermocouples at the inner and outer surfaces of the reaction vessel and an inverse problem analysis unit (102) for determining the temperatures or the heat fluxes at the inner and outer surfaces of the reaction vessel by conducting inverse problem analysis using an unsteady heat equation on the basis of the temperature data inputted into the input unit (101). The inverse problem analysis unit (102) calculates the temperatures T at the positions of the thermocouples by using the unsteady heat equation from the temporary values of the heat fluxes at the inner and outer surfaces of the reaction vessels. Then the inverse problem analysis unit (102) determines, as the heat fluxes, the temporary values of the heat fluxes at which the sum of the squares of the differences between the temperatures Y measured by the thermocouples linearly arranged and the calculated temperatures T is minimum.

Description

Specification

Operation management method, apparatus, computer program, and computer-readable recording medium for reaction vessel

The present invention relates to a reaction vessel operation management method suitable for use in managing the operation of a reaction vessel involving a high-temperature gas reaction or a liquid reaction such as a blast furnace, a steel material heating furnace by combustion, a coal gasification reaction furnace, etc. The present invention relates to an apparatus, a computer program, and a computer-readable recording medium. Background art

When controlling the operation of a reaction vessel involving a high-temperature gas reaction or a liquid reaction such as a blast furnace, a steel heating furnace by combustion, or a coal gasification reaction furnace, one specific example is to monitor the flow of hot metal at the bottom of the blast furnace. In such a case, it is necessary to observe the situation inside the reaction vessel (blast furnace) (for example, combustion behavior) to understand the situation.

Conventionally, the state inside the reaction vessel has been estimated based on the temperature measured by a thermocouple embedded inside the wall of the reaction vessel. For example, if there is a sudden rise in temperature, it is estimated that abnormal heat is generated in the reaction vessel around the thermocouple, and if there is an extreme drop in temperature, heat is generated in the reaction vessel around the thermocouple. This is an empirical method such as estimating that a decrease in the calorific value has occurred such as a reduction in the reaction area.

However, in the above estimation, it is inevitable that a time lag occurs between the timing of the occurrence of the temperature abnormality in the actual reaction vessel and the timing of the temperature measurement. This is because the abnormal temperature in the reaction vessel is transmitted to the surface of the reaction vessel as a change in heat flux, and then part of the heat is accumulated inside the wall material of the reaction vessel, and the heat is gradually transmitted by the heat conduction effect. This is because the temperature change finally occurs in the thermocouple. In principle, the heat conduction phenomenon in a solid having a heat capacity has a slight time delay (non-stationary).

On the other hand, considering the heat conduction phenomenon inside the reaction vessel wall as an unsteady one-dimensional heat conduction inverse problem, one thermocouple temperature change or multiple thermocouple temperature changes arranged in one-dimensional direction Therefore, a method for estimating a change in heat flux on the inner surface of a reaction vessel has been proposed. Figure 35 shows a two-dimensional cross section near the furnace wall of a reaction vessel (heating furnace) in which multiple thermocouples “X” are embedded. Although the boundary is indicated by a broken line in the furnace wall, one-dimensional means that only the heat flow in the direction along the broken line is considered. That is, for example, assuming heat conduction in la → lb → lc or ld → le directions, the heat flux on the furnace inner surface is estimated. At this time, it is general to determine the heat flux on the unknown inner furnace surface, assuming that the cooling condition of the outer furnace surface is known. Of course, it is also possible to reverse the known and unknown boundary conditions.

As the above estimation method, for example, Japanese Patent Application Laid-Open Publication No. 2000-1 — 324 217 discloses an inverse problem analysis of an unsteady one-dimensional heat conduction equation from a thermocouple embedded in a blast furnace hearth. It describes a method for estimating the heat flux.

One of these methods is to estimate the heat flux at the opposite end point from the thermocouple temperature change at one point and the cooling condition (assumed to be known) at the end point. Such cooling conditions are given by the heat transfer coefficient and the temperature of the cooling water.In particular, since the heat transfer coefficient is estimated from the average flow velocity of the cooling water using an empirical correlation formula, uncertain estimated values This may have a negative effect on the accuracy of the heat flux estimate at the opposite end point, estimated using the value in the inverse problem.

Also, as another method, an estimation method using two points of thermocouple temperature change is described.However, since it is a method to solve by giving one of the two points as a fixed temperature boundary condition However, it is difficult to estimate by capturing the relative temperature change between the two points, and it is possible to estimate the heat flux under the fixed temperature boundary condition, but outside of the side selected as the fixed temperature boundary condition The end point heat flux on the extension line cannot be estimated.

Furthermore, in any of the above methods, the change in thickness due to the in-furnace melt attached to the surface of the refractory and the change in heat flux are simultaneously estimated, rather than the method of finding the heat flux at both ends while fixing the analysis length. Method. Introducing a mouthpiece that increases or decreases the amount of adherence by coagulation and dissolution phenomena into the inverse problem analysis firstly complicates the calculation procedure and makes the calculation unstable. Second, if a calculation procedure that changes the analysis length is entered at each time step, uncertainties may be mixed in the method of estimating the temperature distribution before and after the change in the length. Estimation accuracy may be worse I can't deny it. As described above, the conventional inverse problem analysis method is inadequate in many respects, and a new method for simultaneously estimating the heat flux at both ends by fixing the analysis length from multiple thermocouple information has been established. Therefore, a technique for accurately and stably estimating unsteady changes in heat flux is important.

The original unsteady one-dimensional inverse one-dimensional heat conduction problem is to estimate the boundary conditions on the inner and outer surfaces of the furnace at the same time. We can only get an approximate answer to the given boundary condition. For example, temperature fluctuations measured by a certain thermocouple may be caused by a change in heat flux on the inner surface of the reaction vessel as described above, or may be caused by poor contact of a cooling device installed outside the reaction vessel. It cannot be distinguished whether the change is due to a change in heat flux on the outer surface of the reaction vessel. In order to evaluate more rigorously, the heat conduction phenomenon should also occur in the vertical direction across the broken line shown in Fig. 35, and it is necessary to solve the inverse heat conduction problem in two dimensions. In this case, even if the upper and lower boundaries in Fig. 35 are assumed to be adiabatic, it is necessary to construct a two-dimensional inverse problem for estimating the fine heat flux distribution on the left and right boundaries.

In this case, a method of estimating the temperature distribution by trial and error and simultaneously estimating the temperature distribution at both ends is also conceivable, so that the temperature change can be sufficiently expressed from multiple pieces of thermocouple information. However, in such a method, the calculation becomes complicated as the number of thermocouples increases, and it is extremely difficult to obtain a temperature distribution solution that satisfies the measured temperature changes of all thermocouples. In addition, it is difficult to determine the standard for determining the absolute value of the difference between the measured temperature and the calculated temperature for each thermocouple, so it is difficult to generalize the calculation procedure.

As one example of this, from the two thermocouple temperatures,

By applying the method of No. 7 publication, the unknown heat flux is calculated by alternately changing the two end points, and apparently the heat flux of the end point can be estimated at the same time. In other words, the measurement temperature as the fixed temperature boundary condition is alternately calculated repeatedly, and when the measured temperature and the calculated temperature of both thermocouples agree to some extent, both ends in the time step Heat flux solution. However, in this method, it is difficult to determine at which point the absolute value of the difference between the measured temperature and the calculated temperature should be solved for each thermocouple, and in some cases, Ability to express one thermocouple temperature extremely well Even if the other thermocouple temperature cannot be expressed very much, there is a risk that it will be recognized as a solution. In other words, when minimizing the absolute value of the difference between the measured temperature and the calculated temperature at two thermocouple positions, a criterion for how to balance the minimization at two independent thermocouple positions is required. It is difficult to set properly. It goes without saying that if this method is extended to the case of multiple thermocouples, it will be extremely difficult to determine the solution.

When performing inverse problem analysis to simultaneously estimate the heat flux at both ends from multiple thermocouple information, it is necessary to stabilize the inverse problem analysis.

Until now, for example, the time course of the heat flux obtained by inverse problem analysis has been independently plotted and evaluated.However, if the change of the heat flux is large or small, it is very vague, It is difficult to judge how non-stationary changes (rapid changes) are in the state inside the container. The present invention has been made in view of the points mentioned above, and _c to that of the heat flux changes and temperature changes in the inner and outer surfaces of the reaction vessel and can be simultaneously estimated the main purpose is the inverse problem The purpose is to stabilize the analysis and to evaluate the degree of unsteadiness of the state in the reaction vessel. Disclosure of the invention

The operation management method for a reaction container according to the present invention is a method for managing the operation of a reaction container for controlling the operation of a reaction container accompanied by a temperature change reaction, wherein a plurality of the reaction containers are arranged at least in a thickness direction inside a wall of the reaction container. Based on the temperature measured at the measured temperature measurement point, the inverse problem analysis using an unsteady heat conduction equation is performed, thereby obtaining a temperature or a heat flux on the inner surface and the outer surface of the reaction vessel. It has features.

Further, another feature of the operation management method for the reaction vessel of the present invention is that the temperature measured at each of the temperature measurement points, the temperature on the inner surface and the outer surface of the reaction vessel, Or the minimum value of the sum of the squares of the difference between the temperature at each of the temperature measurement points calculated from the assumed value of the heat flux and the unsteady heat conduction equation is the inner surface and outer surface of the reaction vessel. In that the temperature or the heat flux is determined.

Another feature of the operation management method for a reaction vessel of the present invention is that the method includes a step of increasing the number of digits after the decimal point of the temperature data measured at the temperature measurement point, and The point is that the increased number of temperature data is used for the inverse problem analysis. Alternatively, the method includes a step of performing a filtering process on the temperature data measured at the temperature measurement point, and using the temperature data after the filtering process in the inverse problem analysis. Alternatively, the method includes a step of increasing the number of digits after the decimal point of the temperature data measured at the temperature measurement point, and a step of filtering the temperature data with the number of digits after the decimal point increased. Is used in the above inverse problem analysis.

Another feature of the operation management method for a reaction vessel of the present invention is that, based on the temperature data measured at the temperature measurement points, analysis is performed by a steady-state method, whereby the inner surface of the reaction vessel is analyzed. The analysis procedure by the steady-state method for obtaining the temperature or the heat flux, the temperature or the heat flux on the inner surface of the reaction vessel obtained by the inverse problem analysis, and the temperature or the heat flux obtained by the analysis procedure by the steady-state method And a comparison procedure for comparison.

Another feature of the operation management method for a reaction vessel of the present invention is that the inverse problem analysis is an inverse problem analysis using an interpolation function or an external 揷 function that satisfies an unsteady heat conduction equation. On the point.

An operation management apparatus for a reaction vessel according to the present invention is an operation management apparatus for a reaction vessel for managing an operation of a reaction vessel accompanied by a temperature change reaction, and a plurality of the operation management apparatuses are arranged at least in a thickness direction inside a wall of the reaction vessel. A means for determining the temperature or heat flux on the inner surface and the outer surface of the reaction vessel by performing an inverse problem analysis using an unsteady heat conduction equation based on the temperature measured at the measured temperature measurement point. It is characterized by points.

The computer program of the present invention is a computer program for managing the operation of a reaction vessel accompanied by a temperature change reaction, wherein the computer program is measured at least at a plurality of temperature measurement points arranged in the thickness direction inside the wall of the reaction vessel. By performing an inverse problem analysis using the unsteady heat conduction equation based on the temperature, the inner surface of the reaction vessel and It is characterized in that a process for obtaining a temperature or a heat flux on the outer surface is executed. The computer-readable recording medium of the present invention is characterized in that the above-mentioned computer program of the present invention is stored. BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a diagram showing a schematic configuration of an operation management device for a reaction vessel according to the first embodiment.

FIG. 2 is a flowchart for explaining the inverse problem analysis processing.

FIG. 3 is a diagram for explaining an arrangement relationship of thermocouples in an example of the first embodiment.

4A to 4E are diagrams for explaining the analysis results in the example of the first embodiment.

FIG. 5 is a diagram showing a schematic configuration of an operation management device for a reaction vessel according to the second embodiment.

FIG. 6 is a diagram showing a schematic configuration of another operation management device for a reaction vessel in the second embodiment.

FIG. 7 is a diagram for explaining an arrangement relationship of thermocouples in an example of the second embodiment.

8A to 8D are diagrams for explaining the analysis result in the example of the second embodiment.

FIG. 9 is a diagram for explaining the arrangement relationship of thermocouples in another example of the second embodiment.

FIGS. 10A to 10D are diagrams for explaining analysis results in another example of the second embodiment.

FIG. 11 is a diagram showing a schematic configuration of a reaction vessel operation management device according to the third embodiment.

FIG. 12 is a diagram for explaining the analysis by the stationary method.

FIG. 13 is a diagram for explaining the analysis by the stationary method.

FIG. 14 is a diagram for explaining a state in which the amount of heat input suddenly changes. FIG. 15 is a diagram for explaining the problem setting.

FIG. 16 is a characteristic diagram showing a change in heat flux at each cross-sectional position when a heat flux that changes stepwise at a position of 4 m is given.

FIG. 17 is a characteristic diagram showing a temperature change at each cross-sectional position when a heat flux that changes stepwise at a position of 4 m is given.

FIG. 18 is a diagram showing an example in which the horizontal axis is mapped as the non-stationary index and the vertical axis is mapped as the steady heat flux.

FIGS. 19A to 19E are diagrams for describing the analysis results in the example of the third embodiment.

FIG. 20 is a diagram showing an example in which the horizontal axis represents the unsteadiness index and the vertical axis represents the constant heat flux in the example of the third embodiment.

FIG. 21 is a flowchart for explaining the inverse problem analysis processing.

FIG. 22 is a diagram for explaining an arrangement relationship of thermocouples in Example 1 of the third embodiment.

FIG. 23 is a diagram for explaining an arrangement relationship of thermocouples in Example 1 of the third embodiment.

FIGS. 24A and 24B are diagrams showing the results obtained by performing a forward problem analysis with artificial boundary conditions and determining the change over time in thermocouple temperature.

Fig. 25A and Fig. 25B are diagrams showing the results of performing a forward problem analysis with artificial boundary conditions and determining the change over time in thermocouple temperature.

FIG. 26 is a diagram schematically showing a relationship among a reference point, a known temperature point, and an estimated point. FIG. 27 is a diagram schematically showing a relationship among a reference point, a known temperature point, and an estimated point. Figure 28 shows the results of comparing the heat flux given by the forward problem analysis with the heat flux found by the inverse problem analysis.

Figure 29 shows the results of comparing the heat flux given by the forward problem analysis with the heat flux found by the inverse problem analysis.

FIGS. 30A to 30D are diagrams for explaining the analysis results in Example 1 of the fourth embodiment.

FIGS. 31A to 31D illustrate the analysis results in Example 1 of the fourth embodiment. FIG.

FIG. 32 is a diagram schematically showing a relationship among a reference point, a known temperature point, and an estimated point.

FIG. 33 is a diagram for explaining an analysis result in Example 2 of the fourth embodiment.

FIG. 34 is a diagram for explaining the analysis result in Example 2 of the fourth embodiment.

FIG. 35 is a diagram showing a two-dimensional cross section of a reaction vessel in which a plurality of thermocouples are embedded. BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings.

(First Embodiment)

FIG. 1 shows a schematic configuration of the operation management device for a reaction vessel of the present embodiment. As shown in the figure, the operation management device for the reaction vessel has an input section 101 for inputting temperature data measured by a thermocouple embedded in the wall of the reaction vessel (see Fig. 35). Inverse problem analysis to determine the temperature or heat flux on the inner and outer surfaces of the reaction vessel by performing an inverse problem analysis using the transient heat conduction equation based on the temperature data input to the input unit 101 Unit 102 and an output unit 103 for displaying the temperature or heat flux on the inner surface and the outer surface of the reaction vessel calculated by the inverse problem analysis unit 102, for example, on a display (not shown). Have.

Hereinafter, the processing mainly performed in the inverse problem analysis unit 102 will be described in detail. The unsteady heat conduction equation used for the inverse problem analysis is expressed as shown in the following equation (1).

In the formula (l), p is the density of the material in the reaction vessel, c _P is the specific heat of the material in the reaction vessel, τ is the calculated value of the temperature inside the reaction vessel, t is time, and k is the thermal conductivity of the material in the reaction vessel. Represents

Heat conduction inverse problem analysis is based on the unsteady heat conduction equation that governs the calculation domain. Then, assuming the temperature inside the region as known, estimating boundary conditions such as temperature and heat flux at the region boundary. On the other hand, the heat conduction order problem analysis refers to estimating the temperature inside a region from known boundary conditions such as temperature and heat flux at the region boundary.

Five

Examples of the two-dimensional inverse problem analysis method include, for example, a method disclosed by the present applicant in Japanese Patent Application Laid-Open No. 2002-2066958. It can also be applied to title analysis. As an example of one-dimensional inverse problem analysis, an analysis method proposed by Beck et al. Is known (Beck and others, Inverse Heat Conduction, 1985, Wiley, New Yo: rk).

Also, as a recent method of inverse problem analysis, it is conceivable to apply probabilistic estimation methods such as Kalman filter theory, projection filter theory, and the like. At present, this method is considered to be applied to the steady-state heat conduction equation (observation equation), where the left side of equation (1) is set to zero. If possible, a similar inverse problem analysis may be possible. For an example of applying the probability estimation method to this steady-state differential equation, see Nobosaka and others, "Mathematics and Solution of Inverse Problems, Inverse Analysis of Partial Differential Equations" (The University of Tokyo Press (1999)).

In the present embodiment, the concept shown in Japanese Patent Application Laid-Open No. 2002-209658 is used as a method of analyzing the inverse problem. That is, as shown in the following equation (2), the temperature Y measured by each thermocouple arranged in a certain one-dimensional direction (such as la → lb → lc or ld → le shown in Fig. 35) and the reaction Y The assumed value that minimizes the sum of the squares of the difference from the temperature T at each thermocouple position calculated by the transient heat conduction equation from the assumed value of the heat flux on the inner and outer surfaces of the vessel is the inner surface of the reaction vessel. and _t Incidentally obtained as heat flux at the outer surface, J is the number of thermocouples.

MinY Yj-Tjf (2)

Zo = ι In this way, instead of finding a solution (heat flux on the inner and outer surfaces of the reaction vessel) that makes the temperatures Τ and で at multiple thermocouple positions completely coincide, the least squares are satisfied. By finding such a solution, it is possible to estimate a realistic change in heat flux. The reason for this is that the measurement temperature includes various measurement error factors, and it may be practically meaningless to make them completely consistent.

Note that a regularization term may be added to stabilize the calculation. Equation (3) below shows an example of a zero-order regularization term. p is the number of divisions of the estimated heat flux, α. Is a regularization parameter obtained from empirical values. 0∑ () (3)

Below, more specifically, an example of a formulation for estimating the heat flux on the outer surface and the outer surface of the reaction vessel assuming the temperature at multiple thermocouple positions is known, and an example of a calculation procedure are shown below. .

S _m of formula (4) 4 below represents the entire objective function, the following equation (5) represents the objective function representing the deviation of the measured temperature Y and calculated temperature T. Equation (6) below is an objective function added to stabilize the calculation, and has the function of suppressing rapid changes in values in the space division direction. Α in equation (6). And are regularization parameters obtained from certain empirical values.

S _m (q) = S ^r _m (q) + S ^a , _n (q) (4) Z

∑ £ fc n + W-, "+ MW). (5

7 = 1 i = \

P PP,

S ^a _m (q) = a ₀ ∑ (q _k J ² + a _l ∑ y, (q _km -q _k ^ (6)

k

In the above equation (5), the objective function is set so that the square of the difference between the temperature Y measured by a certain thermocouple and the temperature Τ calculated from the assumed value of the heat flux by the heat conduction equation model is minimized. ing. In the above equation (6), an objective function for performing regularization in the spatial direction is set so that the solution is stable even if there is a temperature measurement error. And equation (4) Is used as the overall objective function, as shown in the following equation (7), a minimum point is searched for the unknown heat flux division region.

dS _m (q)

= 0 7)

Here, as shown in Eq. (8), for the purpose of stabilizing the solution, it is assumed that the heat flux value at each time step does not change until a certain future time. The time step varies depending on the thermophysical properties and shape of the target material. In Equation (8), q indicates the heat flux, and it is assumed that the heat flux in the future time m + r _ 1 time step is constant from the heat flux q _m force in the m time step.

q _m =, ₊ ι =… ⁼ 1 = q _m -i + (8) Then, the minimization of equation (7) is expanded using the assumption of equation (8), as shown in equation (9). , Can be expanded into a matrix form.

[X ^T + ( ₀ H ₀ ^T H ₀ + aH _x ^T H,)} = [Χ ^τ ] {Υ-Γ} (9) where Aq = {qq} 丄, = T (q) X ^T X is derived from the first term of the right side of the equation (4), second term following the ^{_{^{Χ Τ Χ (α .Η ο Τ}}} Η 0 + α, Η ^ Η,) is hand side of formula (4) It is derived from the term (the superscript Τ represents the transposed matrix). The configuration of X is shown below as Xj, i, _k as a supplementary expression (10). Here, i, which indicates the number of divisions in the time direction, changes up to the maximum M time steps, j, which indicates the number of thermocouples, changes up to J, and k, which indicates the number of divisions of the heat flux distribution, is k, which is the maximum It changes up to P. The superscript * in equation (9) indicates a reference value in the iterative convergence calculation, T * is a temperature reference value, and q * is a heat flux reference value. In the one-dimensional case, since the boundary conditions at both ends are estimated, the number of divisions k of the heat flux distribution is at most p = 2.

i = l, ..., ... M Number of divisions in the time direction

J '= J Number of thermocouples

k = l, ... p The number of divisions of the heat flux distribution Equation (9) is a simultaneous equation for estimating the change in heat flux when a temperature change occurs. In each time step, this equation (9) Is used to determine the heat flux q at both ends. First, the calculated temperature at the thermocouple position in the previous time step is set as the initial T *, and q is obtained by Eq. (9). This q is given as the boundary condition of the forward problem heat conduction equation model calculated in parallel, and the temperature distribution is calculated. The calculated temperature value obtained here is used as the next temperature reference value T *, and q is revised again (substituting into equation (9) to find q again). This operation is repeated by correcting q and T * until Equation (5) becomes smaller than the fixed residual (convergence), and the heat flux at both ends (final q) at each time step is calculated. . By repeating this calculation procedure, two changes in the heat flux q at both ends can be estimated simultaneously.

Equation (10) represents a kind of sensitivity matrix. In short, it shows the ratio of the magnitude of the change of the calculated temperature T at the thermocouple position to the unit change of the heat flux q at the boundary endpoint. are doing. In equation (10), the value per unit time step can be calculated at each time step by the forward problem calculation performed at the same time as the inverse analysis. In the following, a more desirable solution will be described using a one-dimensional inverse problem analysis as an example. As described above, even if a one-dimensional inverse problem with the heat flux of the two end faces (the inner surface and outer surface of the reaction vessel) as unknown boundary conditions is constructed (formulated), in principle, a solution must be obtained. Can be done.

However, there may be multiple solutions depending on the number of thermocouples and the thermophysical conditions of the materials, and the calculation may be unstable. One of the reasons is that if the combination of “heat flux difference between unknown end faces” can be properly selected, there may be countless combinations of heat flux that express the temperature change at discrete temperature measurement points. Because there is. In particular, heat transfer In the case of a substance with low conductivity, even when estimating the boundary condition that causes the surface temperature to become extremely large or small, if only the temperature change at discrete measurement points is reproduced, one Recognition as a solution can also occur. This not only is impossible as a real phenomenon, but also makes the inverse problem calculation very unstable.

As a practical problem, the temperature of the thermocouple at the start of the inverse problem analysis (the temperature at the discrete measurement points) is given as a known value, but the initial conditions of the temperature distribution in other analysis domains are unknown. Is common. For this reason, the calculation is started from the tentative initial temperature distribution arbitrarily given, and while the calculation steps are proceeding, the actual temperature distribution is searched and estimated, and the temperature distribution is corrected gradually to an appropriate temperature distribution, and stably It is necessary to use a calculation logic that allows the calculation to proceed (for example, the temperature distribution referred to here means, in the calculation procedure of inverse problem analysis, the solution of the above equation (9) must be modified. This is the calculated value of the forward problem heat conduction equation model calculated in parallel). Thus, the uncertainty of the initial temperature distribution is one of the major factors that make the inverse problem calculation unstable. The above indicates that in order to stabilize the inverse problem, it is necessary to provide some surface temperature guideline (constraint condition) in the process of inverse problem analysis. Based on this concept, a method for appropriately giving the constraint conditions will be described with reference to the flowchart in FIG.

First, a temporary heat flux q is given as a heat flux on one of the inner surface and the outer surface of the reaction vessel, here, on the outer surface. As way of giving heat flux q of the temporary, by using the reference temperature T _b and the heat transfer coefficient h,

q = h (T _surf — T _b )

(Step S201).

T _surf indicates the temperature at the unknown boundary, here the outer surface of the reaction vessel. This surface temperature T _surf is usually also used to perform a forward problem analysis in order to correct the heat flux value during the inverse problem analysis, but it is equivalent to the surface temperature obtained in the forward problem analysis.

The reference temperature _Tb is a temperature outside the inside and outside and inside surfaces of the reaction vessel. For example, the cooling condition of the reaction vessel is determined based on the water temperature and the like in the case of water cooling. As a result, the heat flux q on the left side of the above equation can be given as if it were known heat flux information. By thus providing the heat flux information provisional will be given two constraint that references the temperature T _b and the heat transfer coefficient h, ensuring physical plausibility than to provide any heat flux As a result, it is possible to prevent an extreme temperature distribution from occurring.

Next, a temporary heat flux q (= h (T _surf — T _b )) on the outer surface of the reaction vessel is given, and the temperature T, Υ of the above equation (2) or (5) is obtained. The heat flux at the inner surface of the reaction vessel where the sum of the squares of the differences is minimized is calculated as a temporary heat flux at the inner surface of the reaction vessel (step S202). This step is the main calculation procedure of the inverse problem analysis, and the formulation and calculation procedures shown in Equations (4) to (9) can be directly applied as one of the specific solutions. In this case, when solving Equation (9), the provisional heat flux q (= h (T _surf -T _b )) on the outer surface of the reaction vessel is given as a known value, and the provisional heat flux on the inner surface of the reaction vessel is given. This means solving the bundle as unknown.

Here, given the heat flux information on one side (outer surface of the reaction vessel) as described above, the heat flux on the other side (inner surface of the reaction vessel) obtained by inverse problem analysis is one possibility of solution. It just shows. Further, the known and assumed heat transfer coefficient h and the reference temperature T _b is also approximate, the unknown values would otherwise.

Therefore, the heat transfer coefficient h and / or the external reference temperature T _b are changed by several points, that is, the value of the temporary heat flux q on the outer surface of the reaction vessel is shaken by several points (point K), and the reaction is performed. Combination of the temporary heat flux q on the outer surface of the vessel and the heat flux on the inner surface of the reaction vessel that minimizes the sum of the squares of the differences in temperature Τ and 最小 when given each temporary heat flux information q Are obtained (Step S203).

Then, as shown in the following equation (11), the heat flux q on the outer surface of the reaction vessel and the heat flux on the inner surface of the reaction vessel obtained corresponding to the respective heat flux information q Of the K combinations of and Υ, the combination that minimizes the value of the square of the difference between the temperatures Τ and Υ is selected, and that combination is used as the heat flux on the inner and outer surfaces of the reaction vessel (step S 204). ).

J

Μιη Μη∑ (Factory Ί) (1 1)

J k = l, K The square brackets in the above equation (11) show the results of one case calculation in which the heat flux on one side was known and the inverse problem analysis was performed. It means choosing out small results.

By repeating this procedure at each time step, it is possible to sequentially and simultaneously calculate the temporal change of the heat flux on the inner surface and the outer surface of the reaction vessel. As described above, the one-dimensional inverse problem analysis for simultaneously obtaining the heat flux changes on the inner surface and the outer surface of the reaction vessel can be stably executed. If the temperature change and the heat flux change on the inner surface and the outer surface of the reaction vessel can be simultaneously estimated, for example, the temperature fluctuation at a certain temperature measurement point is caused by the heat flux change on the inner surface of the reaction vessel. It is possible to distinguish whether the heat flux is caused by a change in heat flux on the outer surface of the reaction vessel caused by poor contact of a cooling device installed outside the reaction vessel or the like.

The above method is simple to apply to one-dimensional inverse problem analysis, and is often effective as a practical problem. The reason is that the upper and lower ends of the reaction vessel are generally insulated (symmetric) in many cases, and there is no practical problem.

Therefore, inverse problem analysis can be performed assuming one dimension in the thickness direction within the area demarcated by the broken line in Fig. 35, and the results can be combined into two dimensions by combining them vertically.

If we want to strictly consider the heat flow in the vertical direction in Fig. 35, a two-dimensional inverse problem analysis is required. Such two-dimensional analysis consists of making the heat flux divisions at the left and right ends in Fig. 35 finer upward, and finding the minimum heat flux distribution by least squares at the temperature at these thermocouple positions. This is equivalent, and the present invention may be applied in accordance with the same method as the inverse problem formulation disclosed in Japanese Patent Application Laid-Open No. 2002-209658.

In this case, the heat flux at the upper and lower ends in Fig. 35 may be unknown or known, but considering the stability of calculation, an appropriate heat flux (for example, adiabatic Etc.) and it is desirable to make it known. Based on the same idea, extension to three-dimensional analysis can be easily performed.

(Example of the first embodiment)

As a specific example of the first embodiment, according to the above method, a certain metal refining furnace An example of inverse problem analysis of measured temperature data of a thermocouple embedded in a wall will be described. As shown in Fig. 3, the thickness of the furnace wall is 1 m in total, and thermocouples 1 t and 1 s are embedded at 0.1 [m] and 0.2 [m] from the outer end of the furnace. ing. In other words, the position of the thermocouple is arranged to be deviated to the outside of the furnace. The thermophysical properties of the furnace wall material are as follows: constant pressure heat capacity C _P = 0.17 [kcal / kg-K] 7.12 X 10 ² [j / kg-K]) _s energy density = 2 3 0 0 [kg Zm ^3], the thermal conductivity k = 1 8. 2 [kca 1 Roh m. hr .K] (7. 6 2 X 1 0 4 [J / m · hr -K]). The calculation time step was 3 hours.

4A to 4E show measured temperature data and analysis results of the thermocouples 1 s and 1 t. The horizontal axis is the number of days. Figure 4A shows the changes over time of the two thermocouples 1 s and It. According to the results, two places where the temperature is noticeably higher can be observed as enclosed by the ellipse (high temperature 1 and high temperature 2).

However, the results shown in Fig. 4A alone can be used to distinguish whether these high-temperature phenomena 1 and 2 are due to a high temperature inside the furnace or a decrease in the cooling capacity outside the furnace. Can not.

Figures 4B and 4C show the results of calculating the temperature at the furnace inner end (the inner surface of the reactor) and the temperature at the furnace outer end (the outer surface of the reactor) using the inverse problem analysis method described above. . Analyzing the high-temperature phenomenon in this way, the high-temperature phenomenon 1 shows that the inner and outer ends of the furnace were simultaneously heated, and the effect of the reaction activation high temperature in the furnace affected the outer end of the furnace. It can be inferred. On the other hand, in the high temperature phenomenon 2, almost no temperature fluctuation was observed at the inner end of the furnace, and it can be inferred that the temperature was raised simply because the cooling capacity outside the furnace was reduced.

Fig. 4'D shows the change of the heat flux at the outer end and the inner end of the furnace similarly obtained by the inverse problem analysis method. Fig. 4E shows a characteristic diagram converted to the heat transfer coefficient h on the outer end of the furnace. From these results, the heat transfer coefficient h also fluctuated greatly near the high temperature phenomenon 2, and the cooling capacity gradually increased after about 300 days, and dropped sharply near the high temperature phenomenon 2. It can be understood that there is an abnormality in cooling due to some factor.

(Second embodiment) FIG. 5 shows a schematic configuration of the operation management device for the reaction vessel of the present embodiment. In the following, description will be made focusing on differences from the above-described first embodiment, and the same reference numerals will be given to components already described, and detailed description thereof will be omitted. In the figure, reference numeral 201 denotes an arithmetic unit, which performs an operation to increase the number of digits after the decimal point using the temperature data input to the input unit 101, as described later. Then, the inverse problem analysis unit 103 performs an inverse problem analysis using an unsteady heat conduction equation based on the temperature data in which the number of digits after the decimal point has been increased by the arithmetic unit 201, thereby obtaining a reaction vessel. Determine the temperature or heat flux on the inner and outer surfaces. Since the inverse problem analysis used in this embodiment has been described in the first embodiment, the description is omitted here. For example, in order to estimate the “current” change of the heat flux change on the surface of the reaction vessel by the inverse problem analysis described above, it is necessary to estimate the past situation in the reaction vessel as close as possible. For this purpose, it is conceivable to shorten the unit time step of the inverse problem calculation. If the unit time step of the inverse problem calculation is long, it is necessary to estimate a change that goes far back in the past at least for that time step. In addition, since the inverse problem calculation is a calculation result obtained by time averaging in the calculation time step, the restored heat flux change also captures a dull change, and a rapid change below the time step cannot be captured.

However, shortening the unit time step of the inverse problem calculation means that during that short time, the small amount of heat transmitted from the position where the heat flux changes (for example, the inner surface of the blast furnace in contact with the hot metal) to the thermocouple position This means that temperature changes must be captured. In particular, when the position of the thermocouple is far from the position where the heat flux changes, and the thermal conductivity of the material between them is small, the temperature movement in a short time becomes very small.

To theoretically extract the temperature change due to the heat flux change from such a small temperature change and to restore the heat flux change (short-time inverse problem analysis), a temperature measurement method and temperature data processing are required. The method needs some ingenuity.

Therefore, the present inventors have conducted intensive studies in order to be able to estimate the past heat flux distribution as close as possible in a short time step while utilizing temperature data measured by a thermocouple.

In the operation of a blast furnace, etc., since only the temperature change is observed, the global temperature When looking at the flow of data, it is common to evaluate the value by rounding down the temperature data after the decimal point. In addition, even when looking closely at the current temperature change over time, the manufacturer's guaranteed range of the temperature measurement device that converts the thermocouple contact voltage change into temperature may be up to one decimal place in most cases. Often temperature data is used. In other words, the collected and recorded temperature data is coarse, with zero or one decimal place.

However, in order to estimate the boundary condition change (heat flux change) at a distant position that causes a very subtle temperature change (inverse problem analysis), the behavior of the temperature change after the decimal point is estimated. That is very important.

That is, in the inverse problem analysis, the time transition of temperature-the flow of temperature change is more important than the accuracy of temperature itself. If the temperature changes in a staircase, pursuing only the accuracy of the temperature itself, the inverse problem analysis would be unstable. In particular, when aiming for inverse problem analysis in a short time step, an unpredictable step-like temperature change may occur in that time step. Therefore, even if an inverse problem analysis is performed using this stepwise temperature change to obtain a heat flux solution, there is a possibility that a physically impossible solution may be reached. In fact, in most cases the solution diverges, making it impossible to continue the inverse problem analysis.

Generating temperature data with an increased number of decimal places from temperature data with a small number of decimal places in a rational manner is an effective method for smoothing step-like temporal changes. It is.

As one method, the arithmetic unit 201 collects temperature data with zero or one digit below the decimal point with a sampling time shorter than the time step in inverse problem analysis, averages them over time, and performs inverse problem analysis. The representative value of the temperature data used in the calculation time step in. For example, a small digit number of temperatures sampled at 5-minute intervals shorter than the time step (1 hour) in the inverse problem analysis is simply averaged over a 1-hour range, and a representative value of the 1-hour-step temperature data is obtained. I do. This makes it possible to apparently reduce the number of decimal points in the one-hour temperature data. When this method is used, the temperature data used for the inverse problem calculation is based on the temperature data (measured by the thermocouple) with zero decimal places and one decimal place that guarantees the accuracy measured by the thermocouple. The number of decimal places of It is possible to increase.

Also, the number of digits after the decimal point of the temperature data used for the inverse problem calculation may be increased by another method. For example, in a thermocouple, even if the assurance range of the temperature data itself is one decimal place, it is actually calculated based on the conversion formula that converts the voltage at the thermocouple junction into temperature, or the calibration is performed. A common method is to convert the voltage-temperature conversion table to temperature.

In the former method, the calculated temperature value of many digits is rounded off to one digit after the decimal point, and it is actually possible to obtain the number of decimal digits according to the capacity of the computer. For example, as a conversion formula for converting the voltage of a K-type thermocouple into temperature, there is the following formula.

T = a + b · X + c · Χ 2 + d · X 3 + e · X + f · X 5 + g · X 6 + h · X 7 + i · X 8

T: Temperature [° C]

X: Contact voltage [V]

a = 0.22 6 5 8 4 6 0 2

b = 2 4 1 5 2.1 0 9 0 0

c = 6 7 2 3 3. 4 2 4 8

d = 2 2 1 0 3 4 0 .6 8 2

e = — 8 6 0 9 6 3 9.9

f = 4.8 3 5 0 6 X 1 0 ¹⁰

g =-1.18 4 5 2 X 1 0 ¹²

h = ^1.3 8 6 9 0 X 1 0 ¹³

i = -6.3 3 7 0 8 X 1 0 ¹³

By directly converting the contact voltage to the temperature using the above conversion formula, it is possible to easily obtain the decimal part of the temperature data. It is needless to say that the contact voltage here is a true contact voltage after cold junction temperature compensation.

By the way, in addition to increasing the number of digits after the decimal point as described above, a filter 101a is provided in the input section 101 as shown in FIG. To be applied. That is, using the filter 10 la, Correct the temperature data measured in pairs and use the corrected temperature data for inverse problem analysis. If a filter is used, even if the original temperature data has a small number of decimal places, the decimal places can be apparently generated in the temperature data. Calculation of problem analysis is very stable.

What seems to be the most effective in theory is to use a low-pass filter. The mouth-pass filter corrects the measured data in order to remove the influence of fluctuation due to high-frequency noise mixed in the measured data sampled at equal time intervals.

The reason why it is effective to use a low-pass filter to correct the temperature data in the inverse problem analysis is that the change in the heat flux at a position far from the thermocouple occurs while the heat flux is transmitted through the refractory through the heat diffusion phenomenon. This is because, when the temperature has slowed down and transmitted to the thermocouple position, the temperature change is considered to have become extremely large (low-frequency changes are transmitted).

This means that the temperature change at the thermocouple position caused by a change inside the furnace far away is a low frequency change in time. However, high-frequency noise due to other causes is superimposed on the actual thermocouple contact voltage change (original signal before temperature conversion). Therefore, using temperature data that has been processed to remove 髙 -frequency noise from actual measured temperature changes in an inverse problem analysis is a very physically meaningful method. Therefore, this method not only can improve the calculation stability of the inverse problem analysis, but also can improve the accuracy of estimating the heat flux. In the mouth-to-pass filter processing, the number of digits after the decimal point was increased by some other method, as well as the temperature data whose number of digits was increased by taking the above-mentioned time average or using a conversion formula. It is very effective even if it is added to temperature data or original measured temperature data with few decimal places. That is, increasing the number of digits after the decimal point and performing low-pass filtering may be used in combination, thereby synergistically smoothing the temperature change.

A wide variety of filters are conceivable. For example, see RW Hamming's Digital filters, Dover publications Inc. 1998, and the like. There are many other reference materials. As a classic method of a low-pass filter, a method of correcting the temperature at the midpoint using measured temperature data Y sampled at equal time intervals is known. The formulas (12) to (14) below are derived as formalism for the correction. The subscript i indicates the number of times of sampling, which means that the current time i is corrected by the measured temperature before and after.

(1 2)

ί [7,24,34,24,71 (1 6)

96

— 11,6,12,14,12,6,1] (1 7)

— [1,28,78,108,118,108,78,28,1] (1 8) 548 ^L ,,

— 980 [ ^L -11, (19, 138 ,, 168 ,, 178 ,, 168 ,, 138 ,, 88 ,, 18, -11] ■!), 18 ,, 88, 丄 320 [Sh-3, -6 ,,-5,3,21,46,67,74,67, ... 46,21,3, -5, -6, -3] "(20) 丄 [- 1-3-5, -5.-2,6,18,33,47.57,60,57,47.33,18,6, -2. -5, -5, -3, -1] 350 ^L

(21) Equations (12) to (14) show the equations of the three-term method, the five-term method, and the seven-term method, respectively, and the performance as a low-pass filter increases as the number of measured temperature data used for correction increases. Is improved. That is, only lower frequency signals can be extracted. Basically, it can be expressed by the coefficient of each term. 5) It becomes like (17).

In general, as the number of terms increases, the performance as a low-pass filter improves, and the degree of freedom in filter design increases. In other words, since the high-frequency disturbance can be removed over a wide range by the polynomial filter, the calculation of the inverse problem analysis is extremely stable. On the other hand, when the number of terms increases, the measured temperature at several time points before and after the time point must be used to obtain the corrected temperature value at a certain time point, which is substantially retroactive to the past. Therefore, in the case of "estimating the current heat flux by inverse problem analysis.", It means that the "present" itself is pulled back by the low-pass filter. Therefore, there is a trade-off between ensuring the stability of the inverse problem analysis using a low-pass filter and making the “current” estimation time as close to the present as possible, so an appropriate combination should be considered while considering the relationship between the two. You need to choose

From this point of view, using temperature data with as many decimal places as possible, using a low-pass filter with a small number of terms after suppressing the stepwise temperature change, reduces the `` current '' heat flux. It is effective in estimating.

(Example of the second embodiment)

As a specific example of the second embodiment, FIG. 7 shows a one-dimensional transient heat conduction model using a thermocouple embedded in a carbon brick installed on the bottom of the blast furnace bottom. Assuming that, the example of trying the inverse problem analysis is shown schematically. Two thermocouples are embedded on the cooling surface side, and TC 1 indicates a high-temperature thermocouple and TC 2 indicates a low-temperature thermocouple. From the temperature changes measured by these thermocouples TC1 and TC2, the unsteady heat flux q1 on the high-temperature heat flux surface and the unsteady heat flux q2 on the cooling surface are calculated by the inverse problem analysis described above. Estimate at the same time. The position of the high-temperature heat flux surface is a fixed point 4.0 m deep from the cooling surface. The assumed thermophysical properties of the carbon brick are as follows: specific heat C _P = 7 12 J / (kg 'K), density p = 230 kg / m ³ , thermal conductivity k = 21.2 W / ( mK).

FIG. 8A shows the estimation result of the heat flux q1 on the high temperature side obtained in the present example. Fig. 8 A ~

The horizontal axis of 8D represents the date, and shows the results from September 1 to October 1. Actually, the calculation starts before September 1, and ends on October 1st. The time step of the inverse problem analysis is 8 time steps.

Case 1 rounds off the temperature data measured by the thermocouple to one decimal place. This is the calculation result when filter processing is performed on the data with 0 decimal places. Case 2 is the calculation result when filtering the temperature data with two decimal places rounded to one decimal place.

Figures 8B and 8C show plots of the temperature data (temperature data used for inverse problem analysis) after filtering the high-temperature-side thermocouple TC1 and low-temperature-side thermocouple TC2. FIG. 8D shows the temperature difference between case 1 and case 2 (case 1—case 2) at the respective positions of thermocouples T C1 and T C2.

Regarding the filter, in order to stabilize the calculation by applying a low-pass filter with as many terms as possible to past temperature data, the Spencer-type equation (Equation (2 1)) of up to 21 terms is used. A technique is used in which the number of terms is gradually reduced as approaching. Specifically, the expressions (15) to (21) are used in a Windows format notation. That is, the number of terms decreases as the date approaches October 1, and finally equation (15) is used, and no filtering is performed on the last temperature data.

In both Case 1 and Case 2, the past analysis is very stable due to the filter effect, but gradually destabilizes as it approaches the present, and the final estimated heat flux becomes realistic. Is generating an incredibly large vibration. This is considered to indicate that the effect of the low-pass filter gradually decreases and the calculation becomes unstable.

Comparing Case 1 and Case 2, it is clear that Case 2 is able to reduce the magnitude of the final vibration. This indicates that temperature data with more digits after the decimal point can perform relatively stable calculations with a low-pass filter with fewer terms.

In addition, in each case, oscillations were generated in the final estimation result, so when comparing temperature data with the same number of digits, the number of terms in the low-pass filter was reduced, and the temperature data was smoothed as much as possible. It is also shown that doing so is an effective means of obtaining a stable solution. In particular, when a low-pass filter of the form of equations (15) to (21) is used, even if equation (15) is used, no filter is applied to the last data, so the decimal point of the original temperature data Inverse problem solution The solution is stable.

In Cases 1 and 2, inverse problem analysis was attempted without filtering the temperature data at all, but the solution diverged and the calculation could not proceed. Fig. 9 shows a schematic diagram similar to Fig. 7 for cases where the thermocouples are installed at different depths. Figure 10A shows the estimation results of the high-temperature side heat flux q1 when the calculation time step of the inverse problem analysis is set to 8 hours and when it is set to 6 hours. The results of these calculations are extracted from September 1 to October 1 of the long-term calculation results.

The temperature data used for the calculation was one digit after the decimal point, and the filter was smoothed using equation (21). FIGS. 10B and 10C show characteristic diagrams obtained by plotting the temperature data of the high-temperature-side thermocouple TC1 and the low-temperature-side thermocouple TC2 after the smoothing. Further, FIG. 10D shows the difference between the high-temperature side thermocouple temperature and the low-temperature side thermocouple temperature (T C 1 -T C 2) corresponding to the steady state heat flux.

A comparison of the transition of the quasi-stationary heat flux in Fig. 10D and the correspondence between the peaks of the unsteady heat flux estimated by the inverse problem analysis in Fig. 10A shows that the inverse problem analysis is intuitive. It can be seen that the peak time appears earlier in the unsteady heat flux by correcting the delay time (shown by the broken line in Fig. 10A).

The quasi-stationary heat flux in the characteristic diagram in Fig. 10D can be interpreted as the average heat flux passing around the thermocouple position, and the value of the unsteady heat flux estimated at the hot surface 4 m deep The peaks do not always correspond to each other, but in this case, a peak lag of about 2-3 days is observed. In other words, the unsteady heat flux based on the inverse problem analysis detects the movement in the furnace approximately 2-3 days earlier than the conventional steady-state method. Also, comparing the 8-hour step calculation and the 6-hour step calculation in the characteristic diagram of Fig. 10A, the 6-hour step calculation shows a movement with a sharper contour. If the time step is lengthened, only the averaged motion within that time can be captured, so shortening the time step as much as possible is more likely to express the actual internal motion.

(Third embodiment) FIG. 11 shows a schematic configuration of the operation management apparatus for a reaction vessel of the present embodiment. In the following, description will be made focusing on differences from the first embodiment, and the same reference numerals will be given to the components already described, and detailed description thereof will be omitted. In the figure, reference numeral 301 denotes an analysis unit based on the steady-state method. By performing analysis based on the temperature data obtained through the input unit 101 by the steady-state method, the temperature on the inner surface of the reaction vessel is calculated. Or heat flux. Reference numeral 302 denotes a comparison unit which compares the temperature or heat flux obtained by the inverse problem analysis unit 102 with the temperature or heat flux obtained by the analysis unit 301 by the steady-state method. Specifically, a difference between the two is obtained and used as an evaluation index. Then, the output unit 103 displays the result compared by the comparison unit 302 on, for example, a display (not shown). Since the inverse problem analysis used in the present embodiment has been described in the first embodiment, the description is omitted here.

The analysis by the stationary method used in the present embodiment will be described. The temperature at the inner surface of the reaction vessel is obtained from the temperature measurement values at two points in the depth direction (thickness direction of the wall (brick)) in the one-dimensional stationary method. In this case, as shown in FIG. 12, the temperatures at the two points are connected by a straight line, and the temperature at the outside point is the temperature on the inner surface of the reaction vessel. Also, since the heat flux is the slope of the straight line, it can be obtained by multiplying the slope by the thermal conductivity k (the intermediate term in the following equation (22)).

In addition, when the temperature measurement values at more than two points in the depth direction are included, as shown in Fig. 13, for example, a straight line that satisfies the temperature at the plurality of points is obtained by the linear least squares method. The temperature at the outside point is defined as the temperature on the inner surface of the reaction vessel. The heat flux can be obtained by multiplying the slope of the straight line by the thermal conductivity k (the rightmost term in the following equation (22)).

The heat flux (steady heat flux) obtained as a result of the analysis by the steady-state method can be expressed by a straight line, so that it takes the same value regardless of the cross-section, which is the heat flux (unsteady heat flux) obtained as a result of the inverse problem analysis. Bunch).

It is the one-dimensional non-linearity shown in the above equation (1) that governs the heat transfer in the wall thickness direction. Although it is a steady-state heat conduction equation, there is no problem even if the steady-state method is used to easily obtain the approximate average heat flux. However, in practice, due to the heat capacity effect of the brick expressed by the term on the left side of the transient heat conduction equation, the one-dimensional temperature distribution in the brick does not become a linear temperature distribution as in the steady state method, but a temperature gradient distribution. Is represented by a curve with This is the amount of heat is gradually transmitted, not only the heat flow phenomenon caused by the temperature gradient (the effect of the thermal conductivity k), (the effect of heat capacity p C _P) phenomena continue to thermal storage in the bricks also relates It is a character that is.

In particular, near the boundary of the brick in contact with the outside (near the part where the boundary conditions are given), the temperature gradient changes sensitively due to the effect of the outside, so it is easy to largely separate from the straight line of the steady method. As shown in Fig. 14, for example, if the inflow calorific value increases suddenly, the temperature gradient will increase locally, and if the inflow calorie decreases suddenly, the temperature gradient will decrease locally. If such a change is not instantaneous but extends for a long time (steady state), the distribution of the temperature gradient is gradually eliminated and converges on a certain straight line (steady state). The implication of estimating the heat flux on the inner surface of the reaction vessel by inverse problem analysis using the unsteady heat conduction equation is to accurately capture this local change in the temperature gradient. It is important to be able to make decisions.

Here, it is important to compare the unsteady heat flux and temperature at a certain fixed point. If the position of the fixed point to be obtained changes, not only the temperature but also the unsteady heat flux will change. In order to show the state of the change, a problem as shown in Fig. 15 was set, and the change of the heat flux and temperature at each cross-sectional position when the heat flux that changes stepwise at 4 m position was given. investigated. The results are shown in Figures 16 and 17. The initial temperature distribution is given at 27 ° C.

This trial calculation suggests that, for example, using the temperature change at the 2 m and lm positions, the heat flux at the 3 m position is estimated by inverse problem analysis, and the heat flux at the 4 m position is estimated. In estimating, the change in the estimated heat flux is different. 2 m position,

This shows that the 4 m position, which is deeper than the 1 m position, can estimate a sharper change, and that at the 3 m position, only a considerably slowed heat flux can be estimated. I can't.

Therefore, when evaluating the result of inverse problem analysis, "where" This is a very important factor, and the deeper the estimated position is relative to the thermocouple position, the more accurately the change in heat flux can be reproduced. On the other hand, if the estimated position is deeper, the temperature transmitted to the thermocouple position will be lower, and it will be obvious that the inverse problem analysis is more likely to be unstable and it is difficult to obtain a solution.

As described above, the time course of the heat flux at a fixed position obtained by inverse problem analysis has been evaluated by a single plot. It was ambiguous, and it was difficult to judge how unsteady the change in the molten metal flow in the furnace was (a sudden change in the flow).

As a result of intensive studies, the inventors of the present application have found that in order to clarify the evaluation of unsteadiness, the heat flux (unsteady heat flux) obtained by inverse problem analysis and the heat flux obtained by analysis by the stationary method It was found that by plotting and comparing the heat flux (steady heat flux) together, it was very clear.

That is, if the unsteady heat flux is lower than the steady heat flux, it can be estimated that the steady heat flux (average heat flux) will tend to decrease in the future. Conversely, if the unsteady heat flux is higher than the steady heat flux, it can be estimated that the steady heat flux (average heat flux) will tend to increase in the future. Also, if the heat flux difference is large, the unsteadiness is large, so it can be judged that this suggests that the average heat flux will rapidly rise and fall in the future.

The same evaluation can be performed by comparing the solution of the inverse problem analysis and the analysis by the steady-state method for the estimated temperature at the fixed position, instead of comparing the heat flux at the fixed position. Also, by examining the starting point where the heat flux difference between the two begins to change rapidly, it is possible to identify what caused the sudden rise or fall.

This can be very useful information for judging the quality of operation actions taken at that time. In some cases, as long as the operation change does not cause the desired heat flux change, it can also serve as reference data for restoring or otherwise changing operation specifications.

In order to clarify the unsteady change, the difference between the unsteady heat flux (or temperature) at a fixed position and the steady heat flux (or temperature) is used as an indicator of unsteadiness, and There is also a method of evaluating The non-stationarity index is calculated by the following formulas (23), (24) It is possible to define the heat flux difference or the temperature difference at a fixed position as a numerical value, so that a quantitative grasp can be obtained. It is important to clarify at which fixed position the value of the non-stationarity index is defined, and the value changes depending on the defined position, as described above.

# inversion of q _in and _t置! Heat flux

q _in , _stdy : Estimated heat flux by stationary method at fixed position tran-in in ran in, stdy (4)

q _{in! tran} : The solution at 立立 ft

q _inJran : Estimated temperature by stationary method at fixed position Since the inverse problem model based on the unsteady heat conduction equation is a model to the last, it is considered that there is actually no wall for the purpose of evaluating the _{unsteadiness.} It is also possible to determine such a deep position as a fixed position and to perform the unsteady mature conduction inverse problem analysis. If the setting is made deeper in this way, the calculation tends to be unstable, but the unsteady change appears in the sharp, and the starting point of the change can be clearly shown. Also, although the depth is different, it is easier to discuss the same playing field when comparing the results of operation with reactors of the same type by determining the reference position and comparing the analysis results.

If the fixed position reference is fixed at a very shallow position, the unsteadiness may become dull as shown in Fig. 16, and the desired comparison result may not be obtained. In such a case, it is desirable to set the standard for the reactor with the largest brick thickness, even if it is virtually.

In addition, it is possible to set a criticality unsteadiness index, and to set a certain criterion to give an appropriate operation action when the value is exceeded. However, the non-stationary index only estimates the magnitude and directionality of the subsequent changes based on the current steady-state heat flux (steady-state temperature), and therefore depends on the magnitude of the heat flux at that time. The meaning changes. That is, the relationship between both the unsteadiness index and the absolute value of the heat flux is important.

Fig. 18 schematically shows an example of mapping that concept. The horizontal axis shows the unsteadiness index Δ Τ \ „ _、, and the vertical axis shows the steady heat flux, and this operation requires that the steady heat flux be kept above a certain reference value Q. When the results of the time-series analysis are plotted on the map in this figure, it is assumed that the plot changes along the locus indicated by “→”. The last (immediately) 〇 plot indicates a steady heat flux above the reference value. The unsteadyness index ΔT _tra „swings significantly in the negative direction beyond the critical value of ₋₂₀ ° C. This means that the current value of the steady state heat flux is higher than the reference value, but the critical value of the non-stationary index ΔT _{tra 大きく} is much larger than ₁₂₀ ° C, and will be greatly reduced in the future. It can be interpreted that the alarm sounds.

In this example, the critical value of the unsteadyness index ΔT _tran is set to ₁₂₀ ° C. The value depends on the concept of stabilizing the operation, the allowable heat flux change, and the thermophysical properties of the reaction vessel wall. Of course, it changes depending on the value and the estimated position (thickness position). Also, here, the value on the vertical axis is the steady heat flux, but there is no problem even if it is unsteady heat flux.

(Example of the third embodiment)

As a specific example of the third embodiment, as in the second embodiment, FIG. 9 shows a case where a thermocouple embedded in a carbon brick installed in the bottom of the blast furnace bottom is used. An example of an inverse problem analysis is shown, assuming a one-dimensional transient heat conduction model. Two thermocouples are biased toward the cooling surface side. TC 1 indicates a high temperature side thermocouple, and TC 2 indicates a low temperature side thermocouple. From the temperature changes measured by these thermocouples TC1 and TC2, the unsteady heat flux q1 on the high-temperature heat flux surface and the unsteady heat flux q2 on the cooling surface were simultaneously determined by the inverse problem analysis described above. presume. The position of the high-temperature heat flux surface is a fixed point 4. O m deep from the cooling surface. The assumed thermal properties of the carbon brick are as follows: specific heat CP = 7 12 J / (kg 'K), density p = 230 kg / m ³ , thermal conductivity k = 21.2 W / (mK) It is. The time step of the inverse problem analysis was 8 hours, and the temperature data to one decimal place sampled at 5 minute intervals were averaged over 1 hour and used for the calculation.

Figures 19C and 19D show the transition of the temperature at the high-temperature thermocouple TC1 and the temperature at the low-temperature thermocouple TC2 (temperature data used for the inverse problem analysis). The horizontal axis is the date Yes, showing results from September 1 to January 25.

Figure 19A shows the results of the heat flux by the inverse problem analysis on the high-temperature heat flux surface (4 m position) estimated using the above temperature data, and the results of the heat flux by the steady-state method. The transition of the unsteady heat flux by the inverse problem analysis shows larger fluctuations, while the steady heat flux by the steady method changes slowly. Comparing these changes, it can be inferred that from around January 8, the difference in heat flux between the two methods increased, and that there was an unsteady change in the hot metal flow in the furnace.

Figure 19B shows the results of the temperature estimation by the inverse problem analysis on the high-temperature heat flux surface (at a position of 4 m) estimated using the above temperature data, and the temperature estimation by the steady-state method. From this result, it is possible to read the same tendency as in the case of heat flux.

What can be said in common with Figs. 19A and 19B is that the unsteady heat flux (temperature) moves faster than the steady heat flux (temperature). If the unsteady heat flux (temperature) rises (falls), the steady heat flux (temperature) rises (falls) a few days later. Particularly noticeable is the behavior of both parties around January 8th. The same time delay can also be qualitatively confirmed by comparing the thermocouple temperature trends shown in Fig. 19D with the characteristic diagrams in Figs. 19A and 19B.

Figure 19E shows the change in the unsteadiness index Δ _{tran tran at} the high-temperature heat flux surface (4 m position) as a function of temperature. Expressing with such indicators makes it easier to see when the change originated.

FIG. 20 shows the result of _mapping this calculation result between the _unsteadiness index ΔT _tran and the steady heat flux. The results show that the critical value of the unsteadyness index ΔT _{tra 設定} was set to ₁₃₀ ° C. with the lowest reference value of the steady-state heat flux set at ₃₅₀ ° W / m ² , _whereas the critical value of ₁₃₀ ° C. In this case, the steady-state heat flux decreases rapidly after this value is cut, and eventually falls significantly below the reference value. Did not take any action.

From these results, it is suggested that, under these calculation conditions, the absolute value of the critical set value of the unsteadiness index should be set a little smaller. From now on, a trial will be made such that "The critical value of the unsteadyness indicator T _tran should be adjusted to about 15 ° C, and if this value is cut off vigorously, an appropriate operation action will be taken." Stricter operating standards It is required to optimize the set value according to the operation result after the setting.

Unsteady index delta T _{t ra n} are, so show a deviation from stationarity inside fixed point of the furnace. It can be grasped signs of early changes than before. Therefore, if an appropriate action standard can be set by utilizing the characteristics of this indicator, it will lead to a reduction in production costs, but it will be possible to promote marginal operation, which is a bad operating condition. It enables agile operation design to detect signs of deterioration in the furnace at an early stage and take immediate recovery action.

(Fourth embodiment)

The schematic configuration of the reaction vessel operation management device of the present embodiment is the same as that of FIG. 1 described in the first embodiment, but is input to the input unit 101 in the inverse problem analysis unit 102. The temperature or heat flux on the inner and outer surfaces of the reaction vessel by performing inverse problem analysis using an internal function or an external function that satisfies the transient heat conduction equation based on the temperature data It is characterized by the following.

Hereinafter, the processing mainly performed in the inverse problem analysis unit 102 will be described in detail. The unsteady heat conduction equation used for the inverse problem analysis is expressed by the following equation (25). C dT _? D ² T _Ί d ² T _Ί is Γ

p-C _D — = k ^ — + k ,, — + n — (2 5)

ot dx oy In the present embodiment, by using an appropriate interpolation function or an external function that satisfies the above-mentioned unsteady heat conduction equation, the boundary condition on the inner surface and outer surface of the reaction vessel as a simpler method is obtained. The change is estimated. The interpolation function or the outer 揷 function is a function that connects the temperature at the measurement point and expresses a region other than that point, for example, the whole or a part of the analysis region. Linear functions such as linear function approximation and spline interpolation are known as internal functions that cannot be extrapolated. However, functions that can be extrapolated while satisfying the transient heat conduction equation are not known. Interpolation refers to estimating unknown points inside known points, and extrapolation refers to estimating outside and around known points. As shown in FIG. 21, the inverse problem analysis unit 102 first expresses the solution of the unsteady heat conduction equation using a predetermined internal function or external function and parameters (step S 2 101) .

As a result of intensive studies, the inventors of the present application have found that using an interpolation function or an outer 揷 function form that satisfies the non-stationary heat conduction equation expressed by the following equation (26) gives a more physical meaning. It has been found that it is possible to perform internal or extrapolation with a certain degree.

(, y, z, t): exp

+ Then _x

No

In the above equation (26), t represents time, and X, y, and z represent position vector elements, and can be applied to a general three-dimensional coordinate system. τ _χ , τ "τ _ζ , Α _χ , A _y , Α _ζ , X, Υ, and Ζ represent appropriate arbitrary constants, and the optimum value varies depending on the target system. The values of these arbitrary constants Care must be taken in choosing

This function F ( _X , y, z, t) automatically satisfies the transient heat conduction equation (25). When this function F (x, y, z, t) is used to express the solution of the unsteady heat conduction equation in general, it is expressed as the following equation (27).

In the above equation ( ²⁷ ), x ^j , y ^j , and z ^j represent each element of an arbitrary reference position vector, represents an arbitrary reference time, and _x , y, _z, and t are points at which temperature is to be estimated. Position of The elements and time of the turtle. N j is the number of reference position vectors and the number of reference times in the time direction, respectively. These numbers are often the same as the number of temperature measurement points, that is, the number of temperature measurement points by the thermocouple, and the number of samplings of the measurement temperature in the time direction, but it is not always necessary to match them. Les ,. Then, a is a parameter, but if this value is determined, it is possible to determine an arbitrary position vector (X, y, z) and a temperature distribution T (X, y, z, t) at time t. You can. Next, the value of the parameter in the solution of the transient heat conduction equation expressed by the above equation (27) is determined using the temperature information measured by the thermocouple (step S2102). The value of this parameter a can be determined by solving the following simultaneous equation (28).

^N J

X x ^j , y ^k -yz ^l z ^J X-f) = a k'l (28) zo = 1! · = Ι In the above equation (28), a _{ki l} is the temperature T measured by the thermocouple. (x ^k , y ^k , z ^k , t ¹ ), where the subscript k indicates the measurement position and the subscript 1 indicates the sampling time.

By using the method described above, if there are discrete temperature measurement data in the space and time directions, the temperature estimation value over the entire reaction vessel wall region (arbitrary space-time position) governed by the transient heat conduction equation Is obtained.

Here, the heat conduction inverse problem is based on the unsteady heat conduction equation governing the calculation domain, assuming that the temperature inside the domain is known, and the boundary conditions such as temperature and heat flux at the domain boundary or the initial conditions. Points to the problem of estimating On the other hand, the heat conduction order problem refers to the problem of estimating temperature information inside a region based on known boundary conditions. In the above method, the temperature distribution at the wall boundary of the reaction vessel is also estimated at the same time, and although indirect, the boundary between the inner surface and the outer surface of the reaction vessel is obtained from the temperature information measured by the thermocouple. This is the inverse problem of deciding the conditions.

In addition, since the temperature gradient at the boundary can be estimated not only from the temperature distribution at the wall boundary of the reaction vessel but also from the temperature distribution in the vicinity, the heat flux at the wall boundary position of the reaction vessel is consequently obtained. The change can also be estimated.

In addition, since there is no restriction on the number of spatial dimensions in this method, it can be applied as it is to the inverse problem analysis method for 1-, 2-, and 3-dimensional spaces.

(Example 1 of the fourth embodiment)

As a specific example 1 of the fourth embodiment, a one-dimensional unsteady heat conduction equation system was examined. In the one-dimensional case, the governing equation is simplified (A _x = 1.0) as shown in the following equation (29). Further, the interpolation function or the outer function is similarly simplified as in the following equation (30). ·

C dT, d ² T

pc _P — = (2 9)

dt dx

Figs. 22 and 23 show one-dimensional transient heat using thermocouples embedded in carbon bricks installed on the bottom (Fig. 2 2) and side walls (Fig. 2 3) of the blast furnace bottom. A model that attempted an inverse problem analysis assuming conduction is schematically shown. In each case, two thermocouples are embedded toward the cooling surface side, TC1 is a hot-side thermocouple, and TC2 is a low-temperature-side thermocouple. Based on the temperature changes measured by these thermocouples TC1 and TC2, the inverse problem analysis was used to determine the unsteady heat flux q1 on the hot heat flux surface and the unsteady heat flux q2 on the cooling surface. Estimate at the same time. In Fig. 22, the high-temperature heat flux surface position is a fixed point (4.0 m) at a depth of 4.0 ^ 1 from the cooling surface, and in Fig. 23, the high-temperature heat flux surface position is 2.0 m from the cooling surface. The fixed point (x = 2.0 m). The assumed thermal properties of carbon bricks are: specific heat C _P = 7 1 2 JZ (kg ZK), density p = 230 kg / m ³ , thermal conductivity k _x = 21.2 W / (m K).

Here, it is important to set the constant τ X appropriately. So, first,

Perform forward problem analysis with artificial boundary conditions q 1 and q 2 such as 24Α and 25Α. The temperature change of TC1, TC2, and TC2 over time was calculated (Fig. 24B, 25B). ₀ Here, in the forward problem analysis, the implicit solution method of ordinary difference approximation (time step 28800 seconds) Was used. Then, the above-mentioned inverse problem analysis is executed with each thermocouple temperature shown in FIG. 24B or FIG. 25B as a known condition, and the optimum _x and X are searched. The model shown in Fig. 22 was given the condition shown in Fig. 24A, and the model shown in Fig. 23 was given the condition shown in Fig. 25A. In the present embodiment, since the thermocouple interval can be considered to be invariant, it is determined that X = Om—confirmation is appropriate, and a suitable τ _x is selected. When selecting τ _x , it is also an important factor to set the reference position vector and the reference time. Figures 26 and 27 show the reference point (reference position vector and reference time), the known temperature point (the thermocouple position vector whose temperature is being measured and the known temperature time), and the estimated point (temperature estimation position position). The relationship between the distance and the estimated time is schematically shown. In the examples of Figs. 26 and 27, the reference point and the known temperature point are matched, and Fig. 26 shows that three temperature points are used in the time direction and Fig. 27 shows that five temperature points are used in the time direction. I have. In both cases of Figs. 26 and 27, the estimation point selects the point closest to the present in the time direction (shown as "present"), and sets the position vector to the q1 and q2 positions did. In Figs. 26 and 27, the estimated points are indicated by "X". For the model in Fig. 22, the heat fluxes q1 and q2 at the estimation point are obtained with the settings in Fig. 26. For the model in Fig. 23, the heat flux The heat fluxes q 1 and q 2 are obtained, and τ _でき_る that can reproduce the boundary conditions relatively well compared to the heat fluxes 1 and q 2 in Figs. In determining the _c- parameter, the value was determined by solving the simultaneous equations in Eq. (28). In the inverse problem analysis, as shown in Eq. (27), the temperature distribution of the entire region is estimated, so the values of ql and q2 cannot be directly obtained. Therefore, the temperature (T _p ) at the position vector (x _p ) of the estimated point and the temperature (T _{p at} 3. O mm inside of _{X p} , _c ) near the estimated point pole (χ _ρ ) _p , _c ) was estimated and calculated by the following equation (31), and it was assumed that the heat flux q was at the estimated point.

T P—T P, c

(3 1)

^X P ^X P, c First, Fig. 28 shows the results of comparing the heat fluxes q1 and q2 given by the forward problem analysis with the heat fluxes q1 and q2 found by the inverse problem analysis for the model in Fig. 22. The solid lines are q1 (thick line) and q2 (thin line) given by the forward problem, and the plots are the estimated values of q1 (command) and q2 (country) obtained by the inverse analysis. Time step of inverse analysis is 28800 seconds, the value of tau _chi at this time was 1800000 seconds. The value of _χ depends on the unit system of the analysis, but in this analysis, the MKS unit system is used. It can be seen that both ql and q2 reproduce the boundary condition of the forward problem relatively well. There is a comparative margin in the selected value of τ _x , and when τ _x = about 1800000 seconds ± 200000 seconds, the heat flux estimation value did not show any significant deterioration in accuracy. However, _τ χ = 1000000 sec, set to _τ χ = 2400000 sec, etc. Then, obviously estimation accuracy is confirmed to be reduced.

Similarly, Fig. 29 shows the results of comparing q1 and q2 given in the forward problem analysis with q1 and q2 found in the inverse problem analysis for the model in Fig. 23. The solid lines are q 1 (thick line) and q 2 (fine line) given by the forward problem, and the plots are the estimated values of q 1 (♦) and q 2 (garden) obtained by the inverse analysis. Time step of inverse analysis is 28800 seconds, the value of tau _chi at this time was 1000000 seconds. It can be seen that both q 1 and q 2 reproduce the boundary condition of the forward problem relatively well. If _x = 1.800000 seconds ± 200000 seconds, the estimation accuracy will be extremely deteriorated. That is, for the model of FIG. ₂₃ , it was found that the value of τ _た different from that of FIG. Thus, preferred tau _chi, the reference point, the temperature known point, the relative positional relationship and their number estimated point, it can be seen that there is a tendency that a value became different.

Using the value of τ _{求め} obtained as described above, the result of inverse problem analysis using the actual temperature of the blast furnace (heat fluxes q 1 and q 2 from April 1 for about 4 months) , Fig. 30 A

330 D and FIGS. 31A to 31D. Figure 3 0 A~ 3 0 D is the case in FIG 2 models of blast furnace bottom base plate _(τ χ = 1800000 sec), FIG 3 1 Α~ 3 1 D is a blast furnace

^ This is the case of the model in Fig. 23 of the bottom wall ( _τχ = 1000000 seconds). These figures are excerpted from the long-term analysis results. Using the thermocouple TC1 temperature data in the characteristic diagrams of Figs. 30C and 31C, and the thermocouple TC2 temperature data in the characteristic diagrams of Figs. 30D and 31D, the characteristics of Fig. 30A and 31A The heat flux ql on the high temperature side in the figure and the heat flux q2 on the low temperature side in the characteristic diagrams in Figs. 30B and 31B are simultaneously estimated. `` Constant '' in the characteristic diagrams of Fig. 30 A and 31 A The `` ordinary method '' is a method of estimating the once-through heat flux that has been conventionally used, and multiplies the absolute value of the temperature difference between TG 1 and TC 2 by the thermal conductivity k _x to calculate the distance between the TC 1 position and the TC 2 position. It is the value re-divided by the absolute value of In particular, it is noticeable in Figs. 31A to 31D, but it can be seen that ql of the steady-state method changes in the same shape several days later than the ql estimation. This is the effect of the lag time due to the effect of the heat capacity (p _CP ) of the blast furnace carbon brick. In the stationary method, this delay time cannot be taken into account, so that only the average heat flux can be evaluated.However, in this method, the estimation can be made in consideration of this effect, so that the change in the heat flux in the furnace can be made faster. It is possible to detect.

(Example 2 of the fourth embodiment)

As a specific example 2 of the fourth embodiment, an example of estimating “future temperature change” using the model of FIG. 22 will be described. Figure 32 schematically shows the relationship between the reference point, the known temperature point, and the estimated point. In the case of the present embodiment, it means that the future temperature change is estimated in the time direction with the position of the estimation point being the position of TC1 and the position of TC2. The unit time step of the temperature known point (past) and the estimated point (future) is

At 28800 seconds, they are at different positions but arranged at equal intervals as shown in Figure 32. In addition, the reference point is set by shifting the half-hour step by 14400 seconds, and the time step of the reference point is doubled to 57600 seconds. Further, in the present embodiment, the analysis is performed by using the internal function or the external function of the equation (30), assuming 6000000 seconds and X = 0m. Other settings are the same as in the first embodiment.

Figure 33 shows an example of the analysis results. In order to show the features of this method, the temperature changes at the positions of the 〇1 and 〇2 when the artificial boundary conditions ql and q2 (thick solid line right axis) were given (fine solid line left axis) ), The accuracy of the estimation was verified. In this forward problem analysis, the usual implicit difference approximation method (time step 28,800 seconds) was used. The plot (♦, garden) in Fig. 33 shows the estimation results by this method, using the six known temperature points (three TC1 and three TC2) immediately before the plot. This is the result of estimating six estimated points (future points) (see Figure 32). Overall, it has very good estimation performance. However, it can be seen that some points show estimates in completely different directions. A representative example is shown with an ellipse, but the estimated value in this method is “decreased”, but the temperature is actually increased. You. This is because the temperature at the known temperature point is located at the point where the stepped large boundary condition changes, and the known temperature point has a large effect when the heat flux is low (lOOOW / m ² ). It is thought that it is received. Thus, it can be seen that the estimation accuracy decreases when the boundary condition changes extremely significantly, but has extremely good estimation accuracy when there is no significant change in the boundary condition. Figure 34 shows the result of estimating the future point by generating TC1 and TC2 using trapezoidal heat flux as the same result. In this case, it can be seen that the estimation accuracy of the future temperature is extremely good because the change of the boundary condition is smoother than in FIG.

(Other embodiments)

The operation management device for a reaction vessel according to the above-described embodiment is configured by a computer CPU or MPU, RAM, ROM, or the like, and is realized by the operation of a computer program stored in RAM or ROM. Therefore, the computer program itself for realizing the functions of the above-described embodiment on a computer implements the functions of the above-described embodiment, and constitute the present invention.

Further, means for supplying the computer program to a computer, for example, a recording medium storing the computer program constitutes the present invention. As a recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

It should be noted that the shapes and structures of the respective parts shown in the above embodiments are merely examples of the specific embodiments for carrying out the present invention, and these limit the technical scope of the present invention. It must not be interpreted. That is, the present invention can be implemented in various forms without departing from its spirit or its main features. For example, in order to use the present invention in a network environment, all or some of the computer programs may be executed on another computer. Industrial applicability According to the present invention, an inverse problem analysis using an unsteady heat conduction equation is performed based on temperatures measured at least at a plurality of temperature measurement points arranged in the thickness direction inside the wall of the reaction vessel. Temperature changes and heat flux changes on the inner and outer surfaces of the reaction vessel can be estimated simultaneously. Therefore, for example, whether the temperature fluctuation at a certain temperature measurement point is due to a change in the heat flux on the inner surface of the reaction vessel, or outside the reaction vessel caused by poor contact of the cooling device installed outside the reaction vessel, etc. It is possible to distinguish whether the change is due to a change in heat flux on the surface. Also, when performing inverse problem analysis, for example, if the time step in inverse problem analysis is shortened in order to estimate a change in temperature or heat flux in the past as close as possible, the decimal point of the temperature data Increasing the number of digits or applying filter processing makes it possible to capture small temperature changes, and stabilize inverse problem analysis.

Also, for example, by comparing the heat flux on the inner surface of the reaction vessel obtained by the inverse problem analysis with the heat flux on the inner surface of the reaction vessel obtained by the steady-state method, the unsteadiness of the state in the reaction vessel is obtained. Strength can be evaluated.

Claims

The scope of the claims

1. An operation management method for a reaction vessel for managing the operation of a reaction vessel accompanied by a temperature change reaction,

By performing an inverse problem analysis using an unsteady heat conduction equation based on the temperatures measured at least at a plurality of temperature measurement points arranged in the thickness direction inside the reaction vessel wall, A method for managing the operation of a reaction vessel, comprising a step of obtaining a temperature or a heat flux on an inner surface and an outer surface.

2. The temperature measured at each of the above temperature measurement points and the temperature or heat flux on the inner and outer surfaces of the above-mentioned reaction vessel at the above-mentioned temperature measurement point positions calculated by the transient heat conduction equation from the assumed values of the heat flux. 2. The operation management method for a reaction vessel according to claim 1, wherein the assumed value that minimizes the sum of the square of the difference from the temperature is obtained as a temperature or a heat flux on the inner surface and the outer surface of the reaction vessel. .

3. The assumed value of the temperature or heat flux on either the inner surface or the outer surface of the above-mentioned reaction vessel is calculated using the heat transfer coefficient and the reference temperature on the inside of the wall of the reaction vessel and on the outside of the inner and outer surfaces. Wherein the temperature or heat flux at one of the inner surface and the outer surface of the reaction vessel, at which the sum of the squares of the differences is minimized, is calculated as the other assumed value. The operation management method of the reaction vessel described in the above.

4. A plurality of values of the one assumed value obtained by changing at least one of the heat transfer coefficient and the reference temperature, and the other assumed value obtained corresponding to each one assumed value. 4. The reaction according to claim 3, wherein the combination in which the minimum value of the sum of the squares of the differences is smallest among the combinations is the temperature or heat flux on the inner surface and the outer surface of the reaction vessel. Container operation management method.

5. As one of the assumed values, an assumed value of the temperature or heat flux at the outer surface of the reaction vessel is given using the heat transfer coefficient and the reference temperature, and the reference temperature is calculated as 4. The operation management method for a reaction vessel according to claim 3, wherein the method is determined from cooling conditions of the reaction vessel. '

6. The operation management method for a reaction vessel according to claim 1, wherein a plurality of the temperature measurement points are arranged two-dimensionally or three-dimensionally inside a wall of the reaction vessel.

7. The operation management method for a reaction vessel according to claim 6, wherein the two-dimensional or three-dimensional approximation is performed by combining a one-dimensional transient heat conduction equation.

8. The operation management method for a reaction vessel according to claim 6, wherein a two-dimensional unsteady heat conduction equation or a three-dimensional unsteady heat conduction equation is used.

9. Include a procedure to increase the number of decimal places of the temperature data measured at the temperature measurement points,

2. The operation management method for a reaction vessel according to claim 1, wherein the temperature data in which the number of digits after the decimal point is increased is used for the inverse problem analysis.

10. In the procedure to increase the number of decimal places of the above temperature data, temperature data is collected with a sampling time shorter than the calculation time step in the above inverse problem analysis, and they are averaged over time. 10. The operation management method for a reaction vessel according to claim 9, wherein a representative value of the temperature data used in the calculation time step is used.

1 1. There is a procedure to filter the temperature data measured at the above temperature measurement points.

2. The operation management method for a reaction vessel according to claim 1, wherein the temperature data after the filtering is used for the inverse problem analysis.

1 2. The procedure to increase the number of decimal places of the temperature data measured at the above temperature measurement points, Filtering the temperature data with an increased number of digits after the decimal point.

13. The operation management method for a reaction vessel according to claim 11 or 12, wherein the filter processing is a one-pass filter processing.

14. A steady-state analysis procedure for obtaining the temperature or heat flux on the inner surface of the reaction vessel by performing a steady-state analysis based on the temperature data measured at the temperature measurement points,

And a comparison procedure for comparing the temperature or heat flux at the inner surface of the reaction vessel obtained by the inverse problem analysis with the temperature or heat flux obtained by the analysis procedure by the steady-state method. An operation management method for a reaction vessel according to claim 1.

15. The comparison procedure is to calculate a difference between the temperature or heat flux obtained by the inverse problem analysis and the temperature or heat flux obtained by the analysis procedure by the stationary method. 4. The operation management method for a reaction vessel according to 4.

16. The method according to claim 1, wherein the inverse problem analysis is an inverse problem analysis using an interpolation function or an outer function that satisfies an unsteady heat conduction equation.

As an 7. The unsteady heat conduction equation, the density p, the specific heat C _P X direction of the heat conductivity k _x y direction of the heat conductivity k _y z direction of the heat conductivity k _z,

3T _Ί d ² T _Ί d ² T, d ² T

P ' _D2 k _x ~-+ k _v ~~-+ k. ~-P dt ^x dx ^{2 y} dy ² ― dz ² The operation management method for a reaction vessel according to claim 16, wherein

1 8. The above 內揷 function or outer function is the position vector (X, y, z) and time t. X, Υ, Ζ, τ _χ , τ _y , A _x , A _y , A _z are arbitrary. As a constant

The operation management method for a reaction vessel according to claim 17, wherein the method has the following relationship.

1 9. Parameter H, reference position vector (X ^j , y ^j , ₂ , reference time, number of reference position vectors Ν ”·, reference time number Ni, solve the above transient heat conduction equation , N,

T x, y, z, t) = ^a j, i ^ -i (— zo, — zo, ^z — ー ^

19. The operation management method for a reaction vessel according to claim 18, wherein the expression is expressed by zo = 1! = 1.

2 0. k the temperature measurement positions, 1 and temperature sampling time, as the temperature information a _kl measured by the temperature measuring point, the parameter _alpha w,

a _k

10. The operation management method for a reaction vessel according to claim 19, wherein the method is used to determine the reaction vessel.

2 1. Perform a forward problem analysis with appropriate boundary conditions, and use the temperature changes at several points obtained by the analysis to apply an inverse function using an interpolation function or an external を満たす function that satisfies the transient heat conduction equation. Perform problem analysis and determine the values of X, Y, Ζ, _y , τ _z , A _x , A _y , A _z so that the boundary conditions or temperature distribution given in the forward problem analysis can be reproduced most. 19. The operation management method for a reaction vessel according to claim 18, which is characterized in that:

22. A reaction vessel operation control device for controlling the operation of a reaction vessel accompanied by a temperature change reaction,

By performing an inverse problem analysis using an unsteady heat conduction equation based on the temperatures measured at least at a plurality of temperature measurement points arranged in the thickness direction inside the reaction vessel wall, An operation management device for a reaction vessel, comprising: means for determining a temperature or a heat flux on an inner surface and an outer surface.

23. A combi-tab mouth gram for controlling the operation of a reaction vessel with a temperature change reaction,

By performing an inverse problem analysis using an unsteady heat conduction equation on the basis of the temperatures measured at at least a plurality of measurement points of the degree of the Phoenix inside the wall of the above-described reaction vessel, A computer program for executing a process for determining a temperature or a heat flux on an inner surface and an outer surface of a computer.

24. A computer-readable recording medium storing the computer program according to claim 23.