JP2005082862A - Method and device for estimating inner surface position in reaction vessel, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve an estimating accuracy with which unsteady changing behavior of the temperature and the heat flux is caught from an inverse problem analysis by using an unsteady heat-conductivity equation and e.g. the remaining thickness of the furnace wall in a blast furnace is estimated and also, the calculation at this time is stabilized. <P>SOLUTION: In a some time step, the temperature at each thermocouple position, is calculated with the unsteady heat-conductivity equation from an assumed value of the heat flux at the inner surface assumed position and the outer surface position in the blast furnace, and based on the calculated temperature at each thermocouple position and the measured temperature with each thermocouple, the heat fluxes at the inner surface assumed position and the outer surface position and further, a treatment obtaining the temperature given from the heat flux, are performed by changing the inner surface assumed positions in the above reaction vessel at the same time step in plurality of times. Then, a corresponding relation between the temperature obtained at each inner surface assumed position and each fixed length is obtained and the inner surface assumed position becoming 1150°C (the solidifying point temperature of molten iron) is estimated as the inner surface position, and the remaining thickness of the furnace wall in the blast furnace is estimated. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a method, apparatus, and computer program for estimating the inner surface position of a reaction vessel suitable for estimating a remaining thickness that changes due to, for example, erosion of a blast furnace wall or formation of an adhering solidified layer.

  Conventionally, the remaining thickness of the blast furnace wall is calculated by calculating the heat flux from the temperature and distance between the two points and the thermal conductivity of the brick, based on the temperature measured by two thermocouples embedded in the furnace wall, for example. The remaining surface thickness is estimated by assuming the operating surface temperature as the solidification temperature of the hot metal, for example.

  However, in the above conventional method, it is assumed that the temperature distribution in the furnace wall brick is on a straight line connecting two thermocouple temperatures embedded in the brick, and the temperature distribution in the brick is always steady. The heat flux is calculated on the assumption that it is in a state. However, the furnace wall bricks have a large heat capacity, and it takes a long time for the temperature distribution in the brick to reach a steady state. In the method of estimating the remaining thickness assuming that the temperature distribution in the brick is in a steady state, there is a large separation between the actual value.

  In view of the above points, Patent Document 1 discloses an unsteady change behavior of the heat flux on the working surface or the molten solidified deposit layer working surface in the furnace by performing an inverse problem analysis using the unsteady heat conduction equation. A technique for estimating the remaining thickness of the furnace wall is disclosed.

JP 2001-234217 A

  The technique disclosed in Patent Document 1 simultaneously estimates a change in thickness and a change in heat flux due to the in-furnace melt adhering to the furnace wall. However, if logic that increases or decreases the amount of adhesion due to the solidification / dissolution phenomenon is introduced in inverse problem analysis, the calculation procedure becomes complicated and the calculation tends to become unstable, and there are uncertain factors before and after changing the thickness. Since there is a possibility of mixing, the estimation accuracy may be deteriorated.

  The present invention has been made in view of the above points, and captures an unsteady change behavior of temperature and heat flux by inverse problem analysis using an unsteady heat conduction equation to estimate the remaining thickness of a blast furnace wall, for example. The purpose of this is to stabilize the calculation and improve the estimation accuracy.

  The inner surface position estimation method of the present invention estimates the inner surface position of the reaction vessel based on temperatures measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction vessel accompanied by a temperature change reaction. A method for estimating the inner surface position of the reaction vessel, wherein the temperature at each temperature measurement point or the temperature at each of the temperature measurement points according to the unsteady heat conduction equation is calculated from the assumed temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel. A heat flux is calculated, and based on the calculated temperature or heat flux at each temperature measurement point and the temperature measured at each temperature measurement point, the assumed inner surface position and the outer surface position of the reaction vessel. The temperature or heat flux is obtained by changing the assumed inner surface position of the reaction vessel for the same target time.

  Another feature of the method for estimating the inner surface position of the reaction vessel of the present invention is that the temperature at each assumed inner surface position of the reaction vessel is obtained, and the assumed inner surface position at which the predetermined temperature is reached is determined as the inner surface. It is a point to be estimated as a position.

  Another feature of the method for estimating the inner surface position of the reaction vessel according to the present invention is that the temperature measured at each temperature measurement point and the temperature at the assumed inner surface position and outer surface position of the reaction vessel or The above assumed values at which the sum of the squares of the differences from the temperature at each temperature measurement point position calculated from the assumed value of heat flux by the unsteady heat conduction equation is the minimum are the assumed inner surface position and outer surface position of the reaction vessel. It is in the point calculated | required as temperature or heat flux in.

  Another feature of the method for estimating the inner surface position of the reaction vessel of the present invention is that it is used to estimate the remaining thickness of the blast furnace wall that is the reaction vessel.

  The reaction vessel inner surface position estimation apparatus according to the present invention is based on the temperature measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction vessel accompanied by a temperature change reaction. An apparatus for estimating the position of the inner surface of a reaction vessel for estimating a position, wherein the temperature at each assumed temperature and heat flux at the assumed inner surface position and outer surface position of the reaction vessel is measured at each temperature measurement point according to an unsteady heat conduction equation. The temperature or heat flux of the reaction vessel is calculated, and based on the calculated temperature or heat flux at each temperature measurement point and the temperature measured at each temperature measurement point, the assumed position of the inner surface of the reaction vessel and the outer heat flux are calculated. The present invention is characterized in that there is provided means for performing the process of obtaining the temperature or heat flux at the surface position by changing the assumed inner surface position of the reaction vessel for the same target time.

  The computer program of the present invention is for estimating the inner surface position of the reaction vessel based on temperatures measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction vessel accompanied by a temperature change reaction. A computer program for causing a computer to execute processing, wherein the temperature or heat flow at each temperature measurement point is calculated from an assumed value of temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel according to an unsteady heat conduction equation. The bundle is calculated, and based on the calculated temperature or heat flux at each temperature measurement point and the temperature measured at each temperature measurement point, the inner surface assumed position and the outer surface position of the reaction vessel Let the computer execute a process for obtaining temperature or heat flux, and change the assumed inner surface position of the reaction vessel for the same target time. Characterized by a point.

  As described above, according to the present invention, the residual thickness of the blast furnace wall can be estimated, for example, by capturing the unsteady change behavior of temperature and heat flux by inverse problem analysis using the unsteady heat conduction equation. In this case, since the length between the assumed inner surface position and the outer surface position is fixed, the calculation can be stabilized and the estimation accuracy can be improved.

Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 shows the configuration of a blast furnace wall residual thickness estimation apparatus using the reaction vessel inner surface position estimation method according to the present invention. In the figure, 101 is an input unit for inputting temperature data measured by a plurality of thermocouples (see FIG. 2) embedded in the furnace wall of a blast furnace (corresponding to a reaction vessel in the present invention). The

  Reference numeral 102 denotes an inverse problem analysis unit, which assumes the inner surface position of the blast furnace and calculates the temperature at each thermocouple position from the assumed value of the heat flux at the inner surface assumed position and the outer surface position by an unsteady heat conduction equation. Based on the calculated temperature at each thermocouple position and the temperature measured at each thermocouple, the heat flux at the assumed inner surface position and the outer surface position, and the temperature given by the heat flux Ask for. Then, the inverse problem analysis processing is performed by changing the assumed inner surface position of the blast furnace a plurality of times at the same time step (for the same target time).

  103 is a remaining thickness estimation unit, and for each time step, the correspondence between the temperature obtained at each assumed inner surface position of the blast furnace and each fixed length (the length between the outer surface position and the assumed inner surface position) Seeking a relationship. The assumed inner surface position at which the temperature is 1150 ° C. (freezing point temperature of hot metal) is estimated as the inner surface position.

  Reference numeral 104 denotes an output unit which displays the correspondence between the temperature obtained at the assumed inner surface position of the blast furnace and the fixed length output by the remaining thickness estimation unit 103 so as to be visible on the display 105.

  Here, the inverse problem analysis used in this embodiment will be described. As also disclosed in Patent Document 1, the heat conduction phenomenon inside the reaction vessel wall is considered as an unsteady one-dimensional heat conduction inverse problem, and one thermocouple temperature change or a plurality of one-dimensional directions are arranged. A method has been proposed for estimating the heat flux change on the inner surface of the reaction vessel from the thermocouple temperature change.

  FIG. 2 shows a two-dimensional cross section near the blast furnace wall in which a plurality of thermocouples “x” are embedded. Although the boundary is indicated by a broken line in the furnace wall, the one-dimensional means that only the heat flow in the direction (thickness direction) along the broken line is considered. That is, for example, when heat conduction in the directions of 1a → 1b → 1c and 1d → 1e is assumed, the heat flux at the furnace inner surface is estimated. At this time, assuming that the cooling condition of the outer surface of the furnace is known, it is common to obtain the heat flux on the unknown inner surface of the furnace. Of course, it is also possible to reverse the known and unknown boundary conditions.

  However, the original unsteady one-dimensional inverse heat conduction problem is to simultaneously estimate the boundary conditions on the inner and outer surfaces of the furnace, and in the inverse solution method assuming that one of the boundary conditions is known, We can only get an approximate answer to the boundary condition. For example, a reaction that is caused by a temperature fluctuation measured by a certain thermocouple due to a change in the heat flux on the inner surface of the reaction vessel as described above or due to poor contact of a cooling device installed outside the reaction vessel. It cannot be distinguished whether it is due to a heat flux change on the outer surface of the container.

  In order to evaluate more strictly, the heat conduction phenomenon should also occur in the upward direction across the broken line shown in FIG. 2, and it is necessary to solve the inverse heat conduction problem in two dimensions. In this case, even when the upper and lower boundaries in FIG. 2 are assumed to be adiabatic, it is necessary to construct a two-dimensional inverse problem for estimating a fine heat flux distribution at the left and right boundaries.

  Therefore, the applicant of the present application has proposed inverse problem analysis for enabling simultaneous estimation of changes in heat flux and temperature on the inner and outer surfaces of the reaction vessel. Hereinafter, the inverse problem analysis proposed by the present applicant 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 Equation 1, ρ is the density of the reaction vessel material, C _p is the specific heat of the reaction vessel material, T is the calculated value of the temperature inside the reaction vessel, t is time, and k is the thermal conductivity of the reaction vessel material. .

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

In the present embodiment, as an inverse problem analysis method, as shown in the following equation 2, each thermocouple arranged in a certain one-dimensional direction (1a → 1b → 1c, 1d → 1e, etc. shown in FIG. 2) is used. The sum of the squares of the differences between the measured temperature Y _j and the temperature T _j at each thermocouple position calculated by the unsteady heat conduction equation from the assumed heat flux on the inner and outer surfaces of the reaction vessel is The minimum assumed value is determined as the heat flux at the inner and outer surfaces of the reaction vessel. J represents the number of thermocouples, and j represents the thermocouple number (1 to J).

  In this way, instead of obtaining a solution (heat flux on the inner and outer surfaces of the reaction vessel) that perfectly matches the temperatures T and Y at a plurality of thermocouple positions, a solution that satisfies the least squares. Thus, it is possible to estimate a realistic change in heat flux. The reason is that since the measurement temperature data includes various measurement error factors, it can be said that it is practically meaningless to make them completely match.

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

  More specifically, an example of a formulation and calculation procedure for estimating the heat fluxes on the inner surface and the outer surface of the reaction vessel with the temperatures Y at a plurality of thermocouple positions as known will be described.

S _m number 4 below represents the entire objective function of the number 5 below shows the objective function representing the deviation of the measured temperature Y and calculated temperature T. The following Equation 6 is an objective function added to stabilize the calculation, and has a function of suppressing a rapid change in the value in the space division direction. Α ₀ and α ₁ in Equation 6 are regularization parameters obtained from certain empirical values.

  In the above formula 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 T calculated by the heat conduction equation model from the assumed value of the heat flux is minimized. In the above equation 6, an objective function for regularizing the spatial direction is set so that the solution is stable even if there is a temperature measurement error. Then, using Equation 4 as an overall objective function, a minimum point is searched for an unknown heat flux division region as shown in Equation 7 below.

Here, as shown in Equation 8, for the purpose of stabilizing the solution, it is assumed that the heat flux value at each time step remains unchanged until a certain future time. The time step varies depending on the thermophysical properties and shape of the target material. The q number 8 shows the heat flux, the heat flux q _m at m time step, is assumed to be heat flux q _{m + r-1} in the future time m + r-1 time step is constant.

  Then, if the minimization of Expression 7 is expanded using the assumption of Expression 8, it can be expanded into a matrix form as shown in Expression 9.

X ^T X in Formula 9 is derived from the first term on the right side of Formula 4, and the two terms (α ₀ H ₀ ^T H ₀ + α ₁ H ₁ ^T H ₁ ) following X ^T X are the second term on the right side of Formula 4. (The superscript T represents a transposed matrix). The configuration of X is shown as X _{j, i, k at the} bottom as a supplementary equation 10. Here, i indicating the number of divisions in the time direction changes up to maximum M time steps, j indicating the number of thermocouples changes up to J, and k indicating the number of divisions of the heat flux distribution is maximum. It changes to p. Note that the superscript * in Equation 9 indicates a reference value in repeated convergence calculation, T ^* is a temperature reference value, and q ^* is a heat flux reference value. In the case of the one-dimensional case, the boundary condition at both ends is estimated, so the division number k of the heat flux distribution is p = 2 at the maximum.

Equation 9 is a simultaneous equation for estimating a change in heat flux when a temperature change occurs. In each time step, Equation 9 is used to obtain 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 Equation (9). This q is given as a 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 ^* to correct q again (substituting into Equation 9 to obtain q again). This operation is repeated until q 5 is equal to or less than a certain residual (convergence), and correction of q and T ^* is repeated to obtain the heat flux (final q) at both ends in each time step. 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 represents the ratio of the magnitude of the change in the calculated temperature T at the thermocouple position to the unit change in the heat flux q at the boundary end point. Equation 10 can calculate the value per unit time step at each time step by the forward problem calculation calculated simultaneously with the inverse analysis.

  Hereinafter, a more preferable solution will be described by taking a one-dimensional inverse problem analysis as an example. As described above, even if a one-dimensional inverse problem is formulated (formulated) using the heat fluxes at the two end faces (inner and outer surfaces of the reaction vessel) as unknown boundary conditions, a solution can be obtained in principle. Can do.

  However, there may be many solutions depending on the number of thermocouples, the thermophysical condition of the material, etc., and the calculation may become unstable. One reason for this is that if a combination of “difference in heat flux at unknown end faces” can be selected appropriately, there may be an infinite number of heat flux combinations that represent temperature changes at discrete temperature measurement points. Because there is. In particular, in the case of a substance with low thermal conductivity, even if the boundary condition that the surface temperature becomes extremely large or small is estimated, if only the temperature change at the discrete measurement point is reproduced. It can happen that it is recognized as one solution. This is not only impossible as a real phenomenon, but also makes the inverse problem calculation very unstable.

  Moreover, as an actual problem, the temperature of the thermocouple when starting the inverse problem analysis (the temperature of the discrete measurement points) is given as known, but the initial conditions of the temperature distribution in other analysis areas may be unknown. It is common. For this reason, the calculation is started from the provisional initial temperature distribution given arbitrarily, and while proceeding with the calculation step, the actual temperature distribution is searched and estimated, and the calculation is stably performed while gradually correcting to an appropriate temperature distribution. It is required to have a calculation logic that can be advanced (the temperature distribution here is calculated in parallel in order to correct the solution of Equation 9 in the calculation procedure of the inverse problem analysis, for example) Is the calculated value of the forward problem heat conduction equation model). Thus, the fact that the initial temperature distribution is indefinite 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 a standard (constraint condition) of a certain surface temperature in the process of inverse problem analysis. Based on this concept, a method for appropriately giving the constraint condition will be described with reference to the flowchart of FIG.

First, a temporary heat flux q is given as a heat flux on one side of the inner surface and the outer surface of the reaction vessel, here the outer surface. As a method of giving this temporary heat flux q, using the heat transfer coefficient h and the reference temperature T _b ,
q = h (T _surf −T _b )
(Step S201).

T _surf indicates the temperature at an unknown boundary, here the outer surface of the reaction vessel. This surface temperature _Tsurf is usually subjected to forward problem analysis at the same time in order to correct the value of heat flux in the inverse problem analysis process, and corresponds to the surface temperature obtained by this forward problem analysis.

Further, the reference temperature _Tb is a temperature outside the inside and outside surfaces of the reaction vessel. In the present embodiment, the cooling condition of the reaction vessel is determined based on the water temperature or the like for water cooling, for example.

As a result, the heat flux q, which is the left side of the above equation, can be given as known heat flux information. By giving temporary heat flux information in this way, two constraint conditions of the heat transfer coefficient h and the reference temperature T _b are given, and the physical validity is ensured as compared with the case of giving an arbitrary heat flux. Thus, it is possible to prevent an extreme temperature distribution from occurring.

Next, given a temporary heat flux q (= h (T _surf −T _b )) on the outer surface of the reaction vessel, the square of the difference between the temperatures T and Y shown in the above equation 2 or 5 is given. The heat flux on the inner surface of the reaction vessel that minimizes the sum is calculated as a temporary heat flux on 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 procedure shown in Equations 4 to 9 can be applied as they are as one specific solution. 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 known, and the provisional heat flux on the inner surface of the reaction vessel is given. Is solved as unknown.

Here, the heat flux information on one side (outer surface of the reaction vessel) is given as described above, and the heat flux on the opposite side (inner surface of the reaction vessel) obtained by inverse problem analysis indicates the possibility of one solution. It only 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, by changing several points both or one of the heat transfer coefficient h and the external reference temperature T _b, i.e., waving several points the value of the heat flux q provisional outside surface of the reaction vessel (K point), The provisional heat flux q on the outer surface of the reaction vessel and the heat flux on the inner surface of the reaction vessel that minimizes the sum of the squares of the differences between the temperatures T and Y when each provisional heat flux information q is given. K combinations are obtained (step S203).

  And, as shown in the following equation 11, the temporary 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 each temporary heat flux information q Among the K combinations, the combination having the smallest square value of the difference between the temperatures T and Y is selected, and the combination is set as the heat flux on the inner surface and the outer surface of the reaction vessel (step S204).

  The brackets in the above formula show the calculation results of one case where the inverse heat problem analysis was performed with the heat flux on one side known, and it means that the result with the smallest least squares difference is selected from the K case calculations. To do.

  By repeating this procedure at each time step, it is possible to sequentially and simultaneously calculate changes in heat flux with time on the inner and outer surfaces of the reaction vessel.

  As described above, it is possible to stably execute a one-dimensional inverse problem analysis that simultaneously obtains heat flux changes on the inner surface and the outer surface of the reaction vessel. If the temperature change and heat flux change at the inner surface and outer surface of the reaction vessel can be estimated simultaneously, for example, whether the temperature fluctuation at a certain temperature measurement point is due to the heat flux change at the inner surface of the reaction vessel. It is possible to distinguish whether it is due to a change in the heat flux on the outer surface of the reaction vessel caused by poor contact of the cooling device installed outside the vessel.

  The above method is simple when applied to one-dimensional inverse problem analysis, and is often effective as an actual problem. The reason is that, generally, the upper and lower ends of the reaction vessel are often adiabatic (symmetric), and there is no practical problem.

  Therefore, an inverse problem analysis is performed assuming a one-dimensional thickness direction in a range delimited by a broken line in FIG. 2, and the result can be combined in the vertical direction to be two-dimensional.

  To more strictly consider the heat flow in the vertical direction in FIG. 2, a two-dimensional inverse problem analysis is necessary. Such a two-dimensional analysis is equivalent to finely dividing the heat flux at the left and right ends of FIG. 2 upward and obtaining a heat flux distribution that minimizes the temperature at these thermocouple positions in a least-square manner. Yes, the present invention may be applied according to the same method as the inverse problem formulation described above.

  In this case, the heat flux at the upper and lower ends of FIG. 2 may be unknown or known, but considering the stability of calculation, an appropriate heat flux (for example, heat insulation) is determined from physical considerations. It is better to give it and make it known.

  Based on the same idea, the extension to the three-dimensional analysis can be easily performed.

  Hereinafter, a method for estimating the remaining thickness of the blast furnace wall will be described with reference to the flowchart of FIG. According to the inverse problem analysis method described above, the temperature at each thermocouple position is calculated from the assumed value of heat flux at the inner surface (working surface) assumed position and outer surface position of the blast furnace using the unsteady heat conduction equation at a certain time step. Based on the calculated temperature at each thermocouple position and the temperature measured at each thermocouple, the heat flux at the assumed inner surface position and the outer surface position, and the temperature given by the heat flux are Obtain (step S401).

Here, as shown in the above equation 2, the temperature Y _j measured by each thermocouple and the heat flux assumption values at the inner surface assumed position and the outer surface position of the blast furnace are calculated by an unsteady heat conduction equation. Further, the above assumed value that minimizes the sum of the squares of the differences from the temperature T _j at each temperature measurement point position is defined as the heat flux at the assumed inner surface position and the outer surface position of the blast furnace, and the temperature given by the heat flux. However, if the assumed inner surface position (that is, the fixed length) is different, the level satisfying the equation shown in Equation 2 also changes. Therefore, two solutions (inner surface obtained by assuming different fixed lengths) The heat flux at the assumed position and the outer surface position) cannot be compared in the same row.

Considering the _two models (fixed lengths L ₁ and L ₂ ) shown in FIGS. 5A and 5B, the heat flux q at both ends is
q _{1, L1} ≠ q _{1, L2}
q _{2, L1} ≠ q _{2, L2}
And different values. The reason is that the heat flux at both ends obtained by the inverse problem analysis changes if the length is different. In the case of the model of FIG. 5, the heat flux q _{1, L1} > heat flux q _{1, L2.} .

In addition, assuming that the heat flux at the intermediate position (length L ₂ ) in the result of the inverse problem analysis assuming the fixed length L ₁ is q _{1, L2} *, the value is
q _{1, L2} * ≠ q _{1, L2}
Therefore, it does not necessarily coincide with the heat fluxes q ₁ and L ₂ at the same position when the fixed length L ₂ is used. The reason is that the shorter the length, the greater the freedom of distribution, and the easier it is to make the value of the equation shown in Equation 2 smaller.

Accordingly, a plurality of inner surface positions of the blast furnace are assumed, and the temperature at each assumed inner surface position is obtained. That is, in the flowchart of FIG. 4, it is determined whether to change the assumed inner surface position of the blast furnace (step S402), and when changing the assumed inner surface position, the assumed inner surface position is changed (step S403). Returning to step S401, the temperatures at the assumed inner surface position and the outer surface position of the blast furnace are obtained. Thus, for example, as shown in FIG. 6, the fixed length by sequentially changing the L ₁ ~L _n, determine the temperature of the inner surface presumed position and an outer surface located in the case of a fixed length L ₁ ~L _n To go. The range and pitch for changing the assumed inner surface position are appropriately set by the user, for example.

  If the assumed inner surface position of the blast furnace is changed by a predetermined number n, the process proceeds to step S404. In step S404, the temperature obtained at each assumed inner surface position of the blast furnace and each fixed length are plotted, and by performing function interpolation such as spline interpolation, the assumed inner surface position as shown in FIG. Correspondence between the temperature obtained in step 1 and the fixed length is obtained.

  Then, the assumed inner surface position at which the temperature becomes 1150 ° C. (freezing point temperature of the hot metal) is estimated as the inner surface position (step S405). Thereby, the remaining thickness of the blast furnace wall can be estimated.

  Next, it is determined whether or not to move to a different time step (step S406). And when repeating a process at a different time step, after changing a time step (step S407), the process of step S401-S405 is repeated. Thereby, since it can be estimated as the inner surface position at each time step, it is possible to capture the change with time of the remaining thickness of the blast furnace wall. If the process is not repeated at different time steps, the series of processes ends.

(Example)
With reference to FIGS. 8-10, the example which estimates the residual thickness of a certain blast furnace furnace wall is demonstrated. FIG. 8 schematically shows a remaining thickness estimation model in this example. The high temperature side thermocouple T1 and the low temperature side thermocouple T2 are inserted at positions of distances of 0.150 m and 0.050 m from the cooling surface, biased toward the outer surface (cooling surface) side of the blast furnace. In addition, the thermophysical property value of carbon brick is assumed to be constant, and the value is added to the figure.

  At each time step, assuming the assumed inner surface (high temperature surface) position of the blast furnace as the 1.8 m position, the estimated temperature transition at the 1.8 m position is recorded by the inverse problem analysis method described above. Next, the assumed inner surface position is moved away from the cooling surface by 0.2 m, and the estimated temperature transition at the 2.0 m position is recorded by the inverse problem analysis method. This procedure is repeated until the inner surface assumed position is moved away from the cooling surface at a pitch of 0.2 m until the position becomes 5.6 m.

  Using the estimated temperature at each assumed inner surface position obtained at each time step, the correspondence between the estimated temperature and the fixed length is plotted. From this result, using spline interpolation, the assumed inner surface position at 1150 ° C. (freezing point temperature of the hot metal) at each time step is obtained, and it can be estimated that the remaining brick thickness.

  9 and 10 show examples of analysis results by inverse problem analysis using thermocouple temperature change data from July 23rd to October 11th. 9 and 10 are analysis results at different circumferential positions of the blast furnace bottom wall. The graph shown in each figure (a) is the remaining thickness (hot surface position) transition, the graph shown in (b) is the heat flux transition at the high temperature surface, and the graph shown in (c) is the thermocouple temperature used for the analysis. It shows the transition.

  As described in the above-mentioned conventional example, the steady-state method assumes that the position of the intersection where 1150 degrees (freezing point temperature of hot metal) is obtained by connecting two thermocouple temperatures with a straight line is the freezing point position (residual thickness). The effect of the heat capacity of carbon bricks is completely ignored. The estimation results by both methods are completely different, and it is understood that the difference becomes larger as the remaining thickness is thicker, as is apparent from comparison between FIGS.

(Other embodiments)
The inverse problem analysis apparatus described above is composed of a CPU or MPU of a computer, RAM, ROM, RAM, and the like, and is realized by operating a program stored in the RAM, ROM, etc. as described above. .

  Therefore, the program itself realizes the functions of the above-described embodiment, and constitutes the present invention. As a program transmission medium, a communication medium (wired line or wireless line such as an optical fiber) in a computer network (LAN, WAN such as the Internet, wireless communication network, etc.) system for propagating and supplying program information as a carrier wave Can be used.

  Furthermore, means for supplying the above program to a computer, for example, a storage medium storing such a program constitutes the present invention. As such a storage 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 implementation in carrying out the present invention, and these limit the technical scope of the present invention. It should not be interpreted. That is, the present invention can be implemented in various forms without departing from the spirit or the main features thereof. For example, in order to use the present invention in a network environment, some programs may be executed on another computer.

It is a figure which shows the structure of the remaining thickness estimation apparatus of the blast furnace furnace wall to which this invention is applied. It is a figure which shows the example of arrangement | positioning of a thermocouple. It is a flowchart for demonstrating the example of an inverse problem analysis. It is a flowchart for demonstrating the estimation method of the residual thickness of a blast furnace wall. It is a figure for demonstrating two models from which fixed length differs. The fixed length is a diagram showing the state of successively changed L ₁ ~L _n. It is a figure which shows the correspondence of the temperature calculated | required in the inner surface assumed position, and fixed length. It is a figure which shows typically the remaining thickness estimation model in an Example. It is a figure which shows the example of an analysis result in an Example. It is a figure which shows the example of an analysis result in an Example.

Explanation of symbols

101 Input unit 102 Inverse problem analysis unit 103 Remaining thickness estimation unit 104 Output unit

Claims (6)

A reaction vessel inner surface position estimation method for estimating an inner surface position of the reaction vessel based on temperatures measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction vessel accompanied by a temperature change reaction. There,
The temperature or heat flux at each temperature measurement point is calculated from the assumed temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel by the unsteady heat conduction equation, and each calculated temperature measurement is performed. The processing for obtaining the temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel based on the temperature or heat flux at the point and the temperature measured at each temperature measurement point is the same subject. A method for estimating an inner surface position of a reaction vessel, wherein the inner surface assumed position of the reaction vessel is changed with respect to time.   2. The estimation of the inner surface position of the reaction vessel according to claim 1, wherein the temperature at each assumed inner surface position of the reaction vessel is obtained, and the assumed inner surface position at a predetermined temperature is estimated as the inner surface position. Method.   The temperature measured at each temperature measurement point and the temperature at each temperature measurement point calculated by the unsteady heat conduction equation from the assumed temperature or heat flux at the assumed inner and outer surface positions of the reaction vessel. 3. The reaction according to claim 1, wherein the assumed value that minimizes the sum of squares of differences from the temperature is obtained as temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel. Container inner surface position estimation method.   The method for estimating the inner surface position of a reaction vessel according to any one of claims 1 to 3, wherein the method is used to estimate a remaining thickness of a blast furnace wall that is a reaction vessel. An inner surface position estimation device for a reaction container that estimates the inner surface position of the reaction container based on temperatures measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction container with a temperature change reaction. There,
The temperature or heat flux at each temperature measurement point is calculated from the assumed temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel by the unsteady heat conduction equation, and each calculated temperature measurement is performed. The processing for obtaining the temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel based on the temperature or heat flux at the point and the temperature measured at each temperature measurement point is the same subject. An apparatus for estimating an inner surface position of a reaction vessel, comprising means for changing the assumed inner surface position of the reaction vessel with respect to time. A computer for causing a computer to execute a process for estimating the inner surface position of the reaction vessel based on temperatures measured at a plurality of temperature measurement points arranged at least in the thickness direction inside the wall of the reaction vessel with a temperature change reaction A program,
The temperature or heat flux at each temperature measurement point is calculated from the assumed temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel by the unsteady heat conduction equation, and each calculated temperature measurement is performed. Based on the temperature or heat flux at the point and the temperature measured at each temperature measurement point, the computer is caused to execute processing for obtaining the temperature or heat flux at the assumed inner surface position and outer surface position of the reaction vessel. A computer program characterized in that the processing is performed by changing the assumed inner surface position of the reaction vessel for the same target time.

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