JP2007075789A - Method, apparatus, and computer program for estimating temperature or heat flux of reaction container and computer-readable recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate heat fluxes and temperature simultaneously in the inner surface and the outer surface in the heat flow path (thickness) direction even in the case only one thermocouple is installed in a one-dimensional heat flow path from the higher-temperature side surface to the lower-temperature side surface of a reaction container. <P>SOLUTION: In the case an inverse problem analysis is carried out using an unsteady state heat conduction equation from temperature data measured at a plurality of temperature measurement points set dispersedly and two- or three-dimensionally in the wall inside of a reaction container where reaction is carried out at a temperature changing with the lapse of time, the inverse problem analysis is carried out from temperature data measured at a plurality of temperature measurement points existing in one-dimensional heat path from the higher-temperature side surface to the lower-temperature side surface of the reaction container and its periphery. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention is, for example, the temperature of a reaction vessel for managing the operation of a reaction vessel with a change in temperature over time, such as a high temperature gas reaction or liquid reaction, such as a blast furnace, a steel heating furnace by combustion, a coal gasification reaction furnace, or the like. The present invention relates to a heat flux estimation method, apparatus, computer program, and computer-readable recording medium.

  When managing the operation of a reaction vessel with a high temperature gas reaction or liquid reaction, such as a blast furnace, a steel heating furnace by combustion, and a coal gasification reactor, the situation inside the reaction vessel (for example, combustion behavior) is observed and the situation Need to manage.

  Conventionally, the situation in a reaction vessel has been estimated from temperature data (temperature measurement data) measured by a thermocouple embedded in the wall of the reaction vessel. For example, if there is a sudden rise in temperature, it is assumed that abnormal heat generation has occurred in the reaction vessel around the thermocouple. Conversely, if there is an extreme temperature drop, heat generation in the reaction vessel around the thermocouple. This is an empirical method such as estimating that the calorific value is reduced, such as reduction of the reaction zone.

  However, in the estimation as described above, it is inevitable that a time lag occurs between the actual temperature abnormality occurrence timing in the reaction vessel and the temperature measurement timing. This is because the temperature abnormality in the reaction vessel is transmitted to the surface of the reaction vessel as a change in heat flux, and then the temperature is changed in the thermocouple due to heat conduction inside the wall material of the reaction vessel. The phenomenon has a slight time delay (unsteadiness).

  On the other hand, considering the heat conduction phenomenon in the reaction vessel wall as an unsteady one-dimensional heat conduction inverse problem, from one thermocouple temperature change or a plurality of thermocouple temperature changes arranged in a one-dimensional direction, A method for estimating the heat flux change on the inner surface of the reaction vessel has been proposed. FIG. 1 shows a two-dimensional cross section near the furnace wall of a reaction vessel (heating furnace) in which a plurality of thermocouples “◯” 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 the direction of 1a → 1a ′ or 1b → 1b ′, the heat flux on 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 determine the heat flux on the unknown inner surface of the furnace (when there is one temperature measurement point). Of course, it is also possible to reverse the known and unknown boundary conditions.

  As the above estimation method, for example, Patent Document 1 describes a method for estimating the end point heat flux by analyzing the inverse problem of the unsteady one-dimensional heat conduction equation from the thermocouple embedded in the blast furnace hearth. ing. One of these methods is a method of estimating the heat flux at the opposite end point from the temperature change at one point and the cooling condition (assumed to be known) at the end point. Such a cooling condition is given by the heat transfer coefficient and the cooling water temperature. In particular, since the heat transfer coefficient is estimated from the average flow velocity of the cooling water by an empirical correlation equation, an uncertain estimated value. This value may be used to adversely affect the accuracy of the heat flux estimate at the opposite end point estimated using the value.

  As another method, an estimation method using two points of thermocouple temperature change is also described. Since one of the two points is given as a fixed temperature boundary condition and solved, two points are used. It is difficult to estimate by capturing the relative temperature change, and it is possible to estimate the heat flux on the fixed temperature boundary condition, but the end point on the outer extension line on the side selected for the fixed temperature boundary condition The heat flux cannot be estimated.

  Furthermore, in any of the above methods, the method is not a method for obtaining the heat flux at both ends with the analysis length fixed, but a method for simultaneously estimating the change in thickness due to the melt in the furnace adhering to the refractory surface and the change in heat flux. It is. If logic that increases or decreases the amount of adhesion due to the solidification / dissolution phenomenon is introduced into inverse problem analysis, first, there is a problem that the calculation procedure becomes complicated and the calculation tends to become unstable. Second, if a calculation procedure that changes the analysis length at each time step is entered, there is a possibility that indeterminate elements may be mixed in the estimation method of the temperature distribution before and after the change in length. The possibility that the estimation accuracy will deteriorate cannot be denied.

  In this way, the conventional inverse problem analysis method has many inadequate points, and a new method has been established to simultaneously estimate the heat flux at both ends by fixing the analysis length from multiple thermocouple information. Therefore, a technique for accurately and stably estimating changes in unsteady heat flux is important.

  On the other hand, a method of estimating the temperature distribution by trial and error so that the temperature change can be sufficiently expressed from the measured temperatures of a plurality of thermocouples and simultaneously estimating the temperature distribution at both ends can be considered. However, with such a method, the calculation becomes complicated as the number of thermocouples increases, and it becomes extremely difficult to obtain a temperature distribution solution that satisfies the measured temperature changes of all the thermocouples. In addition, it is difficult to generalize the calculation procedure because it is difficult to determine the standard for how much the absolute value of the difference between the measured temperature and the calculated temperature should be reduced in each thermocouple.

  As an example of this, from the two thermocouple temperatures, the method of Patent Document 1 is applied to calculate the unknown heat flux by alternately changing the two end points, and apparently the end point heat flux is estimated at the same time. A way to do this is conceivable. In other words, the measurement temperature as the fixed temperature boundary condition is calculated alternately and repeatedly, and when the measured temperature and the calculated temperature of both thermocouples agree to some extent, the heat flux solution at both ends at that time step is obtained. Is. However, in this method, it is difficult to determine how much the absolute value of the difference between the measured temperature and the calculated temperature should be reduced for each thermocouple. Although the thermocouple temperature is expressed very well, there is a danger of recognizing it as a solution even when the other thermocouple temperature cannot be expressed so much. In other words, when minimizing the absolute value of the difference between the measured temperature and the calculated temperature at the two thermocouple positions, an appropriate criterion is to determine the balance of minimization at the two independent thermocouple positions. Difficult to set. Furthermore, it goes without saying that when this method is extended to the case of a plurality of thermocouples, determination of the solution becomes extremely difficult.

  Next, as an example of a technique for two-dimensional inverse problem analysis, for example, there is one disclosed by the present applicant in Patent Document 2, and this technique can be applied to a one-dimensional inverse problem analysis as it is. An analysis method proposed by Beck et al. Is known as an example of one-dimensional inverse problem analysis (see Non-Patent Document 1).

  In addition, as a recent method of inverse problem analysis, it is conceivable to apply a probabilistic estimation method such as Kalman filter theory or projection filter theory. At present, this method has been studied for application to the steady-state heat conduction equation (observation equation) with zero on the left side of equation (1) to be described later. If configured, the same inverse problem analysis may be possible. As an application example of the probability estimation method to this stationary differential equation, Non-Patent Document 2 is detailed.

  Furthermore, Patent Document 3 has a description of an interpolation function matrix of an unsteady heat conduction equation. However, the interpolation function described here is an expression of an interpolation function generally used in the finite element method or the like, and satisfies the unsteady heat conduction equation as in the present invention. It is completely different from the extrapolation function.

  Further, Patent Document 4 discloses that an inverse problem analysis using an extrapolation function that satisfies the unsteady heat conduction equation is performed based on temperature data measured at a plurality of temperature measurement points inside the reaction vessel, thereby A method for evaluating the heating or cooling characteristics for calculating the temperature distribution or heat flux distribution in or on the surface is described.

JP 2001-234217 A JP 2002-206958 A Japanese Patent Laid-Open No. 10-10064 JP 2005-134383 A J.V.Beck et al., "Inverse Heat Conduction", 1985, Wiley, New York, P1-P280 Tosaka et al., "Mathematical and inverse methods of inverse problems, inverse analysis of partial differential equations", The University of Tokyo Press, 1999, P191-P289

  However, the original unsteady one-dimensional inverse heat conduction problem is to simultaneously estimate the boundary conditions on the inner surface and the outer surface of the furnace, and as in Patent Document 1, the inverse problem assumes that the boundary condition on one side is known. In the solution, only approximate answers of unknown boundary conditions can be obtained. For example, whether the temperature fluctuation of a certain thermocouple is due to the change in the heat flux inside the reaction vessel as described above, or the heat flux outside the reaction vessel caused by poor contact of the cooling device installed outside the reaction vessel It cannot be distinguished whether it is due to change.

  That is, in Patent Document 1, assuming that the heat transfer coefficient on the cooling side is constant, a method for searching for a solution (reaction vessel inner heat flux) in which the change with time of one thermocouple temperature satisfies the unsteady heat conduction equation However, when the heat transfer coefficient on the cooling side is assumed to be constant, it means that “there is no problem on the cooling side”. One thermocouple temperature change is originally determined by the contribution of heat flux on both the cooling side and the inside of the reaction vessel. Therefore, the method of Patent Document 1 assuming the heat flux on the cooling side cannot model the actual situation. there is a possibility.

  In order to evaluate more strictly, the heat conduction phenomenon should also occur in the vertical direction across the broken line shown in FIG. 1, and it is necessary to solve the inverse problem in two dimensions. In this case, even when the upper and lower boundaries in FIG. 1 are assumed to be adiabatic, it is necessary to construct a two-dimensional inverse problem that estimates a fine heat flux distribution at the left and right boundaries.

  Patent Document 2 describes a method for estimating a molten metal surface height of a molten high-temperature liquid in a container using a plurality of thermocouple temperature aging changes arranged in a line in the height direction in a wall surface of a tundish. Yes. This method applies a two-dimensional inverse problem analysis method, and expresses each area above and below the surface of the molten metal with two heat fluxes. ). In this method, a plurality of thermocouples are inserted in the vertical direction, but since only one thermocouple is embedded in the thickness direction of the container wall, the heat transfer coefficient on the cooling surface side in the thickness direction is a constant value. And estimate the two heat fluxes in the vessel. Originally, the heat flux (heat transfer coefficient) on the cooling side in the thickness direction is unknown, but since it is difficult to estimate, an approximate solution assumed to be known is obtained.

  In Patent Document 4, when the temperature measurement points inside the reaction vessel are moderately dispersed inside the reaction vessel on the front and back sides, the temperature distribution or heat flux at a predetermined position on the reaction vessel surface Although the distribution can be estimated well, there are problems that the estimation accuracy is deteriorated and the calculation is likely to be unstable when the temperature measurement points are biased toward the front side or the back side.

  The present invention has been made in view of the above points, and it seems that only one thermocouple serving as a temperature measurement point is installed inside the reaction vessel wall in the vicinity of a predetermined position for estimating temperature and heat flux. Even when the temperature measurement points are biased to the front side or back side, it is possible to stably estimate the temperature and heat flux at a predetermined position on the inner surface, outer surface, or wall of the reaction vessel. It is an object to provide a method, an apparatus, a computer program, and a computer-readable recording medium.

  The method for estimating the temperature or heat flow rate of the reaction vessel according to the present invention is a method of measuring temperature data at a plurality of temperature measurement points distributed in a two-dimensional or three-dimensional manner inside a reaction vessel wall with a temperature-dependent reaction. The temperature or heat flow of the reaction vessel for estimating the temperature or heat flux at a predetermined position on the inner surface, outer surface, or wall inside the reaction vessel by performing an inverse problem analysis using an unsteady heat conduction equation A method for estimating a bundle, which is present around a one-dimensional heat flow path from a high temperature side surface of a reaction vessel to a low temperature side surface passing through the predetermined position from among the plurality of temperature measurement points, or the heat flow path At least three points including temperature measurement points that exist around and on the flow path and have different installation distances from the outer surface in the wall thickness direction of the reaction vessel, and measure at the selected temperature measurement points. Based on temperature data Characterized in that it has a procedure for problem analysis.

  The apparatus for estimating the temperature or heat flux of the reaction vessel according to the present invention is also capable of measuring at a plurality of temperature measurement points installed in a two-dimensional or three-dimensional manner in the reaction vessel wall with a temperature change reaction. By performing an inverse problem analysis using an unsteady heat conduction equation based on the input temperature measurement data and input means for inputting temperature data, the inner surface, outer surface, or inner wall of the reaction vessel An apparatus for estimating the temperature or heat flux of a reaction vessel comprising an estimating means for estimating temperature or heat flux at a predetermined position and an output means for outputting the estimated temperature or heat flux, wherein the plurality of temperature measurements Among the points, the reaction vessel exists around the one-dimensional heat flow path from the high temperature side surface of the reaction vessel to the low temperature side surface passing through the predetermined position, or exists around and on the heat flow path, and the reaction In the wall thickness direction of the container Installation distance from the outer surface comprises a different temperature measuring point, having the features of at least three points, further comprising a point selecting means for selecting as the temperature measuring point temperature measuring data inputted by said input means.

  Further, the computer program of the present invention includes an input process for inputting temperature measurement data at a plurality of temperature measurement points installed in a two-dimensional or three-dimensional manner inside a reaction vessel wall with a temperature change reaction. By performing an inverse problem analysis using an unsteady heat conduction equation based on the input temperature measurement data, the temperature or heat flux at a predetermined position on the inner surface, the outer surface, or the wall of the reaction vessel is calculated. A computer program for causing a computer to execute an estimation process for estimation and an output process for outputting the estimated temperature or heat flux to estimate the temperature or heat flux of the reaction vessel, from among the plurality of temperature measurement points Existing around the one-dimensional heat flow path from the reaction container high temperature side surface to the low temperature side surface passing through the predetermined position, or present around the heat flow path and on the flow path, and Causing the computer to further execute a selection process of selecting at least three points as temperature measurement points of the temperature measurement data input in the input process, including temperature measurement points having different installation distances from the outer surface in the wall thickness direction of the container. It is characterized by.

  Furthermore, the present invention is characterized in that the computer program is recorded on a computer-readable recording medium.

The “temperature measurement data” in the present invention means temperature data measured with a thermocouple or the like.
Further, in the present invention, “a plurality of temperature measurement points that are two-dimensionally distributed” means that a plurality of temperature measurement points do not all exist on the same straight line but are distributed in a plane. This means that three or more temperature measurement points are required.
In addition, “a plurality of temperature measurement points arranged in three dimensions” means that the plurality of temperature measurement points are not all on the same plane and are spatially dispersed. Four or more temperature measurement points are required.

  According to the present invention, when only one thermocouple serving as a temperature measurement point is installed inside the reaction vessel wall in the vicinity of a predetermined position for estimating the temperature and heat flux, or when the temperature measurement point is on the surface side or Even when it is biased toward the back side, it is possible to stably estimate the temperature and heat flux at a predetermined position on the inner surface, outer surface, or wall of the reaction vessel.

  In particular, the insertion positions of a plurality of thermocouples are greatly dispersed in the reaction vessel wall, and if there is only one thermocouple when focusing on the position sandwiched between two boundary wall surfaces, Even when it is difficult to estimate the temperature or heat flux, according to the present invention, it is possible to appropriately separate the effects from both wall surfaces.

  Hereinafter, embodiments of a method or apparatus for estimating temperature or heat flux of a reaction vessel, a computer program, and a computer-readable recording medium according to the present invention will be described with reference to the drawings.

  FIG. 2 shows an example of an apparatus configuration related to the present invention. As shown in FIG. 2, the temperature or heat flux estimation device of the reaction vessel has a plurality of temperature measurement points installed two-dimensionally or three-dimensionally distributed inside the reaction vessel wall with the change in temperature over time. From the input unit 101 to which temperature data (temperature measurement data) measured at the position where the thermocouple is embedded (see FIGS. 1 and 3) and the temperature measurement data input to the input unit 101 are input. A calculation unit 102 that calculates and estimates the temperature or heat flux at a predetermined location in the inner surface, outer surface, or wall of the reaction vessel by performing an inverse problem analysis so as to satisfy the unsteady heat conduction equation; An output unit 103 for displaying, for example, a temperature or heat flux calculated by the unit 102 on a display (not shown) is provided.

  Here, the unsteady heat conduction equation is expressed by the following equation (1).

  The equation governing the heat flow in the reaction vessel wall surface (solid) as shown in FIG. 1 is generally expressed by equation (1) (three-dimensional unsteady heat conduction equation). Here, when only the heat conduction in the direction of 1a → 1a ′ or 1b → 1b ′ is considered, it is called a one-dimensional unsteady heat conduction equation. In this case, only one term on the right side of the equation (1) is considered. Other terms are omitted. Similarly, when the heat flow across the broken line in FIG. 1 is considered, it is referred to as a two-dimensional unsteady heat conduction equation. In this case, it is expressed using any two terms on the right side of equation (1). . Since the selection of the coordinates of x, y, and z can be arbitrarily set, there is no essential difference regardless of which code is used. In the case of the three-dimensional unsteady heat conduction equation, it can be considered that in addition to the heat flow on the plane, the heat flow in the direction perpendicular to the paper surface of FIG.

  When modeling the heat flow in the reaction vessel, it is possible to reduce the computational load by physically inspecting the heat flow in the reaction vessel and selecting and expressing a heat conduction equation with as few orders as possible. Ideal modeling. For example, in the case of FIG. 1, most of the heat flow due to the exothermic reaction in the reactor inside the reaction vessel is from the reaction vessel surface inside the furnace on the high temperature side to the reaction vessel surface outside the furnace on the low temperature side. It can be inferred that the flow is a one-dimensional heat flow (referred to as a heat flow path) in the direction of 1a → 1a ′ or 1b → 1b ′.

  In this case, when the heat flux change at the point 2a inside the furnace and the point 3a outside the furnace is obtained from the thermocouple temperature change of 1a and 1a ′ by inverse problem analysis, it is sufficient if only the one-dimensional unsteady heat conduction equation is used as a basis. It is thought that. Therefore, in the case of FIG. 1, an inverse problem analysis based on a one-dimensional unsteady heat conduction equation is performed for each region divided by a broken line, and the two ends (2a, 3a are applied to each region. It is considered to be a reasonable method to estimate the heat flux at the corresponding position) or the change in temperature over time and evaluate it individually.

  On the other hand, although it can be considered that the main heat flow in the reaction vessel wall is in a one-dimensional direction along the broken line, as shown in FIG. There may be a case where there is only one thermocouple.

  In this case, if the one-dimensional unsteady heat conduction equation is used as a base, the heat flux change at both ends is estimated from the temperature change at one point. However, the one-dimensional inverse problem analysis that estimates the heat flux or temperature change at two points from one temperature change is not only a problem of accuracy but also tends to be unstable.

  Therefore, the present inventors analyzed the inverse problem using a two-dimensional unsteady heat conduction equation that can be considered including the temperature change at the temperature measurement point in the vertical direction across the broken line region. It has been found that changes in temperature or heat flux at predetermined locations within the inner surface, outer surface, and wall can be estimated. For example, the heat flux at the position 2b (or 3b) in FIG. 3 is obtained by inverse problem analysis of a two-dimensional unsteady heat conduction equation using the temperature change of thermocouples such as 1a, 1b ′, 1c, and 1d. Estimate.

  Patent Document 4 also refers to a method for estimating a two-dimensional unsteady heat flux distribution. For example, the thermocouple arrangement shown in FIG. 4 of Patent Document 4 is an ideal arrangement. In the actual thermocouple arrangement in the reaction vessel wall, there are many cases where the thermocouple is biased toward the cooling side outside the reaction vessel or multiple thermocouples are arranged in the height direction, but the number of thermocouples in the thickness direction is limited. As in Patent Document 4, there are not many existing cases in which thermocouples are arranged in a uniform arrangement on the two-dimensional boundary four surfaces. On the other hand, the present invention is effective in cases where it is difficult to freely set the thermocouple arrangement, but it can be inferred from the physical consideration that the main heat flow will be on the one-dimensional heat flow path. is there.

  The details of the embodiment of the present invention will be described with reference to FIG. 3 in the case where the main heat flow is on the one-dimensional heat flow path. In FIG. 3, in the example in which the predetermined position on the reaction vessel surface is 2b (or 3b) and the heat flux at this position is estimated, the temperature measurement point for sampling the temperature measurement data used for the inverse problem analysis over time is selected. Is a reaction passing through the position 2b (or 3b) from among the five temperature measurement points 1a, 1b ′, 1c, 1d, and 1e ′ that are installed in a two-dimensional distribution inside the reaction vessel wall. Around the one-dimensional heat flow path (in this example, a straight line connecting 2b → 1b ′ → 3b) from the high temperature side surface (2b in this example) to the low temperature side surface (3b in this example), or around and the heat flow At least three points including temperature measurement points that exist on the road and have different installation distances from the outer surface in the wall thickness direction of the reaction vessel are selected. That is, 1a, 1b ', 1c, 1a, 1b', 1c, 1d, 1a, 1b ', 1c, 1d, 1e' or 1a, 1c, 1d, 1e ', etc. are selected.

  Similarly, for example, when estimating the heat flux at the 2c (or 3c) position, 1b ′, 1c, 1d, or 1a, 1b ′, 1c, 1d, or 1b ′, 1c, 1d, A temperature measurement point such as 1e 'or 1a, 1b', 1d, 1e 'is selected.

  As a way of selecting the temperature measurement point, when estimating the heat flux at the position 2b (or 3b), a one-dimensional heat flow path from the high temperature side surface of the reaction vessel passing through 2b (or 3b) to the low temperature side surface (this In the example, the thermocouple 1b ′ existing on the straight line connecting 2b → 1b ′ → 3b) is presumed to have the most important temperature information, so it is desirable to include it in the temperature measurement point to be selected.

  Other thermocouples can be selected as appropriate from those existing around the one-dimensional heat flow path, but include temperature measurement points with different installation positions from the outer surface in the wall thickness direction of the reaction vessel is required. This is because the temperature information obtained is poor when the installation position from the outer surface is the same only at the temperature measurement point. This is because only heat flux can often be obtained. Therefore, selections such as 1a, 1c, and 1d are not performed.

In addition, it is preferable to select temperature measurement points in order from the above-described one-dimensional heat flow path passing through a predetermined position for estimating temperature or heat flux because it is considered that more important temperature information is included.
Further, the method of the present invention can be applied not only in the two dimensions as shown in FIG. 3 but also in the three dimensions.

  In addition, it is often preferable to select as many temperature measurement points as possible, but it is preferable that the distance between the temperature measurement points is not excessively widened. Therefore, if the target is a two-dimensional problem, there is a possibility that there is a heat flux contribution from at least four directions, so it is more preferable to select four temperature measurement points. Similarly, if the target is a three-dimensional problem, It is more preferable to select six temperature measurement points since there may be a heat flux contribution from a minimum of six directions.

  As another embodiment of the present invention, a case as shown in FIG. 4 is also conceivable. This is a case where the temperature measurement point (thermocouple installation position, indicated by “◯”) is biased toward the outer surface side (cooling side) of the reaction vessel as compared to FIG. In this case, the distance between the thermocouple installation position and the heat flux q1 (position is Q1) on the surface of the high temperature reaction vessel to be estimated and the heat flux q2 (position is Q2) on the surface of the low temperature reaction vessel. Since the balance is greatly lost, it has been found that the inverse problem analysis of the two-dimensional heat conduction equation alone tends to be very unstable, and there is a high possibility that a physically meaningless solution is obtained. Even in such a case, the present inventors have intensively studied and become an approximate method, but found that it is effective to combine one-dimensional and two-dimensional inverse problem analysis.

  That is, even when the temperature measurement point is extremely biased toward the outer surface of the reaction vessel, at least one of the selected temperature measurement points is from the reaction vessel high temperature side surface passing through the predetermined position toward the low temperature side surface. And at least two of the remaining selected temperature measurement points are on a two-dimensional plane including the one-dimensional heat flow path, and The problem analysis solution can be stabilized to make a physically meaningful solution. In FIG. 4, the thermocouples are installed in a two-dimensional manner from the beginning, but the same is effective even in a case where the thermocouples are arranged in a three-dimensional manner.

  The details will be described with reference to FIG. 4. First, one temperature measurement point “◯” existing on a one-dimensional heat flow path connecting Q1 and Q2 and a two-dimensional plane including this one-dimensional heat flow path. A total of three temperature measurement points “◯” existing in the above are selected.

  Next, the temperature at the predetermined position “Δ” on the one-dimensional heat flow path is predicted from the temperature measurement data at two temperature measurement points existing on the two-dimensional plane.

  Based on the predicted temperature data at this “△” position and the temperature measurement data at the temperature measurement point existing on the one-dimensional heat flow path, the inverse problem analysis using the one-dimensional unsteady heat conduction equation is performed, The heat fluxes q1 and q2 on the inner and outer surfaces of the reaction vessel can be estimated.

  FIG. 5 shows a similar relationship with respect to a cylindrical reaction vessel. 4 and 5, although the coordinate systems are different, a one-dimensional heat flow path from the reaction vessel high temperature side surface to the low temperature side surface direction, which is the main heat conduction heat flow direction, is assumed based on physical considerations (large The direction is assumed to be one-dimensional heat conduction (a line connecting q1 and q2). In this way, even if there is some estimation error, it is possible to capture the rough heat movement in the reaction vessel. In the same way, when estimating the heat flux inside the reaction vessel from the thermocouple temperature arranged in the three-dimensional analysis area, not only the three dimensions but also the two-dimensional, one-dimensional Combined with inverse heat conduction analysis is effective. In this case as well, it is desirable to determine the combination of each other geometrically after judging the main heat flow from physical considerations.

  In addition, the inventors conducted further diligent investigations, and were surrounded by temperature measurement points such as thermocouples when estimating the temperature or heat flux at a predetermined position on the inner surface, outer surface, or wall inside the reaction vessel. It is practically useful to estimate the temperature in the region using an appropriate interpolation function, and to estimate the temperature or heat flux using the estimated temperature, such as a low-order inverse heat conduction problem. I found out.

  In FIG. 4, the region is indicated by a region surrounded by three temperature measurement points “◯” (within a triangular broken line). In the broken line, when considered in the xy local coordinate system, all xy coordinates in the region include xy coordinate values corresponding to three “◯”, and arbitrary points in the broken line are x and y respectively. Since it can be expressed as an intermediate point between three “◯”, it can be considered as a range that can be interpolated. Therefore, the temperature of the “Δ” point can be estimated from the temperature of the “◯” point if an appropriate interpolation function can be selected. In the case of such a triangle, for example, area coordinates used in the finite element method or the like can be applied as a linear interpolation function.

  FIG. 5 shows the case of a cylindrical coordinate system. The temperature measurement points “◯” are set at two points at a position where r is the same, but r is the same (total of 4 points). The area surrounded by the broken line is composed of r concentric circles and a straight line, and the position of the “Δ” point corresponds to the interpolation point in the rθ coordinate system. If an interpolation function can be set, it can be estimated. Any number of interpolation methods can be considered. For each measurement time step temperature, a linear function approximation is performed between the temperatures of each “◯” point, and the temperature value at the coordinate value corresponding to the intermediate value is obtained. The method of deciding can be considered. Further, the measured temperature “◯” point does not necessarily have to be at the apex of the region, and there is no problem even if it is included in the region. In this case, since the number of temperature measurement points (known temperature points) in the region increases, it is possible to use a higher-order interpolation function, and an improvement in interpolation accuracy is expected.

  Furthermore, the present inventors, as one embodiment of the present invention, use an extrapolation function that satisfies the unsteady heat conduction equation. (A) The temperature of the region surrounded by the thermocouple “◯” as described above Can be interpolated to estimate “△”, and (b) As one of the inverse problem analysis methods, it can also be applied to estimate the temperature distribution or heat flux distribution in the block (temperature extrapolation). , Found.

  As for the above (a), the extrapolation function is not a simple interpolation function, but the temperature at the extrapolation point can be estimated while satisfying the unsteady heat conduction equation. There is also an advantage that the temperature “Δ” can be estimated with sufficient accuracy even if it slightly protrudes from the region.

  As for the above (a), estimating the temperature distribution or heat flux distribution in the block is, after all, equivalent to estimating changes in the boundary conditions on the inner and outer surfaces of the reaction vessel. Equivalent here means that, as will be described below, the analysis method using the extrapolation function estimates the temperature distribution at an arbitrary xyz position as shown in equation (5) described later. Means that there is no distinction between being inside the reaction vessel wall and being on the surface of the reaction vessel wall. Therefore, this is an inverse problem analysis in which the boundary condition is estimated from the temperature change.

  Here, the extrapolation function is a function that connects temperatures at measurement points and expresses a region other than that point, for example, the entire analysis region or a part thereof. As interpolation functions that cannot be extrapolated, linear function approximation, spline interpolation, and the like are known. However, functions that can be extrapolated while satisfying the unsteady heat conduction equation have not been known. Interpolation refers to estimating an internal unknown point surrounded by known points, and extrapolation refers to estimation including outside and surrounding of the known point.

Hereinafter, a temperature estimation method using an extrapolation function that satisfies the unsteady heat conduction equation and an inverse problem analysis method will be described.
First, the calculation processing performed in the calculation unit 102 will be described with reference to the flowchart of FIG. The computing unit 102 first expresses the solution of the unsteady heat conduction equation using a predetermined interpolation or extrapolation function and parameters (step S201).

  As a result of intensive studies, the present inventors can perform more physically meaningful extrapolation by using an extrapolation function that satisfies the unsteady heat conduction equation expressed by the following equation (2). I found out.

In the above equation (2), t represents time, and x, y, and z represent position vector elements, and can be applied to a general three-dimensional coordinate system. τ _x , τ _y , τ _z , A _x , A _y , A _z , X, Y, Z represent appropriate arbitrary constants, and the optimum value varies depending on the target system. Care must be taken in selecting the values of these arbitrary constants.

  As another function form, for example, it can be expressed as the following expression (3).

Similarly, in the above equation (3), τ _xy , τ _z , A _xy , A _z , X, Y, and Z represent appropriate arbitrary constants, and the optimum value varies depending on the target system. Needless to say, the relationship between the coordinate systems x, y, and z in the above equations is interchangeable.

  Further, as another function form, for example, it can be expressed as the following expression (4).

Similarly, in the above equation (4), τ _xyz , X, Y, and Z represent appropriate arbitrary constants, and the optimum value varies depending on the target system. Any of the above three types of interpolation / extrapolation functions can be used because any physically meaningful extrapolation can be performed.

  These functions F (x, y, z, t) automatically satisfy the unsteady heat conduction equation (1). When the solution of the unsteady heat conduction equation is generally expressed using this function F (x, y, z, t), it is expressed as the following equation (5).

In the above equation (5), x ^j , y ^j , and z ^j represent each element of an arbitrary reference position vector, t ⁱ represents an arbitrary reference time, and x, y, z, and t are about to estimate temperature. The point position vector elements and time. N _j and N _i are the number of reference position vectors and the number of reference times in the time direction, respectively. These numbers often coincide with the number of temperature information measurement points, that is, the number of temperature measurement points by the thermocouple, and the number of sampling times of the measurement temperature in the time direction, but it is not always necessary to match. Α _{j, i} is a parameter. If this value is determined, an arbitrary position vector (x, y, z) and temperature distribution T (x, y, z, t) at time t can be determined. It can be done.

Next, the value of the parameter α _{j, i in} the solution of the unsteady heat conduction equation expressed by the above equation (5) is determined using the temperature information measured by the thermocouple (step S202). The value of the parameter α _{j, i} can be determined by solving the following simultaneous equations (6).

In the above equation (6), a _k and _l indicate the temperature T (x ^k , y ^k , z ^k , t ^l ) measured by the thermocouple, and the superscript k indicates the measurement position (x ^k , y ^k , z ^k ), and the superscript ^l represents the sampling time t ^l .

  By using the method described above, if there are discrete temperature measurement data in space and time direction, the estimated temperature value in the entire reaction vessel wall area (arbitrary spatiotemporal position) governed by the unsteady heat conduction equation Will be obtained.

  Here, the inverse heat conduction problem is based on the unsteady heat conduction equation that governs the computational domain, and the boundary conditions such as the temperature and heat flux at the boundary of the domain or the initial condition are defined based on the temperature information inside the domain. Refers to the problem to be estimated. On the other hand, the heat conduction order problem refers to a problem of estimating temperature information inside a region based on a known boundary condition.

  In the above method, the temperature distribution at the wall boundary of the reaction vessel is estimated at the same time, and indirectly, the boundary conditions of the inner and outer surfaces of the reaction vessel are determined from the temperature information measured by the thermocouple. It is an inverse problem to decide.

  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 thereof, as a result, the heat flux change at the wall boundary position of the reaction vessel can also be estimated. .

  One of the major features of the present invention is that it is possible to easily estimate the change over time in the temperature distribution of the entire analysis region as well as the inner and outer surfaces of the reaction vessel. In the normal inverse heat conduction problem, it is assumed that not only the temperature of the thermocouple (the temperature of the discrete measurement point) but also the temperature distribution (generally the initial temperature distribution) at a certain time section in other analysis areas is known. As usual, it is formulated. However, as a practical matter, the temperature distribution in the reaction vessel wall is generally unknown regardless of the time axis. Therefore, when the ordinary inverse problem solving method is adopted, it is necessary to add various methods to find a solution stably while searching and estimating an actual temperature distribution as appropriate. However, in principle, the method of the present invention can simply estimate the temporal change of the temperature distribution in the entire analysis region as long as there is a temperature change at discrete measurement points.

  Further, since there is no restriction on the number of spatial dimensions in this method, it can be applied as it is as a spatial two-dimensional or three-dimensional inverse problem analysis method.

  The apparatus for estimating the temperature or heat flux of the reaction vessel of the above-described embodiment is constituted by a computer CPU or MPU, RAM, ROM, hard disk, etc., and the program recorded in the ROM, hard disk, etc. operates, and the above-mentioned means After the temperature data input in step 1 is read into an input unit such as a RAM or a hard disk, the temperature data is transferred to a calculation unit in the program, and the calculation unit calculates the temperature or heat flux at the wall boundary by the means described above. This is realized by calculating and estimating, and then sending the estimated temperature or heat flux data to the output unit. Therefore, the program itself for executing the procedure of the above-described embodiment for the computer executes the procedure of the above-described embodiment, and the program itself constitutes the present invention.

  The temperature measurement point used for the inverse problem analysis can also be selected using a program that causes a computer to execute the procedure. In that case, it can be executed by programming so as to select four points in the order close to the one-dimensional heat flux.

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

  Further, by executing the program supplied by the computer, not only the procedure of the above-described embodiment is executed, but also the program is collaborated with an OS (operating system) or other application software running on the computer. Needless to say, such a program is included in the embodiment of the present invention even when the procedure of the above-described embodiment is executed.

  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 main features thereof. For example, in order to use the present invention in a network environment, all or some of the programs may be executed on another computer.

  Examples of the present invention will be described. A two-dimensional unsteady heat conduction equation system was studied. In the case of two dimensions, the governing equation is simplified as shown in Equation (7). Here, as an inverse problem analysis method, a method using an extrapolation function was adopted. This interpolation / extrapolation function is also simplified as shown in equation (8).

  FIG. 6 schematically shows a model in which an inverse problem analysis is attempted according to the present invention on the assumption of two-dimensional unsteady heat conduction using a thermocouple embedded in a steel reaction vessel wall surface. A steel wall with a thickness of 0.1m continues in the vertical direction in the figure, but in this model, a part of it is extracted. As shown in FIG. 6, the five thermocouples TC0 to TC4 are installed one by one at each height position (y-direction position), and are disposed so as to be biased toward the cooling side.

In this embodiment, the heat fluxes q1 and q2 (positions Q1 and Q2 as positions) at both ends at the height of TC3 are estimated. When the thermocouple positions TC0 to TC4 are displayed in the coordinates of the x and y components with the left corner position as the origin (illustrated as 0), TC0 = (0.045, 0.01), TC1 = (0.075, 0.05), TC2 = (0.045) , 0.09), TC3 = (0.075, 0.13), and TC4 = (0.045, 0.17) (unit is m). The assumed thermal properties of the steel wall are: specific heat C _p = 434 J / (kg · K), density ρ = 7500 kg / m ³ , thermal conductivity (isotropic) k _x = 30.0 W / (m · K) , K _y = 30.0 W / (m · K).

  FIG. 7A shows the change with time of the actual temperature at each thermocouple position. The temperature change of the five thermocouples is shown. Of these, TC0 is far away from the q1, q2, and TC3 positions that are the object of analysis, so it is excluded and one-dimensional from Q1 to Q2. Four temperature measurement points were selected in order from the closest heat flow path. That is, it was judged that the interaction in the heat conduction equation was small between the TC0 and TC3 height positions. Accordingly, the heat fluxes q1 and q2 at the positions Q1 and Q2 were estimated using the four thermocouple temperatures TC1 to TC4 as shown in FIG. 7B.

In the case of a two-dimensional inverse problem, since the temperature distribution of the entire two-dimensional analysis region is estimated (see Equation (5)), the heat flux at the interface must be estimated using this temperature distribution. . Therefore, for the Q1 plane and the Q2 plane, the heat flux is estimated using Equation (9). That is, the position vector of the estimated point temperature at _{(x p) (T p)} , the position vector of the estimated point close proximity (x _p from 3.0mm inner: x _{p, c)} the temperature in (T _{p, c)} the (5 ) And is substituted into equation (9) to calculate the heat flux.

The time step of the inverse problem analysis using the extrapolation function was 12.0 seconds, and the reference position vector was matched with the thermocouple position. In addition, the number of known temperatures in the time direction is 3 points for one thermocouple (12 points in total), and we analyzed the changes over time while advancing the reference time little by little. The heat fluxes q1 and q2 at each end face at the point (current time) were estimated. The reference point in the time direction and the temperature known point are matched. The inverse problem analysis was performed with the parameters in the extrapolation function as X = −2.0 m, Y = 0 m, A _x = 1.0, A _y = 1.0, τ _x = 205800 seconds, and τ _y = 23400 seconds. These parameter values are values determined by combining with appropriate forward problem analysis. Specifically, the inverse problem analysis was performed using the thermocouple temperature change of FIG. 7B, and the result of estimating q1 and q2 is shown in FIG. In these results, the heat flux flowing into the reaction wall is displayed as “positive”, and the heat flux flowing out is displayed as “negative”. The estimation result of q2 shows that the heat flux on the cooling side is separately measured and compared with a heat flux meter, and it is found that it is well expressed.

  On the other hand, when the same inverse problem analysis was attempted using 5 points including TC0 as a block as shown in FIG. 7A, it was found that the estimation accuracy deteriorated. This is probably because the analysis range of one block is too wide. On the other hand, the block range of 3 points of TC4, TC3 and TC2 was not considered. This result shows that the optimal block range varies depending on the nature of the problem (absolute distance / relative relationship of thermocouple position, estimated heat flux, temperature position, etc.). This may indicate that it is necessary to select according to the problem.

  Another embodiment of the present invention will be described. FIG. 9 shows a cross section of a cylindrical reaction vessel (blast furnace). This problem also belongs to the two-dimensional unsteady heat conduction equation system. The inside and outside of the furnace are partitioned by heat-resistant bricks of 2 m (r = 6.0 m to 8.0 m), and the temperature measurement points are extremely biased toward the cooling surface. When these installation thermocouple positions are expressed in the (r, θ) cylindrical coordinate system, 4a = (7.95,45), 4b = (7.85,30), 4c = (7.95,15), 4d = (7.95,0) ), 4e = (7.85,345), 4f = (7.95,330). Here, the unit of r is [m], and the unit of θ is [degree].

  This problem is caused by the fact that although the heat-resistant bricks are very thick, the thermocouple is not installed on the cooling surface, and the location along the r direction, which is considered to be the main heat flow direction. Since only one thermocouple is set, as a target of the two-dimensional inverse problem analysis for obtaining the heat flux q1 (position is Q1) inside the furnace and the heat flux q2 (position is Q2) outside the furnace, It becomes extremely difficult.

  Accordingly, the present inventors firstly used a temperature measurement data that is two-dimensionally expanded and that is a time-dependent change in thermocouple temperature by analysis using a two-dimensional extrapolation function (equation (8)). It was considered to predict the temperature of the virtual thermocouple position on the r-axis that becomes a one-dimensional heat flow path from the high temperature side surface to the low temperature side surface.

  For example, assuming that the thermocouples 4c, 4d, 4e, and 4f indicated by “◯” are one unit, the position of the virtual thermocouple 4d ′ indicated by “Δ” is obtained from the thermocouple temperature change data at these temperature measurement points. (4d ′ coordinate position is (7.85, 0)). Thereafter, the heat flux q1 at the 5d position is estimated from the temporal change of the 4d temperature measurement data and the 4d ′ predicted temperature data by the one-dimensional inverse problem analysis. The position 4d ′ corresponds to a position concentric with 4e and slightly deviates from the region surrounded by the four thermocouples 4c, 4d, 4e, and 4f. However, as shown below, a two-dimensional interpolation function ( It was found that the equation (8) can be estimated relatively well.

The analysis time step in the 4d ′ position temperature estimation using the extrapolation function was 28800 seconds, and the reference position vector was matched with the thermocouple position. In addition, the number of known temperatures in the time direction is 3 points for one thermocouple (12 points in total), and we analyzed the changes over time while advancing the reference time little by little. The temperature at the 4d 'position at the point (current time) was estimated. The reference point in the time direction and the temperature known point are matched. In the analysis using the extrapolation function, the rθ coordinate system cannot be used, but the xy coordinate system shown in FIG. 9 is set, and the coordinates of each thermocouple position are converted and introduced. The parameters in the extrapolation function were X = -13.0 m, Y = 39.0 m, A _x = 1.0, A _y = 1.0, τ _x = 4320000 seconds, and τ _y = 2880000 seconds. These parameter values are values determined by combining with appropriate forward problem analysis. The assumed thermal properties of the heat-resistant brick are as follows: specific heat C _p = 712 J / (kg · K), density ρ = 2300 kg / m ³ , thermal conductivity k _x = 21.2 W / (m · K), thermal conductivity k _y = 21.2 W / (m · K).

  FIG. 10A shows the temperature change of each thermocouple used in the analysis, and FIG. 10B shows the estimated temperature change at the 4d ′ position. The horizontal axis is the date, and the results from July 13 to August 12 are shown.

As an example of the analysis at another heat flux estimation position (5b), the thermocouples 4a, 4b, 4c, and 4d indicated by “◯” are regarded as one unit, and from the thermocouple temperature change data at these positions, “Δ ”Was estimated (the coordinate position of 4b ′ is (7.95, 30)). The analysis conditions are almost the same as those described above, but the parameters in the extrapolation function are X = -10.0 m, Y = -48.0 m, A _x = 1.0, A _y = 1.0, τ _x = 2880000 seconds, The analysis was performed with τ _y = 2880000 seconds. These parameter values are also values determined by combining with appropriate forward problem analysis. Needless to say, the temperature data at the 4b ′ position is used for one-dimensional inverse problem analysis for obtaining the heat flux at the 5b position together with the 4b temperature data.

  Similarly, FIG. 11A shows the temperature change of each thermocouple used in the analysis, and FIG. 11B shows the estimated temperature change at the 4b 'position. The horizontal axis is the date, and the results from July 13 to August 12 are shown.

Next, means for estimating the heat flux at 5d using the measured temperature change and estimated temperature change of 4d and 4d ', and heat flow at 5b using the measured temperature change and estimated temperature change of 4b and 4b' The means for estimating the bundle was estimated by inverse problem analysis using a one-dimensional interpolation function. In the case of one dimension, the governing equation is simplified as shown in Equation (10). Similarly, the extrapolation function is simplified as shown in Expression (11) (A _x = 1.0).

  FIG. 12 schematically shows a model in which an inverse problem analysis is attempted according to the present invention, assuming a one-dimensional unsteady heat conduction using a thermocouple embedded in a heat-resistant brick. TC1 is a high temperature side thermocouple (4b or 4d ') TC2 is a low temperature side thermocouple (4b' or 4d). From the temperature changes measured by these thermocouples TC1 and TC2, the unsteady heat flux q1 at the high temperature heat flux surface and the unsteady heat flux q2 at the cooling surface are simultaneously estimated by the inverse problem analysis shown in the present invention. To do. Originally, since it is a one-dimensional cylinder, it cannot be expressed strictly by equation (10), but since the inner diameter of the container is extremely large, an approximate solution was obtained.

FIG. 13 schematically shows the relationship among a reference point (reference position vector and reference time), a temperature known point (temperature measurement thermocouple position vector and temperature known time), and an estimated point (temperature estimation position vector and estimated time). Is shown. The reference point and the temperature known point are made to coincide with each other, indicating that three temperature known points in the time direction are used. As the estimation point, a point closest to the current time (shown as “current”) is selected in the time direction, and the position vectors are set at positions q1 and q2. The time step is 28800 seconds. The heat flux was calculated from equation (9) from the temperature distribution obtained from equation (5). The inverse problem analysis was performed with the parameters in the extrapolation function set to X = -0.5m and τ _x = 940000 seconds. These parameter values are values determined by combining with appropriate forward problem analysis. The assumed thermal properties of the heat-resistant brick are specific heat C _p = 712 J / (kg · K), density ρ = 2300 kg / m ³ , and thermal conductivity k _x = 21.2 W / (m · K).

  FIG. 14 shows the result of estimating the heat flux q1 at the positions 5b and 5d. Looking at this plot, a sharp drop in the heat flux is observed on July 23, particularly in the heat flux q2 at the 5d position. This corresponds to a blast furnace off-air day (an outage date), and it can be determined that this sudden drop is a good view of a decrease in heat flux accompanying a decrease in the furnace bottom hot metal flow velocity.

In this embodiment, a spatial two-dimensional example has been shown. However, as the present invention proposes a spatial three-dimensional problem as shown in equations (1) to (6), it is extended to three dimensions. Is extremely easy.
In the present invention, it is difficult to freely set the two-dimensional or three-dimensional thermocouple arrangement, but it can be inferred from the physical consideration that the main heat flow will be on the one-dimensional heat flow path. Even in such a case, it is possible to appropriately estimate the heat flux / temperature of the inner and outer surfaces of the reaction vessel.

It is a figure which shows the two-dimensional cross section near the furnace wall of the reaction container in which the several thermocouple was embedded. It is a figure which shows the structure of the inverse problem analysis apparatus in this Embodiment. It is a figure which shows the two-dimensional cross section near the furnace wall of the reaction container in which the several thermocouple was embedded. It is a figure explaining the application method in this Embodiment. It is a figure explaining another application method in this Embodiment. FIG. 3 is a diagram showing the arrangement relationship of thermocouples in Example 1. FIG. 6 is a diagram for showing changes in actual temperature of five thermocouples in Example 1. FIG. 4 is a diagram for showing changes in actual temperature of four thermocouples in Example 1. It is a figure for demonstrating the analysis result by the actual data in Example 1. FIG. FIG. 6 is a diagram showing the arrangement relationship of thermocouples in Example 2. FIG. 4 is a diagram for showing changes in actual temperature of four thermocouples in Example 2. It is a figure for showing the temperature estimation result of the virtual thermocouple position in Example 2. FIG. FIG. 9 is a diagram for showing four thermocouple actual temperature changes in another combination in Example 2; It is a figure for showing the temperature estimation result of another virtual thermocouple position in Example 2. FIG. 6 is a diagram illustrating a thermocouple arrangement relationship in a one-dimensional direction in Embodiment 2. FIG. FIG. 10 is a diagram for explaining an inverse problem analysis method according to the second embodiment. It is a figure for demonstrating the analysis result by the actual data in Example 2. FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Input part 102 Temperature or heat flux calculation part by inverse problem analysis 103 Output part

Claims (14)

Inverse problem analysis using unsteady heat conduction equation based on temperature measurement data at multiple temperature measurement points installed in two or three-dimensional distribution inside the reaction vessel wall with temperature-dependent reaction A method for estimating the temperature or heat flux of the reaction vessel for estimating the temperature or heat flux at a predetermined position inside the reaction vessel, the inner surface, the outer surface, or the inside of the wall,
Among the plurality of temperature measurement points, it exists around a one-dimensional heat flow path from the reaction container high temperature side surface to the low temperature side surface passing through the predetermined position, or exists around and on the heat flow path. And at least three points including temperature measurement points having different installation distances from the outer surface in the wall thickness direction of the reaction vessel, and the inverse problem based on temperature measurement data at the selected temperature measurement points A method for estimating a temperature or heat flux of a reaction vessel characterized by performing analysis.   At least one of the selected temperature measurement points is present on a one-dimensional heat flow path from the reaction vessel high temperature side surface to the low temperature side surface passing through the predetermined position, and the remaining selected temperature measurement points. 2. The method for estimating temperature or heat flux of a reaction vessel according to claim 1, wherein at least two points are present on a two-dimensional plane including the one-dimensional heat flow path.   From the temperature measurement data at at least one temperature measurement point existing on the one-dimensional heat flow path and the temperature measurement data at at least two selected temperature measurement points existing on the two-dimensional plane, the one-dimensional A temperature at a predetermined position on the heat flow path is predicted, and the one-dimensional unsteady heat conduction equation is calculated based on the predicted temperature data and temperature measurement data at a temperature measurement point existing on the one-dimensional heat flow path. The temperature or heat flux of the reaction vessel according to claim 2, wherein the inverse problem analysis used is performed, and the temperature or heat flux at a predetermined position inside the reaction vessel is determined. Estimation method.   The temperature or heat flux of the reaction vessel according to any one of claims 1 to 3, wherein the selection of the at least three temperature measurement points is selected in the order close to the one-dimensional heat flow path. Estimation method.   The method for estimating the temperature or heat flux of a reaction vessel according to any one of claims 1 to 4, wherein an interpolation function that satisfies the unsteady heat conduction equation is used when performing the inverse problem analysis. The unsteady heat conduction equation is expressed by the following equation as density ρ, specific heat C _p , heat conductivity k _{x in} the x direction, heat conductivity k _{y in the y} direction, and heat conductivity k _{z in the} z direction. The method for estimating the temperature or heat flux of the reaction vessel according to any one of claims 1 to 5.

The interpolation / extrapolation function is a position vector (x, y, z) and time t, and X, Y, Z, τ _x , τ _y , τ _z , A _x , A _y , A _z are arbitrary constants, 7. The method for estimating the temperature or heat flux of a reaction vessel according to claim 5 or 6, wherein the method has an equation relationship.

The interpolation / extrapolation function has a relationship as shown in the following equation, with a position vector (x, y, z) and time t, and X, Y, Z, τ _xy , τ _z , A _xy , and A _z as arbitrary constants. The method of estimating the temperature or heat flux of the reaction vessel according to claim 5 or 6.

The interpolating function is a position vector (x, y, z), time t, and X, Y, Z, and τ _xyz are arbitrary constants, and has a relation of the following expression. The method of estimating the temperature or heat flux of the reaction vessel as described in 1.

The solution of the unsteady heat conduction equation is defined as parameter α _{j, i} , reference position vector (x _j , y _j , z _j ), reference time t _i , reference position vector number N _j , and reference time number N _i. The method for estimating the temperature or heat flux of the reaction vessel according to any one of claims 7 to 9, wherein the method is expressed by the following equation.

The parameter α _{j, i} is determined using the following equation, where k is a temperature information measurement position, l is a temperature sampling time, and temperature information a _{k, l} is measured at a temperature information measurement point. Item 11. The method for estimating the temperature or heat flux of the reaction vessel according to Item 10.

Input means for inputting temperature measurement data at a plurality of temperature measurement points distributed in a two-dimensional or three-dimensional manner inside a reaction vessel wall with a temperature change reaction, and the input temperature measurement data Based on the above, the estimation means for estimating the temperature or heat flux at a predetermined position inside the inner surface, outer surface, or wall of the reaction vessel by performing an inverse problem analysis using an unsteady heat conduction equation, and the estimated An apparatus for estimating the temperature or heat flux of a reaction vessel comprising an output means for outputting temperature or heat flux,
Among the plurality of temperature measurement points, it exists around a one-dimensional heat flow path from the reaction container high temperature side surface to the low temperature side surface passing through the predetermined position, or exists around and on the heat flow path. And a selection means for selecting at least three points as temperature measurement points of temperature measurement data input by the input means, including temperature measurement points having different installation distances from the outer surface in the wall thickness direction of the reaction vessel. An apparatus for estimating the temperature or heat flux of a reaction vessel. An input process for inputting temperature measurement data at a plurality of temperature measurement points distributed in a two-dimensional or three-dimensional manner inside the wall of the reaction vessel accompanied by a temperature change reaction, and the input temperature measurement data Based on the estimation process for estimating the temperature or heat flux at a predetermined position in the inner surface, outer surface, or wall of the reaction vessel by performing an inverse problem analysis using an unsteady heat conduction equation, and the estimated A computer program for causing a computer to execute an output process for outputting temperature or heat flux to estimate the temperature or heat flux of a reaction vessel,
Among the plurality of temperature measurement points, it exists around a one-dimensional heat flow path from the reaction container high temperature side surface to the low temperature side surface passing through the predetermined position, or exists around and on the heat flow path. And a selection process of selecting at least three points as temperature measurement points of the temperature measurement data input in the input process, including temperature measurement points having different installation distances from the outer surface in the wall thickness direction of the reaction vessel. A computer program for the temperature or heat flux of a reaction vessel, which is executed by a computer.   A computer-readable recording medium, wherein the computer program according to claim 13 is recorded.

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