JPH0420969B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for determining a heating pattern of a material that minimizes fuel consumption in temperature control of a heating furnace in a hot rolling line.

[Conventional technology]

Conventionally, as a method for determining the temperature rise curve online for temperature control of this type of heating furnace, for example, as shown in Japanese Patent Application Laid-Open No. 75533/1983,
Using both nonlinear models, one that calculates the material temperature from the furnace temperature and the other that calculates the fuel flow rate from the furnace and material temperatures, the furnace temperature is varied in steps in order to perform nonlinear fuel minimization. A method is used in which linearization is performed using a perturbation simulation method (a method in which a linearization coefficient is determined by performing simulation in a reference state and a perturbed state), and the temperature rise curve of the material is determined from the results.

[Problem that the invention seeks to solve]

In the conventional method for determining material temperature rise curves for heating furnaces as described above, the number of furnace temperature calculation zones is generally greater than the number of zones in which fuel flow rate can be controlled. There was a problem that the furnace temperature and temperature rise curve were not always in a realistic pattern.

In addition, when determining the linearization coefficient and temperature increase pattern, the simulation is performed by ignoring heat loss to the furnace wall, furnace wall temperature distribution, etc., and changing the furnace temperature in steps without considering the response delay of the furnace. As a result, there was a problem in that a temperature increase curve was determined that was far from the actual temperature increase trend of the material and the furnace condition.

In addition, because the effects of extraction suspension (interruption) during unsteady operation are not incorporated into the optimization logic, there is no manual operation to lower the furnace temperature setting, which worsens the fuel consumption rate. Problems also arose.

This invention was made in order to solve the above-mentioned problems, and it is possible to create a temperature rise curve that is feasible and corresponds to the actual conditions, and that lowers the set furnace temperature during unsteady operation with extraction pauses. The purpose of this invention is to obtain a method for determining the material temperature rise curve of a heating furnace.

[Means for solving problems]

The method for determining a material temperature rise line for a heating furnace according to the present invention includes a model that calculates the furnace temperature using an unsteady heat balance formula based on the fuel flow rate, a model that calculates the furnace wall temperature distribution based on the furnace temperature, and a model that calculates the furnace wall temperature distribution based on the furnace temperature. In order to minimize the fuel, we use a perturbation method simulation in which the fuel flow rate is changed in steps, and an evaluation using the LP (linear programming) method. The temperature rise curve is determined by incorporating the fuel flow rate and the effects of unsteady operation into the function.

[Effect]

In this invention, 3 including the furnace wall temperature distribution
We use two nonlinear models to determine the heating curve using the so-called perturbation method simulation for fuel minimization, which is both feasible and corresponds to the actual conditions, and also for extraction pauses. It becomes possible to determine a temperature increase curve that lowers the set furnace temperature during unsteady operation.

〔Example〕

The principle of this invention will be explained below. The furnace temperature calculation model is constructed as follows.

As shown in FIG. 1, the heating furnace is divided into n pieces in the furnace length direction, and the following heat balance equation is established for each divided mesh.

c ₁・dt _gi ／dt…Furnace temperature change =Q ₁ …Sensible heat of fuel and air +H _g・W ₁ …Fuel calorific value +G _i+1・cpg・T _gi+1 …Exhaust gas calorific value from upstream −G _i・C _pg・T _gi ...Calorific value of exhaust gas to downstream + _o 〓 ^j=1 K _1ij {T _gj +273） ⁴ −(T _gi +273 ⁴ }...Radiation from other mesh furnace temperatures + _o 〓 ^k=1 K _2ik {(T _wk +273) ⁴ −(T _gi +273 ⁴ }... Radiation from the furnace wall + _n 〓 ^l=1 K _3il {(T _sl +273) ⁴ − (T _gi +273 ⁴ }... Radiation to the material +C ₂ ( T _wi −T _gi ) +C ₃ (T _si −T _gi )...Convection to the furnace wall and materials -Q _wi ...Skids cooling water loss...(1) Here, H _g is the calorific value per unit flow rate of fuel, C _pg
is the exhaust gas specific heat, G _i is the exhaust gas flow rate of each mesh, K _1ij , K _2ik , and K _3il are the radiation exchange coefficients, respectively.
C ₁ , C ₂ and C ₃ are constants. Further, n is the number of furnace length divisions, and m is the number of slabs.

The above equation (1) can be transformed as follows if the fuel flow rate w is given and the furnace wall temperature and slab temperature are known.

dt _gi / dt= _o 〓 ^j=1 Aij (T _gj +273) ⁴ + _o 〓 ^K B _ik・T _gk +c _i (i=1...n) ...(2) This is an n-element simultaneous nonlinear differential equation However, by using the temperature distribution in the furnace one step before as a starting value, discretizing it with respect to time, and converging it using Newton's method, etc., it is possible to easily calculate a new temperature distribution in the furnace.

In addition, the material temperature model is the well-known 2
From the dimensional heat conduction equation, it can be expressed as follows.

dT _sl /dt=λ _s /c _s・r _s (d ² T _sl /dx ² +d ² T _sl /dY ² )
...(3) The boundary conditions at the surface are Here, X represents the material thickness direction, Y represents the material width direction, and d ₁ and d ₂ represent the material thickness and material width, respectively. In addition, c _s , λ _s , and r _s are the specific heat of the material, respectively,
These are the thermal conductivity and specific gravity, and q _s is the surface heat flux of the material, which can be expressed by the following formula.

q _s = _o 〓 ⁱ⁼¹ k _3il {(T _gi +273) ⁴ − (T _sl +273) ⁴ }+c ₃ (T _sl −T _gl )……(5) Equation (3) is the boundary of equation (4) can be solved using the normal difference method.

As shown in FIG. 1, the furnace wall temperature model can be expressed as follows using a one-dimensional heat conduction equation in the thickness direction only within the mesh for each division in the longitudinal direction of the furnace.

dT _w ／dt＝λ _w ／c _w・r _w・d ² T _w ／dx ² …(6) The boundary condition at the furnace inner surface is dT _w ／dx｜x=0=1/λ _w・_o 〓 ^{i =1} K _2ij {(T _gi +273) ⁴ −(T _w +273) ⁴ } +c ₂ (T _gi −T _w ) ...(7) The boundary condition on the outer surface of the furnace is dT _w /dx | x=d ₃ = 1/λ _w・H _OUT・(T _w −T _air ……(8
) Here, x is the thickness direction of the furnace wall, d ₃ is the thickness of the furnace wall,
c _w , r _w , and λ _w represent the specific heat, thermal conductivity, and specific gravity of the furnace wall, H _OUT represents the external thermal conductivity, and T _air represents the external temperature. Equation (6) can also be solved by a normal difference equation by using the boundary conditions of Equations (7) and (8).

By using the above three models in combination, if the fuel flow rate is given, the future values of the furnace temperature, material temperature, furnace wall temperature, and the future values of the three will be calculated using the current values of the furnace temperature, material temperature, and furnace wall temperature as initial values. Temperature can be calculated.

Next, a method for determining a temperature increase curve for a material that minimizes fuel consumption will be explained based on FIG. 2. In addition, 1 is the 1st step of temperature rise curve determination, 2 is the similar 2nd step, 3 is the similar 3rd step, 4 is the similar 4th step, 5 is the furnace temperature calculation model, 6 is the furnace wall temperature calculation model, and 7 is the same Material temperature calculation model, 8 is the calculation of the furnace temperature at the material passing position, 9 is the minimum temperature, calculation of the uniformity degree, 10 is the calculation of the linearization coefficient, 11 is the calculation of linear programming (LP), and 12 is the extraction of the material. This is a calculation to determine the temperature rise curve until the temperature rises. The degree of uniformity of heat is the temperature difference between the highest temperature (between skids) and the lowest temperature (between skids) in one material. A skid is a beam used for transporting slabs in a heating furnace.The contact portion of this beam is called the skid portion, and the non-contact portion (between the skids) is called the skid-to-skid portion.

First, as the 1st step 1, by repeatedly using three models 5, 6, and 7 for the time until all the materials are extracted at the current flow rate W _K ⁰ , the lowest temperature _s ⁰ at the time of each material extraction, The degree of soaking (maximum temperature - minimum temperature) ΔT _s ⁰ and the average material temperature T _bi ⁰ at the outlet side of the calculation zone in the furnace can be calculated.

Next, as the second step 2, by changing the above fuel flow rate by ΔW _k ^* in a stepwise manner for each fuel flow rate control zone, the lowest temperature at each material extraction time at each flow rate change is determined as in the first step 1. _s ^K , soaking degree ΔT _s ^K ,
The material average temperature T _b ^K at each zone outlet position can be calculated.

Next, as a third step 3, the following linearization coefficient calculation 10 is executed. By the procedure in step 2, the minimum temperature of each material at the time of extraction, the soaking degree, and the average temperature in each calculation zone when each material passes, which are solutions of the nonlinear equation, can be linearized as follows.

_s = _s ⁰ + _KMAX 〓 ^K=1 P _1K・ΔW _K ……(9) ΔT _s = ΔT _s + _KMAX 〓 ^K=1 P _2K・ΔW _K ……(10) T _bi ＝T _bi ⁰ + _KMAX 〓 ^K=1 P _3iK・ΔW _K ……(11) Here, KMAX is the number of fuel flow control bands,
P _1K , P _2K , and P _3iK are linearization coefficients when the flow rate is changed, and are given as follows.

P _1K = (T _S ^K − T _S ⁰ )/ΔW _K ^* ……(12) P _2K = (ΔT _S ^K − ΔT _S ⁰ )/ΔW _K ^* ……(13) P _3iK = (T _bi ^K − T _bi ⁰ ) / ΔW _K ^* ... (14) Furthermore, each fuel flow rate can be expressed as W _K = W _K ⁰ + ΔW _K , where ΔW _K is the amount of change in each control band.

The constraints in determining the temperature rise curve are as follows due to metallurgical constraints of the material and constraints on furnace operation.

_SMIN ≦ _s ≦ _SMAX ∆T _SMIN ≦∆T _s ≦∆T _SMAX T _biMIN ≦T _bi ≦T _biMAX W _KMIN ≦W _K ≦W _KMAX ... (15) Here, the subscripts MIN and MAX indicate the respective lower and upper limits. It shows. The evaluation function for optimization is fuel minimization, and the effect of unsteady operation, that is, the extension of each reactor zone time, is incorporated into the following equation.

Φ＝ _KMAX 〓 ^K=1 w _K・Δt _K ……(16) Minimization of Equation (16) under the constraint condition of Equation (15) is carried out by using ordinary linear programming (LP) calculation Equation (11). It is possible to ask for it.

The flow rate of the above solution is the optimal flow rate W _kppt for each material,
Linear programming (LP) is performed based on this flow rate as the 4th step.
By substituting into calculation (11), the temperature rise curve of the material until extraction can be calculated.

Next, heating furnace control based on an embodiment of the present invention will be explained with reference to FIG.

In FIG. 3, a combustion burner 105 and a furnace temperature detector 104 are arranged in a heating furnace 101 divided into a plurality of control zones, and each control zone is set by a furnace temperature setting means 106. The flow rate is controlled by a fuel flow rate controller 103 so that the temperature reaches the set temperature. Reference numeral 102 denotes a material information means, which instructs the furnace temperature setting means 106 with material information such as the dimensions, weight, extraction temperature, and conveyance information of the material in the furnace.

The furnace temperature setting means 106 is the current temperature calculation means 20.
, temperature increase curve determining means 21 and set furnace temperature calculating means 22
It consists of , and is activated periodically. The current temperature calculation means 20 calculates the current material temperature using a furnace temperature calculation model 5, a furnace wall temperature calculation model 6, and a material temperature calculation model 7 based on the material information. The temperature rise curve determining means 21 determines the temperature rise curve for each material under fuel minimization, as described in the explanation of the present invention.

The set furnace temperature calculation means 22 compares the target temperature increase record for each material with the current temperature, calculates the furnace temperature of each control zone, and instructs the fuel flow rate controller 103 to set the furnace temperature.

〔Effect of the invention〕

As explained above, according to the present invention, fuel minimization is achieved by using three nonlinear models: a furnace temperature calculation means, a furnace wall calculation means, and a material temperature calculation means, and by providing an evaluation function that takes unsteady operation into consideration. In order to do this, we use perturbation method simulation to determine the temperature rise curve, which not only determines the temperature rise curve of the material that is feasible and corresponds to the actual conditions, but also allows us to set it even during unsteady operation. It becomes possible to determine a temperature increase curve that lowers the furnace temperature. Therefore, the extraction temperature of each material can be precisely controlled and the fuel consumption rate can be reduced.

[Brief explanation of drawings]

Figure 1 is a schematic diagram showing the zone division of the furnace temperature calculation, Figure 2 is an explanatory diagram to explain the method of determining the temperature rise curve of the material that minimizes the amount of fuel, and Figure 3 is an illustration of the method of determining the heating curve of the material that minimizes the amount of fuel. FIG. 1 is an overall configuration diagram showing an example. 5: furnace temperature calculation model, 6: furnace wall temperature calculation model, 7: material temperature calculation model, 20: current temperature calculation means, 21: temperature rise curve calculation means, 22: set furnace temperature calculation means, 101: heating furnace, 103: Fuel flow rate controller, 104: Furnace temperature detector, 105: Combustion burner, 106: Furnace temperature setting means.

Claims (1)

[Claims] 1. In the heating control of a continuous heating furnace having multiple control zones, a first calculation means calculates the time change in the furnace temperature using an unsteady heat balance formula based on the fuel flow rate; a second calculation means for calculating, a third calculation means for calculating the temporal change in the internal temperature of the material from the furnace temperature;
a fourth calculation means for calculating the average temperature at the time of material extraction, the degree of soaking, and each furnace temperature at the time of material passage at the current fuel flow rate of each control zone using the respective calculation means; Using each calculation means, the fuel flow rate in each control zone is changed by a certain constant value from the current flow rate,
Calculate the minimum temperature when extracting the material, the degree of soaking, and the average temperature when passing through each calculation zone, and compare this with the fourth
A fifth calculation means for calculating a linearization coefficient around the current flow rate based on the result of the calculation means, using the coefficient to minimize and extract the fuel required to burn up the material under the restrictive conditions of furnace operation. A sixth calculating means for calculating the optimum fuel flow rate by incorporating the influence of the stoppage into the optimization evaluation function in consideration of unsteady operations in which a stoppage (interruption) is scheduled; A seventh calculation means for determining a temperature rise curve of a heating furnace, and a target temperature rise curve of a material in the furnace necessary for combustion control of the heating furnace is determined by these calculation means. Curve determination method.