JPS6041124B2 - How to operate a blast furnace - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method of operating a blast furnace that reduces erosion of the blast furnace bottom and makes it possible to extend the life of the blast furnace.

In recent years, in pursuit of high productivity, blast furnaces have become larger and operating conditions have become more severe, which hastened the destruction of the bottom refractories and shortened the life of blast furnaces. Therefore, in blast furnace operation under conditions of low economic growth, it is important to maintain stable operation, extend the life of the blast furnace, and reduce the unit price of pig iron. In order to ensure stable operation and extend the life of the blast furnace, it is essential to constantly monitor the corrosion status of the bottom refractory during blast furnace operation and to take prompt and appropriate measures to protect the eroded areas. Multiple thermocouples are installed at the bottom of the blast furnace. In order to estimate the furnace bottom erosion line, the finite element method was adopted as a simple one-dimensional heat transfer calculation or a two-dimensional heat transfer calculation using the actually measured temperatures detected by thermocouples at various parts of the hearth bottom. Estimating the erosion line at the corner of the hearth bottom is impossible using one-dimensional heat transfer calculations, so the blast furnace hearth is simplified as a ball-symmetric body (simply referred to as an ``axis-symmetric body'') with the vertical axis of the furnace as its axis of symmetry. However, two-dimensional heat transfer calculations are essential. The finite element method has generally been used for this two-dimensional heat transfer calculation, but this is a very time-consuming and tedious task. In general domain methods such as the finite element method and the finite difference method, in the case of axisymmetric problems, the axis of symmetry is set as 1 as shown in Figure 1, and
For example, the meridian cross section 2 of 8=0 shown by diagonal lines is divided into elements, and variables (temperatures) are determined so that each element satisfies the heat conduction equation.

Therefore, in estimating the erosion line, first consider the meridian cross section 2 of the hearth bottom at the actual temperature measurement position as shown in FIG. 2, and appropriately assume the erosion line 5. The region of meridian cross section 2 in FIG. 2 is divided into elements, and the temperature of each part is calculated. It is generally believed that the refractory erosion line 5 coincides with the isotherm of the iron-carbon eutectic temperature (approximately 1150°C), so this temperature of 1150°C is given as the boundary condition on the erosion line 5. The other boundaries are given respective bottom cooling conditions. FIG. 2 shows an example of the calculation results obtained by this method, and provides each isotherm. Next, the calculated value and the actual measured value at the position of the bottom-embedded thermometer 6 are compared. The temperature range where there is a difference between them, for example 1
If it is larger than pi○, move the erosion line 5 a little, divide the new calculation area 2 again, and repeat the above operation. Repeat this until the calculated value and the measured value match within a certain temperature range at all the positions of the hearth bottom thermometer 6, and then
Determine. According to this method, estimating one erosion line 5 from the actual measurement value of the hearth bottom thermometer 6 at a certain point in time requires a large number of steps (one engineer) x (half a day) x (1 week). Needless to say, this calculation requires an electronic computer, and since a large amount of data is input each time, a fairly large computer is essential. Furthermore, it is impossible to automatically move the erosion line 5 and automatically input the division of internal elements, but the algorithm to execute it would be complicated, and each time the internal elements other than the thermometer 6 position Unnecessary temperature calculations are also added, resulting in a large calculation cost. In this way, it takes a lot of time to estimate the erosion line 5 on the hearth bottom using conventional domain methods such as the finite element method. However, it is impossible to take prompt and appropriate measures to protect the hearth bottom. Furthermore, since there are generally multiple blast furnaces in a steelworks, it is impossible to manage the furnace bodies by constantly monitoring the bottom conditions of all of those blast furnaces, taking long-term protection measures, and quickly responding to abnormalities. . Under these circumstances, the inventor focused on the fact that an axisymmetric problem can be converted from a two-dimensional problem to a one-dimensional problem by a numerical calculation method called the boundary element method, which has recently begun to be actively researched.

That is, as shown in FIG. 3, the boundary line 4 of the meridian cross section 2 (for example, the intersection line between the meridian cross section at 0=0 and the boundary surface of the axisymmetric region) is divided into elements, and each element (i.e., line segment) 9 is divided into elements. It is sufficient to satisfy the boundary integral equation corresponding to the heat conduction equation.
Figure 4 shows an example of the heat transfer calculation at the hearth bottom obtained by the boundary element method and each isotherm. As can be seen from Figure 4, in the boundary element method, the heat transfer problem can be solved by dividing only boundary line 4 (including boundary lines if the bricks are of different types) into elements. The internal temperature can also be determined using the obtained boundary variables, namely temperature and heat flow.

In this way, the boundary element method does not require element division of the inside of the region, that is, the furnace bottom brick 8, and it becomes possible to automate the estimation of the erosion line 5 of the furnace bottom brick 8. The process of estimating the erosion line 5 is the same as the finite element method described above, but by applying the boundary element method, there is no need to divide the interior into elements for each movement of the erosion line 5, and calculation of the internal temperature is also possible. This can be done only using the position of the thermometer 6 buried in the bottom of the hearth, eliminating any unnecessary calculations.

By applying this calculation method, one case can be solved in one to two minutes calculation time (true erosion line:
This not only reduces man-hours and calculation costs, but also enables the bottom management of all furnaces and speeds up action in the event of an abnormality such as a rise in bottom temperature, resulting in significant benefits such as extending the life of the blast furnace. can be raised.

As mentioned above, the inventor: ■ Boundary element method reduces the dimension of the heat transfer problem by one, so we reduce the wisteria symmetry problem to a one-dimensional problem, and ■ In this way, we use this to estimate the erosion line at the bottom of the blast furnace. We focused on the fact that this process can be easily automated, allowing for online management of the furnace body and, in turn, extending the life of the furnace.

Below, we describe the calculation principle of the boundary element method and a method that applies it to estimate the erosion status of blast furnace bottom bricks online, and to speed up the management of multiple blast furnace bodies and actions in the event of an abnormality.

The boundary element method has various other names such as boundary integral method, boundary integral equation method, singular point solution method, Green's function method, and marginal integral finite element method, but the calculation principle is that the governing differential equation of the field is reduced to an integral equation on the boundary, which is then discretized and divided into elements using a method similar to the numerical solution method known as the finite element method to obtain values. includes all of them. Computational Principles This paper describes the formulation, discretization, and solution of axisymmetric potential problems (steady heat transfer problems) using the boundary element method.

○}Formulation Consider an axially symmetric region ○ as shown in FIG. 5, and let its boundary surface be r (=r, 10r2 10r3).

The governing equations and boundary conditions of the potential problem are expressed as follows. Governing equation: ▽2u (umpire) = 0
0} Here, u (for) is the potential at an arbitrary point 4 within the circle, u ({) and q (之) are the potential and flow velocity at an arbitrary point 4 on r, and u.

,q. denotes a defined value, ua and h are the ambient potential and (heat) transfer coefficient. In the case of heat transfer problems, the potential u is the temperature and the flow east q is the heat flow east.

The integral equation on the boundary for the problem under consideration is C(no i
)・u(くi)十′′ru(く)・q・(之i,4)d
r='Jrq({)・uoKi,ku)dr becomes'.

Here, i,4 represents an arbitrary point on r, and C(ku)
When the boundary is smooth, C(kui)=0.5, and when it is not smooth, its value can be indirectly determined from the equipotential condition. The weighting function u·(2i, ku) or u·(ru, ku) satisfies the following differential equation corresponding to the expression {kawako} in an infinite medium and is called the fundamental solution. ▽2u・(
¥i, half) 18 (graduation, no i): 0 (4} Here, mi i, bu represents an arbitrary point in Q, and 6 (komi-ro) is Djr
It is a delta function of ac.

The solution of equation [4} for a three-dimensional isotropic object and q・(Winter i
, fist) is expressed as follows. u・(winter i, and)=1
/4 汀R '5}q・(Winter i, graduation) = 6
u* (Winter 1, Mu)/anni (1/4 汀R2) (aR
/an) (6} Here, R=l - il, which represents the distance between point i, where the unit concentrated load is applied, and other points.

On the equation side, [6}' also holds true for point 2i, on r. In an axially symmetric problem, both the potential and the flow are constant regardless of the circumferential direction. Therefore, as shown in FIG. 5, the equation {kalpa, {9, [6; Here, as shown in FIG. 5, points 2j,
Let the points corresponding to 8=8'=0 be respectively i, year, and the outward unit normal at the point year be Wataru=(possible, n2, old 3). Since a=0, the point 2=0, and the outward unit normal 9 at the point is expressed by 9 as follows. Q=(
n,, mountain, n3) = (city, cosa, city lsino, million 3)
(7) Also, since it is 0' axially symmetric, Ai instead of Ai
(8=0) is considered without loss of generality.

Therefore, when 8=0 and the normal direction derivatives of R and R in the equation {51, (2) are expressed in a cylindrical coordinate system, the following is obtained. R=
l4-Ai = [〆+r'2ichiko rcos80 (Z1Z')2] ground
■aR/6n=(r-rcos8) old 1/R+(Z-Z
) flea/R side, ku: (r, a,
Z), ne=(r', 0, Z).

Now, u, q on the intersection line S between the 8=0 plane including the Z axis and
Letting the values of u and q be respectively, since they are axially symmetrical, it becomes as follows. u(etc); u(be), u({i): u(4
;) q({)=q({), q(etc.)=q(Ai) 0
0, the cylindrical coordinate system expression for the formula leg is C(Ai)・u(
Length i) + ′′rcu (year), anti-j, 4), IJld
rC=JJrcq(Z)・old・(father i, 4)・IJld
rc(11).

Here, rc, old.・(4i, stop), を・(之i, father)
are the cylindrical coordinate system expressions of r, u・(Ai, 4), q・(4, tile i), respectively, and! J! is the Jacobian associated with coordinate transformation. (2) Discretization and solution Equation (11) is an integral equation regarding the potential u and the flow q on the intersection line S of the 8=0 plane including the Z axis and r.

Therefore, just like a two-dimensional problem, by dividing S into elements, a discretized algebraic equation is obtained, and by solving this, the problem is solved. However, the integration regarding the cage in equation (11) needs to be performed on the rotating body surface rC, resulting in double integration. Now, S is divided into N boundary elements, and the amount of nodes at node i is expressed as j, aj. Assume that u and q within an element are expressed as follows using an inner function. u(4)=
? (4)・Q,q(be)=◇(Z)・9
(12) Here, 9 is the column vector of nodes u and q, respectively.

By substituting equation (12) into equation (11), the following discretized algebraic equation is obtained.

- - To N N C''4i) -u (Ai) 12Hij・mountain=i≧・(thin.
・qi j=1 However, Gij:'Jr.

j○(4). 6 (Yuzu 4)・IJlarc
(1 heart Gii=J'rCi○(4)
・古・(之i,4)・IJldrC
(15). Here, for example, r is expressed as follows based on the relationship between r and Z on the boundary element (line segment) j shown in FIG. 5 and the variable conversion of Z. r=aZ ten b=a・△j・t+aZj ten b (1 mother here, △Z
i=Zj+, -Zj, and a and b represent the slope and intercept of element i on the 6=0 plane.

When element j is represented as a vector using equation (16), upper = (
a・△Zi・t+aatenb)coso・ten(△Zj+
t10Zj)・half (17). here,
1, J, depth x,, x2, is a unit vector in the cedar axis direction. Using this, Wataru on the equation side and IJI of equation (11) can be expressed as follows. Weight = (△Zj/li) (↓-a
Winter) (1 is IJ I:li・(a・△Zi・t
10aZj1b) (19D, where li is the length of element j,
lj: [(rM-r,)20(△Zj)2] It is rare.
Also, dr=ljl・drc=IJl・dhi・dt, and the formulas [5}, [61, [hunch, '9', (18), (19
) into equations (14) and (15), and when 0=0 to 2, t
By performing integration between = 0 and 1, 100 ij and Gi
j can be evaluated. It is possible to evaluate equations (14) and (15) in exactly the same way for boundary elements on a plane where Z=fixed. For all boundary nodes, the formula (
13) Considering that the value of u is defined on r, and the value of q is defined on r2 and r3, there are N unknowns and the algebraic equation for the entire system is as follows: Become.

Mufuyu=E (20) Here, now the coefficient matrix, X and F are column vectors containing only unknown nodal quantities and only known quantities, respectively.

Equation (20) can be solved for X. The potential at any point within 0 can be calculated by the following equation using the amount of nodes on the boundary.

N N u (winter i) ni Z Gij・qj‐Z Hij・uj
(21) j=l j〒1 The calculation principle above can be summarized as follows.

■ Combine the governing differential equation (Laplace equation) of the steady heat conduction problem {11 with the boundary condition [21] to create a weighted residual expression.

■ This weighted residual expression is converted into the integral equation on the boundary '3
Convert to '.

■ Taking into consideration the axial symmetry, formula {31 is transformed into a cylindrical coordinate system expression (
11).

(2) In order to numerically solve the solution of equation (11), the boundary surface of the region ○ (FIG. 5) is divided into rc elements to obtain the discretized algebraic equation of equation (13).

■ Coefficient stand ij of equation (,3). G; j (Formula (14), (
15)) Each boundary element surface rd divided to evaluate
is expressed as an auxiliary variable by a vector (Equation (17)).

(1) Using equation (17), equations (14) and (15) can be converted into double integrals, and their values can be determined numerically.

■ Considering equation (13) for each element rcj, an algebraic equation (20) with N unknowns and N equations is created,
Solving this will determine all temperatures and heat flow east on the boundary.

■ The temperature inside the region ○ is calculated using the temperature on the boundary and the heat flow east.
Calculated by equation (21).

Applications of the boundary element method are as follows.

[1] A numerical calculation method called the boundary element method solves a heat transfer problem in an axisymmetric region (variables, that is, temperature and heat flow east, are independent of the circumferential direction, and the problem is solved for one meridional cross section of the region, so it is a two-dimensional problem. ) is converted into an integration problem on the boundary of the meridional section of the wisteria-symmetric region (the boundary can be expressed as a line segment, so it becomes a -dimensional problem).

'21 Since the bottom of the blast furnace (brickwork section 8) is considered to be an axially symmetrical body, the boundary 4 of the meridian section (plane including the position of the bottom-embedded thermometer 6) where the bottom is located is as shown in Fig. 4. Divide into 9 minute boundary elements (line segments).

'3' Consider the internal surface of the brickwork 8 at the time of blast furnace construction as the initial position of the erosion line 5, and set the iron-carbon system eutectic temperature 115 as the boundary condition of the node 10 on the boundary element 9 of that part.
Give 0qo.

'41 For the node 101 on the element 9 on the other external boundary, external cooling conditions (heat removal amount or cooling heat transfer coefficient) are given.

(51) Since the node 10 on each boundary element 9 is given one of temperature, heat flow, or heat transfer coefficient as a boundary condition, the problem can be defined and solved.

That is, the problem can be solved by the boundary element method, and the temperature and heat flow east at the nodes 10 on all the boundary elements 9 are determined. '
61 Node 10 on each boundary element 9 determined in this way
The temperature at the position of each thermometer 6 buried in the hearth bottom is calculated using the temperature at the bottom of the furnace and the heat flow east by an equation derived by the boundary element method.

{71 Compare the calculated value and the actual measured value at the position of thermometer 6, and if the difference is within a predetermined temperature range (for example, 1ooo) at all thermometer 6 positions, the erosion as originally assumed Let line 5 be the true erosion line 11 on the thermometer side.

'8} If the difference between the calculated value and the measured value at even one point is larger than that range, the erosion line 5 near that thermometer 6
automatically moves according to the temperature difference.

(2) Execute the process of leg ~'7'' above based on the new erosion line 5.

[IQ] Repeat the process of [3} to '7) until the conditions are satisfied at all thermometer 6 positions, and determine the true erosion line 11.

(11) Since the calculation time required to estimate the true erosion line 11 from the measured values at a certain time is 1 to 2 minutes, the estimated furnace of the buried surface of the thermometer 6 can be calculated online from the measured values from moment to moment. The bottom erosion line 11 is displayed on a CRT and is immediately reported to the reactor operator.

(12) This makes it possible to constantly monitor the erosion situation at the bottom of the blast furnace and quickly and accurately take short-term and long-term protection measures for the more eroded areas.

(13) For example, for the expected amount of erosion on the side wall of the bottom of the furnace,
Implement refractory protection measures for eroded areas using the following steps:

Table 1. The numerical values in the table of implementation guidelines for protection measures for furnace bottom side wall bricks represent increases and decreases with respect to the standard amount K.

It goes without saying that the numerical values shown in the implementation conditions and countermeasures differ depending on each blast furnace. (1 pile) If the expected thickness of the remaining brick increases due to the implementation of protective measures (i.e., a solidified layer of melt gun, coke, brick fragments, etc. is formed on the working surface of the brick), proceed from step m according to the thickness. Protection measures will be relaxed to 1.

(15) Previously, judgments were made based on the readings on the thermometer, but even if the readings were the same, the thickness of the remaining bricks would vary depending on the bricks used and the cooling conditions. It was difficult to quickly judge whether the situation was dangerous or not.

That is, conventionally, each time the temperature at each part of the furnace bottom rose, a large amount of man-hours were required off-line to predict the state of erosion, making it difficult to take protective measures quickly and accurately. (16) However, according to the present invention, the corrosion state of the hearth bottom can be constantly monitored, so it is possible to quickly and accurately implement the countermeasures shown in Table 1.

Furnace bottom brick erosion line 1 based on a certain actual measurement value of the thermometer 6 buried in the bottom of a large blast furnace of 5,000 tons of Nissan pig iron
An example of No. 1 is shown in FIG.

A meridian cross section including the position of the thermometer 6 buried in the hearth bottom is considered, and its boundary 4 is divided into elements 9.

The inner surface of the brickwork 8 during blast furnace construction is the initial position of the erosion line 5, and the boundary node 101 above it is set as the boundary condition 1.
Give 150oo. Boundary nodes 10' on the outer surface of the other bottom bricks 8 provide the respective cooling conditions. Applying the boundary element method, calculate the temperature and heat flow east at all boundary nodes 10, and the thermometer 6
Calculate the temperature at location. The movement of the erosion line 5 is repeated until the measured values of the thermometer 6 and the calculated values all match within a certain range, and as a result, a true erosion line 11 as shown in FIG. 6 is determined. If the initial position of erosion line 5 and the determined position of erosion line 11 are far apart, the calculation time required for estimation will be close to 2 minutes, but if constant estimation is performed, it will take 1 to 2 minutes.
The true erosion line 11 is determined by repeating the process several times, and the calculation time is about 10 to 2 hours.

In the above-mentioned blast furnace with an average pig iron tapping capacity of 500 m/day, the bottom side wall temperature rose rapidly about 7 months after firing, and the estimated remaining thickness of the bricks at that time was less than 1.0 mm.

For this reason, Table 1. Short-term measures shown in step 1■
,■ were taken, and ■■ was carried out at the same time. After implementing countermeasure ■■, the progress of erosion of the bricks stopped in about 5 days, and the remaining thickness showed an increasing tendency (formation of a solidified layer of pig iron, coke, brick fragments, etc. on the working surface of the bricks). Therefore, about 9 days after implementing the countermeasures, countermeasures ■■ were gradually relaxed, and about 15 days later, countermeasures ■■ were stopped. Measures ■■ were continued after that, and after about 30 days, the estimated brick thickness exceeded 1, so measures ■ and ■ were also discontinued, and normal operations resumed. With conventional methods, it is impossible to estimate the true erosion line 11 in such a short time.
Therefore, it has been difficult not only to display the erosion state online and take quick protective measures in the event of an abnormality, but also to manage the furnace bodies of multiple blast furnaces over a long period of time. As a result, the corrosion status of the blast furnace bottom can be monitored at all times, allowing for quick and short-term long-term and short-term bottom protection measures.
In addition, it becomes possible to easily extend the life of the bottom refractory and, ultimately, the life of the blast furnace.

[Brief explanation of the drawing]

Figure 1 shows the calculation area (shaded area) using the finite element method and equal domain method.
2 is a hearth temperature distribution diagram showing an example of hearth heat transfer calculation by the finite element method, and FIG. 3 is an explanatory diagram showing the calculation area (cross-sectional boundary line) by the boundary element method. Figure 4 is a hearth temperature distribution diagram showing an example of hearth heat transfer calculation using the boundary element method, and Figure 5 is an axially symmetric region Q, boundary surface r, and r
FIG. 6 is an explanatory diagram showing an intersection line S between the x2=0 (8=0) plane and the x2=0 (8=0) plane, and FIG. 6 is an explanatory diagram of an example of estimating the erosion line at the bottom of the blast furnace. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6

Claims (1)

[Claims] 1 Using the boundary element method, conduct a heat transfer analysis of the blast furnace hearth as an axisymmetric body with the vertical axis of the furnace as the axis of symmetry, predict the hearth bottom erosion shape, and predict the growth of local erosion in the hearth bottom erosion shape. 1. A method for operating a blast furnace, comprising: selecting operating conditions that prevent this, and operating the blast furnace under the operating conditions.