Title of Invention

A PROCESS FOR DETERMINING CHARGING SCHEDULE OF A BLAST FURNACE FOR CONTROLLING STABLE OPERATION THEREOF

Abstract

The main object of the present invention is to provide a convenient way to quickly explore the effect of changing parameters on the burden distribution. The applicability of this approach is confined within a judicious range of the bench marked condition. For example the value assigned to the blockage parameter of the dynamic arch holds good only within a reasonable range of the charge weight. The present invention thus provides a process for optimizing operation of a blast furnace by simulating the burden distribution therein, comprising the steps of: estimating initial discharge velocity in incremental steps; calculating bounced trajectory of the particles; estimating heap formation after the charge particles on stock-line; and estimating ore/coke ratios along the radius of the blast furnace, for providing information regarding prediction of concomitant gas distribution in the shaft of the blast furnace.

Full Text

-2- FIELD OF APPLICATION The present invention relates to a process for optimizing operation of a blast furnace by simulating the burden distribution therein. In particular, it relates to simulation of the burden distribution in blast furnaces, so as to obtain a satisfactory charging schedule, that will provide stable operation. BACKGROUND OF THE INVENTION The operation of blast furnaces is largely governed by the distribution of the gas flow inside the furnace. This has a pronounced effect on the reactions, the thermal conditions as well as the pressure gradients in the lumpy zone. These factors in turn affect the smooth working of the furnace. Control of the blast furnace operation thus vests in the gas flow pattern, which can be only indirectly manipulated by the distribution of the burden, so as to adjust the distribution of the porosity in the various layers. In addition, the burden distribution directly influences the structure of the cohesive zone, where most of the chemical reactions occur. -3- Direct measurement of various in-furnace phenomena has been studied with the aid of advanced monitoring and recording techniques. The iron and steel institute of Japan have reported this. Data is required from comprehensive instrumentation for measuring (1) the geometry of the cohesive zone, (2) the distribution of the gas velocity, (3) the flow of the molten hot metal and slag, (4) the movement of the cohesive zone. Detectors to measure some of these furnace variables have been developed, such as (1) vertical probes for the cohesive zone, (2) sampling of the ascending reducing gases and (3) the descending solids, (4) profilometers for the blast furnace burden1 etc. The above-burden and in-burden probes record temperatures and gas compositions at different radial positions, from which information about the gas and burden distribution can be inferred. Measurements from such detectors have enabled stable operation of large blast furnaces. However, the instrumentation cited in the previous paragraph is not available in most commercial blast furnaces. A number of experimental results have been reported. Small-scale experiments, with a sector of the blast furnace2' 3 constructed according to dimensional similarity, provide an insight into the process of burden formation. Full-scale models2' 4 provide more reliable results, but even here a degree of approximation is inevitable, as it is necessary to work with a sector model (in order to obtain a view of the burden section). This effectively precludes experimental models of a rotating chute, because the swirling component of the discharge velocity cannot be accommodated in a sector model. -4- The large quantities of the charge materials required in full-scale experiments, means that such studies are expensive and time consuming. Scaled down experiments are simpler, but a fresh experiment has to be performed for every change in the charging pattern, material properties such as particle size, or the position of the stock-line, or in the rate of descent of the burden (matl, T, rev, dprt, hel11, hell2, rdchlst, dscnlst). The most convenient approach is to simulate the trajectories of the charge particles as they fall from the chute, by numerical calculation. After the particles have been tracked to the point of impact with the stock-line, the formation of the heap has to be computed, considering segregation of the material and rolling of the particles1'5. Since this is a purely numerical technique, specific values have to be assigned to a large number of parameters such as the coefficient of restitution and the coefficient of friction of individual particles with individual surfaces, repose angles, particle sizes etc. (corr, mu, rpang, dprt (1/2/3). The specific values required for the numerical solution, such as the coefficients of restitution and friction, and the repose angles of the various charge materials have to be experimentally determined. In addition there are a number of empirical parameters, such as the radial distribution of the burden descent rate, whose value has to be given. For this reason, pilot experiments are required to validate the theoretical solution. However once that is done a programmed processor can be used to predict the burden distribution for different charging schedules, on line. -5- The high temperatures and abrasive nature of the materials in an operating blast furnace make direct measurement of the internal state of the furnace difficult, although some modern furnaces have been equipped with sophisticated instrumentation for this purpose. SUMMARY OF THE INVENTION The main object of the present invention is to provide a convenient way to quickly explore the effect of changing parameters on the burden distribution. The applicability of this approach is confined within a judicious range of the bench marked condition. For example the value assigned to the blockage parameter of the dynamic arch holds good only within a reasonable range of the charge weight. The present invention thus provides a process for optimizing operation of a blast furnace by simulating the burden distribution therein, comprising the steps of: estimating initial discharge velocity in incremental steps; calculating bounced trajectory of the particles; estimating heap formation after the charge particles on stock-line; and estimating ore/coke ratios along the radius of the blast furnace, for providing information regarding prediction of concomitant gas distribution in the shaft of the blast furnace. -6- BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS The invention can now be described in detail with the help of the figures of the accompanying drawings in which: Figure 1 shows nomenclature of geometric variables. Figure 2 shows the initial discharge velocity in the dynamic arch theory, and in the hydrostatic head formulation. Figure 3 shows bounced velocity in the Paul Wurth rotating chute. Figure 4 shows heap formation at the stock-line (kase = 0, -2). Figure 5 shows a simulated burden distribution, together with calculated ratios. Figure 6 Enlarged view of the simulated burden distribution, showing the charges filled with close packed circles of the particle sizes. -7- DETAILED DESCRIPTION The simulation of the burden distribution can be done by tracing the path of descent of the charge, and the formation of the heap at the stock-line in a processor (computer). This method can be used to simulate the burden distribution in any blast furnace. The geometrical and other operating parameters are specified through a set of interactive menus. The list of variables for the geometrical parameters (hell to horl6) have been shown in Table 1 and shown schematically in Figure 1. The processor can be programmed to simulate the burden for a single charge or for a set of upto 10 individual charges. This has been shown in the charging schedule in the list of variables (Table 3) (Mat I, kolr, T, Rev, 10-0), with a provision to repeat the set a number of times. Calculations of both the movable throat armor as well as the Paul Wurth rotating chute are supported, which includes the effect of the swirling component of the velocity. The radial distribution of the burden descent can be specified in the program (Table 4). The system automatically lowers the burden by an appropriate amount between charges (rdchlst, dscnlst), so as to retain the vertical probe at a constant level (hor!6, hell/12). The individual ore, coke, sinter layers, as well as the ore/coke ratios are graphically displayed (Figure. 5). -8- A provision has been kept to incrementally change some of the empirical parameters (e.g. kfact in Table 1 and vfact in Table 2). This is required in order to calibrate these parameters against observed results. The procedure followed is described in the following sections. Section (1) describes the initial discharge velocity. Section (2) describes the bounced path of the particles after striking the throat armor or the walls. Section (3) treats the formation of heaps at the stock-line. Section (4) describes the ore/coke ratio. 1. INITIAL DISCHARGE VELOCITY This can simulate the particle trajectories, based on two theories. The theory for the discharge velocity based on the dynamic arch is described in Appendix 1. Under this theory, the discharge velocity is governed by the opening of the large bell. It is possible to simulate the effect of increasing bell opening, by adjusting the values for the initial, final and incremental bell opening. The software will then show the trajectories of the particles, starting from the initial bell opening and incrementing the bell opening in step upto the final bell opening. As the bell opening increases, the discharge velocity is predicted to increase, causing the trajectory to spread further outwards from the center. -9- The program can alternatively be switched, to calculate the initial discharge velocity based on the hydrostatic head of the burden materials in the hopper. When the burden begins to flow out, the particles are assumed to be ejected with a velocity governed by the pressure of the material in the hopper (the hydrostatic head). As the hopper empties, the hydrostatic head falls, so that the discharge velocity is reduced, and the trajectory comes closer to the centre. This process is discretised into steps, and the velocity for each step is assumed constant throughout that step. The volume discharged in each step is assumed constant, neglecting the effect of the sloping hopper wall, and is taken as a proportion of the full hopper volume multiplied with the ratio of the step increment to the total hopper height. The trajectory of the particles is calculated for each step, from the full hopper condition (maximum velocity), to the empty hopper condition (minimum). Passing through the bell opening, the particles move along the large bell to its edge, and attain an initial velocity for free fall in the throat space. The materials then strike the burden surface, the throat wall or the movable armor, to form a burden profile. The incremental discharge volume is shown at each step. Since the material discharged in the previous steps governs the burden profile, this shows the skewing of the peak away from the centre as the bell opening increases for the dynamic arch theory. For the hydrostatic head formulation, the skewing is towards the centre, as the velocity of discharge tapers off as the hopper empties. This has been shown in Figure 2. -10- In the case of simulating the Paul Wurth mechanism, the flags are set to bypass the process of incremental volume discharges, and the entire charge volume is set to follow a single trajectory. The quantities (halb1/2/3) in the dynamic arch theory can be assigned suitable values in the operating menus (Table 1), depending on the user perception of the accuracy required. A larger number of steps (with a smaller step increment) will increase the computation time. A similar consideration applies to the quantities (hhl/2/3), in the hydrostatic head theory. The quantities (kfact 1/2/3) are the empirical blockage parameters in the dynamic arch theory, and (vfact 1/2/3) are the velocity factors in the hydrostatic head formulation. The software can be programmed to increment these parameters in small increments and show the concomitant trajectories. This provision is provided in order to calibrate with observed data. Once an appropriate values for these factors have been finalized, the process for incremental checking of these values can be bypassed. -11- Thus the changed trajectories for each incremental step are computed. By this means, the observed splaying of the descent trajectory can be faithfully simulated. 2. THE BOUNCED TRAJECTORY The trajectory of the particles in the throat is assumed to be governed by the equations of free fall, neglecting the effects of the gas velocity. The procedure is straightforward in the case of the movable throat armor, as the particles follow a parabolic path in 2 dimensions. The total distance of fall is divided into segments of equal vertical drops of (dfytot/nstept=9048/50=180.96=181 mm). As long as there are no impacts, the vertical component of the velocity is incremented, depending on the total distance of fall (dfystp). In case of impacts and subsequent bouncing off, the vertical step is adjusted so that the following step commences from an equal segment spacing. The point of the start of free fall is updated, and dfystp is computed from this updated start of free fall. The time in this vertical segment is computed, depending on the incoming velocity and the drop in the segment. This time is then used to derive the position increments from the updated start of free fall (dfx/dfy). This will continue till all the (ntstep = 50) segments have been completed, or the particle comes to rest on the stock-line. In each segment, the particle is assumed to move in a straight line. The total number of steps (ntstep) is user specified. -12- While each segment of the trajectory is being computed, it is checked for intersection with the armor, the throat wall, and the stock-line. An intersection indicates an impact of the particles with an obstruction. A normal to the surface of impact is constructed, and the tangential and normal components of the incoming velocity are computed. The bounced trajectory is calculated in the software, by reversing the direction of the normal component and multiplying it with the appropriate coefficient of restitution (cors11-33), as shown in Appendix 2. The procedure is more complicated in the case of the Paul Wurth chute. The Corriolis forces drive the charge particles up the side of the rotating chute, so that the discharge point changes from the default location at the bottom of the chute. Moreover, since the chute is rotating there is a swirling velocity, which is indicated by the Vz value (Vx is radial and Vy is taken as the vertical component of the velocity). With only the radial and vertical components (Vx, Vy), the particle trajectory will be confined to a radial section. Because of the swirling component (Vz) however, the trajectory plane will be out-of-center (Figure 3). The swirling component will increase, with increasing (nrpm), the speed of rotation of the chute. -13- If the particle impacts against the wall of the furnace, the swirling velocity will result in the particle bouncing into a trajectory whose plane is different from that of the incoming trajectory. Depending on the magnitude of the swirling velocity (nrpm), this can result in the particle bouncing repeatedly against the wall and tracing a spiral trajectory as it descends. The simulation of the trajectories in such cases is done with an appropriate modification to the procedure shown in Appendix 2, as the path still lies in a vertical plane (albeit being out-of center). The coordinates of the particle in its trajectory (PCENT 1) will contain (X and Z) values. The elevation (Y) remains the same as in the axis symmetric case for the movable throat armor, with the total distance of fall (dfystp) continuing to be incremented in steps of (dfytot/nstep = 181 mm), till the particle bounces against an obstruction. However, the calculation of the point of impact with the sloping walls of the furnace is an exercise in solid geometry, involving the intersection of a line in 3D with the frustum of a cone. When there is an obstruction. the bounced velocity has to be evaluated which involves calculating the normal to the surface. -14- Fortunately, this procedure is simplified as the possible obstructing surfaces (Figure 1. stock shield line, ring platform line, and the stock-line), are all axis symmetric. 1. Stock shield line p 103 (hor 9, hel 1) - p 104 (hor 9, hel 9) 2. Ring platform line p 104 (hor 9, hel 9) - p 105 (hor 10, hel 10) 3. Stock-line (hel 11, hel 12) After calculating the normal, the tangential and the normal components of the incoming velocity are evaluated. For this purpose the angle of incidence is found from 3 points, a point on the incoming trajectory, the point of intersection and the point where the normal intersects the centerline. Since these points do not lie in a radial plane, the angle is estimated from the triangle defining the 3 points. The normal component of the incoming velocity is modified by the appropriate coefficient of restitution of the charge material and the obstructing surface, to give the normal component of the velocity after bouncing. The transversal incoming velocity of the particle remains unchanged. With these two velocity components, the straight segment of the trajectory after bouncing is constructed. The procedure has been shown in Figure 3 and Appendix 3. -15- Checking for obstructions is performed during the calculation of each segment of the trajectory. The stock-line is initially defined as a straight line, which may be horizontal or tilted at an angle (hel 11, hel 12), However, as fresh material is dumped on the stock-line, the corresponding line segments of the heaps are added into an array, which represents the changed stock-line. The checking for intersections is done against each of these line segments. If there is intersection here, then the trajectory is terminated (corr = 0). The point of impact is stored, for use in the calculation of the burden heap. When the path from the initial discharge impinges on an obstruction the particles trace a bounced path. For the 2 dimensional case with a movable throat armor, this has been described in the section 2. (THE BOUNCED TRAJECTORY) and in (Appendix,2). For calculation of the bounced trajectory in 3 dimensions. This occurs with a Paul Wurth discharge mechanism. This requires modification of the method in claim 2. It has been described in the section 2. (THE BOUNCED TRAJECTORY} and in (Appendix. 3). 3. FORMATION OF HEAPS AT STOCK-LINE The stock-line is defined as a list of points comprising the boundary of the previous charges deposited on the initial stock-line (hel 11, hel 12). This list is updated each time a fresh charge is added. There is a provision to consider the burden decent, which is specified as a set of points in the input menus (rdchlst, dscnlst). At the end of the simulation of a discharge, the updated stock-line list is lowered by the amount specified in the burden descent, to form the current stock-line. The procedure for tracing the trajectory of the particle upto Intersection with the stock-line was described in the previous section. -16- Several cases can arise, depending on the angle of the stock-line segment at the point of impingent. The particles will stick to the point of impingement (kase = 0, 1, -1) if the stock-line slope is less than or equal to the repose angle, but in the case that it exceeds the repose angle of the material, the particles will roll down the slope, either towards the center-line side (kase = 2) or towards the wall side (kase = -2). The points where the particles will come to rest are determined. For (kase = 0, 1, -1) a cone defined by the repose angle (rpang), is constructed at the point where the particle trajectory impinges on the stock-line, by measuring a distance of (defdis = 100 mm) vertically upwards on the trajectory segment (ptrj O-ptrj 1). The intersection of the two sides of the cone with the stock-line list is also determined. The charge is assumed to form an annular ring on the stock-line, with a cross section of the cone. The volume of material in this cone is estimated by drawing vertical slices and multiplying with the circumference of the circle centered at the centre-line. This slicing procedure is required, as the stock-line can comprise of numerous peaks and shallows. A sufficiently large number of slices (100 say) are made, the depth from the repose cone to the -17- underlying stock-line is calculated for each slice, and multiplication with the circular perimeter of each slice gives the incremental volume due to that slice. If the computed volume (vdschrg 3) is less than the charge volume (vdschrg 1), the apex of the cone is incremented by a further step increment (defdis), and the procedure is repeated, till the entire charge volume is accounted for. The accuracy of this procedure is governed by the setting of this parameter (defdis). A smaller value will require a larger number of iterations, but will provide better accuracy. For (kase = 2, -2), the slope of the stock-line at the point of impingement exceeds the repose angle of the material, and slopes towards the center-line or towards the wall side. The point where the particles will come to rest are determined by tracking the stock-line till an opposing slope is encountered, where the particles can come to rest. As the particles accumulate at this local minimum elevation, the profile of the accumulated charge is constructed by drawing parallel lines at the slope of the repose angle. These lines are drawn by measuring off (defdis) distances from the lowest point, along the incoming stock-line slope. The slicing procedure is repeated to calculate the incremental volumes. As before, the process continues till the entire charge volume is accounted for. Figure 4 illustrates the procedure for two cases (kase = 0, -2). -18- Estimating the heap formation after the charge particles reach the stock-line involves estimating the change in the inter-surface between successive charges for all the previous charges, as the burden descends in the blast furnace, to arrive at the current stock-line. 4. ORE COKE RATIO Figure 5 illustrates a burden distribution that has been simulated by the software. There is a provision to draw the distribution with each charge color coded to a pre-selected specification. Where monochromatic representation is required, the individual charges may be filled with circles drawn to the specified particle sizes (dprt). This has been shown in Figure 6, which is an enlarged representation of the burden in Figure 5. The simulated burden distribution makes it possible to obtain various other numerical values that are useful for predicting the behavior of the blast furnace. The Figure by the side of the burden distribution has been obtained by segregating the individual ore, coke and sinter charges. This makes it possible to see at a glance the total height of any of these materials, at a specific radius. In the composite Figure of these individual segregations, the final profile is the same as the top of the burden distribution, but the arrangement below groups the charges so that all the ore, coke, and sinter layers are together. -19- The set of 4 Figures at the top, display the segregated charge data scaled as a ratio with the total height of materials at a radius. This means that the top line will be flat at 100 %. i The set of 4 Figures at the bottom displays the ratio of a particular material to the amount of coke at a particular radius. Such visual representations of numerical data, are particularly useful to experienced operators, and enable them to anticipate problems. In addition, various combinations of charges can be simulated, in order to form a strong centre. The simulation exercise demonstrates the sensitivity of the burden profile to changing notch positions of the throat armor, or the chute angle of a Paul Wurth mechanism. A heap discharged at mid radius in one of the initial charges can seriously influence the subsequent burden distribution by blocking the trajectory of subsequent charges. This further increases the height of the heap at mid radius, thus compounding the effect. A logical extension of this work would be to use the simulation procedure, to conjure up a charging schedule that matches a preset: ore/coke radial distribution. This would eliminate the trial and error simulation of various charging schedules in order to arrive at an acceptable solution. Instead the operator would specify the central working condition that was desired, and the software would provide the ideal charging schedule. -20- Appendix 1. Dynamic arch theory of granular material flow through opening. Extracted from Ref[i], Large bell [ hell mm [Absolute elevation BF top ] [ hor2 mm [Absolute horizontal Large bell] [ hel2 mm [Absolute elevation Large bell] [ bslp mm [Slope length along Bell bottm] [\ bang degrees [Angle with vert of Bell bottm] [ \ Isld mm [Sliding dist after strike bell] [ \ Lhets degrees [Angle of bell lip to bell surf] \ he 1-5 mm * [ I nit abs elevation Lip ring t] \ I hh mm [Large bell opening] \ V (hor2+-bslp*sin(bangr)a-lsld*sin(bangr+thetar) Radius of lip (hel4-bslp*cos(bangr)-lsld*cos(bangr+thetar) Elevation lip We consider burden materials present in a large bell hopper. The erge bell lowers at a prescribed speed from a closed position to reach a position corresponding to a prescribed large bell stroke. According to experimental results, at an early stage of this large bell descent, there exists a period when no particles flow out. This period lasts until the horizontal clearance at the lower edge of the hopper wall reaches about four times the mean size of the burden to be discharged. When the burden begins to flow out of this hopper, a dynamic arch contacting both the hopper wall and the large bell, is formed at a level close to the edge of the hopper wall. Above the dynamic arch, particles constituting the burden i nterfore with each other as they descend slowly towards this arch. Passing through this dynamic arch, the particle fall freely, till they reach and strike the large bell. Subsequently they move along the large bell to its edge, and attain an initial velocity for free fall in the throat space. ud=sqrt(g*(hh-vfact*dprt*tan(thetarl))) where: hh>vfact*dprt* tan{thetarl) ud:The descending velocity at the level of the dynamic arch hh mm [Large bell opening ] vfact=kfact dimensionless [Empirical param blockage factor] dprt mm [Mean size of particles ] thetarl (0.5*pi-pi/180*bang), sufix "r" indicating radians bang deg [Angle with vert of Bell btm] ue: The velocity of particles striking the large bell surface after the free fall from the dynamic arch ue=sqrt(ud*ud+g*hh) It is assumed that the average fall distance is 0.5*hh. Assuming non-elastic collision of particles with the large bell surface, we obtain the initial velocity ue*sin (thetarl) of particles moving along this surface, and the velocity at the edge of the large bell as follows. xx=sin(thetarl)-muf*cos(thetarl} muf dimensionless [Coeff friction particLe /bell surface ] yy=2.0*g*(lsld+0.5*hh*sin(thetarl)) lsld mm [Sliding dLst after strike bell] vd=sqrt (ue + sin (thetarl ) 'ue* sin (thetarl) +yy*xx) 21 Appendix 2. Procedure for calculating the bounced path in 2D. Let us assume that in the 31st segment of the parabolic trajectory [P0-P1], there is an impact with the wall of the furnace [P2-P3]. The drop in each segment [181 mm] is obtained from the total distance of fall and the number of specif. i.ed steps [dfytot=9048, nstept = 50], and the drop from the bell lip to the start of this segment [PO] is Idl'ystp= (3J-1) 9048/50 = 5429 ram]. + 7, 31154,0 + PI gives the Cartesian coordinates of the planar projection, at the termination of the 31st segment. The planar coordinates of the point of intersection, is updated as the end point, of the trajectory before impact [P1]. The free fall upto the point of impact had started at an elevation of [hel40=36583 mm],[at the lip of the bell]. - + Elevation view; PO Start of segment \ P2 Incoming\ |Impeding wall TrajectoryA 1 pangle2=Angle P0-P1-P3 \ I panglen=Angle X-Pl-N Normal point N \ I PI X /|\ Updated PI: Point of impact Outgoing / | Trajectory/ | Bounced / ( / ' P3 PI P0 ' / Initial PI: End of segment The vertical component of the velocity depends on the initial vertical velocity [2597 mm/sec], and the distance of free fall upto the point of impact [36583-31288=5295 mm][vdy3=sqr(2.597-2+2+9.81+5.295)=10.518 m/sec] The planar total velocity is the vector sum of the X & Y components: [vd3=sqr(2.029^2+10.518^2)=10.711 m/sec] The angle from the trajectory at the point of impact, to the impeding wall is: [pangle2=169 deg; measured in the anticlockwise direction] And the angle from the positive X axis to the normal to the wall is: [panglen=186 deg; measured in the anticlockwise direction] [pangle3-265 deg; measured in the anticlockwise direction] + After bouncing, the transverse planar velocity would be [vdt3=vd3*Cos(pangle2)=10.711+Cos(169)=10.509 m/sec] The normal velocity, considering the coefficient of restitution, is: [vdn3=vd3*Sin{pang]e2) *cors=10.71l*Sin(169)*0.3-0,62 2 m/sec] And the total planar velocity would be [vd3 = sqr(vdt3^2-t-vdn3'2}=sqr (10 . 509 ^2-( 0 . 622"2 ) =10 . 527 m/sec] The bounced trajectory is obtained by measuring a line along the furnace wall from the impact point P1, proportional to the transverse velocity [vdt3] and then measuring a line normal to the wall proportional to the normal velocity Ivdn3]. Extending this line til] intersection with the end segment horizontal, gives the point P0' which is the start of the next section of the trajectory. -22- Appendix 3. Procedure for calculating the bounced path in 3D. Let there be an impact in the 31st segment;. The starting point of the 31st segment corresponds to the termination point of. the 30th segment, and this is stored as the point [PCEHT0:3103, 31335,2231; . The termination point of the 31st segment is calculated [PCENTl=3137, 3115-3, 2278], A point on the line [FCENT0-PCENT1 ] can be expressed paremetrically as-X=3103+34*kl; Z=2231+47*k] ; Y=31335- 181*kl The radius of the wall at any level can be obtained form the geometrical parameters of the furnace. ( 3487 :hor9 mm [Absolute horz Stock Shield bot]) ( 34575 :hel9 mm [Absolute elev stock Shield bot]) { =188 :horlO mm [Absolute horz Ring Platfrm bot]) 18543 :hellO mm [Absolute elev Ping Platfrm bot]) The radius (B) can be expressed parametrically in terms of a quantity (k2) as: (XA2+Z"2) ~0,5=R=34 87+1701*k2; Y=3457 5-16032**2 Equating R & Y, gives 2 equations for solving kl & k2 (3103+34*kl)"2+(2231+47*kl) "2= (X"2 +Z"2) =R"2= (3487 + 1701 *k2) ^2=31335- 181*kl= Y =3 457 5-16032*k2 A value of (0 The normal to the surface of the cone at a level (Y=34575-16032* k2) will meet the centre line at (PNCNT): X=0;Z=0,Y=34575-16032*k2-(3487 + 1701*k2)* (5188-3487)/ (34575-18543) =34 205-16212*k2=30883 Now 3 points are known, the starting point of the segment of the trajectory (PCENTO), the point of impact (PCENT1) and a point on the normal (PNCNT). This defines the plane of the incoming particle trajectory, and also the plane of the bounced centrifugal trajectory. The angle of incidence is evaluated from the triangular area (PCENTO-PCENT1-PNCNT) in terms of the line lengths: a2 (distance pcentO pcentl)= 49.3356 a3 (distance pcentl pnent) =3857.4108 a4 (distance pnent pcentO) =3862.6283 al=0.5Ma2+a3+a4) =3884.6873 asqr2=al*(al-a2)*(al-a3)+(al-a4)=896469924 3 area2=sqrt(asqr2)=94 682 sininc=(2*area2)/a2/a3 =0.9950413 cosinc=sqrt(1.0-sininc*sininc)=0.0994 62 6 pangine=atan (sininc/cosinc) 84.29 deg Now the bounced velocity, after impact, can be calculated. Prior to impact, the velocity components were evaluated as: (VDX1/VDY3O/VDZ1=2O29, 10518, 2778 min/sec say). The total velocity was (vd30= sqrt (vdxl**2+vdy3'*2+vdzl**2)] =sqrt(2029*"2+10518**2+2778**2) =11.066 m/sec The tangential component parallel to the impeding wall, remains unchanged after impact, and is: vdt3=vd30*sin (panginc) =11066*sin (84.29) =]1.011 m/sec. And the component normal to the impeding wall, after impact is: vdn3=cors*vd3*cos(panginc)=0.3*11066*cos(84.29)=0.330 m/sec. The total velocity after impact becomes vd3==11.016 m/sec. Next, a point on the normal is located by dropping a perpendicular from the start point PCENTO, on to the normal. This will simply divide the line PCENT1-PNCNT, in a ratio of: prp=- PCENT0-PCENT1 'cosine/ PCENT1-PNCNT= a2'cosinc/a3 =4 9.33 56*0.0994 626/38 57.4108=0.001272 The normal point (PNCNT) is now updated in proportion to: Pncnt [X]=PCENT1 [X]+ (PNCNT [X]-PCENTl [X] ) *prp 3112+ ( 0- 3112)*0.001272= 3108 Pnent [Y]=PCENT1 i Y ] -" ( PNCNT [Y] -1'CENT] [Y] ) *prp 31288 i- ( 3088 3- 31288) *0.001272 = 31287 Pncnt [Z!=PCENT1 [ 2] + (PNCNT [Z] -PCENTl [Z] ) *prp 2243+ ( 0- 2243)'0.001272= 2240 Tne distances, arc also updated. d3 (disiance PCENTl Pncnt) = 5.0990 d4 ( (distance Pnent PCENTO) -= 49.6588 -2 5- In the case of perfectly elastic impact [cors=l], the angle of incidence becomes equa] to the angle of reflection. However, for non-elastic impact, the angles are unequal. The plane of the incident segment of the trajectory, the normal, and the reflected trajectory segment, is cop]snar. To find the reflected line, the points PCENTO and Pncnt are used. The point Pncnt was redefined as the foot of the perpendicular from PCENTO onto the normal. This line is extended to Prefl [say], so that PCENTl-Prefl defines the reflected path. Then, the ratio of the line PCENTO-Pncnt / PCENTl-Pncnt will equal the ratio of the transversal velocity to the normal velocity before impact. On similar lines, the ratio of the line Prefl-Pncnt / PCENTl-Pncnt will equal the ratio of the transversal velocity to the normal velocity after impact Prefl-Pncnt / Pcentl-Pncnt = Prefl-Pncnt / a3 = vdt3 / vdn3 Prefl-Pncnt= a3 * vdt3 / vdn3= 5.0990* 11011/ 330 = 170.1366 The points Prefl,Pncnt s PCENTO are collinear. The length of the line Prefl-Pcent0= the line Prefl-Pncnt+ the line Pncnt-PCENTO = Prefl-Pncnt+ a4= 170.1366+49.6588= 219.7954 The ratio of Prefl-PcentO / Pncnt-PcentO = prpl. Then prpl=219.7954/a4= 219.7954/49.6588=4.4261 The coordinates of the point Frefl, defining the reflected path, can now be calculated, as PCENTO and Pncnt are known. PCENTO [3103,31335,2231], Pncnt {3108,31287,2240] Prefl(X]= 3103+( 3108*- 3103)*4.4261= 3125 Prefl [Y] =31335+ (3128"'-31335) +4.4261=31123 Prefl[2]= 2231+( 2240- 2231)*4 . 4261= 2271 Since the point of impact fPCENTl 3112,312e8,2243], and the point on the reflected trajectory [Prefl 3125,31123,2271] are known, and also the total velocity after impact [vd3 11016 mm/sec], the Cartesian components of the velocity can be evaluated: a3= (distance PCENTl-Prefl)=167.8630 mm dum= (Prefl[X]-PCENT1[X])/a3= (3125-3112)/167.8630=0.07 74 4 4 vdx3=vd3'dum=11016*0-077444=853 mm/sec dum= (Prefl[Y]-PCENT1(Y] ]/a3= ( 31123-31288)/167.8 638-0.982 9 39 vdy3=vd3*dum=11016*(-0.982939)=-10828 mm/sec dum= (Prefl[Z]-Pcentl12])/a3= (2271-224 3)/167.8 630=0.1668026 vdz3=vd3*dum=11016*[0.166802 6)=1837 mm/sec The coordinates of the point of impact are stored in horO,helO,hzcO. This is also updated into the new start point of the next segment of the trajectory [PCENTO]. The velocities after impact are similarly also updated into the starting velocity of the next segment [vdxl/yl/zl] . + The trajectory :n each segment as checked for intersection with each of the following lines. It is possible that the trajectory impacts against more than one of these lines, in which case, the first [closest] impact point 13 considered, as the others will be masked. FLGlNT is a flag, which indicates the active surface against which impact has occurred. FLG1NT= 1, Check intersection with Movable armour line pl01-pl02 2; Check intersection with Stock Shield line plO3-plO4 3; Check intersection with Ring Platfrm line pl04-pl05 -24- LIST OF VARIABLES FOR GEOMETRY: ( 39005 :hell mm [Absolute elevation BF top ]) ( 167 :hor2 mm [Absolute horizonti Large bell]) ( 39636 :hel2 nun [Absolute elevation Large bell]) ( 1881 :bslp mm [Slope length along Bell bottm]) ( 44 :bang degrees [Angle with vert of Bell bottm]) ( 38636 :he14 mm [Init abs elevation Lip ring t]) ( 3700 :hor5 mm [Absolute horizonti Armour hin]) ( 37665 :helb mm [Absolute elevation Armour hin]) ( 3424 :hor6 mm [Absolute horizonti Armour top]) ( 36915 :hei6 mm [Absolute elevation Armour top]) ( 35715 :hel7 mm [Absolute elevation Armour bot]) ( 36315 :hei8 mm [Absolute elevation Actuat Rod]) ( 3487 :hor9 mm [Absolute horz Stock Shield bot]) ( 34575 :hel9 mm [Absolute elev Stock Shield bot]) ( 5188 :horl0 mm [Absolute horz Ring Platfrm bot]) ( 18543 :hell0 mm [Absolute elev Ring Platfrm bot]) ( 29938 :helll mm [Absolute elev Stock line Outer]) ( 29938 :hell2 mm [Absolute elev Stock line Inner]) ( 16053 :hell3 mm [Aba elev Belly bottom Bosch tp] ) ( 4500 :horl4 mm [Abs horz Bosch bottom Hearth t]) ( 12553 :hell4 mm [Abs elev Bosch bottom Hearth t]) ( 12053 :hell5 mm [Absolute elev Hearth bottom ]) ( 3200 :hor16 mm [Abs radius of vertical probe ]) ( 2.1563E+03 :workvol m cube [Working volume of the Blast Fn]) ( 3.65E+05 :tuyrara mm square [Cross sect area of one tuyere ]} ( 28 :numtuyr dimensionless[Number of tuyeres ]} ( 10 :nmhrprb dimensionless[Number of horizontal probes ]) ( 9 :nrpm rpm [Rpm of rotating chute ]) ( 1000 :grdbrdx mm [Border mark on x grid distance]) ( 1000 :grdbrdy mm [Border mark on y grid distance]) ' 500 :grdshx mm [Border mark length on x grid ]) ( 500 :grdshy mm [Border mark length on y grid ]) ( 100 :sizfnt dimensionless [Pixel size of lettering ]) ( 60 idnotch mm [Dist advance for 1 notch ActRd]) ( 0 :notch dimensionless [Notch setting of Actuator Rod ]) ( 9810 :g mm/secA2 [Acceleration due to gravity ]) ( 4 :tspacn mm [Spacing between adjacent lump]) ( 0 :halbl mm [Initial opening of large bell ]) ( 700 :halb2 mm [Final opening of large bell ]) ( 700 :halb3 mm [Increment opening large bell ]) ( 4.00E+00 :kfactl dimensionless [Max empirical param blockage ]) { 3.00E+00 :kfact2 dimensionless [Min empirical param blockage ]) ( 2.00E+00 :kfact3 dimensionless [Decrement emp param blockage }) ( 0 :lsld mm [Sliding dist after strike bell]) ( 2209 :hhl mm [Initial hopper height ]) i 209 :hh2 mm [Final hopper height ]) ( 100 : hh3 mm [ Decrement hopper height ] } ( 9048 :dfytot mm [Total distance of fall ]) ( 100 :defd.is mm [Increment heap dist for volume]) ( 6 :theta degrees [Angle of bell lip to bell surf]) Table: I List of variables for specifying the Blast Furnace geometry -25- LIST OF VARIABLES FOR PARTICLE PROPERTIES: ( 1.00E+00 :vfacti dimensionless [Max value of vel factor ]) ( 9.00E-01 :vfact2 dimensionless [Min value of vel factor ]) ( 3.00E-01 :vfact3 dimensionless [Decrement for vel factor ]) ( 50 :ntstep dimensionless [Number of vertical drop steps ]) ( 1 :lmnp dimensionless [Lump 12 3 for Ore/Coke/Sintr ]) ( 22 :dprtl mm [Mean size of Ore particles ]) ( 55 :dprt2 mm [Mean size of Coke particles ]) ( 17 :dprt3 mm [Mean size of Sinter particles ]) ( 4.00E-01 :mu] dimensionless [Coeff friction Ore /bell surf ]) ( 3.00E-01 :mu2 dimensionless [Coeff friction Coke/bell surf ]) ( 2.00E-01 :mu3 dimensionless [Coeff friction Sint/bell surf J) ( 32 :rpangl degrees [Repose angle of Ore particles ]) ( 37 :rpang2 degrees [Repose angle Coke particles ]) ( 27 :rpang3 degrees [Repose angle Sinter particles ]) ( 3.50E+00 :denstl T per cub mtr [Density of Ore particles ]) ( 5.60E-01 :denst2 T per cub mtr [Density of Coke , particles ]) ( 2.40E+00 :denst3 T per cub mtr [Density of Sinter particles ]) ( 200 :nskipl number [Nos skips or rotations for Ore]) ( 3 :nskip2 number [Nos skips or rotations for Cok]) ( 2 :nskip3 number [Nos skips or rotations Sinter ]) ( 4.00E+00 :weigtl T per skip/rot[Ore in one skip or rotation]) ( 3.33E+00 :weigt2 T per skip/rot[Coke in one skip or rotation]) ( 1.20E+01 :weigt3 T per skip/rot[Sinter in one skip or rotation]) ( 1 :kolorl character [Colour of lines to show Ore ]) { 2 :kolor2 character [Colour of lines to show Coke ]) ( 4 : ko.l or3 character [Colour of lines to show Sinter] ) ( 3.00E-01 :corsll dimensionless [Coef restitution Ore/Armour ]) ( 3.00E-01 :cors12 dimensionless [Coef restitution Ore/Stck Shi ]) ( 3.00E-01 :cors33 dimensionless [Coef restitution Ore/Ring Pit ]) ( 3.00E-01 :cors21 dimensionless [Coef restitution Cok/Armour ]) ( 3.00E-01 :cors22 dimensionless [Coef restitution Cok/Stck Shl ]) ( 3.00E-01 :cors23 dimensionless [Coef restitution Cok/Ring Pit ]) { 3.00E-01 :cors31 dimensionless [Coef restitution Sin/Armour ]) ( 3.00E-01 :cors32 dimensionless [Coef restitution Sin/Stck Shi ]) ( 3.00E-01 :cors33 dimensionless [Coef restitution Sin/Ring Pit ]) Tablc:2 List of variables for specifying the particle properties ore/coke/sinter] -26- i Charging Schedule Variables: 5C4 : Indicates the serial number or the charge Matl: Indicates the nature of the charged material with the code Ore=l, Coke=2, Sinter=3. Kolr: Indicates the colour in which the trajectory, and the burden heap for this charge will be drawn. The colour code is: 1:Red, 2:Yellow, 3:Green, 4:Cyan, 5:Blue, 6:Magenta, 7:White, 8:Black 9:Matt, 10:Orange. T : Specifies the weight of this charge in metric tonnes Rev : This is a reversing option, to indicate whether the charging should proceed in the order of 10 to 0 [Rev=l], or friom 0 to 10 [Rev=2] . 10-0: The program can simulate both the movable throat armour, as well as the Paul Wurth rotating chute. In the former case, the columns 10 to 0 indicate the notch position of the armour, and the values in the columns indicate the proportion of the total charge [T] to be discharged at these notch settings. In the latter case, the column headings 10 to 0 indicate equal annular area rings at the stock-line and the column values are the respective proportions of the charge. (SC# Mat1 kolr T Rev 10 9 8 76543210 ) {122 11.0 251 2 00 222 100 ) ( 2 1 4 35.0 250 0 00 124 317 ) (323 15.0 102230012100 ) (437 45.0 100 000 124 319 ) { 5 ] 5 55.0 153 0 00 100 310 } (621 26.0 151 2 00 222 100 ) (736 43.0 103 2 50 270 040 ) (828 14.0 101 2 00 021 506 ) (919 25.0 106300252100 ) (10310 14.0 131 2 00 305 000 } Tablc:3 List or variables for specifying the charging schedule -28- WE CLAIM 1. A process for optimizing operation of a blast furnace by simulating the burden distribution therein, comprising the steps of: - estimating initial discharge velocity in incremental steps; - calculating bounced trajectory of the particles; - estimating heap formation after the charge particles on stock-line; and - estimating ore/coke ratios along the radius of the blast furnace, for providing information regarding prediction of concomitant gas distribution in the shaft of the blast furnace. 2. The process as claimed in claim 1, wherein said estimating step of initial discharge velocity comprises computation of changed trajectory for each incremental step for simulating the descent trajectory faithfully. -29- 3. The process as claimed in claim 1, wherein the bounced trajectory is calculated in two dimensions. 4. The process as claimed in claim 1, wherein the bounce trajectory is in three dimensions. 5. The process as claimed in claim 1, wherein estimating the heap formation comprises estimation of the change in the inter-surface between successive charges for all the previous charges, as the burden descends down to arrive at the current stock line. 6. A process for optimizing operation of a blast furnace by simulating the burden distribution therein, substantially as herein described and illustrated in the accompanying drawings. The main object of the present invention is to provide a convenient way to quickly explore the effect of changing parameters on the burden distribution. The applicability of this approach is confined within a judicious range of the bench marked condition. For example the value assigned to the blockage parameter of the dynamic arch holds good only within a reasonable range of the charge weight. The present invention thus provides a process for optimizing operation of a blast furnace by simulating the burden distribution therein, comprising the steps of: estimating initial discharge velocity in incremental steps; calculating bounced trajectory of the particles; estimating heap formation after the charge particles on stock-line; and estimating ore/coke ratios along the radius of the blast furnace, for providing information regarding prediction of concomitant gas distribution in the shaft of the blast furnace.

Documents:

00959-kol-2006-abstract.pdf

00959-kol-2006-claims.pdf

00959-kol-2006-correspondence others-1.1.pdf

00959-kol-2006-correspondence others.pdf

00959-kol-2006-description(complete).pdf

00959-kol-2006-drawings.pdf

00959-kol-2006-form-1-1.1.pdf

00959-kol-2006-form-1.pdf

00959-kol-2006-form-2.pdf

00959-kol-2006-form-3.pdf

00959-kol-2006-g.p.a.pdf

959-KOL-2006-(22-08-2012)-FORM-27.pdf

959-KOL-2006-(29-11-2011)-FORM-27.pdf

959-kol-2006-amanded claims.pdf

959-KOL-2006-CORRESPONDENCE.1.3.pdf

959-kol-2006-examination report reply recieved.pdf

959-KOL-2006-EXAMINATION REPORT.1.3.pdf

959-KOL-2006-FORM 18.1.3.pdf

959-KOL-2006-FORM 3.1.3.pdf

959-KOL-2006-GPA.1.3.pdf

959-KOL-2006-GRANTED-ABSTRACT.pdf

959-KOL-2006-GRANTED-CLAIMS.pdf

959-KOL-2006-GRANTED-DESCRIPTION (COMPLETE).pdf

959-KOL-2006-GRANTED-DRAWINGS.pdf

959-KOL-2006-GRANTED-FORM 1.pdf

959-KOL-2006-GRANTED-FORM 2.pdf

959-KOL-2006-GRANTED-LETTER PATENT.pdf

959-KOL-2006-GRANTED-SPECIFICATION.pdf

959-KOL-2006-REPLY TO EXAMINATION REPORT.1.3.pdf

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