U.P.B. Sci. Bull., Series B, Vol. 78, Iss. 3, 2016 ISSN

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1 U.P.B. Sci. Bull., Series B, Vol. 78, Iss. 3, 2016 ISSN MATHEMATICAL MODEL OF CORRELATION BETWEEN THE INJECTION PARAMETERS IN THE BLAST FURNACES CRUCIBLE AND THE MAIN OBJECTIVE FUNCTIONS OF THE PIG IRON OBTAINING PROCESS Victor ANDREI 1, Nicolae CONSTANTIN 2, Cristian DOBRESCU 3 This paper aims at presenting a mathematical model for correlating the parameters which intervene in the phsic-chemical processes that take place in the blast furnaces crucible, when using auxiliar fuels. The presented mathematical model establishes correlations between the injection parameters described below, containing a number of equations so that an of the injection parameters can appear as an independent input variable (x j ), but also as an output function (). The correlations are presented: = f ( x j ), i = 1... n, as well as dependencies: x j = f (, xi ), i = 1... n, j = 1... n, i j. Kewords: blast furnace,, auxiliar fuels, tar, oil pitch 1. Introduction The equations for the mathematical model were established having as basis actual operating data from the 1700 m 3 ARCELOR MITTAL Galati blast furnace. For the calculation premises for the injection parameters the following achievable values were considered: - Theoretical specific consumption (with 0% humidit), K t(, of 600 [kg/t]; - Tar hourl flow injected in the tueres, D gdr(, of [kg/h]; - Oil pitch hourl flow injected in the tueres, D cls(, of [kg/h]; - Methane gas hourl flow injected in the tueres, D gm(, of [Nm 3 /h]. 1 PhD. assistant, Dept. of IMOMM, Universit POLITEHNICA of Bucharest, Romania, victorandrei11@ahoo.com 2 PhD, Dept. IMOMM, Universit POLITEHNICA of Bucharest, Romania, nctin2014@ahoo.com 3 PhD, Dept. IMOMM, Universit POLITEHNICA of Bucharest, Romania, cristiandobrescu@ahoo.com

2 196 Victor Andrei, Nicolae Constantin, Cristian Dobrescu 2. Preliminaries The mathematical model contains calculation relations through which the hourl flow of tar, methane gas and oil pitch are being transformed into specific consumption, compared to a tone of pig iron. The theoretical temperature in the combustion area is presented as an objective function, T za(f) as a dependenc on the input parameter values, X i. It can also be used in the mathematical model as an input variable with predicted values, T za(, values that are obtained from real data processing operation of blast furnaces. In the equations of the mathematical model the specific heats of air, C a, water vapors, C w, and furnace gases, C gf, appear as variables, whose values, depending on the temperature, are found in the scientific literature [1],[2]. For the furnace gas specific heat the following relation was considered: 4 C gf = ( T za ( 273) 10, [kj/kg K] (1) The calculation compositions for tar and oil pitch are presented in Table 1 and Table2. Table 1 Calculation composition for tar C unbound C total CH 4 C 2 H 2 H 2 O 55% 55.2% 13.6% 28.8% 5% Table 2 Calculation composition for oil pitch C unbound C total CH 4 C 2 H 2 H 2 O 43% 43.2% 15% 16% 5% For the replacement index of through tar, methane gas and oil pitch the following values were considered [3]: tar I =1.08, [kg /kg tar] (2) CH I 4 =1, [kg /Nm 3 CH 4 ] (3) oil pitch I =1.04, [kg /kg oil pitch] (4) The selected values for the calculation of these replacement ratios can be corrected depending on the functioning of the blast furnace Mathematical model Hourl production of iron is determined using the relation:

3 Mathematical model of correlation between the injection parameters [ ] obtaining process 197 Q f ni =, [t/h] (5) 24 where Q f represents theoretical quantit of iron obtained from a loading unit, [t/ui], n i - number of units loaded in the blast furnace in one da. The specific consumption of tar G dr, methane gas G m, and oil pitch Cls is determined using the equations: Dgdr( Gdr =, [kg/t] (6) Dgm( Gm =, [Nm 3 /t] (7) Dcls( Cls =, [kg/t] (8) The equivalent quantit of replaced b auxiliar fuels was computed using the following equation: tar CH4 Cls Kte = I Gdr + I Gm + I Cls, [kg/t] (9) Thus the specific consumption of phsical technical is determined using the relationship: Ktf = Kt( Kte, [kg/t] (10) The hourl consumption of technological with humidit W i is expressed b: 100 K th = Ktf, [kg/h] (11) 100 Wi The quantit of technological with humidit, W i (usuall 1-3%), that is introduced in the loading unit is determined using the relationship: 100 Kth Kui =, [kg/ui] (12) 100 Wi Using the combustion thermal balance in the crucible of the blast furnace, various forms of heat equalit is generated b the main input parameters and the residual heat with the gas in the furnace. From this balance, a functional relationship between the input parameters and the main objective functions can be extracted. Hourl gas flow, with a % of O 2 used for the gasification of and other auxiliar fuels that has to be introduced in the furnace, is determined using the relationship:

4 198 Victor Andrei, Nicolae Constantin, Cristian Dobrescu Dgh = Ck Kth Dgdr( Dgm( + Dcls( + 1 % [ O ] (0.729Ck Kth Dgdr( Dgm( Dcls( ) 2 where C k represents the content of the unbound carbon of dr produced b its technical analsis (usuall this value is between 84% and 88%). The theoretical temperature can be determined with the following relationship: Tza( f ) = {15.912Ck Kth Dgdr( + 439Dgm( Dcls( (14) + Dah[( Ca ϕ CH O ) ( Ta 273) 25.8ϕ ]} Cgf D 2 gh where T a and ϕ represent the air temperature injected in the crucible and its humidit [%]. From the thermal balance area of the crucible from which T za( f ) = f ( xi ) was extracted, a time relationship can also be extracted: X j = f ( Tza(, X i ), representing the model of influence on a X j component of the other input parameters X i and of the resulting function T za(f) that became T za(, therefore bearing the predicted values in accordance with the furnace operational requirements [4],[5]. B linearizing the complex expressions, through the method of partial derivatives around a point on the optimum value of the objective function, the following relationship was determined: n Y = a0 + = ε i i X 1 i (15) where a 0 - numerical coefficient; εi - bias coefficient that expresses the influence of the independent parameter X i on the resulting function Y. A positive value (+) of the coefficient ε indicates a proportional dependenc between X i and Y, also a negative value (-) shows an inverse dependenc, respectivel forε i > 0, the increase of X i leads to the increase of Y and forε i < 0, the increase of X i leads to a decrease of Y. The absolute value of the coefficient ε i shows, for several values of (, the influence share of the X i coefficient over the function Y, meaning that ε 1 > ε 2 shows an influence greater of X 1 over Y than X 2. Dependencies between parameters that intervene in the combustion zone are depicted in the following linear equations: (13)

5 Mathematical model of correlation between the injection parameters [ ] obtaining process 199 Tza( f ) = 0.031Ktf Dgdr( Dgm( Dcls( Dah Kth( f ) = 31.70Tza( 1.143Dgdr( 0.317Dgm( 0.809Dcls( 0.219Dah (16) (17) Dgdr( f ) = 0.425Tza( 0.874Kth 0.277Dgm( 0.707Dcls( 0.219Dah (18) Dgm( f ) = 99.98Tza( 2.996Kth 3.606Dgdr( 2.551Dcls( 0.793Dah (19) Dcls( f ) = 39.18Tza( 1.174Kth 1.74Dgdr( 0.39Dgm( 0.31Dah Dah( f ) = Tza( 3.77Kth 4.546Dgdr( 1.26Dcls( 3.21Dcls( Tza( f ) = Tza( Ktf Dgdr( Dgm( Dcls( Dah where T za theoretical temperature from the combustion zone, [K] W gdr - water content from tar and the steam used at injecting the tar. [%] D gdr, D gm, D Cls technological specific consumption, [kg/t]; D ah - hourl air flow necessar for burning the fuel at the tueres, [Nm 3 /h]; (20) (21) (22) 3. Conclusions The equations were obtained from the mass and energ balances, applied in the combustion zone in the furnace crucible, starting with the phsic-chemical relationships between the parameters in the combustion zone (C k, K tf, D gdr, D gm, D Cls, O 2 ) as defined above. For the s replacement ratio through various auxiliar fuels, values were used that were adopted b all field specialists, values confirmed b the furnace real data. The presented mathematical model is used for the process of obtaining pig iron in the blast furnace, assisted b the computer.

6 200 Victor Andrei, Nicolae Constantin, Cristian Dobrescu If in the process simulation using an initial input set of values, abnormal results are obtained, then a new set of values is used that can lead to results similar to those obtained in the real practice. The simulation is done using the equations from the model; out of the simulation, important conclusions are drawn and the correction coefficient for some equations can be determined. A model can be obtained that can precisel reproduce the development of the process in the combustion area of the blast furnace. This model can contribute to the implementation of the advanced techniques regarding the obtainment of pig iron in optimal conditions, through a perfect correlation of the injection parameters. The mathematical model presented in the paper represents a computer software support that can be used to conduct dnamic and conversational processes in the furnace. B this date no furnace is being full conducted using process computers. Maximum productivit, in conditions of minimum specific consumption, could be obtained using a conversational sstem. Acknowledgement The work has been funded b the Sectoral Operational Programme Human Resources Development of the Ministr of European Funds through the Financial Agreement POSDRU/159/1.5/S/ R E F E R E N C E S [1]. N. Constantin, Blast furnace process intensification b gas circulation improvement, in order to ensure productivit growth and energ and metallurgical econom, Ph. D. Thesis, Bucharest, 1994 [2]. F. Pettersson, H. Saxén, Model for economic optimization of iron production in the blast furnace, ISIJ International 46 (2006) [3]. N. Constantin, V. Geantă, D. Bunea, R. Şaban, Metode analitice şi grafice pentru determinarea rapidă a consumurilor de cocs la furnale în cazul utilizării diverşilor combustibili auxiliar (Analtical and graphical methods for quick determination of the consumption of in blast furnaces when using various auxiliar fuels), Metalurgia Revue, nr. 9-12, 1990, pag , ISSN [4]. N. Constantin, D. Ioniţă, A. Semenescu, C. V. Semenescu, Analtical methods for blast furnace iron making optimization b optimal correlation of rate with blowing parameters in the racewa, Metalurgia Revue nr.6/2003, pag [5]. N. Constantin, V. Geantă, R. Şaban, D. Bunea, Stabilirea prin modelare matematică a consumului teoretic optim de cocs la furnale, în funcţie de componenţa încărcăturii" (Establishing through mathematical modeling the optimal theoretical consumption of in blast furnaces, depending on the composition of the load), Metalurgia Revue, nr. 6, 1991, pag 14-17, ISSN