MATHEMATICAL MODELLING OF BLAST FURNACE

Abstract

Blast furnace is a moving bed noncatalytic reactor, used widely for producing pig iron. Burden feed consisting of iron ore, coke and flux enters the furnace from top and moves downwards. While the hot air blast introduced through the tuyeres at the bottom of furnace, moves upwards. Many transfer and rate processes take place during the countercurrent sojourn of gas and solids in the furnace. Overall process of making pig iron requires large amount of heat, which is supplied by the hot gases produced during the combustion of coke with hot air blast. Due to the increasing emphasis on energy conservation and pollution control, there is a need to understand and analyse the blast furnace process so that the problems associated with its operation, design and control could be solved. Mathematical modelling is an attractive tool for the analysis and simulation of systems as the models are based upon fundamental laws of conservation of mass, momentum and energy. Properly formulated models provide sufficient insight about the processes occuring in the system and also assist in quantifying them. Thus, it is desirable to develop a mathematical model of the complex blast furnace process. In the present thesis, a One-dimensional mathematical model of the shaft region of blast furnace has been developed. The shaft encompasses stack, belly and bosh. Its model consists of ten nonlinear partial differential equations (time-dependent convection equations), one ordinary differential equation and four algebraic equations. In the model eight chemical reactions have been considered, which also include the reaction of SiO gas with carbon dissolved in molten pig iron. This model is capable of predicting the behaviour and performance under ii unsteady state as well as steady state operations. For its numerical solution, initial and boundary conditions, and appropriate constitutive relationships are required. In view of the above, a procedure for computing the material and energy balances of a blast furnace has been developed and programmed. The program calculates the boundary conditions of the proposed mathematical model by using the generally available plant data and also computes the parameters of streams, which are difficult to measure and are normally not known. During the process few significant results and relationships have also been obtained, which are mentioned below. A methodology for computing the molar flow rate of SiO gas formed in the combustion zone. An empirical relationship for calculating the melting temperature of coke ash for the specified Al 0 and SiO contents. Simplified relationships for the direct calculation of adiabatic flame temperature, tuyere gas temperature, and top gas temperature. Besides, it has been clearly demonstrated by computations that the tuyere gas temperature is approximately 250 K less than the adiabatic flame temperature. Hence, it is not advisable to use adiabatic flame temperature in place of tuyere gas temperature in modelling studies. Constitutive relationships play an important role in modelling and simulation of engineering systems. For blast furnace process, their number is quite large. Correlations for various parameters used in the model have been discussed and derived. Their limitations have also been pointed out. Further, the heat of reaction varies with temperature, and there exists wide variation in temperature within the furnace. Therefore, the correlations for heats of reactions as a function of temperature have been derived so that the effect of variation in heats iii of reactions on the behaviour of furnace could be studied. The model has been transformed into steady state model by setting time derivatives equal to zero. Resulting model equations consist of eleven nonlinear ordinary differential equations. In the present work, it was decided to obtain the numerical solution of the model under steady state conditions only. These model equations constitute a Boundary Value Problem (BVP), which is generally difficult to solve in comparison to an Initial Value Problem (IVP). Since developed model consists of many adjustable parameters pertaining to the maldistribution of gas and solids, and uncertainties associated with the constitutive relationships, therefore, the model equations have been solved as an IVP and the iterations have been stopped by matching the calculated and given boundary conditions at one of the end. A computer program has been developed for the simulation of steady state model. It has been our experience that the numerical solution of the model is very sensitive to the adjustable parameters and slight variation in their values might lead to nonconvergence of the numerical scheme adapted to solve it as a BVP. An industrial blast furnace was selected for testing the model predictions. Its dimensions and four sets of operating data were taken from the literature. In order to ascertain the correctness of the proposed model, longitudinal profiles of all the process variables, namely compositions, fractional conversions, temperatures and pressure have been computed, and are in accordance with those reported in the literature. These have also been explained on the basis of assumptions underlying the model. It has been observed that the change in heats of reactions as a result of variation in temperature has appreciable effect on the model predictions in higher temperature zones (1000 K or above) . Therefore, it is necessary to account for this effect in the model. This conclusion is in contrast to most of the earlier modelling studies in iv which heats of reactions were considered constant and taken at the reference temperature (298 K). It is our view that the proposed model may be used for the analysis of blast furnace process and optimization of its productivity, provided actual plant data could be made available for estimating the adjustable parameters of the model. Then the model may also be used for studying its dynamic behaviour and developing suitable control strategies.