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This paper presents a method by which the maximum possible rate of pulverized coal injection (PCI) in blast furnace can be predicted. The method is based on a two-step approach. First, a first principle simulation model of the blast furnace is used to generate data sets for the development of a linear model of pulverized coal injection rate. The data has been generated randomly in MATLAB software within the range of operating parameters (constraints) of the blast furnace. After that , the coefficients of the function have been determined. The inputs and the resulting outputs formed the data on which the linear optimization model was developed. Next, the linear model was used for maximizing the pulverized coal rate injection by optimizing the other variables. Two operating Indian Blast Furnaces have been chosen to validate the optimization model.

Reduction of fuel consumption, increase of the blast furnace capacity and productivity are the main factors, which determine the development of the iron making industry. The decrease of coke rate is the most important factor for reduction of hot metal production cost as well as from environmental perspectives. This problem can be resolved by improvements in utilization of gas heat and reduction potential by rationalizing gas distribution in the furnace cross-section. In recent iron making blast furnaces, pulverized coal is increasingly injected as a supplementary fuel in replacement of coke [

There are several problems in blow pipes and tuyeres due to low combustibility of coal compared to oil and natural gas. The former would have unburnt coal particles trapped in the coke bed interstices and change the gas stream distribution in the burden. This leads to problems in tuyere and blow pipe failures [

Few investigations have been performed related to coal combustion efficiency in terms of coal properties and blast conditions. Yamaguchi et al. [

Pettersson et al. [_{2} emissions. This method is based on genetic algorithm. Discrete element method analysis of blast furnace and solids motion around raceway was studied by Natsui et al. [

So far, no concrete work has been done to know the maximum coal injection rate in blast furnace due to complex nature of raceway phenomena including combustion of coke and coal particles. In previous investigation [

In the present study, an optimization model has been developed for the prediction of maximum possible rate of pulverized coal and optimum blast parameters for specified condition. The results are examined using some practical data of coal injection in Indian blast furnace. Sensitivity tests of the model parameters are also being conducted in the range of conditions expected in operating blast furnaces.

Our final aim was to find the optimization model for pulverized coal injection into the blast furnace. First, we have developed a raceway model. The raceway model is one dimensional and static. It is based on mass and heat balance.

The role of reduced order model is to replace the more rigorous mathematical model of a system or a process by a model that is considerably “smaller” than the original multidimensional model; but still describes at least approximately, key aspects of the system of process. Usually this model is one-dimensional and computationally amenable for real time plant applications.

The reduced order model of the raceway has been developed for real time applications in an operating blast furnace involving combustion of coke and PC. In order to keep the model computationally tractable and suitable for real time predictions, the following assumptions have been used.

1) One dimensional axisymmetric steady state conditions with radial variation of the process variables (temperature and compositions, etc.).

2) Density, viscosity and diffusivity of the gas depend on temperature and composition.

3) Total fuel rate (coke + PC) has been considered to be constant. This implies that replacement ratio of PC is 1, which essentially indicates that the amount of coke saved is replaced with an equal amount of PC during operation.

4) Combustion of coke takes place only after complete combustion of pulverized coal.

The molar flow rate of blast has been calculated approximately by the average flow rate of gas before and after combustion under the given operating conditions. Before combustion the flow rate of gas can be expressed as:

F 1 = V b 22.4 [ 0.21 + O 2 e n ] + W s t + W N 2 (1)

After the combustion of total fuel, the flow rate of gas is:

F 2 = ( N N 2 + N CO + N H 2 ) (2)

From Equations (1) and (2), the average flow rate of gas (F), based on the cross section of the hearth [

F = 2 ( F 1 + F 2 ) π D h 2 (3)

With regard to the flow rate in the vicinity of the upper boundary, the following approximate relationship between the vertical component F_{y}, and the horizontal component F_{x}, can be established at any location along the tuyere axis [

F y F = 2.3 e r f ( 0.5 F x F − 2 ) + 2.9 (4)

The major quantum of outflow rate of gas through the combustion zone has been estimated by F_{y} multiplied by an empirical coefficient ξ. This coefficient represents the fractional area of effective outflow surface and is estimated to be 0.25.

The principal combustion reactions occurring in the tuyere zone could be given as:

(i) C + O 2 → CO 2

(ii) C + CO 2 → 2 CO

(iii) C + H 2 O → H 2 + CO

(iv) H 2 + 1 2 O 2 → H 2 O

The water-gas shift reaction ( CO + H 2 O → CO 2 + H 2 ) has been neglected since the reaction (iii) is the predominant reaction in the combustion zone.

The species reaction (O_{2}; CO_{2}; H_{2}O; CO and H_{2}) rate, r_{i} can be expressed as follows:

r i = − ε d C g i d θ = − ε d ( P y i / R T g ) d θ ( i = 1 , 2 , 3 , 4 , 5 ) (5)

r 1 = R 1 * + 1 2 R 4 * (6)

r 2 = − R 1 * + R 2 * (7)

r 3 = − r 5 = R 3 * − R 4 * (8)

r 4 = − 2 R 2 * − R 3 * (9)

Overall reaction rate may be written as:

R * = k i C g i ( i = 1 , 3 ) (10)

The expression for rate constant k i based on the unit volume of the combustion zone may be presented as:

k i = 1 1 k f i a + 1 η i k m i ρ b ( i = 1 , 3 ) (11)

The mass transfer coefficient k_{fi} can be expressed as follows:

k f i = ( D i ϕ d p ) S h ( i = 1 , 3 ) (12)

The following relationship may be applied to the high Reynolds number (Re_{p}) region:

S h = 1.5 R e p 0.55 (13)

The chemical rate constant for reaction (i) of a single carbon particle can be expressed as [

K m 1 = 6.53 × 10 5 ( a / ρ b ) T m exp ( − 22140 / T m ) (14)

The chemical rate constant for reaction (ii) is

K m 2 = 8.31 × 10 9 exp ( − 30190 / T m ) (15)

The chemical rate constant for the reaction (iii) is given as

k m 3 = 13.4 T m exp ( − 17310 / T m ) (16)

The reaction (iv) is fast among the four chain reactions but it would stop after attaining equilibrium state. The critical oxygen content, y 1 * , may be nearly 5 % with respect to the initial oxygen content during combustion in the tuyere zone. Thus the reaction rate may be expressed as

R 4 = R 3 at y 1 ≥ y 1 * , R 4 = 0 at y 1 < y 1 * (17)

Using the concept of reduced order model, the steady state heat and mass transfer model has been developed in the combustion zone.

A differential one dimensional control volume is considered. On this volume, the mole balance for the total gas flow is given as:

− d ( F x ) d x = 4 F y ξ D T + ( α ∑ i = 1 5 r i + β ∑ i = 1 5 r i ) (18)

The relationship between F_{y} and F_{x} has been provided in Equation (4).

For each component of the gaseous species, the mass balance during combustion of pulverized coal and coke can be represented as:

d y i d x = y i ( α ∑ i = 1 5 r i + β ∑ i = 1 5 r i ) − ( α r i + β r i ) F x (19)

The differential heat balance equation incorporating both pulverized coal and coke combustion in an integrated manner can be expressed as:

d T g d x = α ( ∑ i = 1 4 R i ( − Δ H i ) + c p c T c ∑ i = 1 3 R i + c p g T g ∑ i = 1 5 r i − π D T h g c ( T g − T c ) F x ( c p g + T g ∂ c p g ∂ T g ) ) + β { ∑ i = 1 4 R i ( − Δ H i ) + c c T c ∑ i = 1 3 R i − π D T h g c ( T g − T c o a l ) − ( H d e v ∗ P C I ∗ V M ∗ P D ) F x ( c p g + T g ∂ c p g ∂ T g ) } (20)

The above formulation takes into account bulk transport of heat with gas flow, heat exchange between gas and solid and heat generated by chemical reactions.

The temperature of the coke particles in the combustion zone has been assumed to be related to the surrounding gas temperature [

T c = 0.8 T g (21)

Boundary conditions:

Boundary condition for coke particles at the tuyere nose (x = 0);

y 10 = ( 0.21 + O 2 e n ) (22)

y 20 = y 40 = y 50 = 0 (23)

y 30 = ( W s t ∗ 22.4 ) / ( 18 ∗ 1000 ) (24)

F x 0 = F 1 / ( π D T 2 n / 4 ) (25)

T 0 = T b (26)

Boundary condition for coal particle at tuyere nose (x = 0),

y 10 = ( ( ( 0.21 + O 2 e n ) ∗ V b ) / 22.4 ) − 2 × V M V M + ( V b / 22.4 ) (27)

y 20 = V M / ( V M + ( V b / 22.4 ) ) (28)

y 30 = ( 2 ∗ V M ) / ( V M + ( V b / 22.4 ) ) (29)

y 40 = y 50 = 0 (30)

F x 0 = F 1 / ( π D T 2 n / 4 ) (31)

T 0 = T b (32)

where, subscript 0 represents the condition at the tuyere nose.

Numerical solution of the above equations using proper boundary conditions gives radial temperature and composition profile of the gas in the raceway zone of Blast Furnace.

The following equation has been used to estimate the depth of raceway cavity.

D R D T = k R ( ρ g u g 2 T r P T a ρ b g d p ) 1 / 2 (33)

where, empirical constant,k_{R} = 0.18 when PCI has been used and k_{R} = 0.27 when only coke has been considered. These constants have been tuned for the present real time model with respect to the plant operating data.

The ordinary differential equations of the raceway model have been solved using 4^{th} order Runga-Kutta method. The solver algorithm has been implemented in C++ computer code to simulate the process. Numerical simulation of the raceway was carried out using data from literature to establish its predictive capability. Model formulation was suitably modified to match the model output with those reported in literature. Subsequently, data from an Indian operating blast furnace were utilized to tune the adjustable parameters of the reduced order model (heat transfer coefficient between gas and coke, mass transfer coefficient, rate constant of chemical reaction, diffusivity of gas component, etc.) so as to make it amenable for application under Indian blast furnace operating conditions. Subsequent calculations were terminated at the raceway penetration depth (Equation (33)).

The objective function can be expressed in terms of various operational parameter including raceway parameters. Raceway Adiabatic Flame Temperature (RAFT), Steam addition, O_{2} enrichment, Blast volume, Blast temperature, Volatile matter in coal and carbon % in coal are the most important parameters of raceway zone of blast furnace. Keeping in mind the parameters, the following linear objective function has been developed from first principle based above model data sets:

f ( x ) max = a 0 + ∑ a i x i

where a_{0}, a_{i} are coefficients and x_{i} are different process variables.

Subject to: x min ≤ x i ≤ x max _{ }

Where f(x) = PCI rate (kg/thm)

i = 1 to 7.

The variables are:

x_{1} = Raceway Adiabatic Flame Temperature (RAFT (K));

x_{2} = Steam addition (tons/hr);

x_{3} = O_{2} enrichment (%);

x_{4} = Blast volume (Nm^{3}/min);

x_{5} = Blast temp (K);

x_{6} = Volatile Matter (VM) in coal (%);

x_{7} = Carbon in coal (%).

Pulverized coal injection (PCI) is an effective way to decrease the amount of coke and environmental problems in a blast furnace. Here, an optimization framework has been developed for the prediction of maximum possible rate of pulverized coal injection and optimum blast parameters for specified conditions. The optimization method is based on a two-step approach. First, a first principle simulation model of the blast furnace is used to generate data sets. The inputs and the resulting outputs formed the data on which the linear optimization model was developed. Next, the linear model was used for maximizing the pulverized coal rate injection by optimizing the other variables using Luus-Jaakola method. Luus-Jaakola is a direct search optimization technique to solve many optimization problems of chemical and biochemical processes.

The results are examined using some practical data of coal injection in two operating Indian blast furnaces. Sensitivity tests of the model parameters are also being conducted in the range of conditions expected in operating blast furnaces. As the goal of the work was to find the maximum rate of pulverized coal injection into the blast furnace, an important step in the analysis was the formulation of raceway model. The raceway model is static and one-dimensional with respect to the coordinate is based on mass and heat balance.

Various operating parameters and their range of two Indian integrated steel

Variables | Range |
---|---|

RAFT (K) | 2200 - 2400 |

Steam addition (t/hr) | 0 - 16 |

O_{2} enrichment (%) | 0 - 4 |

Blast volume (Nm^{3}/min) | 3000 - 4200 |

Blast temperature (˚C) | 850 - 1050 |

Volatile Matter (%) | 25 - 30 |

Carbon in coal (%) | 55 - 65 |

Case 1 | ||
---|---|---|

Variable Constraints RAFT (K) = 2380 - 2430 Steam (tons/hr) = 4 - 5 O_{2} (%) = 2 - 4 Blast Volume (Nm^{3}/min) = 2350 - 2380 Blast Temperature (K) = 1470 - 1500 VM (%) = 19 - 20 C in PCI (%) = 71 - 72 Output: - Plant values (kg/thm): 118.65 Optimized PCI (kg/thm): 135 | ||

Variables | Plant Values | Model Output |

RAFT (K) | 2393 | 2397 |

Steam addition (t/hr) | 4.14 | 4.38 |

O_{2} enrichment (%) | 2.95 | 3.08 |

Blast volume (Nm^{3}/min) | 2360 | 2353 |

Blast temperature (˚C) | 1473 | 1486 |

Volatile Matter (%) | 19.24 | 19.14 |

Carbon in coal (%) | 71.10 | 71.61 |

Case 2 | ||
---|---|---|

Variable Constraints RAFT (K) = 2320 - 2360 Steam (tons/hr) = 2.7 - 3.0 O_{2} (%) = 2.8 - 3.0 Blast Volume (Nm^{3}/min) = 2500 - 2550 Blast Temperature (K) = 1470 - 1500 VM (%) = 19 - 20 C in PCI (%) = 70 - 71 Output:- Plant values: 135(kg/thm) Optimized PCI (Kg/thm): 146 | ||

Variables | Plant Values | Model Output |

RAFT (K) | 2333 | 2355 |

Steam addition (t/hr) | 2.78 | 2.91 |

O_{2} enrichment (%) | 2.91 | 2.91 |

Blast volume (Nm^{3}/min) | 2516 | 2517 |

Blast temperature (˚C) | 1473 | 1497 |

Volatile Matter (%) | 19.22 | 19.79 |

Carbon in coal (%) | 70.76 | 70.23 |

plant have been taken for investigation. It has been done to testify the model performance. The results have been shown in

An optimization method has been developed for raceway zone of blast furnace to predict the maximum permissible coal injection rate in certain operating blast conditions. It is based on fundamental models of raceway for data generation and an optimization technique. The capability of prediction has been demonstrated by two case studies. The model predictions are reasonably good. The linear objective function has been formulated based on large amount of data. The data has been generated randomly in MATLAB software within the range of operating parameters (constraints). After that, the coefficients of the function have been determined. Two large Indian steel plants have chosen to validate the objective function and to show the results. The designated plants are operating below optimized conditions as per results from optimization technique. This model is in generic nature and can be used in any operating blast furnace to predict maximum permissible PCI rate with available constraints. This work will help to operate the blast furnace with PCI without any difficulty. It will also reduce the cost and maintain steady operation of the blast furnaces.

The authors thankfully acknowledge the financial assistance received from Ministry of Steel, Govt. of India, under Steel Development Fund scheme for carrying out the present work as a part of a research project. The authors also wish to thank Director, CSIR-National Metallurgical Laboratory, for his kind permission to publish this paper.

The authors declare no conflicts of interest regarding the publication of this paper.

Sau, D.C., Murmu, R., Senapati, P. and Sutar, H. (2021) Optimization of Raceway Parameters in Iron Making Blast Furnace for Maximizing the Pulverized Coal Injection (PCI) Rate. Advances in Chemical Engineering and Science, 11, 141-153. https://doi.org/10.4236/aces.2021.112009

a Specific surface area, (m^{2}/m^{3}(bed))

c_{pc}_{ } Specific heat of coke, (J/mol∙K)

c_{pg} Specific heat of gas, (J/mol∙K)

C_{gi} Concentration of gas component, (mol/m^{3} (bed))

d_{p} Diameter of coke particle, (m)

D_{h} Diameter of hearth, (m)

D_{R} Raceway depth, (m)

D_{i} Diffusivity of gas component, (m^{2}/sec)

D_{T} Tuyere diameter, (m)

V_{b} Blast volume in dry base, (m^{3}/sec)

F Average flow rate of gas, (mol/m^{2}∙sec)

F_{1} Gas flow rate before combustion, (K-mol/sec)

F_{2} Gas flow rate after combustion, (K-mol/sec)

F_{x} Gas flow rate in x-direction, (K-mol/m^{2}∙sec)

F_{y} Gas flow rate in y-direction, (K-mol/m^{2}∙sec)

h_{gc} Heat transfer coefficient between gas and coke, (W/m^{2}∙K)

ΔH_{i} Heat of reaction, (J/mol)

H_{dev} Heat of volatilization (J/mol)

i Gas component

k_{i} Rate constant of chemical reaction, ((mol/m^{3})^{1-n}/sec)

k_{fi} Mass transfer coefficient, (m/K)

k_{mi} Chemical reaction rate constant, (m^{3}/mol-sec)

n No. of tuyere, (−)

N_{CO} Amount of CO after combustion (K-mol/sec)

N H 2 Amount of H_{2} after combustion K-(mol/sec)

N N 2 Amount of N_{2} after combustion (mol/sec)

P Pressure in raceway zone, (K-mol/m sec^{2})

P_{D} Productivity, (tons/hr)

r_{i} Rate of consumption of gas component, (mol/m^{3}(bed)∙sec)

R_{i} Rate of reaction, (mol/m^{2}∙sec)

Re_{p} Particle Reynolds number, (−)

R Gas constant (J/K.mol)

Sh Sherwood number, (−)

T_{a} Ambient temperature (K)

T_{b} Blast temperature (K)

T_{c} Temperature of coke particle, (K)

T_{coal} Temperature of coal particle, (K)

T_{g} Temperature of gas, (K)

T_{m} Mean temperature of coke and gas, (K)

T_{r} Raceway gas temperature (K)

u_{g} Velocity of bosh gas (m/s)

VM Volatile Matter, (−)

O_{2en} Oxygen enrichment, (−)

W_{st} Amount of steam addition, (K-mol/sec)

W N 2 Amount of N_{2} (K-mol/sec)

x Distance in x-direction

y Mole fraction of gas component, (−)

thm Ton of hot metal

η i Effectiveness factor, (−)

ρ b Bulk density of coke, (kg/m^{3}(bed))

ρ g Density of bosh gas, (kg/m3)

ξ Fractional area of the effective outflow surface, (−)

φ Sphericity of particle, (−)

α Fraction of coke rate (−)

β Fraction of coal rate (−)

ε Voidage of the combustion is zone (−)

θ Time (sec)