In this work, slab-heating process by two tunnel furnaces of Tata Steel Ltd. India [Furnace A and Furnace B] at continuous thin slab caster and rolling has been considered. The slab heating is carried out at both the furnaces by air-fuel combustion. The length of each furnace is approximately 239 meter ( Figure 1 ) and “Furnace B” has swivel over operation technique where, slabs are shifted from furnace B to furnace A, for uninterrupted slab feeding facilities to a single hot rolling operation line ( Figure 2 ). The objective of this roller base tunnel type continuous furnace is to maintain desired rolling temperature throughout the furnace length. It also enables continuous operation of slab heating for uninterrupted rolling operation. The slab entry temperature into tunnel type furnace varies between 900˚C - 950˚C whereas, slab exit temperature is commonly between 1100˚C - 1150˚C for both the furnaces. It indicates, required heat or energy input should be between 12% - 18% of total heat input for achieving desired slab out temperature from the furnace. The entire furnace is divided into several zones which are namely Zone1 to Zone9 for furnace A and Zone1 to Zone8 for furnace B. Each zone consists of three thermocouples (TC) in alternative furnace walls ( Figure 3 ). In order to operate such a huge furnace, these zones are combinedly divided into three virtual sections for both the furnaces i.e., for furnace A: Zone1 to Zone3 are considered as Section1, Zone4 to Zone7 are considered as Section2 and Zone8 to Zone9 are considered as Section3. Similarly, for furnace B: Zone1 to Zone3 are considered as Section1, Zone4 to Zone7 are considered as Section2 and Zone8 is considered as Section3. Three recuperators are attached with the three sections respectively of each furnace for recovering the heat from exiting flue gas, which is predominantly used as recycled heat input into the furnace. Both the furnaces are operating on roller base for pushing stocks from charging to discharging point through the furnace. There are 218 rolls in Furnace-A and 214 rolls for Furnace-B, which are embedded with refractory and continuously cooled by inflow of water. The temperature range for inlet water is in the range of 250˚C to 350˚C.

In an integrated steel plant, mixed gas is commonly used as combustion agent where byproduct gases from coke oven, blast furnace and Linz-Donawitz furnace (LD) are mixed with a proportion based on availability. Zheng et al. [15] has suggested an optimized model for the users of byproduct gas, considering fluctuation in Calorific Value (CV) and supply patterns. Authors have explained the various reasons for inconsistent CV of mixed gas. Hence, instantaneous variation in CV requires dynamic analysis of mixed gas composition at an every instance before combustion so that fuel consumption can be optimized.

As shown in Table 1 , the variation in mixed gas composition results in fluctuation in CV leading to the variation in combusting character. To circumvent this issue, CV for every instance has been calculated based on the basic governing equation of combustions as given in Eq. 1.

$\begin{array}{l}\text{Calorific}\text{Value}\\ ={\displaystyle {\sum }_{i=1}^n\text{Volume}\%\text{of}\text{Component}i\times \text{Calorific}\text{Value}\text{of}\text{Component}i}\end{array}$ (1)

where:

n: Number of gas Components;

Volume % of Component i: Volume percentage of gas component i;

Calorific Value of Component i: Calorific value of gas component i in energy units.

Figure 4 shows hourly variation of CV for a single day, ranging from 2000 Gcal to 2300 Gcal. However, mixed gas property depends upon various other factors i.e., gas temperature, density, specific heat, and viscosity. Figure 5 shows the property variation of same flue gas with respect to temperature. Hence, variation in CV has been considered for the present model to achieve accurate prediction of heat transfer.

A complete combustion process of mixed gas with preheated air with a base value ratio namely a stoichiometric combustion, generates desired heat for reheating the stock. To achieve the optimum ratio considering the variation in CV for such a huge furnace with multiple zones is a key challenge for a steel plant. Kangvanskol et al. has described in his article that, for achieving a stoichiometric combustion is practically not possible due to the limitation of the air and fuel mixing, variation in CV and combustion time [16] [17] . Hence, optimum excess air $\lambda$ must be provided for the complete combustion of unburned fuel inside the furnace. The percentage of excess air can be measured based on following Eq: 2.

$\lambda =\frac{A{F}_{actual}}{A{F}_{stoic}}$ (2)

where, $A{F}_{actual}$ refers to actual air-fuel ratio and $A{F}_{stoic}$ refers to the base value ratio or stoichiometric air-fuel ratio. In industrial practice, input of excess air is controlled based on the measurement of online oxygen analyzer. It usually operates at the flue gas exit to obtain the actual volume percentage of oxygen in it and apparently maintained under 3 vol%. The variation in vol% of produced flue gas depends on the percentage of input excess air. Figure 6 shows a typical linear correlation in terms of vol% between combustion air (input air), excess air and flue gas. This means supply of excessive air generates high volume of flue gas, leading to more heat content. This heat is lost while the flue gas leaves the system, which basically leads to lower efficiency of furnace. There are other various disadvantages of additional excess air into the system, such as a) localized cooling of heated zone as well as stock, b) excess gas consumption during maintaining of air-fuel ratio, c) reduction in flame temperature, and d) more carbon footprint. In this present study, the input of excess air percentage has been optimized depending upon the varying CV of mixed gas and stoichiometric air-fuel ratio. A feedback model has been introduced for each zone of the furnace, which measures the difference of input air-fuel ratio with respect to stoichiometric ratio over varying CV for each and every instance. The output of feedback model controls the system in such a manner that both ratios should be nearer to each other. Figure 7 shows a complete algorithm of the above-mentioned feedback model. However, due to industrial environment and practical point of view, a relaxation of 5% - 10% in variation between two ratios has been incorporated into the model. This relaxation percentage also follows a comparison node where the relaxed percentage is decided upon the best time performance of furnace. The decision node controls the adjustment of input air-fuel ratio based on feedback of all the input and resulted nodes.

The produced heat due to combustion of fuel, undergoes to industrial process typically leaves the system as flue gas, which contains maximum percentage of heat Q_f. The remaining heat is transferred to the atmosphere as various losses like furnace wall losses or skin losses Q_s, opening losses during stock in and out (door opening) Q_d and cooling system losses (water is used as coolant in the skids/rolls/doors usually) Q_w [18] . The quantity of consumed heat Q_c by the stock can be estimated from the following equation Eq: 3.

$Q_c=m{C}_p\left(T_2-T_1\right)$ (3)

where, Q_c is the quantity of heat in kJ, m is the mass of the material in kg, C_p is the mean specific heat, T₁ and T₂ are the initial and final desired temperature of the charge. Similarly, rate of heat losses due to cooling system Q_w as well as rate of heat transfer from the walls or skins of the furnace Q_s can also be estimated from the equations Eq: 3 and Eq: 4 respectively. The radiative heat loss due to the door opening Q_d can be obtained with the help of total radiation factor chart [19] .

$Q_s=-k\cdot A\cdot \frac{\text{d}T}{\text{d}x}$ (4)

where, k is the thermal conductivity in watt/m-K, A is the area of the furnace walls in m² and dT/dx is the variation in temperature gradient with respect to wall thickness. According to the law of energy conservation, the total input heat H must be equal to the sum of consumed heat Q_c by the stock and the sum of various heat losses Eq: 5.

$H=Q_c+{\displaystyle {\sum }_{i=1}^n{Q}_s}+{\displaystyle {\sum }_{j=1}^p\left(Q_w+Q_d\right)}+Q_f$ (5)

where,

n: Number of furnace walls exposed to atmosphere.

p: Number of skids/rolls/doors

From the Eq: 5 it is obvious that to increase the efficiency of a reheating furnace, heat losses must be as minimum so that the maximum input heat can be utilized for heating the charged material. In the present study, it has been considered that the material of furnace wall and charging stock both are individually homogeneous and isotropic. Due to door opening at furnace entry as well as furnace exit, heat loss does not vary significantly while a slab enters the furnace or leaves the soaking zone. This is because of fixed door opening height. Note that subsection 2.1, where the furnace dimension and operation details has been described also contains detail of roll cooling system. The heat losses also take place due to the roll cooling where water is used as cooling medium. In this case ΔT has been calculated using Eq: 3 based on water inlet temperature (T₁) and outlet temperature (T₂). Here, C_p the specific heat of water and m is the mass flow rate of water. In general, Erosion of refractory lining on the outer surface of the rolls results in additional heat loss from the furnace. This can be evident from the pattern of ΔT.

Efficiency of recuperator ${\eta }_{recup}$ is an important feature which has a relation with thermal efficiency η_C of the reheating furnace. A higher ${\eta }_{recup}$ indicates higher heat recovery from the flue gas exit, which is typically used for preheating combustion air or input mixed gas or both [20] [21] . In the referenced article, authors have explained how the thermal efficiency η_C depends on enthalpy released by combustion, furnace ability to extract energy from combustion of air-fuel mix and recuperator efficiency ${\eta }_{recup}$. The volumetric thermal capacity $s\left(T\right)$ of flue gas and combustion air $a\left(T\right)$ can be measured from the Eq: 6 and Eq: 7.

$s\left(T\right)=V_{flue}\times {\rho }_{flue}\times C_{p\left(flue\right)}\times T$ (6)

where, $s\left(T\right)$ is the thermal capacity of flue gas at temperature T in KJ, $V_{flue}$ is the flue gas volume in m³, ${\rho }_{flue}$ is the flue gas density and $C_{p\left(flue\right)}$ is the specific heat of flue gas at same temperature.

$a\left(T\right)=V_{air}\times {\rho }_{air}\times C_{p\left(air\right)}\times T$ (7)

where, $a\left(T\right)$ is the thermal capacity of combustion air at temperature T in KJ, $V_{air}$ is the combustion air volume in m³, ${\rho }_{air}$ is the combustion air density and $C_{p\left(air\right)}$ is the specific heat of combustion air at same temperature. Using Eq:6 and Eq:7 the thermal efficiency ${\eta }_C$ of tunnel furnace and efficiency of each recuperator ${\eta }_{recup}$ has been estimated from Eq:8 and Eq:9 respectively.

${\eta }_C={\displaystyle {\sum }_{sec=1}^n\frac{{10}^6-\left({\theta }_1-T_{ambient}\right)\times s\left(T\right)+\left(T_{combair}-T_{ambient}\right)\times a\left(T\right)}{n\times {10}^6}\times 100\%}$ (8)

${\eta }_{recup}=\frac{a\left(T\right)\times \left(T_{combair}-T_{ambient}\right)}{s\left(T\right)\times V_{frac}\times \left({\theta }_1-{\theta }_2\right)}$ (9)

where, n is the number of sections inside the furnace, $T_{combair}$ and $T_{ambient}$ are the combustion air temperature and ambient temperature in ˚C, $V_{frac}$ is the volume fraction of flue gas $V_{flue}$ and combustion air $V_{air}$, ${\theta }_1$ and ${\theta }_2$ are the flue gas temperature before and after the recuperator respectively in ˚C. The overall heat loss in terms of percentage due to flue gas has been estimated from the following Eq:10.

$Q_f=100\%-{\eta }_C$ (10)

where, $Q_f$ heat loss due to flue gas in %. For estimating the real time furnace efficiency and heat losses, all the above equations have been integrated as additional node to the model. A parallel activity of model, during furnace runtime has been scheduled for each furnace and model output is visualized invariably to mitigate the abnormal behavior of furnace. It is worthy to mention another important aspect by Seong et al. [22] where authors have explained that high temperature corrosion on heat exchanger pipe of a recuperator is a very serious problem resulting in degradation of recuperator performance. This high temperature corrosion predominantly occurs due to oxidation, sulfidation and presence of molten salt. To improve the consistency of recuperator performance, the authors have suggested a Cr3C2-NiCr coating in carbide form, and Ni-45Cr-4Ti as an alloy coating for heat exchanger pipes of recuperator. The suggested coating has an excellent resistivity of corrosion at high temperature.