Controlling Chemical composition in BOF (Steel making) using Kalman Filter

Welcome to the next edition of my newsletter.

During my college days the first time when I heard about the Kalman filter and how it can be made use of stuck me right at the moment. However at that point of time I did not have the experience nor the required infrastructure to proceed with it. But little did I know I had already made the foundation to work on a pet project using Kalman filter. I along with the esteemed professors made a model using the CFD/Matlab to simulate the complete process of a Basic Oxygen Furnace and Electric Arc Furnace. This model was used to determine and control the chemical composition of the steel. With this model we used to make a lot of analysis. The access to that particular software is still available for me which made this newsletter possible. This edition of my newsletter looks at how Kalman filter can be used to control the chemical composition in steel making. (The focus in this edition is Basic Oxygen Furnace)

What is Kalman Filter?

It is an algorithm used for estimating. The estimate is based on a number of measurements over a good period of time. It is predominantly used for estimating which involves noise. This filter tends to reduce/minimize these levels in order to achieve a near accurate measurements.

Key Concepts of Kalman Filter

I am not trying to explain this part here in order to fit my work within the maximum limit of linkedin newsletter. However there are many websites which explains this.

The Set Up

Important Reaction models in in Basic Oxygen Furnace

1)??? Carbon Oxidation- In both BOF and EAF processes, carbon oxidation is central because it reduces the carbon content in molten steel. The reaction can be expressed as: C+O2→CO+CO2

The rate of carbon oxidation depends on the oxygen flow rate and the temperature. The model for carbon concentration over time can be given by: Ck=Ck?1?rCO2?Δt

where rCO2=kC?f(O2,T) and

·? kC is the reaction rate constant for carbon oxidation,

·? f(O2,T) is a function that accounts for the oxygen flow rate and temperature dependence of the reaction.

Temperature Dependence: The rate constant kC follows the Arrhenius equation:

kC=AC?e?EC/RT

where

AC is the pre-exponential factor,

·? EC_CEC is the activation energy for carbon oxidation,

·? R is the gas constant,

·? T is the temperature.

2)??? Silicon Oxidation- Silicon in molten steel oxidizes to form silica, which joins the slag phase (Well, one of the first thing that is taught in steel making is the better the slag you make the better the steel it is!!!)

Si+O2→SiO2

The rate of silicon oxidation is:

Sik=Sik?1?rSiO2?Δt

where rSiO2=kSi?f(O2,T) with kSi as the silicon oxidation rate constant.

3)??? Sulphur Removal - Sulphur is removed from molten steel via slag-metal reactions, forming calcium sulphide: S+CaO→CaS+O2

the rate of sulphur removal depends on the slag composition and temperature:

Sk=S(k?1)?r(CaS)?Δt

where rCaS=kS?f(CaO,T) with kS as the sulphur removal rate constant, and f(CaO,T)f(CaO, T)f(CaO,T) represents the effect of flux addition and temperature on sulphur removal.

Constructing the State Transition Matrix:

The state vector xk represents the concentrations of elements like carbon, silicon, sulphur, etc., at each time step k:

Given the reaction rates above, we model the change in each element over time using the state transition matrix Fk:

xk=Fkx(k-1)+wk

where wk represents the process noise, accounting for uncertainties in reaction rates and external influences (e.g., additions of fluxes).

Observation Models

The observation model relates the measured variables (sensor data) to the state vector xk.

zk=HkXk+vk

where:

• zk is the sensor measurement vector (e.g., carbon and silicon concentrations),
• Hk is the observation matrix,
• vk is the measurement noise.

Step by Step

1)??? Initialize State and Covariances: At the start of the process, initialize the state vector x0 based on the known composition of inputs (e.g., molten iron in BOF,) and set initial values for P0, Q, and R.

2)??? Monitor Process and Update in Real-Time:

• During oxygen blowing (BOF)), the Kalman Filter continuously predicts and updates the composition of key elements.
• Sensor data (e.g., carbon from off-gas analysis, temperature from thermocouples) is fed into the Kalman Filter, which corrects predictions based on actual measurements

For this analysis purposes, the CFD model takes into account through a feedback loop mechanism

?3)??? Control Adjustments:

• Oxygen Flow: If carbon levels deviate from the target, the control system can adjust the oxygen flow rate to correct the carbon content.
• Alloy Additions: When the estimated concentrations of alloying elements (e.g., chromium, nickel in EAF) are low, the control system can time alloy additions to achieve the desired steel grade.
• Flux Additions: Based on sulphur and phosphorus estimates, fluxes like lime or dolomite can be added to the slag to enhance impurity removal.

4)??? Feedback - The real-time estimates of the Kalman Filter can be displayed on a control panel, allowing operators to monitor composition trends and make additional manual adjustments if needed.

Final Output and Benefits

By continuously refining the estimates, the Kalman Filter:

• Improves accuracy of final steel composition: Ensuring tighter adherence to desired alloy specifications.
• Optimizes resource usage: Reduces excessive oxygen flow, fluxes, and alloy additions, resulting in cost savings.
• Enhances process stability and efficiency: Minimizes manual interventions, reduces variability in steel quality, and shortens process cycle times.

Based on the BOF model that was developed (CFD) the comparisons were made with and without Kalman filter. This clearly suggested Kalman filter helps in better composition control.

Happy to discuss and learn!

And, to all my friends back in India, This year, aim for zero defects in happiness and maximum tensile strength in patience. May your bonding with family be as tough as a well-welded joint, and your joy corrosion-resistant! Here's to a shining, stress-free, all-conquering Diwali!

Wishing you a festival filled with resilience, laughter, and high yield strength! "HAPPY DIWALI"