exploring the design set points of refining operation … · control the levels of sulfur and...

1 Copyright © 2015 by ASME

Proceedings of IDETC 2015 International Design Engineering Technical Conferences &

Computers and Information in Engineering Conference August 2-5, 2015, Boston, Massachusetts, USA

DETC2015-46265

EXPLORING THE DESIGN SET POINTS OF REFINING OPERATION IN LADLE FOR COST EFFECTIVE DESULFURIZATION AND INCLUSION REMOVAL

Rishabh Shukla Tata Consultancy Services, Pune, India

Ravikiran Anapagaddi* Tata Consultancy Services, Pune, India

Amarendra K. Singh

Department of Materials Science and Engineering Indian Institute of Technology, Kanpur, U.P., India

Jitesh H. Panchal School of Mechanical Engineering

Purdue University, West Lafayette, Indiana, USA

Janet K. Allen The Systems Realization Laboratory @ OU

The University of Oklahoma, Norman, OK, USA

Farrokh Mistree The Systems Realization Laboratory @ OU

The University of Oklahoma, Norman, OK, USA

ABSTRACT This paper is motivated by a need identified by steel makers, namely, the need to produce steel products with new and often more stringent set of specifications and enhanced performances (such as fatigue life and corrosion behavior) using existing equipment cost-effectively. Manufacturing a steel product involves series of unit operations, each having a significant bearing on the properties of the end product. This paper focuses on studying the effect of one such unit operation, namely, ladle refining. The performance like corrosion behavior and fatigue life and properties of advanced high strength steel are greatly influenced by its cleanliness and by maintaining composition within specified bounds. Cleanliness of steel is assessed in terms of the count and nature of inclusions present and the levels of tramp elements such as sulfur, phosphorus and total oxygen present in the liquid steel. The desired composition is maintained with respect to alloying elements (Ni, Cr, Mn, etc.) that are added to impart certain properties to the steel. The ladle furnace is one of the key unit operations for carrying out deoxidation and desulfurization to maintain the levels of oxygen and sulfur within a tolerable limit. Deoxidation reaction during refining lead to formation of a number of which are deleterious in nature and should be removed. The effectiveness of the ladle operation is thus influenced by conflicting goals such as inclusion removal efficiency, desulfurization and the cost of refining.

George Box is reputed to have observed that all models are wrong and some are useful. In keeping with George Box’s observation we suggest that our challenge is to determine the set points for the ladle unit operation using computational models that at best capture the essence of reality but not reality itself. Therefore, the need is to find solutions that are relatively insensitive to the inherent uncertainties embodied in the computational model while satisficing the conflicting goals. In this paper we present a method for visualizing and exploring the solution space using the compromise Decision Support Problem (cDSP) as a decision model. We illustrate the efficacy of our method, for use by steel producers, by determining the set points for a ladle, in an industrial setting.

*Currently, Grace Davison Chemical India Pvt. Ltd., Chennai, India. Keywords: Ladle refining, response surface models, compromise Decision Support Problem, ternary plots NOMENCLATURE

X1 Initial Temperature , K X2 Refining Time, min X3 Holding Duration, min X4 Teeming Duration, min X5 Start time of purging, % X6 End time of purging, %


X7 Higher level of purging, Nl/min X8 Lower level of purging, % X9 First arcing intensity, MW X10 Second arcing intensity, MW X11 Start first arcing, % X12 Start second arcing, % X13 Duration first arcing, % X14 Duration second arcing, % n Inclusion count r Size of inclusion, micron a Characteristics of Inclusion Distribution b Characteristics of Inclusion Distribution Ɛ Stirring Density M Weight of Steel, tonnes V Steel Flow Rate, m3/s H Ladle Height, m Po Pressure on top surface, atm Ks Rate constant for desulfurization reaction, s-1 di

+, di- Deviation Variables

Z Deviation Function Tout Steel Out Temperature, K Cost Cost of Refining, $/tonne Costmax Maximum Refining Cost, $/tonne S Sulfur Content, ppm SMax Maximum Sulfur Content, ppm Ƞ Inclusion Removal Efficiency, % ȠTarget Target Inclusion Removal Efficiency, % Wi Weights on Each Goal wS Weight on Sulfur Goal wC Weight on Cost Goal wE Weight on Inclusion Removal Efficiency

Goal

1. FRAME OF REFERENCE Demand for high quality and cost-effective steel is increasing so as to meet the requirements of industries and overcome the challenges posed by other advanced materials. Steel producers are striving for cost effective steel production with desired properties and performance requirements such as corrosion behavior, spring back and fatigue life. The performance and properties of advanced high strength steel are greatly influenced by its cleanliness and composition. Cleanliness of steel is assessed in terms of the count and nature of inclusions present, and the level of tramp elements. The precision in maintaining the desired composition with respect to alloying elements greatly influences the properties of steel. Ladle furnace proves to be one of the key operations for meeting these objectives of composition and controlling levels of tramp elements. Desulfurization and deoxidation occurs during refining to control the levels of sulfur and oxygen within tolerable limits. Deoxidation leads to formation of inclusion of different types, size and shape that are deleterious in nature and therefore should be removed. The requirement thus is to ensure careful control of individual process parameters of each unit process involved in steel making [1].

Efforts are going on to develop a platform based on integrated systems engineering approach [2-3] which will make it possible to address such complex problems. The idea is to (a)

reduce time, cost and effort incurred in development of new materials and their manufacturing processes and (b) facilitating attainment of suitable end properties and performance specification of the products (corrosion behavior, fatigue life, spring back etc.)

Steel manufacturing comprises of a number of processing steps such as ladle refining, tundish processing, continuous casting, rolling, heat treatment etc., which requires attention and proper control. Among these, ladle refining is a crucial step as it facilitates the attainment of proper composition and inclusion level in the liquid steel, which prevents the formation of cracks or defects during further downstream processing and ensuring good quality in the final product.

George Box [4] is reputed to have observed that all models are wrong and some are useful. In keeping with George Box’s observation we suggest that our challenge is to determine the set points for the ladle unit operation using computational models that at best capture the essence of reality but not reality itself. Therefore, there is a need to find solutions that are relatively insensitive to the inherent uncertainties embodied in the computational model while satisficing the conflicting goals.

In this paper we present a method for visualizing and exploring the process design space using the compromise Decision Support Problem (cDSP) construct [5-6]. We describe the exploration of the process design space for the crucial ladle unit operation. Lumped models are used to develop response surface models (RSM) for critical output parameters such as cost, inclusion distribution and output temperature as a function of different process design variables. These RSMs are used to instantiate the cDSP to explore the design space bounded by constraints and limits for various design variables including arcing duration and intensity, purging duration and intensity, holding and teeming time. The cDSP is exercised for different scenarios. The numerical results so obtained are illustrated as ternary plots. These plots are then used to identify the feasible process design space.

The paper is organized as follows. In Section 2 we briefly cover the state of art of ladle refining and provide a glimpse of the relevant work carried out by other researchers. The targeted problem and solution strategy is presented in Section 3. Details of computational analysis models and the associated response surface models are provided in Section 4. The mathematical formulation of the cDSP is discussed in Section 5. The efficacy of ternary plots in process design exploration is discussed in Section 6. The key findings along with closing comments are included in Section 7.

2. LADLE REFINING – STATE OF THE ART The process of ladle refining is very complex and crucial for the production of clean steel. The steel from basic oxygen furnace (BOF) or electric arc furnace (EAF) is tapped into the ladle where a number of operations are carried out to meet the compositional and cleanliness requirements. Alloying and slag forming additives are added to ensure that required composition is met. Desulfurization takes place in ladle and the sulfur content is brought down to the required level. To facilitate sulfur removal, argon purging is done which enhances the kinetics of desulfurization at the slag-metal interface. There is


continuous heat loss from ladle and solid additives are added, which result in heat loss/gain from the steel melt. Therefore, arcing is carried out at regular time intervals to maintain the heat content in steel required for subsequent casting. Apart from maintaining superheat, compositional requirements and facilitating adequate deoxidation and sulfur removal, ladle plays an important role in maintaining the cleanliness of steel. The incoming steel from BOF/EAF consists of inclusions of different sizes, shapes and morphologies. New exogenous and endogenous inclusions (endogenous inclusions are formed as a result of deoxidation) are formed during ladle processing. These inclusions need to be brought down to a lower level so as to ensure that no problem is faced during downstream processing of steel and the performance of final products is not affected, which is successfully achieved in ladle.

As mentioned earlier, the effectiveness of ladle refining is reckoned using parameters such as total oxygen level and inclusion removal efficiency, desulfurization and the cost of refining. Desulfurization is affected by argon purging rate [7], which in turn increases the cost of refining. Inclusion removal is dependent on the operating temperature, holding and teeming duration. Higher holding and teeming duration result in higher inclusion removal but also affect the cost and superheat requirements. Therefore, these parameters are selected on the basis of compromise between all the requirements. Higher intensity of argon purging increases the slag/steel interfacial area and thus facilitates sulfur removal [8]. But, the increased level of purging might lead to slag eye opening, resulting in oxygen pick up and thereby formation of inclusions, which is deleterious for steel. We observe that the requirements to which a ladle is subjected are conflicting in nature, and there is a need to model the process so as to design the process leading to a satisficing solution.

3. PROBLEM DESCRIPTION AND SOLUTION STRATEGY

Our aim is to predict a set of processing variables during ladle refining in order to find a satisficing solution that would meet the conflicting requirements of inclusion removal, desulfurization/deoxidation and cost of refining. The process design variables considered in the present study are temperature of steel, purging intensity and duration, arcing intensity and duration, holding and teeming time. Cost, final sulfur content and inclusion removal should be in agreement with the target specified (the target formulation is presented later). Additionally, following constraints must be satisfied, which have been identified based on experience and from literature [8-9]. 1. Arcing is done after the addition of deoxidizers, slag

additives and ferro-alloys and other alloying elements to supply additional heat needed for melting the added solid. Arcing power should be higher initially when higher amount of additions are made and less towards the end of the operation when batch with lower amount of additives are added.

2. At the end of the ladle operation the required amount of desulfurization and deoxidation must have occurred so that

the final sulfur and oxygen content in steel meets the requirements.

3. Total time of purging must be more than 80% of the total ladle operating time.

4. Arcing should not be continuously done for 12-15 minutes. To meet the requirement of minimizing cost, maximizing

inclusion removal and attaining suitable desulfurization along with satisfying a set of constraints, a mathematical construct capable of handling multiple objectives and constraints is required. The cDSP construct is used to serve the purpose. Chemistry control model based on mass balance approach is used to predict the amount of slag and alloying additives to be added. Lumped models are used to develop response surface models for different goals and constraints as a function of design variables. These RSMs are then linked with cDSP construct to develop an optimization framework which is used to explore the design space of ladle refining and to predict the operating parameters to meet the requirements of inclusion removal, cost and desulfurization. The solution strategy is explained in Figure 1.

FIGURE 1 SOLUTION STRATEGY

4. MODELS 4.1. Mathematical Models

Mathematical models have been developed to model various phenomena taking place during ladle refining.

(a) Thermal Model: Maintaining desired amount of superheat

in the steel melt requires tracking heat loss and heat gain during the process of refining. Heat gain occurs due to addition of some alloying additives such as Al that results in occurrence of deoxidation that are exothermic reactions. Heat loss occurs due to various reasons such as alloying additions, convective and radiative loss, and heat loss during purging, holding and teeming. Exothermic reactions occurring in ladle and supplied arcing serves as the source of heat. The thermal model is used for the prediction of temperature considering the effect of series of aforesaid phenomena [10].

(b) Chemistry control model: Steel poured in ladle has some composition and is accompanied by carry over slag (COS) of a particular composition. The aim of ladle refining is to produce steel melt of a desired composition with respect to


alloying and tramp elements and to achieve this, alloying additives are added. Additives get dissolved in steel and reactions occur between slag and steel to meet the desired composition. Desulfurization and deoxidation occurs during the refining that results in maintaining the level of sulfur and oxygen within tolerable limits. These reactions occur at slag/steel interface and to facilitate slag/steel reaction, we need to maintain basicity and fluidity level of slag [11], which in turn depends on the composition of slag. Slag additives are added to maintain the target composition of slag. The chemistry model makes use of simple mass balance approach [12] to predict the amount of slag and alloying additions required. Empirical equations have been used to bring in the effects of oxygen and nitrogen pick up and incorporate the kinetics of slag metal reactions such as desulfurization while predicting the steel chemistry.

(c) Inclusion evolution model: Steel coming to ladle from basic oxygen furnace or electric arc furnace has certain level of inclusions. Inclusions are also formed during refining, owing to refractory erosion and deoxidation reactions, which add to the inclusion level in steel. Equation 1 is used to represent the inclusion distribution of steel in ladle and thereby we have used parameters a and b for characterizing inclusion distribution in our model.

(1)

where, n = inclusion count, and r = size of inclusion (in microns)

These inclusions are deleterious and create challenges during the subsequent downstream processing. Also, performance such as corrosion behaviour and fatigue life of many steel products are dependent on the type, size and distribution of inclusions. Thus, it becomes essential to carry out refining so as to restrict the level of inclusions within a tolerable limit. A population balance based method is used to study the behaviour of inclusions during ladle refining [13] and to study the effect of process design parameters on inclusion removal efficiency. For the current problem, the coefficients used in the inclusion evolution model are with respect to Al2O3 and for spherical inclusions. These coefficients can be tuned in the future to include inclusions of other types and shapes in our model.

Ladle refining is a transient process and is highly complex is nature. Certain assumptions have been made in developing these models to simplify the process. These assumptions are listed below: 1. Temperature is considered to be uniform throughout ladle,

i.e., no spatial variation of temperature is considered in the melt. This assumption is made because argon purging is continuously done (not when arcing is going on) which homogenizes the liquid steel.

2. Chemistry predictions are based on the mass balance approach. The additives get partitioned between slag and steel. This partition greatly influences the additions that have to be made for meeting desired steel and slag composition. The partition coefficient depends on the chemistry of steel and slag, and the temperature of steel. It varies throughout the refining process. In the current

chemistry model, we have considered average partition coefficient values for each element. The average partition coefficients have been calculated using the available data on average BOF slag chemistry, average LF out chemistry and additions made during ladle refining. The chemistry model will be improved in the future by incorporation of transient partition coefficients to further enhance the predictions of chemistry model.

4.2. Response Surface Models (RSM) Response surface models have been developed to represent the output parameters of ladle as a function of the process design variables. The ranges of process design variables for which simplified models are developed are provided in Table 1.

TABLE 1 RANGES OF PROCESS DESIGN VARIABLES

Sr. No.

Variables Range

1 X1, Initial Temperature 1830-1880 K 2 X2, Refining Time 25-75 min 3 X3, Holding Duration 40-70 min 4 X4, Teeming Duration 40-70 min 5 X5, Start time of purging 1-12.5 (% of X2 ) 6 X6, End time of purging 87.5-99(% of X2 ) 7 X7, Higher level of purging 200-500 Nl/min 8 X8, Lower level of purging 30-50 (% of X7) 9 X9, First arcing intensity 10-20 MW 10 X10, Second arcing intensity 5-10MW 11 X11, Start first arcing 5-15 (% of X2 ) 12 X12, Start second arcing 70-80 (% of X2 ) 13 X13, Duration first arcing 10-20 (% of X2 ) 14 X14, Duration second arcing 10-20 (% of X2 )

The response surface models (RSMs) can be developed in numerous ways. We have used the second-order polynomial function in Equation 2 to represent the responses generated from the thermal and inclusion evolution model, as functions of the process design variables. The strategy adopted for development of response surface models is depicted in Figure 2.

FIGURE 2 RESPONSE SURFACE MODEL DEVELOPMENT STRATEGY


∑ ∑∑ ∑ (2)

Full factorials have been used to capture the complete

information of ladle refining. Developed models have been used to generate data required for formulation and validation of the response surface models. Regression analysis of the generated data is carried out to represent each response as a function of the involved processing variables. Statistical tests such as F-test and t-test have been carried out for sensitivity analysis, thereby discarding the input parameters which have least effect on the output function. The response surface equations developed are summarized in Table 2. The output values predicted by the RSMs have been compared against the same obtained using the detailed models, and a good agreement between two is observed. Comparison is shown in Figures 3 and 4, and the R2 values are reported in Table 2. Further details of constructing response surface models and design of experiments are described in Reference [14].

TABLE 2 RESPONSE SURFACE MODELS

R2 Response Equations

0.98 ∆

19.39 0.013 0.0640.57 0.57 0.020.009 2.39 10 7.6510

0.99

21.94 0.002 0.0060.0018 0.0024 0.030.023 5.36 100.0003 0.46 6.72

0.995 0.0008

0.977

0.83 0.83 0.0006

0.0006

Where,

/100

/100

/100

/100

100 /

100 /

FIGURE 3 COMPARISON OF TEMPERATURE PREDICTION

FIGURE 4 COMPARISON OF COST PREDICTION

5. THE CDSP FOR LADLE REFINING In this section we describe the mathematical formulation of the compromise DSP for ladle refining. The design of ladle also has a significant influence on the efficiency of ladle refining. But, once a plant is set up, design of equipment (ladle in this case) is not changed as this is very costly. For this reason, we are not exploring ladle design parameters and have considered a fixed value for the same. The values for these have been determined based on literature review and experience. Given the equipment setup cannot be changed, once the plant is up and running, an important consideration is how to carry out refining operation (or any other unit operation) in a way to tackle the need of changed set of requirements. For example, suppose the steel mill is producing a steel product within specified limit of inclusion and sulfur content. Now, consider a scenario where manufacturers, as per customer requirements, want to produce the same steel product with lower or higher tolerable limit of inclusions and sulfur content. The unit operation where inclusions and sulfur is controlled is ladle refining. The task is to change the operating conditions of the unit operation so as to meet the changed requirements. However, the equipment design is fixed in an industry which means that the process designer only has the flexibility to modify the process design variables and achieve the task. To address the above stated example (which is one such possibility), we talk about


exploration of the solution space using cDSP construct and identify the design set points that will lead to meeting the desired requirement specs. To replicate an industrial scenario, we have considered fixed equipment parameters and explore the process design variables in our formulation. Process design variables considered and their ranges are given in Table 1. Next, we explain the reason for selecting these variables.

Ladle refining involves the addition of alloying and slag additives, which is required for meeting target steel and slag composition. Industrial practice is to add these additives in batches as there is lot of uncertainty surrounding weight and composition of COS and weight of steel melt. In the current formulation, we consider the predicted additives to be added in two batches. 70% of predicted amount is added in the first batch which is towards start of refining and remaining amount is added in the second batch during later stages of refining [15]. Additions get dissolved in around 3 minutes and result in loss of heat, so additions are accompanied by arcing to compensate for the heat loss. Arcing requirement will be less if additions are less and vice-versa. For this reason, we have considered two levels of arcing with varying intensity, one towards the beginning and other during the later stages of refining as a process design variable in our formulation. Purging is done to facilitate sulfur removal and homogenization of bath. The intensity of purging is kept low when arcing is done to prevent excess heat loss. For this reason, we have considered two intensity levels for argon purging in our formulation. Refining time is important to ensure sufficient time is available for desulfurization, deoxidation reactions and inclusion removal. Holding and teeming time is considered as a variable in our formulation because these parameters affect the superheat and inclusion removal and also have a significant bearing on the productivity of a plant. An important point to mention here is that this is one way of formulating the problem that has been described above. We can adopt a different formulation strategy and explore the process accordingly. For example, we can consider addition to be made in three batches.

Mathematical formulation of the cDSP also requires specification of goals and constraints involved in the system that is being studied. The performance of the ladle is assessed in terms of inclusion removal efficiency, desulfurization and cost of refining. These parameters have been considered as goals in the formulation (Equations 15-17). Response surface models have been used for calculation of inclusion removal efficiency and cost of refining. An empirical model (Equation 3-5) has been used for calculation of desulfurization. This gives a relation for desulfurization rate constant as a function of purging rate [8].

14.231 log 1

1.48

(3)

. , if <60 (4)

. , if >80 (5) where, k= 8*10-6

Processing constraints that need to be satisfied are provided in Equations 6-14. The constraints are based on what is available in the published literature and from industrial practice communicated to the authors by steel operators. All the constraints must be satisfied to obtain a feasible solution. The aim here is to explore the process design space and identify set points of ladle refining to meet the specified requirements on cost, sulfur content and inclusion control. The important thing to keep in mind is that equipment design is kept fixed and exploration is done only for the available range of process design variables. The reason for choosing a fixed equipment and need of exploration has been established above. Next, we discuss the mathematical form of the cDSP. Given Fixed design parameters: Ladle Height = 3.97 m, Ladle

Top Outer Diameter = 3.476 m, Ladle Top Inner Diameter = 3.476 m

Number of refractory layers, thickness, conductivity and density is fixed

= 100

CostMax= 150, = 25 ppm (parts per million): Maximum value of cost and sulfur is decided based on the maximum value attained in the entire space

Response surface models and range of process design variables (Table 1). The value of these variables have been normalized between 0-1 and then used in the cDSP formulation.

Number of design variables = 14, Goals = 3, Constraints = 10

Find The value of process design variables: Xi,i= 1,…,14; the

details of these variables have been provided in Table 1.

The value of deviation variables: di ,di‐,i= 1,….,3 Satisfy Bounds on process design variables:

0 ≤ Xi ≤ 1, i=1,….,14 (Normalized value based on range provided in Table 1)

Process Design Constraints:

Minimum Temperature (K): 1820 0 (6)

Maximum Temperature (K): 1860 0 (7)

Minimum Cost ($/tonne): 50 0 (8)

Maximum Cost ($/tonne): 350 0 (9)

Arcing Intensity(MW): 0.8 0(10)

Lower Purging Restriction (Nl/min) 200 0.01

0 (11)


Total Purging Duration (% of X2):

80 0 (12)

First Arcing Limit (min):

12 0.01 0 (13)

Second Arcing Limit (min):

12 0.01 0 (14)

Goals:

Goal on Minimization of Cost, G1:

⁄ 0 (15)

; here = 0.

Goal on Minimization of Sulfur, G2:

⁄ 0 (16)

; here = 0.

Goal on Maximization of Efficiency, G3:

⁄ 1 (17)

; here = 0.

Minimize In the compromise DSP, the aim is to minimize the under or over achievement in a goal from the target. This is achieved by minimizing the deviation function which is constructed using Archimedean approach as shown below. The deviation function (Z) provides an indication of the extent to which a specific goal has been achieved.

, ; 1 , 0 1, . . ,3

(18) Here, di ,di‐are the deviation variables. di

+ is a measure of the over achievement and di

- is a measure of the under achievement in a specific goal. The objective of the cDSP formulation is to minimize the deviation variables, which in turn implies that achieved value of a goal is closer to its specified target value.

We have talked about the conflicting goals involved in ladle refining, established the need of process design exploration and have explained the cDSP formulation being used to address the problem. In next section, we exercise different scenarios varying the weights assigned to each goal in the cDSP formulation. Numerical results of these scenarios are then used to construct ternary plots. We have illustrated how these plots can be used by a process designer to explore the design space and identify the set points that will result in meeting the specified requirements.

6. RESULTS AND DISCUSSION We have exercised different scenarios using cDSP. In each

scenario, different weights are assigned to each goal as per their relative importance. Details of some of the exercised scenarios are provided in Table 3.

Scenario 1, 2 and 3 represents a case where the process designer is interested in meeting target with respect to one of the goal, i.e., any one of sulfur, cost or efficiency. Scenario 4 represents a case where the process designer wants to meet the sulfur and cost requirement. The goal on inclusion efficiency is not so critical so no weight is assigned to same. Scenarios 5 and 6 are representative of a case where the goals on cost and sulfur are less critical. All the goals are equally important in Scenario 7, so equal weights are assigned to each of them. Numerical results obtained after exercising these scenarios include predicted design set points and achieved value of each goal. The information, thus obtained, is used to construct ternary plots (explained later). We believe that ternary plots are helpful in exploring the designs space. Consider a case where a process designer knows about his/her preference structure. In such a case, he/she needs to assign the weights to each goal (cost, sulfur and efficiency) and run the cDSP. The set points, thus predicted, are the values of the process design variables at which refining must be carried out to meet the requirements on cost, sulfur removal and inclusion removal efficiency. However, if the process designer is not sure about his/her preference structure i.e., what weights should be assigned to each goal in the cDSP formulation. The first task in this case is to identify the weights to be assigned as per the requirements of the process. Ternary plots are useful to provide an answer to this question. The details of constructing ternary plots are provided in Reference [16-18]. Next, we discuss how to use ternary plots (constructed using information available from exercising various scenarios) for identifying the weights to be assigned, thereby predicting the set points for ladle refining.

TABLE 3 SCENARIOS EXERCISED Scenarios wC wS wE

1 1 0 0 2 0 0 1 3 0 1 0 4 0.5 0.5 0 5 0 0.5 0.5 6 0.5 0 0.5 7 0.33 0.33 0.33

Ternary Plots Different weights are assigned to each goal in the cDSP formulation (Section 5) and model is executed for different scenarios (Table 3). The obtained information is collated to construct ternary plots for each goal. Maximum and minimum achieved value of each goal in the entire scenario is provided in Table 4. Figure 5-7 are the ternary plots for cost, sulfur content and inclusion removal efficiency respectively. The axes represent weights assigned to each goal and color code represents achieved value of corresponding goal for which ternary plot is constructed.


FIGURE 5 TERNARY PLOT FOR COST

FIGURE 6 TERNARY PLOT FOR SULFUR

FIGURE 7 TERNARY PLOT FOR INCLUSION REMOVAL EFFICIENCY

TABLE 4 MAXIMUM AND MINIMUM ACHIEVED VALUES OF

GOALS

Goal Minimum Value Maximum Value Cost ($/tonne) 90 99 Sulfur (ppm) 10 20

Inclusion Removal

Efficiency (%) 80 86

Next, we discuss how the ternary plots are used to identify the weights to be assigned and thereby predict the design set points. Let us consider the following scenarios: 1. Process designer is interested in designing a process so as

to have cost of refining equal to or less than 50 % of the maximum achieved value (Table 4). The region of interest is identified in the ternary plot and is shown with a green dashed line (see Figure 5). The designer needs to select weights for each goal from this region and run the cDSP model. The design set points so predicted will lead to having cost of refining as less than50 % of maximum possible value.

2. Process designer is interested in designing a process so as to have final sulfur content equal to or less than 30 % of the maximum achieved value (Table 4). The region of interest is identified in the ternary plot and is shown with a yellow dashed line (see Figure 6).Weights have to be decided as per this region and same should be used to run the cDSP model. The predicted design set points is the solution of interest at which ladle refining must be carried out to have required level of sulfur in the steel melt.

3. The interest of the process designer is to carry out ladle refining to facilitate inclusion removal and have efficiency equal to or more than 80 % of the maximum achieved value (Table 4). The region of interest is marked in the ternary plot of

inclusion removal efficiency and is shown with a white dashed line (Figure 7). First we select any point in this region and identify the weights for each goal (done by drawing perpendicular to each axes), which is then used in the cDSP model and executed. The predicted design set points is the solution of interest at which ladle refining must be carried out to have required level of inclusions in the steel melt.

The above discussions illustrate how to identify weights and thereby predicting the design set points in order to meet specific requirement of ladle refining. Now, let us consider a scenario where a designer wants to operate refining in a way to meet all the aforesaid three requirements. Next, we discuss using ternary plots to identify if a solution is possible or not. If yes, what are the values of process design variables at which refining must be carried out to achieve the requirements.

The region of interest (identified above in points 1, 2, 3) is superimposed in a single ternary plot (see Figure 8).


FIGURE 8 SUPERIMPOSED TERNARY PLOT Observations with respect to achievement of goals are discussed below: 1. Goal G2 and G3: We see in Figure 8 that there is an overlap

between the feasibility region of sulfur and efficiency, which means the requirements on sulfur content and inclusion removal efficiency can be simultaneously met. The region is shown in ternary plot which is the area enclosed within the white dashed line in the direction of arrow. We have to select a set of weights from this region and run the model, which in turn will give us the design set points at which refining must be carried out to meet sulfur and inclusion requirements.

2. Goal G1 and G2: We see in Figure 8 that there is a small overlap area between the feasibility region sulfur and cost, which means we can have the desired sulfur content in liquid steel within specified cost of refining. The region is shown in ternary plot which is the area enclosed between yellow and green dashed line and we have two small feasibility areas, one along the left edge and other is in the bottom right corner. We have to select a set of weights from this region and run the model, which in turn will give us the design set points at which refining must be carried out to facilitate cost effective sulfur removal.

3. Goal G2 and G3: There is no overlap between the feasibility region of cost and efficiency. This implies that we cannot have inclusion removal efficiency equal to or more than 80 %, and incur less than 50 % for cost of refining.

Also, there is no possibility of achieving all the three requirements simultaneously (see Figure 8, no area of overlap within all three feasibility regions). This is important information for a process designer and clearly alludes to the efficacy of the method, namely, making it possible for a process designer to look at ways to increase the solution space that includes

1. modifying the design space by relaxing the constraints and bounds on the system variables, and

2. modifying the aspiration space by modifying the goals

and then exercising the cDSP again. 7. CLOSING REMARKS In this paper, we have described a method to visualize and explore the solution space of one unit operation in a steel-making process, namely, the ladle.. The trade-offs between achievement of sulfur, inclusion removal efficiency and cost of refining is demonstrated. It is shown that cost of refining increases in order to have lower sulfur content. The reason for this observation is the increase in argon purging requirements to facilitate sulfur removal. A number of useful observations with respect to operability of ladle refining can be drawn using the suggested framework. Our method involves exercising the cDSP for various scenarios, analyzing the results, modifying the design and aspiration spaces (if necessary) and iterating to a decision to implement or stop.

Our decision model (the cDSP) includes information on additives to be added, arcing strategy to be adopted, argon purging to be done and set points for refining, holding and teeming time to meet the specified requirements of ladle refining operation. The current trend in the industry is to identify this information solely on the basis of experience and operating practices. Our method, augments operating practice through prediction based on computational models that are anchored in physics of each phenomena thereby reducing the time and cost of determining the set points. Going forward, we aim to further improve the physics-based models in order to address more complexities and impose more realistic processing constraints which will help to improve upon the accuracy of the obtained solution.

We have used our method to explore the solution space associated with the tundish and the caster [16 and 17]. Work is underway to instantiate cDSPs for exploring the solution space for other unit operations of steel manufacturing, namely, reheating, rolling and annealing. Our aim, using an ICME based platform that is under development, is to simulate the entire steel product manufacturing chain, explore the solution space and determine the set points for various unit operations in the process chain thereby reducing the time and cost involved determining the set-points for the unit operations.

ACKNOWLEDGMENTS The authors thank TRDDC, Tata Consultancy Services, Pune for supporting this work. Janet Allen and Farrokh Mistree gratefully acknowledge financial support from the John and Mary Moore Chair and the L.A. Comp Chair at the University of Oklahoma. F. Mistree and J.K. Allen gratefully acknowledge support from NSF Grant CMMI 1258439.

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18. Shukla R., Kulkarni N., Gautham B. P., Singh A. K., Allen J. K., Panchal J. H., and Mistree F., 2015, “Design exploration of engineered materials, products and its associated manufacturing processes”, JOM, Vol. 67 (1), pp 94-107.

exploring the design set points of refining operation … · control the levels of sulfur and...

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