철강 공정의 일정계획: II. 환경 친화적 일정계획

이 동엽, 문 성득, 박 선원

한국과학기술원 화학공학과

Scheduling of Primary Steelmaking processes:

Part II. Environmentally Friendly Scheduling

Dong-Yup Lee, Sungdeuk Moon and Sunwon Park

Dept. of Chem. Eng., KAIST

1. Introduction

Steelmaking industry is known to be a highly energy and environment-intensive industry. Therefore, with the necessity of efficient scheduling of the process, environmental impacts have to be taken into account for a decision-making. In order to meet these two objectives, a systematic methodology is needed. In this study, the methodology to consider simultaneously environmental impacts and scheduling of primary steelmaking process is addressed.

2. Methodology

Environmental Impact Issues in Batch/Semicontinuous Plants

A key characteristic of batch plants is their inherent operational flexibility in utilizing available resources. For given resources over a long-term or short-term horizon, the individual company can maximize the total profit by efficient algorithms for production planning and operation scheduling. However, at the same time, among the available resources unit equipment or manufacturing facilities are potential candidates for waste generation. According to the sequence of unit operation and amount of a batch for each unit, the different amounts of emissions could be discharged. Also, although units have the same task for the operation, each unit could release different amounts and kinds of emissions, according to its size, type and cycle time. From this point of view, environmentally friendly sequences of processing tasks can exist. These environmental impacts caused by different sequences or amount of batch are considered in the scheduling stage. In addition, in order to quantify and evaluate environmental impacts a Life Cycle Assessment (LCA)[1] approach is used.

Multiobjective Optimization

In this study, a systematic methodology for incorporating environmental consideration in the scheduling of primary steelmaking processes is presented. The methodology embeds principles of LCA within a general multi-objective formulation for the scheduling of multipurpose batch plants.

The general mathematical problem, which involves continuous and discrete variables, to identify the Pareto solutions can be formulated as the multiobjective MILP problem[2] (P).

[eqn: &~~~~~~~~min f_1 (x, y) # & s.t. ~h(x,y)=0, ~g(x,y)<=0 # & ~~~~f_2 (x,y) <= epsilon _2 , DOTSLOW , f_n (x,y) <= epsilon _n # & ~~~~x IN X , y IN Y = LEFT { 0, 1 RIGHT }^m # & ~~~~epsilon_2 IN LEFT [ epsilon_2^lower , epsilon_2^upper RIGHT ] , DOTSLOW , epsilon_n IN LEFT [ epsilon_n^lower , epsilon_n^upper RIGHT ]]	(P)

where the parameter ranges [eqn: LEFT [ epsilon ^lower , epsilon^upper RIGHT ]] result from the optimization of each scalar objective separately. By changing the constrained level □, the Pareto points are generated.

3. Application to Steelmaking Processes

As shown in Fig. 1, two different steels, products A and B, are manufactured by treatment through LMF1 (RH type) and LMF2 (AP type), respectively. In addition, three different shapes, slabs, plate, and hot rolled coil for each product are produced finally. Scrap is generated while fitting a plate or a coil to suitable width and recycled to BOF. Also each unit discharges emissions such as SOx, NOx, CO, CO2, etc. when it is operated. This emission inventory is obtained by LCA. In this work, among the 7 air emissions and 16 water emissions presented in Table 1, 6 air emissions including CO, CO2, SOx, NOx, Dust, and Zn and 4 water emissions including Ni, Cd, Pb, and As are considered to quantify environmental impacts since other emissions are investigated to have less effects on environment via the screening LCA.

Table 1. Emissions inventory for the problem

Equipment	Air emissions	Water emissions	Solid emissions
BOF, LMF, CC	Zn, HCl, SOx, NOx, CO, CO2, Dust	COD, Zn++, Ni++, Cu++, Fe++ Pb++, As3++, Cd++, NH4+, Org, F-, CN-, Cl-, H+, P, C6H14	Scales, Sludge, Slag
RF, HPR	HCl, SOx, NOx, CO CO2, Dust	COD, Zn++, Ni++, Cu++, Fe++ Pb++, As3++, Cd++, NH4+, Org, F-, CN-, Cl-, H+, P, C6H14, S--	Scales
RF, HSM	HCl, SOx, NOx, CO CO2, Dust	COD, Zn++, Ni++, Cu++, Fe++ Pb++, As3++, Cd++, NH4+, Org, F-, CN-, Cl-, H+, P, C6H14, S--	Scales

On the basis of the scheduling model presented by Moon et al.[3], a novel multiobjective MILP model for the short-term scheduling of primary steelmaking process is proposed adding on environmental model obtained from LCA results. Here, CST95 method[4] is used to identify and quantify environmental impacts. In addition to the short-term scheduling model presented by Moon et al., the environmental model for the primary steelmaking process can be stated as follows:

Given:

(1) set of emissions such as SOx, NOx, CO2, etc., indexed l=1,...,L

(2) set of environmental impact criteria such as Human Toxicity, Global Warming, etc., indexed m=1,...,M

(3) environmental regulation

Minimize: the makespan (total processing time), MS,

Maximize: the profit, PR, and

Minimize: the environmental impact of m criteria, EIm

Environmental Regulation Constraints

[eqn: SUM from { i IN I} SUM from { k IN K} LEFT ( SUM from { j IN J_i} Va_ikj W_ijl +Vy_i,plate,k W_i,HPR,l +Vy_i,coil,k W_i,HSM,l RIGHT ) <= beta_l]	(1)

Eq. (1) expresses the total amount of waste for emission l is constrained by environmental regulation, □l.

Additional Objective 1: Maximization of Profit, PR =

[eqn: SUM from { i IN I} SUM from { s IN S_i} SUM from { k IN K} Vy_isk PRICE_is - SUM from { i IN I} SUM from { k IN K} SUM from { j = J_i - LEFT { HPR,HSM RIGHT } } Va_ikj OC_ij - SUM from { i IN I} SUM from { k IN K} SUM from { s IN S_i} SUM from { j = LEFT { HPR,HSM RIGHT } } Vy_isk OC_ij]	(2)

The shapes s, slabs, plates, and coils, of product i are considered as the final product to be delivered to customers. The first term of eq. (2) denotes the total sale price on the market and the other two terms are total operating costs.

Additional Objective 2: Minimization of Environmental Impacts, EI

[eqn: EI_m = SUM from { l IN L} SUM from { i IN I} SUM from { k IN K} CTF_ml LEFT ( SUM from { j IN J_i} Va_ikj W_ijl +Vy_i,plate,k W_i,HPR,l +Vy_i,coil,k W_i,HSM,l RIGHT )]	(3)

where l is emission inventory and m is environmental impact criteria such as Human toxicity, Ecotoxicity, etc.

The □-constraint method[2] is used in the present work to generate the Pareto set of the problem. The minimization of PR is selected as a primary objective function and is optimized while the other objective functions, i.e. the minimization of MS and the minimization of EI are converted into constraints Eqs. (4) and (5). And then the problem can be solved for multiple □-values to generate Pareto solutions.

[eqn: EI <= epsilon_1]	(4)

[eqn: MS <= epsilon_2]	(5)

Results

The three objectives, MS, EI and PR, are considered simultaneously. There are several categories for the assessment of environmental impacts. Here, among them human toxicity is considered as environmental impact criterion. In order to evaluate Human toxicity, CST95 is used. The reference substance for human toxicity is arbitrarily retained as the effect through inhalation of lead emitted to air (Pbair). The Pareto surface obtained by simultaneous consideration of three objectives are shown in Fig. 2. As shown in Fig. 2, we can see that the environmental impacts of the process becomes large in proportion to profit.

4. Conclusions

In this work, the methodology for scheduling of steelmaking processes considering environmental impacts is presented. Through LCA, environmental impacts for steelmaking processes are obtained and are embedded in a multiobjective formulation so as to investigate the effect of environmental impact on the scheduling of the processes. The analysis of optimization results shows that the environmental burden of the process becomes large in proportion to profit and we need to follow the operation schedule considering the environmental effects according to the environmental policy of companies. This work is expected to help a steelmaking company to operate the process environmentally friendly as well as efficiently.

References

[1] ISO/DIS 14040, "Environmental Management - Life Cycle Assessment Part 1: Principles and Framework", 1997.

[2] Lee, D.-Y., "Environmentally friendly scheduling for primary steelmaking processes", MS. dissertation, KAIST, 2000.

[3] Moon, S., Lee, D.-Y. and Park, S., "Mathematical Model for Scheduling of Primary Steelmaking Process", Korea-France Workshop at Cheju Island, Feb., 2000.

[4] Jolliet, O. and Crettaz, P., "Critical Surface-Time 95, a Life Cycle Assessment Methodology including fate and exposure", Swiss Federal Institute of Soil and Water Management, July, 1997.

Fig. 1. Aggregated environmental impact  assessment in primary steelmaking process

Fig. 2. Pateto surface for the problem.