Plant-wide Optimal Byproduct Gas Distribution and Holder Level Control in the Iron and Steel Making Process

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1 Korean J. Chem. Eng., 20(3), (2003) Plan-wide Opimal Byproduc as Disribuion and Holder Level Conrol in he Iron and Seel Making Process Jeong Hwan Kim, Heui-Seok Yi* and Chonghun Han Deparmen of Chemical Engineering, *School of Environmenal Science and Engineering, Pohang Universiy of Science and Technology, San 31 Hyoja, Pohang, Kyungbuk , Korea (Received 18 July 2002 acceped 24 Sepember 2002) Absrac A new plan-wide muliperiod opimizaion approach is proposed for opimal byproduc gas disribuion o preven unfavorable byproduc gas emission and equipmen rip and simulaneously o maximize he efficiency of energy resource usage in he iron and seel making process. Compared wih he previous approach, he proposed approach finds he opimal rade off among conflicing objecives such as holder level conrol, minimizaion of oil consumpion and number of burner swiching, and he maximizaion of generaing elecriciy. To consider he differen fuel load change operaion according o he fuel ypes, boh ineger and coninuous variables are used. Case sudies were performed o verify he usefulness of he proposed approach, and he resuls show good performance in erms of he reduced number of burner swiching which leads o he reducion of oal cos and producing operaion-easy soluions. Key words: Plan-wide Opimizaion, Byproduc as, Holder Level Conrol, Opimal Disribuion, Iron and Seel Making Process INTRODUCTION Fig. 1. Simplified byproduc gas flow in he iron and seel making process. To whom correspondence should be addressed. chan@posech.ac.kr Energy cos consiues abou 20% of he oal operaion cos in he iron and seel making process. Thus efficien use of energy is very imporan. In he iron and seel making process, several ypes of energy sources such as byproduc gases, oil, elecriciy, and LN (Liquefied Naural as) are used. The byproduc gases are generaed as byproducs, and are used as imporan energy sources wihou paying addiional cos o purchase. However, here exis unbalances beween he amoun of he generaion and consumpion of he byproduc gases a ime scale, and byproduc gas holders serve as a buffer uni o solve emporal unbalances beween he generaion and consumpion of byproduc gases. Because of he limi on holder capaciy, emporal excess or shorages of byproduc gas happen. As shown in Fig. 1, he excess or shorage of byproduc gases can be adjused by changing he supply of byproduc gases from gas holders o power plan, where byproduc gases are used o generae process seam and elecriciy. In he power plan, each boiler has differen efficiencies. Therefore, he opimal operaion ha can preven, or a leas minimize, he loss of byproduc gases and efficien use of byproduc gases is very imporan and indispensable in he iron and seel making process. Alhough much research has been done on he opimizaion of iron and seel making processes, i is mainly on scheduling and producion planning problems, and lile is repored on he opimizaion of he byproduc gas supply and disribuion. Akimoo e al. [1991] proposed an MILP (Mixed Ineger Linear Programming) model for opimal byproduc gas supply in he iron and seel making process. The opimizaion model reflecs process consrains by assigning appropriae penaly funcions for he siuaion ha is no preferred such as excess or shorage of byproduc gases, oil usage, flucuaion of gas amoun in he holder, simulaneous changeover of fuels ec. In his model, oal amoun of fuel load change is deermined by opimizaion model, bu he disribuion of fuels o each boiler is no calculaed because no consideraion was given o he efficiencies of boilers and demands for seam and elecriciy. Fukuda e al. [1986] proposed an opimal energy disribuion conrol mehod for he seel works by energy demand forecasing and opimizaion. ARMAX (Auo Regressive Moving Average wih Exogenous variable) model was used for forecasing, and gradien descen mehod was used for opimizaion. Bemporad and Morari [1999] proposed a framework for modeling and conrolling he mixed logical dynamical sysems, and applied i o he gas sup- 429

2 430 J. H. Kim e al. ply sysem a he seel works. Sinha e al. [1995] used MILP o opimally allocae he resource for profi maximizaion, and significan amoun of benefi is repored by applying i o Taa Seel. Consideraion of he sarup and shudown cos in he opimizaion formulaion was inroduced in he opimizaion modeling. Hui and Naori [1996] presened a mixed ineger programming model for an indusrial uiliy sysem ha includes sarup and shudown coss o find more exac opimum soluions by inroducing equipmen sarup and shudown coss. Iyer and rossmann [1997, 1998] proposed he bilevel decomposiion mehod o solve he muliperiod opimizaion problem for uiliy plans and considered he swiching cos beween periods. Kim and Han [2001] proposed a heurisics combined dynamic programming approach o solve he muliperiod planning problem for a uiliy plan. Yi e al. [2000] also used his concep in planning problems. Lee e al. [2001] proposed an MILP model for scheduling of non-sequenial bach processes. Singh e al. [2000] proposed ime horizon based real ime opimizaion (RTO) approach for he gasoline blending process, which is similar o model predicive conrol (MPC). Blending horizon and sochasic model of disurbances were incorporaed ino he opimizaion model. In his paper, an improved model is proposed for solving opimal byproduc gas disribuion in he iron and seel making process where discree fuel load changes, penaly for sarup and shudown of he burner. Compared wih he previous approach, his research simulaneously opimizes he holder levels ha are iner-correlaed and byproduc gas disribuion of he supplied byproduc gases in erms of oal cos reducion. A case sudy was performed o verify he usefulness of he proposed approach. PROCESS DESCRIPTION As shown in Fig. 1, several ypes of byproduc gases such as Blas Furnace as (BF), Coke Oven as (CO), Lindz-Donawiz as (LD), and Corex Furnace as (CF) are produced as a byproduc in he iron and seel making process. The byproduc gases are primarily supplied o he seel making process, and some are supplied o he power plan. The paerns of he generaion of each byproduc gases are differen. Some of byproduc gases are generaed irregularly, and ohers wih a consan generaion paern and amoun. The consumpion of byproduc gases a he seel making process is performed according o he producion schedule, and here is lile flexibiliy o change i. Owing o he combinaion of limied capaciy of byproduc gas holders and irregular generaion of byproduc gases, excess or shorage of byproduc gases a holder occurs. This can resul in he holder booser rip or unfavorable byproduc gas emission o air, which is an economic loss. These unbalances are compensaed for by changing he supply of byproduc gases from each gas holder o he power plan by changing he rae of byproduc gas consumpions a each boiler. Byproduc gases supplied o boilers a he power plan generae seam o be used for generaing elecriciy and process seams. Oil is used when he byproduc gases are insufficien o supply for generaing he required amoun of elecriciy, bu i is no preferable because addiional fuel cos is required. Each boiler in he power plan has differen characerisics in capaciies, efficiencies, and available fuel ypes. Therefore, an opimal allocaion of byproduc gases considering he differen condiion of each boiler is required o maximize he efficiency of byproduc gas usage. The sable operaion of he boiler o avoid backfires or incomplee combusion from unsable operaion is also imporan. For he sable operaion of he boiler, frequen swiching of he burner such as urn-on or urn-off is no favorable. Opimum operaion in erms of byproduc gas supply sysem as a whole requires he following condiions. 1. The Holder level of each byproduc gas should be kep wihin he operaion range o avoid unfavorable byproduc gas emission and holder booser rip. 2. Minimum number of sarup/shudown of a boiler is desired. 3. Minimum amoun of oil consumpion is preferred. 4. Minimum flucuaion of holder level is preferred. 5. Efficien use of a boiler o produce more elecriciy considering efficiencies of boilers and urbines is required. 6. The supply of oal energy o each boiler o generae elecriciy should be larger han he required amoun of elecriciy demand o avoid paying high penaly o a power company. The opimizaion model resuling from considering various objecives becomes a muli-objecive programming model. Tradeoff among conflicing objecives exiss and he opimal radeoff should be found for he oal cos minimizaion. For example, o reduce he holder level deviaion from he normal operaion level, a large number of fuel load change is required, bu his is no preferable in erms of boiler operaion. Fig. 2 shows he holder level conrol by opimal fuel load change during he planning horizon. For he sysem where ypes of byproduc gas holders exis, fuel load change for each burner during he planning horizon is deermined o minimize he oal cos. MATHEMATICAL FORMULATION FOR OPTIMAL BYPRODUCT AS DISTRIBUTION Fig. 2. Holder level conrol by opimal fuel load change. May, 2003

3 Plan-wide Opimal Byproduc as Disribuion and Holder Level Conrol in he Iron and Seel Making Process 431 Objecive Funcion C Oil P NB P Oil F i, + w P HH S HH, + w P LL S LL, + w Min lim H S H, Oil 1i Ni 1,, Fi, P P + w L S L, + w P d+ S d+, + w P NB d S d, + w SW N i, 1 P NB + w 2s + ( j 2,, i + k 2,, i ) + w 3s + [ ( j 3,, i + k 3,, i )] P C elec ( P PD ) 1i 1 1 (1) Consrains F i F i, 1 for, F H i, + F Oil i, H Oil B Q i, for i, h r, + h e, 1 h min h h max for, h h C 1 F i, d * i seam seam ( H in,, i ) Cp F i, + Cp Oil Oil F i, F S i, H oui,, h h max S HH, S HH, for, 0 for, S HH, S HH, h h H S H, S H, for, 0 for, S H, S H, h min S LL, h S LL, S LL, for, 0 for, S LL, h L h S L, S L, for, 0 for, S L, S L, h h N d + d +, N i, + 1 N i, N i, N i N i + j 1,, i N i + + +, j 1,, i + j 2,, i + j 3,, i + j 2,, i, k 1,, i k 1,, i k 2,, i + j 3,, i + k 2,, i k 3,, i + for d +, d 0 for i, + k 3,, i for for, for, for, i, N i, N i, 1 SW + i, SW i, SW Oil+ Oil i, SW i, F min F i, ηi + SW i, SW i, for,, i,,, 0 for F max for i, 1i 1, for i,,, i (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) The objecive is o minimize he oal cos during he planning horizon, which is composed of fuel cos, various penaly coss, and seam producion benefi. Fuel cos is composed of oil consumpion cos and byproduc gas consumpion cos. Because byproduc gas does no require addiional purchasing cos, i has zero operaion cos. The penaly cos is imposed on he holder booser rip, unfavorable byproduc gas emission, frequen boiler burner on/off, simulaneous fuel load change in he same boiler, and deviaions from he normal operaion holder levels for each byproduc gas. The linear penaly funcion is used for he deviaion from he normal average operaion level for reduced compuaion ime. According o he relaive imporance among each cos funcion, he weigh for each cos funcion is differenly imposed. eneral ineger variables N i, are used o represen he number of burners used a each boilers, and binary variables j + 1,, i, j + 2,, i, j + 3,, i, k 1,, i, k 2,, i, k 3,, i are used o represen he muliple burner on and off a he same boiler. Because a raher large number of fuel load changes are required o adjus he byproduc gas holder level, discree amoun of fuel load change, burner level fuel load change, is made and he use of ineger var- iables reflecs his operaion heurisic. On he whole, fuel load change for oil is represened by coninuous variables due o is coninuous fuel load change. The opimal byproduc gas disribuion for he planning horizon is found o minimize he oal cos given holder level predicion, elecriciy demand predicion, and he presen opera- ion daa. As he operaion siuaion changes, such as he uni fuel cos change, he relaive imporance among each cos funcion changes, and his changing informaion is refleced by changing weighs. The relaive weighs among cos funcions can be deermined by process expers. The opimal rade among conflicing cos funcions is found for he pre-deermined coefficiens. Eq. (2) shows he maerial balance beween he oal amoun of byproduc gases a he ih boiler and is oal consumpion. Eq. (3) is he consrains for supplying more energy wih byproduc gases or oil han elecriciy demands a he ih boiler a period. Eq. (4) shows he holder operaion range o avoid holder booser rip or unfavorable byproduc gas emission. Eq. (5) shows he ime varying byproduc gas amoun relaionship wih generaion, consumpion of byproduc gases a he iron and seel making process, and flow rae enered ino he power plan. Eq. (6) shows he energy balance for he seam producion a ih boiler. Eqs. (7)-(10) show he consrains for mainaining holder level wihin he operaion range. According o he deviaion of holder level, a differen penaly is imposed. For he holder level which goes over he maximum and minimum operaion level, he larges penaly is imposed, and he holder level which is wihin he high or low operaion region, a large penaly is imposed. For he deviaion wihin he operaion range a small penaly is imposed [Eq. (11)]. Slack variables are used o represen he gas emission, holder booser rip, high or low operaion, and deviaion. Eq. (12) shows he number of operaing burners a he ih boiler and a ime using byproduc gas. Eqs. (13) o (16) check he simulaneous (wo a a ime or hree a a ime) burner level changes. Eq. (17) shows he number of swichings of burners beween ime periods from 1 o a each boiler using byproduc gas. Eq. (18) shows he minimum byproduc gas inpu a each boiler for he sable operaion of boilers a ime. CASE STUDY A case sudy was performed o verify he usefulness of he proposed approach using he simulaed model of an iron and seel making process, and he resuls were compared wih hose by a previous approach [Akimoo e al., 1991], which deermines he oal fuel load change a each period and no opimal disribuion is made. The disinguishing difference beween he previous and proposed approach is he opimizaion model srucure. The previous one uses coninuous variables for fuel load change, while he proposed one uses boh discree and coninuous variables according o he fuel ypes used in he process. To compare he performance of he proposed approach wih he previous approach, i is assumed ha he Korean J. Chem. Eng.(Vol. 20, No. 3)

4 432 J. H. Kim e al. oal amoun of adjusing byproduc gases ha is deermined from he previous approach is disribued o each boiler considering efficiencies, energy demand, and he number of swichings of burner wih coninuous fuel load change. The planning horizon is composed of five periods, and each period is five minues. Fig. 2 shows he gas flow diagram for he case sudy. Two ypes of byproduc gases are generaed from he process, and some porion of he byproduc gas is supplied o he seel making process, and he remaining are sen o he power plan. Four boilers exis a he power plan. Table 1 shows he operaion range of holders o reflec he operaion heurisic of using classified holder level region for he holder level mainenance. Table 2 shows he fuel load change Table 1. Operaion limi of he byproduc gas holder A as B as LL operaion limi (Nm 3 /h) 40,000 30,000 L operaion limi (Nm 3 /h) 50,000 40,000 Cener operaion (Nm 3 /h) 70,000 60,000 H operaion limi (Nm 3 /h) 90,000 80,000 HH operaion limi (Nm 3 /h) 100,000 90,000 Table 2. Burner level of byproduc gas fuel load change (Nm 3 /h) Boiler 1 Boiler 2 Boiler 3 Boiler 4 A as 27,000 27,000 27,000 27,000 B as 10,000 10,000 10,000 10,000 Table 3. Low heaing value of fuels A gas (kcal/nm 3 ) B gas (kcal/nm 3 ) Oil (kcal/l) Low heaing value 750 2,000 9,300 Table 4. Efficiencies of each boiler Boiler 1 Boiler 2 Boiler 3 Boiler 4 Efficiency Fig. 4. Comparison of A gas holder level change. uni for byproduc gases a each boiler. Table 3 shows he low heaing values of fuels. Table 4 shows he differen efficiencies of each boiler a he power plan. The case sudy deals wih he siuaion where boh byproduc gas holders are expeced o experience he unfavorable emission or shorage of gases. Fig. 3 and Fig. 4 show he holder level predicion and he opimized resul for proposed approach and he previous approach for A gas and B gas, respecively. The holder level predicion shows ha A gas is expeced o increase and gas discharge is expeced a ime period 5. On he whole, he B gas holder level operaes a a less low level, and i is expeced o go o he lower risky region a ime period 3. Therefore, o avoid gas discharge and holder booser rip, opimizaion is performed. The resul shows ha boh holder levels are flucuaing wihin he operaion limi during he planning horizon, bu he deviaion of he holder level from he normal operaion level by proposed approach shows larger deviaion han he previous approach. This is because he proposed one deermines he opimum poin by considering he penaly for he frequen burner on/off and discree load change while previous approach does no consider he frequen fuel load change. Fig. 5 and Fig. 6 show he opimum fuel flow rae resuls during he planning horizon by he proposed approach, and Fig. 7 and Fig. 8 show he resul by he previous approach, respecively. The pro- Fig. 3. Process diagram of he case 1. Fig. 5. Comparison of B gas holder level change. May, 2003

5 Plan-wide Opimal Byproduc as Disribuion and Holder Level Conrol in he Iron and Seel Making Process 433 Fig. 6. A gas flowrae change by proposed approach. Fig. 9. B gas flowrae change by previous approach. Fig. 7. B gas flowrae change by proposed approach. posed approach performs he hree imes burner swiching: B gas burner urn-off a he firs period, and wo A gas burner urn-on a he second period. The resul from he previous approach experiences six imes of swiching: B gas burner urn-off a he firs period, and five A gas burner urn-ons a he second and hird periods. Comparing he fuel load change resul shows ha he proposed approach performs a reduced number of swichings han he previous approach. By changing he flow raes of he byproduc gases by urning he burner on or off, he holder levels are mainained wihin he operaion range, and also he elecriciy demands for each boiler a each period are saisfied. Simulaneous urn off of he burner a he same boiler, which is no good in erms of he fuel load increasing ime han he disribued fuel load increasing, was avoided. Fig. 9 shows he disribuion of byproduc gas o each boiler a period 3. The byproduc gas disribuion resul shows ha he disribuion is made o maximize he efficiency of energy use. The larges amoun of hea energy of byproduc gases is allocaed o he boiler ha has he highes efficiency (Boiler No. 4). The resul also shows ha he fuel load change is performed by considering he efficiency of he boiler. When he fuel load is increased, he mos efficien burner (burner in No. 4 boiler) is firs urned on, and hen he nex efficien one (burner in No. 2 boiler) is urned on. On he conrary, when reducing he fuel load, he mos inefficien one (burner in No. 1 boiler) is firs urned off, and hen he nex inefficien one is urned off. Here, we assumed he efficiency of he burner is same as in he same boiler. Table 5 shows he cos comparison of he wo approaches. The resuls show ha oil was no used, holder booser rip and byproduc gas emission did no occur, and simulaneous changeover was no carried ou in boh resuls. The difference is in he swiching cos, deviaion, and elecriciy generaed. The previous approach shows a small deviaion cos and a lile more profi from elecric- Fig 8. A gas flowrae change by previous approach. Table 5. Cos comparison (Won) Previous Proposed Oil consumpion cos 0 0 Holder booser rip penaly 0 0 Unfavorable byproduc gas emission 0 0 High operaion penaly 0 0 Low operaion penaly 0 0 Deviaion penaly 441, ,125 Burner swiching cos 420, ,000 Elecriciy generaion benefi 321, ,727 Toal cos 540, ,897 Annual oal cos difference 129,648,000 won/yr Korean J. Chem. Eng.(Vol. 20, No. 3)

6 434 J. H. Kim e al. w : penaly weigh [won/penaly] Fig. 10. Byproduc gas disribuion resul a period 3. iy generaion, bu loses much by he frequen burner operaion. The previous approach focuses on he reducion of he oil consumpion, mainaining he normal operaion gas amoun ha is relaed wih he holder par, bu a consideraion of he opimal operaion of he power plan usage was no included. Overall, he proposed approach finds he opimal rade off among several coss, and i shows he lower oal cos. CONCLUSION To achieve plan-wide opimal operaion under he flucuaing unbalance of byproduc gas amoun and operaion condiion change in he iron and seel making process, a new muli-period opimizaion model was proposed. The proposed approach simulaneously opimizes he byproduc gas holder level and he disribuion of he byproduc gases o each boiler o minimize he oal cos. Compared wih he previous approach, he proposed approach shows good performance in erms of he oal cos reducion by searching opimal rade off among conflicing objecives, and produces an operaion-easy opimum soluion. ACKNOWLEDMENT This work was financially suppored by POSCO, and he auhors appreciae grea help from Young Jai Kim, Kyung Hak Yoon, and In Su Kang (POSCO). NOMENCLATURE C : uni cos [won] Cp : hea capaciy [kcal/nm 3 ] d : deviaion of byproduc gas amoun from normal amoun [Nm 3 ] F : flow rae [Nm 3 /h] H : enhalpy [kcal/kg] h : gas amoun in he holder [Nm 3 ] SW : burner swiching [-] : ime period [min] reek Leers η i : efficiency of ih boiler [-] Superscrips and Subscrips 2s : wo burner experience simulaneous swiching a he same boiler 3s : hree burner experiences simulaneous swiching a he same boiler : byproduc gases H : high level operaion HH : unfavorable byproduc gas emission i : boiler L : low level operaion LL : holder booser rip oil : heavy oil sm : seam eneral Ineger Variables N i, : number of operaing burner a boiler i a ime + SW i, : number of gas burner urn on a boiler i a ime : number of gas burner urn off a boiler i a ime SW i, Binary Ineger Variables + j 1,, i + j 2,, i + j 3,, i k 1,, i k 2,, i k 3,, i 1 if one gas burner urned on a boiler i a ime 1 if wo gas burner simulaneously urned on a he same boiler i a ime 1 if hree gas burner simulaneously urned on a he same boiler i a ime 1 if one gas burner urned off a boiler i a ime 1 if wo gas burner simulaneously urned off a he same boiler i a ime 1 if hree gas burner simulaneously urned off a he same boiler i a ime REFERENCES Akimoo, K., Sannomiya, N., Nishikawa, Y. and Tsuda, T., An Opimal as Supply for a Power Plan using a Mixed Ineger Programming Model, Auomaica, 27, 513 (1991). Bemporad, A. and Morari, M., Conrol of Sysems Inegraing Logic, Dynamics, and Consrains, Auomaica, 35, 407 (1999). Fukuda, K., Makino, H., Suzuki, Y. and Ishida, S., Opimal Energy Disribuion Conrol a he Seel Works, IFAC Simulaion of Conrol Sysems, Vienna, Ausria, 337 (1986). Hui, C. and Naori, Y., An Indusrial Applicaion using Mixed Ineger Programming Technique: A Muli-period Uiliy Sysem Model, Comp. Chem. Eng., 20, S1577 (1996). Iyer, R. R. and rossmann, I. E., Opimal Muliperiod Operaional Planning for Uiliy Sysems, Comp. Chem. Eng., 21, 787 (1997). Iyer, R. R. and rossmann, I. E., Synhesis and Operaional Planning May, 2003

7 Plan-wide Opimal Byproduc as Disribuion and Holder Level Conrol in he Iron and Seel Making Process 435 of Uiliy Sysems for Muliperiod Operaion, Comp. Chem. Eng., 22, 979 (1998). Kim, J. H. and Han, C., Shor-erm Muliperiod Opimal Planning of Uiliy Sysems using Heurisics and Dynamic Programming, Ind. Eng. Chem. Res., 40, 1928 (2001). Lee, H., Kim, S., Lee, E. and Lee, I., MILP Scheduling Model for Mulipurpose Bach Processes Considering Various Inermediae Sorage Policies, Korean J. Chem. Eng., 18(4), 422 (2001). Singh, A., Forbes, J. F., Vermeer, P. J. and Woo, S. S., Model-based Real-ime Opimizaion of Auomoive asoline Blending Operaions, J. of Process Conrol, 10, 43 (2000). Sinha,. P., Chandrasekaran, B. S., Mier, N., Dua,., Singh, S. B., Choudhury, A. R. and Roy, P. N., Sraegic and Operaional Managemen wih Opimizaion a Taa Seel, INTERFACES, 25, 6 (1995). Yi, H. and Han, C., The Inegraion of Complee Replanning and Rulebased Repairing for Opimal Operaion of Uiliy Plans, Korean J. Chem. Eng., 18(4), 442 (2001). Korean J. Chem. Eng.(Vol. 20, No. 3)