Article pubs.acs.org/IECR
Optimal Shut-Down Policy for Air Separation Units in Integrated Steel Enterprises during a Blast Furnace Blow-Down Peikun Zhang† and Li Wang*,†,‡ †
School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China Beijing Engineering Research Center for Energy Saving and Environmental Protection, Beijing 100083, China
‡
S Supporting Information *
ABSTRACT: Optimal shut-down policy for air separation units (ASUs) in the oxygen distribution system is studied for the integrated steel enterprises with a captive oxygen plant during a blast furnace blow-down. A multiperiod mixed-integer linear programming (MILP) model was proposed, which includes the minimum time constraints for ASU shut-down and start-up and the zero vent constraint of gaseous oxygen. When the decision variables are scheduled simultaneously, such as the on/off states of the fixed-load compressors and ASUs, the rate of the variable-load compressors, and the rate of liquefaction units, the model can easily offer the on-site manager a solution to operate the facilities in the oxygen distribution system while avoiding oxygen venting and minimizing the pressure levels of the high-pressure network in the buffer system, thereby reducing the overall energy consumption for oxygen production. The applicability of the model was demonstrated and justified using a real-world case study.
1. INTRODUCTION The annual crude steel output in China amounted to 803.8 Mt in 2015 (represents 49.5% of the world crude steel production), and there is a pressing need to increase the energy efficiency in this energy-intensive industry. Steel production needs a great amount of high-purity gaseous oxygen (GOX), which is commonly supplied by cryogenic air separation units (ASUs). ASUs are power-intensive equipment that require a significant amount of power consumption, and GOX consumption is a critical determinant in the electricity consumption of iron- and steel-making processes. Most of the integrated steel enterprises in China have a captive oxygen plant that operates on a set of large-scale ASUs to provide GOX. Except for a GOX cylinder needed for minor uses and liquid oxygen (LOX) delivered by trucks, most of the oxygen generated in a captive oxygen plant can be supplied to the unique on-site user, that is, the integrated steel enterprise. Because the captive oxygen plant has many facilities (e.g., ASUs, compressors, and liquefiers) that differ in the function and technical specification, the scheduling of these units to meet the demand with uncertainty is a major challenge facing managers. In such a scenario, oxygen imbalances between demand and supply usually occur and lead to GOX vents. When the GOX supplied is larger than that consumed, excessive production occurs. Conversely, when a GOX shortage occurs, this threatens safe production. Because of the lack of efficient tools for optimal operations, managers always pursue excessive productions with a considerable amount of GOX vent in many integrated steel enterprises, which is safe overall but leaves a considerable amount of wasted © XXXX American Chemical Society
electricity. The more GOX is vented, the larger the unit energy consumption of steel production. Energy costs are the only real costs encountered in ASUs because the raw material (atmospheric air) is taken directly from the atmosphere such that if ASUs were capable of producing oxygen in more efficient manners, energy costs could be significantly reduced. Thus, good scheduling can avoid GOX vent and is an important approach for improving the efficiency of energy utilization in integrated steel enterprises. Many studies have been conducted for the enterprise-wide production optimization of ASUs. Manenti and Rovaglio1 analyzed the scheduling problem on a large-scale system for the production industrial gases such as oxygen, nitrogen, and argon under complex power contractual obligations, which consists of two ASU fields, a branched network structures, and a pipeline for GOX supply for gas and liquid product distribution. Glankwamdee et al.2 developed a variety of formulations for the flexible optimization of industrial gas distribution and production. The model effectiveness was tested using the data from Air Products. Manenti and Manca3 discussed the development, detection, and description of operating transients within MILP architecture for enterprise-wide optimization. Manenti4 proposed an alternative approach for handling uncertainties in both plant-wide and enterprise-wide optimizaReceived: Revised: Accepted: Published: A
October 16, 2016 December 27, 2016 February 7, 2017 February 7, 2017 DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
Figure 1. Diagrammatic sketch of the oxygen distribution system in integrated steel enterprises.
tion problems. D’Isanto et al.5 proposed a novel approach for ensuring the use of mixed-integer optimization for the network management, which was validated by a nitrogen supply related case for the Thyssen−Krupp steel mill placed in Terni (Italy). Manenti et al.6 introduced the general concepts of supply chain management from a perspective which the corporate optimum imposed on the ASUs was significantly different than those dictated by a single ASU optimization result. The mathematical corporate model was described, and the numerical results and a comparison between plant-level and enterprise-level decisions were discussed. Manenti and Rovaglio7 investigated the mixedinteger modeling and optimization issues by means of a multiscale approach for an existing ASU network. The most significant result was the demonstration and quantification of the improved flexibility in plants when enterprise-wide optimization was applied. It was particularly useful in helping the latter track increasingly volatile market dynamics and monetize those fluctuations. Marchetti et al.8 developed an MILP formulation for both the simultaneous coordination of production and distribution decisions in industrial gases supply chains. The resulting formulation allowed the prompt examination of different scenarios such as changes in electricity pricing or disruptions in plant operations. Rossi et al.9 proposed a general model that was specifically designed to work online and determine the optimal assignments for production site output to customer demand in the supply chain. The model can be easily combined with the rolling horizon technique to mitigate any uncertainties in the demand. The model was tested using a case that was based on a portion of the real supply chain and production network of Linde Gas Italia. Han et al.10 proposed a two-stage predictive scheduling method to optimize oxygen and nitrogen usage and an MILP model was established to obtain the optimal energy scheduling solution. Puranik et al.11 presented optimization methodology that determined the efficient production and distribution decisions in the face of fluctuating electricity prices and contractual obligations. This
methodology relied on the global optimization of a mixedinteger nonlinear programming (MINLP) model that represented the network operations. Zhou et al.12 analyzed an air separation process with different types of ASUs and, together with vaporizers and liquefiers, developed an MILP model that optimized scheduling of multiple sets of ASUs with a frequent load change operation. However, most of the above-mentioned studies reported on industrial gas companies, with only a few concerned about the oxygen distribution system of integrated steel enterprises with a captive oxygen plant. As compared to an industrial gas company, an integrated steel enterprise operates optimally in the oxygen distribution system in three different conditions. First, an industrial gas company generally has numerous users, whereas the captive oxygen plant has only one on-site user. Therefore, the long-term demands of an integrated steel enterprise are steadier than that of an industrial gas company. However, the demands of integrated steel enterprises may fluctuate more than that of an industrial gas company in a short-term view because the iron and steel production equipment requires periodic maintenance. Second, the industrial gas company follows under time-varying electricity pricing schemes (real-time prices or time-of-use rates), whereas integrated steel enterprises have a relatively stable electrical price given that the majority of consumed electricity is gathered from power stations owned by the enterprise. Third, the industrial gas company has a different contractual obligation from the captive oxygen plant. In an industrial gas company, ASU operations are bound by the demand for specific components such as oxygen and argon. Argon contracts may overproduce and vent GOX as necessary because the argon is very difficult to separate from the atmospheric air, which only contains 0.93% argon. For the captive oxygen plant, the ASU production is only driven by the oxygen consumption of local iron and steel enterprises. Considering the peculiarities mentioned above, further studies are necessary to investigate B
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research the optimization of the oxygen distribution system in integrated steel enterprises.
procedure adjustments are complicated, oxygen supply scheduling still provides many possibilities and opportunities. In contrast, on the demand side, the consumption of oxygen is inherently unsteady and irregular because of the behaviors of those in the consumption department, which primarily includes iron- and steel-making users. An integrated steel enterprise using the blast furnace-oxygen steelmaking route, which is the primary source for worldwide steel production, pursues the following steps for primary steel production: iron production by blast furnaces (BFs) for the conversion of ore to iron melt; steel production by basic oxygen furnaces (BOFs) for the conversion of iron melt to molten steel; casting for molten steel solidification; roughing or billet rolling for block size reductions; and product rolling for finished shapes. The majority of GOX consumption occurs in the first two steps; therefore, the iron and steel plants are the two main users in the integrated still enterprise. The usage modes in iron and steel plants have led to two types of oxygen demand uncertainties, namely, the basic fluctuation and the steep decline. The basic fluctuation refers to oxygen demands that always swing above or below the average level at given amplitude limit. It is primarily caused by the batch productions of BOFs in steel plants, where sets of BOFs produce molten steel in batch modes, and have varying GOX blowing times and degrees of operation succession. The steep decline is attributed to BF blow-downs in iron plants. BF blow-down maintenance is periodically encountered in iron plants and significantly decreases GOX demands. The presence of a BF blow-down hinders the production of iron melt for an extended amount of time. Likewise, oxygen is no longer needed until the oxygenenriched air is once again blown into the BF. A monthly scheduled BF blow-down typically lasts 18−20 h, and after a preparatory period the oxygen consumption can reach the normal level. Commonly, an unscheduled BF maintenance has a longer duration than a scheduled one. During a BF blowdown, the demand of GOX from iron plants significantly decreases. The return of BFs to produce iron normally following a blow-down has relatively low conventional levels in terms of iron melt production and GOX consumption and still requires hours to resume conventional GOX demands. Furthermore, as a supplier of iron melt, the BF also affects the downstream steel-making step in the corresponding steel plant. During a BF blow-down, molten iron melt produced by iron plants is insufficient as the crude material for BOFs and thus effectively lower the GOX demands of steel plants. The BOFs of the corresponding steel plant are turned off and maintained. Following a BF blow-down, thereby causing the demand of GOX to gradually decrease to zero until the end of the BF blow-down where it gradually returns to its conventional levels. For both types of above-mentioned demands, the reasoning for scheduling differs with each demand. For the basic fluctuation demand, the production capacity and oxygen demand essentially match, with the unbalanced status usually appearing for a short time duration and can be compensated using a buffer system. In this situation, scheduling targets change in the ASU loads according to the varying demands and thus avoid the GOX vent. On the contrary, the steep decline demand experiences a long-term mismatch between the oxygen production capacity and oxygen demand, which cannot be counterbalanced by a buffer system. In this situation, the shutdown of the ASU is necessary to return the oxygen distribution system to balance. Because the freedom degree of shutting down the ASU is provided by optimal ASU on/off planning,
2. PROBLEM STATEMENT GOX is a major production factor in iron and steel production, which is dispatched by the oxygen distribution system to all users over the integrated steel enterprise (Figure 1). By running several large-scale ASUs, we can provide three categories of oxygen products in this system: the high-pressure GOX (HPGOX), the normal-pressure GOX (NP-GOX), and the LOX. In Figure 1, the green solid line, red dash-dot line, and blue dot line indicate the NP-GOX, HP-GOX, and LOX, respectively. NP-GOX is generated directly from ASUs, part of which flows into the liquefiers and iron plants, and flows into the vent port if excessive production occurs. The rest of the NP-GOX is compressed to become HP-GOX, which is mainly used by the steel plants. The LOX can be produced from ASUs as well as liquefiers, a portion of which is dispatched by trucks and the rest of which is kept in the cryogenic tanks for liquid storage and reserved for emergency gasification via evaporators. Imbalances between the supply and demand sides in this system are caused by differences in production characteristics between the two sides. On the supply side, the oxygen is produced by ASUs that provide a large amount of high-purity industrial gases such as oxygen. The ASUs can take a large amount of the atmospheric air to compression, cooling, purification, and liquefaction, after which air is divided into its primary products by cryogenic distillation. The rate of oxygen production from the ASUs is relatively steady because the air separation process was designed with a fixed-rate to maximize the efficiency of operations such that an ASU load has minimal changes within a limited range. In theory, a typical ASU can change its load from 80% to 105% of the design point at a full variation speed of no more than 0.25% per minute.13,14 In practice, the load variation range and speed also rely on specific circumstances, such as the agility of the equipment and operating skills of the on-site managers. Moreover, a constant amount of oxygen can be reduced if an ASU is shut down, though this requires a longer waiting time to reach the required purity of the products during the start-up because it is physically infeasible to efficiently change the operating conditions of an ASU given the strong inertia of the mass and energy holdups. Therefore, to address the potential imbalance between the steady supply and uncertain demand, a buffer system is also present in captive oxygen plants. The buffer system consists of the high-pressure network and a liquid backup system, which has a string of facilities such as compressors, spherical vessels for HP-GOX storage, liquefiers, and cryogenic LOX tanks. On one hand, the GOX can be compressed into the high-pressure network and can solve transient imbalances by swinging the gas pressure between its upper and lower limit ranges. On the other hand, the backup system can also liquefy the GOX for long-term storage, where it is first introduced into the liquefiers for liquefication then flows into cryogenic LOX tanks and kept in reserve. When there is a severe shortage of GOX, the LOX can be evaporated to maintain the pressure of the high-pressure network within its tight limits. However, given that LOX production results in additional costs for the liquefiers, the evaporation can only be started during emergent occasions such as ASU shut-downs caused by malfunction interruptions. Though the capacity of the buffer system is limited and the C
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about 0.25% in theory.13 However, in practice, the load variation also relies on specific circumstances such as equipment flexibility, operator experience, and reliability considerations and thus may be unachievable. Moreover, in captive oxygen plants, the frequent load change in ASUs is not preferred because large-scale ASUs must avoid wide and persistent oscillations in their operating conditions to save the unit life cycle, as well as create easier work condition for field and control-room operators.16 To establish the model, the following items need to be formally defined: • A planning horizon that consists of a set of equal-interval time periods, t ∈ T, as presented in Figure 3, and a timeinterval length Δt is given.
the objective of the scheduling should be no longer limited to avoiding the GOX vent, but to minimize the pressure of the buffer system with that of the zero GOX vent as a model constraint. Recently, Zhang et al.15 proposed an MILP model that can minimize the GOX vent by adjusting the ASU loads and the variables involved in the buffer system such as the pressure of HP-GOX, all of which was considered the starting point for the present study. However, because their model was developed to implement the schedule task with a basic fluctuation demand, the on/off state of the ASU was not considered as a decision variable but was rather part of the given conditions. For scheduling tasks with a deep decline demand caused by BF blow-downs, tentative calculations under various given conditions are required and the previous model would only play a subfunction role in each of the tentative calculations. Apparently, their optimization process was the blind search and was inefficient for the scenarios with deep decline demands. Therefore, given that BF blow-downs typically results in large amounts of GOX vents, the purpose of the present study is to develop a model in which the start-up and shut-down of ASUs are modeled explicitly, thereby efficiently solving the scheduling problem for deeply decline demands caused by BF blow-downs.
Figure 3. Planning horizon with time-interval length Δt.
• A set of ASUs, i ∈ NA, that supply NP-GOX ANPG and i HP-GOX AHPG are given. The minimal production time i after the ASU i start-up (minimal run time), AUtj, and the minimal time required to return online again following an ASU i shut-down (minimal off time), ADtj, are also given. • A set of liquefiers, m ∈ NL, that have a maximum (minimum) liquefaction rate by using NP-GOX LNPGmax m (LNPGmin ) or HP-GOX LHPGmax (LHPGmin ) as the raw gas m m m are provided. • A set of fixed-load compressors, j ∈ NC, with a fixed rated load, Cj, are given. The minimal operating time after the compressor j start-up (minimal run time), CUtj, and the minimal time required to return online following the compressor j shut-down (minimal off time), CDtj, are also given. • A set of variable-load compressors, h ∈ NB, with a min maximum (minimum) compression rate, Bmax h (Bh ), and a load change speed, vh, for load change are given. • A set of sphere vessels, f ∈ NF, that have a capacity, Vf, and a maximum (minimum) allowable operation pressure, Pmax (Pmin), for HP-GOX storage are given. • A given NP-GOX (HP-GOX) demand, DNPG (DHPG ), for t t time period t. The decision variables of the scheduling problem, which need to be determined, are • the operating status of the ASUs: ati, xti, and yti NPG • the NP- and HP-GOX feed rates into liquefiers, lm,t and HPG lm,t • the operating status of fixed-load compressors: ctj, wtj, and ztj • the compression rate of the variable-load compressors, bh,t • the pressure levels of the high-pressure network, pt • the GOX vent rate, et The objective is to minimize the overall pressures of the high-pressure network in the buffer system of the oxygen distribution system for the entire planning horizon. The NPand HP-GOX demands from the iron and steel plants should
3. MODEL The model in Figure 2 was designed to solve the scheduling problem in the oxygen distribution system, which includes
Figure 2. Oxygen gas distribution flowsheet in a captive oxygen plant.
ASUs, compressors, liquefiers, and sphere vessels. The LOX storage and gasification facilities for LOX evaporation in the emergent shortage case were omitted from the model for simplicity because the production capacity of oxygen exceeds the oxygen demand during a BF blow-down. Furthermore, the ASUs are assumed to be operating at a fixed load (at the design point) for three reasons. First, during a BF blow-down with oxygen overproduction, production cutback can be realized by an ASU shut-down instead of the ASU load change. Second, ASUs have been conventionally designed to generate products with a fixed output (design point) to maximize operation efficiencies. Third, the research shows that automatic load change technology is achievable with a load change velocity of D
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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experience, and the ASU agility. Likewise, for oxygen production purity, various Tstart values such as 2, 4, and 6 h i were previously reported in literature.12,17,18 In the production node, the ASU must maintain a minimum time of Trun i before it can move to the “shut-down transition” node, and this limit is principally imposed to reduce stress on the equipment. The ASU can immediately switch from the production node to the shut-down transition node but must stay in the shut-down transition node for a relatively brief period, i.e., Tshut i . After shutdown, the ASU can stay in the off node for a period of Toff i . According to on-site operation experiences and historical data, 14 Toff in cold start-up scenarios. i is usually less than 36 h On the basis of the above analysis, the minimum run, AUti, and off time, ADti, can be given by the following equations.
be fully satisfied. A complete list of variables and parameters for the model are also provided in the Nomenclature. 3.1. Start-Up Constraints for ASUs. An ASU cannot be at start-up and shut-down states in the same time step. The minimal run and shut-down times are defined by three binary integer variables. ⎧1, if ASU i is in production at time t ait = ⎨ ⎩ 0, otherwise ⎪
⎪
⎧1, if ASU i starts up at the beginning of time t xit = ⎨ ⎩ 0, otherwise ⎪
⎪
⎧1, if ASU i shuts down at the beginning of time t yit = ⎨ ⎩ 0, otherwise ⎪
AUt i = Tirun
⎪
ADt i = Tishut + Tioff + Tistart
As shown in eqs 1 and 2, the start-up constraints of ASU i at time step t are functions of the unit start-up and shut-down decision variables. ait − ait − 1 = xit − yit xit
+
yit
≤1
∀ i ∈ NA, t ∈ 1, ..., T
∀ i ∈ NA, t ∈ 1, ..., T
∀ i ∈ NA
(3)
∀ i ∈ NA
(4)
The minimum run and minimum off time constraints for ASU i are functions of the unit start-up/shut-down variables, as provided in eqs 5 and 6.
(1)
xit +
(2)
t + AUt i − 1
∑
yik ≤ 1
∀ i ∈ NA, t ∈ 2, ..., T
xik ≤ 1
∀ i ∈ NA, t ∈ 2, ..., T
(5)
k=t+1
3.2. Minimum Run and Shut-Down Times for ASUs. A significant amount of time, ADti, is required to reach the required production purities when a cryogenic ASU is started up after a shut-down. The present study considers a cold startup mode for the start-up and shut-down operations of the ASU because the time scales of the cold start-up model match with those of the BF blow-down. A cold start-up mode means the ASU will have been shut down for a brief period of time (a temporary break such as an interruption and scheduled shutdown) before the next start-up and is characterized by the presence of liquid in the column sumps for the entire time it is switched off. When an ASU is started without any liquid, this is characterized as a warm start-up mode. The warm start-up scenario is a start-up after a relatively long shut-down period, of which the time required to restart the ASU may exceed the planning horizon, and is not considered in this study. The dynamics of the ASU in terms of its switching behavior can be visualized with a state graph, Figure 4. Figure 4
yit +
t + ADti − 1
∑ k=t+1
(6)
3.3. Operating Constraints of Liquefaction Units. In captive oxygen plants, liquefaction units were originally built to continuously liquefy nitrogen gas, which is another gas product in the plant. Because of the relatively lower boiling point of liquid nitrogen (LIN), LOX can be directly produced via a heat exchanger. The raw gas consumed by liquefiers can be either NPG NP-GOX lm,t or HP-GOX lHPG m,t . Though the liquefaction units always liquefy the nitrogen at a fixed rate,19 the product ratios of LOX and LIN can be changed as required. This indicates that the liquefaction rate of NP- (HP-) GOX can change from the maximal capacity LNPGmax (LHPGmax ) to the minimum rate m m HPGmin LNPGmin (L ), which is limited by strict contractual m m obligations, as shown by eqs 7 and 8. Moreover, given that the GOX flow requires liquefication and is directly introduced from the pipeline by passing through a heat exchanger and a valve, it is appropriate to assume an unlimited load change speed for the GOX liquefaction rate. NPGmax LmNPGmin ≤ lmNPG , t ≤ Lm
∀ m ∈ NL, t ∈ 1, ..., T (7)
LmHPGmin
≤
lmHPG ,t
≤
LmHPGmax
∀ m ∈ NL, t ∈ 1, ..., T (8)
3.4. Constraints of Compressor Start-Up. There are two kinds of compressors in the system if the compression rate can be varied, namely, the fixed-load compressors discussed in sections 3.4 and 3.5 and the variable-load compressors discussed in section 3.6. Fixed-load compressors can be shut down and started up when necessary. Given that a compressor cannot have start-up and shut-down states in the same time step, the minimum run and shut-down times are defined by three sets of binary decision variables, namely, ctj, wtj, and ztj, which indicate the on/ off status, the start-up status, and the shut-down status of the compressors, respectively.
Figure 4. State graph of an ASU in the cold start-up scenario.
illustrates the cold start-up scenario with four different nodes of operating states, namely, off, start-up transition, production, and shut-down transition. The ASU can switch from off to start-up transition immediately. The process must remain for an amount of time, Tstart i , in the start-up transition node before it can be moved to the production node. Tstart is mainly required i to top up the liquid hold level in the column and reestablish the desired production purities. Tstart depends on the duration of i the switched-off state Toff of ASU, the on-site operator i E
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research c jt
⎧1, if compressor j is operating at time t =⎨ ⎩ 0, otherwise ⎪
i=1
⎪
(9) (10)
3.5. Minimum Run and Shut-Down Time for Compressors. To save the compressor life cycle and create easier work conditions for field and control room users, an operating mode that can frequently turn on/off the compressor is not preferred. Therefore, the operating constraints of the minimum run time, CUtj, and off time, CDtj, are considered such that the model reduces stress on the compressors and avoids persistent oscillations in their operations. Equations 11 and 12 present the minimum run and minimum off time constraints for compressor j, which are functions of the compressor start-up/shut-down variables.
∑
z jk ≤ 1
+
∑
wjk
NC
i=1
− (11)
j=1
∀ j ∈ NC, t ∈ 2, ..., T
≤1
3.6. Operating Constraints of the Variable-Load Compressors. The variable-load compressors can change the load in limited flow rate ranges and are considered to be always on a running status except when it is maintaining. Usually, the compression rate can vary from 80% to 105% of the design point rate,14 as constrained by eq 13. Furthermore, a variableload compressor has a limited load change speed. This study assumed a linear relationship between the transition time and the load change speed, as given in eq 14. Bhmin ≤ bh , t ≤ Bhmax
∀ h ∈ NB, t ∈ 1, ..., T
(13)
bh , t − 1 − vhΔt ≤ bh , t ≤ bh , t − 1 + vhΔt ∀ h ∈ NB, t ∈ 1, ..., T
NB
NL
pt − pt − 1 44.6RT Δt
h=1
m=1
∑ Vf
= DtHPG
∀ t ∈ 1, ..., T (17)
f =1
∀ t ∈ 1, ..., T
(18)
3.9. Objective Function. The main purpose of the present paper is to minimize the disadvantage caused by GOX overproduction. Because the GOX store process inside the high-pressure network is done by compressing excessive GOX into the high-pressure network by an increase in its pressure, the immediate consequence with overproduction is the pressure increase of the high-pressure network. Due to the limited capacity of the high-pressure network, small overproduction often causes dramatic rises in pressure levels. Crucially, the pressure increase causes all the compressors operating at high discharge pressures, which means even a small pressure rise would increase the energy consumption of a large amount of oxygen which requires compression (the excessive GOX, the HP-GOX liquefied, and the HP-GOX consumed). Therefore, the disadvantage caused by GOX overproduction is the energy usage increase of the compressors. Accordingly, to minimize this disadvantage, the objective can be directly the minimization of the compression energy usage or be indirectly the minimization of the pressure. To minimize the total compression energy usage, the objective function should be the eq 19 with the assumption that all the compressors are two-stage with the same inner efficiency. However, the nonlinearity of eq 19 makes the model solution excessively difficult (requires a long-elapsed time), which significantly reduces the model performance, particularly
(12)
k=t+1
(16)
NF
P min ≤ pt ≤ P max
t + CDt j − 1
z jt
(15)
∀ t ∈ 1, ..., T
NA
∀ j ∈ NC, t ∈ 2, ..., T
k=t+1
h=1
∑ AiHPGai ,t + ∑ cj ,tCj + ∑ bh,t − ∑ lmHPG ,t
t + CUt j − 1
wjt +
j=1
3.8. Mass Balance of the High-Pressure Network. The high-pressure network consists of the HP-GOX storage vessels and the HP-GOX pipelines. A certain amount of GOX can be temporarily stored inside the high-pressure network, which is done by compressing excessive GOX into the high-pressure network by an increase in the pressure, pt. On the basis of the assumptions of omitting the pressure drop of gas flow and ignoring the effect of the pressure change on the compressor load, the amount of GOX stored can be linearly calculated from the pressure change, and the material balance relationship of the high-pressure network can be given by eq 17. In eq 17, the sum of the HP-GOX produced and the NP-GOX compressed is subtracted from the sum of the HP-GOX liquefied and the HP-GOX stored is equal to the HP-GOX demand. Meanwhile, the pressure inside the high-pressure network must be strictly maintained within the allowable range required by the metallurgical process and the safety concerns constraints (eq 18).
The start-up constraints of compressor j at time step t, which are presented in eqs 9 and 10, are functions of the unit start-up and shut-down variables.
∀ j ∈ NC , t ∈ 1, ..., T
m=1
et = 0
⎪
wjt + z jt ≤ 1
NB
Furthermore, the conditions given in eq 16 should be met in production because the NP-GOX demand from the on-site users such as BFs must always be satisfied and a zero GOX vent is desired.
⎧1, if compressor j shuts down at the beginning of time t z jt = ⎨ ⎩ 0, otherwise
∀ j ∈ NC , t ∈ 1, ..., T
NC
∀ t ∈ 1, ..., T
⎧1, if compressor j starts up at the beginning of ⎪ t wj = ⎨ time t ⎪ ⎩ 0, otherwise
c jt − c jt − 1 = wjt − z jt
NL
NA
NPG ∑ AiNPGai , t − ∑ lmNPG , t − ∑ cj , t Cj − ∑ bh , t − et = Dt
⎪
(14)
3.7. Mass Balance of the Normal-Pressure Network. Constant pressure conditions in the normal-pressure network allows the omission of buffer capabilities in the normal-pressure network to render a mass balance relationship, as shown in eq 15, where the difference between the GOX produced and the sum of the GOX liquefied, compressed, and vented is equal to the NP-GOX demand. F
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research for the scheduling tasks for emergent situations such as an unscheduled BF blow-down, which requires rapid decisions. By combining and analyzing the eqs 17 and 19, we can be notice that the pressure pt decrease has the benefit of reducing the NC NB values of both the terms (Σ j=1 c j,t C j + Σ h=1 b h,t ) and κ − 1/2κ ⎤ ⎡ pt − 1⎥ in eq 19 and thereby decreases the ⎢⎣ 1.01325 × 105 ⎦ value of the objective function. Therefore, to facilitate the model solution, the objective function of this study is modified to minimize the overall pressure of the high-pressure network as given by eq 20; then the whole problem turns to the MILP problem instead of MINLP. The modified objective function (eq 20) conforms to the on-site experience of the industrial filed, where the pressure of the high-pressure network is a key indicator of the management performance of the oxygen distribution system. Moreover, the calculations show that the model with eq 19 has a very close result to that with eq 20 but needs considerable more time for solution, which can be justified by the MILP and MINLP model files and result files attached as the online support material of this paper (the model files were built on the basis of the case study in the next section).
(
)
⎧ NC ⎪ Y = Min ∑ ⎨(∑ cj , tCj + ⎪ t=1 ⎩ j=1 T
Figure 5. GOX demand during the planning horizon for case study.
Table 1. Parameters of the ASUs NP-GOX output [(kNm3)/h] HP-GOX output [(kNm3)/h] minimal run time (h) minimal off time (h) initial status (on/off)
⎡⎛ ⎤⎫ pt ⎪ ⎞κ − 1/2κ ⎥⎬ ⎟ − 1 ∑ bh , t )⎢⎜⎝ 5⎠ ⎪ ⎢⎣ 1.01325 × 10 ⎦⎥⎭ h=1 NB
(19) T
Y = Min ∑ pt t=1
(20)
a
4. CASE STUDY The oxygen distribution system of a large integrated steel enterprise was considered. The oxygen distribution system consisted of eight large-scale ASUs, most of which (ASUs A1− A5 and A8) produce NP-GOX and one (A6) that produces HP-GOX. There are two liquefaction units, one of which (L1) takes NP-GOX as the raw material while the other (L2) takes HP-GOX. In this case, the GOX demand is mainly from the iron plants, the steel plants, and other users such as electric arc furnaces. We focused on the scheduling problem of an optimal shut-down policy during a BF blow-down period, which is a common maintenance situation that leads to significant fluctuations in the GOX demand and usually results in large GOX vents. Figure 5 presents changes in GOX demand during a BF blow-down, where 48 time periods are present in the total scheduling horizon and each period represents 1 h. Tables 1−4 give the main operating parameters and initial data of the facilities involved. The load change ranges of the compressors were derived from the thorough analysis of historical data of real-world equipment. Moreover, although facilities (ASUs A1− A3 and compressor C7) under maintenance status during the entire planning horizon are given in the tables, they are not considered in the scheduling model. The minimum off time, as presented in section 3.2, is the sum of the required time during shut-down transition, the time of the switched-off state, and the required time for start-up transition, which varies and depends on the on-site operator’s experience and the ASU’s agility. In this case, a typical minimum off-time length of 24 h for an ASU (Table 1) was considered. The MILP model consists of 336 continuous nonnegative variables, 1968 binary integer variables, and 2881
A1
A2
A3
A4
A5
A6
A7
A8
30
30
30
30
50
0
60
60
0
0
0
0
0
60
0
0
24
24
24
24
24
24
24
24
24
24
on
on
on
on
on
offa
offa
offa
Maintained during the entire planning horizon.
Table 2. Parameters of the Liquefaction Units maximal NP-GOX rate [(kNm3)/h] maximal HP-GOX rate [(kNm3)/h] minimal NP-GOX rate [(kNm3)/h] minimal HP-GOX rate [(kNm3)/h]
L1
L2
7.159 0 1 0
0 8.8 0 0
Table 3. Parameters of the Compressors variable load rated load [(kNm3)/h] maximal rate [(kNm3)/h] minimal rate [(kNm3)/h] minimal run time (h) minimal off time (h) initial rate [(kNm3)/h]
C1
C2
C3
C4
C5
C6
C7
√ 60 63
√ 30 31.5
× 17
× 17
× 17
× 17
× 17
48
24 6 3 on
6 3 on
6 3 on
6 3 on
offa
62.2
30.6
Maintained during the entire planning horizon; √, available; ×, not available.
a
Table 4. Parameters of the High-Pressure Network in the Buffer System
volume (m3) pressure upper limit (MPa) pressure lower limit (MPa) initiation pressure (MPa) G
vessel V1−V6
vessel V7−V16
pipeline
400 × 6 3.0 1.6 2.53
650 × 10 3.0 1.6 2.53
450 3.0 1.6 2.53
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research constraints and has been solved in around 3 min on an Intel Core i5-3470
[email protected] GHz by Lingo 16.0 software (solver type: branch-and-bound solver). The global optimum results are presented in Figures 6−9. Figure 6 displays the scheduling results of the ASUs (A4− A8) considered in the model. Three ASUs (A5, A6, and A8)
Figure 6. Scheduling results of the ASU on/off status during the planning horizon.
were involved in the shut-down and start-up operations. In comparing the on/off status in Figure 6 for the following discussions, we can divide the planning horizon into three time periods: the first−ninth periods, the 10th−29th periods, and the 30th−48th periods. In the first time segment, Figure 6 illustrates a single ASU (A5) that was shut down during the majority of the segment. This observation contradicts common reasoning because it suggests a possible supply shortage before the BF blow-down from the ASU shut-down. However, the result can be justified by the addition of a buffer system. After the ASU A5 was shut down, the pressure declines as the time was extended (Figure 7a) such that the model attempted to clear out the buffer system and reduce the pressure of the high-pressure network to its lower limit, which follows the optimization objective. Although the ASU outputs were less than the demands (Figure 7b), the balance between the supply and demand was retained by the buffer capacity. The GOX compression rate was reduced by turning off compressors C3−C6 and putting compressors C1 and C2 into working at low loads, which was consistent with the aforementioned statement regarding the buffer capacity (Figure 8). Because the above-mentioned facilities sufficiently balance the systems, both the liquefiers operated at low loads during most of the segment (Figure 9). Therefore, the ASU shut-down in the first time segment was an overall scheduling result, which is the model decision for minimizing the total pressure of the entirety of the planning horizon. In the second time segment, Figure 6 shows two ASUs (A5 and A6) having been shut down to meet the demand decline caused by the BF blow-down. Despite this, the ASU outputs were still slightly more than the demands (Figure 7b) such that the difference between the stable outputs and the fluctuant demands were eliminated by three approaches, namely, the load change of ASU, the pressure swing of the high-pressure network in the buffer system, and the liquefaction using a liquefier. The present study preferred and selected liquefaction given that pressure swings are not preferred by the optimization
Figure 7. Global scheduling results of the oxygen distribution system.
Figure 8. Scheduling results of the compressor loads and statuses during the planning horizon.
objective, and the ASUs are assumed to serve at a design point fixed load. The presence of liquefiers with sizable capacities and sufficient speeds for load change are presented in Figure 9, H
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
5. CONCLUSIONS The present study studied the scheduling problem for the optimal ASU shut-down policy of the oxygen distribution system during a BF blow-down period in integrated steel enterprises. A simultaneous multiperiod MILP model was proposed, which included the minimum time constraints for the ASU shut-down and start-up as well as the zero oxygen vent constraint. When the decision variables are scheduled simultaneously, such as the on/off states of the fixed-load compressors and ASUs, the rate of the variable-load compressors, and the rate of liquefaction units, the model easily provides the on-site manager a solution to operate the facilities in the oxygen distribution system by avoiding GOX vent and minimizing the overall pressure levels of the highpressure network, thereby reducing the overall energy consumption in the system. The proposed model notably offers the possibility of inserting a reasonable minimum start-up time that reflects the detailed physical-chemical procedure in ASUs for an enterprise-wide planning of an ASU shut-down. The case study demonstrated the applicability of the proposed model in dealing with ASU shut-down scheduling problems and planning the operations for complex networks during a BF blow-down. This helps managers during the decision-making process in terms of allowing the integrated steel enterprise to deal with massive economic losses from avoiding oxygen vents during excessive production and high-pressure statuses for the high-pressure network in the buffer system.
Figure 9. Scheduling results of the liquefier rates during the planning horizon.
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where the real demand curve (the sum of the demand and the liquefied rate) improved and smoothened, thereby matching the output curve more closely (Figure 7c). Thus, the pressure curve in Figure 7a was kept at very low levels near the lower limit. Although the load change in the ASU eliminated differences between the outputs and demands as well as the liquefiers, it was still energy-inefficient given that the ASU was conventionally designed to maximize the operation efficiency. Small load changes could still extensively effect on the overall ASU output; thereby increasing the unit energy consumption of oxygen production. In contrast, the energy cost brought by liquefiers is only limited to the energy consumption of the liquefiers themselves and can be excluded from the overall energy cost of the oxygen distribution system because the liquefaction cost would eventually be passed onto the product of the LOX and can be recovered by liquid sale. In the third time segment, the ASU A5 moved from the off state to the production mode (Figure 6), while a single ASU (A6 or A8) remained at the off state during the majority of the segment following the blow-down because the molten iron output and oxygen consumption from the BF was still smaller than the conventional levels even after the BF returned to production. Figure 7a illustrates a small hump of pressure emerging at the beginning of this time segment (after the ASU A5 was online and before the ASU A6 was online). The change rate in the step increase for the ASU outputs, which was a result of the restart in ASU A5, was significantly faster than the gradual rise in demand. Thus, although the liquefiers worked under the full liquefaction rate (Figure 9), high-pressure network were still required to ensure the balance between the supply and demand. Moreover, to cooperate with this action, all the compressors operated under high loads until the ASU A6 came online and served its HP-GOX (Figure 8). In brief, this case justified the applicability of the proposed optimization model in providing the optimal shut-down policy of ASUs in the oxygen distribution system during a BF blow-down.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b03999. readme.txt; lingo model for calculations-MILP.txt; model_results-MILP.xlsx; lingo model for calculationsMINLP.txt; model_results-MINLP.xlsx (ZIP)
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AUTHOR INFORMATION
Corresponding Author
*L. Wang. Telephone: +86 10 6233 2566. E-mail: liwang@me. ustb.edu.cn. ORCID
Peikun Zhang: 0000-0003-4184-5950 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the National Natural Science Foundation of China (NSFC, Grant No. 51306015), and the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP, Grant No. 20130006120015) for financial support. Mr. Chenhao Zhou and Mr. Zhengqiang Li of the Baosteel Group Co., Ltd., are gratefully acknowledged for their useful feedback and valuable suggestions. We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.
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NOMENCLATURE
Sets
f = sphere vessel ( f = 1, ..., NF) h = variable-load compressor (h = 1, ..., NB) i = ASU (i = 1, ..., NA) I
DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research j = fixed-load compressor (j = 1, ..., NC) m = liquefier (m = 1, ..., NL) t = period (t = 1, ..., T)
Making Level to Improve the Enterprise-Wide Production Flexibility. AIChE J. 2013, 59 (5), 1588. (7) Manenti, F.; Rovaglio, M. Market-Driven Operational Optimization of Industrial Gas Supply Chains. Comput. Chem. Eng. 2013, 56, 128. (8) Marchetti, P. A.; Gupta, V.; Grossmann, I. E.; Cook, L.; Valton, P. M.; Singh, T.; Li, T.; André, J. Simultaneous Production and Distribution of Industrial Gas Supply-Chains. Comput. Chem. Eng. 2014, 69, 39. (9) Rossi, F.; Manenti, F.; Reklaitis, G. A General Modular Framework for the Integrated Optimal Management of an Industrial Gases Supply-Chain and Its Production Systems. Comput. Chem. Eng. 2015, 82, 84. (10) Han, Z.; Zhao, J.; Wang, W.; Liu, Y. A Two-Stage Method for Predicting and Scheduling Energy in an Oxygen/nitrogen System of the Steel Industry. Control Eng. Pract. 2016, 52, 35. (11) Puranik, Y.; Kilinc, M.; Sahinidis, N. V.; Li, T.; Gopalakrishnan, A.; Besancon, B. Global Optimization of an Industrial Gas Network Operation. AIChE J. 2016, 62 (9), 3215. (12) Zhou, D.; Zhou, K.; Zhu, L.; Zhao, J.; Xu, Z.; Shao, Z.; Chen, X. Optimal Scheduling of Multiple Sets of Air Separation Units with Frequent Load-Change Operation. Sep. Purif. Technol. 2017, 172, 178. (13) Xu, Z.; Zhao, J.; Chen, X.; Shao, Z.; Qian, J.; Zhu, L.; Zhou, Z.; Qin, H. Automatic Load Change System of Cryogenic Air Separation Process. Sep. Purif. Technol. 2011, 81 (3), 451. (14) Li, H. Oxygen Technology, 2nd ed.; Metallurgical Industry Press: Beijing, China, 2009. (15) Zhang, P.; Wang, L.; Tong, L. MILP-Based Optimization of Oxygen Distribution System in Integrated Steel Mills. Comput. Chem. Eng. 2016, 93, 175. (16) Manenti, F.; Rossi, F.; Croce, G.; Grottoli, M. G.; Altavilla, M. Intensifying Air Separation Units. Chem. Eng. Trans. 2012, 35, 1249. (17) Mitra, S.; Grossmann, I. E.; Pinto, J. M.; Arora, N. Optimal Production Planning under Time-Sensitive Electricity Prices for Continuous Power-Intensive Processes. Comput. Chem. Eng. 2012, 38, 171. (18) Zhang, Q.; Sundaramoorthy, A.; Grossmann, I. E.; Pinto, J. M. A Discrete-Time Scheduling Model for Continuous Power-Intensive Process Networks with Various Power Contracts. Comput. Chem. Eng. 2016, 84, 382. (19) Li, Y.; Wang, X.; Ding, Y. A Cryogen-based Peak-shaving Technology: Systematic Approach and Techno-economic Analysis. Int. J. Energy Res. 2013, 37, 547.
Parameters
Δt = time-interval length (h) ANPG = NP-GOX rated output of ASU i [(Nm3)/h] i HPG Ai = HP-GOX rated output of ASU i [(Nm3)/h] ADti = minimal off time of ASU i (h) AUti = minimal run time of ASU i (h) Bmin = minimal rate of variable-load compressor h [(Nm3)/ h h] Bmax = maximal rate of variable-load compressor h [(Nm3)/ h h] Cj = rated load of fixed-load compressor j [(Nm3)/h] CDtj = minimal off time of fixed-load compressor j (h) CUtj = minimal run time of fixed-load compressor j (h) DNPG = demand of NP-GOX at time t [(Nm3)/h] t DHPG = demand of HP-GOX at time t [(Nm3)/h] t max P = upper limit of pressure of high-pressure network (Pa) Pmin = lower limit of pressure of high-pressure network (Pa) LNPGmax = maximum NP-GOX rate to liquefier m [(Nm3)/h] m LHPGmax = maximum HP-GOX rate to liquefier m [(Nm3)/h] m NPGmin Lm = minimum NP-GOX rate to liquefier m [(Nm3)/h] HPGmin = minimum HP-GOX rate to liquefier m [(Nm3)/h] Lm R = 8.31446 m3·Pa·K−1·mol−1 (ideal gas constant) T = temperature (K) Vf = capacity of vessel f for gas storage (m3) vh = load change speed of variable-load compressor h (Nm3/ h2) κ = polytropic index of oxygen compression process (a real number) Continuous Variables
bh,t = load of variable-load compressor h at time t (Nm3/h) et = oxygen vent rate at time t [(Nm3)/h] 3 lNPG m,t = NP-GOX rate to liquefier m at time t [(Nm )/h] HPG lm,t = HP-GOX rate to liquefier m at time t [(Nm3)/h] pt = pressure of high-pressure network at time t (Pa) Binary Variables
ati = operating status of ASU i at time t ctj = operating status of fixed-load compressor j at time t wtj = start-up status of fixed-load compressor j at time t xti = start-up status of ASU i at time t yti = shut-down status of ASU i at time t ztj = shut-down status of fixed-load compressor j at time t
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REFERENCES
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DOI: 10.1021/acs.iecr.6b03999 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
