Preventive Optimization Framework for Unexpected Equipment

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Ind. Eng. Chem. Res. 2002, 41, 6070-6081

PROCESS DESIGN AND CONTROL Preventive Optimization Framework for Unexpected Equipment Failures in the Utility System with Quantitative Emergency Handling Constraints Jeong Hwan Kim,† Sangjun Ju,† Heui-Seok Yi,‡ In-Su Han,† and Chonghun Han*,† Department of Chemical Engineering and School of Environmental Science and Engineering, Pohang University of Science and Technology, San 31 Hyoja, Pohang, Kyungbuk 790-784, Korea

A preventive optimization framework is proposed to find the optimal operation that can avoid plant shutdown in the case of unexpected equipment failures in the utility system. To find the optimal solution in terms of both operation cost reduction and emergency handling capability improvement, emergency handling constraints that consider the present system’s capability of avoiding plant shutdown by performing predetermined emergency response actions are incorporated into the conventional optimization model. To verify the proposed approach, simulation case studies were performed and their results were compared with those of the equal load allocation method and the conventional optimization approach. The simulation results show that the proposed approach successfully handles the emergency situation with reduced total cost by simultaneous consideration of process robustness and operating cost. This idea can be generally applied to other processes by adopting appropriate emergency handling constraints into the optimization formulations. 1. Introduction The utility system in the chemical complex is as important as the human heart. All production plants rely on a consistent supply of steam and electricity, which requires expensive operating costs in the utility plant for its continuous production. Therefore, the optimal operation of the utility system requires satisfication of two objectives. One is to minimize the total operating cost, and the other is to consistently provide steam and electricity to the production plant. To achieve these objectives, many research works have been proposed such as thermodynamic approaches, mathematical programming, and rule-based approaches. Among various approaches, the mathematical programming has been widely used for its advantage of providing a common framework for solving different classes of problems in a systematic manner.1 Previous studies on the optimization of the utility systems based on the mathematical programming are mainly concerned with formulating optimization problems to minimize the total cost by either deterministic or stochastic approaches and with developing an efficient algorithm to solve them. A deterministic approach assumes the deterministic, i.e., fixed, values for the parameters in the model such as demands, efficiencies of equipment, etc. Cho2 proposed an optimization method, where the capacities and efficiencies of the boilers are taken into account, to * To whom all correspondence should be addressed. Tel: +82-54-279-2279. Fax: +82-54-279-5528. E-mail: chan@ postech.ac.kr. † Department of Chemical Engineering. ‡ School of Environmental Science and Engineering.

reduce the fuel consumption by allocating optimal loads to the boilers. Ito et al.3 presented an operational planning model for gas-turbine cogeneration plants that include startup and shutdown costs to find more exact optimum solutions by introducing equipment startup/shutdown costs. Hui and Natori4 have presented a mixed-integer linear programming (MILP) formulation to determine the best combination of equipment to be added to the existing utility system that can maximize the total profit through the planning horizon. The difference of unit electricity cost between day and night, seasonal steam, and electricity demands were employed in their formulation. Kalitventzeff5 presented a mixedinteger nonlinear programming (MINLP) formulation for the management planning of utility networks for chemical plants. Prokopakis and Maroulis6 introduced the transition function to remove the discontinuities stemming from the equipment operation range limit and thus transformed the MINLP to nonlinear programming (NLP) for shorter computation time to use in real-time optimization for an industrial utility system. Iyer and Grossmann7,8 proposed the two-stage algorithm using a bilevel decomposition method and the modified shortest path algorithm with a partial enumeration to reduce the computation time, where switching cost between periods is considered. Kim et al.9 proposed the bilevel programming approach where heuristics-combined dynamic programming is used to find the optimum solution, and Kim and Han10 improved this approach by introducing successive refinement steps to consider the transition cost between two connected periods. Recently, Yi et al.11 proposed a two-level optimization model, which is composed of the MILP model to determine the

10.1021/ie020059+ CCC: $22.00 © 2002 American Chemical Society Published on Web 11/02/2002

Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 6071

Figure 1. Causes and portions of industrial chemical plant accidents in Korea.

optimal configuration of pumps and the NLP model to determine the optimal steam load allocation at steam generation part, to consider the internal and external utility demand of steam and electricity. Yi and Han12 proposed the integration of complete replanning and plan repairing which is constructed by a rule-based system to handle the prediction errors for energy demands during multiperiod operational planning. Many research works have been made by a stochastic approach to handle the uncertainties in demands, prices, etc. Papalexandri et al.13 suggested a multiperiod optimization method to handle the uncertainties of energy demands and efficiencies of equipment in the utility plant. In their works, two-mode demands for midweek and weekend were introduced to find the optimal solution that is robust enough to model uncertainty and is flexible enough to accommodate variable energy demands. Bansal et al.14 proposed a simultaneous design and control optimization for a large-scale, complex, mixed-integer dynamic model under timevarying disturbances and parametric uncertainties. Although previous optimization approaches have provided the optimum solution to minimizing the total operating cost by considering the various characteristics of the utility systems, the optimization results are true under the major assumption that the process does not experience any kinds of equipment failures during the operation horizon. However, major equipment shutdown may happen, and it can result in the process shutdown, which results in an enormous loss. The statistical data show that unexpected equipment failure is one of the major causes of chemical plant accidents, as shown in Figure 1,15 and it should be appropriately handled in the optimization framework. To prevent equipment failure or, at least, to minimize its effect on the total cost by determining optimal maintenance time and activity, many researches on preventive maintenance optimization have been proposed. Sanmarti et al.16 presented a preventive maintenance scheduling approach for multipurpose batch plants under equipment failure uncertainty, where the effects of equipment failures on the production schedule are minimized by computing the reliability indexes and avoiding the use of equipment with low reliabilities. Dedopoulos and Shah17 presented a two-step solution procedure to determine the optimal preventive maintenance policy. In the first step, a short-term stochastic scheduling problem is solved to find the expected profitability at each period, and in the second step, a long-term maintenance optimization problem is solved to determine the time at which preventive maintenance

is performed. Recently, Vassiliadis and Pistikopoulos18 proposed a MINLP model to find optimal preventive maintenance policies in continuous process operations under parametric uncertainty to maximize the system effectiveness measure. The interactions of maintenance, process characteristics, and process uncertainty were considered, and introducing the availability threshold value reduced the computation time. Although the preventive maintenance approaches provide a quantitative method to minimizing the impact of equipment failures or to reducing the frequency of equipment failures using the rate functions for expected equipment failures during a scheduling or planning, it is difficult to predict when the equipment failure will happen. Generally, the rate of equipment failures at a specific operating period cannot be exactly predicted because it is not just a function of time but also a function of temperature, pressure, chemical concentrations, number of startups and shutdowns, etc., in chemical processes.19 Therefore, the preventive maintenance approaches are not effective for the optimization of utility plants where unexpected equipment failures happen and cannot be easily predicted. Therefore, the optimization framework that can handle unexpected equipment failure and obtain economic benefit by efficient operation is required. In this study, we present a new optimization framework that finds the optimal solution that is robust to the unexpected equipment failure with minimum operating cost. Emergency handling constraints that consider the present system’s capability of avoiding plant shutdown were added to the conventional optimization (CO) model. Incorporation of emergency handling constraints in the model constrains the feasible solution space so that the optimal solution can be determined to avoid process shutdown under the assumption that emergency response actions are performed during the emergency situation. To verify the effectiveness of the proposed optimization formulations, several case studies were carried out and their results were compared with those of the equal load allocation (ELA) method and the CO approach. 2. Description of the Utility Systems A utility plant supplies several types of steams and electric power to the down steam production processes in a chemical complex. Typically, the utility plant consists of the steam generation part and the steam distribution part, as shown in Figure 2. At the steam generation part, the boilers produce superheated steam by burning fuels. Because each boiler has different efficiencies, the optimal allocation of steam to each boiler is required to minimize the total cost of the fuel consumed.2 At the steam distribution part, superheated steam is distributed to the production processes through turbines and letdown valves to satisfy several types of steam and electricity demands. Steams that are not used to supply the process demands are condensed by cooling water, recycled to a deaerator, and reused as boiler feedwater. 3. Emergency Situations and Emergency Response Actions in the Utility Systems Emergency situations occurring in a chemical plant are very dangerous and greatly damaging to property because they may result in the whole process shutdown,

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Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002

Figure 2. Emergency response actions in the utility system under an emergency situation.

leakage of toxic chemicals, or tank explosions if not appropriately handled within a certain amount of time. The emergency situations might happen for various reasons including operation errors, unexpected equipment failures, design errors, process defects, etc.15 In this study, the emergency situations caused by unexpected equipment failures in the utility plants are the major concern. In the utility plant, boilers and turbines are the most important equipment. Especially, the failure of the boilers causes much harm to the production processes because it leads to a failure to produce the required amount of steam to the production processes. Figure 2 shows an emergency situation arising from unexpected equipment failure in the utility plant. When one of the running boilers fails unexpectedly, the total production rate of steam at the boilers decreases, and the pressure of the XPS header goes down below the allowed minimum operating pressure. This impact is propagated to the production processes. The pressure drop at the XPS header decreases the pressures of the distributed steams (HPS, high-pressure steam; MPS, medium-pressure steam; LPS, low-pressure steam), and it can result in the malfunction of the production process equipment such as reactors and heat exchangers, where specified qualities of steam are required for a normal operation of the process. To avoid equipment breakdown, plants are shut down according to its priority before they reach the minimum allowable steam-deficiency limit. When unexpected equipment failure happens, the steam and energy balance is broken. To recover the steam and energy balance quickly, emergency response actions are immediately performed during the emer-

gency situation,20-23 and Figure 2 shows the emergency response actions performed in the system. Emergency Response Actions. 1. Steam production rates of the remaining boilers are increased to their maximum to compensate quickly for the deficient amount of steam. 2. The steam flow rate to the turbine to be used for in-house electricity generation is decreased, and more steam is supplied to the production plant, directly. 3. Steam and electricity demands from the production plant are temporarily reduced to their tolerable limits by slowing down the production process to avoid the plant shutdown. 4. Electricity is imported from an external power company to compensate for the power shortage. If the sudden steam shortage can be supplemented within a certain amount of time, the process shutdown can be avoided. However, the steam production rates cannot be drastically increased to their desired values in a short period of time because of the mechanical limitation of the boilers. A period of time within which the production process can endure the shortage of steam supply is defined as the process buffer time in this study. The process buffer time depends on the type of production process and is usually within a few minutes. According to the present operation status, the plant shutdown can be avoided by emergency response action or cannot be avoided even with emergency response actions. If the present operation status has the capability of dealing with unexpected failure, then plant shutdown is avoided by performing emergency response actions, and vice versa. Therefore, it is very important


Figure 3. Overall structure of considering an emergency situation.

not only considering the economic operation at the present time which previous approaches2-13 have mainly focused on but also considering the capability of avoiding plant shutdown under emergency situations. 4. Emergency-Considered Optimization (ECO) for the Utility Systems 4.1. Overall Structure of Considering an Emergency Situation. To find the optimal solution that considers an emergency situation, the ECO framework is proposed. Figure 3 shows the overall structure of considering an emergency situation in the utility systems. Two ways of considering an emergency situation are possible. One is to strictly prohibit the process shutdown by incorporating emergency handling constraints as hard constraints (ECO-I), and the other is to allow the process shutdown by incorporating them as penalty functions (ECO-II). The decision on which formulation to use depends on the impact when the process shutdown happens. If the process shutdown results in the critical unfavorable effect such as an environmental problem or damage of an operator’s health and safety, the formulation of allowing process shutdown (ECO-II) cannot be chosen. Therefore, the investigation on the impact of process shutdown is first made, which includes the investigation on the process buffer time, mechanical limitation on the increase of the steam production rate, frequency of equipment failure, and penalty cost for the process shutdown, and is performed to find how long the plant can endure the emergency situation without experiencing plant shut-

down and how quickly the deficient amount of steam can be supplied. This information can be obtained from a process expert and operation data. Then, the decision on which formulation to use based on this investigation is made. If the optimization result of ECO-I or -II produces a feasible solution, it is implemented into the process. If it does not produce a feasible solution because of the limited capacity of the present steam production system, the addition of new boilers to the present steam production system can be considered to improve the emergency handling capability. Process buffer time analysis, which is applied to ECO for various process buffer times, is performed to find out the chance of improving the emergency handling capability of the present process. Then, the optimal size of the boiler to be added is determined on the basis of the result of process buffer time analysis, and ECO is applied with the changed emergency handling constraints. In the formulation of the ECO, the following points are assumed. Assumptions. 1. Steam cannot be purchased from outside; thus, failure of steam supply results in the shutdown of the process. 2. Electricity can be purchased from an external electric power company. 3. The penalty cost for the shutdown of the process is given and has a fixed value. 4. The frequency of the shutdown of the equipment can be calculated from the historical operation data. 5. The boiler efficiency curve is regressed as a quadratic function of the steam production flow rate. 6. Predetermined emergency response actions are performed during the emergency situation when the equipment failure happens. 4.2. ECO-I. The ECO-I formulation finds the optimal solution where process shutdown is strictly prohibited and the total operating cost is minimized. To reflect the nonlinearity arising from energy balance, boiler efficiency relationship, and emergency handling constraints, ECO-I is formulated as a NLP. Because the emergency situation where two or more of the boilers unexpectedly fails at the same time rarely happens, the emergency situation where only one of the boilers unexpectedly fails is considered in the formulation, but the same idea can be applied to multiple equipment failure by appropriate modification of the formulations.

[( NB

min J1 ) XD

∑ i)1

)

in Hout Fout - Hin i i i Fi

ηBi Cp im Max +

{PexCex + PimC

+P

CF +

Cpp} + WUCW +

NB

im,e im fuf C + PMax+,e Cpp} ∑ j {Pi i j)1

]

(1)

This is subject to the following: (1) Model equations and operating conditions:

∑Fink - ∑Fout k ) 0, k ) 1, 2, ..., NE out ∑Hink Fink - ∑Hout k Fk ) 0, k ) 1, 2, ..., NE

(2) (3)

ΩL,k e Uk(F,T,P) e ΩU,k, k ) 1, 2, ..., NE

(4)

ηBi ) ai(FBi )2 + biFBi + ci, i ) 1, 2, ..., NB

(5)

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(2) Steam and electricity supply constraints: NTB

G Qr,k g QD ∑ r, k)1

r ) 1, 2, ..., NS

(6)

NTB

PG )

HP XP HP MP HP MP ηTB ∑ k [Fk (Hk - Hk ) + Fk (Hk - Hk ) + k)1 MP LP cond cond (HLP )] (7) FLP k (Hk - Hk ) + Fk k - Hk

PG - PD ) Pex - Pim PexPim ) 0

Pex, Pim g 0

Pim - PMax ) PMax+ - PMax-

(8) (9)

PMax+, PMax- g 0 (10)

Figure 4. Unit electricity cost change.

(3) Emergency handling constraints: NTB

∑ k)1

NB

G Qr,k - FBj +

∑ i*j

NTB

∆FtBp,i +

IG ∆Qr,k g Qr,L, ∑ k)1

r ) 1, 2, ..., NS, j ) index of boiler tripped (11)

where

∆FtBp,i ) FBi {(1 + νi)tp,i - 1}, i ) 1, 2, ..., NB

(12)

log(Fmax,i/Fi) , i ) 1, 2, ..., NB log(1 + νi)

(13)

tmax,i )

tp,i ) min(tb, tmax,i), i ) 1, 2, ..., NB

(14)

IG e ∆Qr,k ) Fr,k - Fr,k, k ) 1, 2, ..., NTB, r ) 1, 2, ..., NS (15) NTB

PG,e ) i

HP,e HP ηTB (HXP ∑ k {Fk k - Hk ) + k)1

MP LP,e LP (HHP (HMP FMP,e k k - Hk ) + Fk k - Hk ) + cond (HLP )} (16) Fcond,e k k - Hk

PG,e - PD,e ) Pex,e - Pim,e i i i Pex,e Pim,e )0 i i

im,e Pex,e g0 i , Pi

(17) (18)

- PMax ) PMax+,e - PMax-,e Pim,e i i i i Max+,e

Pi

, PMax-,e g 0 (19) i

In the formulation, the objective is to minimize the total operation cost that consists of oil consumption cost, electricity consumption cost, water usage cost, and the expected electricity import cost under an emergency. The electricity consumption cost is formulated to reflect the unit electricity price change as shown in Figure 4. For the peak electricity demand that is larger than the contract maximum electricity demand PMax, large penalty Cpp is imposed, and the different unit electricity price for importing Cim and exporting Cex is multiplied by the quantity of electricity imported and sold, respectively. Slack variables PMax+, PMax-, Pex, and Pim are introduced to formulate the amount of electricity used over the peak load, below the peak load, as export, and as import, respectively. In addition to the operation

Figure 5. In-house electricity generation using a multistage turbine.

electricity cost, the expected electricity cost under an emergency situation is considered because the reduced amount of electricity generation due to boiler failure can lead to the excessive import of electricity over contract. The inclusion of the expected electricity importing cost finds the optimal solution that can avoid the excess import of electricity. The decision variables (XD) are steam production rates at each boiler FBi . The process configuration, process buffer time, and demands on steam and electricity are given. Equations 2-5 represent the model equations and operating conditions, eqs 6-10 are steam and electricity supply constraints, and eqs 11-19 are emergency handling constraints. The material and energy balances (described in eqs 2 and 3, respectively) for all of the equipment (k ) 1, 2, ..., NE), such as the header, boiler, turbine, pump, and heat exchangers, should be satisfied, and the operating conditions (mass flow rates, temperatures, and pressures) of all of the equipment should be operated within the normal operating ranges as shown in eq 4. Equation 5 is the boiler efficiency regressed as a quadratic function of the steam production rate for each boiler i. The generation rate of each steam type r should satisfy the present steam demand of type r as in eq 6. In-house electricity generation using a multistage turbine can be schematically understood as in Figure 5. The amount of power generated is the sum of the enthalpy difference between the input and output of steam multiplied by turbine efficiencies, and eq 7 represents the amount of in-house electricity generation. When an emergency situation happens, the amount of steam extraction is increased to its maximum to supply more steam to the production, and as a result a smaller amount of steam is supplied to condensing steam flow where the enthalpy difference is large; thus, the amount of in-house electricity generation is reduced. Equations 8-10 are auxiliary equations to represent the power deficit or surplus. According to the difference between


Figure 6. Schematic diagram of an increase in the steam production rate.

in-house generation and electricity demand and the unit costs, the electricity to generate and import is determined to minimize the total cost. Equation 11 denotes the emergency handling constraints that find the optimal steam flow rates that can avoid process shutdown when one of the running boilers unexpectedly fails. Equations 12-19 are the auxiliary variables associated with this constraint. The emergency handling constraint represents the fact that plant shutdown can be avoided only if the deficient amount of process steams can be complemented during the process buffer time and steam supplies are maintained over the minimum steam demands of Qr,L. Steams are supplied by increasing the steam production rate of the remaining running boilers and by reducing the in-house electricity generation, i.e., increasing the steam flow rate to each process steam header. The resulting steam supply after the process buffer time is equal to the left-hand side in eq 11, and the reduced steam demands from the production plant by slowing down the production rate are as much as the right-hand side in eq 11. However, because of the mechanical limitation of the boiler, boilers cannot increase their steam production rate drastically, and there is a maximum steam production increasing rate vi for each boiler. As a result, the steam production rate of the boiler exponentially increases at a fixed increasing rate of υi as described in eq 12. Another physical constraint is the maximum steam production limit of each boiler Fmax,i due to the capacity limit of the boilers, and the maximum time of steam production increase tmax,i exists, which is the time period to increase the steam production from the present steam production rate Fi to the maximum steam production rate Fmax,i (eq 13). Therefore, the actual increase of steam production of the remaining boiler under an emergency situation is made during the steam production time tp,i, which is the minimum value between the process buffer time tb and the maximum steam production increase time tmax,i (eq 14), and the increased steam production rate ∆Fi during the process buffer time is calculated as in eq 12. Figure 6 shows the increase of the steam production rate by increasing the steam production rate with the remaining boiler. If the maximum steam production time of a boiler is shorter than the process buffer time, the steam production time of the boiler is equal to the maximum steam production time of the boiler, and vice versa, which is shown in Figure 7. According to the present steam production rate of each boiler, the actual steam production time of each boiler varies, and it directly affects the capability of deficient steam makeup to avoid the whole process shutdown. Equation 15 shows the amount of increased steam of type r by reducing in-house generation. The

Figure 7. Increase of the steam production rate during a production time.

steam flow rate to the process steam header is increased to its maximum, and the reduced electricity is complemented by importing electricity from the external power company. Equation 16 represents the amount of electricity generation under an emergency situation, and eqs 17-19 are the auxiliary equations. Emergency handling constraints show that the determination of optimal steam production rates of each boiler is important and should be reflected in the optimization formulation to prevent whole process shutdown, because the steam production rate of each boiler is the only variable that can be optimized for preventing process shutdown for the given process where Fmax,i, υi, and tb are predetermined. 4.3. ECO-II. ECO-II finds the optimal solution where process shutdown is considered for the optimal tradeoff between the operating cost reduction from efficient load allocation and the penalty cost increase from process shutdown. ECO-II is formulated as MINLP as follows.

[∑( NB

min J2 ) XD

i)1 ex

ηiCpi im Max+

{P C + P C ex

)

in Hout Fout - Hin i i i Fi

im

+P

CF +

Cpp} + WUCW +

NB

∑ j)1

NB

im,e im fuf C + PMax+,e Cpp} + CPSD j {Pi i

yPSD,j fuf ∑ j j)1

]

(20)

This is subject to the following: (1) Model equations, operating conditions, and steam and electricity supply constraints: eqs 2-10. (2) Emergency handling constraints: NTB

yPSD,j ) 0 if

∑Q

G r,k

k)1

yPSD,j ) 1 otherwise

NB

- FBj +

∑ ∆F i*j

B tp,i

NTB

+

∑ ∆Q

IG r,k

k)1

g Qr,L

}

for j ) 1, 2, ..., NB, r ) 1, 2, ..., NS (21)

and auxiliary equations: eqs 12-19. The objective is to minimize the total cost where the penalty cost for a plant shutdown is added to the operation cost. CPSD is a unit process shutdown penalty cost. It includes the cost for repairing and restartup of the tripped boilers, production loss penalty cost due to the process shutdown, and customer dissatisfaction due to delayed delivery. fuf j is an average boiler failure

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Table 1. Cost Data total cost ) operating cost + penalty cost ) fuel cost + electricity cost + water cost + process shutdown penalty cost operating cost unit fuel cost [won/tons of B-C oil] 200 000 unit electricity import cost [won/MW] 60 000 unit electricity export cost [won/MW] 20 000 excess electricity import cost [won/MW] 1 000 000 unit water cost [won/ton] 2 000 penalty cost unit process shutdown penalty cost [won] 75 000 000

Table 2. Coefficients of the Boiler Efficiency Curve boiler 1

boiler 2

boiler 3

boiler 4

boiler 5

ai -0.0000077 -0.0000012 -0.000011 -0.000011 -0.000011 bi 0.0005 -0.0002 0.0019 0.001863 0.0019 ci 0.89 0.802 0.842 0.872 0.812 Table 3. Steam and Power Demands

HPS (395 °C, 45 bar, tons/h) MPS (285 °C,11.5 bar, tons/h) LPS (210 °C, 3.3 bar, tons/h) electricity (MW)

normal operation

emergency situation

175 75 65 60

170 70 60 55

frequency. Similar to ECO-I, the emergency situation where only one of the running boilers unexpectedly fails is considered in the formulation. The decision variables are the flow rates of the steam generated by the boilers. The constraints are similar to those of the ECO-I formulation except that the emergency handling constraints for preventing process shutdown are replaced by soft constraints in the objective function. 5. Case Studies The proposed optimization approach was applied to a simulated model of the industrial-scale utility system at Hyundai Petrochemical Co. in Korea. The utility system consists of five boilers and two turbines. The maximum steam production-increasing rate of the ith boiler υi is assumed to be 5% for all of the boilers. Tables 1 and 2 show the unit cost data and coefficients of the boiler efficiency curve used in the case studies, respectively. The efficiency of the turbines was assumed to be 0.12 for both turbines. The data used in the case study for steam and electricity demands from the production process at normal operation and under an emergency situation are tabulated in Table 3. 5.1. Application of ECO-I. The case studies for ECO-I were carried out, and the optimization results were compared with other operation strategies: the CO, where the emergency handling constraints are not considered in the optimization formulation, and the ELA, where steam generation rates are equally allocated to all of the boilers, which is common in the industrial field. The capacities of the boilers are the same, and the maximum steam production rate of the ith boiler Fmax,i is 150 tons/h for all of the boilers. The process buffer time for the case study is assumed to be 4.4 min. The frequency of unexpected boiler failure is assumed to be one time per year for all boilers. Table 4 shows the optimization result of the major equipment in the system. The result shows that the optimum steam production rates of the boiler are different in each method. This difference affects the emergency handling capability and operating cost. Because the boiler efficiencies are different, the different steam production loads result in the difference in the operation cost and the amount of deficient steam

makeup during the process buffer time, which is directly related with the emergency handling capability. The different amounts of steam makeup also lead to the different amounts of in-house generation and affect the amount of electricity import that should be maintained within the maximum import limit for avoiding high penalty. Table 5 shows a comparison of the emergency handling capability when the no. 3 boiler unexpectedly fails. ECO-I and ELA can handle the emergency situation, while CO cannot handle the emergency situation because it cannot produce the required minimum amount of HPS during the process buffer time, although it satisfies the steam demands for MPS and LPS. Table 6 shows a comparison of the total cost. The results show that CO shows the lowest operation cost, ELA shows the highest operation cost, and ECO-I shows a slightly higher cost than that of CO. This is because CO finds the optimal operation by only considering the operating cost reduction and ELA does not consider the different efficiencies of the boilers. The results show that the ECO-I finds the optimum solution that is robust to the unexpected equipment failure, reduces the operation cost, and is closely related to the present operation’s capability of steam makeup during the process buffer time. In the next section, to analyze the effect of the process buffer time on the optimization results, simulation studies for various process buffer times were performed and the optimization results are compared with other approaches. 5.2. Process Buffer Time Analysis with ECO-I. Figure 8 shows the results of optimal steam load allocation by applying ECO-I for various process buffer times. The results show that the optimum steam loads by ECO-I are different for the different process buffer times even for the same steam and electricity demands and the process buffer time belongs to one of three characteristic regions: regions A-C. For the process whose tb is in region A, the process buffer time is too short to make up for the deficient amount of steam due to the limited capability of the present steam production system, and no feasible solution exists. For the process whose tb is in region B, optimal solutions exist that can avoid process shutdown with a minimized operating cost. In region C, there exist optimal solutions, but the same optimal values are obtained regardless of the process buffer time because the emergency handling constraint (eq 11) is not active because of the high process buffer time. Table 7 summarizes a comparison of the emergency handling capabilities of the three operation strategies. For the process whose tb is in region A, no operation strategies can handle the emergency situation when one of the boilers experiences failure. Consequently, the shutdown of the whole process cannot be avoided by optimal operation of the present steam production system. Because the process buffer time is an inherent characteristic of a process and cannot be changed, the only solution to this situation is either to increase the capacities of the boilers or to install another boiler, and a detailed discussion on this appears in section 5.3. In region B, the process shutdown can be avoided by ELA and ECO-I, while it cannot be avoided by CO if one of the running boilers in the parentheses unexpectedly fails. For example, the process whose buffer time is equal to 4.0 min should drift to shutdown when one of the boilers 3-5 fails unexpectedly. In region C, all of

Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 6077 Table 4. Comparison of the Optimization Results of Major Equipment flow rate [tons/h]

boiler 1 inlet boiler 2 inlet boiler 3 inlet boiler 4 inlet boiler 5 inlet boiler 1 outlet boiler 2 outlet boiler 3 outlet boiler 4 outlet boiler 5 outlet XPS outlet turbine 1 inlet turbine 1 ext 1 turbine 1 ext 2 turbine 1 ext 3 turbine 1 cond turbine 2 inlet turbine 2 ext 1 turbine 2 ext 2 turbine 2 ext 3 turbine 2 cond HPS header MPS header LPS header BLR feedwater deaerator out

ECO-I

CO

ELA

temp [°C]

91 60 118 119 112 91 60 118 119 112 500 225 78.8 31.5 29.3 85.5 275 97.3 43.5 35.8 99.5 175 75 65 315 500

84.9 60 118.6 126.5 110.0 84.9 60 118.6 126.5 110.0 500 225 78.8 31.5 29.3 85.5 275 97.3 43.5 35.8 99.5 175 75 65 315 500

100 100 100 100 100 100 100 100 100 100 500 225 78.8 31.5 29.3 85.5 275 97.3 43.5 35.8 99.5 175 75 65 315 500

120 120 120 120 120 510 510 510 510 510 510 510 395 240 160 84 510 395 240 160 84 395 240 160 30 99

pressure [bar]

vapor fraction

125 125 125 125 125 106.6 106.6 106.6 106.6 106.6 106.6 106.6 45 11.5 4.3 1 106.6 45 11.5 4.3 1 45 11.5 4.3 1 1

0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

generated electricity [MW]

27.20

34.54

Table 5. Comparison of the Emergency Handling Capabilitiesa ELA remaining boiler increase in-house generation slowing down the production process total process steam supply emergency handling capability

CO

ECO-I

HPS

MPS

LPS

HPS

MPS

LPS

HPS

MPS

LPS

175.2 3.51 5 178.7 Y

74.2 1.62 5 80.8 Y

65.1 1.30 5 71.4 Y

164.2 3.28 5 172.5b N

69.5 1.52 5 76.2 N

61.0 1.22 5 67.2 N

167.3 3.35 5 175.7 Y

70.8 1.55 5 77.4 Y

62.2 1.24 5 68.4 Y

a Y denotes that it produces the required steam demands within the buffer time. N denotes that it fails to produce the required steam demands within the buffer time. b Does not meet the minimum allowable steam demand.

Table 6. Comparison of the Total Cost (Units: won/h) ELA

CO

ECO-I

fuel cost 8 043 987 7 932 613 7 935 998 electricity cost -35 064 -35 064 -35 064 water cost 630 000 630 000 630 000 expected emergency electricity 219 243 219 import cost total cost 8 639 142 8 527 793 8 531 153

the operation strategies can handle the emergency situation by performing emergency response actions because the process buffer time is sufficiently long to cope with the process shutdown. Therefore, ECO-I and ELA produces more robust optimum solutions than CO. Figure 9 shows a comparison of the total operating costs of the three operation strategies. For the process whose tb is in regions B and C, CO shows the lowest total operating cost while ELA shows the highest total operating cost. The total operating cost of ECO-I is higher than that of CO in region B and is equal to that of CO in region C because the emergency handling constraint is not active in region C. It is a natural result that CO yields the best performance in terms of the total operating cost among the three operation strategies because the emergency handling constraints are not incorporated. However, CO cannot be applied to the utility system in which the boilers frequently fail to produce steam.

Figure 8. Optimal boiler load allocation by ECO-I for various process buffer times.

While the total operating costs of ELA and CO remain the same for the different process buffer times, that of ECO-I decreases as the process buffer time increases. This is because the feasible region is increased as the process buffer time increases, and a more economic solution is found within the larger feasible region. Figure 10 shows the changes of the feasible region of the optimal solutions of ECO-I as the process buffer time decreases. As the process buffer time decreases, the

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Table 7. Comparison of the Emergency Handling Capabilities for Various Process Buffer Timesa region A region B

region C

buffer time [min]

ELA

ECO-I

CO

before 3.5 3.5 3.6 4.0 4.4 4.8 5.1 after 5.1

N N Y Y Y Y Y Y

N N Y Y Y Y Y Y

N N N(3,4,5) N(3,4,5) N(3,4) N(4) Y Y

a Y denotes that it produces the required steam demands within the buffer time. N denotes that it fails to produce the required steam demands within the buffer time.

Figure 9. Total cost comparison for various process buffer times.

Figure 10. Feasible region change for various process buffer times.

emergency handling constraints becomes active and the feasible region is reduced. Depending on the process, emergency constraints can be more strict or redundant than other conventional constraints, such as material balances, energy balances, equipment operation range limit, etc., that previous approaches have included in their optimization formulation of the utility systems.2-12 Therefore, the solutions found without considering emergency constraints become infeasible in terms of the emergency handling capability when the process has more strict conditions due to emergency handling constraints. For the process whose buffer time is in region B, the emergency handling constraint should be employed to the optimization formulation to find the optimum solution in the reduced feasible region. 5.3. Application of ECO-II. The optimization studies are performed for the same process as that in section

5.1 using ECO-II, and the optimization results are compared with those from ECO-I. The frequency of unexpected equipment failure of the boiler is assumed to be one time per year for all boilers. Table 8 shows the optimal steam production rate by each approach and process shutdown frequency in the case of unexpected boiler failures. ECO-I experiences no process shutdown, while ECO-II and CO experience process shutdown one and two times, respectively. Table 9 shows the total cost comparison of ECO-II with ECO-I and CO. The operation with ECO-II results in a decrease of the operating cost but an increase of the penalty cost. Process shutdown occurs one time when one of the boilers in the parentheses unexpectedly fails. The total cost is reduced because ECO-II finds the optimal tradeoff between the increase of the economic benefit from efficient operation and the loss from reduced emergency handling capability. For the process where the equipment failure rate is very low and process shutdown can be allowed for the economic operation, ECO-II can be applied to find the optimum steam production rate whose total cost is lower than that of ECO-I. 5.4. Effect of the Steam Production Configuration on the Emergency Handling Capability. As shown in the previous case studies, the capability of handling unexpected equipment failure of the present steam production system is an important factor in determining an optimal operation and is closely related to the steam production configuration. To analyze the relationship between the configuration of the steam production system and the emergency handling capability, a simulation case study was performed. Figure 11 shows the different configuration types of the steam production system, each of which produces the same amount of steam of 500 tons/h to the header: (a) the configuration of the same boiler capacities and (b) the configuration of the different boiler capacities. The upper bar and lower bar represent the maximum and minimum steam production rate at each boiler, respectively. Process buffer time analysis was made for configurations a and b by ECO-I, and a comparison of the emergency handling capability was made by comparing the minimum process buffer time that each configuration can handle. Figure 12 shows the process buffer time analysis result for the b configuration. Comparing the result with that of the same boiler capacity configuration, which is shown in Figure 7, reveals that the emergency handling capability varies depending on the configuration and is better in the same capacity configuration than in the different capacity configuration. The minimum process buffer time by the same capacity boiler configuration is 3.6 min, while that of the different capacity boiler configuration is 4.7 min. The simulation result implies that the configuration of the steam production system can make a big difference for the process whose process buffer time is between 3.6 and 4.7 min when unexpected equipment failure happens. Although the difference of the minimum process buffer time that each configuration can handle is only about 70 s, it can be a critical time under an emergency situation that determines the process shutdown or not. In the industrial field, an ELA with the same capacity configuration boiler system is preferred for its advantage of emergency handling capability and operation

Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 6079 Table 8. Comparison of the Optimal Production Rates and Process Shutdown Rates optimal steam production rate [tons/h]

cause of process shutdown

boiler no. 1 boiler no. 2 boiler no. 3 boiler no. 4 boiler no. 5 failed boiler steam supply failure

process shutdown rate [number/year]

ECO-I

ECO-II

CO

100 61 114 115 110 none none 0

91 60 116 123 110 (B3) HPS shortage 1

85 60 119 126 110 (B3 and B4) HPS shortage 2

Table 9. Total Cost Comparisona

ECO-I ECO-II CO

operating cost [won/year]

penalty cost [won/year]

total cost [won/year]

68 332 441 223 68 236 360 908 68 222 125 301

0 75 000 000 150 000 000

68 332 441 223 68 311 360 980 68 372 125 301

a Equipment shutdown frequency: one time per year. Working hours: 8000 h/year.

Figure 13. Minimum process buffer time change by addition of a boiler.

Figure 11. Various configurations of the steam production system in the utility system.

Figure 12. Optimal boiler load allocation by ECO-I for the different capacity boiler configuration.

simplicity. However, ELA does not provide an optimum solution in terms of the operation cost reduction, but ECO provides an optimum solution by simultaneously considering process safety and efficient operation. Therefore, ECO is a good strategy for use in the industrial field for the operation cost reduction and emergency handling capability. The result of a simulation case study implies the chance of improving the emergency handling capability by modifying the present steam production system. For

the process whose process buffer time is in region A, where process shutdown cannot be avoided for the equipment trip, the addition of a new boiler to the present steam production system can be considered to improve the emergency handling capability. Figure 11c shows this situation, where the optimal size of the new equipment is found to improve the emergency handling capability of the present steam production configuration. For the process whose process buffer time is 4 min, the configuration b cannot handle the emergency situation as shown in Figure 12, where 4.7 min is the minimum process buffer time that the present configuration can handle the emergency situation. To have the steam production system that can avoid process shutdown for unexpected boiler failure, the minimum size of the boiler to add to the present boiler configuration was found by process buffer time analysis using ECO-I. Figure 13 shows that the addition of a new boiler lowers the minimum process buffer time that the new steam generation system can handle for the unexpected equipment failure and prevents process shutdown. Addition of a boiler whose capacity is larger than 30 tons/h changes the minimum allowable process buffer time from 4.7 to 4 min, and the process can handle the emergency situation. This result shows that the addition of a backup boiler can increase the emergency handling capability of the present system. However, this result only shows the idea of increasing the process buffer time by addition of a new boiler for a particular fixed steam demand. So, for the real application, various steam demands should be considered, and, of course, other considerations such as the design factor should be considered. 6. Conclusions We noticed the fact that the present operation status has a close relationship with the emergency handling

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capability of avoiding plant shutdown under an emergency situation and proposed a new preventive optimization model to consider both economic operation at the present time and robust operation to avoid the plant shutdown under an emergency situation from unexpected equipment failure. The incorporation of emergency handling constraints that takes into account the process buffer time, mechanical limitation of steam production system, and emergency response actions under an emergency situation into the optimization formulation gives the optimal solutions that are robust to unexpected equipment failure. According to the process characteristics, emergency constraints are considered as hard or soft constraints in the formulation, and the optimization case studies were performed to compare the usefulness of the proposed approach with other operation approaches including ELA and CO. Compared with other operation methods, the proposed approach gives the lowest total cost by simultaneous consideration of the efficiency of operation and the emergency handling capability. The quantitative analysis for the present boiler configuration also provides the information on the size of the boiler to be added to the present configuration to improve the emergency handling capability of the process. This idea can be generally applied to other processes by adopting appropriate emergency handling constraints into the optimization formulations.

tb ) process buffer time [min] ηBi ) efficiency of boiler i ηTB k ) efficiency of turbine k υi ) maximum steam production increasing rate of the ith boiler [%/min] ΩL,k ) lower operation bound for the equipment k ΩU,k ) upper operation bound for the equipment k Continuous Variables

Nomenclature

FBi ) flow rate of the steam produced by the ith boiler [tons/h] Fin k ) stream flow rate into the unit k [tons/h] Fout k ) stream flow rate from the unit k [tons/h] e Fr,k ) increased stream flow rate at the kth turbine of steam type r when an emergency situation happens [tons/h] ∆FtBp,i ) increased rate of steam production by the remaining boilers during the production time [tons/h] Hin k ) specific enthalpy of the steam into the unit k [kJ/ ton] Hout k ) specific enthalpy of the steam from the unit k [kJ/ ton] J1 ) value of the objective function of ECO-I [won/h] J2 ) value of the objective function of ECO-II [won/h] PG ) in-house electric power generation [MW] PG,e ) in-house electric power generation under an emeri gency situation [MW] G Qr,k ) steam generation rate for type r by the kth equipment [tons/h] IG ∆Qr,k ) steam generation increase by reducing in-house electricity generation for type r by the kth equipment [tons/h] tp,i ) steam production time of the ith boiler [min] tmax,i ) maximum time of increasing the steam production rate of the ith boiler [min] Uk(F,T,P) ) operation range of equipment k for the flow rate, temperature, and pressure WU ) water usage [tons/h]

Sets

Slack Variables

i, j ) boiler indexes k ) equipment index (k ) 1, ..., NE) XD ) vector of decision variables: Fi (i ) 1, ..., NB)

Pex ) amount of power export [MW] Pex,e ) amount of power surplus under an emergency i situation when the ith boiler fails [MW] Pim ) amount of power import [MW] Pim,e ) amount of power import under an emergency i situation when the ith boiler fails [MW] PMax- ) amount of power import below the peak load [MW] PMax-,e ) amount of power import below the peak load i under an emergency situation when the ith boiler fails [MW] PMax+ ) amount of power import over the peak load [MW] ) amount of power import over the peak load PMax+,e i under an emergency situation when the ith boiler fails [MW]

Acknowledgment This work was financially supported by the Brain Korea 21 project and IMT2000-00015993 from Ministry of Commerce, Industry and Energy (MOICE). The authors also appreciate the great help from Moo Ho Lee (Hyundai Information Technology Co. Ltd.) and Sang Hyun You (Hyundai Petrochemical Co. Ltd.).

Parameters ai, bi, ci ) coefficients of the efficiency of the ith boiler Cex ) unit cost of the electric power export [won/MW‚h] CF ) unit cost of fuel [won/ton] Cim ) unit cost of the electric power import [won/MW‚h] Cpp ) unit penalty for being over the electric power peak load [won/MW‚h] CPSD ) unit cost of process shutdown [won/shutdown] CW ) unit cost of water [won/ton] Cp ) low heating value of the fuel [kJ/ton] fuf j ) frequency of unexpected failure of the jth boiler [shutdown/year] Fmax,i ) maximum steam production rate of the ith boiler [ton/h] NB ) number of boilers NE ) number of equipment NS ) number of steam types NTB ) number of turbines PD ) electric power demand [MW] PD,e ) electric power demand under an emergency situation [MW] PMax ) contract electric power peak load [MW] QD r ) steam demand of type r [ton/h] Qr,L ) minimum allowable steam demand of type r [ton/h]

Integer Variables yPSD,j ) 1 if a process shutdown happens because of an unexpected trip of the jth boiler and is 0 otherwise

Literature Cited (1) Papoulias, S. A.; Grossmann, I. E. A structural optimization approach in process synthesissI. Comput. Chem. Eng. 1983, 7, 695. (2) Cho, C. H. Optimum boiler load allocation. Instrum. Technol. 1978, Oct, 55-58.

Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 6081 (3) Ito, K.; Yokoyama, R.; Horii, S.; Matsumoto, Y.; Adagi, S. An optimal operational planning model for gas turbine cogeneration plants. International Gas Turbine Congress, Tokyo, 1987. (4) Hui, C.; Natori, Y. An industrial application using mixedinteger programming technique: A multi-period utility system model. Comput. Chem. Eng. 1996, 20, S1577. (5) Kalitventzeff, B. Mixed integer nonlinear programming and its application to the management of utility networks. Eng. Opt. 1991, 18, 183. (6) Prokopakis, G. J.; Maroulis, Z. B. Real-time management and optimization of industrial utilities systems. Comput. Chem. Eng. 1996, 20, S623. (7) Iyer, R. R.; Grossmann, I. E. Optimal multiperiod operational planning for utility systems. Comput. Chem. Eng. 1997, 21, 787. (8) Iyer, R. R.; Grossmann, I. E. Synthesis and operational planning of utility systems for multiperiod operation. Comput. Chem. Eng. 1998, 22, 973. (9) Kim, J. H.; Lee, M. H.; Han, C.; Kim, S.; You, S. Multiperiod planning for utility systems using dynamic programming. Comput. Chem. Eng. 1999, 23, S519. (10) Kim, J. H.; Han, C. Short-term multiperiod optimal planning of utility systems using heuristics and dynamic programming. Ind. Eng. Chem. Res. 2001, 40, 1928. (11) Yi, H. S.; Han, C.; Yeo, Y. K.; Optimal multiperiod planning of utility systems considering the discrete/continuous variance in internal energy demand based on the decomposition method. J. Chem. Eng. Jpn. 2001, 33, 456. (12) Yi, H. S.; Han, C. The integration of complete replanning and rule based reparing for optimal operation of utility plants. Korean J. Chem. Eng. 2001, 18, 442. (13) Papalexandri, K. P.; Pistikopoulous, E. N.; Kalitvenzeff, B. Modelling and optimization aspects in energy management and plant operation with variable energy demands-application to industrial problems. Comput. Chem. Eng. 1998, 22, 1319.

(14) Bansal, V.; Perkins, J. D.; Pistikopoulos, E. N.; Ross, R.; Schijndel, J. M. G, Simultaneous design and control optimization under uncertainty. Comput. Chem. Eng. 2000, 24, 261. (15) Kang, S. J. Trends in major industrial accidents in Korea. J. Loss Prevent. Process Ind. 1999, 12, 75. (16) Sanmarti, E.; Espuna, A.; Puigjaner, L. Batch production and preventive maintenance scheduling under equipment failure uncertainty. Comput. Chem. Eng. 1997, 21, 1157. (17) Dedopoulos, I. T.; Shah, N. Preventive maintenance policy optimization for multipurpose plant equipment. Comput. Chem. Eng. 1995, 19, S693. (18) Vassiliadis, C. G.; Pistikopoulos, E. N. Maintenance scheduling and process optimization under uncertainty. Comput. Chem. Eng. 2001, 25, 217. (19) Tan, J. S.; Kramer, M. A. A General framework for preventive maintenance optimization in chemical process operations. Comput. Chem. Eng. 1997, 21, 1451. (20) Allen, J. W.; Bruce, F. W. Power Generation Operation and Control; John Wiley & Sons: New York, 1996. (21) Everett, B. W.; Herbert, B. L.; Thomas, F. L. Steam Plant Operation, 7th ed.; McGraw-Hill: New York, 1998. (22) Joseph, L. K.; Irvin, N. H. IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications; The Institute of Electrical and Electronics Engineers, Inc.: Piscataway, NJ, 1980. (23) Sam, G. D. The Control of Boilers, 2nd ed.; Instrument Society of America: 1991.

Received for review January 22, 2002 Revised manuscript received August 28, 2002 Accepted September 25, 2002 IE020059+

Preventive Optimization Framework for Unexpected Equipment

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