Proactive Scheduling Strategy Applied to Decoking Operations of an

3024

Ind. Eng. Chem. Res. 2009, 48, 3024–3032

Proactive Scheduling Strategy Applied to Decoking Operations of an Industrial Naphtha Cracking Furnace System Heejin Lim Office of Strategy Consulting, Consulting Center, Samsung SDS, Gyeonggi-Do, 463-870, Korea

Jaein Choi System Engineering Team, Memory DiVision, Samsung Electronics Co., Ltd., Kyung-gi 445-970, Korea

Matthew Realff and Jay H. Lee* School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Sunwon Park Department of Chemical and Biomolecular Engineering, KAIST, Daejeon 305-701, Korea

The scheduling of decoking operations in a naphtha cracking furnace system is an important issue to ethylene producers, because excessive coke deposits inside the furnace coils can negatively impact plant safety and productivity. For optimal scheduling, accurate online estimation of the thickness of the deposited coke is essential. In practice, the coke thickness can be estimated from various furnace operating variables, but measurement errors and unexpected changes in the coke growth rate cause significant uncertainties in the estimation. Errors in the coke thickness estimate manifest themselves as gaps between the model prediction and actual measured values of key operating variables such as the pressure drop and the tube temperature. To handle the potential conflicts in an established schedule caused by the uncertainties, we propose to use a “proactive” scheduling strategy. In “reactive” scheduling, rescheduling is performed whenever an unexpected operational problem causes an unscheduled decoking operation, thus making a standing schedule no longer viable. On the other hand, in the “proactive” scheduling strategy, model information, as well as measurement information, are used to determine appropriate rescheduling points before actual operational problems arise. Under the proposed proactive scheduling strategy, the model predictions of the pressure drop and the tube temperature are compared against their measurements while the plant is operating according to a current decoking schedule. Whenever the gap between the model prediction and the measurement is larger than a given threshold value, the model is updated based on the measurements and the scheduling problem is solved again with the updated model information. The new scheduling solution is applied to the operation until the next scheduling point is found. This proactive scheduling procedure is applied to a simulated system of multiple furnaces. The advantages of the proactive scheduling strategy, in terms of productivity and risk management, are shown by comparing it with a reactive scheduling strategy and a heuristic decoking strategy over a large number of scenarios. 1. Introduction In an industrial naphtha cracking center (NCC) that is producing ethylene, propylene, and other petrochemicals, the cracking furnace is the most important unit; it determines the product yield while consuming about half of the total energy spent in the ethylene production process. A typical setup includes several furnaces being operated simultaneously. During operation, coke is formed and deposited on the inner surface of the pyrolysis coils in the furnace. The deposited coke decreases the thermal efficiency of the coils and, therefore, the productivity of the furnace. To restore the productivity, the furnace requires periodic “decoking”. If a decoking intervalsthe operation time between two successive decoking operationssis too long, deposited coke in the coils reduces the furnace production efficiency of the furnace. Conversely, if it is too short, the actual production time would decrease, because of the decreased number of operating days for the furnaces.1 However, in industrial NCCs, scheduling of the decoking operation across * To whom correspondence should be addressed. Tel.: +1-404-3852148. Fax: +1-404-894-2866. E-mail address: [email protected].

the parallel units, although important for a safe and effective operation, is not done systematically. In our previous work,1 we formulated a mixed-integer nonlinear programming (MINLP) for optimal scheduling of decoking operations in a multiple furnace system under a deterministic scenario. We considered three solution strategies of the MINLP, and among them, the sequential solution of mixed-integer linear programming (MILP) and nonlinear programming (NLP) was identified as being the most effective, in terms of computational load and optimality gap. In real operations, however, model errors can make such a model-based optimal schedule suboptimal or even infeasible. For the scheduling, coke thickness is the most important variable, which determines an appropriate decoking point. In practice, coke thickness cannot be measured directly without cutting the coils. In addition, the deposits have a tendency to be distributed unevenly throughout the tube, making measurement at a single point not representative. The coke thickness can be estimated indirectly through measurements of the product yields, tube skin temperature, and pressure drop. However, such

10.1021/ie800331z CCC: $40.75  2009 American Chemical Society Published on Web 02/13/2009

Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 3025

an estimated coke thickness will always have uncertainties about it, because of inevitable measurement errors and irregular coke deposition rates, which are caused by uneven inner surface and bending structure of coils.2-4 Sometimes, the sudden appearance of a hot spot in the coil wall causes an unexpected rise in the coke growth rate.5 To be applicable to real operations, the previous deterministic scheduling strategy1 must be modified to account for these uncertainties. Researchers have proposed several rescheduling strategies, such as the rolling horizon method and the reactive scheduling method, to address uncertain events that arise during operation. In the rolling horizon method, a new schedule within a moving time window is obtained periodically.6-10 The solution reliability of this method is highly dependent on the size of the moving horizon and uncertain event occurrences.11 To overcome this problem, the reactive scheduling strategy was proposed.12-16 Because all these strategies were focused on batch processes, they are not naturally suited to the furnace system, which is a part of a continuous processing system. In this paper, we propose a “proactive” scheduling strategy, by modifying the deterministic scheduling strategy in our previous work to handle mismatches that result from the uncertainties.1 In this new strategy, we monitor the gap between the measured values and model predictions of the tube skin temperature and pressure drop. We check the size of the gap against chosen threshold values, in addition to checking the operating limits of the tube skin temperature and the pressure drop. If the differences are larger than the given threshold values, or the tube skin temperature or the pressure drop reaches its respective operating limit, rescheduling is triggered by resolving the deterministic scheduling problem but with an updated value of the current coke thickness. The performance of the proactive scheduling strategy is compared against those of heuristics-based and reactive scheduling strategies. It is shown that the proactive scheduling strategy gives a much more consistent performance with significantly less spread of the profit value in the presence of uncertainty. 2. Decoking Scheduling Strategies under Uncertainty 2.1. Uncertain Nature of the Naphtha Cracking Furnace System. A major source of uncertainties in the furnace is the uneven coke growth rate inside the coil. There have been many studies about the mechanisms of coke formation and its dependence on the operating conditions.2,3,17-20 The coke growth rate is mainly affected by the tube temperature, pressure, feed flow rate, and feed composition.18,19 Coke is known to have a tendency to deposit heavily in a coil bend, where the diameter of the coil changes or the coil is bent.17 In the coil bend, the mass flux and pressure are changing.21,22 The temperature of the coil is nonuniform throughout the coil, because firing nozzles are placed at the bottom and side walls of the furnace. The nonuniform distribution of temperature and pressure makes coke deposit heavily on certain sections of the coil. Those sections are subjected to especially high temperatures by the insulation effect of the coke and develop so-called “hot spots”.20 Because of the high temperature at the hot spots, coke deposition is further accelerated, thus creating a spiral of increased temperature and accelerated coke deposition. Because hot spots decrease the durability of the coils and increase the coke growth rate, they can jeopardize safe and continuous operation of a furnace system. A major problem in a practical furnace system is that one cannot measure the coke thickness directly without cutting the coils of the furnace. The coke thickness can be estimated from

the operating conditions of the furnace system, but the exact distribution of coke thickness inside the coils cannot be predicted from them. Thus, an unexpected event such as the formation of a hot spot cannot be predicted before it manifests itself as a major problem in the operation. If a fixed decoking schedule is applied to a real furnace system without modification, such unpredictable events can bring severe safety and operational problems. To avoid critical safety problems, emergency shutdowns and unscheduled decoking operations are unavoidable. Because these emergency measures can disturb an established decoking schedule, a rescheduling strategy is required for an industrial furnace system. 2.2. Previous Rescheduling Strategies. Many rescheduling strategies have been proposed to handle unpredictable events during the operation under a predictive schedule. The rolling horizon method and the reactive scheduling method are two such representative methods. In the rolling horizon method, rescheduling is performed periodically by resolving the scheduling problem on a fixed-size, moving horizon after the scheduling information has been updated.7 This method has been applied toseveralonlineproductionplanningandschedulingproblems.6,8-10 However, unpredictable events can occur between the rescheduling points. In addition, its robustness and optimality are highly dependent on the size of the moving horizon and unpredictable event occurrences.11 To increase the rescheduling efficiency during the operation, the reactive scheduling method was introduced. In reactive scheduling, a schedule is modified to accommodate unexpected changes in the operation whenever an unpredictable event forces the schedule to be no longer feasible.15 Thus, in this strategy, rescheduling is triggered by an unpredicted event.12-14,16 Because all these strategies are focused on batch processes, they are not especially suitable for the furnace system, which is a part of the continuous system of a NCC. In the furnace system, uncertain events such as an unscheduled decoking operation and an emergency shutdown can cause severe problems in the downstream processes. Thus, it is highly desirable that these events be predicted before they occur and the decoking schedule be adjusted to accommodate them or even to prevent them from happening. For this, we introduce the “proactive” scheduling strategy next. 2.3. Proactive Scheduling Strategy. The basic concept of proactive scheduling is described in the work by Park.23 The key idea is to use the observed data to update the relevant parameters in real time. The main motivation is to exploit the time and spatial correlations that exist in typical plants so that changes that force rescheduling can be predicted ahead of time. This gives the decision-maker an extra leverage to change the schedule in a proactive manner. In proactive scheduling, a deterministic scheduling problem is solved repeatedly to revise the schedule, because the parameters are continually updated and significant errors in the model prediction are detected. Figure 1 shows the flowchart of the proactive scheduling strategy. The first schedule is given by the initial scheduling parameters. At each unit time, the deviation of the operating conditions from the model prediction is checked. If the deviation is insignificant (i.e., falls within some threshold value), the previously obtained schedule continues to be applied to the system. Otherwise, rescheduling is performed with the updated model parameters and applied from that point onward. In this paper, we develop a “‘proactive” decoking scheduling strategy for the furnace system by modifying the deterministic decoking scheduling strategy in our previous work.1 In this new strategy, we monitor the gap between the measured values and

3026 Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009

model predictions of the tube skin temperature and pressure drop against given threshold values (denoted hereafter as R and β, representing the tube skin temperature and pressure drop thresholds, respectively). If they exceed the limits or if the tube skin temperature or the pressure drop reaches its respective operating limit, rescheduling is triggered by resolving the deterministic scheduling problem but with an updated value of the current coke thickness. 3. Online Test of the Proactive Scheduling Strategy 3.1. Development of the Plant Model. To test the performance of the proactive scheduling method, we create a “simulated plant”, which has uncertain behavior characteristic of the real plant. The furnace system we study is composed of 10 identical units in parallel. The furnace model that we use is based on the data obtained with a commercial NCC simulator called CRACKER; it is the same system that we used in our previous study. (See Lim et al.1 for details.) The main uncertainty in the system is the coke growth rate, which can vary with time.24 Uneven growth of the coke thickness, which is indirectly measured by the tube skin temperature, has been observed in many industrial NCCs.20 For the purpose of simulation study, we model this behavior with a Markov chain, which is capable of capturing time-correlated behavior.25,26 The model that we adopt is focused on the following wellknown coke growth patterns: (i) reduced coke growth rate after each decoking operation17 and (ii) self-accelerating coke growth pattern after a hot spot formation.20 In this paper, we assume that the coke growth rate at any given time can be represented by one of the four states: L (low), M (medium), H (high), and E (extra high). After a decoking operation, the coke inside the coils is removed and, hence, the coke growth rate is set to state L (representing the low growth rate). From there on, the state of the coke growth rate evolves according to a given probability transition matrix. Hence, the conditional probability distribution vector for the coke growth rate (p) is represented as follows:

where Pa,b denotes the probability of coke growth rate from state a to state b after one sample interval and xi,t is the state vector that indicates the current state (i is an index for the furnace unit and t is an index for time). For example, if the current state of the growth rate is M (xi,t ) [0, 1, 0, 0]T), the probability distribution of the coke growth rate state at the next time, pi,t+1, is [PM,L, PM,M, PM,H, PM,E]T. Diagonal elements of the probability matrix jP represents the probability of remaining in the same state through the next time. Thus, large values of the diagonal elements reflect the likelihood of the growth rate state to remain at a same state rather than to transition to another state. To model the selfaccelerating coke growth pattern, the fourth diagonal term of the probability matrix, PE,E, is set to a large value. Because PE,E is closer to 1, the extra high coke growth rate mode will last longer.

Figure 1. Flowchart of the proactive scheduling strategy.

j can be In practice, the coke growth rate transition matrix P obtained from historical furnace operating data. In this study, we chose

[

0.68 0.23 j) P 0.087 0.003

0.22 0.62 0.15 0.01

0.15 0.24 0.54 0.07

0.05 0.15 0.3 0.5

]

(2)

In the plant simulation, after the current coke growth rate state is determined, the current coke growth rate is set to a representative value of each state. The representative coke growth rate of the ith furnace at time t (Rcoke,i,t) is represented as follows: Rcoke,i,t ) Rcoke + [RˆL RˆM RˆH RˆE ]xi,t ) Rcoke + [-0.285 0 0.21 1.5 ]xi,t

(3)

These parameters were obtained from the simulation data of an industrial naphtha cracking furnaces system in Korea by CRACKER,27 which is a furnace simulator. 3.2. Simulation. With the underlying Markov chain model of the coke growth rate, the performance of various scheduling algorithms can be tested in simulation. At the beginning of a simulated run, we assume that we only have an “estimated” value of the coke thickness, based on the operating conditions. The coke thickness of each furnace is initialized by the coke growth rate sequence generated by the underlying Markov chain, assuming the last decoking operation was performed on some past day that is randomly chosen. Using these initial coke thicknesses, an initial decoking schedule is obtained by solving the MINLP problem as described in our previous work.1 We follow the given schedule until the first decoking/rescheduling point is found. If one of the furnaces is decoked by the given decoking/ rescheduling criteria, the coke growth rate state of the decoked furnace is set to the state L after the decoking, and then, from there, it evolves according to the Markov chain model presented in the previous section. At each time, the coke growth rate state is determined from random sampling of the condition probability distribution vector pi,t, and the corresponding coke thickness from eq 3 is used. The next conditional probability vector xi,t+1 is again calculated using eq 1, and this repeats until the next decoking day. Figure 2 describes the simulation data generation procedure.


Figure 2. Data generation procedure for the simulation.

Of course, it is assumed that the “actual” coke growth rate state sequences are unknown to the scheduler. Instead, for scheduling, measured operating data (assumed here to contain measurement errors of normally distributed random numbers with a mean of 0 and variance of 1) may be used to calculate a coke thickness estimate based on the model. 3.3. Performance Comparison. The proposed proactive decoking scheduling strategy is compared with a heuristic strategy and a reactive scheduling strategy. All these strategies are tested over 15 scenarios, each with a different initial coke thickness. For a fair comparison of the scheduling strategies, the same initial coke thickness and same coke growth state sequences are applied to each strategy until each of the three strategies finds a different decoking point. The details of the heuristic strategy and the reactive scheduling strategy that we used are given below. 3.3.1. Heuristic Decoking Strategy. In a real operation, there are operating limits on the tube skin temperature and the pressure drop. If a furnace reaches a maximum limit of the tube skin U ) or the pressure drop (∆PU) during the temperature (T skin operation, the furnace is removed from the operation and decoked.1 The “heuristic decoking strategy” for the decoking decision is based on this practice. In this strategy, decoking is measure U measure performed whenever T skin,i,t g T skin or ∆P i,t g ∆PU. Hence, decoking is decided by the observed plant data. This strategy requires some additional criteria, given the constraint that no more than one furnace can be decoked at a time.1 In the case that multiple furnaces reach one of the maximum operating limits on a same day, we apply the following two criteria to determine the order of decoking. First, a furnace reaching the pressure drop limit has the priority over those reaching the maximum tube skin temperature. Second, if there are further conflicts, the furnace that has the highest operating value is decoked first. This heuristic strategy does not require a model and has no predictive capability. When a furnace is decoked, the remaining furnaces that are in operation equally share the extra product load, because there is no information to bias the distribution otherwise.

3.3.2. Reactive Decoking Scheduling Strategy. Under the reactive scheduling strategy, rescheduling is triggered by an unscheduled decoking. Under this strategy, unscheduled decoking is performed whenever the operating limits are exceeded unexpectedly under a given decoking schedule. When an unscheduled decoking occurs, a new decoking schedule after this point is calculated and applied to the plant operation. We call this point a “rescheduling point”. At the rescheduling point, the coke thickness for the decoked furnace is set to zero, because the coke has been removed through the decoking operation. The coke thicknesses of the other furnaces remain the same as the model output of the previous scheduling solution. With the new coke thickness values, a new decoking schedule is calculated and applied to the plant. In this strategy, there is no update of the model except the coke thickness of the decoked furnace. 3.3.3. Proactive Decoking Scheduling Strategy. Under this strategy, the decoking criteria for the reactive scheduling strategy still applies. In addition, the validity of the model that is used to optimize the current schedule is checked each time. For this, the model’s prediction of the tube skin temperature and the pressure drop are compared against their measured values. If the gap for either exceeds its respective threshold value, rescheduling is triggered. Because the coke thickness cannot be measured directly, its value is re-estimated using the equation for the rescheduling. The previous schedule then is discarded and the new decoking schedule is applied until the next proactive scheduling point is found. In this strategy, the main tuning parameters are R and β, which are the threshold values. Small values of R and β require tighter predictions by the model and, hence, have a tendency to trigger rescheduling more frequently. 4. Computational Results In scheduling the furnace production and decoking operations, the operators want to maximize the productivity while maintaining a safe operation. A schedule, no matter how attractive it may be in terms of profit, cannot be applied to the real operation if it compromises the safety of the plant. Maximum tube skin temperature and pressure drop limits imposed in the decoking criteria have direct implications on the operational safety. Therefore, selecting the proper values for them is of paramount importance. In this section, the proposed proactive scheduling strategy is compared with the described reactive scheduling strategy and the heuristic decoking strategy. For this, we compare their performances (in terms of profit value and risk manageability), averaged over a large number of scenarios. The proposed strategies are first compared under same operating limits. Next, for a fairer comparison, the tuning parameters of rescheduling/decoking criteria for each strategy are adjusted, to operate the furnaces without any emergency alarm. 4.1. Decoking Scheduling under Same Operating Limits. In this section, the three strategies share the same operating limits as follows: U ) (1) Proactive scheduling: R )20 K, β ) 0.3 kPa, T skin U max max T skin , ∆P ) ∆P ; U max (2) Reactive scheduling: T skin ) T skin , ∆PU ) ∆Pmax; and U max (3) Heuristic operation: T skin ) T skin , ∆PU ) ∆Pmax. The parameters of the proactive scheduling (R and β) are selected based on the maximum measurement errors of the tube skin temperature and the pressure drop. A total of 15 cases are studied for each strategy: 3 different stochastic realizations are simulated for each of 5 different initial coke thicknesses. The measured operating data of a plant can be different from their true values, because of measurement errors; therefore, a dangerous situation may occur when an actual violation of the


Figure 3. Tube skin temperature profile under a heuristic decoking solution for the first realization of case 5.

Figure 4. Pressure drop profile under a heuristic decoking solution for the first realization of case 5.

operating limit is not reflected in the measured value. In this comparison, an “(emergency) alarm” is defined as the case in which the true operating values reach the operating limits, which causes significant problems. In the furnace system operation, the operators do not know the true operating values exactly, but they can detect the alarm condition by examining other indicators, such as the color of the heated cracking coils. To compare risk manageability under each strategy, we can examine the number of alarms within a given time horizon (120 days). Another performance measure that we use for comparison is a weighted sum of the total production amount of ethylene and propylene (reflecting the total profit) within the time horizon, which also is the objective function of the optimization that we solve for the scheduling.1 Figures 3-8 show the tube skin temperature and pressure drop profiles of an example case for the three strategies. Figures 3 and 4 show one solution example of the heuristic decoking strategy. In the strategy, the furnace is decoked when an alarm condition is found. Unscheduled decoking operations that are caused by alarms are shown on day 27 in Figure 3 and on day 93 in Figure 4. In Figures 5-6, rescheduling points are identified as vertical lines on the graphs. These figures include all rescheduling points, including those triggered by the operating conditions of the furnaces. Figures 5 and 6 respectively show

the profiles of the tube skin temperature and pressure drop when the reactive scheduling strategy is applied. On day 65 in Figure 6, the pressure drop exceeds its operating limit (dashed line) and decoking is performed. Figures 7 and 8 are examples of the cases under the proactive scheduling strategy. They show that mismatches in the tube skin temperature and the pressure drop between their measured values and model predictions trigger rescheduling under the proactive scheduling strategy. In these figures, the gap between the model prediction (solid line) and plant measurements (short dashed line) is larger than the given threshold values (R for the tube skin temperature or β for the pressure drop, respectively). When the proactive rescheduling limits are exceeded, the coke thickness of the model for the MINLP-based deterministic decoking scheduling is updated, based on the measured plant data, to follow the plant operation trajectories. Figures 9 and 10 are the Gantt charts of the proactive and reactive scheduling solutions in the first realization of case 5. The average of the total decoking days under the proactive scheduling is similar to that observed under the reactive scheduling, as reported in Table 1. The rescheduling points for the reactive scheduling solution in Figure 9 are different from those under the proactive scheduling solution in Figure 10. According to the rescheduling criterion of the reactive schedul-


Figure 5. Tube skin temperature profile under a reactive scheduling solution for the first realization of case 5.

Figure 6. Pressure drop profile under a reactive scheduling solution for the first realization of case 5.

Figure 7. Tube skin temperature profile under a proactive scheduling solution for the first realization of case 5.

ing strategy, decoking is performed whenever a rescheduling point is found in Figure 9. However, under the proactive

scheduling strategy, some rescheduling points are accompanied with immediate decoking of the furnace but some are not, as


Figure 8. Pressure drop profile under a proactive scheduling solution for the first realization of case 5.

Figure 9. Gantt chart under the reactive scheduling for the first realization of case 5.

Figure 10. Gantt chart under the proactive scheduling for the first realization of case 5.

can be observed from Figure 10. At those rescheduling points without immediate decoking, the model is updated, based on the measured plant data, and a new schedule is obtained, because the gap between the model predictions and measured data exceeded the limits. Table 2 shows the average values for the profits and the number of alarms. Also reported are the standard deviations calculated with the data from the 15 cases. The standard deviations, denoted as Std.Dev., are obtained from the equation

Std.Dev. )

∑ x - (∑ x)

n

2

2

n(n - 1)

Under the heuristic strategy, one operates the furnaces until they reach their operation limits, but that yields the smallest average profit. For the tube skin temperature and the pressure drop, the average number of alarms under the heuristic strategy is 3.0 and 3.7 times greater than the number of alarms under the

proactive strategy, respectively. Hence, the heuristic strategy causes more alarm conditions than the reactive and the proactive strategies. These results also show that the heuristic decoking strategy gives the fewest number of decoking days, as shown in Table 1, but the worst overall performance. Comparing the proactive scheduling with the reactive scheduling, we find that the average profit and the number of emergency alarms are similar but slightly less for the proactive schedule, as can be seen from Table 2. The standard deviation of the profits under the proactive strategy in Table 2 is significantly smaller than that under the heuristic strategy and is also somewhat smaller than that under the reactive scheduling. From Table 1, we can also see that the proactive strategy requires more instances of rescheduling than does the reactive strategy. 4.2. Performance Comparison under Safe Operation. In the previous results, the three strategies shared the same max operating limits (T skin , ∆Pmax). Under these conditions, the furnaces can experience emergency alarm conditions, because

Ind. Eng. Chem. Res., Vol. 48, No. 6, 2009 3031 Table 1. Average Number of Rescheduling and Decoking Days strategy

average total number of decoking days

average number of rescheduling points

heuristic reactive proactive

20.9 26.2 25.0

9.5 11.9

Table 2. Average Profit and Number of Alarms for the Three Strategies Profit

Number of Alarms

strategy

value

Std.Dev.

for Tskin

for ∆P

heuristic reactive proactive

100.0 101.0 100.5

8.7 3.9 3.2

9.5 3.6 2.9

4.1 1.7 1.1

Table 3. Computational Results under the Scheduling/Decoking Criteria Adjusted for the No-Alarm Condition Average average number average number Objective Function of decoking of rescheduling strategy value Std.Dev. days points heuristic reactive proactive

100.0 101.1 101.7

8.6 26.3 2.9

24.6 30.5 26.7

9.3 18.5

of measurement errors, as reported in Table 2. For a fairer comparison, the proposed rescheduling strategies should be readjusted to give the same number of emergency alarms, because safety is the most important issue in furnace operation. Generally, there is a tradeoff: To increase the safety, one must sacrifice the profit, and vice versa. In the plant operation, the furnace system is operated to push the profit as high as possible while satisfying the minimum safety condition. Here, we define the minimum safety condition as having no alarm and, hence, we compare the performance of the three strategies under this safety requirement. To achieve this, the parameters of the decoking criteria for the three strategies are readjusted. The tuning parameters for the proactive strategy are the threshold values for the tube skin temperature (R) and pressure drop (β), and the gap allowed between the model prediction and plant observation. For the reactive and heuristic strategies, the maximum pressure drop U (∆PU) and tube skin temperature (T skin ) values for decoking are decreased. By trial and error, the parameters were reduced to give no-alarm condition. Similar to that observed in the previous section, the average profits for the 15 cases of different initial coke thicknesses are compared. Under the proactive scheduling, only the R and β values are detuned and the maximum limits of the tube skin temperature and the pressure drop are maintained at their original values. Under the reactive scheduling strategy, the maximum operating limits are detuned by the amounts of maximum measurement errors. For the heuristic strategy, the limit values for the safe operation under the heuristic decoking strategy are obtained by trial and error. The maximum operating limits so chosen were lower than those for the reactive scheduling. The final rescheduling/decoking criteria are as follows: (1) Proactive scheduling: R )15 K and β ) 0.25 kPa; U max (2) Reactive scheduling: T skin ) T skin - 5, ∆PU ) ∆Pmax 0.05; and U max (3) Heuristic scheduling: T skin ) T skin - 10, ∆PU ) ∆Pmax - 0.1. The computational results under the new criteria are compared in Table 3, where the average profit, the average number of decoking days, and the average number of rescheduling under the three strategies are reported. The proactive strategy gives the maximum average profit value and the smallest standard deviations, compared to the other

Figure 11. Profit distribution histogram of the 15 test cases for the three strategies.

strategies. The reactive strategy gives a smaller average profit than does the proactive strategy. More importantly, the profit values for the reactive scheduling solutions show a very large standard deviation. The profit variations are also shown in Figure 11. From this, we see that the profits achieved by the reactive scheduling strategy are highly variable, depending on the initial coke thicknesses. This means that the reactive scheduling strategy may give a very poor result if the initial coke thickness is estimated poorly. Compared with the standard deviation for the reactive scheduling strategy in Table 2, the standard deviation for the same case in Table 3 is significantly larger. This means that the reactive scheduling strategy is very sensitive to boundary conditions as well as the initial coke thickness. Despite the uncertainty, the proactive decoking scheduling strategy consistently gives a good profit value. Although the proactive strategy requires twice as many rescheduling points as reactive scheduling, it exhibits a more-stable profit pattern under uncertainties in the initial coke thickness. 5. Conclusion Scheduling of decoking operations in the cracking furnace system is an important issue for ethylene producers, because it affects operational safety and productivity. In practice, measurement errors and unexpected changes in the coke growth rate can cause problems when applying a fixed decoking schedule to the real operation. Because of the uncertainties, the gap between the model prediction and the plant observation continually increases. To handle the uncertainties, the proactive scheduling strategy is proposed. This strategy utilizes the model prediction data, together with the measured plant data, to determine rescheduling points. Under the proactive scheduling strategy, a rescheduling point is decided by whether the gap between the model prediction and the measured data exceeds a chosen threshold value. At each rescheduling point, the parameters are updated and the scheduling problem is resolved. The performance of the proactive scheduling strategy is compared with that of the reactive scheduling and heuristic decoking strategies by simulating a large number of scenarios. When same operating limits are applied to all the strategies, the reactive strategy and the proactive strategy showed a similar level of profits and number of emergency alarms. The parameters of the decoking criteria then are readjusted to result in no-emergency-alarm conditions, to ensure safe operation. In this case, the reactive and proactive strategies give higher profits than the heuristic strategy. However, the main difference is that the profits under the reactive strategy are much more variable, with respect to the initial coke thicknesses. This can be an important disadvantage for the reactive strategy, because, in practice, an estimated coke thickness value always has uncertainties.


Nomenclature General Notations y ) model output C ) coke thickness ∆P ) pressure drop ∆PU ) maximum operating limit of pressure drop through coils M ) mode vector Pa,b ) probability of coke growth rate from state a to state b Pri,t ) conditional probability vector of furnace i at time t j ) coke growth transition matrix P Rcoke ) representative coke growth rate Rˆ ) an element of representative coke growth rate Rcoke T skin ) tube skin temperature U T Skin ) maximum operating limit of tube skin temperature Greek Letters R ) maximum gap limit of tube skin temperature between model prediction and plant observation β ) maximum gap limit of pressure drop between model prediction and plant observation Subscripts coke ) coke thickness E ) extra high state of coke growth rate H ) high state of coke growth rate L ) low state of coke growth rate M ) medium state of coke growth rate i ) furnace number t ) discrete time Superscripts max ) maximum bound min ) minimum bound

Acknowledgment This work was supported by the BK21 Project. J.H.L. gratefully acknowledges the financial support from the U.S. National Science Foundation (under Grant No. CTS-0301993). Literature Cited (1) Lim, H.; Choi, J.; Realff, M. J.; Lee, J. H.; Park, S. Development of Optimal Decoking Scheduling Strategies for an Industrial Naphtha Cracking Furnace System. Ind. Eng. Chem. Res. 2006, 45 (16), 5738–5747. (2) Sundaram, K. M.; Froment, G. F. Kinetics of coke deposition in the termal cracking of propane. Chem. Eng. Sci. 1979, 34, 635–644. (3) Sundaram, K. M.; Van Damme, P. S.; Froment, G. F. Coke deposition in the thermal cracking of ethane. AIChE J. 1981, 27 (6), 946– 951. (4) Renjun, Z.; Qiangkun, L.; Huicai, L.; Fenghui, N. Investigation of coke deposition during the pyropysis of hydrocarbon. Ind. Eng. Chem. Res. 1987, 26, 2528–2532. (5) Bennett, M. J.; Price, J. B. A physical and chemical examination of an ethylene steam cracker coke and of the underlying pyrolysis tube. J. Mater. Sci. 1981, 16, 170–188. (6) Peeta, S.; Mahmassani, H. S. Multiple user classes real-time traffic assignment for online operationssa rolling horizon solution framework. Transp. Res., Part C: Emerging Technol. 1995, 3 (2), 83–98.

(7) Dimitriadis, A. D.; Shah, N.; Pantelides, C. C. RTN-based rolling horizon algorithm for medium term scheduling of multipurpose plants. Comput. Chem. Eng. 1997, 21, S1061–S1066. (8) Stauffer, L.; Liebling, Th. M. Rolling horizon scheduling in a rollingmill. Ann. Oper. Res. 1997, 69, 323–349. (9) Kimms, A. Stability measures for polling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing. Omega: Int. J. Manage. Sci. 1998, 26 (3), 355–366. (10) Jaillet, P.; Bard, J. F.; Huang, L.; Dror, M. Delivery cost approximations for inventory routing problems in a rolling horizon framework. Transport. Sci. 2002, 36 (3), 292–300. (11) Millar, H. H. The impact of rolling horizon planning on the cost of industrial fishing activity. Comput. Oper. Res. 1998, 25 (10), 825–837. (12) Rodrigues, M. T. M.; Gimeno, L.; Passos, C. A. S.; Campos, M. D. Reactive scheduling approach for multipurpose chemical batch plants. Comput. Chem. Eng. 1996, 20, S1215–S1220. (13) Sanmarti, E.; Huercio, A.; Sepuna, A.; Puigjaner, L. A combined scheduling/reactive scheduling strategy to minimize the effect of process operations uncertainty in batch plants. Comput. Chem. Eng. 1996, 20, S1263–S1268. (14) Vin, J. P.; Ierapetritou, M. G. A new approach for efficient rescheduling of multiproduct batch plants. Ind. Eng. Chem. Res. 2000, 39, 4228–4238. (15) Sun, J.; Xue, D. A dynamic reactive scheduling mechanism for responding to changes of production orders and manufactring resources. Comput. Ind. 2001, 46, 189–207. (16) Mendez, C. A.; Cerda, J. Dynamic scheduling in multiproduct batch plants. Comput. Chem. Eng. 2003, 27, 1247–1259. (17) Froment, G. F. Coke formation in the thermal cracking of hydrocarbons. ReV. Chem. Eng. 1990, 6 (4), 293–928. (18) Kopinke, F. D.; Zimmermann, G.; Reyniers, G. C.; Froment, G. F. Relative rates of coke formation from hydrocarbons in steam cracking of naphtha. 2. Paraffins, naphthenes, mono-, di-, and cycloolefins, and acetylenes. Ind. Eng. Chem. Res. 1993, 32 (1), 56–61. (19) Kopinke, F. D.; Zimmermann, G.; Reyniers, G. C.; Froment, G. F. Relative rates of coke formation from hydrocarbons in steam cracking of naphtha. 3. Aromatic-hydrocarbons. Ind. Eng. Chem. Res. 1993, 32 (11), 2620–2625. (20) Garg, A. Troubleshooting Fired Heaters. Presented at the AIChE 2001 Spring National Meeting, Houston, TX, 2001. (21) Albright, L. F.; Marek, J. C. Coke formation during pyrolysis: roles of residence time, reactor geometry, and time of operation. Ind. Eng. Chem. Res. 1988, 27 (5), 743–751. (22) Plehiers, P. M.; Reyniers, G. C.; Froment, G. F. Simulation of the run length of an ethane cracking furnace. Ind. Eng. Chem. Res. 1990, 29, 636–641. (23) Park, H. Efficient Planning and Scheduling for Large Scale Production Plants, Ph.D. Thesis, KAIST, Daejeon, Korea, 2001. (24) Jain, V.; Grossmann, I. E. Cyclic scheduling of continuous parallelprocess units with decaying performance. AIChE J. 1998, 44 (7), 1623– 1636. (25) Choi, J.; Lee, J. H.; Realff, M. J. An algorithmic framework for improving heuristic solutions. Part II. A new version of the stochastic traveling salesman problem. Comput. Chem. Eng. 2004, 28, 1297–1307. (26) Choi, J.; Lee, J. H.; Realff, M. J. Dynamic Programming in a Heuristically Confined State Space: A Stochastic Resource Constrained Project Scheduling Application. Comput. Chem. Eng. 2004, 28 (6-7), 1039– 1058. (27) Joo, E.; Lee, K.; Lee, M.; Park, S. CRACKERsA PC based simulator for industrial cracking furnaces. Comput. Chem. Eng. 2000, 24, 1523–1528.

ReceiVed for reView February 28, 2008 ReVised manuscript receiVed June 24, 2008 Accepted September 17, 2008 IE800331Z

Proactive Scheduling Strategy Applied to Decoking Operations of an

Recommend Documents