Integrated Proactive and Reactive Scheduling for Refinery Front-End

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 12192−12206

pubs.acs.org/IECR

Integrated Proactive and Reactive Scheduling for Refinery FrontEnd Crude Movement with Consideration of Unit Maintenance Honglin Qu,† Sujing Wang,‡ and Qiang Xu*,† †

Dan F. Smith Department of Chemical Engineering and ‡Department of Computer Science, Lamar University, Beaumont, Texas 77710, United States

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S Supporting Information *

ABSTRACT: A typical front-end crude supply process of refineries encompasses many units, such as vessels, port-side storage tanks, long-distance pipeline, refinery-side charging tanks, and crude distillation units. In reality, the performance of these units will inevitably decay; thus, unit maintenance plans should be well integrated with normal crude movement schedules. In this paper, a novel methodology has been proposed to dynamically and simultaneously determine the optimal schedule of crude movement and unit maintenance operations. Specifically, both proactive scheduling for multiple preventive maintenance tasks and reactive scheduling for emergent corrective maintenance tasks are systematically integrated. Accordingly, the developed mixed-integer nonlinear programming (MINLP) model will optimize the operation schedule for the front-end crude supply process via minimizing the total operating cost during the scheduling time horizon. Meanwhile, it can also determine the optimal unit maintenance schedule, which will identify the best opportunities of not only isolating units from process system to perform maintenance but also resuming their services after maintenance. The model can simultaneously handle multiple unit maintenance tasks while satisfying all strict constraints for crude transferring, storing, blending, and processing operations. The efficacy of the developed methodology and the MINLP model has been demonstrated through various case studies.

1. INTRODUCTION Refinery plays an important role in meeting the growing energy demand from various commercial and industrial activities. Due to global competition, rigorous environmental regulation, and volatile crude/oil product market, the supply chain of crudes and petrochemicals needs advanced decision support more than ever to secure raw material supply, alleviate emerging concerns over sustainability, and hedge against various uncertainties. Substantial research efforts have been devoted into this area, and significant benefits have been accomplished through maximizing process profitability,1 minimizing environmental impact,2,3 and enhancing operation robustness.4−6 The crude supply chain generally involves upstream crude exploitation, midstream refining and processing, and downstream product distribution. The front-end crude movement of refineries is a critically important section to the entire supply chain, which covers crude importing by vessels, unloading and storing in port-side storage tanks (STs), transferring via long-distance pipeline (LDPL), blending in refinery-side charging tanks (CTs), and continuously feeding crude distillation units (CDUs) (see Figure 1). Since optimal and smooth operations of this section heavily depend on the appropriate scheduling, studies on front-end crude scheduling (FECS) have been extensively performed in recent years with great accomplishments.7−10 It should be noted that FECS involves substantial key units, such as STs, LDPL, CTs, and CDUs. In reality, these units are © 2019 American Chemical Society

not always under normal status. Their performance will inevitably decay along with the processing time. Due to this reason, units need regular maintenance to ensure their efficient working performance. Otherwise, overused units with low efficiency would aggravate on-site operational burdens, adversely affect the process safety, and eventually lead to local unit malfunction or even severe plant incidents. Figure 1 illustrates some types of units that need to be frequently maintained. Certainly, different types of unit maintenance operations will be performed under respective concerned situations. Generally, the maintenance operations can be classified into two categories: preventive maintenance (PM) and corrective maintenance (CM).11 PM refers to the priorrecovery action implemented on units that are still capable of handling normal duties but with low processing efficiency or at high risk of malfunction. CM indicates the postremedial action, such as repair and replacement, after the reveal of unit failure or other uncertainties. A feasible schedule is crucial to perform unit maintenance within the crude supply process. Thus, it is vital to make a proper schedule of crude movement and maintenance operations, Received: Revised: Accepted: Published: 12192

May 4, 2019 June 11, 2019 June 14, 2019 June 14, 2019 DOI: 10.1021/acs.iecr.9b02449 Ind. Eng. Chem. Res. 2019, 58, 12192−12206

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Industrial & Engineering Chemistry Research

Figure 1. Illustration of the studied problem.

probability distribution functions to reveal the underlying relation of working time and unit failure chance. Laggoune et al. utilized Weibull distribution to estimate the system reliability along with time.24 This obtained trend was incorporated with other process constraints, and the developed model was applied to continuous operating units to minimize the operating cost. These studies implicitly focused on the proactive scheduling of the time-based maintenance (TBM), for which the unit life was predicted according to experts’ experience and/or mathematical models. However, concerns on TBM arose from the perspective of principle and practice, such as unrealistic model assumption and insufficient data collection. As comparison, the condition-based maintenance (CBM) relied on the real-time condition monitoring, which could accurately track the decaying progress and dynamically capture the indication of unit failure. Thus, even though CBM could be more expensive due to its continuous condition monitoring and huge data processing, it still dominated TBM in many realistic aspects.25 Safari and Sadjadi integrated the condition-based maintenance policy into a flowshop scheduling problem, where the unit condition was continuously monitored at equidistant intervals and PM would be carried out right after the condition threshold was reached.26 This concept of CBM was also adopted in a stochastic scheduling problem.27 The reactive scheduling of CM aims at timely adjusting or updating current operation schedules in response to emerging unit failure or uncertainties. Newly obtained schedules should ensure the effective implementation of CM and the continuous completion of leftover production operations. In addition, reactive schedules have to be promptly determined, so that new events can be timely responded, and subsequent operations can be explicitly guided. In the context of plant production, Vin and Ierapetritou proposed a two-stage procedure to deal with the reactive scheduling work for multiproduct batch plants, where a deterministic schedule was established at the first stage and disturbances (e.g., unit breakdown) were systematically incorporated at the second stage.28 To expedite the reactive scheduling process, Janak and Floudas developed a new mathematical framework, in which unaffected operations would remain fixed during the rescheduling.29 This framework was applied to address the unit breakdown and sudden order

which can not only recover performance and resume service for maintenance needed units in a timely manner but also perform normal operations with less process impact and/or minimum total operating cost. By following such schedules, severe upsets and potential infeasibility of ongoing operations will be avoided; meanwhile, the entire crude supply process can be operated in a cost-effective way. In real applications, the scheduling activity should be dynamic, which means that it needs to respond to any new requests of PM and CM. In addition, the scenario that multiple units need maintenance should be considered as well. Historically, mathematical programming techniques were widely employed to determine optimal schedules and plans in a variety of engineering fields, such as plant production, job manufacturing, product transportation, process safety, and so on.12−18 As to unit maintenance management, the proactive scheduling of PM is to determine the integrated schedule of production and maintenance prior to failure emerging, in which PM is well coordinated with normal operations. According to different maintenance policies, proactive scheduling has been extensively investigated. For the purpose of convenience, PM could be periodically planned at a fixed time interval. However, such a policy was too rigid, neglecting the impact of external factors, such as environmental changes; therefore, huge discrepancies could be caused after a long period of production.19 To address this concern, Castro et al. considered a flexible range of working time between adjacent maintenance operations and developed an MILP model to optimize the maintenance plan for a gas engine power plant.20 Instead of the working time, the production batch and processed material could also be used to characterize the yield decay and determine the optimal production and maintenance plan of a biopharmaceutical process.21 Kopanos et al. investigated the effect of different maintenance policies, i.e., runtime-based, fixed, and flexible policies, on the compressor network in an air separation plant.22 Furthermore, Fitouhi and Nourelfath proposed an age matrix to represent the effective status of each unit at the beginning of the scheduling period according to the selected maintenance policy and employed the heuristic simulated annealing algorithm to solve the large-size maintenance scheduling problems of multistate systems.23 Researchers also analyzed historical failure data and fitted them into suitable 12193

DOI: 10.1021/acs.iecr.9b02449 Ind. Eng. Chem. Res. 2019, 58, 12192−12206

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dynamically and simultaneously determine the optimal schedule for both crude movement and unit maintenance operations. Specifically, both proactive scheduling for PM tasks and reactive scheduling for emergent CM tasks are systematically integrated. Accordingly, an MINLP model with continuous time formulation has been developed to optimize the operation schedule for the front-end crude supply process via minimizing the overall operating cost during the scheduling time horizon. Meanwhile, it can also determine the optimal unit maintenance schedule, which will identify the best opportunities of not only isolating units from process system to perform maintenance but also resuming their services after maintenances. It is capable of handling multiple maintenance tasks, which are well scheduled without any time overlap, and unit inventories are managed within the system without the use of backup units. In addition, all strict constraints for multi crudes transferring, storing, blending, and processing operations are also satisfied. The efficacy of the proposed methodology and the developed model has been investigated through multiple case studies, where the developed MINLP models have been solved by BARON with a global optimality gap of 0.1%.

issues in a large-scale industrial batch plant, and optimal reactive schedules could be obtained in reasonable time. Furthermore, Li and Ierapetritou treated CM and other relatively frequent events as uncertain parameters and derived multiparametric programming models, which was solved prior to the event occurrence, and the response time could be significantly reduced.30 Focusing on the crude supply process, Zhang and Xu studied the reactive scheduling of crude oil operations under multiple uncertain scenarios and developed an nonconvex MINLP model with continuous-time and global-event formulation.31 Moreover, Zhang et al. suggested an innovative full rescheduling strategy (FRS) based on previous partial rescheduling strategy (PRS), where operations of all units regardless of their status would be involved in the rescheduling. Through comparison, it turned out that FRS could result in an enlarged feasible range associated with the failure occurrence timing; thus, it could be more flexible and robust in practice.32 In summary, great scientific contributions have been made to unit maintenance management in terms of effective maintenance policies, suitable algorithms, significant process reliability, optimal economic performance, etc. However, few studies have been reported to address unit maintenance issues for the complex crude supply process. Although Zhang et al. reported their works on short-term crude operations under unit malfunction, they focused on CM and reactive scheduling without the consideration of the cost-effective PM and flexible proactive scheduling.31,32 Some researchers simultaneously considered PM and CM operations,33 but the scheduling problem was solved using reinforcement learning method, which was generally by the means of heuristic methods and could not ensure the optimality. It should be noted that the front-end crude supply process involves substantial units with large throughput and complex operations. It is very difficult to predict the exact time when a unit needs the maintenance. Thus, plants will usually plan a conservative time period to perform unit PM tasks based on the trend of unit operating conditions or key performance indexes. Within this time period, the unit PM task could flexibly start at any time when the best maintenance opportunity comes; i.e., maintenance resources such as manpower, maintenance equipment, and utility are ready. Single PM task might be easy to schedule. However, when multiple PM tasks with different maintenance requirements are assigned in the same scheduling time horizon, how to effectively and efficiently organize a maintenance schedule together with the normal crude movement schedule becomes very challenging. Thus, a proactive scheduling strategy has to be employed to optimally plan all PM tasks. In reality, maintenance resources are usually limited, which implies that two or more maintenance tasks cannot be simultaneously performed. Certainly, emergent unit failure may occur at any time, which should be considered as well. Under such a CM request, a reactive scheduling strategy as developed in Zhang’s work32 is adopted, which can immediately handle this urgent CM task and reschedule all other leftover PM tasks. This integrated proactive and reactive scheduling strategy for different PM and CM tasks will be very general to deal with unit maintenance issues in industrial processes. And to the best of our knowledge, studies on the integrated proactive and reactive scheduling work with deterministic models are still lacking for the front-end crude supply process. In this paper, a novel methodology has been proposed for the optimal scheduling of refinery front-end crude movement with consideration of unit maintenance management. It can

2. PROBLEM STATEMENT In this work, the font-end crude supply process for an inland refinery as illustrated in Figure 1 will be studied. As normal operations, various crudes are shipped to the port, where they are unloaded through berths into port-side STs. The crudes in STs will be transferred via LDPL to refinery-side CTs, where blending operations will take place. After that, crudes will be fed into CDUs, which is the beginning of formal processing in the refinery. Note that the feeding operations of each CDU should be continuous. All tank units need some brine settling time (BST) after they have received new crudes, during which they are unavailable of discharging. For CTs, specifications of blending operations on key components are enforced to satisfy processing requirements of CDUs. For the unit maintenance management, the timing to perform unit maintenance operations and resume their services, as well as how to handle the inventory of these units, should be optimally determined. The proactive scheduling of all PM tasks will be performed and integrated with the crude movement schedule. When emergent failure occurs for certain units, the current schedule needs to be updated correspondingly. Thus, the reactive scheduling strategy will be immediately employed to handle the emergent CM tasks as well as the leftover PM tasks. Again, the unit maintenance plan should also be integrated with the updated crude movement schedule. Both scheduling and rescheduling objectives are to minimize the total operating cost for all crude movement and unit maintenance operations. For better understanding of this study, some terminologies used in this work should be clarified in advance. (i) Time event: This work employs continuous time formulation. A time event refers to the unit-specific time window for crude transfer or unit maintenance operations. Note that time event n of unit i should be ahead of time event n + 1 without any time overlap. (ii) Maintenance task: When a unit needs maintenance, both PM and CM, a maintenance task will be assigned. The duration of PM tasks and different types of CM tasks can be estimated based on historical records and given prior to scheduling. Note that each maintenance task has to be completed within the entire scheduling time horizon, and 12194


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Figure 2. Methodology framework.

(6) The maintenance for tank units needs preparation, i.e., draining out the leftover inventory to downstream units; (7) A unit will be isolated and out of service during its maintenance. Assumptions. (1) No time cost for switching feed source to a unit; (2) Ideal blending for tank units; (3) All maintenance tasks are completed within the scheduling time horizon. Given Information. (1) The scheduling time horizon; (2) Unit maintenance tasks and their time durations; (3) Fractions of key components in each crude; (4) Vessel information, including arrival time, carried crude types, and volumes;

the starting/ending time of maintenance tasks will be optimally determined in this work. Based on the above description, operation rules, assumptions, given information, and information to be determined of this scheduling problem are summarized as follows. Operation Rules. (1) One unit can supply at most one downstream unit at one time event; (2) One unit can be fed by at most one upstream unit at one time event; (3) Tank units cannot simultaneously charge and receive crudes; (4) CDUs should be operated continuously; (5) Two or more maintenance tasks cannot be performed at one time event; 12195


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4.1. Proactive Scheduling Model for PM tasks. During PM tasks, units will be off function. For the ease of modeling, maintenance operations are treated as pseudo transfer operations. Specifically, a pseudo unit is introduced to set up pseudo transfer with this off-function unit during its maintenance. This pseudo transfer operation has the same starting and ending time as the real maintenance operation, but there is no actual crude flow. The purpose of such a modeling method is to unify the mathematical formulations of unit maintenance (i.e., pseudo transfer) and normal crude transfer and efficiently integrate the two operations, which would benefit the model solving. This method will be applied to the modeling of CM tasks as well. UNTr and UNTp are defined as the sets of real and pseudo units, u. UNTr contains multiple elements, and UNTp has only one element. According to unit types, elements in UNTr can be classified into subset V (vessels), ST (storage tanks), CT (charging tanks), and CDU (crude distillation units). In addition, based on the crude flow direction, these units can be further categorized as set CU (charging units that can charge downstream units) and RU (receiving units that can receive crudes from upstream units) as shown in eqs 1 and 2.

(5) Capacity, initial inventory and operation specs of STs, LDPL, and CTs; (6) Feeding flow rate range of each unit; (7) Economic data, including demurrage, unloading, transfersetup, and inventory cost. Information To Be Determined. (1) The detailed crude movement schedule, including specific timing and transferred volume from vessel unloading all the way to feeding CDUs; (2) The detailed unit maintenance schedule for all maintenance tasks; (3) The inventory and composition inside STs, LDPL, and CTs.

3. GENERAL METHODOLOGY Figure 2 shows the proposed methodology framework of this study. As displayed, there are three major stages of works: (i) information collection, (ii) model development and proactive scheduling, and (iii) schedule execution and reactive scheduling. After the starting point, critical information will be collected, including process and economic data, vessel and tank initial inventory data, and requested PM tasks in the first stage. After that, the collected information will be fed into the model as developed in the second stage to determine the optimal schedule of front-end crude movement and unit maintenance operations. In the second stage, the MINLP model is developed based on operation rules and unit maintenance requirements. Its objective function is to minimize the total operating cost during the given scheduling time horizon with the completion of all requested maintenance tasks. Note that all PM tasks will be proactively scheduled to determine the best operating timing. If the obtained solution is feasible, it will be identified as the optimal solution and passed to the next stage for implementation; otherwise, troubleshooting will be conducted. During the implementation of the obtained proactive schedule in the third stage, all unit performances will be realtime monitored. If no emergent CM task is requested, the schedule will be continuously executed. Otherwise, if a unit failure occurs, then a CM task will be requested, which should be immediately handled, and the reactive scheduling strategy will be performed. Following the methodology, the leftover PM tasks and the emerging CM task, as well as the current unit operating condition and unit inventory information, will be collected and reinitialized in the model. Then the model will be solved to reactively determine the optimal schedule of front-end crude movement and unit maintenance operations for both emerging CM and leftover PM tasks. Note that the reactive schedule has the same time horizon as that in the previous proactive schedule. After the completion of obtained proactive or reactive schedules, the developed methodology will end or initiate a new schedule.

CU = {u|u ∈ V ∪ ST ∪ CT}

(1)

RU = {u|u ∈ ST ∪ CT ∪ CDU}

(2)

Particularly, CU(u) denotes the set of all real units that can charge unit u; similarly, RU(u) represents the set of all real units that can receive crudes from unit u. Plus the pseudo unit, the set of total charging units, TCU, is defined in eq 3. TCU(u) indicates the set of all units (both real and pseudo) that can charge unit u. TCU = {u|u ∈ CU ∪ UNTp}

(3)

4.1.1. Constraints for Operation Integrality. Binary variable X(u, u′, n) is used to represent both real and pseudo transfer operations. If a transfer operation is scheduled from unit u to unit u′ at time event n, it equals 1; otherwise, it equals 0. Note that for a pseudo transfer operation, the pseudo unit is defined as the upstream unit, and it will charge units that need maintenance. The parameter MR(u) can indicate whether or not unit u needs maintenance in the scheduling time horizon, and it should be given in advance. If MR(u) = 1, it means that one pseudo transfer operation will be scheduled for unit u; if MR(u) = 0, there will be no such a pseudo transfer operation. Accordingly, pseudo transfer operations can be constrained by eqs 4 and 5.

∑

X(u′, u , n) = MR(u), ∀ u′ ∈ UNTp; u ∈ RU

n∈N ,n≥1

(4)

4. MODEL DEVELOPMENT The integrated scheduling model is developed based on our previous works9,34 with significant modifications to address the modeling of maintenance tasks and the integration with other transfer operations, as well as the proactive and reactive scheduling. For the sake of conciseness, only the newly developed model with respect to the proactive and reactive scheduling of unit maintenance is presented below. The model sections regarding general logic, vessel unloading, material balance, and LDPL transfer are summarized in Supporting Information, which readers can refer to for more details.

X(u′, u , n) ≤ MR(u), ∀ u′ ∈ UNTp; u ∈ RU; n ∈ N, n ≥ 1

(5)

At a time event, one unit can charge at most one downstream unit; meanwhile, one unit can receive crudes from at most one upstream unit. Note that the pseudo unit cannot set up multiple pseudo transfers at one time event as well. The two constraints are expressed in eqs 6 and 7. In addition, tank units cannot simultaneously receive and charge crudes at the same time event, which is formulated in eq 8. 12196


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∑

X(u , u′, n) ≤ 1, ∀ u ∈ TCU; n ∈ N , n ≥ 1

Ts(u , u′, n) + H(1 − X(u , u′, n)) ≥ Te(u″ , u′, n′)

u ′∈ RU(u)

− H(1 − X(u″ , u′, n′)), ∀ u′ ∈ RU, u , u″

(6)

∑

∈ TCU(u′); n , n′ ∈ N , n > n′ ≥ 1 X(u , u′, n) ≤ 1, ∀ u′ ∈ RU; n ∈ N , n ≥ 1

The sequence of charging and receiving operations of intermediate units (STs or CTs) follows eqs 16 and 17. For unit u′, its receiving operation at a later time event should be after its charging operation at an earlier time event. Since the brine settling time (BST) is considered, the charging operation at a later time event should be after the completion of receiving operations at an early time event and the settling operation.

u ∈ TCU(u ′)

(7)

X(u , u′, n) + X(u′, u″ , n) ≤ 1, ∀ u ∈ TCU(u′), u′ ∈ ST ∪ CT, u″ ∈ RU(u′); n ∈ N , n ≥ 1

(8)

4.1.2. Constraints for Unit Operation Timing and Sequencing. For each transfer operation (both real and pseudo), its ending time (Te(u, u′, n)) should be after its starting time (Ts(u, u′, n)). If one transfer operation is scheduled, then its operation duration cannot exceed the scheduling time horizon, H. The two logic are expressed by eqs 9 and 10.

Ts(u , u′, n) + H(1 − X(u , u′, n)) ≥ Te(u′, u″ , n′) − H(1 − X(u′, u″ , n′)), ∀ u ∈ TCU(u′), u′ ∈ ST ∪ CT, u″ ∈ RU(u′); n , n′ ∈ N , n > n′ ≥ 1 (16)

Ts(u′, u″ , n′) + H(1 − X(u′, u″ , n′)) ≥ Te(u , u′, n)

Ts(u , u′, n) ≤ Te(u , u′, n), ∀ u ∈ TCU, u′ ∈ RU(u); n ∈ N , n ≥ 1

− H(1 − X(u , u′, n)) + BSTX(u , u′ , n), ∀

(9)

u ∈ TCU(u′), u′ ∈ RU(u′); n , n′ ∈ N , n′ > n ≥ 1 (17)

Te(u , u′, n) − Ts(u , u′, n) ≤ HX(u , u′, n), ∀ u ∈ TCU, u′ ∈ RU(u); n ∈ N , n ≥ 1

4.1.3. Constraints for Maintenance Requirement. Note that the crude inventory of a tank should be completely drained in order to perform maintenance tasks. The tank inventory should remain empty during the maintenance. Thus, once a pseudo transfer operation is determined for unit u at time event n (X(u′, u, n) = 1), its inventory at time event n − 1 and n (Invt(u, n − 1) and Invt(u, n)) should be enforced as zero, which are formulated in eqs 18 and 19.

(10)

The given parameter Tm(u) represents the maintenance duration of each unit. If a pseudo transfer operation is determined (i.e., X(u, u′, n) = 1), its duration should be exactly equal to Tm(u); otherwise, it will be relaxed, as constrained by eqs 11 and 12. Te(u , u′, n) − Ts(u , u′, n)

Inv t(u , n − 1) ≤ Inv max(u)(1 − X (u′ , u , n)), ∀

≤ Tm(u′)X(u , u′, n) + H(1 − X(u , u′, n)), ∀ u ∈ UNTp, u′ ∈ RU; n ∈ N, n ≥ 1

u ∈ ST ∪ CT, u′ (11)

∈ UNTp; n ∈ N , n ≥ 1

Te(u , u′, n) − Ts(u , u′, n) ≥ Tm(u′)X(u , u′, n), ∀ u ∈ UNTp, u′ ∈ RU; n ∈ N , n ≥ 1

∑

(12)

u ∈ ST ∪ CT, u′ ∈ UNTp ; n ∈ N , n ≥ 1 (19)

As aforementioned, there is no actual crude flow for pseudo transfer operations. Thus, for each pseudo transfer operation, the total transferred volume (Vt(u, u′, n)) and volumes of each type of crudes (Vc(u, u′, c,n)) should be zero. The two constraints are expressed by eqs 20 and 21.

Te(u , u′, n) − Ts(u , u′, n)

V t(u , u′, n) = 0, ∀ u ∈ UNTp, u′

u ∈ TCU(u ′) n ∈ N , n ≥ 1

= H , ∀ u′ ∈ CDU

(13)

∈ RU(u); n ∈ N , n ≥ 1

The charging or receiving operations should be well sequenced. For unit u, its charging operation at a later time event should be after that at an earlier time event. For unit u′, its receiving operation at a later time event should be after that at an earlier time event. The two constraints are shown in eqs 14 and 15.

(20)

V c(u , u′, c , n) = 0, ∀ u ∈ UNTp, u′ ∈ RU(u); c ∈ C ; n ∈ N , n ≥ 1

(21)

4.1.4. Objective Function. The model objective is to minimize the total operating cost (TOC), which encompasses vessel demurrage cost, crude unloading cost, transfer setup cost, and tank inventory cost, as expressed in eqs 22 and 23. Note that if a maintenance task is requested, its cost has already been fixed as a constant. Thus, the maintenance cost is not included in the objective function.

Ts(u , u′, n) + H(1 − X(u , u′, n)) ≥ Te(u , u″ , n′) − H(1 − X(u , u″ , n′)), ∀ u ∈ TCU, u′ , u″ ∈ RU(u); n , n′ ∈ N , n > n′ ≥ 1

(18)

Inv t(u , n) ≤ Inv max(u)(1 − X (u′ , u , n)), ∀

Since CDUs are required to be continuously fed, the summation of all charging operation time to a CDU, including the duration of a potential pseudo transfer operation (i.e., the maintenance time of CDU), should equal the scheduling time horizon as shown in eq 13.

∑

(15)

(14) 12197


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Figure 3. Structure of the studied front-end crude supply process.

Obj = min TOC

Ts(u , u′ , n) ≤ Inv 0(u′)/FRlo(u′) + H(1 − X (uu′ , n)), ∀

(22)

u ∈ UNTp, u′ ∈ EU ∩ (ST ∪ CT); n

TOC = C dem ∑ (TV s(v) − TV arr(v)) v∈V ´ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ Ö≠ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÆ Vessel Demerrage Cost

∈ N, n ≥ 1

Ts(u , u′, n) ≥ Inv 0(u′)/FRup(u′) − H(1 − X(u , u′, n)) ∀

+ C unld ∑ (TV e(v) − TV s(v)) v∈V ´ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ ≠ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÆ Crude Unloading Cost + C set

∑

∑

∑

(24)

u ∈ UNTp, u′ ∈ EU ∩ (ST ∪ CT); n ∈ N, n ≥ 1

X (u , u′, n)

´ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ≠ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÆ Transfer Setup Cost

(25)

u ∈ CU u ′∈ RU(u) n ∈ N , n ≥ 1

Ts(u , u′, n) ≤ H(1 − X(u , u′, n)), ∀ u ∈ UNTp, u′

ij ij yzyzz j H + ∑ jjjjjC inv(u)jjjjj ∑ Inv(u , n) + Inv 0(u)zzzzzzzzzz jn∈N ,n≥1 zz |N | + 1 u ∈ ST ∪ CT j k ≠ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ {{Æ k ´ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ Tank Inventory Cost

∈ EU ∩ CDU; n ∈ N , n ≥ 1

(26)

It should also be noted that for units in DU, their PM tasks need be completed within the left part of original horizon, i.e., from 0 to H − T* based on the new time horizon. Thus, the starting time of their pseudo transfer operations is constrained by eq 27, where parameter Tstart(u) denotes the starting time, which equals H − T* − Tm(u).

(23)

In summary, eqs 1−23 as well as all equations listed in the Supporting Information (eqs S1−S69) compose the MINLP model of the proactive scheduling for PM tasks. The nonlinearities arise from the crude blending inside tanks and transferred volume as presented in eqs S10 and S19. 4.2. Reactive Scheduling Model for CM Tasks. During the execution of obtained schedule from the developed scheduling model, emergent unit failures may occur at any time. Under the occurrence of such a unit failure, a CM task will be placed to trigger the reactive scheduling. Here, two new sets are defined: set EU (emergent units) includes the malfunctioning units, and set DU (delayed units) contains units that have leftover PM tasks. When a CM task is requested at T* (0 < T* < H), all unit operating conditions and inventory information will be updated. Note that the CM task should be immediately handled in the reactive scheduling. If the CM task is for a tank unit, its current inventory will be first drained. The starting time of the pseudo transfer operation (maintenance) is bounded by the initial inventory and discharging flow rate range as shown in eqs 24 and 25. If the CM task is for other units like a CDU, the pseudo transfer operation (maintenance) will be set up at the beginning of the new horizon as expressed by eq 26.

Ts(u , u′, n) ≤ T start(u′) + H(1 − X(u , u′, n)), ∀ u ∈ UNTp , u′ ∈ DU; n ∈ N , n ≥ 1 (27)

In summary, eqs 1−27 as well as all equations in Supporting Information compose the reactive scheduling model for the CM and all the leftover PM tasks.

5. CASE STUDIES The efficacy of the developed MINLP scheduling model has been tested through three case studies. Case I is a 12-day scheduling problem, in which one unit requests a PM task. Case II addresses a 14-day scheduling problem, where three PM tasks are requested by three units, respectively. Case III is an integrated proactive and reactive scheduling problem based on Case II, where a new unit requires CM task during the implementation of the original schedule. For these three case studies, the same front-end crude supply process of a refinery is employed as shown in Figure 3, which consists of three vessels, 12198


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Industrial & Engineering Chemistry Research one berth, three port-side STs, one LDPL, four refinery-side CTs, and two CDUs. Details of this front-end crude supply process, including unit capacity, feeding flow rate range, unit maintenance duration, crude properties, blending specs, economic cost, etc., are provided in Table 1. For each case,

Table 2. Process Information for Case I

400 Mbbl

BST

0.1 days

storage tanks

capacity (Mbbl)

charging tanks

capacity (Mbbl)

ST1 ST2 ST3

[0, 1000] [0, 1000] [0, 1000]

CT1 CT2 CT3 CT4 Flow Rate Range: (Mbbl/day)

[0, 1000] [0, 1000] [0, 1000] [0, 1000]

crude unloading charging CDU

[0,500] charging CTs [88, 92] Unit Maintenance Duration: (day)

[170,190]

1 CT 2 Crude Type and Key Indexes

1

ST CDU

k1 (%)

crude C1 C3 C5 C7

0.71 C2 1.08 C4 1.45 C6 1.73 Specs on Key Indexes k1 (%)

charging tank CT1 CT3

crude

charging tank

[0.70, 1.03] CT2 [1.20, 1.47] CT4 Economic Cost

demurrage ($/day) unloading ($/day) transfer-setup ($/time)

30000 10000 20000

maintenance request

CT2

arrival time (day)

volume (Mbbl)

crude composition

ST1 ST2 ST3 charging tanks CT1 CT2 CT3 CT4

0 600 100% C1 4 600 100% C2 8 600 100% C6 initial inventory (Mbbl) initial composition 600 600 600 initial inventory (Mbbl)

100% C2 100% C5 100% C7 initial composition

400 500 400 500 Long-Distance Pipeline Profile

100% C1 100% C3 100% C4 100% C7

initial LDPL slot

inventory (Mbbl)

composition

l1 l2

200 200

100% C2 100% C5

The overall computation time is 3640 CPU s (661 clock s), and the objective function of TOC is $4.436 × 105. The Gantt chart and pipeline profile of the obtained schedule are displayed in Figure 4. The scheduled crude transfer operations and PM operation are illustrated in Figure 4a. In the figure, the horizontal axis represents the scheduling time, and the vertical axis represents crude receiving units. Each bar denotes a crude transfer operation. The colors and filling patterns indicate the associated operating time event and source units, which can be referred to from the explanatory legends. The number nearby each bar is the transferred crude volume. The maintenance operation as well as its preparation is highlighted in red color. As displayed, every vessel carries 600 Mbbl of crudes to the port. Following the schedule, V1 will be unloaded to ST1. Since ST1 holds a plenty of inventory initially, it has to charge 210 Mbbl of crudes to CT1 from day 0.00 to day 1.11. After that, ST1 has enough space to take over all the crudes from V1. As to V2 and V3, they will be unloaded right after their arrivals. CT2 requests a PM task. As shown, it will be scheduled to charge CDU1 from day 0.00 to day 5.68 to prepare for its maintenance operation. Followed by its deinventory, CT2 will be isolated to start its 1day maintenance operation from day 5.68 to day 6.68. After that, its function will be restored, and CT2 is scheduled to receive 200 Mbbl of crudes from day 6.95 to day 8.00. Note that during the entire PM task (preparation−maintenance−return), the tank inventory of CT2 is managed within the system without the use of any external units. As aforementioned, the two CDUs should be continuously fed during the scheduling time horizon. After the charging of CT2, CDU1 is supplied by CT1 from day 5.68 to day 12.00 with 560 Mbbl of crudes. CDU2 is first fed by CT4 from day 0.00 to day 4.89 with 450 Mbbl of crudes, and then its feeding unit is switched to CT3 for the rest of the scheduling time horizon, which supplies 652 Mbbl of crudes. The movement of crude slots inside the LDPL has been presented in Figure 4b, where the horizontal and vertical axes represent the pipeline coordinate and the scheduling time, respectively. As shown, there are two initial crude slots inside the LDPL, l1 and l2. Each one has a volume of 200 Mbbl. From day 0.00 to day 1.11, ST1 charges 210 Mbbl of crudes to LDPL as the new slot l3; meanwhile, all crude of l1 and 10 Mbbl of l2 are pushed into CT1. Next, from day 1.11 to day 2.70, ST2 feeds

k1 (%) 0.94 1.20 1.59

k1 (%) [0.92, 1.15] [1.50, 1.82]

ST inventory ($/day·Mbbl) CT inventory ($/day·Mbbl)

12 days

vessels V1 V2 V3 storage tanks

Table 1. Process and Economic Data of the Studied FrontEnd Crude Supply Process long-distance pipeline

time horizon

5 10

the scheduling model is programmed with GAMS version 25.1.2 installed on a Inter 3.6 GHz Windows PC with 12.0 GB memory. All scheduling models are solved using the global MINLP solver, BARON35, with parallel computing of eight threads. The optimality gap is set as 0.1%. Optimal schedules of the three cases can be determined within reasonable computation time, and these schedules are illustrated below. 5.1. Case I: 12-Day Scheduling Time Horizon with One PM Task. 5.1.1. Results of Obtained Transfer and Maintenance Schedule. Case I is a 12-day scheduling problem, in which unit CT2 requests one PM task and the maintenance duration is 1 day. The process information for Case I, such as vessel arrival time and initial unit inventory, is listed in Table 2. In this case, 5 time events (0−4) in total are assigned to time event set N. Time event 0 corresponds the origin of the scheduling time horizon; time events 1−4 associated with different units will be individually optimized. Less time events will result in a problem with smaller size; thus, less computation time is expected. However, too few time events will lead to undesired local optimality or even infeasible solutions. Therefore, the determination of time event is a trade-off between solving time and solution quality. This study is developed based on our previous work with new consideration of unit maintenance operations;9 thus, one more time event is assigned in this case. This developed scheduling model has 9120 constraints, 2975 continuous variables, and 292 binary variables. 12199


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Figure 4. Gantt chart and pipeline profile for Case I.

302 Mbbl of crudes into the LDPL, generating slot l4. Associated with this feeding, the leftover crudes of l2 and 112 Mbbl of l3 are pushed into CT3. At last, ST3 injects 200 Mbbl of crudes to the LDPL, which forms slot l5. The leftover l3 and 102 Mbbl of l4 are discharged into CT2. At the end of the scheduling time horizon, 200 Mbbl of l4 and 200 Mbbl of l5 are left in the LDPL. 5.1.2. In-Depth Analysis on the Economic Effect of PM Timing. The timing of maintenance tasks will certainly affect the total operating cost. Through the scheduling model based on section 4.1, the timing of all PM tasks will be optimally determined. To further investigate the effect of PM timing on TOC, the PM timing can be intentionally perturbed by a fixed interval, and the corresponding TOC can be identified for each scenario with different fixed PM timings. The trend of TOC with respect to different PM timings will be explicitly figured out. For this purpose, a parameter Tfix(u) is introduced to denote the starting time of the PM task for unit u. Two new constraints, eqs

28 and 29, will be added to the model developed in section 4.1 to form a new scheduling model for this in-depth analysis. Ts(u , u′, n) ≤ T fix(u′) + H(1 − X(u , u′, n)), ∀ u ∈ UNTp, u′ ∈ RU; n ∈ N , n ≥ 1

(28)

Ts(u , u′, n) ≥ T fix(u′) − H(1 − X(u , u′, n)), ∀ u ∈ UNTp, u′ ∈ RU; n ∈ N , n ≥ 1

(29)

For Case I, the starting time of the PM task requested by CT2 will be manipulated by a step increase of 0.5 day from day 0. Accordingly, multiple scheduling scenarios has been generated. The obtained TOC and corresponding PM timing of each scenario are plotted in Figure 5. As shown, feasible solutions can be obtained when the PM timing changes from day 5.5 to day 10.5. The minimum TOC is $4.436 × 105, corresponding to the PM starting time at day 5.68, which is the optimal solution identified in the previous section of 5.1.1. By changing the PM 12200


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Figure 5. Relation of TOC vs varied PM timing.

starting time from day 5.68 to day 10.5, the TOC increases from $4.436 × 105 to $4.81 × 105 by up to 8%. This trend can be explained as follows: completing the PM task earlier indicates that the tank can resume its function earlier; thus, more operational flexibility will be granted to the entire system, which could benefit the overall operations and save more operating cost. It is observed that no feasible schedules can be identified in the beginning time period (from day 0 to day 5) and the ending time period (from day 11 to day 12). The reason for infeasibility in the beginning time period is that the PM task requires the deinventory operation, which needs more than 5 days for CT2 to complete. For the infeasibility in the ending time period, it is because the PM task needs 1 day to complete the maintenance, so that PM cannot start after day 11. In addition, CTs have to maintain their minimal inventory at the end of the scheduling time horizon. Thus, it need some time to complete the charging operations after its PM task. From Figure 5, it is obvious that the obtained schedule in section 5.1.1 is optimal, which proves the effectiveness of our developed scheduling model. Meanwhile, it highlights that the PM timing should be optimally selected, since it has significant economic effect on TOC. 5.2. Case II: 14-Day Scheduling Time Horizon with Three PM Tasks. Compared with Case I, a larger scheduling problem in Case II has been studied, where the scheduling time horizon is 14 days and 3 PM tasks are requested by 3 units of ST1, CT2, and CDU1. The maintenance durations of both ST1 and CT2 are 1 day, and that of CDU is 2 days. The detailed process information on Case II is provided in Table 3. Since Case II has a longer scheduling time horizon and more unit maintenance tasks are requested, 6 time events in total (0−5) are employed. For this problem, the developed scheduling model has 12 573 constraints, 3 671 continuous variables, and 375 binary variables. The optimal solution with a TOC of $4.051 × 105 has been identified in 11 893 CPU s (2 019 clock s). The Gantt chart and pipeline profile of the optimal schedule of Case II are shown in Figure 6. Figures 6a and 6b have the same axes and explanatory legends as those in Figure 4a and 4b. As shown in Figure 6a, each of the three vessels transports 500 Mbbl of

Table 3. Process Information for Case II time horizon

14 days

maintenance request

ST1, CT2, and CDU1

vessels

arrival time (day)

volume (Mbbl)

crude composition

V1 V2 V3 storage tanks

1 500 5 500 10 500 initial inventory (Mbbl)


ST1 ST2 ST3 charging tanks

400 600 400 initial inventory (Mbbl)


CT1 CT2 CT3 CT4

500 100% C2 400 100% C3 500 50% C4 and 50% C5 400 100% C6 Long-Distance Pipeline Profile

initial LDPL slot

inventory (Mbbl)

composition

l1 l2

300 100

100% C3 100% C4

crudes to the port and unloads their crudes to STs right after their arrivals. Three transfer operations are scheduled via the LDPL, and the two CDUs are consecutively supplied by CTs. As to the three PM tasks, CT2 is scheduled to charge CDU1 at the beginning of the time horizon. After the deinventory operation, CT2 will have 1-day maintenance from day 4.35 to day 5.35. ST1 feeds CT1 254 Mbbl of crudes at first, and then it charges to CT2 with the leftover of its inventory. After that it will be isolated for its maintenance from day 9.00 to day 10.00. Right after the maintenance, it resumes its function and receives 500 Mbbl crudes from V3. The PM task of CDU1 is scheduled from day 12.00 to day 14.00 after being fed by CT1. In this case, the three PM tasks are scheduled without any time overlaps as enforced by the operation rules. Note that inventories of the two tank units, ST1 and CT2, are managed without the help of any external storage units during the scheduling time horizon; 12201


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Figure 6. Gantt chart and pipeline profile for Case II.

scheduling as proposed by our methodology framework. According to Figure 6a, vessels 1 and 2 have been unloaded, and the PM task of CT2 has been completed; meanwhile, the inventory of ST1 has been partially drained prior to day 7. Thus, the emergent CM task and original PM tasks for ST1 and CDU1 should be handled in this reactive scheduling problem. Process information has to be reinitialized, which includes unit inventory, crude composition, and vessel arrival time, as provided in Table 4. Since Case III is based on and compared with Case II, 6 time events (0−5) are assigned in this case as well. Note that the new scheduling time horizon still lasts 14 days, and it will set the previous day 7.00 as day 0.00 for the rescheduling problem. To comply with the in-time maintenance requirement (see eq 29), the two PM operations need to be completed within the first 7 days (H − T*) in the new time horizon. For this rescheduling problem, the developed model has 14 686 constraints, 3 666 continuous variables, and 430 binary variables. The optimal solution is obtained in 20 045 CPU s; since parallel computing is employed, the clock time is 3 060 s. For an MINLP problem with such a large size, this computation time is reasonable. Moreover, compared with the

meanwhile, they are scheduled to resume their normal operations and receive new crudes after their maintenance operations. In Figure 6b, two slots initially exist in the LDPL, l1 with 300 Mbbl of volume and l2 with 100 Mbbl of volume. As aforementioned, three transfer operations via the LDPL are scheduled. From day 0.00 to day 2.57, ST2 feeds 488 Mbbl of crudes into CT3. In the next 1.49 days, ST1 supplies 254 Mbbl of crudes to CT1. From day 8.23 to day 9.00, ST1 injects another 146 Mbbl of crudes into CT2. Here, the two injections from ST1 correspond to two deinventory operations in Figure 6a. At the end of the scheduling time horizon, 254 Mbbl of l4 and 146 Mbbl of l5 are left in the LDPL, and they act as the initial pipeline slots in the next scheduling problem. 5.3. Case III: 14-Day Scheduling Time Horizon with One Emergent CM Task. Case III addresses a reactive scheduling problem for an emergent unit failure and its corresponding CM task. Case III is based on the solution of Case II. It is assumed that during the execution of the schedule of Case II, a sudden unit failure of CT3 occurs at day 7.00. Hence, an emergent CM task for CT3 will trigger the reactive 12202


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The optimal reschedule is represented using Gantt chart and pipeline profile as shown in Figure 7. For the sake of easy understanding, the operations of the first 7 days from the original schedule (Case II) is still provided in Figure 7a, which correspond to the time range from day −7.00 to day 0.00. In the reactive schedule (from day 0.00 to day 14.00), CT3 starts the deinventory operation by charging its crudes to CDU2 at day 0.00 in response to its CM task. All 686 Mbbl of inventory are transferred. Right after its deinventory, CT3 will receive its 1-day CM operation from day 7.80 to day 8.80. As shown, the PM of CDU1 is rescheduled to the beginning of the new schedule, from day 0.00 to day 2.00. Meanwhile, ST1 starts to drain to CT2 at the time origin as well, and the 146 Mbbl of leftover inventory inside ST1 are transferred from day 0.00 to day 0.77. After the completeness of CDU1’s maintenance, ST1 receives its PM from day 2.00 to day 3.00. In this schedule, the three maintenance operations are well arranged without any time overlap. Again, all inventories of maintained tank units have been handled within the front-end crude supply system without the use of extra backup units, and these units are able to resume the designated function, receiving and storing new crudes, after their maintenance tasks. In the meantime, the refinery could still run normally under upsets from those CM and PM tasks. As displayed in Figure 7b, four new slots are generated in this schedule. Through the reinitialization, there are two slots

Table 4. Process Information for Case III time horizon

14 days

time of failure realization (T*)

day 7

uncompleted PM request

ST1 and CDU1

new CM request

CT3

vessels

arrival time (day)

volume (Mbbl)

crude composition

V3 storage tanks

3 initial inventory (Mbbl)

ST1 ST2 ST3 charging tanks CT1 CT2 CT3 CT4 initial LDPL slot l1 l2

146 612 900 initial inventory (Mbbl)

500 100% C5 initial composition 100% C2 82% C3 and 18% C4 56% C2 and 44% C6 initial composition

500 66% C2 and 34% C4 0 − 616 31% C3, 44% C4 and 25% C5 50 100% C6 inventory (Mbbl) composition 146 254

100% C4 100% C2

14-day time horizon, the computation time is negligible. The obtained optimal schedule has a TOC of $3.529 × 105.

Figure 7. Gantt chart and pipeline profile for Case III. 12203



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present in the LDPL. l3 is charged by ST1 in the first 0.77 day, which corresponds to the deinventory operation of ST1; and l1 with 146 Mbbl of crudes is discharged into CT2. l4 with 490 Mbbl of volume is fed by ST2 from day 0.77 to day 3.56 into the LDPL. Correspondingly, 254 Mbbl of l2, 146 Mbbl of l3, and 90 Mbbl of l4 are supplied into CT1. From day 3.66 to day 7.09, ST3 charges 652 Mbbl of l5 into the pipeline, and 400 Mbbl of l4 and 252 Mbbl of l5 are discharged into CT2. At last, ST3 sends 50 Mbbl of l6 into the LDPL, and 50 Mbbl of l5 is pushed into CT3. At the end of the rescheduling horizon, 350 Mbbl of l5 and 50 Mbbl of l6 are left inside the LDPL, which compose the initial status of the LDPL for the next scheduling problem.

ACKNOWLEDGMENTS This work was supported in part by Graduate Student Scholarship and Anita Riddle Faculty Fellowship from Lamar University in Beaumont, TX.

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NOMENCLATURE INDICES: c∈C crude types k∈K key indices l∈L pipeline slots n∈N time events U ∈ UNT units, including vessels, port-side storage tanks, refinery-side charging tanks, and crude distillation units

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6. CONCLUDING REMARKS

SETS: C CDU ⊂ UNT CT ⊂ UNT CU ⊂ UNT K L Lini ⊂ L

In this work, a novel methodology has been proposed for the optimal scheduling of refinery front-end crude movement with consideration of unit maintenance management. It can dynamically and simultaneously handle multiple maintenance tasks and meanwhile ensure the smooth running of the front-end crude supply process under upsets from maintenance operations. Specifically, both the proactive scheduling for PM tasks and the reactive scheduling for emergent CM tasks are systematically integrated. Accordingly, an MINLP model with continuous time formulation has been developed to optimize the operation schedule for crude supply process via minimizing the overall operating cost during the scheduling time horizon. The development of this study can determine the optimal unit maintenance schedule, which will identify the best opportunities of not only isolating units from process system to perform maintenance but also resuming their services after maintenance. Meanwhile, it is capable of handling multiple maintenance tasks, which can be well scheduled without any time overlap. The inventory of maintenance needed units is also managed within the system without the use of external backup units, while still satisfying all strict constraints for crude transferring, storing, blending, and processing operations. Through three case studies, the developed methodology and MINLP model exhibits excellent performance on solving the integrated scheduling problem, and the optimal solution can be effectively and efficiently determined.

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Lnew ⊂ L N RU ⊂ UNT ST ⊂ UNT TCU UNTr UNTp V ⊂ UNT

■

set of crude oil types set of crude distillation units set of refinery-side charging tanks set of charging units that can feed other units set of key indices (e.g., sulfur content) set of pipeline slots set of initial pipeline slots that exist within the pipeline before scheduling starts set of pipeline slots that may be fed to the pipeline during the scheduling time horizon set of global time events set of receiving units that are fed by other units set of port-side storage tanks set of total charging units including CU and pseudo units set of all real units including vessels, STs, CTs and CDUs set of pseudo units set of vessels

PARAMETERS: BST brine settling time Cdem vessel demurrage cost Cunld crude unloading cost Cset transfer setup cost for crude transfers from vessels to ST, from ST to CTs, and from CTs to CDUs Cinv inventory cost FRlo(u)/FRup(u) lower/upper bounds of flow rate for charging unit u f 0(u,c) initial volume fraction of crude c in unit u f k(c,k) the fraction of key index k of crude c f k,lo(u,k)/f k,up(u,k) minimum/maximum fraction of key index k in unit u H scheduling time horizon Invmin(u)/Invmax(u) minimum/maximum inventory capacity of unit u Inv0(u) initial inventory of unit u Inv0(l) initial inventory of slot l MR(u) the maintenance request of unit u S/M the lower/upper bound to activate constraints (big-M method) T* the timing of realizing unit failure Tfix(u) the fixed maintenance timing of unit u Tm(u) the maintenance duration of unit u Tstart(u) the latest time for the delayed unit u to start its maintenance operation

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b02449. Model sections regarding general logic, vessel unloading, material balance, and LDPL transfer, as well as variable bounds (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Phone: 409-880-7818. Fax: 409-880-2197. E-mail: Qiang.xu@ lamar.edu. ORCID

Qiang Xu: 0000-0002-2252-0838 Notes

The authors declare no competing financial interest. 12204


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Industrial & Engineering Chemistry Research TVarr(v) VDc,up(l,c,n) VDt,up(l,l′,n) VOL

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(2) Ugalde-Salas, P.; Díaz-Alvarado, F.; Flores, S. A.; Ramírez, H. An Optimization Model To Incorporate CO2 Emissions in the Scheduling of Crude Oil Operations. Ind. Eng. Chem. Res. 2018, 57 (33), 11342− 11349. (3) Xu, J.; Qu, H.; Zhang, J.; Wang, S.; Xu, Q. Emission Conscious Scheduling of Crude Unloading, Transferring, and Processing for Petroleum Refineries. In Computer Aided Chemical Engineering; Eden, M. R., Ierapetritou, M. G., Towler, G. P., Eds.; Elsevier: Amsterdam, 2018; Vol. 44, pp 1219−1224. (4) Ji, X.; Huang, S.; Grossmann, I. E. Integrated Operational and Financial Hedging for Risk Management in Crude Oil Procurement. Ind. Eng. Chem. Res. 2015, 54 (37), 9191−9201. (5) Xu, J.; Qu, H.; Wang, S.; Xu, Q. A New Proactive Scheduling Methodology for Front-End Crude Oil and Refinery Operations under Uncertainty of Shipping Delay. Ind. Eng. Chem. Res. 2017, 56 (28), 8041−8053. (6) Yang, Y.; Barton, P. I. Integrated crude selection and refinery optimization under uncertainty. AIChE J. 2016, 62 (4), 1038−1053. (7) Chen, X.; Grossmann, I.; Zheng, L. A comparative study of continuous-time models for scheduling of crude oil operations in inland refineries. Comput. Chem. Eng. 2012, 44, 141−167. (8) Li, J.; Misener, R.; Floudas, C. A. Continuous-time modeling and global optimization approach for scheduling of crude oil operations. AIChE J. 2012, 58 (1), 205−226. (9) Qu, H.; Xu, J.; Wang, S.; Xu, Q. A novel MINLP model of frontend crude scheduling for refinery with consideration of inherent upset minimization. Comput. Chem. Eng. 2018, 117, 42−62. (10) Qu, H.; Xu, J.; Wang, S.; Xu, Q. Optimal Front-end Crude Schedule for Refineries under Consideration of Inherent Upset Reduction. In Computer Aided Chemical Engineering; Elsevier: Amsterdam, 2018; pp 1315−1320. (11) Wang, H. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research 2002, 139 (3), 469− 489. (12) Castro, P. M.; Grossmann, I. E. From time representation in scheduling to the solution of strip packing problems. Comput. Chem. Eng. 2012, 44, 45−57. (13) Gao, X.; Jiang, Y.; Chen, T.; Huang, D. Optimizing scheduling of refinery operations based on piecewise linear models. Comput. Chem. Eng. 2015, 75, 105−119. (14) Pan, X.; Tang, W.; Karim, M. N. Detection of Multiple Leaks in a Natural Gas Pipeline Using Observer and Mixed-Integer Partial Differential Equation-Constrained Optimization. Ind. Eng. Chem. Res. 2017, 56 (41), 11839−11846. (15) Qu, H.; Wang, S.; Xu, Q. A new method of cyclic hoist scheduling for multi-recipe and multi-stage material handling processes. Comput. Chem. Eng. 2016, 90, 171−187. (16) Qu, H.; Wang, S.; Xu, Q. Simultaneous 2D hoist scheduling and production line design for multi-recipe and multi-stage material handling processes. Chem. Eng. Sci. 2017, 167, 251−264. (17) Qu, H.; Xu, J.; Wang, S.; Xu, Q. Dynamic Routing Optimization for Chemical Hazardous Material Transportation under Uncertainties. Ind. Eng. Chem. Res. 2018, 57 (31), 10500−10517. (18) Zhang, Q.; Grossmann, I. E.; Heuberger, C. F.; Sundaramoorthy, A.; Pinto, J. M. Air separation with cryogenic energy storage: Optimal scheduling considering electric energy and reserve markets. AIChE J. 2015, 61 (5), 1547−1558. (19) Ruiz, R.; Carlos García-Díaz, J.; Maroto, C. Considering scheduling and preventive maintenance in the flowshop sequencing problem. Computers & Operations Research 2007, 34 (11), 3314−3330. (20) Castro, P. M.; Grossmann, I. E.; Veldhuizen, P.; Esplin, D. Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programming. AIChE J. 2014, 60 (6), 2083− 2097. (21) Vieira, M.; Pinto-Varela, T.; Barbosa-Póvoa, A. P. Production and maintenance planning optimization in biopharmaceutical processes under performance decay using a continuous-time formulation: A multi-objective approach. Comput. Chem. Eng. 2017, 107, 111−139.

arrival time of vessel v upper bound of the discharged volume of crude c pushed by slot l at time event n upper bound of the discharged volume of slot l′ pushed by slot l at time event n volume of the LDPL

0−1 CONTINUOUS VARIABLES: XL(l,u,n) it is 1 if slot l is pushing crudes into charging tank u at time event n; otherwise, it is 0. CONTINUOUS VARIABLES: f(u,c,n) volume fraction of crude c in unit u at the end of time event n f l(l,c) volume fraction of crude c in slot l Invc(u,c,n) inventory of crude c inside unit u at the end of time event n Invk(u,k,n) the level of key index k in charging unit u at the end of time event n Invt(u,n) total inventory of unit u at the end of time event n Invl(l,l′,n) the inventory of slot l′ after slot l has been fed during time event n TOC the total operating cost Ts(u,u′,n) starting time of a crude transfer from unit u to unit u′ at time event n Te(u,u′,n) ending time of a crude transfer from unit u to unit u′ at time event n TVs(v) starting time of unloading a vessel v during the scheduling time horizon TVe(v) ending time of unloading a vessel v during the scheduling time horizon Vt(u,u′,n) total volume transferred from unit u to unit u′ at time event n Vc(u,u′,c,n) volume of crude c transferred from unit u to unit u′ at time event n V1c(u,u′,c,n) corrected volume of crude c transferred from ST u to CT u′ at time event n VDt(l, l′, n) discharged volume of slot l′ after slot l has been fed during time event n VDc(l,c,n) discharged volume of crude c pushed by slot l at time event n VLt(u,l,n) volume of slot l charged by ST u at time event n VLc(u,l,c,n) volume of crude c in slot l charged by ST u at time event n VL1c(l,u,c,n) volume of crude c in slot l discharged into CT u at time event n

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BINARY VARIABLES: X(u,u′,n) it is 1 if unit u transfers crudes to unit u′ at time event n; otherwise, it is 0. W(u,l,n) it is 1 if unit u charges slot l into LDPL at time event n; otherwise, it is 0. Y(l,l′,n) it is 1 if slot l pushed out slot l′ at time event n; otherwise, it is 0. Z(l,l′,n) it is 1 if slot l′ has inventory left in the pipeline after slot l has been fed at time event n; otherwise, it is 0.

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REFERENCES

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