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A New Proactive Scheduling Methodology for Front-End Crude Oil and Refinery Operations under Uncertainty of Shipping Delay Jialin Xu,† 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 S Supporting Information *

ABSTRACT: Crude oil planning and scheduling is crucial to petroleum refineries because of the potential for significant economic benefits. In reality, however, crude oil scheduling activities are highly vulnerable to disruptions caused by various uncertainties. In this paper, a new proactive scheduling methodology simultaneously covering crude unloading, transferring, and processing (CUTP) has been developed. The CUTP scheduling methodology is to maximize the total profit subject to various inventory, operation, transportation, and production constraints, while maintaining the refinery normal operating conditions under the uncertainty of crude shipping delays. To quantify shipping delay uncertainties, a combined feasibility index has been developed and embedded into the developed continuous-time mixed-integer nonlinear programming scheduling model, which is solved by the global solver of ANTIGONE. In addition, the relationship between the total profit and the minimum flexibility threshold is also given. The efficacy of this study has been demonstrated by industrial-scale case studies.

1. INTRODUCTION The petroleum industry plays an important role in the economic development of the country. The supply chain management system consists of oil and gas exploration, shipping, loading, storage, blending, refining, transportation, and sale. The schematic of the overall system is shown in Figure 1. Within the entire supply chain, many decisions need to be made, such as what types of crudes are purchased, what product portfolios are produced, and how to determine the product distribution for internal use or sold to external customers. Therefore, advanced decision-supporting techniques such as planning and scheduling are needed to cope with challenges in crude oil supply chain management. Scheduling is the process of arranging, controlling and optimizing work and workloads in a production or manufacturing process. In manufacturing, the purpose of scheduling is to minimize the production time and costs, by telling a production facility when and what to make, with which staff, and on which equipment. Since the 1950s, mathematical programming has been implemented in long-term decision making for crude planning to optimize both production and crude purchasing plan. Crude planning and scheduling is very important to a petroleum refinery because of the potential realization of large cost savings. It has been studied and practiced for a long time, © XXXX American Chemical Society

especially in the last two decades, driven by increasingly intensive global competitions, more volatile feedstock and product markets, as well as stricter environmental regulations. As shown in Figure 1, the scope of this study contains two major sections: (i) front-end crude transfer, which covers the crude unloading from vessels to portside storage tanks at onshore berths and the crude transferring to charging tanks of an inland refinery to prepare blends for plant processing with satisfied property specifications; (ii) crude processing in the refinery, which includes crude distillation, reforming, cracking, hydrotreating, blending, gas processing, sulfur recovering, as well as refinery product blending and storage. Obviously, the supply chain management for a petroleum refinery should consider the simultaneous scheduling of front-end crude transfers and in-plant processing. Many published studies have addressed these two major sections. Ierapetritou and Floudas proposed a novel continuous-time formulation for short-term scheduling problems, which decoupled the task events from the unit events.1,2 Jia et al. used the Received: Revised: Accepted: Published: A

April 10, 2017 June 8, 2017 June 16, 2017 June 19, 2017 DOI: 10.1021/acs.iecr.7b01496 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematic of overall supply chain management system in petroleum industry.

plants under the uncertainty of crude oil shipping delays.19 An integrated optimization model of refinery production has been proposed by Zhao et al. to decompose the integrated model of the two systems into a MILP model and a NLP model, which are then solved iteratively through variables transferring to further reduce the solution time.20 Very recently, a large-scale MILP model for strategic planning optimization was proposed by Elia et al. for a network of natural gas to liquids (GTL) systems, which was solved by a rolling horizon strategy.21 Meanwhile, Gao et al. studied refinery scheduling by employing a piecewise linear (PWL) partitioning and modeling strategy to help solve the original MINLP problem.22 Actually, there’s a potential opportunity to improve the refinery profitability if these two parts could be optimally integrated. However, it is not an easy task because of the domino effect with the crude flows from upstream to downstream units and the differences between their densities, sulfur contents, product yields, etc. In addition, simultaneous scheduling is a big challenge; development and integration of two different large-scale models is complicated. In reality, the crude scheduling activities are highly vulnerable to disruptions brought by various uncertainties, which can be regarded as the Achilles heel of planning and scheduling. For example, the shipping delay of crude vessels may disrupt the associated activities and cause the originally well-set schedule operations to become suboptimal or even infeasible. Various techniques have been developed for hedging against uncertainties, such as recourse-based classical stochastic programming,23 probabilistic or chance-constraint programming,24 robust stochastic programming,25 stochastic dynamic programming,26 fuzzy programming,27 flexibility analysis and optimization,28,29 and multiparametric programming for mixed-integer quadratic programming.30−32 To characterize the inherent capability of a refinery for handling the delivery delay uncertainties, the property-based and quantity-based operational flexibility indexes and their combination are introduced in this paper. The combined flexibility index (CFI) range will be added as a constraint in the optimization model to maximize the gross profit, which will be introduced in the following context later. Obviously, a large flexibility index is desirable for production operation; however, it may induce more crude oil inventory and slower cash flow. Therefore, the optimization of the front-end and refinery crude-oil operations should proactively take the production flexibility into account and know

continuous-time method to build a mixed-integer linear programming (MILP) scheduling model for inland refineries with both storage and charging tanks, in which nonlinear constraints were relaxed to generate a MILP model.3,4 Similarly, Reddy et al. presented continuous-time formulation for crude oil scheduling of refineries incorporating those real characteristics, including single buoy mooring (SBM) station, multiparcel vessels, brine settling, and a multitank feeding one or more columns.5 An iterative algorithm was adopted to eliminate the crude composition discrepancy problem. Shah presented a discrete-time MILP model to address the production-driven crude oil scheduling.6 Lee et al. minimized operational costs for inland refineries by formulating a discrete-time-based MILP model via linearization of bilinear crude blending constraints.7 Li et al. solved the developed scheduling model with a global optimization algorithm and considered 15 volume- and weightbased property indices that were linearly additive for marineaccess refineries.8 Chryssolouris et al. proposed an integrated simulation-based approach for refinery short-term scheduling with tank farm, inventory, and distillation management.9 Besides all realistic characteristics mentioned above, Zhang and Xu proposed an effective two-stage reactive scheduling methodology for short-term crude oil operations to manage crude movements from ship unloading to distillation processing under various uncertainties, such as shipping delay, crude mixture demand change, and tank unavailability.10 Also, a new continuous-time crude scheduling model has been developed by Zhang et al. to address long-distance pipeline transportation and other realistic considerations for crude unloading using an OA-based iterative algorithm.11 Refinery production scheduling addresses in-plant crude oil processing, which is also an important part of petroleum supply chain management.12−14 Pinto et al. presented a general modeling framework for petroleum supply chain optimization.15,16 The model framework could integrate oilfield, crude oil supply, petroleum processing, and product distribution models into a large supply chain model. Mendez et al. proposed a simultaneous optimization approach for blending and scheduling of refinery plant, which could be either a discretetime or continuous-time formulation.17 Yüzgeç et al. developed a model predictive control (MPC) strategy presented to determine the optimal control decisions for the short-term refinery scheduling problem.18 Zhang et al. developed a general mixed integer nonlinear programming (MINLP) model to address the optimal crude oil blending and purchase planning in refinery B

DOI: 10.1021/acs.iecr.7b01496 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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CDU feed with satisfied blending requirements.19 However, in some cases, the PFI may be overestimated. Under such situations, QFI reflects the actual sustainable time. Thus, a new index, CFI, is introduced, which gives a more accurate quantification of the production flexibility. This CFI is used to address the shipping delay in the model. More detailed explanation on flexibility indexes has been provided in the model constraints section. The studied CUTP scheduling problem is summarized below: Given Information: (1) Detailed CUTP configurations including process units and facilities and the connecting structures of the frontend crude transfer section and the refinery processing section. Note that major process facilities of a refinery have been illustrated by previous work.35 (2) Initial operating status and process specifications of each CUTP unit and facility, such as tank capacities, crude transfer rate limits, and feed/product quality constraints of major refinery facilities. (3) Crude shipping information including number of vessels, crude types, volumes of each crude parcel, and vessel arrival time. (4) Properties of crude oils and blending products including densities, sulfur contents, light oil yields, and segregation policies such as property index ranges. (5) Economic data including demurrage cost (vessel waiting cost); unloading cost; CDU changeover cost; utility costs; front-end tank setup and inventory costs; and prices of crude oil, utilities, and refinery products. Information To Be Determined: (1) A detailed unloading schedule for each vessel, including information on transfer connections, timings, and volumes. (2) A detailed crude transfer schedule from storage tanks to charging tanks and from charging tanks to refinery CDUs, including transfer connections, timings, volumes, and properties. (3) Inventory and crude composition profiles at each storage and charging tanks. (4) Operating schedules of various refinery processing facilities. (5) Detailed refinery product quantity and quality profiles. (6) CUTP economic results including front-end crude unloading, transferring, and storage costs; refinery processing costs; refinery product revenue; and total profit. Operating Constraints: (1) A parcel can be unloaded to at most one storage tank at a time event; however, it can be unloaded into multiple tanks across consecutive time events. (2) A storage or charging tank cannot simultaneously receive and send out crudes. (3) A charging tank can feed at most one refinery CDU, and a CDU can receive feed from at most one charging tank at a time event. (4) Properties of crudes fed to refinery CDUs should satisfy certain requirements. (5) Final refinery products after blending operations should satisfy certain quality requirements. Assumptions: (1) Perfect mixing is assumed in crude storage and charging tanks as well as refinery blend headers.

in-depth about the relation between the plant profitability and production flexibility. In this research, a new large-scale continuous-time scheduling model has been developed for crude unloading, transferring, and processing (CUTP) systems to simulate and optimize the front-end and refinery crude-oil operations simultaneously. The general objective of the proposed CUTP model is to maximize the total production profit under uncertainty of shipping delay; meanwhile, operation and product specifications, inventory limits, and production demands have to be satisfied. The scheduling model is a large-scale mixed integer nonlinear programming problem. To efficiently solve large-scale systems without compromising problem complexity, a general mixedinteger nonlinear global optimization solver, ANTIGONE, has been employed.33 In addition, the insight of the relationship between the total profit and the minimum flexibility threshold has also been provided. The efficacy of the proposed scheduling model has been demonstrated by industrial-scale case studies.

2. PROBLEM STATEMENT The scope of the studied CUTP scheduling process is illustrated in Figure 1. To help better understand the developed continuous-time methodology, several important terminologies in this study need to be clarified. Time Event: In this study, the unit-based time event is defined for unit-to-unit operations including crude unloading, transferring, and processing. To align time events on a continuous-time base, any input−output operations associated with a unit at time event n occurs earlier than those arranged at time event n + 1. Thus, the operating time window of event n for a unit will be determined by its scheduled input−output operations at time event n. In other words, the time event can be regarded as an “identif ier” that facilitates the alignment of different activities along the scheduling time horizon. The more detailed explanation for time event can be found in a previous paper.34 Refinery Processing Status Transition (RPST): During the CUTP scheduling, the blend type of crudes from charging tanks to refinery crude distillation units (CDUs) may change associated with different time events. The CDU feed type change will cause the refinery to have different operating statuses and production yields. Such a refinery processing status transition is called RPST. A RPST should take the whole refinery some time to complete the status transition, and it should satisfy crude mass balance during the transition. A fixed RPST time has been considered in our CUTP scheduling model. The more detailed explanation for RPST can be found in a previous paper.35 Property-Based Flexibility Index (PFI): The inventoryrelated production flexibility index can be classified into two categories: PFI and QFI. PFI is the minimum time duration to sustain CDU feeds with the satisfied sulfur content requirement by using up all the crude oil inventories. Quantity-Based Flexibility Index (QFI): The time duration to sustain CDU feeds with satisfied quantity requirements is that which constrains only the quantity of crude oil inventories. Both property-based and quantity-based flexibility indexes are inventory-related variables and functions of time, which give the conservative estimation of how long the inventory can sustain the refinery operation if no new crude oil is imported. Combined Flexibility Index (CFI): A combined flexibility index is developed to quantify the shipping delay uncertainty. It means the minimum time duration based on the current inventory without receiving any new crude oil to sustain the C


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Industrial & Engineering Chemistry Research (2) A fixed value of RPST time is assumed in the CUTP scheduling model.

After the modeling solution is identified as feasible and the range of CFI is obtained, the maximum gross profit will be identified, where eq 14 is employed as the sole objective function. During this step, the profit maximization and the customized minimum CFIn will be considered simultaneously. Thus, an threshold expectation of the minimum CFIn can be set and added as a constraint in the optimization model, where the objective function is to maximize the gross profit as shown in eq 14. This makes the optimization more applicable in terms of having taken into account shipping delay uncertainty. For comparison, the optimization results with and without customized CFI are presented and discussed. The branch-and-cut global optimization method has been employed to obtain the optimal solution of the developed MINLP scheduling model.

3. METHODOLOGY FRAMEWORK Figure 2 gives the general framework of the developed CUTP scheduling methodology. The general objective of this study is

4. CUTP SCHEDULING MODEL The whole scheduling model can be separated into three parts: (i) a front-end crude oil transfer model, which includes equations and constraints covering crude movement from vessels to portside storage tanks, inland charging tanks, and refinery CDUs; (ii) a refinery crude processing model, which addresses the detailed processing strategy based on the given input of crude blends; (iii) flexibility index constraints, which present the detailed constraints associated with different flexibility indexes. 4.1. Front-End Crude Transfer Model. The front-end crude transfer scheduling model is mainly borrowed from a previous study35 with modest modifications. It involves integrality constraints for operating practices; logic constraints; transportation and capacity constraints; time constraints for vessels, parcel unloading, storage and charging tanks; and material balance constraints for crude parcels and tanks; as well as variable upper and lower bounds. The RPST model is also included in the front-end crude transfer scheduling model, which addresses issues of transitional time and mass balance because of the refinery operating status change associated with different refinery feeds. The detailed front-end crude scheduling model constraints similar to the previous study are summarized in part A of the Supporting Information. 4.2. Refinery Crude Processing Model. The refinery crude processing model is also borrowed from the previous study,35 which addresses the detailed processing strategy based on the given input of crude blends. Property mixing functions, mixing unit model, reactor model, separator model, plant feedstock and output model, inventory unit model, as well as plant utility balance constraints are included in this submodel. Because the integrated crude scheduling model is very complicated, for conciseness, only those newly developed model equations from this study are discussed in detail in the following section. The detailed refinery crude processing model constraints similar to the previous study are summarized in part B of the Supporting Information. 4.3. Flexibility Indexes Constraints. The proposed flexibility indexes are associated with the crude-oil inventory. This means the minimum time duration based on the current inventory without receiving any new crude oil to sustain the CDU feed with satisfied blending requirements. According to the CDU feed requirements, the inventory-related production flexibility index can be classified into two categories: the property-based (i.e., sulfur content) flexibility index and the quantity-based flexibility index. 4.3.1. Property-Based Flexibility Index. FOct(unt, n) and f(unt, k, n) represent the flow rate and the sulfur content of

Figure 2. General methodology framework.

to maximize refinery profit under shipping delay uncertainty. The profit maximization and the production flexibility maximization are generally two contradictory aspects that should be well-balanced. Generally, the methodology starts from collecting economic, process, and initial operating data. Based on the collected data, a continuous-time CUTP scheduling model will be developed, which consists of three sub models: (i) front-end crude transfer model; (ii) refinery processing status transitional model, also called RPST model; and (iii) refinery crude processing model. Then a CFI model needs to be developed to quantify the shipping delay tolerance. After that, the upper and lower bounds of the CFI will be identified, where eqs 15 and 16 are independently employed as an objective function to solve the corresponding model. During the modeling solution identification, various data is needed, including the price data, inventory data, and production specifications. If the solver finds a feasible range of CFI, the studied problem is feasible, otherwise, the studied problem is infeasible and thus it is unnecessary to continue. Troubleshooting will be performed on specific sections, which is mainly about refinement of the developed model in case any discrepancies occur in any possible studied cases. D


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Figure 3. Schematic diagram of the studied front-end crude transfer process. Reprinted with permission from ref 35. Copyright 2017 Elsevier.

Figure 4. Schematic diagram of the studied refinery plant. Reprinted with permission from ref 35. Copyright 2017 Elsevier.

The property-based flexibility index, PFIn, is the minimum time duration to sustain CDU feeds with the satisfied sulfur content requirement by using up all the crude-oil inventories that belong to Cl. Because PFIn should be as small as possible, the crude oils with high sulfur contents employed for blending operation should belong to Ch, and each charging tank outflow rate should reach the upper bound of FOct,up(unt, n). This is just the way of calculating PFIn based on the worst case scenario in order to identify the smallest value of PFIn, which has nothing to do with controlling daily refinery feed rate. Therefore, eqs 3 and 4 present the total mass balance and sulfur balance related to PFIn.

blended oils from the charging tanks directed to CDUs, respectively, at time event n. FOct (unt, n) and f(unt, k, n) should be within the refinery specifications. Thus, the upper and lower bounds of FOct(unt, n) are defined as FOct,up(unt, n) and FOct,lo(unt, n), respectively. Similarly, f up(unt, k, n) and f lo(unt, k, n) are upper and lower bounds of f(unt, k, n), respectively. Note that any component crude oil c (c ∈ C) has its own sulfur content defined as ICKc(c, k). According to the comparison between ICKc(c, k) and f up(unt, k, n), the total crude set C implies two subsets: the lower sulfur-content set Cl and the highest sulfur-content set Ch as defined in eqs 1 and 2. C l = {c|c ∈ C , ICKc ≤ min f up (unt, k , n)} unt

c′

(1)

PFIn

c

C h = {c′|c′ ∈ C , ICK = max ICK (c , k)} c

∑ unt ∈ DU

(2)

FOct,up(unt, n) = EX n +

∑ Ec ,n , ∀ n ∈ N c ∈ Cl

(3) E


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Figure 5. Front-end scheduling result of case 3.

∑

PFIn

(FOct,up(unt, n)f up (unt, k , n))

unt ∈ DU

= EX n ICKc ′ +

∑ (Ec ,n ICKc), ∀ n ∈ N , c′ ∈ Ch (4)

c ∈ Cl

Ec , n =

Inv sct, c(unt, c , n), ∀ n ∈ N

∑

(5)

unt ∈ SCT

where Ec,n is the inventory of the crude c in all storage tanks and charging tanks at time event n, as illustrated in eq 5; EXn is the estimated amount of the highest sulfur crude for the feasible blending operation at time event n. It is an intermediate variable, which could be solved by eq 6 as below.

∑

EX n = PFIn

FOct,up(unt, n) −

unt ∈ DU

∑ Ec ,n , ∀ n ∈ N c ∈ Cl

(6)

Substituting eq 6 into eq 4 gives the formula of PFIn in eq 7. Note that PFIn is a function of time because the crude oil inventory, Ec,n, will change with time. PFIn =

∑ (Ec , n(ICKc′ − ICKc))/ c ∈ Cl

∑

(FOct,up(unt, n)(ICKc ′ − f up (unt, k , n))),

unt ∈ DU

∀ n ∈ N , c′ ∈ C h

(7)

Equations 8 and 9 give the limits of the effluent amount and effluent sulfur content of each charging tank. Note that every refinery will have its own physical processing capacity. Thus, eq 8 provides the daily upper and lower bounds for the refinery feed amount, which somehow are also indirectly affected by product market demands.

Figure 6. Front-end inventory profiles of (a) storage tanks and (b) charging tanks for case 3.

f lo (unt, k , n) ≤ f (unt, k , n) ≤ f up (unt, k , n), ∀ n ∈ N , ∀ unt ∈ DU

4.3.2. Quantity-Based Flexibility Index. The quantity-based flexibility index, QFIn, is the minimum time duration to sustain CDU feeds with satisfied quantity requirements. It constrains

FOct,lo (unt, n) ≤ FOct (unt, n) ≤ FOct,up(unt, n), ∀ n ∈ N , ∀ unt ∈ DU

(9)

(8) F


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only the quantity of crude oil inventories, which is calculated by eq 10.

Table 1. Scheduling Result of Refinery Imports and Exports for Case 3a time event crude oil 1 crude oil 2 gasoline medium gasoline diesel kerosene dry gas liquefied petroleum gas polypropylene benzene naphtha petroleum coke sulfur catalytic coking hydrogen fuel gas utility fuel gas utility fuel oil fresh water desalinated water recycled water deoxygen water low-pressure steam medium-pressure steam electricity (MW·h) condensed water high-pressure steam a

1

2

Crude Oil 69.69 45.82 72.32 118.34 Main Product 15.73 15.66 25.73 33.94 65.76 74.41 8.98 12.66 0.23 0.16 3.39 3.81 1.42 1.70 4.14 5.08 0.23 0.32 3.57 1.56 0.48 0.51 3.53 4.22 0.28 0.27 6.03 6.83 1.53 1.87 Main Utility Import 39.67 49.04 10.29 10.75 3241.68 3724.70 30.30 35.82 3.09 3.85 4.56 4.02 7280.86 8329.47 Main Utility Export 13.34 14.37 0.24 0.24

3

4

QFIn =

∑ Ec ,n/ ∑ c∈C

209.95 48.47

161.94 185.44

33.52 37.77 123.25 10.97 0.83 6.46 2.45 6.87 0.28 12.69 0.98 6.06 0.61 11.32 2.53

37.87 64.01 160.40 22.40 0.55 8.28 3.50 10.21 0.57 8.17 1.17 8.67 0.66 14.72 3.76

64.65 21.42 5955.66 53.17 4.98 11.33 13477.94

97.89 24.92 7930.34 74.37 7.62 10.88 17803.30

26.81 0.53

32.44 0.57

FOct,up(unt, n), ∀ n ∈ N (10)

unt ∈ DU

Both property-based and quantity-based flexibility indexes are inventory-related variables and functions of time, which give the conservative estimation of how long the inventory at time event n can sustain the refinery operation if no new crude oils are imported. 4.3.3. Combined Flexibility Index. During the derivations of PFIn, the estimated value of the highest sulfur crude EXn has no upper limit. In some cases, the EXt may exceed the amount of sour oil inventories. Thus, the PFIn may be overestimated. Under such situations, QFIn reflects the actual sustainable time. Thus, a combined flexibility index, CFIn, defined by eq 11 gives a more accurate production flexibility. CFIn = min(PFIn, QFI n), ∀ n ∈ N

(11)

4.3.4. Blending Constraints. The total mass-balance constraint and sulfur balance constraint for each CDU are shown in eqs 12 and 13, respectively.

∑ ∑ V c(unt, unt′, c , n) = FOct (unt, n), unt ∈ CT c ∈ C

∀ unt′ ∈ DUunt, n ∈ N , n ≥ 1

(12)

∑ ∑ (V c(unt, unt′, c , n)ICKc(c , k)) unt ∈ CT c ∈ C

= FOct (unt, n)f (unt, k , n), ∀ unt′ ∈ DUunt , n ∈ N , n ≥ 1 (13)

4.4. Objective Function of CUTP model. 4.4.1. Primary Objective Function. The primary objective function of the CUTP model is to maximize the total profit of the studied

The unit of these solution results is kiloton if not specified.

Figure 7. Optimization results of main refinery products for four time events of case 3. G


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are two secondary objective functions related to inventoryrelated production flexibility, as shown in eqs 15 and 16.

Table 2. Refinery Economic Results of Case 3 time event crude oil 1 crude oil 2 subtotal gasoline medium gasoline diesel kerosene dry gas liquefied petroleum gas polypropylene benzene naphtha petroleum coke sulfur subtotal fresh water desalinated water recycled water deoxygen water low-pressure steam medium-pressure steam electricity subtotal main utility sell condensed water high-pressure steam subtotal crude oil buy product sell operation cost front-end operation cost a

1

2

Crude Oil Buy −29 545.89 −19 426.34 −26 773.96 −43 812.13 −56 319.85 −63 238.47 Main Product Sell 9707.66 9667.54 16 334.07 21 551.05 42 914.32 48 560.62 6336.80 8928.10 28.41 20.13 2512.45 2821.33

3

4

−89 015.02 −17 944.82 −106 959.84

−68 660.17 −68 650.63 −137 310.80

20 689.43 23 977.63 80 432.30 7740.04 102.63 4784.18

23 376.53 40 636.77 104 676.39 15 803.91 67.55 6134.48

1957.62 2342.82 4530.37 5559.35 141.98 200.01 377.18 164.94 50.78 53.96 84 891.65 99 869.84 Main Utility Buy −209.83 −259.41 −36.32 −37.95 −57.05 −65.55 −213.77 −252.72 −5.45 −6.80

3366.34 7506.88 173.46 1342.18 103.79 150 218.85

4810.82 11167.92 354.33 864.39 123.26 208 016.34

−341.97 −75.62 −104.82 −375.09 −8.79

−517.82 −87.95 −139.57 −524.70 −13.44

−12.07

−10.63

−29.97

−28.78

−642.17 −1176.65

−734.66 −1367.73

−1188.75 −2125.01

−1570.25 −2882.52

0.12 0.42

0.13 0.42

0.24 0.93

0.29 1.01

0.54 0.54 1.17 Economic Performance Summarya 363,828.97 profit 542,998.16 profit/sell 11,468.46 utility/sell 3918.40 crude/sell

5. CASE STUDY 5.1. Given Data. The developed scheduling methodology has been demonstrated through an industrial-size CUTP problem. The problem consists of three single-parcel vessels carrying their respective crudes, one single docking berth, four storage tanks (ST), four charging tanks (CT), and a refinery plant starting from two CDUs. The detailed crude oil transfer network and schematic diagram of the studied refinery plant are presented in Figures 3 and 4, respectively.35 The refinery process includes crude distillation, reforming, cracking, hydrotreating, blending, gas processing, product blending, and sulfur recovery facilities. The case study has neglected the inventory change of each refinery processing unit. The specified scheduling time horizon is 15 days. The brine settling time (BST) for front-end tank operations is 0.1 day. For simplicity, the frontend crude unloading and transferring data, crude property data, refinery product specifications, and economic data of the studied CTUP case are the same as those in the previous study,35 and they have been provided by Tables 1−4 from that paper. Only the sulfur content upper limit of crude mixtures changes from 0.2 to 0.15. The obtained CUTP model is developed as an MINLP model. The nonlinearity in the MINLP model mainly comes from crude oil and refinery product blending sections. It has been programmed and solved in GAMS v24.8.3 on an Intel 3.6 GHz Windows PC with 12.0 GB memory. The optimization solver ANTIGONE (solver based on the branch-and-cut global optimization algorithm) is adopted to solve the MINLP problems.33 5.2. Identification of the Range of CFI. As shown in Figure 2, the step after the development of a continuous-time CUTP scheduling model is to identify the flexibility range of the case study by solving the models with eqs 15 and 16 as objective functions, respectively. In the CFI range identification step, the objective function is to maximize or minimize CFI, not maximize gross profit. These two problems are indicated as case 1 and case 2 in the following discussion. The minimum value of CFI is 0. This is understandable because CFI is defined as the minimum time duration; it should be a non-negative number. The gross profit under the minimum CFI is $43,715.50 K. The upper bound of CFI is identified as 2.16, which is within the scheduling time horizon. Therefore, the maximum delay time of a crude delivery that the refinery plant can sustain is 2.16 days if no new crude oils are

1.30 167,703.92 30.88% 1.39% 67.00%

n

n

−

∑ (cost_OPn) n

(16)

where CFIn is already defined in eq 11. Note that each secondary objective function can be used to replace the primary objective function of eq 14 to form a new optimization problem with the same constraints. When eq 15 is used as the objective function, the problem will be maximizing the CFI instead of maximizing profit with other constraints remaining the same. While eq 16 is used as the objective function, the problem will be minimizing the CFI with other constraints remaining the same. The solutions of the optimization problems based on the objective function of eqs 15 and 16 will identify the upper and lower bounds, respectively, of CFIn.

∑ Sale_POn + Sale_UOn)

∑ (cost_FDn + cost_UDn + ∑

min min CFIn n

system, which is defined in eq 14. It contains three main items. The first summation item of eq 14 represents the total refinery revenue, which includes plant product sale income and utility sale income. The second summation item of eq 14 represents the total refinery cost, which includes feedstock costs, utility costs, and plant inventory costs. The third summation item of eq 14 represents the front-end crude operational cost. Detailed explanation of each item can be found in part B of the Supporting Information.

−

(15)

n

Unit of these economic results is k$.

max Profit =

max min CFIn

ΔIVu , n)

u ∈ UINV

(14)

4.4.2. Secondary Objective Functions. Besides the primary objective function for maximizing the plant gross profit, there H


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Figure 8. Front-end scheduling result of case 4.

Table 3. Scheduling Result of Refinery Imports and Exports for Case 4a time event crude oil 1 crude oil 2 gasoline medium gasoline diesel kerosene dry gas liquefied petroleum gas polypropylene benzene naphtha petroleum coke sulfur catalytic coking hydrogen fuel gas utility fuel gas utility fuel oil fresh water desalinated water recycled water deoxygen water low-pressure steam medium-pressure steam electricity (MW·h)

Figure 9. Front-end inventory profiles of (a) storage tanks and (b) charging tanks for case 4.

condensed water high-pressure steam

imported. The gross profit under the maximum CFI is $53,860.59 K. As mentioned previously, the general objective of this study is to maximize profit under shipping delay uncertainty. Thus, the profit maximization and the production flexibility maximization are two contradictory aspects that should be well balanced. In order to highlight the merit of the proposed flexibility index, two different scenarios are performed.

a

1

2

Crude Oil 73.02 209.80 72.32 116.42 Main Product 16.21 38.94 26.14 53.89 67.38 153.01 9.08 17.52 0.24 0.77 3.48 7.97 1.45 3.19 4.23 9.13 0.23 0.45 3.77 11.86 0.49 1.17 3.60 7.90 0.29 0.70 6.18 14.06 1.56 3.36 Main Utility Import 40.44 86.62 10.59 25.20 3318.91 7480.21 30.97 68.48 3.15 6.72 4.73 12.25 7456.32 16867.74 Main Utility Export 13.71 32.17 0.25 0.60

3

4

84.08 59.32

158.47 145.49

16.56 24.73 66.77 8.27 0.30 3.48 1.42 4.09 0.21 4.60 0.50 3.51 0.29 6.15 1.51

34.21 54.09 141.09 18.59 0.54 7.30 3.03 8.80 0.48 8.35 1.04 7.51 0.60 12.94 3.24

38.84 10.79 3283.98 30.35 3.02 5.07 7399.83

84.08 22.33 6947.12 64.67 6.54 10.10 15615.87

13.91 0.25

28.87 0.52

The unit of these solution results is kiloton if not specified.

In scenario 1, the flexibility index is not considered. Scenario 2 simultaneously considers flexibility index and profit maximization. I


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Figure 10. Optimization results of main refinery products for four time events of case 4.

5.3. Scenario 1: Profit Optimization without Flexibility Consideration. The flexibility range calculation indicates the studied problem is a feasible problem, whose optimal solution must exist. In order to highlight the merit of the proposed flexibility index, the simultaneous optimization of front-end and refinery crude-oil processing without flexibility consideration is conducted. The optimization model has less constraint than the previous model for the identification of CFI range. This problem is presented as case 3: profit maximization without flexibility consideration 5.3.1. Results of Front-End Crude Scheduling. The optimal Gantt chart of front-end scheduling result for the CUTP scheduling model without flexibility consideration is presented in Figure 5. As shown, the scheduling time is adopted as the horizontal axis, and crude “receiving units” are adopted as the vertical axis category. The numbers close to the schedule bars represent the total volumes (Mbbl) transferred. Here, various filling patterns indicate the source units of crude transfers, while different colors denote specific time events when particular operations occur. Overall, four time events are adopted for the CUTP scheduling case. Small black schedule bars represent the RPST time. For example, as for the first green schedule bar in the figure, it means at time event 1, a total volume of 1000 MbbL crude oil is fed from parcel 1 to storage tank 2 from day 0 to day 1.1. Other schedule bars can be recognized in the same way. It can be seen in the optimal Gantt chart that two refinery CDUs have utilized all four time events, and they are continuously operated during the entire scheduling time horizon. RPST time is located where a crude changeover does occur. It is possible that a CDU may skip certain time events, but it still can ensure its continuous operations with the left nonsuccessive time events. Comparatively, crude movements from parcels to storage tanks and from storage tanks to charging tanks take a smaller portion of the entire scheduling time horizon. Tank inventory profiles based on storage tanks and

charging tanks are presented in panels a and b of Figure 6, respectively. As illustrated in these two figures, all storage tank and charging tank inventories change with different time events but within their capacity constraints, which is [100, 2000] for storage tanks and [0, 1500] for charging tanks. 5.3.2. Results of Refinery Processing. The scheduling results of refinery imports and exports for case 3 are presented in Table 1. The refinery main imports contain two types of crude oils and various utilities such as four types of water, two grades of steam, and electricity. The refinery main exports include major products such as gasoline, diesel, kerosene, and benzene and utilities like condensed water and high-pressure steam. Figure 7 shows the scheduling result of case 3 based on production of main refinery products for all four time events. It can be seen that diesel and gasoline are the main products of this refinery compared to others like kerosene, liquefied petroleum gas, utility fuel gas, etc. Meanwhile, it is obvious that production from time events 3 and 4 are more than those from time events 1 and 2. This corresponds to the total volumes of crudes transferred in different time events from Figure 5, in which time events 3 and 4 have more CDU inlets. 5.3.3. Economic Results Analysis. Table 2 gives refinery economic results for case 3. Detailed economic results in terms of crude oil buy, main product sell, main utility buy, and main utility sell in different time events are shown in this table. The subtotal results of each category in different time events are also presented. Based on the proposed CUTP methodology without flexibility consideration, the optimal solution gives the maximum total gross profit of $167,703.92 K. This results from the total revenue from products sale of $542,998.16 K, minus crude oil purchase of $363,828.97 K, and minus operational cost of $11,468.46 K, in which the front-end operational cost is $3918.40 K. In comparison, ratios of the gross profit, total net utility income, and crude purchasing cost over the total revenue are 30.88%, 1.39%, and 67.00%, respectively. This matches the reality that the major expenditure of a refinery is J


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different time events. Thus, a RPST time is located between any pair of these time events. Similar to the former case, crude movements from parcels to storage tanks and from storage tanks to charging tanks take a relatively smaller portion of the entire scheduling time horizon. As seen from Figures 5 and 8, there are many differences for the front-end scheduling results between cases 3 and 4. Tank inventory profiles of storage tanks and charging tanks are illustrated in panels a and b of Figure 9, respectively. All storage tank and charging tank inventories change with different time events but are still within their capacity constraints. 5.4.2. Results of Refinery Processing. The scheduling results of refinery imports and exports for case 4 are presented in Table 3. A refinery plant may have over 20 products, which include diesel, gasoline, petroleum coke, kerosene, and naphtha etc. Figure 10 shows the scheduling result of case 4 based on main products produced for all four time events. It is obvious that productions from time events 1 and 3 are relatively small compared to those from time events 2 and 4. The reason is that time events 2 and 4 have more CDU inlets based on the total volumes of crudes transferred in different time events, which can be retrieved from Figure 8. The product distribution in 4 time events is pretty different for cases 3 and 4. However, one thing in common is that diesel and gasoline have covered almost three-quarters of the refinery products. That is a normal sense of a refinery. Other products include kerosene, liquefied petroleum gas, utility fuel gas, petroleum coke, benzene, catalytic coking, utility fuel oil, polypropylene, sulfur, hydrogen fuel gas, naphtha, dry gas, etc. 5.4.3. Economic Results Analysis. Table 4 shows refinery economic solutions for case 4. Detailed economic results as well as subtotal results of each category in different time events are presented in this table. Based on the proposed CUTP methodology with combined flexibility consideration, the optimal solution gives the maximum total gross profit of $165,763.35 K. It results from the total revenue from product sale of $545,516.77 K, minus crude oil purchase of $368,438.65 K, and minus operational cost of $11,316.56 K, in which the frontend operational cost is $3716.10 K. In comparison, ratios of the gross profit, total net utility income, and crude purchasing cost over the total revenue are 30.39%, 1.39%, and 67.54%, respectively. This also matches the reality that the major expenditure of a refinery is for crude purchasing. One thing should be noted by comparing economic results is that case 4 has less profit than

Table 4. Refinery Economic Results of Case 4 time event crude oil 1 crude oil 2 subtotal gasoline medium gasoline diesel kerosene dry gas liquefied petroleum gas polypropylene benzene naphtha petroleum coke sulfur subtotal Fresh Water Desalinated Water Recycled Water Deoxygen Water Low-pressure Steam Medium-pressure Steam Electricity Subtotal condensed water high-pressure steam subtotal crude oil buy product sell operation cost front-end operation cost a

1

2

Crude Oil Buy −30959.44 −88950.16 −26773.96 −43098.00 −57733.40 −132048.15 Main Product Sell 10003.35 24035.19 16595.02 34214.76 43969.58 99853.67 6408.76 12360.36 29.89 95.47 2575.41 5901.16

3

4

−35648.66 −21961.60 −57610.26

−67186.84 −53860.00 −121046.84

10219.40 15698.54 43574.75 5831.66 37.17 2577.64

21119.07 34341.74 92077.29 13115.95 66.57 5404.89

2000.27 4621.13 143.83 399.29 52.27 86798.79 Main −213.93 −37.37 −58.41 −218.52 −5.55

4384.36 9982.56 277.17 1254.58 123.36 192482.63 Utility Buy −458.19 −88.95 −131.65 −483.14 −11.86

1949.37 4472.42 130.87 486.57 53.11 85031.50

4169.75 9619.52 294.45 883.11 110.03 181202.37

−205.44 −38.08 −57.80 −214.09 −5.33

−444.80 −78.81 −122.27 −456.24 −11.53

−12.51

−32.41

−13.42

−26.73

−657.65 −1203.94 Main 0.12 0.43

−1487.73 −2693.94 Utility Sell 0.28 1.06

−652.66 −1186.83

−1377.32 −2517.71

0.12 0.45

0.25 0.92

0.55 1.34 0.57 Economic Performance Summarya 368,438.65 profit 545,516.77 profit/sell 11,316.56 utility/sell 3716.10 crude/sell

1.17 165,763.35 30.39% 1.39% 67.54%

Unit of these economic results is k$.

for crude purchasing. It should be noted that this profit is gross profit because it does not consider some direct costs like labor, supervision, payroll, maintenance, and royalties, as well as indirect costs like depreciation, taxes, and insurance. 5.4. Scenario 2: Profit Optimization with Flexibility Consideration. Simultaneous optimization of front-end and refinery crude-oil processing with combined flexibility consideration to highlight the merit of the proposed flexibility index is conducted in this section as case 4: profit maximization with CFI. In this step, the CFI range [0, 2.16] will be added as a constraint in the optimization model to maximize the gross profit. 5.4.1. Results of Front-End Crude Scheduling. The optimal Gantt chart of front-end scheduling result for the CUTP scheduling model with combined flexibility consideration is presented in Figure 8. It can be seen in the optimal Gantt chart that two refinery CDUs have utilized all four time events, and they are continuously operated during the entire scheduling time horizon. In addition, both CDU1 and CDU 2 have received different types of crude blends from charging tanks at

Figure 11. Relationship between the total profit and the minimum flexibility threshold. K


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Industrial & Engineering Chemistry Research Table 5. Computational Results for Case Studies no. of cases 1 2 3 4

case description minimize CFI maximize CFI profit maximization without CFI profit maximization with CFI

no. of binary variables

no. of continuous variables

no. of constraints

nonzeros

profit (k$)

solution time (sec.)

74 74 74

1882 1882 1868

3179 3179 3153

11 812 11 812 11 678

43,715.496 53,860.585 167,703.916

22 25 41

74

1902

3187

11 844

165,763.353

43

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case 3, and the gross profit decreases by 1.16%. Therefore, flexibility indexes will decrease the optimal refinery profit, which will be discussed in detail in the following section. 5.4.4. Profit Maximization with Customized CFI. To make the optimization results applicable, the inventory-related flexibility should be considered. On the basis of the identified CFI range, the plant may select an appropriate time as the minimum flexibility threshold (i.e., min CFIn≥ the threshold)

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

Qiang Xu: 0000-0002-2252-0838 Notes

n

The authors declare no competing financial interest.

to ensure that the refinery production has a designated flexibility at any time. For this case study, the minimum flexibility threshold is designated from 0 to 2.16 days. With the same computing hardware and GAMS solver, the average solving time for these cases is about 232.8 s. Figure 11 shows the relationship between the plant gross profit and the minimum flexibility threshold. The gross profit monotonically decreases with the increase of minimum flexibility threshold. It is reasonable because with more flexibility, more oil will be required in the inventory to support such operational flexibility; this will increase inventory cost and also eliminate opportunities to make profit from processing these available inventories. More flexibility indexes will decrease the optimal refinery profit, which demonstrates the fact that the profit maximization and the production flexibility maximization are two contradictory aspects that should be well balanced. Sometimes a win−win situation can be achieved. It actually provides support for not only the refinery but also other plants to manage operational risks. The computational results of all case studies are summarized in Table 5.

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ACKNOWLEDGMENTS This work was partially supported by the Center for Advances in Port Management, President Visionary Project, and Anita Riddle Faculty Fellowship from Lamar University.

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NOMENCLATURE

Indices

c ∈ C = crude types k ∈ K = key components n ∈ N = global time events unt ∈ UNT = all the units including parcels, tanks, and CDUs Sets

C = set of crude oil types Cl = set of crude oil with lower sulfur content Ch = set of crude oil with highest sulfur content CT ⊂ UNT = set of charging tanks DU ⊂ UNT = set of distillation CDUs K = set of key components (e.g., sulfur concentration) N = set of global time events SCT = ST ∪ CT = union of storage and charging tank sets ST ⊂ UNT = set of storage tanks UNT = P ∪ ST ∪ CT ∪ DU = set of all the units including parcels, tanks, and CDUs UINV = inventory unit set

6. CONCLUDING REMARKS A systematic methodology for simultaneous scheduling of front-end crude transfer and refinery processing has been developed to simulate and optimize the CUTP system under uncertainty of shipping delay. This work has three major contributions: (i) Simultaneous scheduling of front-end crude transfer and refinery processing with shipping delay uncertainty has been achieved. (ii) The shipping delay uncertainty has been taken into account to avoid refinery shut-down events by introducing an inventory-related time flexibility index. (iii) The relationship between the total profit and the minimum flexibility threshold is also given for a plant to manage its operational risks. It greatly increases the potential profitability and production flexibility of refineries. The efficacy of the proposed methodology and CUTP model has been demonstrated by large-scale case studies.

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AUTHOR INFORMATION

Corresponding Author

Parameters

FOct,lo (unt, n)/FOct,up (unt, n) = lower/upper bounds of flow rate from charging tanks to CDUs unt at time event n f lo (unt, k, n)/f up (unt, k, n) = lower/upper bounds of key component k (sulfur content) transferred from charging tanks to CDUs unt at time event n Continuous Variables

profit = total gross profit during the scheduling time horizon Invsct,c (unt, c, n) = inventory of crude c inside a tank unt ∈ SCT at the end of time event n Vc (unt′, unt, c, n) = volume of crude c transferred from units unt′ to unt at time event n PFIn = property-based flexibility index QFIn = quantity-based flexibility index CFIn = combined flexibility index FOct (unt, n) = flow rate of blended oils transferred from all charging tanks to distillation CDUs unt at time event n

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b01496. Detailed front-end crude scheduling model constraints and refinery crude processing model constraints similar to the previous study with additional nomenclature (PDF) L


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f (unt, k, n) = sulfur content (key component k) transferred from charging tanks to CDUs unt at time event n ICKc (c, k) = sulfur content/key component k in crude c Ec,n = inventory of the crude at time event EXn = estimated amount of the highest sulfur crude for the feasible blending operation at time event Cost_FDn = total cost for plant feedstock purchase during time event n Cost_UDn = total cost for plant utility purchase during time event n Cost_OPn = total operational cost for front-end crude oil transfer during time event n ΔIVu,n = inventory value increment Sale_POn = total sale value of plant products produced during time event n Sale_UOn = total sale value of plant utilities produced during time event n

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