AU2014100521A4 - Short-term scheduling method of crude oil operations in refinery for systems with two transportation pipelines - Google Patents
Short-term scheduling method of crude oil operations in refinery for systems with two transportation pipelines Download PDFInfo
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Abstract
Abstract: In some refineries, it needs to process both low and high fusion point crude oil types. For such refineries, often the storage tanks are located at two geographically different sites, one for low fusion point crude oil and the other for high fusion point crude oil. With two storage tank sites, there are two pipelines for different types of crude oil transportation. The constraints resulted from the high fusion point oil transportation are difficult to deal with. The present invention conducts the scheduling analysis for such a system in the control theory perspective. Due to the hybrid property of the process, the system is modeled by a hybrid Petri net. With this model, schedulability conditions are obtained and scheduling method is presented, and one can transport as much high fusion point crude oil with a single setup as possible. Furthermore, efficient algorithms are presented for calculating the amount of high fusion point crude oil that can be transported. Abstract Figure: FIG. 2 Refining Scheduling Schedulability Analysis Detailed Scheduling Hybrid Petri Net Model The Crude Oil Operation Process Crude oil operations Production a Pipeline #2 Pipeline #1 Site #1 Ca ing Distillers production landr pushed C aru i trg tanks units hedr pout Docket No.: UM1139AUOO 39
Description
Short-Term Scheduling Method of Crude Oil Operations in Refinery for Systems with Two Transportation Pipelines Inventors: NaiQi Wu, MengChu Zhou, and LiPing Bai Field of the Invention: [0001] The present invention relates generally to a method for scheduling crude oil operations in refinery. More particularly, the present invention relates to a short-term scheduling method of crude oil operations in refinery for systems with two transportation pipelines. Background: [0002] The following references are cited in the specification. Disclosures of these references are incorporated herein by reference in their entirety. [0003] List of References: Bechtel, PIMS (Process Industry Modeling System) User's manual, Version 6.0. Houston, TX: Bechtel Corp, 1993. H. Chen and H.-M. Hanisch, "Analysis of hybrid system based on hybrid net condition/event system model," Discrete Event Dynamic Systems: Theory and Applications, vol. 11, 163-185, 2001. R. David and H. Alla, "On hybrid Petri nets," Discrete Event Dynamic Systems: Theory and Applications, vol. 11, 9-40, 2001. C. A. Floudas and X. Lin, "Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review", Computers and Chemical Engineering, vol. 28, 2109-2129, 2004. K. Glismann and G. Gruhn, "Short-term scheduling and recipe optimization of blending processes," Computers and Chemical Engineering, vol. 25, 627-634, 2001. M. G. Ierapetritou and C. A. Floudas, Effective continuous-time formulation for short-term scheduling, part 2: Continuous and semicontinuous processes, Industrial and Engineering Chemical Research, vol. 37, 4360-4374, 1998. DocketNo.: UM1139AUOO 1 Z. Jia, M. Ierapetritou, and J. D. Kelly, "Refinery short-term scheduling using continuous time formation: crude oil operations," Industrial and Engineering Chemical Research, vol. 42, 3085-3097, 2003. Z. Jia and M. Ierapetritou, Efficient short-term scheduling of refinery operations based on a continuous time formulation, Computers and Chemical Engineering, vol. 28, 1001-1019, 2004. R. Karuppiah, K. C. Furmanb, and I. E. Grossmann, Global optimization for scheduling refinery crude oil operations, Computers and Chemical Engineering, vol. 32, 2745-2766, 2008. H. Lee, J. M. Pinto, I. E. Grossmann, and S. Park, "Mixed integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management," Industrial and Engineering Chemical Research, vol. 35, 1630-1641, 1996. W. K. Li, W. H. Chi, and B. Hua, Scheduling crude oil unloading, storage, and processing, Industrial and Engineering Chemistry Research, vol. 41, 6723-6734, 2002. T. Murata, "Petri nets: Properties, analysis and applications", Proceedings of the IEEE, vol. 77, no. 4, pp. 541-580, 1989. C. A. Mendez, I. E. Grossmann, I. Harjunkoski, and P. Kabore, A simultaneous optimization approach for off-line blending and scheduling of oil-refinery operations, Computers and Chemical Engineering, vol. 30, no. 4, 614-634, 2006. L. F. L. Moro, Process technology in the petroleum industry - current situation and future trends, Computers & Chemical Engineering, vol. 27, 1303-1305, 2003. R. Pelham and C. Pharris, Refinery operation and control: a future vision, Hydrocarbon Processing, vol. 75, no. 7, 89-94, 1996. J. M. Pinto, M. Joly, and L. F. L. Moro, "Planning and scheduling models for refinery operations," Computers and Chemical Engineering, vol. 24, 2259-2276, 2000. R. Rejowski and J. M. Pinto, Scheduling of a multiproduct pipeline system, Computers and Chemical Engineering, vol. 27, no. 8-9, 1229-1246, 2003. G. K. D. Saharidisa, M. Minouxb, and Y. Dallery, Scheduling of loading and unloading of crude oil in a refinery using event-based discrete time formulation, Computers and Chemical Engineering, vol. 33, 1413-1426, 2009. Docket No.: UMlI39AUOO 2 N. Shah, "Mathematical programming techniques for crude oil scheduling," Computers and Chemical Engineering, vol. 20, Suppl. S1227-1232, 1996. N. Shah, G. K. D. Saharidis, Z. Jia, and M. G. Ierapetritou, Centralized - decentralized optimization for refinery scheduling, Computers and Chemical Engineering, vol. 33, 2091-2105, 2009. M. Silva and L. Recalde, "Petri nets and integrality relaxations: a view of continuous Petri net models," IEEE Transactions on Systems, Man, and Cybernetics, Part C, vol. 32, no. 4, 317-327, 2002. J. Wang, Timed Petri Nets: Theory and Application, Kluwer Academic Publishers, 1998. N. Q. Wu, M. C. Zhou, and F. Chu, "Short-term scheduling for refinery process: bridging the gap between theory and applications," International Journal of Intelligent Control and Systems, Vol. 10, No. 2, pp. 162-174, June 2005. N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, Short-term schedulability analysis of crude oil operations in refinery with oil residency time constraint using Petri nets, IEEE Trans. on Systems, Man, and Cybernetics: Part C, Vol. 38, No. 6, pp. 765-778, 2008a. N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, Short-term schedulability analysis of multiple distiller crude oil operations in refinery with oil residency time constraint, IEEE Transactions on Systems, Man, & Cybernetics, Part C, vol. 39, no. 1, 1-16, 2009. N. Q. Wu, N., M. C. Zhou, and F. Chu, "A Petri net based heuristic algorithm for realizability of target refining schedules in oil refinery," IEEE Trans. on Automation Science and Engineering, Vol. 5, No. 4, pp. 661-676, 2008b. N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, Hybrid Petri net modeling and schedulability analysis of high fusion point oil transportation under tank grouping strategy for crude oil operations in refinery, IEEE Transactions on Systems, Man, and Cybernetics, Part C, vol. 40, no. 2, 159-175, 2010a. N. Q. Wu, F. Chu, C. B. Chu, and M. C. Zhou, Tank cycling and scheduling analysis of high fusion point oil transportation for crude oil operations in refinery, Computers & Chemical Engineering, vol. 34, no. 4, 529-543, 2010b. N. Q. Wu, C. B. Chu, F. Chu, and M. C. Zhou, Schedulability analysis of short-term scheduling for crude oil operations in refinery with oil residency time and Docket No.: UM1139AUOO 3 charging-tank-switch-overlap constraints, IEEE Transactions on Automation Science and Engineering, vol. 8, no. 1, 190-204, 2011. N. Q. Wu and M. C. Zhou, System modeling and control with resource-oriented Petri nets, CRC Press, Taylor & Francis Group, New York, October 2009. U. Yuzgec, A. Palazoglu, and J. A. Romagnoli, Refinery scheduling of crude oil unloading, storage and processing using a model predictive control strategy, Computers & Chemical Engineering, vol. 34, 1671-1686, 2010. M. C. Zhou and K. Venkatesh, Modeling, Smulation and Control of Flexible Manufacturing Systems: A Petri Net Approach, World Scientific, Singapore, 1998. [0004] Refinery belongs to a typical process industry. With increasing globalization, it is necessary to develop effective techniques for the operations of process industries to remain competitive [Moro, 2003]. There are three levels in the operation of a processing plant: production planning, production scheduling, and process control. There are existing advanced control systems for process control at the process control level, and planning techniques are well-developed using linear programming-based commercial software [Bechtel, 1993; and Pelham and Pharris, 1996] at the production planning level. However, although great deal of research has been done in the area short-term scheduling at the production scheduling level in the passed several decades, it still lacks effective techniques and software tools [Moro, 2003; and Honkomp et al., 2000]. In fact, in practice, short-term scheduling in a refinery is still done manually by planners. Thus, it is necessary to bridge the gap between the process control and production planning such that all three levels can be integrated. A short-term schedule for oil refinery should provide all the activities in details for the whole scheduling horizon, which makes the short-term scheduling problem extremely difficult as pointed out by Honkomp et al. [2000]. Furthermore, it is subject to various constraints, including physical and process constraints. If any of them is violated, a short-term schedule becomes infeasible. [0005] The process of refinery contains both discrete event and continuous variables, hence is a hybrid process. Due to the discrete decisions involved, a short-term scheduling problem of refiner is inherently combinatorial in nature, and is known to belong to a set of NP-complete problems [Floudas and Lin, 2004]. Thus, it is better to use approximation methods such as those for discrete production scheduling. However, unlike general Docket No.: UM1139AUOO 4 scheduling problems, where the jobs to be scheduled are well-defined and the time taken for each job is known in advance, for short-term scheduling in refinery, the jobs to be scheduled are unknown at the beginning. One knows the system states only. A schedule for refinery operations should defines the jobs and determines their sequence as well. Hence, heuristic and mate-heuristic methods used in discrete production scheduling, such as TABU search, genetic algorithm (GA), revolutionary algorithm, and the like, are not usable. Therefore, to solve the problem, mathematical programming models and exact solution methods are developed. [0006] Based on the time description, there are mainly two categories of mathematical programming models: discrete-time and continuous-time ones. The former divides the scheduling horizon into a number of time intervals with uniform time durations. An event, such as start and end of an operation, should happen at the boundary of a time interval. Then, exact solution method is used to obtain an optimal short-term schedule. The representative work can be found in [Shah, 1996; Lee et al., 1996; Pinto et al., 2000; Glismann and Grahn, 2001; Jia et al., 2003; Rejowski and Pinto, 2003; Saharidisa et al., 2009; Mendez et al. 2006, and Yuzgec et al., 2010]. In such models, the uniform time interval must be small enough so as to obtain acceptable accuracy. This leads to a huge number of binary variables for real-world applications that are difficult or even impossible to solve [Floudas and Lin, 2004 and Wu et al., 2011]. Continuous-time models are adopted in [Jia and Ierapetritou, 2003 and 2004; Li et al., 2002; Ierapetritou and Floudas, 1998; Karuppiah et al., 2008; and Shah et al., 2009] to reduce the number of discrete variables. With these methods, although the number of discrete variables is significantly reduced, the drawback is that there exist nonlinear constraints [Pinto et al., 2000]. Also, these methods require the knowledge of the number of discrete events that occur during the scheduling horizon and iterative methods are necessary to determine such a number [Floudas and Lin, 2004]. Hence, these methods are not applicable to real-world problems either. [0007] To make the problem solvable, most of discrete-time and continuous-time models must make special assumptions, which, unfortunately, make the solutions inefficient or unrealistic for real world cases [Mendez et al., 2006]. Moreover, they often ignore such constraints as the oil residency time and high fusion crude oil transportation constraints, which is infeasible. Due to the fact that short-term scheduling problem involves discrete Docket No.: UM1139AUOO 5 decisions and is inherently combinatorial in nature [Floudas et al., 2004], although there is significant progress in theory for such problem, there is a serious gap between theory and applications [Wu et al., 2005]. Therefore, it is very crucial to search for effective techniques that can overcome the difficulty such that they can be applicable to practical cases. [0008] Short-term scheduling for crude oil operations is one of the most difficult scheduling problems in oil refinery plant operations. As pointed out by Honkomp et al. [2000], it is the extremely high level of details that makes the short-term scheduling so difficulty. It should also be noticed that, for short-term scheduling of crude oil operations, the objectives include minimizing oil unloading from tankers, tanker waiting, and inventory cost, and maximizing production [Lee et al., 1996; Pinto et al., 2000; Jia et al., 2003; and Jia and Ierapetritou, 2004]. This implies that the optimization involves only in refining scheduling, but is independent of the detailed scheduling. Thus, the short-term scheduling problem for crude oil operations may be divided into two sub-problems hierarchically [Wu et al., 2008a and 2009]. At the upper level, it finds a refining schedule to optimize the objectives, such as minimum crude oil inventory and maximal productivity. For each distiller, a refining schedule determines the production rate, crude oil types, amount for each type to be processed, and the process sequence without generating a detailed schedule. At the lower level, it provides a detailed schedule to realize a given refining one. [0009] However, with various constraints to be satisfied, the two-level method raises two new problems: 1) how could the refining schedule found be guaranteed to be realizable, because, at the upper level, it does not determine a detailed schedule; and 2) how could a detailed schedule be found when a refining schedule is realizable. To solve these problems, a two-level architecture as shown in FIG. 1 is proposed by Wu et al. [2008a, 2008b, 2009, 2010a, and 2010b]. In this architecture, the crude oil operation process is modeled by a hybrid Petri net (PN). Based on the PN model, schedulability analysis is made from a control theory perspective to obtain the schedulability conditions. With the PN model and schedulability conditions obtained, detailed short-term schedule can be found for a given realizable refining schedule. Meanwhile, the schedulability conditions can be treated as constraints for the refining scheduling at the upper level such that the obtained optimal refining schedule is realizable. DocketNo.: UM1139AUOO 6 Summary of the Invention: [0008] Accordingly, a first aspect of the presently claimed invention is to provide a method for scheduling oil refining operation. [0009] According to an embodiment of the presently claimed invention, the method comprises: generating a Petri net model based on an oil refining operation system; generating a set of conditions based on the Petri net model; providing one or more initial states of the oil refining operation system; determining at least one expected refining schedule based on the initial states and one or more of the conditions; and determining at least one detailed refining schedule based on the expected refining schedule and one or more of the conditions. [0010] Preferably, the oil refining operation system comprises storage tanks, pipelines, charging tanks, and distillers. The Petri net model comprises Petri nets for the storage tanks, the pipelines, the charging tanks, and the distillers. [0011] According to an embodiment of the presently claimed invention, the pipelines include at least one first pipeline for transporting a first oil, and at least one second pipeline for transporting a second oil. [0012] A second aspect of the presently claimed invention is to provide a computer-readable medium whose contents cause a computing system to perform the method for scheduling oil refining operation of the present invention. Brief Description of the Drawings: [0013] Embodiments of the present invention are described in more detail hereinafter with reference to the drawings, in which: [0014] FIG. 1 shows a two-level operation architecture according to a prior art; [0015] FIG. 2 is a schematic diagram for illustration of an oil refinery process according to an embodiment of the presently claimed invention; [0016] FIG. 3 shows icons in a Petri net model according to an embodiment of the presently claimed invention; [0017] FIG. 4 is a Petri net for a tank according to an embodiment of the presently claimed invention; Docket No.: UM139AUOO 7 [0018] FIG. 5 is a Petri net for Pipeline #1 according to an embodiment of the presently claimed invention; [0019] FIG. 6 is a Petri net for Pipeline #2 according to an embodiment of the presently claimed invention; [0020] FIG. 7 is a Petri net for an overall system according to an embodiment of the presently claimed invention; [0021] FIG. 8 is a PN model of a two-distiller system for processing both low and high fusion point oil according to an embodiment of the presently claimed invention; [0022] FIG. 9 is a PN model for the proof of Theorem D.2 according to an embodiment of the presently claimed invention; [0023] FIG. 10 is an expected refining schedule according to an embodiment of the presently claimed invention; [0024] FIG. 11 is a detailed schedule for distiller feeding according to an embodiment of the presently claimed invention; [0025] FIG. 12 is a detailed schedule for tank charging via Pipeline #2 according to an embodiment of the presently claimed invention; and [0026] FIG. 13 is a detailed schedule for tank charging via Pipeline #1 according to an embodiment of the presently claimed invention. Detailed Description of Preferred Embodiments: [0027] In the following description, short-term scheduling methods of crude oil operations in refinery for systems with two transportation pipelines are set forth as preferred examples. It will be apparent to those skilled in the art that modifications, including additions and/or substitutions maybe made without departing from the scope and spirit of the invention. Specific details may be omitted so as not to obscure the invention; however, the disclosure is written to enable one skilled in the art to practice the teachings herein without undue experimentation. [0028] A. Introduction [0029] In some cases, for a refinery, the storage tanks are located at one site. All the types of crude oil should be unloaded into these storage tanks first and than delivered to the Docket No.: UM1139AUOO 8 charging tanks. There is a pipeline used to transport crude oil from the storage tanks to charging tanks. For this case, schedulability analysis is made and schedulability conditions are obtained under the assumption that there is no high fusion point oil to be processed [Wu et al., 2008b, 2009, and 2011]. When high fusion point oil is required to be processed, there is a high cost to set up the transportation of high fusion point oil from the storage tanks to charging tanks such that the short-term scheduling problem of crude oil operation is much complicated. Thus, it is necessary to know the schedulability conditions and how much crude oil can be transported with a single set up so as to minimize the transportation cost. This problem is solved in [Wu et al., 2010a and 2010b] for different scheduling strategies. With these results, it is ready to search for effective technique for refining scheduling such that software tool can be developed. [0030] For many other cases, due to the special requirement for high fusion point crude oil unloading from a tanker, the storage tanks are located at two geographically different sites. The tanks at one site are used for the storage of crude oil with low fusion point while the tanks at the other site are for high fusion point, respectively. With two sites of storage tanks, there are two pipelines, one transports crude oil from storage tanks at one site to the charging tanks. Notice that the storage tanks at one site store only the crude oil types with high fusion point, one of the pipeline is used to transport such crude oil. To transport crude oil with high fusion point, the pipeline should be heated first by using hot crude oil with low fusion point that flows from the charging tanks to storage tanks such that the high fusion point oil can flow through the pipeline. Often, after the transportation of a parcel of high fusion point oil to the charging tanks, the pipeline goes to idle state. However, a type of high fusion point oil cannot stay in the pipeline without flowing, otherwise the oil would be frozen and block the pipeline. Thus, it is necessary to send a certain amount of low fusion point oil from the storage tanks to the pipeline such that high fusion point oil in the pipeline can be flushed out of the pipeline. In this way, the oil follow in this pipeline becomes bidirectional. Therefore, some charging tanks should be used for oil transportation but not for charging, leading to more charging tank requirement. Hence, the scheduling problem is much more complicated. To reduce the operation cost, it requires transporting the high fusion point crude oil of a type that is in the storage tanks at a time to the refinery plant with single setup. Docket No.: UM1139AUOO 9 [0031] B. The Process and Scheduling Problem [0032] B.1 The Processes of Crude Oil Operations [0033] Oil refinery processes contain mainly three stages as shown in FIG. 2: 1) crude oil operations; 2) production; and 3) final product delivering. Because short-term scheduling for crude oil operations is one of the most difficult scheduling problems in operating a refinery, the present invention discusses crude oil operations only. [0034] At the crude oil operation stage, crude oil is carried to a dock near to the refinery plant by crude oil tankers, where the crude oil is unloaded into storage tanks. The crude oil in the storage tanks is transported to charging tanks in the refinery plant through pipelines. From the charging tanks, crude oil is fed into distillers for distillation. Often, a refinery processes various types of crude oil including high fusion point oil that has fusion point higher than 30'C and it is in a solid state under ordinary temperature. In general, there is no deep-water dock to hold large crude oil tankers in the nearby area of a refinery. Hence, a site is built for crude oil tanker unloading and crude oil storing. At such a site, the docking area is located in the sea with a distance from the land such that large oil tanker can enter the area to make the crude oil transportation economically acceptable. To unload the crude oil from a tanker to the storage tanks, an undersea pipeline is constructed. Site #1 in FIG.2 is used to represent such a site. [0035] However, the temperature under sea is always below 30'C such that high fusion point crude oil cannot be unloaded through such a pipeline. Thus, a refinery that should process high fusion point crude oil has to use a port that is near enough to the land such that a pipeline in the air can be built. Such a port is often small and can berth only small crude tankers. In FIG. 2, Site #2 denotes such a facility. Because the transportation cost is relatively high by using small crude tankers, only high fusion point oil is carried to Site #2 and low fusion crude oil is carried to Site #1. [0036] The components are different with different types of crude oil and different types of crude oil have different set point for distillation. When two different types of oil are mixed it should be treated as a new type of oil. Hence, crude oil can be unloaded into only an empty storage tank unless the same type of crude oil is in it. After a storage or charging tank is charged, before the crude oil in the tank can be discharged, it must stay in it for a certain Docket No.: UM1139AUOO 10 amount of time to separate the brine. This is referred to as time delay oil residency time (RT). When crude oil is transported through a pipeline to charging tanks, different types of crude oil may be mixed to obtain suitable components for distillation. However, here a mixture is not considered to be same as a new type of crude oil. Usually, a pipeline takes tens of kilometers long with capacity of tens of thousand cubic meters. It is full of crude oil all the time and cannot be emptied. Crude oil in the pipeline should be taken as inventory and cannot be neglected. At each site, there are a number of crude oil types to be processed. These types of oil are delivered from storage tanks to charging tanks via a pipeline. Hence, it needs to switch from one type of oil to another from time to time. There may be a number of crude oil segments of different types that stay in the pipeline or are flowing through it. When crude oil is transported via a pipeline, the pipeline can feed one charging tank at a time. Besides, a tank cannot receive and send oil simultaneously for both storage and charging tanks. [0037] To prevent high fusion point crude oil from being frozen during its transportation through Pipeline #2, the pipeline should be heated before high fusion point crude oil can be charged into the pipeline. It can be heated only by hot crude oil that is flowing through it. Thus, pipeline #2 is heated by sending a certain amount of hot low fusion point crude oil such that the oil flows through the pipeline from the charging tanks to the storage tanks at Site #2. When the pipeline is hot enough the heated high fusion point crude oil in the storage tanks at Site #2 can be delivered to the charging tanks at the plant via the pipeline. When there is crude oil with high fusion point in the pipeline, the oil in it must be kept flowing; otherwise when the pipeline and oil in it cools down, the oil turns solid. This requirement is referred to as a high fusion point oil transportation constraint. Hence, according to a schedule, after a parcel of high fusion point crude oil is sent to the pipeline, another parcel of low fusion point crude oil in the storage tanks at Site #2 must be sent to the pipeline so that the high fusion point crude oil can go out of the pipeline. This requires that there are enough low fusion point crude oil in the storage tanks at Site #2 and enough charging tank space at the plant. It follows from the above requirements that the setup cost for transporting high fusion point crude oil is very high and it needs additional tanks. Thus, in scheduling crude oil operations for such a system, when high fusion point crude oil is transported from storage tanks at Site #2 to charging tanks, it is desired that it can be Docket No.: UMll39AUOO 11 transported as much as possible, or at least with an expected amount by a single setup. [0038] It follows from the above discussion that, to schedule crude oil operations, it is subject to the following resource and process constraints. The former include: 1) the limited number of storage and charging tanks and the capacity of each tank; 2) the limited flow rate of oil unloading and oil transportation through the pipelines; and 3) the available amount of various crude oil types in storage and charging tanks, and in coming tankers. The latter include: 1) a distiller should be kept in working all the time uninterruptedly unless a maintenance is necessary; 2) at least one charging tank should be dedicated to feed a distiller at any time; 3) a tank cannot be charged and discharged simultaneously; 4) oil residency time constraint for any tank after charging; and 5) high fusion point oil transportation constraint. [0039] B.2 The Short-Term Scheduling Problem [0040] A short-term schedule of crude oil operations comprises a series of operations. For each operation to take place, a decision should be made to determine the task and time duration for the operation. Thus, to describe a short-term schedule, an operation decision is to be defined first. [0041] Definition B.1: OD = (COT, , S, D, INT = [a, b]) is defined as an operation decision, where COT= crude oil type; (= volume of crude oil to be unloaded from a tanker to a storage tank, or transported from a source tank to a destination tank, or fed from a charging tank to a distiller; S = the source from which the crude oil is to be delivered; D = the destination to which the crude oil is to be delivered; and INT is a time interval in which a and b are the start and end time points of the operation. [0042] The flow rate in delivering crude oil during [a, b] can be variable. However, in reality, to make a schedule to be easily implemented it is kept as a constant for a single operation. Thus, given volume ( and time interval [a, b] in an OD, (/(b - a) is determined and used as its flow rate. [0043] There are four types of ODs: crude oil unloading, transportation via pipelines #1 or #2, and feeding, denoted by ODU, ODTL, ODTH, and ODF, respectively, and their time interval for ODU, ODTL, ODTH, and ODF is denoted as [a, p], [A, p], [y, r], and [c, ,r], respectively. For ODU, S is a tanker and D is a storage tank. For ODTL, S is a storage tank, D is a charging tank and the transportation must be via pipeline #1. For ODTH, S and D can be Docket No.: UM1139AUOO 12 both storage and charging tanks and the transportation must be via pipeline #2. For ODF, S is a charging tank and D is a distiller. ODFki denotes the i-th OD for feeding distiller k for a schedule. To describe a short-term schedule for crude oil operations, let g = c1(p - a),f= I(p - A), r = g(r7 - y), and h = /(7c - c) denote flow rates for a tanker unloading, transportation via pipelines #1 and #2, and distiller feeding decided by ODs, respectively. Also let K be the set of distillers. Let [.r, r1] be the schedule horizon that often lasts for a week or ten days. Given the system state at r, i.e., the inventory of crude oil and state of all the devices, and information of tanker arrival, it needs to know if there exists a system state at a time point r E [r, ru] and time interval [r, rd] such that during [, rd] a required amount of high fusion crude oil at Site #2 can be transported to the charging tanks. Notice that [r, rd] may cross over two schedule horizons and let F= [r, r] = [r, ri]u [r, rd] be the schedule duration considered and be the volume of high fusion crude oil required to be transported. With 'known, it is useful to optimize a refining schedule. STi, ST2, and CT denote the storage tanks at Site #1 and #2, and charging tanks respectively. Then, the short-term scheduling problem for the situation considered in the present invention is to find a series of ODs described as follows. SCHD = [ODU 1 , ..., ODUw, ODTLI, ..., ODTLz, ODTH, ..., ODTHu, ODF 1 ,..., ODFK} (B.1) Subject to opk1 = rs, 7rkl = 0 k2, ... , rk(i-1) = Ski, ... , and 7ckn e,for bk eK (B.2) 3i andj with 1 i <j U such that COT e ODTH,, c ODTH , S, e ODTH4 ,Dk e ODTHk,Sk e ST2, Dk E CT, for i ! k j ,+... + = T(B.3) the resource and process constraints given above. [0044] Constraint (B.2) requires that the schedule should cover the entire scheduling duration and a distiller cannot be stopped. Constraint (B.3) guarantees that the required amount of high fusion crude oil is transported by a single setup. Notice also that r e [rs, re] and r = rd - r are variables that should be determined by the schedule. [0045] Because of a number of constraints and the combinatorial nature, problem (B.1) is NP-hard [Floudas et al., 2004]. Thus, it is difficult to find a feasible schedule. Notice that Docket No.: UM1139AUOO 13 an operation decision OD in a schedule transfers the system from one state to another. If a state is reached such that one or more constraints are violated, this state is said to be an infeasible state. If a state is not infeasible, it must be feasible. If a state is feasible itself, but no matter what ODs are applied thereafter, the system will enter an infeasible state. Then, such a state is called an unsafe state, otherwise it is a safe one. A safe state guarantees the existence of a feasible schedule. Meanwhile, if there is a criterion of safe state it is easy to find a feasible schedule with control theory perspective. With this observation, the scheduling problem (B.1) is presented from the control theory perspective. [0046] C. Hybrid Petri Net Modeling [0047] To make scheduling analysis for crude oil operations in the control theory perspective, a model is necessary. Because there are both discrete event and continuous variables, such a model must be hybrid one. Although hybrid PN models exist, for instance [Chen and Hanish, 2001; David and Alla, 2001; and Silva and Recalde, 2002], they cannot be applied here directly because of the special constraints and requirements for the problem here as discussed above. For example, in their work, a pipeline is treated just as a tank. In this way, the segments of different oil types in a pipeline cannot be identified. Thus, it is not suitable for the scheduling purpose here. For schedulability analysis, hybrid PN is developed to model crude oil operations in [Wu et al., 2008a, 2008b, 2009, and 2011]. Nevertheless, in those models, no high fusion crude oil transportation is considered. In [Wu et al., 2010a and 2010b] high fusion crude oil transportation is considered, but there both high fusion and low fusion oil types are transported via a single pipeline, and oil flow is unidirectional, which is different from the situation discussed here. To describe the processes of crude oil operations considered here, the device models presented in [Wu et al., 2008a and 2009] are used for tanks and Pipeline #1, and a new hybrid PN for Pipeline #2 is developed for the overall model for the system. A reader is referred as to [Murata, 1989; Zhou and Venkatesh, 1998; Wang, 1998; Wu and Zhou, 2009] for the basic knowledge of PN. [0048] Because of the hybrid properties of the system, in the PN model, both discrete and continuous places, and discrete and continuous transitions are used. Colors are used to identify the crude oil types in the model. Also, time aspect should be described for the scheduling purpose. Thus, the PN model presented here is a kind of colored-timed PN (CTPN) Docket No.: UM1139AUOO 14 defined as CTPN = (P = PDUPCjPE, T = TDUT7uTC, I, 0, H, <$, Mo), where PD, PC, and PE are sets of discrete, continuous, and enforcing places; TD, TT, and Tc are sets of discrete, timed, and continuous transitions; I: PxT -+ {0, 1} and 0: PxT -> {0, 1} are input and output functions; H: Px T -+ {0, 1 } is an inhibitor function; O(p) and <0(t) represent the color sets of the places in P and transitions in T; and Mo is the initial marking, respectively. The icons are shown in FIG. 3. [0049] With these elements defined, the modeling of tanks and pipelines is presented. Then, the overall PNmodel is obtained based on the models for devices. [0050] C.1 Models for Tanks and Pipelines [0051] Referring to the models for tanks and Pipeline #1 developed in [Wu et al., 2008a and 2009]. A tank is modeled by a PN shown in FIG. 4. Two continuous places ps and pc are used to model the state of a tank. A token in either ps or pc or both represents that there is crude oil in the tank. However, a token in ps represents that the oil in the tank is not ready for discharging, and it is ready only if p, has a token and ps is empty. The token in p3 is used to model the residual capacity of a tank at a marking. Continuous transitions ti and t 3 model the processes of filling to and discharging from a tank. Timed transition t 2 together with the inhibitor arc (ps, t 3 ) guarantees that the RT constraint is always satisfied. By the token in discrete place p4, only one of transitions ti and t 3 can fire at a time, which prevents a tank from being filled and discharged simultaneously. [0052] The PN model in FIG. 5 describes the behavior of Pipeline #1 that transports crude oil in storage tanks at Site #1 to charging tanks uni-directly. Places p, p2, and p3 are used to describe the number of different oil segments in the pipeline. The number of such places in the model means the number of segments of crude oil of different types. It can be set as the largest number of crude oil segments that may occur. Immediate transitions t 1 and t 2 mean that when t 1 is enabled and fires, a token in P2 is removed immediately, and when t 2 is enabled and fires, a token enters p2 immediately. In this way, different oil types in the pipeline can be properly identified. [0053] Continuous transitions yn to y,% and yol to yok are used to model the behavior that crude oil flows into and out of the pipeline with a given flow rate. Let Y = {yn, ... , yNI and Yo = {yol, ... , yok}. When one of transition in Yo is firing, the token volume in p, is Docket No.: UM1139AUOO 15 continuously decreasing, until pi is emptied. Then, t 1 is enabled and fires, the token in P2 is moved into p, immediately, so one transition in To can fire continuously. When one transition in Y1, say yn, fires, a token goes into p3 immediately. With crude oil mixing in transportation through the pipeline not considered, only one transition in Y and one transition in Yo can fire at a time. Thus, the pipeline is modeled by a macro transition y. Then, place pi in y can be denoted as p1(y). When y fires, it implies that one transition in Y and one transition in Yo fire with the same rate simultaneously. [0054] The PN model shown in FIG. 6 describes the behavior of the Pipeline #2 where places Ps-sIk are for the storage tanks at Site #2 and pcl-ck for the charging tanks. As the model for Pipeline #1 shown in FIG. 5, continuous places p1, p2, and p3 are used to identify crude oil segments of different types in the pipeline. Because crude oil can flow through Pipeline #2 bi-directionally, continuous transitions xy, to xIk and z-1 to zRI are used for crude oil flowing into the pipeline from storage and charging tanks, respectively, while zo to zok and xol to xOk for crude oil flowing out of the pipeline into storage and charging tanks. Let X = {xIj, ... , xrk}, Xo = {xoI, ... , xok}, Z= {zz[, ... , zrk}, and Zo = {zol, ... , zok}. [0055] The main function of Pipeline #2 is to transport the high fusion point crude oil. Hence, it is very important for the model to describe the high fusion point oil transportation constraint. To do so, an enforcing place p4 is put into tpipetine2. Every time, a token enters p3 by firing a transition in X, a token with the same color and volume goes into p4 too. When there is a token representing a high fusion point crude oil type in p4, it enforces that one of transition in Xo must fire, which requires firing of one of transitions in Xi too. When the token representing a high fusion point crude oil type in a continuous place in tppezine2 goes out of tppeline 2 by firing a transition in Xo, the token in p 4 is removed too. In this way, the behavior of the pipeline is well modeled. [0056] It should be noticed that, at any time, only one transition in X and one in X 0 , or one transition in Zr and one in Zo can fire. When they fire, it is done simultaneously and has the same firing rate. Thus, the pipeline is described by two macro-transitions x and z for different oil flowing directions as shown in FIG. 6. Then, a place p in the model can be denoted as p(x) or p(z) when the crude oil is delivered from storage tanks to charging tanks or in the opposite direction. Docket No.: UM1139AUOO 16 [0057] C.2 PN Model for the Overall System [0058] With the device models presented above, the PN model for the overall system with two storage tanks for each site and two charging tanks is given in FIG. 7. For simplicity, the discrete place and its associated arcs, and the inhibitor arc in a tank PN model are omitted. Also omitted are pi3 for tank i. A storage tank i at Site #1 must be discharged via Pipeline #1, it is described by {tii, ta 2 , y, Pis, Pic, pis}. A storage tank i at Site #2 must be discharged via Pipeline #2. However, it can be charged by a tanker or via Pipeline #2. Hence, it is described by {tij, t 2 , X, Pis, Pic, pi3} for charging by a tanker, and by {z, t 2 , x, pis, Pic, pi3} for charging via Pipeline #2. Similarly, a charging tank i is described by { v, til, , pis, Pi,, pi3}, where v = y and v = x when it is charged via Pipeline #1 and Pipeline #2, respectively; and Vg = t 2 and y' = z when it feeds a distiller and is discharged via Pipeline #2, respectively. [0059] If a tanker carries k types of crude oil, then k tokens are created with their respective volumes. Then, such a token can enter p1 (p2) by firing tj (t 2 ). However, a token can be moved into p, (p2) from t 1 (t 2 ) only if pi (P2) is empty. Places p3 and p4 represent two distillers. From the definition of a short-term schedule, it is known that the firing of a continuous transition in the PN model must be triggered by an OD. Thus, the dynamics of crude oil flow in the PN model should be governed by the flow rate given in OD. This can be modeled by the transition enabling and firing rules that are defined below. [0060] C.3 Transition Enabling and Firing Rules [0061] Let *t (*p) denote the set of input places of transition t (input transitions of place p) and t* (p*) the set of output places of t (output transitions ofp). Further, let V(M(p)) be the token volume (the volume of material) in p at marking M. First, the transition enabling and firing rules for discrete transitions are defined. In the model, for a discrete transition I*t I =I t'1 = 1. [0062] Definition C.1: A discrete transition (including the discrete ones in y, x, and z) t with * t = pi and t* = p is said to be enabled at marking M if M(pi) > 1 and M(pj) = 0. When t fires, M is changed into M' with M'(pi) = M(pi) - 1 and M'(pj) = M(pj). [0063] In this definition, it requires that t's output place is empty that is similar to finite capacity PN. However, it should be pointed out that, in general PN, tokens are discrete, but the tokens in the PN model here may be discrete or continuous. To fire a discrete Docket No.: UM1139AUOO 17 transition, all tokens in the model are treated as discrete one. By Definition C. 1, when some part of oil in p, in FIG. 5 is discharged, there is still a token in p, and transition t 1 cannot fire, so a token inp2 cannot go to p'. Only when all the oil inp, is discharged such that p, is empty, then t 1 can fire and a token in p2 can go to pi. In this way, the pipeline behavior is properly described. A timed transition is used only in the PN for a tank to guarantee the RT before oil in a tank can be discharged. Assume that the time associated with a timed transition is A, the definition is presented below. [0064] Definition C.2: A timed transition t is said to be enabled at marking M if M(pi) > 1, Vp E t. When t starts to fire at time , M is changed into M' such that: 1) at r, M'(pi) = M(pi) - 1, ifpi E *t n PD, and M'(pi) = M(pi) if p; E *t n Pc; 2) at r+ A, M'(pi) = M(pi) - 1 and V(M'(pi)) = 0, pi e *t n Pc; and 3) at r + A, M'(pj) = 1 for Vpj e t* and V(M'(py)) = V(M(p;)) + V(M(pi)), for pi e * t, p; e t*, pi e Pc, and p; e Pc. [0065] When a timed transition t fires, there may be a token in its output place pj. Then, the token in the input place pi enters pj, these two tokens merge into one with the volume being the sum. In this way, it models such a fact that when a tank is neither full nor empty, this tank can still be charged. When it is charged, the volume of oil should be added. Meanwhile, the time delay associated with the timed transition guarantees the RT constraint. [0066] To distinguish multiple types of crude oil, colors are introduced into the PN model. Let o e 0 to denote the color of a crude oil type and say that a token in place p representing crude oil type i has color (p and the number tokens in p with color y; at marking M is denoted by M(p, qo), and the volume for this token at marking M is denoted by V(M(p, ([)). Hence, V(M(p, p)) = 0 is equivalent to M(p, (p) = 0. If a continuous transition t is firing to move crude oil type i from a place to another, it is said t is firing with color (p. A continuous transition must fire with a color. As discussed above, the volume of a token in p3 in FIG. 4 models the capacity of a tank available. Let 0 denote the color for such a token. In other words, p3 in each tank's PN has the same color as the token in ps and/or pc. Further, let 01c P be the set of colors for crude oil types with low fusion point and 0 2 c P be the set of colors for crude oil types with high fusion point with 01r 02 = 0 and 01 u 02= 0. [0067] Definition C.3: A continuous transition (including transitions in Y, Yo, X, Xo,
Z
1 , and Zo in y, x, and z) t is said to be enabled with color q' at marking M if the following Docket No.: UM1139AUOO 18 conditions are satisfied: 1)M(p, pi) 1 or M(p, 0) 1, for Vp e *t; and 2) K(p) e t* for somej, then M(K(ps), pi) 1 or M(K(pc), p) > 1, or M(K(ps)) = M(K(pe)) = 0. [0068] By 1), it says that, if p ePc, there must be crude oil with a right color or the tank to be charged must not be full. Ifp ePE, it implies that firing t will consume a token inp. By 2), it says that the oil in K(ps) has color q', that is same as that inp e *t. This implies that if there is crude oil in a tank, only the same type of crude oil can be charged into it. However, if a tank is empty, any type of crude oil can be charged into it. When a continuous transition t is enabled and triggered by an OD, it can then fire. This firing must be associated with a flow rate given by the OD, i.e., the flow of crude oil is governed by a flow rate. The firing rules for continuous transitions below describe this dynamics. Assuming that t's firing with color 7; begins at time TI, ends at 2, re[i, zn], and the flow rate isf the marking changes as follows: At ri, ifp e *t PD M'(p)= M(p) -1 (C.1) At r, ifp e t* rPD M'(p)= M(p) + 1 ( C.2 ) At r e [z, r], ifp E 't n Pc or p EPE, and M(p, pi) 1 V(M'(p, pi)) = V(M(p, (P)) - (r -rI)f ( C.3 ) Ifp e *t n Pc, and M(p, 0) 1 V(M'(p, 0))= V(M(p, 6)) - (r--r)f (C.4) Ifp e t* n Pc orp ePE, and M(p, Vi) 1 V(M'(p, p0))= V(M(p, q;)) + (r- r])f (C.5) Ifp e t* n Pc orp ePE, and M(p, pi) = 0 M'(p, pi) = 1 and V(M'(p, (o)) = (r- -r)f (C.6) [0069] Because any continuous transition firing leads to a crude oil operation determined by an OD, expressions (C.1) through (C.6) describe the dynamics of crude oil flow in the PN model for the system. Notice that, with (C.5) and (C.6), when a transition t in
X
1 fires with color pi, a token with color 9; and volume that flows through t is moved into t's output enforcing place. From (C.3), such a token can be removed by firing transitions in Xo. Docket No.: UM1139AUOO 19 With the PN model developed above, some constraints can be guaranteed by the transition enabling and firing rules, but the first and fifth process constraints are not. Thus, liveness of the model is defined to describe such constraints. [0070] Definition C.4: The PN model for the system is said to be live if and only if: 1) Let Pdsl denote the set of places representing the distillers and IPdsll= h. Then, at any time z (or at any marking M) for any pi E Pdsl, there exists a ti E *pi such that ti is in firing or enabled and {ti} r {t 2 } r ... r {t} = 0. 2) If M(p 4 (x), (R) > 0, oP e 02, and p4(x) e PE, at marking M, there exists at least a transition t E p 4 (x) * that is in firing or enabled. [0071] By Definition C.4, a non-live state is an infeasible state resulting from an infeasible schedule. Thus, it is necessary to schedule crude oil operations such that the PN model is live. If a schedule can be found such that the PN is live, the system is schedulable. It should be pointed out that the conditions in Definition C.4 are very easy to check. Thus, the PNmodel developed here is an effective tool for scheduling the system. [0072] D. Scheduling Analysis [0073] With the PN model developed in the last section, this section carries out scheduling analysis for conditions under which a feasible short-term schedule exists and the amount of high fusion point crude oil at Site #2 can be transported to the charging tanks by a single setup. As discussed above, it is the detailed scheduling that makes the problem difficult. The feeding rates to the distillers are determined by a refining schedule according to the crude oil availability during the scheduling horizon. Hence, if the feeding rates to the distillers are known it implies that there is always enough crude oil in the storage tanks to be processed when needed. Thus, schedule feasibility is independent of the number of storage tanks and their capacity, and the key is to schedule the crude oil transportation and feeding. [0074] With the concept of liveness of the PN model and the schedule problem given (B.1), to find a feasible schedule is to generate a series of ODs such that the PN is live. The existence of a feasible short-term schedule is dependent on the state of the system and it can be defined as schedulability [Wu et al., 2008a and 2009]. A system of crude oil operations with initial state Mo is said to be schedulable if there exists a feasible short-term schedule for a horizon [0, oo). A state M of a system is said to be safe if, with M as initial state, the system Docket No.: UMIl39AUOO 20 is schedulable. Therefore, to obtain a feasible schedule is to analyze the schedulability or the safeness of the system. Following this concept, the schedulability conditions are analyzed such that a feasible detailed schedule can be obtained. [0075] When there is high fusion point oil in Pipeline #2 it must be discharged from the pipeline. Let A denote the capacity of Pipeline #2. In a refinery, a variety of crude oil types is to be processed and there are multiple distillers, each of which processes different type of crude oil at a time. In fact, if two distillers process the same type of oil at a time, these two distillers can be fed by the same charging tanks. Hence, they can be treated as one distiller when scheduling. Among the distillers, often only one can processes high fusion point crude oil. It is the case addressed in the present invention. Further, let DS; denote distiller i, and L, p, X, fdsl, and D be the maximal crude oil transportation rate of the Pipeline #1, the maximal crude oil transportation rate of the Pipeline #2, the minimal crude oil transportation rate of the Pipeline #2, the feeding rate to distiller DS, and the oil residency time, respectively, and a; = D x fds. These parameters have significant impact on the short-term scheduling. [0076] As discussed above, before transporting high fusion point crude oil from storage tanks at Site #2 to charging tanks via Pipeline #2, some hot low fusion point oil should flow through Pipeline #2 from the charging tanks to the storage tanks. Let Vht denote the necessary volume of hot oil that should flow through the pipeline. It should be pointed out that, to heat the pipeline, Vho,> A must be held. The goal here is to make sure how much high fusion point oil at Site #2 can be transported to the charging tanks by a single setup. Because high fusion point oil transportation begins at the time when hot oil in the charging tanks begins to charge to Pipeline #2, let this time point be o and discuss scheduling problem with ro being the starting time. The conditions are presented under which there exists feasible schedule for the distillers that process low fusion point crude oil. Since the capacity of a pipeline is tens of thousand cubic meters, Alp> Q and (Vot + A)/(2p) > D. Generally, for any i, p fds, leading to A > p x S fds xD = ai. Let C = max[( "' + Q)fdl, VI,] and the 2p result is presented below. [0077] Theorem D.1: For a two-distiller system with DS, for processing low fusion point oil and DS 2 being able to process high fusion crude oil, assume that: 1) the feeding rate Docket No.: UM1139AUOO 21 of DS, is fds, for crude oil with color 9p e 1 ; 2) there are three charging tanks TK 1 3 with capacities C, C, C 2 C, and C 3 C; 3) initially, the volume of oil with color 'p' e 0 in TKI,
TK
2 , and TK 3 is (i = Vor, 2 = (V, +A + 2)fdsi, and 4s = 0 with the oil in TK is heated, and 2p the oil in TK, and TK 2 is ready for discharging; and 4) v fds1. Then, there exists a feasible schedule for feeding DS,. [0078] Proof: With the PN model shown in FIG. 8, it can schedule the system as follows. As shown in FIG. 8, at the initial marking Mo (time ro), Mo(pe) = M(p 2 e) = 1, V(Mo(pc, p,)) = (, V(Mo(p 2 e, p,)) = 2, and Mo(p 3 s) = Mo(p 3 e) = 0. At this marking, t 22 fires with rate fdsl to feed p, (DS,), z with rate p and volume Vhit to heat Pipeline #2, and y with color pi, rate v, and volume (Vhot + A)xfds,/(2p) to charge P3s. At time T = ro + (VIot + A)xfds,/(2vp), marking MI is reached such that M(p 3 s) = 1 and V(M(p 3 s, q',)) = (V,t + A)xfds 8 /(2p). At this time the firing of y is stopped and t 3 s starts its firing. At time T2 = ro + (Vhot + A)/(2p) + £, marking M 2 is reached such that M 2 (p 2 e) = M 2 (p 2 ) = 0. Because L u:fds, 2 - i = (Vhot + A)/(2p) + D - (Vhot + A)xfdsi/(2up) fl. Thus, the firing of t 3 l must end, or
M
2 (pe) = 1 and M 2 (ps) = 0. It implies that t 32 is enabled. Thus, t 3 2 fires with ratefds, to feed p, and meanwhile fire y with color 9i, rate v, and volume (Vhot + A)xfds,/(2p) to charge p2s. At time rs = ro + Vot/p, marking M 3 is reached such that M 3 (pe) = M(ps) = 0 and x fires with rate p, color p2 e 02, and volume A to fill Pipeline #2 so that the oil in the pipeline is delivered to ps. Then, at time r 4 = ro + (Vhit + A)/p, marking M 4 is reached such that M 4 (ps) = 1 and V(M 4 (ps, 91)) = A, and tu starts its firing. At time r5 = '2+ (Vot + A)/(2p) = ro + (VOt + A)/(2p) + £2 + (Vot + A)/(2p) = ro + (VOt + A)/p + , marking M 5 is reached such that M(p 3 e) = M(p 3 s) = 0, M(p 2 s) = 1, V(M5(p 2 s, P)) = (Vhot + A)xfds1/(2p), and t 2 1 starts its firing. Because rs - z4 = £, at marking M 5 , the firing of tn ends. Thus, at this marking, t1 2 fires to feed pi and y fires to charge P3s, with rate v and volume A. Then, after plc is emptied and P3s is charged, t 22 fires to feed pi and y fires to charge pis. This process can be repeated, thus there is a feasible schedule such thatpi can be fed uninterruptedly. [0079] As stated in Theorem D.1, the key is the number of available charging tanks and the initial state. It requires that at To the oil in TK, and TK 2 should be (; = Vt, 2 = Docket No.: UM1139AUOO 22 (Vh,. +A + Q)fdl, respectively, and the capacity of these tanks should be at least C = 2p max[( "'+ A + Q)fds, V,]. In practice, these conditions can be easily satisfied. Take a real 2p industrial refinery as example, where Vhot = 25,000tons, A = 18,000tons, d = 4h, p 625tons/h, and fdsi is no more than 420tons/h. Thus, ' is about 16,000tons. In this refinery, most tanks have capacity from 20,000tons to 34,000tons. Thus, capacity condition can be satisfied. Furthermore, in practice, it is desired to charge a tank as full as possible. Hence, one can manage to make the initial condition satisfied. Of course, some time two small tanks with oil volume Vot can be used to heat Pipeline #2 and the system is still schedulable. According to Theorem D. 1, it is easy to show that feasible schedule exists for feeding DS 1 . Let H= ((V, 20 t + A)/p + D)/(2D), 1a;= ((Vhot + A)/p + Df)xfds/2. Because (Vhot + A)/p lasts for tens of hours and Dis about several hours, H 2 holds. [0080] Theorem D.2: For a three-distiller system with DS, and DS 2 for processing low fusion point oil and DS 3 being able to process high fusion crude oil, assume that: 1) the feeding rates of DS, and DS 2 are fdsl and fds2 with fdsl fds2 for crude oil with color (p] E 0 1 and (p2 e 0 1 , respectively; 2) there are six charging tanks TK 1
-
6 ; 3) initially, the volume of oil with color (p, e D 1 in TKI, TK 2 , and TK 3 is ; = Vh 0 t and 2 = 3 =Ha, with the oil in TK is heated, the volume of oil with color V2 E P 1 in TK 4 and TK 5 is 4 = (s =Ha 2 , and 6 = 0 for
TK
6 , and the oil in TK 1 , TK 2 , and TK 4 is ready for discharging; and 4) v fdsJ + fds2. Then, there exists a feasible schedule for feeding DS, and DS 2 . [0081] Proof: With the PN model shown in FIG. 9, it can schedule the system as follows. As shown in FIG. 9, at the initial marking Mo (time ro), Mo(p]e) = Mo(p 2 e)= Mo(p 3 )= Mo(p 4 ) = M(ps) = 1, V(Mo(pi, 0i)) = Viht, V(0o(p 2 c, (0)) = V(Mo(p 3 , (M)) = 17a, V(4o( 4 , (ps)) = V(Mo(pss, 'p2)) = Ha 2 , and Mo(p 6 s) = Mo(p 6 e) = 0. At this marking, t 2 2 and t 42 are fired with ratefdas andfds2 to feed pi (DSI) and p2 (DS 2 ), respectively, z fires with rate p and volume Vh 0 t to heat Pipeline #2, and y with color (o2, rate v, and volume Ha 2 to charge p6s. At the same time t 31 and t 51 begin to fire. Then, at time rl = ro + (Ha 2 )/v, M, is reached such that MI(p6s) = 1, V(M (p 6 , (p2)) = Ha, and t 6 o begins to fire. At time r2 = ro + (Hal)/fdsI = Zo + (Ha2)/fds2, M 2 is reached such that M 2 (p 2 c) = M 2 (p 4 c)= 0. At this marking, because (Ha)/fads Docket No.: UM1139AUOO 23 = (Ha2)/fds2 = (HJfds1)fds1 = H2 > Q, the firing of t 31 and tsi must end. This implies that
M
2 (p 3 ) = M 2 (psc) = 1 and M 2 (p 3 s)= M 2 (pss) = 0, or t 2 and t 52 are enabled. Thus, t 32 and ts 2 are fired with ratefds1 andfds2 to feed pi and p2, respectively, at the same time y fires with color p02, rate v, and volume Ha to charge p4s and then with color (], rate v, and volume FHa to charge p 2 ,. At time r2= To + V 0 t/p, marking M is reached such that M 3 (pje) = M 3 (pis) = 0 and x fires with rate p, color (p3 e 0 2 , and volume A to fill Pipeline #2 so that the oil in the pipeline is delivered to pis. Then, at time r4 = To + (Vhat + A)/p, marking M 4 is reached such that M 4 (pls) = 1 and V(M 4 (pls, q7')) = A, and tul starts its firing. At time rs = ro + 2(Hai)/fds; = zo + 2(Ha 2 )/fds2, M 5 is reached such that M5(p 3 s) = M(p 5 ) = 0, Ms(p 4 s) = M5(p 2 s) = Ms(p 6 e) =1, V(M5( ps, 92)) = Ha 2 , and V(M5(p 2 s, 91)) = Haz. Notice that rs - 4 = 2( Ha)/fds - (Vhot + A)/p =l, or at M 5 , t 12 is enabled. Thus, at M 5 , t 12 and t 62 are fired with rate fds; and fds2 to feed p, and p2, respectively, at the same time y fires with color 92, rate o, and volume Ha 2 to charge pSS. Then, after marking MA 6 reached such that M6(p6c) = 0, y fires with color (or, rate v, and volume Hal to charge pis. Then, whenever a charging tank i e {1, 2, 3} is emptied there is oil in another tank e {1, 2, 3} ready for feeding pl, and tank i is charged by firing y with color (i, rate v, and volume Ha. The similar situation occurs when a tank k e {4, 5, 6} is emptied. In this way, pi and p2 can be uninterruptedly fed without violating any constraint. [0082] It should be pointed out that for any h= ((Vhot + A)/p + D)/(2) Theorem D.2 holds. Thus, to obtain a feasible schedule it needs only to charge a charging such that it is as full as possible. Let G be an integer and G > 0 such that H/(2G) = b and 1 b < 2. Further let H = 2b, then H/H = G and H > 2. Then, let K be an integer with K > 2, the following result is for the general situation. [0083] Theorem D.3: For a (K+l)-distiller system with DS-K for processing low fusion point oil and DSK+1 being able to process high fusion crude oil, assume that: 1) the feeding rate of DSi, i e {1, 2, ... , K}, for crude oil with color (i e 01, andfdsl # ... fdsK and fdsK < fds + .. .+ fds(K-1); 2) there are 3K-1 charging tanks TK1-(3K-1) for low fusion point oil feeding with TK 3 (i-1)+1, TK 3
(-
1
)+
2 , and TK 3 (i-l)+ 3 for DSi, i e {1, 2, ... , (K-1)}, and TKK-2 and TKK-1 for DSK; 3) initially, the volume of oil with color (] E 01 in TKI, TK 2 , and TK 3 is ' = Vht and ; = ; =Ha, with the oil in TK, is heated, the volume of oil with color 9oi e 0 1 in
TK
3 (i-l)+l, TK 3 (i- 1
)+
2 , and TK 3 (i-1)+ 3 , i E {2, ... , (K-1)}, is 13(i-1)+1 = ,(i-1)+2 =Hai, 3 (i-)+3 =0, Docket No.: UMll39AUOO 24 3 K-2 =HaK, and 3K-1 = 0, and the oil in TKI, TK 2 , and TK 3 (i-1)+1, i E {2, ... , K} is ready for discharging; and 4) o !fds1 + ... +fdK. Then, there exists a feasible schedule for feeding DS, i E {1, 2, ... , K}. [0084] Proof. As in FIG. 8 and FIG. 9, {pis, til, Pic, t 2 } is used to model a charging tank TKi. Then, the system can be scheduled as follows. At the initial marking Mo (time ro), MO(P(3(i1)+1)c) = 1, i E 1, 2, ... , K}, Mo(p 2 e) = 1, Mo(p3s) = 1, MO(P( 3 (i-l)+ 2 )s) = 1, i E {2, ... , (K-1)}, V(Mo(pjc, (oi)) = V 1
,
0 , V(Mo(p 2 , (0)) = V(Mo(p 3 s, quj)) = lz, V(Mo(p( 3
(-
1 l)+l)c, (i)) = V(Mo(p( 3 (i- 1
)+
2 )s, (2)) = Hai, i E {2, ... , (K-1)}, V(Mo(p(3K-2)c, pK)) = HaK, and the other places are empty. At this marking, t 22 fires with rate fds1 to feed p1, t( 3 (i-1)+1) 2 with rate fdsi to feed pi, i e {1, 2, ... , K}, respectively, fire z with rate p and volume V,io to heat Pipeline #2, and fire y with color eoK, rate v, and volume HaK to charge P(3K-1)s, and then with color (Pi, rate v, and volume Hai to charge P(3(i-1)+3)s, 2 i (K-1), sequentially. Then, at time ri = ro + (Hai)/fdst, i e {2, ... , K}, M is reached such that M(p( 3 (i-l)+1)) = 0, i e {2, ... , K}. Notice that 1 = zo= (Hai)/fdsi = H.D> 2f, leading to M(P( 3 (i-l)+ 2 )c) = 1, i E {2, ... , (K-1)}, or t( 3 (i-1)+ 2
)
2 , i E {2, (K-1)}, are enabled. Further, because fdsK <fds + . . .+ fds(K-1), (HaK)/O HfD (fds + .+ fdsK)/ 2 1) HD(fdsl + ... +fdsK)/ 2 (fdsl ..+fsK) = DQholds. This implies that M(P(3K-1)c) = 1, or t(3K-1)c is enabled. Thus, at this marking, t( 3 (i-1)+ 2
)
2 fires with ratefdst to feed pi, i e {1, 2, ... , K}, respectively, and y fires with color 9K, rate v, and volume HaK to charge P(3K-2)s, and then with color (oi, rate v, and volume Hai to charge P(3(i-1)+1s3, 2 i (K-1), sequentially. For tanks
TK
3 (i-l)+l, TK 3
(-
1 l)+ 2 , TK 3 (i-l)+ 3 , i E {2, ... , (K-1)}, TKK-2, and TKK-1, marking M is similar to Mo. This implies that the above process for feedingpi, i e {2, ... , (K-1)}, can be repeated. Thus, it needs only to show that the system can be scheduled such that p, can be uninterruptedly fed. After repeating G times for the above process for feeding pi, i e {2, ... , K}, M 2 is reached such that Mi 2 (p 2 c) = 0, M 2 (p 3 c) = 1 and t 32 is enabled. With L !fdsl + ... +fdK, at this marking, t 32 fires to feed p1, and y fires with color op, rate v, and volume Ha to charge P2, after charging the K-1 tanks for feeding pi, i e {2, ... , K} by firing y. Then, after repeating another G times for the above process for feeding pi, i e {2, ... , K}, M 3 is reached such that M(p 3 c) = 0 and M 2 (p 2 s) = 1. As shown in the proof of Theorem D.2, at this marking M 3 (pic) = 1 and M3(pis) = M 3 (p 3 ) = 0, or t 12 is enabled. Thus, at this marking, t 1 2 fires to feed pi, and y fires with color e91, rate v, and volume Ha to charge p3s, after charging the K-1 tanks for feeding pi, Docket No.: UM1139AUOO 25 i E {2, ... , K} by firing y. In this way, when M 4 is reached such that M 4 (pic) = 0, t 22 must be enabled. Hence, t 2 2 fires to feed p1 and at the same time fire y with color rp1, rate v, and volume Hal to charge pls. By repeating this process, a feasible schedule is obtained for the system. [0085] It should be noticed that, in this theorem, it is required that fds1 # .. # fdsK. However, as shown in [Wu et al., 2009] that iffds1 = ... =fdsK the system is easier to schedule thanfds1 # . . #fdK. Thus, Theorem D.3 considers the most difficult situation. [0086] It should be pointed out that the initial state of the system has great effect on obtaining a feasible schedule. In the proof of Theorem D.3, it requires that, at the initial state, the volume of oil in a tank is Hai, and that the volume Hai occupies only a small space of the tank. It presents a schedulable boundary. By doing so, it leads to frequent switch from transporting one type of crude oil to another type of oil, and frequent switch from one charging tank to another for feeding a distiller. This is undesirable as it increases processing cost. If initially there is more oil in the charging tanks and each time more oil is charged into a tank, it is easier to obtain a feasible schedule. Thus, in practice, a tank can be filled as full as possible. From Theorem D.3, it is also known that the number of charging tanks is an important kind of resources. By this theorem, one distiller needs two charging tanks and each other one needs three charging tanks. By conditionfdK <ds1 + .. .+fd(K-1), the distiller whose feeding rate is the largest one must have three charging tanks. However, if there are more charging tanks as required by the theorem, the system would be easier to be scheduled. [0087] It should also be pointed out that if the type of oil in TK 1 is different from that in TK 2 at the initial state the schedule is same. This assumption is made for the sake of simplicity in showing the theorem. [0088] Theorems D.1 through D.3 do not address the amount of high fusion crude oil in Site #2 that can be transported into the charging tanks via Pipeline #2 by a single setup. The amount of high fusion point oil that can be transported from Site #2 to the charging tanks is greatly dependent on the number of charging tanks that are used for feeding the distiller that processing high fusion point oil. The case with two charging tanks is presented below. [0089] Theorem D.4: Assume that: 1) the conditions for feeding the low fusion point oil processing distillers given in one of the Theorems D.1 through D.3 are satisfied; 2) there is Docket No.: UM1139AUOO 26 one distiller DS 2 that is able to process high fusion point crude oil with feeding ratef; 3) there are two charging tanks TK 4 and TK 6 for this distiller with capacities C 4 andC 5 , respectively; 4) initially, the volume of oil with color e92 e 0 in TK 4 and TK 5 are '4 and ';, respectively, with ;4f (Vhot + A)/p and (, + ;)/f> (V,t + A)/p + D, and 5) after finishing the oil in TK 4 and
TK
5 , DS 2 starts processing oil with color ep3e 02, a type of high fusion point oil. Then, the amount of high fusion crude oil in Site #2 transported into the charging tanks by a single setup is qi= max[p((, + c5)/f- (Vct + A)/p - d), C 4 ]. [0090] Proof: The PN by removing p6s, t 61 , p6c, and t 6 2 from the PN shown in FIG. 8 describe this case. At the initial marking Mo (time ro), Mo(p]c) = Mo(p 4 c) = Mo(pse) = 1, V(Mo(p 1 e, (P)) = Vot, V(Mo(p 4 c, 92)) = 4, and V(Mo(pse, (2)) = ;. At this marking, t 42 fires with rate f to feed p2. At time r= ro + ,/f, marking M, is reached such that Mo(p 4 c) = 0. This time t 52 fires with rate f to feed p2. At Mo, z fires with rate p and volume Vhit to heat Pipeline #2 by using the oil in plc. At time z-2 = z + Vhot/p, marking M 2 is reached such that M 2 (pic) =
M
3 (ps) = 0 and x fires with rate p and color (o3 e 0 2 to discharge the oil with color 91 e 0 1 in Pipeline #2 into pis. Then, at time r 3 = ro + (VOt + A)/p, marking M 3 is reached such that
M
3 (p 1 s) = 1, M 3 (p 4 (x), (o3) = 1, and V(M(ps, (1)) = A. With M(p 4 (x), e3) = 1, it requires to fire x continuously. With the assumption of 4/f ! (Vhot + A)/p, r 3 - r1 0. This implies that
M
3 (p 4 s) = M(p4e) = 0, or p4s can be charged. Hence, x can continue its firing. Then, at time r 4 = ro + (Q + Q)/f, M 4 is reached such that M 4 (p 5 s) = M 4 (pse) = 0, or TIC is emptied. To make the schedule feasible, the charging of ps, by firing x should be stopped before r 4 - . In other words, the time duration for charging p4s by firing x is r 4 - d - r 3 = (G + 5)/f - (Vhot + A)/p D. Because (4 + 5)/f (Vot + A)/p + Q, (, + ;.5)/f- (Vhot + A)/p - D > 0. To transport as much oil with color eo3 e ' 2 as possible, x fires with rate p, the maximal flow rate of Pipeline #2. Thus, consider the capacity of TKI, the amount of high fusion crude oil in Site #2 transported into the charging tanks by a single setup is ig= max[p((Q + 5)/f - (Vhot + A)/p d2), C 4 ]. After charging yf by firing x, x fires with a color ( e 1 and volume A such that all the oil in Pipeline #2 with (3 e 0 2 is discharged. [0091] The high fusion point crude oil is carried to Site #2 by small tankers. To make the high fusion point crude oil transportation into the charging tanks being done economically, it often requires transporting the amount of oil that is carried to the storage tanks via a tanker Docket No.: UM1139AUOO 27 by a single setup. It follows from Theorem D.4 that, with two charging tanks for feeding DS 2 , at most one tank of oil with high fusion point can be transported to the charging tanks. This is much less than the volume of a tanker and it is not economically feasible. Next, the case with three charging tanks for feeding DS 2 is presented with the following definition: = { imod3+3, if imod3#0 (D.1) 6, if imod3=0 Let C,a = max(C 4 , C 5 , C 6 ) and Cmin = min(C 4 , C 5 , C 6 ), results are as follows. [0092] Theorem D.5: Assume that: 1) the conditions for feeding the low fusion point oil processing distillers given in one of the Theorems D.1 through D.3 are satisfied; 2) there is one distiller DS 2 for processing high fusion point crude oil with feeding rate f 3) there are three charging tanks TK4- 6 for this distiller with capacities C 4 , C 5 , and C 6 , respectively; 4) initially, the volume of oil with color p2 E P 1 in TK 4 and TK 5 are 4 and 5, respectively, with Glf < (Vot + A + C 6 )/p and (; + {5)/f> (Vot + A + C 6 )/p + d, and TK 6 is empty; 5) Cmajp < Cmin/f; and 6) after finishing the oil in TK 4 and TK 5 , DS 2 starts processing oil with color ep3 E2, a type of high fusion point oil. Then, there exists a feasible schedule such that the amount of high fusion point crude oil qi in Site #2 transported into the charging tanks by a single setup can be calculated by Algorithm D. 1 below. [0093] Algorithm D. 1: Finding the amount of high fusion point crude oil that can be transported into the charging tanks by a single setup with three charging tanks 1) Initialization: r= (Vho, + A + C 6 )/p, h = ;/f; g = (; + s + C 6 )/f and yi= C 6 . 2) Filling TK 4 : let i= 4 a) If r+ C 4 /X + DQ& g, r= r+ C 4 /X, h = h +51/f g = g + C 4 /f, y= V+ C 4 , and i = i + 1. Then, go to 3); b) If r+C 4 /p+ s f g< r+C 4 /X+ Q, 8=C 4 /(g-Q - ), r= r+C 4 /,h=h+{s/f, g= g + C 4 /f, y= + C 4 , and i= i+ 1. Then, go to 3) 3) Letj = f(i) and k = f(i + 1) 4) Filling TK a) If h i r and r+ Ci/X + DQ g, r =r+ C/X, h = h + C/f, g = g + Clf, y= V+ Ci, and i= i+ 1. Then, go to 3); b) Ifh Randd r+Ci 1 p+D:g<r+CI/X+f,P=Cjl(g-Q-f),r=z+C/p,h=h+ Docket No.: UM1139AUOO 28 Ck/f g = g + C;/f; V= + C;, and i= i+ 1. Then, go to 3); c) Ifh> rgoto 5). 5) Return . [0094] Proof With the PN model shown in FIG. 8, the system can be scheduled as follows. As shown in FIG. 8, at the initial marking Mo (time ro), Mo(pIc)= Mo(p 4 ) = Mo(pse) = 1, V(Mo(pe, 91)) = Vhot, V(Mo(p 4 c, 92)) = ;, V(Mo(psc, (2)) = ;s, and Mo(p 6 s) = Mo(p 6 c) = 0. At this marking, t 42 fires with rate f to feed p2 and at time rT = r 0 + /f, marking M, is reached such that Mo(p 4 ) = 0. This time t 52 fires with ratef to feed p2. Meanwhile, starting at ro, z fires with rate p and volume Vhot to heat Pipeline #2 by using the oil inpc. At time r2 = ro + Voorp, marking M 2 is reached such that M 2 (pl,) = M3(ps) = 0 and x fires with rate p and color 03 e 0 2 to discharge the oil with color (or e P, in Pipeline #2 into ps. Then, at time r3 = To + (VIOt + A)/p, marking M 3 is reached such that M 3 (ps) = 1, M 3 (p 4 (x), p3) = 1, and V(M 3 (ps, 9,)) = A. With M 3 (p 4 (x), (p3) = 1, it requires to continue the firing of x. At this marking, because M(p 6 s) = M(p 6 c) = 0, x can continue its firing to charge p6s with (3 e 0 2 . Then, at time T4 = ro + (Vil,, + A + C 6 )/p, marking M 4 is reached such that M 4 (p 6 s)= 1 and V(M 4 (p 6 s, 92)) = C 6 . When M 5 is reached such that Pse is emptied at time rs = ro + (4 + (s)/f, by assumption, (4 + ;5)/f (VIhot + A + C 6 )/p + Q, t 62 is enabled and can fire to feed p2. This implies that charging p6s with volume C 6 is feasible, so that Vy = C 6 as given by Step 1) in Algorithm D.1. Also, by 4/f (Vhat + A + C 6 )/p, it means that, at M 4 , M 4 (p 4 (x), (93) = 1, M 4 (p 4 ) = M 4 (p 4 ) = 0 or TK 4 is emptied. Thus, x can continue its firing with color (93 to charge p4s, or this is a feasible marking. Furthermore, it follows from Cmax/p Cmin/f that C4/p C 6 /f With (14 + (s)/f (V,t + A + C 6 )/p + 2 in mind, this implies that when M 6 is reached such that M(p 6 e) = 0, M 6 (p 4 c) = 1 and V(M 6 (p 4 e, (p3)) = C4 must hold ifp4s, is charged with rate p. In other words, when TK 6 is emptied the oil in TK 4 is ready for feeding P2. Thus, charging TK 4 with volume C 4 is feasible and the volume of oil with (3 e P2 transported becomes Vg = Vf + C 4 as given by Step 2) in Algorithm D. 1. In Step 2), if r + C 4 / + D2 g holds, TK 4 is charged with rate x and it is still feasible. However, if r + C41 + S g does not hold, but r + C4/p + D2 g < T + C4/, + 12,
TK
4 should be charged with rate p = C4/(g - D - r). When TKj is feasibly charged, the next charging tank TK; can be attempted to be charged. In Step 4), if h r T holds this tank can be feasibly charged with volume C; and the charging rate can be X or P= C;/(g - 1 - T) similar to Docket No.: UM1139AUOO 29 that in Step 2). Thus the volume of oil with (p3 E 02 transported becomes y= V+ C;. If h > r it implies that TK; is not emptied yet. Thus, it cannot be charged and x fires with a color qP e 01 and volume A such that all the oil in Pipeline #2 with (03 e 0 2 is discharged. Hence, the schedule is feasible and, by Algorithm D.1, V gives the volume of oil with V3 E 02 transported from Site #2 to the charging tanks. [0095] To transport high fusion point crude oil from Site #2 into the charging tanks as much as possible by a single setup, it is desirable to charge each tank to capacity. Assumption (; + ;s)/f (Vot + A + C 6 )/p + D guarantees that TK 6 can be charged to capacity when it is charged for the first time. Because of Cmax/p ! Cmin/f if TK 6 is charged to capacity for the first time, the following tanks can also be charged to capacity only if they can be charged. Thus, the assumption of (G + (s)/f (V,,t + A + C 6 )/p + D is very important. This implies the appropriate states can be selected to start the high fusion point oil transportation such that the volume of oil transported is maximized. It is known that for a large refinery in China, the capacities of charging tanks range from 20,000 tons to 34,000 tons, f is no more than 350 tons/h, p= 625 tons/h, X = 420 tons/h, and Q = 4.0 h. Thus, 4 +,(s = 44,520 (tons) is enough, which is not difficult to be satisfied. Also, Cmax/p= 34000/625 = 54.4 20000/350 = 57.14 = Cmin/f This means that the assumptions in Theorem D.5 are reasonable in practice. Also, as for Theorem D.3, initially if the type of oil in TK 4 is different from that in TK 5 , the schedule is unchanged. [0096] It follows from the theorem that Vf is dependent on the variables 4, 5, f, p, X,
C
4 , C 5 , C 6 , and Q, which is a complex function with so many variables. However, Algorithm D. 1 gives an efficient way to calculate it. Let V(M(TK 4 , TK 5 , TK 6 )) denote the volume of oil in all the three tanks TK 4 , TK 5 , and TK 6 at marking Mi. From the proof of Theorem D.5, it is known that V(M 4
(TK
4 , TK 5 , TK 6 )) reaches the minimal value. Then, because of the difference between p and f or Z and f V(Mi(TK 4 , TK 5 , TK 6 )) increases with the increase of i. When it reaches some value there is no tank to be charged. It is from this observation that, in Algorithm D. 1, the rate for charging a tank to slowdown the increase of V(M 4
(TK
4 , TK 5 , TK 6 )) is minimized. Thus, Algorithm D.1 maximizes the amount of high fusion point oil that can be transported. With Theorem D.5, in practice, if the value of 4 + (5 is appropriate, more than three tanks of oil can be transported, which is more than the volume that can be carried into Docket No.: UJM1139AUOO 30 Site #2 t by a tanker. Thus, often three charging tanks for feeding DS 2 are enough. Some time more high fusion point crude oil should be transported from Site #2 to the charging tanks. Thus, more than three charging tanks for feeding DS 2 are necessary and the result for the case of four-charging-tank is presented. For the discussion, first define: 6(i) = i mod 4 + 4 (D.2) [0097] Theorem D. 6: Assume that: 1) the conditions for feeding the low fusion point oil processing distillers given in one of the Theorems D. 1 through D.3 are satisfied; 2) there is one distiller DS 2 for processing high fusion crude oil with feeding rate f; 3) there are four charging tanks TK 4 .7 for this distiller with capacities C 4 , C 5 , C 6 , and C 7 , respectively; 4) initially, the volume of oil with color 92 E P 1 in TK 4 and TK 5 are 4 and 45, respectively, with 4/f < (Vhot + A + C 6 + C 7 )/p and (Q + 5)/f > (VOt + A + C6)/p + D, and TK 6 and TK 7 are empty; 5) Cmax /p Cmin If; and 6) after finishing the oil in TK 4 and TK 5 , DS 2 starts processing oil with color eo3 e 2, a type of high fusion point oil. Then, there exists a feasible schedule such that the amount of high fusion crude oil q' in Site #2 transported into the charging tanks by a single setup can be calculated by Algorithm D.2 below. [0100] Algorithm D.2: Finding the amount of high fusion crude point oil that can be transported into the charging tanks by a single setup with four charging tanks 1) Initialization: r= (Vot + A + C 6 + C 7 )/p, h = ;/f; g = (4 + ; + C 6 + C 7 )/f and y= C 6 +
C
7 ; 2) Filling TK 4 : let i = 4 a) If r+ C 4 /X+ Q &g, r= r+ C 4 /X, h =h +4%fg=g+ C 4 /f V/= y+ C 4 , and i= i+ 1. Then, go to 3); b) If r+ C 4 /p + D ! g < r+ C 4 /X+ l, p= C 4 /(g - d - r), r= r+ C 4 /p,, h = h + 5/f; g= g + C 4 /f; y= /+ C 4 , and i = i + 1. Then, go to 3) 3) Letj= 6(i) and k= 6(i+ 1) 4) Filling TK a) If h ! r and r+ CjiX + DQ: g, =r+ Ci/X, h = h + Cf, g = g + Clf y= V+ Ci, and i= i+ 1. Then, go to 3); b) If h r and r+ Cilp+ D < g < r+ CjiX + D , = Cil(g - D - r), r= z+ Cilp, h = h + Ckf, g = g + C;/fy= y+ C;, and i= i+ 1. Then, go to 3); DocketNo.: UM1139AUOO 31 c) If h > r go to 5). 5) Return V. [0101] Proof It is similar to the proof of Theorem D.5 and it is omitted. [0102] With four charging tanks for DS 2 , if 4 + 5 is same, V(M 4
(TK
4 , TK 5 , TK 6 )) for the three-tank case must be equal to V(M 4
(TK
4 , TK 5 , TK 6 , TK 7 )) for the four-tank case. This implies that there is more space to offset the increase of V(M 4
(TK
4 , TK 5 , TK 6 , TK 7 )) caused by the difference between p andf or X and f Thus, much more high fusion point oil at Site #2 can be transported into the charging tanks. [0103] With y calculated, if V> , the requirement can be met, otherwise it is not. [0104] E. Industrial Case Study [0105] This case problem is a practical application scenario from a large-scale refinery in China. The refinery has four distillers DS 1 , DS 2 , DS 3 , and DS 4 with DS 2 being able to processing high fusion point crude oil. For the case problem, initially there are 11 charging tanks available for distiller feeding. The initial state for the 11 charging tanks is shown in Table 1. The maximal flow rate of Pipeline #1 is v = 1,250 tons/h, and the maximal and minimal flow rates of Pipeline #2 are p = 625 tons/h and X = 420 tons/h, respectively. The feeding rates of the distillers are 250 tons/h, 334 tons/h, 250 tons/h, and 625 tons/h, respectively. It is also known that Vot = 25,000 tons, A = 18,000 tons, and D = 4 h. There is 134,000 tons of oil #11 in tanks at Site #2, which is a type of high fusion point crude oil. At Site #1, there is 24,000 tons of oil #4, 136,000 tons of oil #8, 118,000 tons of oil #9, and 80,000 tons of oil #10. Table 1: The initial state for the charging tanks Tank Capacity Type of oil Volume of oil in the tank (ton) filled (ton) TKI 20,000 0
TK
2 34,000 Oil #1 16,000
TK
3 34,000 Oil #2 26,000
TK
4 25,000 0
TK
5 30,000 Oil #3 25,000
TK
6 34,000 Oil #5 15,000
TK
7 20,000 Oil #4 17,000
TK
8 30,000 Oil #6 25,000
T
9 34,000 Oil #7 22,000 Docket No.: UM1139AUOO 32 TIKo 34,000 Oil #8 19,000 TKI 20,000 0 [0106] In the next period, after processing the oil in TK 2 and TK 3 , DS 2 needs to processing crude oil #11. Thus, it is desired to transport all the oil #11 at Site #2 into the charging tanks, or V1= 134,000 tons. It is scheduled that the oil in TK 5 is to be processed by DSI, the oil in TK 6 and TK 7 for DS 3 , and the oil in TK 9 and TKo for DS 4 . For the available oil at Site #1, it is scheduled as: the 24,000 tons of oil #4 is for DS], 84,000 tons of oil #8 and 118,000 tons of #9 for DS 4 , 52,000 tons of oil #8 for DS, and 80,000 tons of oil #10 for DS 3 . To transport high fusion point oil via Pipeline #2, 25,000 tons of oil in TK 8 that is heated is prepared for heating Pipeline #2. Consider the conditions given in Theorem D.5, TK 8 can be used for DS 3 . Thus, an expected refining schedule is created as shown in FIG. 10. [0107] With TK 2 , TK 3 , and TKI for feeding DS 2 , 16000/f= 16000/334 = 47.9 < (Vhot + A + C 6 )/p = (25000 + 18000 + 20000)/625 = 100.8 and (16000 + 26000)/f = 42000/334 = 125.8 > (Vhot + A + C 6 )/p+ D = 104.8. Also, 34000/625 = 54.4 < 20000/334 = 59.9, or Cm/p Cmin/fis satisfied. Thus, all the conditions given in Theorem D.5 are satisfied. Now, consider the conditions given in Theorem D.3. H= ((Vhot + A)/p + Q)/(2) = (43000/625 + 4)/8 = 9.1 and a = D x fdS3 = 4 x 250 = 1000. For DS 3 , EHaj = 9100. The volume of oil in TK 6 and TK7 is 15000 tons and 17000 tons that is greater than 9100. There are three distillers for processing low fusion point oil and there are 11 charging tanks for these three distillers. Because fdsl = 250 <fds3 +fds4 = 250 + 625 = 855, TK 4 and TK 5 for DS2, TK6- 8 for DS 3 , and TK9.
11 are used for DS 4 . In this way, the charging tank requirement is satisfied. Also, v = 1250 >fdsl +fd3 + fds4 = 1105. Thus, all the conditions given in Theorem D.3 are satisfied. [0108] The remaining problem is if the high fusion oil Wat Site #2 can be transported into the charging tanks. By Algorithm D. 1, it is found that V/ > V Thus, the system can be scheduled according to the requirements. Following the scheduling methods given in the proof of Theorems D.3 and D.5, the feasible detailed schedule is obtained as shown in FIGs. 11, 12, and 13. In FIG. 12, the shade one denotes the oil flow from a charging tank to a storage tanks. As discussed above, in the schedule the charging tanks are charged to capacity except that there is no enough oil of the same type to do so. [0109] The case problem has large number of variables and is very complex. Such Docket No.: UM1139AUOO 33 practical application problem is very difficult to solve. However, by the approach proposed, such problem can be solved efficiently. This shows the efficiency of the proposed approach. With this case problem, it also shows that, by selecting appropriate state, it can transport large amount of high fusion point crude oil from Site #2 to the charging tanks. [0110] F. Conclusions [0111] Because of its combinatorial nature and the detailed scheduling requirements, short-term scheduling for crude oil operations in a refinery belongs to the NP-complete problems [Floudas et al., 2004]. Furthermore, there are a variety of constraints including resource and process ones, leading to large number of discrete variables. With these constraints, in fact, it is hard to find a feasible schedule that is essential to the short-term scheduling problem for crude oil operations. Besides, transportation of high fusion point crude oil results in high cost because of the high cost setup. Thus, it is desired that the volume to be transported by a single setup should be large enough. With a two pipelines, one for low fusion point oil transportation and the other for high fusion point oil transportation, the problem is further complicated. There is no existing model and method that deal with such issues. [0112] Unlike the mathematical programming models, the short-term scheduling problem for crude oil operations is studied from a control theory perspective. By this concept, the short-term scheduling problem of crude oil operations can be solved in a hierarchical way. At the upper level, it finds a refining schedule and, at the lower level, a detailed schedule is found to realize the refining schedule and reduce detailed schedule cost. [0113] In the present invention, a study is conducted on the short-term scheduling problem of crude oil operations for a two-pipeline system, one for low fusion point oil transportation and the other for high fusion oil transportation. The goal is to obtain a feasible schedule such that it can transport as much high fusion point crude oil as possible by a single setup so as to reduce the operation cost. Following the control theory perspective concept, by modeling the system with a hybrid Petri net, conditions and method are presented to obtain a feasible schedule and to maximize the amount of high fusion point oil that can be transported. It shows that the amount of high fusion point oil that can be transported is greatly dependent on the initial state. Thus, the initial conditions for starting high fusion crude oil transportation Docket No.: UM1139AUOO 34 are carefully prepared. Also, the scheduling approach presented in the present invention is efficient. [0114] In some embodiments, the present invention includes a computer storage medium having computer instructions or software codes stored therein which can be used to program a computer or microprocessor to perform any of the processes of the present invention. The storage medium can include, but is not limited to, floppy disks, optical discs, Blu-ray Disc, DVD, CD-ROMs, and magneto-optical disks, ROMs, RAMs, flash memory devices, or any type of media or device suitable for storing instructions, codes, and/or data. [0115] The foregoing description of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations will be apparent to the practitioner skilled in the art. [0116] The embodiments disclosed herein may be implemented using general purpose or specialized computing devices, computer processors, or electronic circuitries including but not limited to digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), and other programmable logic devices configured or programmed according to the teachings of the present disclosure. Computer instructions or software codes running in the general purpose or specialized computing devices, computer processors, or programmable logic devices can readily be prepared by practitioners skilled in the software or electronic art based on the teachings of the present disclosure. [0117] In some embodiments, the present invention includes computer storage media having computer instructions or software codes stored therein which can be used to program computers or microprocessors to perform any of the processes of the present invention. The storage media can include, but are not limited to, floppy disks, optical discs, Blu-ray Disc, DVD, CD-ROMs, and magneto-optical disks, ROMs, RAMs, flash memory devices, or any type of media or devices suitable for storing instructions, codes, and/or data. [0118] The present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiment is therefore to be considered in all respects as illustrative and not restrictive. The scope of the invention is indicated by the appended claims rather than by the foregoing description, and all DocketNo.: UM1139AUOO 35 changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Docket No.: UM1139AUOO 36
Claims (5)
1. A computer implementable method for scheduling an oil refining operation, comprising: generating, by a processor, a Petri net model based on an oil refining operation system; generating, by a processor, a set of conditions based on the Petri net model; providing, by a processor, one or more initial states of the oil refining operation system; determining, by a processor, at least one expected refining schedule based on the initial states and one or more of the conditions; and determining, by a processor, at least one detailed refining schedule based on the expected refining schedule and one or more of the conditions.
2. The method of claim 1, wherein the oil refining operation system comprises one or more storage tanks, one or more pipelines, one or more charging tanks, and one or more distillers.
3. The method of claim 2, wherein the Petri net model comprises one or more Petri nets for the one or more storage tanks, one or more Petri nets for the one or more pipelines, one or more Petri nets for the one or more charging tanks, and one or more Petri nets for the one or more distillers.
4. The method of claim 2, wherein the pipelines include at least one first pipeline for transporting a first oil, and at least one second pipeline for transporting a second oil.
5. A computer-readable medium whose contents cause a computing system to perform the method of any one of claims 1 to 4. Docket No.: UM1139AUOO 38
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170083028A1 (en) * | 2015-09-20 | 2017-03-23 | Macau University Of Science And Technology | Linear Programming-based Approach to Scheduling of Crude Oil Operations in Refinery for Energy Efficiency Optimization |
| CN109212977A (en) * | 2018-11-20 | 2019-01-15 | 常州大学 | A kind of mixed control method based on Petri network |
| CN109740983A (en) * | 2018-12-26 | 2019-05-10 | 中国石油大学(北京) | A kind of product oil dispatching method and device based on pressure control |
| CN112361224A (en) * | 2020-10-21 | 2021-02-12 | 中国石油化工股份有限公司 | Intelligent generation method of oil and gas pipeline emergency repair scheme driven by SPN method |
-
2014
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20170083028A1 (en) * | 2015-09-20 | 2017-03-23 | Macau University Of Science And Technology | Linear Programming-based Approach to Scheduling of Crude Oil Operations in Refinery for Energy Efficiency Optimization |
| US9957959B2 (en) * | 2015-09-20 | 2018-05-01 | Macau University Of Science And Technology | Linear programming-based approach to scheduling of crude oil operations in refinery for energy efficiency optimization |
| CN109212977A (en) * | 2018-11-20 | 2019-01-15 | 常州大学 | A kind of mixed control method based on Petri network |
| CN109212977B (en) * | 2018-11-20 | 2021-02-26 | 常州大学 | Petri net-based hybrid control method |
| CN109740983A (en) * | 2018-12-26 | 2019-05-10 | 中国石油大学(北京) | A kind of product oil dispatching method and device based on pressure control |
| CN112361224A (en) * | 2020-10-21 | 2021-02-12 | 中国石油化工股份有限公司 | Intelligent generation method of oil and gas pipeline emergency repair scheme driven by SPN method |
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