MILP Model for the Tank Farm Operation Problem of Finished

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A MILP Model for the Tank Farm Operation Problem of Finished Products in Refineries Guilherme Alceu Schneider, Flavio Neves, Leandro Magatão, and Lúcia Valéria Ramos de Arruda Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04354 • Publication Date (Web): 13 Oct 2016 Downloaded from http://pubs.acs.org on October 15, 2016

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Industrial & Engineering Chemistry Research

A MILP Model for the Tank Farm Operation Problem of Finished Products in Refineries Guilherme A. Schneider, Flávio Neves-Jr, Leandro Magatão*, and Lúcia V.R. Arruda Abstract —1 this paper presents a MILP model with continuous time representation to address the Tank Farm Operation Problem (TFOP) of finished products in refineries. Real scenarios are considered, which were obtained from the planning of refineries and the external pipeline network scheduling, proposed by (1). The developed MILP model determines the scheduling of loading and unloading operations in the tank farm of finished products at each refinery, but is subjected to time-window constraints. A decomposition approach has been applied and multiproduct scenarios proposed by (1) were broken in single product scenarios. Each one of these scenarios is related with tank farm in a specific refinery. Therefore, they are presenting volumes and values of stored inventories, maximum capacity tanks, and start and end times to product movements at the refinery interfaces (production, demand, and pipelines). The proposed MILP model searches a scheduling that minimizes the movements within the refinery tank farm in order to respect the imposed operational and structural constraints. Further, for making feasible the scheduling in a smaller computational time, an iterative algorithm is developed and a new model approach, named MILP-IA, is added within the solution process. The results allow us to analyze the model computational time, the temporal and structural violations, and the number of product movements for each scenario. For the studied cases, we can also check for attending to time and monthly volume constraints to each interface. Finally, the results also indicate that the proposed MILP-IA approach finds solutions in computational times in the order of minutes. The obtained solutions contribute to improve the transfer and storage activities (TS) on two main points: (i) they minimize the number of movements, facilitating the plant operational tasks (searching for routes); and, (ii) they provide feedback to the pipeline scheduling, creating a collaborative integration between refinery subsystems, linking all information about internal and external product movements at refineries.

Keywords — MILP, Continuous Time Representation, Tank Farm Operation Problem, Scheduling, Refineries.

1

Schneider, G.A. Federal University of Technology – Parana (UTFPR), Curitiba, Paraná, Brazil, [email protected] Neves-Jr, F. Federal University of Technology – Parana (UTFPR), Curitiba, Paraná, Brazil, [email protected] Magatão*, L. Federal University of Technology – Parana (UTFPR), Curitiba, Paraná, Brazil, [email protected] (corresponding author) Arruda, L.V.R. Federal University of Technology – Parana (UTFPR), Curitiba, Paraná, Brazil, [email protected]

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I. INTRODUCTION The oil and derivatives move respecting the limitations of infrastructure (e.g., available tanks) is a currently problem for the transfer and storage (TS) area, in refineries. An important word for TS systems is efficiency; this requires exploration, refining, and distribution of petroleum to operate with high performance and quality. What translates into how to transport and store oil and oil products in order to take advantage of the physical infrastructure (pipelines and tanks) facilities (refineries, ports or terminals) from volumes and movement periods planned by the company (2), (3). In this context, planning and scheduling are keywords commonly found in the oil industry. They are related to the company strategic, tactical, and operational levels and so they are important procedures for coordination of the entire refinery operations. The planning uses aggregate information and it determines longer campaigns with monthly term, six-monthly or even yearly period and, generally, it takes into account the company’s policy (what to do?) and seeks to minimize cost and maximize profit. In turn, the scheduling works with operational tasks and refers to a shorter period of time. It is an activity that seeks to make possible production procedures in the factory environment (how to do?), where the activities compete for limited resources and utilities. The scheduling uses more detailed information and it seeks to define how it should be the sequencing of tasks and allocation of equipment to execute the campaign at time (4), (5). Planning and scheduling seek to find an operating point that makes the system more efficient from an economic point of view, without changing the structure (loops, valves, pumps, pipes, lines, etc.) (1). However, scheduling problems are often very complex, where the use of combinatorial optimization techniques to obtain solutions is common. This motivates the development of computational tools to assist decision making. It is also worth noting that the scheduling is strongly linked to the production area of the company and, therefore, it is related to simulation and computational optimization (6), (1). Following this line, some authors point out that the Mathematical Programming (MP) is an effective approach to scheduling problems. The use of MP models brings the benefit of translating the problem (formalized by equations and inequalities) in order to explicit the relationships between the several scenario components and to allow a thorough analysis to avoid under-utilization of plant production capacity (2), (7). ACS Paragon Plus Environment

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Some computational tools based on Linear Programming models are used to assist the decision making in refineries (planning), among these, we can cite RPMS (Refinery and Petrochemical Modeling System) by Honeywell and the software PIMS (Process Industry Modeling System) by AspenTech® (8), (9). However, scheduling problems deal with complex situations and scheduling models use binary variables for decision making. Moreover, some scenarios can require a model with nonlinear equations. As a result, optimization models based on MILP (Mixed Integer Linear Programming) and MINLP (Mixed Integer Non-Linear Programming) techniques are commonly used to solve scheduling problems in refineries (10), (11), (12), (13), (3), (14). Figure 1 illustrates the Standard Refinery System involved in the transport/storage/processing products in a refinery. This system can be divided into four stages (subsystems): the crude-oil unloading and blending; the production unit operations; the product blending and lifting (shipping) (subsystem where this paper is focused); and, the external pipeline network. In each of these subsystems, movements of crude-oil and oil derivatives occur. The coordination of these movements require the implementation of efficient models to planning and scheduling.

Figure 1. Standard Refinery System.



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A. The crude-oil unloading and blending (subsystem 1) and the production unit operations (subsystem 2) The first stage is related to the unloading of crude-oil from vessels to storage tanks and then to the loading of crude-oil from storage tanks to charging tanks and, finally, from these last tanks to distillation units (CDU). For this first stage, the main information used as parameters involves: the arrival timetable of the vessels; product composition and initial inventory of tanks; the product specification and demand to distillation towers. In general for this stage, the goal is to determine the schedule of the ship unloading, the allocation of tanks in terminals and refineries, times and volumes to move products between these elements, prioritizing distillation profit maximization or operational costs minimization due to delays in unloading ships, waiting time at sea, or even changes in distillation towers. The works of (15), (16), (17), (18), (19), (20), (10), (21), (22), (23), (24), (25), (26) address the scheduling problem for the crude-oil unloading and blending (subsystem 1). The second stage refers to the production unit operations that transform crude oil into fuels and other derivatives. Chemical reactions modifying the crude oil occur into process units, which are interlinked, requiring the movement of products. The two main units that compose this stage are (27): CDU (crude distillation unit) and FCC (fluidize-bed catalytic cracking). The by-products resulting from this stage go to GG (gasoline blending) and DB (diesel oil blending), which are units of the third stage (the product blending and lifting sub-system). According to (28), the main characteristic of the scheduling at this stage is the product flow between the several process units, in which a unit output product serves as an entrance to another unit, even in an environment where a group of process units simultaneously produce multiple products. The works of (27) and (28), also in (29), (30), and (31) deal with the scheduling of the subsystem 2, where the focus is maintaining operations continuity by reinforcing the idea that stops are undesirable in the production stage. B. The product blending and lifting (shipping) – subsystem 3. The third stage is related to the product blending and lifting (shipping). It involves the scheduling of gasoline blending and diesel oil blending (BS), the scheduling of final storage tanks (finished product tanks) and shipment of finished products to the local client (lifting of the final products). The BS unit ACS Paragon Plus Environment

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should make control of the consumption of the intermediate products (generated by processes from subsystem 2) such that efficient mixing is performed to obtain final products within desired specifications (minimize giveaway). The set of tanks to store finished products composes the refinery tank farm addressed within this article. The tank farm receives products from blending (production), and it sends the final products to the local market (demand). Furthermore, the tank farm structure is also used to perform the re-pumping of products that pass through the internal lines of the refinery and to support transportation scheduling by pipeline network interconnecting, possibly, various refineries (external pipeline network). The scheduling of these storage tanks involves the management of tank operations based on inventory profiles. At the beginning, each tank has assigned an initial product inventory (opening stock) and, during the scheduling horizon (H), the tank stock curve should respect its physical capacity and rules of operations. These rules mean, for example, a tank cannot send and receive simultaneously; and, after any receiving operation, a tank should store the product for a time period needed to product specification (setup time or settling time). At the end, the complete tank management should provide solutions that meet the volume values set for continuous movements, production (originating from the blending system) and demand (lifting of the final products), and for incoming and outgoing batches related to the external pipeline network. The work developed in (32) approaches the Tank Farm Operation Problem (TFOP) applying mathematical programming with continuous time representation. The authors address the problem of tanks’ assignment in order to meet the continuous production and local demand, respecting structural limits of resources and the operational characteristics of the process, which make the tank farm management a complex activity. The tanks are dedicated by product and the solution allows verifying the evolution of inventories in each one individually. The model computational time was considered reasonable for scenarios with H (scheduling horizon) of two weeks. The scheduling optimization in refineries is considered as a complex problem to be addressed in a monolithic form, and, therefore, an approach based on subsystems’ decomposition becomes attractive in those cases. Some works (10), (11), (33) propose solutions addressing more than one stage ACS Paragon Plus Environment


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simultaneously, adopting simplifications to deal with real-world problems. Moreover, in the last few decades, a smaller number of works approaching the scheduling of blending and distribution problem (the product blending and lifting) has emerged. As examples, the authors in (34) mention the work of (35), (36), and (37). Finally, this recent study (34) proposes a scheduling model for the diesel blending and distribution with a hybrid temporal representation (discrete and continuous) approach. The scheduling horizon H is divided into equal periods of time (fixed time points) representing demand service milestones and, according to the authors, the hybrid approach that also use the continuous representation, ensured the temporal flexibility to adapt the movements’ operations. C. The external pipeline network (subsystem 4). As in the internal refinery operations, the scheduling of product transport by modals (railways, waterways, roads, and pipelines) is responsible for operations’ coordination (how to do?). More detailed information is used to determine how the tasks’ sequencing and resources’ allocation should be in order to execute the campaign at one time (1), (2). In particular, since the seminal work of (38), the literature related to pipeline-scheduling problems has evolved and a series of contributions can be found, such as: (2), (39), (40), (41), (42), (43), (44), (45), (46). The great majority of related works apply Mixed Integer Linear Programming (MILP) models to address pipeline-scheduling problems in different scenarios. Some woks apply Mixed Integer Non-Linear Programming (MINLP) in pipelinescheduling problems to reduce operational costs for control of the flow rate profile (47), (48). Other applications include problems of product transport between refineries and terminals in a mesh/network structure herein called the external pipeline network, for instance: (1), (49), (50), (51). Generally, these studies present models that consider, in their formulations, operational and structural characteristics for the TS problem in an external pipeline network. Features as pipeline flow rates, flow reversion, product compatibility, and other constraints are also considered and the model goal is to attain a feasible operational schedule to the complete pipeline network. According to the authors, solutions presenting “low” computational time are obtained by decomposition techniques (problem division into parts that are individually solved) and by hybrid models (which combine different solution methods).


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As above introduced, the scheduling of internal movement operations of the refinery (the crude-oil unloading and blending, the production unit operations, and the product blending and lifting) and TS operations of refineries, ports, and terminals (the external pipeline network) are much explored in recent years. However, there are still gaps to attain the entire system integration, so that the whole chain of optimized decisions can contribute to the final operator, who should to implement all appropriate alignments (search for routes) of the tank-end products. Among the schedulers (subsystems 1, 2, BS, and external pipeline network) and the search for routes (which connects the tanks) there is the question of how to make proper use of the tank farm resources (scheduler of tanks). That is, what is the best inventory management to support TS operation at a tank farm? So that, the occupation of tanks has to be the most appropriate possible; also, it has to comply with the scheduling of product receiving and sending by the refinery. The answer to this question is addressed in this paper. The proposed model intends to determine the best policy for the use of storage tanks (Tank Farm highlighted in Figure 1), or end tanks, that is, tanks storing products to be sent to customers. The tankage will be considered individually, this fact makes possible to know loading and unloading in each tank during the considered period. The scheduling will be solved for each individual tank (“tank to tank” approach) from real data of receiving and delivery movements of the refinery (domestic production, final clients demand, and movements generated by the pipeline network scheduling). For this, all information about the movements programming (flow rates, times, volumes) is taken into account and all operational characteristics of the tank farm will be respected. Therefore, the paper focuses on the scheduling of loading and unloading operations in each individual tank that belongs to the tank farm of finished products. The external pipeline network scheduling is, within the considered problem, an important input parameter to be respected. However, a decomposition approach has been applied and multi product scenarios considered by pipeline scheduling were broken in single product scenarios. In addition, storage necessities for the refinery production and the supply of local demand from tanks are other factors that influence the scheduling of each individual tank. This is a TFOP (Tank Farm Operation Problem) that considers production, demand, and pipeline scheduling movements. ACS Paragon Plus Environment


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The other paper sections are organized as follows: the description made in Section II addresses issues relating to input to the tanks’ scheduling. This involves the integration that occurs between production, demand, external network pipeline and tank farm features, the explanation about pipelines’ scheduler, the details on the amount of available resources and the volume of handled product at each stage are also presented. The concepts and rules (temporal and operational) inherent to TS process in tanks, which guide the model design, are also detailed. Section III presents the model assumptions, the sets, indexes, variables, parameters, and formulation of the MILP mathematical model proposed in this paper to solve the scheduling in storage tanks. Sections IV, V, and VI present the results obtained from real scenarios, considering the aspects of time and operational constraints of the problem and computational aspects of the model. They also have the dimensions of the addressed problems and the approach of the iterative algorithm to find solutions in smaller computational times. Finally, in section VII will be the final remarks.

II. PROBLEM DESCRIPTION Figure 2 shows the hierarchy of data streams to the TS operations occurring in refineries. In this figure, scenarios are influenced by information ranging from the strategic to the operational level. They are: pipeline scheduling (optimization of transfers between refineries, ports, and terminals), tank farm operation model (optimization of product moves to load and unload tanks), and routing to operate the tank farm operation model (finding the best routes to ensure the product movements inside refinery). The external pipeline network scheduler (system supporting pipeline feasible scheduling), or pipelines’ scheduler, generates the movements into and out of pipelines at refineries, informing the volumes and the start time (ts) and end time (te) of all movements between refineries. This pipeline scheduling takes into account refinery data, considering only the aggregate capacity per product to the tank farm. The scheduler of the tanks (tank farm operation model) also creates volumes and times to the movements, but in this case these variables are related to loading and unloading of each individual tank (movements inside the refinery). In turn, the tools supporting search for better routes (routing)


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need to receive information about product movements to load and unload tanks. For each loading (origin-tank) and unloading (tank-destination) movement it is also important to know the involved product volume and the start time (ts) and end time (te) of the operation. This information assures a successful operation of the scheduled movement through the extensive network formed by pipe segments and set of valves inside the refinery tank farm. The times and volumes handled by production and for product demand, the opening stocks and tank capacities are known refinery data that serve as parameters for the proposed model. In short, the refinery planning and the external pipeline network scheduler provide a database for the tank farm operation model proposed in this work. The results of tank farm operation model can be checked by routing procedures, however this latter stage is not contemplated in this paper.

Figure 2. Scheduling Problems at Refineries – Hierarchy of Data Streams to the TS Operations.

D. External pipeline network scheduler. In (1), the authors propose a model to pipeline network scheduling. The proposed model uses MP techniques, specifically MILP, and heuristics to optimize the product movement of a real pipeline network. The network consists of thirty pipelines linking fourteen entities (refineries, ports, final clients, and distribution terminals) that move many petroleum products. ACS Paragon Plus Environment


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The model proposed in (1) considers structural information and operational rules of the pipeline network (pumps, cross-product interface, demand services, pipelines’ dimensions, and tank aggregated capacity in each entity) as well as make use of the information about production and demand. This model (1) computes times, volumes, and flow rates of movements that come in and out of each entity, through pipelines. Therefore, refineries provide not only information about domestic production and local demand, but they also provide detailed information about conditions of the monthly movements from pipelines. Each of these movements corresponds to a certain volume that is transported during a set time period from a source to a destination. The scenarios presented in this paper deal with continuous movements (without time interruption) of batches (batches’ delivery takes place one after the other). The production must be continuous as previously explained because subsystem 2 units break-down are costly to the refining process. On the other hand, the movements related to pipelines and to local demand are not necessarily continuous in time. The batches to be moved to pipelines are generated by the pipelines’ scheduler proposed by (1) and demanded batches must occur such that local market is met during H. Thus, four types of refinery tank farm interfaces are defined within this article, namely: Production (P), demand (D), input pipelines (X), and output pipelines (Y), as shown in Figure 4. The monthly volumes of production (P) and of demand (D) are set by the refinery planning itself. On the other hand, the movements of input pipelines (X) and output pipelines (Y) are solutions found by the external pipeline network scheduler, thus are input parameters for the considered model. Figure 3 illustrates the connections of the refined products tank farm and de considered interfaces, namely P, X, D, and Y. Within the article, we considered specific products (see Table I: PD1, PD2, PD3, and PD4). For this group of products, each refinery has interface with just one input (interface X) and one output (interface Y) pipeline. A set of tanks is dedicated for each involved product. Thus, the single product scenario of each refinery has its own tank farm. For instance, the set of tanks dedicated to PD1can be used for sending/receiving operations involving the four interfaces (P-X-D-Y), but only with PD1. Thus, the exchange of products between tanks is not allowed within the presented article. Then, as indicated by the figure, the scenario for PD1 involves the light blue operations, for PD2 the ACS Paragon Plus Environment

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orange, and for PDn the green ones. The receiving from production (P) occurs during the entire scenario (one moth in studied cases) without interruption. The sending to demand (D) also occurs during the entire scenario, but can be broken into different batches.

Figure 3. Tank Farm: Input and Output Interfaces

The scenarios presented in Table I are coming from two databases: monthly planning defined by the refinery and the solution found by pipelines’ scheduler proposed by (1). The values presented are parameters to the tank farm operation model proposed in this work. These scenarios were obtained for two different months (M1 and M2) in four refineries (R1, R2, R3, and R4) which move four types of products (PD1, PD2, PD3, and PD4), all are diesel group. The INTERFACE column represents the origins and destinations of the product throughout the H. Furthermore, it is presented the number of tanks that are allocated (NUMBER OF TANKS column) to receive and send product (tanks dedicated to each product) at the beginning of the programming horizon H. It is also informed the aggregate capacity by product in each refinery, tank capacity in m³, which is used to product movement during H (AGGREGATE CAP. column). The last two table columns show the total volumes entering and exiting the refinery. Note that, in general, the scenarios deal with a large quantity of product movement and display an imbalance between the total of received and delivered product. At the end of each set of movements, a residual amount of volume remains in tanks, so the difference between what goes in and out of the refinery has positive or negative balance that increases or decreases the opening stock to the next analysis. It is important to emphasize that the tanks are dedicated by product (single product), with no exchange of products during H. For example, scenario 10 refers to movements of PD4 product in ACS Paragon Plus Environment


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refinery R4 for the month M1. The scenario involves six tanks with aggregate capacity of 103,548m3; a monthly total input of 323,280m3 of PD4 is given by production; monthly, a total output of 311,097m3 of PD4 is sent to demand and by means of output pipeline.

TABLE I. MOVEMENTS SCENARIOS BY PRODUCT NUMBER OF TANKS SCENARIO

MONTH

REFINERY

PRODUCT

DEDICATED TO EACH PRODUCT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

R1 R2 M1 R3 R4 R1

R2 M2 R3 R4

PD1 PD1 PD2 PD3 PD4 PD1 PD3 PD4 PD2 PD4 PD3 PD4 PD1 PD2 PD3 PD4 PD3 PD4 PD2 PD4

5 9 3 4 5 3 2 8 4 6 3 3 9 3 4 4 3 9 4 5

TOTAL AGGREGATE CAP. (m3)

INTERFACE

96508 254810 61903 68079 130082 52628 58513 192093 67924 103548 25970 58560 264072 27539 68079 109682 69661 207217 67924 98291

P-Y P-X-D P-Y P-D-Y P-X-D-Y X-D D P-D-Y P-D-Y P-D-Y P-Y P-Y P-D-Y P-Y P-D-Y P-X-D P-D P-D-Y P-D-Y P-D-Y

INPUT

OUTPUT

(m3)

(m3)

63360 671860 58320 101520 196380 42000 0 367920 104400 323280 29520 80640 650880 77760 87840 184607 5760 397440 120960 300240

70400 688320 55619 110588 242780 38880 9360 347289 104880 311097 25956 85700 644030 71112 86539 186480 10800 382192 131130 302443

Figure 4, Table II, and Table III are presented in order to exemplify the problem data. Thus, the considered individual network entities and the definition of operations to be performed are indicated. Figure 4 shows the flow curves and added inventory to the scenario 1. In this case, the tank farm handles operations through two interfaces (P-Y), supply from production (P) and delivery to pipeline (Y). As shown in Figure 4a, receiving operation (P) runs with constant flow rate during H (720 hours), but the shipping operations (Y) occur at different times (discontinuous operations by batch). Figure 4b shows the evolution of aggregate product stock curve. This curve behavior is due to the effect of the two types of operation (continuous and by batch). Two time periods (p1 and p2) are highlighted in figures 4a and 4b, and these periods are the same in both graphs.


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During the period p1, product movements occur only from the production (P) to tanks in a continuous operation, thereby this product receiving increases the stock curve in the period. In the period p2, simultaneous to the continued receiving (P), there is also a sending operation of batches through pipeline (Y). In this case, the sending flow rate exceeds that receipt, and this reflects in the decaying curve of the aggregate product stock PD1 (see Table I).

a)

Flow Rate Curve

b) Aggregate Inventory Curve

Figure 4. Product Movements in Refinery – Case 1.

Table II details the movement parameters to scenario 1. Each row represents an operation, pointing the flow rate values, start time and end time, the total volume handled in the period and the involved interfaces. The first line refers to the continuous production (P), where the flow rate is constant throughout H. The remaining table rows relate to sending operations through pipelines (Y). Seven ACS Paragon Plus Environment


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product batches are sent by refinery. The batches’ sending has constant flow rate, but it produces different volumes, because these sending operations occur at different times and with specific duration within the H. Each batch sending is defined by the model proposed in (1). The production (P) is a single operation that occurs during H. The output pipeline (Y) consists of a group of operations with duration and sequence established by the external pipeline network scheduler. The batch indicated in the table (*) is the same as the one highlighted in Figure 3a, which refers to the period p2. TABLE II. OPERATIONS PARAMETERS – SCENARIO 1 FLOW RATE (m³/h) 88 400 400 400 400 *400 400 400

START TIME (h) 0 0 38 254 287 396 553 589

END TIME (h) 720 30 41 279 317 426 583 617

VOLUME (m³) 63360 12000 1200 10000 12000 12000 12000 11200

INTERFACE P Y Y Y Y Y Y Y

The model proposed by (1) considers local production and local demand (P and D interfaces) as input parameters and it computes receiving and sending movements through pipelines (X and Y interfaces). However, the model (1) considers the sum of each product stock in all tanks as a single value, generating a monthly schedule respecting the storage aggregate capacities. The tank farm operation model herein proposed considers each tank individually, regarding both: inventory evolution along H; and, structural constraints and opening stocks. Each storage tank of finished product is dedicated to a single product, although it can send and receive via any of the types of operations (interfaces P, X, D, and Y). Figure 5 illustrates the scenario 5 of Table I, the unique considered scenario that has connections with the four types of interfaces (P, X, D, and Y). The scenario presents a set of five tanks dedicated to PD4. There is a connection to a continuous production operation (P), a discontinuous demand operation (D), seven receiving operations from pipeline (X), and five sending operations to pipeline (Y). It is important to emphasize that the proposed MILP model considers each scenario individually, as exemplified by Figure 5.


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Figure 5. Tank Farm: Input and Output Interfaces Running a Single-product – Scenario 5

The considered approach assumes that each individual tank is dedicated to a specific product. This hypothesis does not conflict with the one used by the pipeline scheduler (1), which considers an aggregated tankage dedicated to each product. Then, it turns out that, indirectly, the pipeline scheduler also takes each individual tank dedicated to a product. Thus, in each scenario the refinery tank farm is dedicated per product and can interface with any operation, as shown in Figure 6. From the refinery tank farm point of view, each move can be a product supply, from production (P) or pipeline (X), or it can be a product delivery to local demand (D) or to pipeline (Y). Figure 6 illustrates the tank farm scenario, where alignments (links) between tanks and interfaces can be observed, forming four origindestination pairs: production-tank; pipeline-tank; tank-demand; and, tank-pipeline. At the scenarios herein presented, operational conditions in which pipelines need to be supplied by a finished product tank were isolated from the pipeline scheduler database. Thus, within the considered data, a pipeline is necessarily supplied by a finished product tank. In a complementary way, the considered pipeline inputs (X) are necessarily sent to tanks. TANK FARM Production (P)

T1

Demand (D)

T2 Pipeline (X)

Pipeline (Y)

Tn

Figure 6. Tank Farm: Input and Output with Internal Alignments.



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Table III exemplifies a tank initial situation. The table shows the initial conditions of each refinery tank to a movement involving production and sending by pipelines (scenario 1 of Table I). Each row has four columns referring to each tank name (tag’s), its capacity value (physical limitation of the tank), and the opening stock (stored volume, residue due to previous operation). The same type of initial condition is considered for other scenarios. However, each scenario has its own set of tanks (no sharing of resources), with different capacities and opening stocks.

TABLE III. OPENING STOCK IN TANKS - SCENARIO 1 TANK

NAME

CAPACITY (m3)

OPENING STOCK (m3)

1 2 3 4 5

T1_C1 T2_C1 T3_C1 T4_C1 T5_C1

19821 20397 18740 18342 19208

30 19059 5262 33 218

The work of Terrazas-Moreno, Grossmann and Wassick (32) also focus on a tank farm operation model. The referenced authors indicate a significant set of operational issues that made the tank farm management a complex problem. They mention that, for instance, tanks cannot send and receive products simultaneously. In addition, the authors highlight that, in order to make viable loading and unloading procedures in each tank, available internal lines in the refinery have to be provided to connect each tank to the necessary input/output point. This fact involves a routing problem, indicated in Figure 2. Indeed, within the presented paper we aid routing procedures as we tried to minimize the number of internal movements (factor 3 of equation 1). In (32) the authors considered the receiving from production and the sending to local demand by means of dedicated tanks. In the proposed work, we also considered a set of dedicated tanks per product, however we have to take into account the additional feature of addressing the temporal and volumetric demands imposed by the pipeline scheduler (1).

E. Temporal issue Some factors must be considered to investigate the time issue of a MILP derived model. In (52) it is mentioned that models seek to arrange for scheduling events over time, respecting the maximum ACS Paragon Plus Environment

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capacities of resources. The authors explore the temporal issue in depth and they classify the different types of time representations. The differences between these representations are analyzed and it is emphasized that, although some may be more general than others, they are always oriented to meet an arbitrary criterion of precedence between tasks of a process. Moreover, the link between variables must take place to ensure correct tasks’ precedences and matching events with times established by the process. These characteristics introduce complexity in the model formulation. For instance, efficient MILP modeling of sequence-dependent switchovers for discrete-time scheduling problems are addressed by (53). In the paper herein proposed, a continuous-time approach is used to address the temporal issue that mainly refers to the fit of receiving and sending operations at refinery with the loading and unloading events in each tank. So, the loading and unloading of a tank (internal movement at the refinery) should occur synchronized with operations arising from the interfaces (synchronization between movements). The first obstacle is related to the setup time (settling period). In (54) the authors use a mathematical programming approach to manage inventory issues. They mention that one important point in modeling is related to the product operational cycle (fill-hold/haul-draw). They validate the proposed formulation in different applications that involve inventory management. In an analogous way, within the tankage management, it can be said that a tank has to first receive a product (the resource has to be filled), then the tank has to wait for a certain time (setup time) and, after this time that can be a fixed or a variable amount, the product can be draw. In the considered problem, after any product receiving, the tank content should remain in rest at least 4 hours before the next event occurs. The setup time is a refinery tank farm operating condition. It is a waiting time in the meanwhile product analysis are performed to ensure product specifications for customers. Figure 7 shows the tank stock profile, highlighting setup time.



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Figure 7. Tank Inventory: Highlight to the 4-Hour Setup Time.

The other concern of temporal issue is related to movements’ synchronization. The proposed model addresses tank farm operations, more precisely the final tanks operations, considering the receiving and sending operations by pipelines, which adds hard constraints to modeling features. This condition requires that loading and unloading tank events respect the times and the flow rates imposed by the pipelines’ scheduler proposed by (1). Figure 8 helps the problem understanding. Figure 8a illustrates how the loading and unloading events occur from shipping or receiving during continuous operations (e.g. internal production). Continuous operation is broken down into batches, which are translated as a loading or unloading event in tanks. As the internal operation is considered uninterrupted, some breaks occur in tankage, one after another, without time gap in between. In this figure, the batch (m1, m2, and m3) are allocated to three tanks (T1, T2, and T3). Each break corresponds to a tank change. Thus, m1, m2, and m3 occur in sequence without temporal gap. Figure 8b illustrates how the loading and unloading events should occur from the deliveries and receipts during discontinuous operations (e.g. batch through pipelines). The discontinued operations are due to batches scheduling and, in this case, it is natural that the breaks may have temporal gaps. However, as in continuous operation, very large discontinuous operations may be broken into smaller batches to allow the storage in several tanks. In these situations, the behavior should be similar to what occurs in the continuous operations, meaning a sequence of batches is loaded or unloaded to/from different tanks. In Figure 8b, three batches (m1, m2, and m3) occur in sequence, but there is a time gap between m1, m2, and m3. The external batch m1 was broken into two internal batches referred as m1a and m1b; each one was received by a different tank, T1 and T3, respectively. In this case, the T3 tank will be used in two stages, first to receive the batch m1b and then to receive the batch m3. It is called “internal batch” any movement related to the loading or


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unloading in a tank. In addition, it is called “external batch” any movement caused by the external pipeline network scheduler. Time violations during continuous operations mean extrapolating the scheduling horizon (H) limit. For discontinuous operation, start and end time violations mean not to respect the periods set by the pipelines’ scheduler. The model solution must comply with time periods imposed for continuous movements and discontinuous movements (pipelines’ operations). For this, “big” batches can be broken in small batches if necessary, ensuring the time and volume values. Practical details of scheduling and undesirable operational tendencies (such as product shortage) are not easily noticed in short term solutions (a period of a few days). Therefore, higher programming horizons (e.g. 30 days) can provide solutions that enable anticipating supply problems in demand or production. Thus, schedulers in their daily activities can take preventive measures rather than corrective ones, which increase the financial cost (1). To take into account these aspects, the scheduling horizon (H) adopted in this study corresponds to 30 days, or 720 hours.

a)

Movements Synchronization during Continuous Operation

b) Movements Synchronization during Discontinuous Operation

Figure 8: Movements Synchronization



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III. MATHEMATICAL MODEL The proposed model relies on some assumptions, which are presented within this section. The mathematical formulation for the MILP proposed model is also presented. The model is applied to solve the tank farm operation problem of finished products in refineries. F. Proposed MILP Model Assumptions From problem description and considering the time issue inherent to the problem addressed, the MILP model assumptions are: A1: the programming horizon (H) is monthly (720 hours or 30 days). A2: the tanks are dedicated by product; there is no product exchange between tanks during H. A3: opening stocks of tanks are known. A4: the type of product allocated to each tank is known. A5: the tank cannot send and receive simultaneously. A6: the setup times are respected (see Figure 5). A7: each “operation” to be performed is a priori set for the model. An operation has known flow parameters such as FLOW RATE, START, END, and VOLUME for a specific interface (P, D, X, and Y). Each row in Table II illustrates an operation to be considered. A8: The model proposed by (1) imposes time windows for each operation. Thus, the MILP model herein proposed is limited to this condition and must respect these time windows, as well as volumes and flow rates of these operations. A9: production operation is continuous during the entire H. A10: there is an available route to each origin-destination movement in the refinery (productiontank, pipeline-tank, tank-demand, and tank-pipeline). A11: each input movement represents the product pumping from production-tank or pipeline-tank pair. A12: each output movement is a product pumping from tank-demand or tank-pipeline pair. A13: each tank can receive only from one origin in each loading event. A14: each tank can only send to a destination in each unloading event. ACS Paragon Plus Environment

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A15: the scheduling of the tanks should help the refinery programming activity, minimizing the number of internal moves at the tank farm. Thus, the set of assumptions limits the model scope and the usage of such model is dependent upon parameters provided by higher order systems, indicated in Figure 2. G. Indexes: • tk Tank. • op

Operation.

• bt

Batch.

H. Sets: • TK

Set of Tanks.

• OPP

Set of Production Operations.

• OPX

Set of Input Pipelines’ Operations.

• OPD

Set of Demand Operations.

• OPY

Set of Output Pipelines’ Operations.

• OPI

Set of Input Operations (OPP ∪ OPX).

• OPO

Set of Outbound Operations (OPD ∪ OPY).

• OP

OPI ∪ OPO.

• BT

Set of Batches.

I. Binary variables: • wtk,bt

indicates whether the tank tk is waiting in bt batch.

• lutk,op,bt

indicates whether the tank tk is active (loading/unloading) in bt batch for op operation.

J. Continuous variables • Stktk,bt

product volume in the tank tk in batch bt (m3).

• vLUtk,op,bt

volume of loading and unloading the tank tk in batch bt for op operation (m3).

• tsBTop,bt

start time of the batch bt during the period of operation op (h).

• teBTop,bt

end time of the batch bt during the period of operation op (h). ACS Paragon Plus Environment


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• tsLUtk,bt

start time of the event (loading/unloading) in tank tk in the batch bt (h).

• teLUtk,bt

end time of the event (loading/unloading) in tank tk in the batch bt (h).

• cvMintk,bt

violation of the minimum tank capacity tk in the batch bt (m3).

• cvMaxtk,bt

violation of the maximum tank capacity tk in the batch bt (m3).

• tvMinop,bt

temporal violation at onset of operation op in the batch bt (h).

• tvMaxop,bt

temporal violation of end of operation op in the batch bt (h).

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The domain of all continuous variables is given in R+. K. Parameters: • STOREDtk

Opening stock of tank tk at the beginning of the H (m3).

• TOTALop

Monthly volume of each operation op (m3)

• STARTop

Start time of the operation op (h).

• ENDop

End time of the operation op (h).

• MAXCAPtk

Maximum volume capacity of the tank tk (m3).

• MINCAPtk

Minimum volume capacity of the tank tk (m3).

• MIN_P

Minimum number of movements in production (P).

• MIN_X

Minimum number of movements in entry pipelines (X).

• MIN_D

Minimum number of movements in the demand (D).

• MIN_Y

Minimum number of movements in the exit pipelines (Y).

• MIN_T

Total minimum number of movements.

• FLOWop

Nominal flow rate of operation op (m3/h).

• MAXFLOWop Maximum flow rate of operation op (m3/h). • SETUP

Setup time after any product receiving in tank (4 hours).

• m

Small value (e.g. 10-2, guarantees minimum value to some BIG-M formulations).

• M

Large value (e.g. 10+6, used in BIG-M formulations).

• α

Weight of time violation variables in the objective function (OF); value choice for α is presented in section L. ACS Paragon Plus Environment

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The model seeks the solution for each individual scenario (single product) and the model dimensions are setting exogenously. The sets are defined as follows: set of tanks (TK) corresponds to the number of tanks that are allocated for each scenario (Table I), set of operations (OP) corresponds to minimum number of movements for each scenario (Table V), set of batches (BT) is postulated with 30 elements. This value was adopted after preliminary tests in scenario 5, which has all the four possible interfaces P-X-D-Y into the same scenario. We run this MILP model increasing the number of batches from 1 to 40, in unitary steps, and observed convergence issues, which were rather stable after a value of twenty elements. Then we tested the minimum number for the set of batches in all considered scenarios and notice that, for feasibility issues, the adopted value of 30 elements would be conservative and, thus, adequate for all tested scenarios. Each operation is broken into batches, according to the set of batches, since only a few of these batches tend to be indeed assigned. It is important to mention that the BT set (Batch) embraces all internal movements (occurring inside the refinery). Each element referenced by bt index is an occurrence of movement with initial and ending time. When a true movement occurs, the batch has length and volume greater than zero due to activation of binary variable (lutk,op,bt = 1). On the contrary, when the batch binary variable is not enabled (lutk,op,bt = 0), thus the batch duration and volume are null. •

Objective Function (OF): The objective function (OF), equation (1), tries to minimize the tanks’ capacity violations (factor 1),

temporal violations of operations (factor 2), and the number of movements within the tank farm (factor 3). The tankage activity aims to manage the inventory of tanks, being major issue not exceeding each tank structural limits. This violation is given by the sum of the values assumed by cvMintk,bt and cvMaxtk,bt. Another relevant point, as earlier mentioned, is the temporal question related to movements (input and output) of products within the refinery. In this sense, the solution must respect temporal issues of movements and all true batches must respect their time limits. To achieve this goal, OF seeks to minimize the violations presented by the sum of tvMinop,bt and tvMaxop,bt variables. The α factor is a temporal violation weight and it is further explored in section L. The minimization of the number of internal movements (lutk,op,bt) is also a goal. This goal highlights that the smaller the number of ACS Paragon Plus Environment


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movements, the less is the exchange of routes (alignments), which facilitates tankage operations, helping the operators’ job. minimize z =

+cvMaxtk ,bt ) + α ⋅ ∑ ∑ (tvMinop,bt +tvMaxop,bt ) + ∑ ∑ ∑ lutk ,op,bt (1 ∈TK op∈OP bt∈BT op∈OP bt∈BT 1444442444443 14 4444 42444444 3 tk1 4442444 3 ) factor 1

∑ ∑ (cvMin

tk∈TK bt∈BT

tk ,bt

factor 2

•

factor 3

Tank Operational Cycle: Equation (2) and inequality (3) set the tank operating cycle. The model considers that a tank can take

two states: one can be in standby (wtk,bt = 1), with remaining stock; or may be in loading or unloading event, receiving or sending a batch in some operation (lutk,op,bt = 1). As these two states are mutually exclusive, equation (2) formulates this condition. The inequality (3) defines that only one tank can receive or send a determined batch operation, thereby observing an operational condition of the tank.

∑ lu

tk ,op ,bt

+ wtk ,bt = 1

∀ tk ∈ TK , bt ∈ BT

(2)

∑ lu

tk , op , bt

≤1

∀ op ∈ OP , bt ∈ BT

(3)

op∈OP

tk ∈TK

•

Minimum Number of Transactions: The OF main goal is to minimize the movements. However the inequalities (4)-(8) require a

minimum number of movements for each interface {P, X, D, Y} and a minimum number of total movements. These inequalities set practical lower bounds for the model search space. The minimum values (MIN_P, MIN_X, MIN_D, MIN_Y, and MIN_T) are parameters obtained from each scenario information. The solution is unpractical if some variables assume values below these limits. It is important to notice the use of different sets (OPP, OPX, OPD, OPY, and OP) within constraints (4)-(8).

∑ ∑ ∑ lu

tk ∈TK op ∈OPP bt ∈ BT

tk , op ,bt

(4)

∑ ∑ ∑ lu

tk , op ,bt

≥MIN_X

(5)

∑ ∑ ∑ lu

tk , op , bt

≥MIN_D

(6)

∑ ∑ ∑ lu

tk , op , bt

≥MIN_Y

(7)

tk ∈TK op ∈OPX bt ∈ BT

tk ∈TK op ∈OPD bt ∈ BT

tk ∈TK op ∈OPY bt ∈ BT

∑ ∑ ∑ lu

tk ∈TK op ∈OP bt ∈ BT

•

≥MIN_P

tk , op , bt

≥MIN_T

(8)

Movements Calculation: ACS Paragon Plus Environment

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The inequalities (9)-(11) drive the volume of movements that take place inside the refinery. The inequalities (9) and (10) define a range for the handled volume. It must have a minimum value between (m) and maximum tank capacity that has been assigned to operation (MAXCAPtk). Although, the inequality (11) shows that the sum of volumes of all batches should reach, at least, the amount required for the operation during the H (TOTALop), respecting a scenario condition. vLUtk ,op,bt ≥ m ⋅ lutk ,op,bt

∀ tk ∈ TK , op ∈ OP , bt ∈ BT

(9)

vLUtk ,op,bt ≤ MAXCAPtk ⋅ lutk ,op,bt


(10)

∀ op ∈ OP

(11)

∑ ∑ vLU

tk ∈TK bt ∈ BT

•

tk , op , bt

≥ TOTAL op

Mass Balance in each Tank: Equations (12) and (13) establish the mass balance in each tank. Equation (12) shows that the value

of the stock (Stktk,bt) is updated to every batch (bt); it is incremented when a load (input operation belonging to OPI) occurs; and, it is decremented when a tank discharge occurs (output operation belonging to OPO). The equation (13) approaches the boundary condition for the first batch. In this case, the increment or decrement is made from the amount of opening stock of each tank (STOREDtk). Stk tk , bt = Stk tk , bt −1 +

∑ vLU

op ∈ OPI

Stk tk ,bt = STORED tk +

•

tk , op , bt

∑ vLU

op ∈OPI

−

tk , op ,bt

∑ vLU

op ∈OPO

−

tk , op , bt

∑ vLU

op ∈OPO

tk , op , bt

∀ tk ∈ TK , bt ∈ BT | bt ≥ 2

(12)

∀ tk ∈ TK , bt ∈ BT | bt = 1

(13)

Tank Capacity Violation: The inequalities (14) and (15) handle with tank capacity violations (variables used in OF). The goal

is to prevent movements causing stock tank overcomes its structural capabilities (MINCAPtk and MAXCAPtk), which requires operational actions to circumvent tank overflow problems.

•

Stktk ,bt ≥ MINCAPtk − cvMintk ,bt


(14)

Stktk ,bt ≤ MAXCAPtk + cvMaxtk ,bt


(15)

Timing and Sequencing of each Batch: Equation (16) and inequalities (17)-(22) ensure the timing and sequencing of batch operations.

Equation (16) computes batch times based on moved volumes (vLUtk,op,bt ) and flow rate of operation



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(FLOWop). This flow rate is the same for all batches from production P and from pipeline X-Y. However, the D demand, even though a single transaction, can have batches with different flow rates. Herein, the demand database supplied by the refinery planning is monthly. This feature can be improved in case of more detailed demand data being readily available. However, for some scenarios, we know that the volumes do not cover the whole month, since they have low volume values (e.g., scenarios 6, 7, and 17 of Table I). We also know that the demand is not a continuous operation as production, but is geared to meet the customer at scheduled delivery periods and these do not necessarily follow a regular basis. Thus, we used the operating range of demands that defines each batch from a nominal value (minimum) and a maximum value of flow rate. In this case the batch time duration is computed by inequalities (17) and (18). These inequalities show that the duration of each demand batch (teBTop,bt - tsBTop,bt) should occur between a nominal minimum and maximum flow rate; i.e., each demand batch operates with a flow rate chosen in the range of FLOWop (nominal flow rate) and MAXFLOWop (maximum flow rate). The inequalities (19) and (20) rule the sequence of batches, guaranteeing a positive value to batch time duration, time interval, (19). In addition, each batch occurs after the end of the previous batch (20). The inequalities (21) and (22) establish the temporal violations (tvMinop,bt and tvMaxop,bt). Although violations can occur at the frontiers of start and end times (STARTop and ENDop) of operations as a model relaxation, these violations should be avoided or, ideally, annulled. Therefore these variables are minimized in the OF. The frontiers of start and end times of production (P) and demand (D) correspond, respectively, to the horizon H limits (either 0 or 720 h). On the other hand, the frontiers of start and end times of pipelines’ movements are defined by the external pipeline network scheduler (interfaces X and Y). teBT op , bt = tsBT op , bt + teBT op ,bt ≤ tsBT op ,bt + teBT op ,bt ≥ tsBT op ,bt +

teBTop,bt ≥ tsBTop,bt tsBTop,bt ≥ teBTop,bt −1

∑ vLU

tk ∈TK

tk , op , bt

∑ vLU

tk ∈TK

∑ vLU

tk ∈TK

tk , op ,bt

tk ,op ,bt

/ FLOW op / FLOW op / MAXFLOW op

∀ op ∈ ( OPI ∪ OPY ), bt ∈ BT

(16)

∀ op ∈ OPD , bt ∈ BT

(17)

∀ op ∈ OPD , bt ∈ BT

(18)

∀op ∈ OP, bt ∈ BT

(19)

∀ op ∈ OP , bt ∈ BT | bt ≥ 2


(20)

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tsBT op , bt + tvMin op , bt ≥ START op − M .(1 − teBTop , bt − tvMax op ,bt ≤ END op + M .(1 −

•

∑ lu

tk ∈TK

∑ lu

tk ∈TK

tk , op , bt

tk , op , bt

)

)


(21)


(22)

Timing and Sequencing of Events: The inequalities (23)-(26) ensure the timing and sequencing of loading and unloading tanks’ events.

The inequalities (23) and (24) treat the standby situation in the tank (wtk,bt = 1). In this case the event duration is considered null (tsLUtk,bt = teLUtk,bt), or loading and unloading movements do not occur. The inequality (25) ensures coherence between beginning and end of an event; its duration (time interval) assumes a positive value. The inequality (26) establishes the sequence of loading and unloading tanks’ events, adding the setup time (SETUP) after the occurrence of a receiving event (op ∈ OPI). tsLUtk ,bt ≤ teLUtk ,bt + M (1 − wtk ,bt )


(23)

tsLUtk ,bt ≥ teLUtk ,bt − M (1 − wtk ,bt )


(24)

teLUtk ,bt ≥ tsLUtk ,bt

∀tk ∈ TK , bt ∈ BT

(25)

∀ tk ∈ TK , bt ∈ BT | bt ≥ 2

(26)

tsLU

•

tk ,bt

≥ teLU

tk ,bt −1

+ SETUP .

∑ lu

op ∈OPI

tk , op ,bt −1

Temporal Link Between Batches and Events: The inequalities (27)-(30) link times of batches with times of events in the tanks. When a batch bt is

linked to the tk tank event, the temporal variables that mark the beginning and end of a batch (tsBTop,bt and teBTop,bt) and an event (tsLUtk,bt and teLUtk,bt) should match. In other words, if the batch is true (lutk,op,bt = 1), there must be a synchronism between the times; otherwise, the condition is relaxed. tsLUtk ,bt ≤ tsBTop,bt + M (1 − lutk ,op,bt )


(27)

tsLUtk ,bt ≥ tsBTop,bt − M (1 − lutk ,op,bt )


(28)

teLUtk ,bt ≤ teBTop,bt + M (1 − lutk ,op,bt )


(29)

teLUtk ,bt ≥ teBTop,bt − M (1 − lutk ,op,bt )


(30)



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IV. MILP MODEL RESULTS The MILP model results were found from the implementation and computational resolution in the IBM ILOG CPLEX Optimization Studio 12.6. The platform chosen to run the model and to generate the solutions was a Desktop PC with i5 2.2 GHz processor and 4 GB of RAM. The results focus, mainly, on the choice of the α coefficient value at OF (appropriate weighting for time violations) and on the analysis of computational results from the proposed models (dimensions of the addressed problems). L. Choice of the α Coefficient Value at OF: The coefficient α at OF (1) is related to time violations. Its magnitude adjusts the values of time violations in relation to tanks’ capacity violations. For example, a violation of 10m3 in tank capacity that supports 30,000m3 is a relatively small value. However, a violation of 10h at the beginning or end time of a batch during 50 hours is a considerable amount. Thus, time parcel and, consequently, time violations, must have an adequate representation in the OF composition, justifying the weighting of time violations by the coefficient α. The MILP model presented in section III is applied to the Table I scenarios. Each scenario has been evaluated for four α values, namely α = 1, 10, 100, and 1000. Figure 9 shows the results of all tests, totaling 80 printed dots (4 tests for each scenario). Each point represents the value of time and tanks’ capacity violations in each test. The chart axes represent the normalized values of the sum of time violations (TV (%)) and the sum of tanks’ violations (CV (%)). These values are minimized in the OF. It can be seen that many scenarios presented time violations in tests with α = 1. On the other hand, many tank capacity violations are perceived in scenarios where it was applied α = 1000. This shows that the increase in α values causes the violations undergo a knee point, which suggests as best possible options α = 10 and α = 100.


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Figure 9. Effect of the α value in violation values.

One of the model’s goals is that violations be NULL. This condition correspond to the curve origin in Figure 9. Thus the distance value (D) among each curve dot and the point {A,B} = (0,0) is computed. The results are shown in Table IV, where for each α value, the sum values (SUM), average (MEAN), and median (MEDIAN) distances of the 20 dots (Table I scenario violations) are shown. It may be noted that α = 100 generates nearest points of origin; therefore, this value is chosen to weight time violations in OF. TABLE IV. DISTANCE FROM CURVE DOTS TO ORIGIN { A,B} = (0,0).

D= α 1 10 100 1000

(A

SUM(D) 398.8495 196.7417 164.3871 261.4706

2

+ B2

)

MEAN(D)

19.9425 9.8371 8.2194 13.0735

MEDIAN(D) 7.8034 0.1350 0 2.8710

M. Analysis of Computational Results: Table V shows problems’ characteristics highlighting two groups of information about each scenario: the minimum number of moves and the dimensions of the generated models.



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The minimum number of movements is referred to the fewest number of batches that must occur for each interface (MIN_P, MIN_X, MIN_D, and MIN_Y), MIN_T is the minimum sum of all interfaces. These parameters are part of the MILP model (inequalities 4 – 8). The values are defined as the minimum number of moves needed to perform receiving and sending operations. A scenario with movements lower than these limits is unpractical. Initially, these values are equal to the number of each interface operation, defined in the scenario, which is a conservative assumption. The limits to pipeline operations (X – Y) are obtained from (1). To production and demand (P – D), the minimum value is assigned from the number of operations. For example, the scenario given in Table II (scenario 1) presents movements from production and to output pipelines (Y) and it has the following minimum values: MIN_P = 1, MIN_X = 0, MIN_D = 0, MIN_Y = 7, MIN_T = 8. From these minimum values, more movements for each interface may appear. However, this is a result from tanks’ scheduling computed by the MILP proposed model, which allows breaking (batches) operations in more batches during H. When observing the number of constraints (CT), total variables (V), and binary variables (BV) it is possible to evidence the size of the addressed models. Even for the scenarios where generated models are relatively smaller, there is a significant number of constraints and variables. We highlight scenarios 8, 10, 13, and 18 showing more than 20,000 constraints each, all these operations have to move through three interfaces (P-D-Y). The scenario 5 can be also detached, which operates by moving through four interfaces (P-X-D-Y) and having a large number of constraints (16,350). Or even scenarios as 1 and 12, which show operations of two interfaces (P-Y), but they have over 10,000 restrictions each. The variables number (V and BV) follows the size of the presented constraints, most of the time, values in the order of thousands of variables. The Table VI shows the quantitative results of the MILP model when applied to the listed scenarios. The following values are shown to each scenario: the objective function (OF), integrality gap (GAP) in %, computational time (T) in seconds, the capacity violations (CV) and time violations (TV), elements of the OF, and feasible number of movements to the scenario. The T computational time is the total run time. The CV column shows the sum of all violations in capacity of tanks, in m3. The columns PV, XV, ACS Paragon Plus Environment

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DV, and YV show the sum of the time violations (TV), in hours, for each interface. The columns PF, XF, DF, YF, and TF show the achievable movement number, i.e., the movements computed by the MILP model for each interface. In this case, batch operations are fractionated in smaller batches, so that the tank scheduling is detailed addressed. According to the results of Table VI, most scenarios achieve a solution without time or tank capacity violations. Four scenarios present tank capacity violations, however such violations are small compared with the aggregate capacity values (see Table I). The aggregate tanks capacity for scenarios 1, 6, 11, and 16 are 96,508m³, 52,628m³, 25,970m³, and 109,682m³, respectively. When compared to the violations’ values of 6,063m³, 2,276m³, 943m³, and 1,148m³, it is possible to conclude that violations were relatively small. On the other hand, the time violations had significant values in three scenarios (3, 14, and 19). All violations correspond to output movements by pipelines (Y interface). Although it is desirable to avoid temporal violations, second term of objective function in (1), violations on the movements start and end times do not invalidate the tankage at the refinery under analysis. These occurrences represent a feedback information to pipeline scheduling model from (1), since the operational times of the Y interface come from this pipelines’ scheduler.

TABLE V. CHARACTERISTICS OF ADDRESSED PROBLEMS. SCENARIO 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

MINIMUM NUMBER OF MOVEMENTS MIN_P MIN_X MIN_D MIN_Y MIN_T 1 0 0 7 8 1 6 1 0 8 1 0 0 5 6 1 0 1 6 8 1 7 1 5 14 0 3 1 0 4 0 0 1 0 1 1 0 1 10 12 1 0 1 7 9 1 0 1 14 16 1 0 0 4 5 1 0 0 11 12 1 0 1 8 10 1 0 0 6 7 1 0 1 6 8 1 6 1 0 8 1 0 1 0 2 1 0 1 10 12 1 0 1 10 12 1 0 1 13 15

MODELS’ DIMENSIONS CT V BV 11519 4921 1620 16586 6901 2430 5042 2341 630 8191 3601 1080 16350 6781 2250 3632 1741 450 1472 841 180 21387 8641 3120 10950 4681 1500 21629 8761 3060 4322 2041 540 11761 5041 1560 20186 8221 2970 5762 2641 720 8191 3601 1080 9870 4261 1350 2192 1141 270 23786 9541 3510 14190 5941 1950 17430 7201 2400



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TABLE VI. QUANTITATIVE RESULTS OF MILP MODEL

SCENARIO

OF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

12.213 40.000 21.394 16.000 23.000 5.455 1.000 31.000 16.000 44.000 9.189 18.000 40.000 41.708 18.000 16.230 2.000 33.000 51.147 37.000

GAP (%) 9.9 2.5 62.6 12.5 13.0 8.3 0.0 6.5 18.8 9.1 34.7 16.7 2.5 76.0 22.2 13.7 0.0 6.1 66.8 16.2

T (s)

CV (m3)

6288.17 36000.00 7348.40 13928.25 10262.50 2862.01 0.03 36000.00 8529.05 36000.00 28584.84 15476.15 36000.00 36000.00 6515.55 36000.00 0.20 20191.96 25134.55 36000.00

6063 0 0 0 0 2276 0 0 0 0 943 0 0 0 0 1148 0 0 0 0

VIOLATIONS TV (h) PV XV DV 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

YV 0 0 6.39 0 0 0 0 0 0 0 0 0 0 13.71 0 0 0 0 19.15 0

PF 4 15 8 7 5 0 0 13 7 20 5 7 18 15 7 4 1 15 16 16

NUMBER OF FEASIBLE MOVEMENTS XF DF YF 0 0 7 6 19 0 0 0 7 0 1 8 7 6 5 3 2 0 0 1 0 0 5 13 0 1 8 0 3 21 0 0 4 0 0 11 0 14 8 0 0 13 0 1 10 6 6 0 0 1 0 0 7 11 0 1 15 0 3 18

TF 11 40 15 16 23 5 1 31 16 44 9 18 40 28 18 16 2 33 32 37

The MILP model also returns the feasible movements’ number. As the OF also aims to minimize movements number, the values computed by the model for PF, XF, DF, YF, and TF are the minimal movements for each interface. The values of PF, XF, DF, YF, and TF present in table VI are considerably larger than the values of MIN_P, MIN_X, MIN_D, MIN_Y, MIN_T, MILP model parameters, at Table V. As shown in E section (Temporal issue), the synchronism of continuous or discontinuous movements requires, in many cases, breaking batches to make the movement feasible. In the presented scenarios, the columns referring to movements in the X interface (MIN_X in Table V and XF in Table VI) have the same batches number. Five scenarios do not present batches breaking during movements in Y interface (scenario 1, 5, 11, 12, and 13). Production operations (P) and demand (D) are initially labeled with a minimum value of one (1), indicating the presence or absence of the operation. But the MILP model result produces breaks in batches of these operations to make feasible tankage scheduling. The used database provides monthly information about demanded volumes. Therefore, within the proposed paper, the demand requirements are met flexibly. The batches for demand requirements have a flexible flowrate in an operational range, as indicated in inequalities (17) and (18). The MILP model ACS Paragon Plus Environment

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considers the demand (D) as an operation that uses different flow rates for each real batch, respecting the minimum nominal (FLOWop) and maximum nominal limit values (MAXFLOWop) to operation flow rates. Tables VII and VIII highlight those situations where some scenarios have demand operation. Table VII has nine columns: SCENARIO, INTERFACE, REQUIRED_VOLUME, VOLUME/H, BATCH, FLOW RATE, DURATION, TIME, and VOLUME. The SCENARIO and INTERFACE columns show three scenarios (6, 7, and 17) that have demand operation in X-D (6), D (7) and P-D (17) interfaces. The REQUIRED_VOLUME column shows the total product in m³ to be sent as required by refinery demand planning. The column VOLUME/H is the desired volume divided by H (720 hours), corresponding to the nominal flow rate value FLOWop. The BATCH column shows the number of demanded batches occurring in the scenario, the FLOW RATE column shows flow rate actually used to perform these batches’ movements. The DURATION column presents these movements’ duration. The TIME column shows the start and end times for each batch; and, the VOLUME column shows the real volume sent in the MILP model solution. In the case of table VII, all demand batches respect the maximum flow rate value (400m³/h), thus the demand operation contributes to find a tankage solution, by releasing routes use (alignments) for other movements. In this case, demand batches can start and end at any time within the H and they are not fixed to much lower flow rates than the nominal one, as it is the case in scenarios 6, 7, and 17, which respectively compute impractical (no operational) flow rates of 54, 13, and 15m³/h. Table VII also features, highlighted (*), the required volume values (REQUIRED_VOLUME) and reached (VOLUME) to the scenario 6. It can be observed differences in values, which show that the refinery delivers more product than needed. In fact, this can occur with demand operations (D), since inequalities (17) and (18) allowed an operational flow rate range. In addition, inequality (11) establishes that the final reached volume has to be greater than or equal the required volume, namely TOTALop. It is noteworthy that such an event does not violate the OF and it does not fail to reach the model goals. This can occur if there is an available tank with the product and it is not necessary to change alignments. An alignment can be defined as an active route, that is, an internal pipe segments that is used to transport a product between a pair tank/interface. Then a new movement is not inserted. ACS Paragon Plus Environment


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It is also worth remembering that if inequality (11) is replaced by an equation (equality), it would make the formulation more restrictive, since empty the tank means enabling for availability other loading, which contributes to the solution. TABLE VII. DEMAND BATCHES – MAXIMUM FLOW RATE SCENARIO

INTERFACE

REQUIRED VOLUME/H VOLUME (m3/h ) (m3)

BATCH

FLOW RATE (m3/h)

DURATION (h)

6

X- D

(*) 38880

54

2

400

35.69

75.83

7

D

9360

13

1

400

23.40

-----

P- D

10800

15

1

400

27.00

-----

17

TIME (h) BATCH 1 BATCH 2

393.31 429.00 696.60 720.00 0.00 – 27.00

VOLUME (m3)

463.00 538.83 ---------

(*) 44608

---------

10800

9360

Table VIII shows three scenarios (8, 13, and 16) where demand interface makes use of intermediate flow rates (between FLOWop and MAXFLOWop). FLOW RATE column shows these flow values, and the scenario 8 has two batches with maximum flow rate and three intermediate flow rates; the scenario 13 had ten batches with maximum flow rates and four intermediate flow rates; the scenario 16 with three maximum flows rates, with two intermediate, and one with minimum flow rate. This shows that the flow rate release to demand operation does not necessarily force maximum flow rate use. However, it is evident that the demand is not an uninterrupted operation as during production. This also shows the practical effect of flexible demand; Table VIII presents demand batches with maximum, minimum, and intermediate flow rates, respecting the imposed operating range by inequalities (17) and (18). TABLE VIII. DEMAND BATCHES – INTERMEDIARY FLOW RATES SCENARIO

INTERFACE

VOLUME

FLOW RATE VALUES PRESENTED BY DEMAND BATCHES (m3/h)

NUMBER OF

3

8 13 16

P-D-Y P-D-Y P- X- D

(m ) BATCHES 126000 5 523440 14 186480 6

MAX

400.00 1163.50 800.00

--------1022.59 ---------

INT

367.47 1008.71 ---------

MIN

316.25 1002.58 577.00

238.15 985.20 477.75

----------------259

The model run time limit was set to 36,000 seconds (T), or 10 hours. However, in some scenarios the model did not reach a solution in this time presenting a burst of memory capacity before attaining this time limit. These values are shown on T column at Table VI. Moreover, the integrality gap for these scenarios has not also reached a null value within the available processing time. Thus, an iterative algorithm is developed in order to improve the model computational time. The MILP – IA proposed approach is described in the following section. ACS Paragon Plus Environment

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V. ITERATIVE ALGORITHM (MILP – IA) The iterative algorithm intends to improve the model computational time, using information computed by the model itself as input parameters for a new model run. Set movement variables to their minimum values (MIN_P, MIN_X, MIN_D, MIN_Y, and MIN_T) tends to contribute to solution convergence, avoiding searches in regions with unpractical solutions. In each iteration, these values of minimal movements are updated as values for PF, XF, DF, YF, TF of previous interactions, changing up the lower bounds. The results in Table VI (PF, XF, DF, YF, and TF) show that tankage implementation requires a larger movements’ number than those set out in Table V. Thus, this fact suggests that the values found in Table VI for PF, XF, DF, YF, and TF are closer to a better feasible solution than the minimum values suggested in Table V. However, there is no guarantee these values of Table VI are the optimal solution values, even in scenarios that were performed for 10 hours. Thus, the proposed iterative algorithm MILP – IA looks for a feasible solution with acceptable computational time for refinery activity scheduling. Therefore, the MILP model is informed in a feedback loop with new values for the movements’ minimum. An end condition is also introduced to stop computation, if the solution cannot be improved. Figure 10 shows the iterative algorithm flowchart used to improve the computational solution time presented in Table VI. The algorithm has three variables (m1, m2, and m_ret) and two parameters (MIN_T and k). The m1 variable saves the total movements’ number for the best solution; for each iteration, m2 is the considered movements’ minimum limit, and m_ret is the achievable movements’ number that is returned by the model for each iteration. The MIN_T parameter is the value presented in Table V and it is a characteristic of each scenario. It is used as minimum limit only to the first iteration. The parameter k is a coefficient that multiplies movements’ number of the last found solution in order to define the minimum threshold value for the next iteration. The algorithm is stopped when the optimal is attained or when it reaches the stop criterion. Such criterion is satisfied when the total movements’ number found in the iteration (m_ret) cannot be greater than movements’ number of the previous iteration m1. Each iteration (m_ret feedback) runs during a time called cycle time, or loop time (LT). ACS Paragon Plus Environment


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Table IX shows tests’ results for the choice of the k coefficient value. Scenario 5 is chosen for this test. This scenario presents movements involving four interfaces (P-X-D-Y). The scenario has been evaluated for five values of k, namely k = 0.9; 0.8; 0.7; 0.6; and, 0.5. The table shows eight columns herein mentioned: K (referring to the coefficient k values); OF values and GAP resulting from the iterative process at the last iteration; LT shows the loop time of 2900s for this scenario; T is the total time to find the solution; N is the iteration number until the algorithm reaches the stop criterion; VIOLATIONS column shows capacity violations CV and time violation TV; and, finally, achievable movements’ numbers is given by PF, XF, DF, YF, and TF. In particular, the LT value equals to 2900s corresponds to the adopted search time for the scenario 5 iterative solution. After this time, the solution value does not improve anymore. This fact was observed during the computational tests of Table VI. Thus, the value of 2900s was adopted as the loop time for the scenario 5. In Table IX, the test with k = 0.7 shows the best result. Although the lower GAP for k = 0.9, with k = 0.7 it was possible to reach a smaller computational time performing only two iterative algorithm cycles. In addition, there was no time or capacity violations and it is the solution with fewer movements. Begin

m1 = m2 = MIN_T

m_ret = Run Model (m2)

YES

Optimal NO

NO

m_ret > m1 YES

m1= m_ret

m2 = m_ret . k

End

Figure 10. Flowchart - Iterative Algorithm.


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TABLE IX. PERCENTAGE ASSESSMENT OF MINIMUM MOVEMENTS ADEQUACY – SCENARIO 5 (P-X-D-Y)

K

OF

0.9 0.8 0.7 0.6 0.5

24.000 23.475 22.000 24.972 23.000

GAP (%) 8.3 14.8 9.1 19.9 13.0

LT (s)

T (s)

N

2900

8783.79 5916.01 5807.53 5807.95 5808.65

3 2 2 2 2

CV (m3) 0 2376 0 0 0

VIOLATIONS TV (h) PV XV DV 0 0 0 0 0 0 0 0 0 0 0.97 0 0 0 0

YV 0 0 0 0 0

ACHIEVABLE NUMBER (FEASIBLE) OF MOVEMENTS PF XF DF YF TF 5 7 7 5 24 5 7 6 5 23 3 7 7 5 22 4 8 7 5 24 4 7 7 5 23

VI. MILP – IA RESULTS Table X shows the results of MILP–IA model for the same scenarios presented in Table V. Table X is a similar table to Table VI, added with the LT column showing the loop time for each scenario. The LT loop time values were experimentally obtained during model convergence to a final solution. The loop time corresponds to the moment in which the search algorithm converges. The results for scenario 1 show an increase in the OF value (12.213 in Table VI to 13.000 in Table X), caused by a greater movements’ number, meanwhile there are no more capacity violations (CV), as shown in Table VI. The scenario 5 results to a better solution than the previous one (no iterative algorithm), if we compare OF values (23.000 versus 22.000). The movements are reordered by interface, achieving a fewer movements’ number without violations occurrence. The scenarios 6 and 16 results show small changes in the OF value, due to small variations of tank capacity violations. On the other hand, the scenario 19 results showed a significant change in the OF value (51.147 versus 59.795) due to variation in time violations (YV). In this case, the time violation, given in hours, is more significant than the capacity violations, given in m³. The model seeks to minimize capacity and time violations, where hours (h) outweigh volume (m³). The α coefficient in OF reinforces the time factor, as reflected in the observed OF value at scenario 19. It is worth highlighting the results from scenarios 7 and 17, which are small scenarios compared to others. In such cases, the search reaches the optimal solution during the first iteration loop. Thus, as shown in the Figure 8 flowchart, the iteration is interrupted and the T total time value does not reach the LT loop time value. In general, the MILP model (Table VI) and MILP – IA model (Table X) results are similar in relation to interest variables presented in the OF (1): the total number of movements and the violations. The main advantage of the MILP – IA model is the computational time reduction to find a solution. ACS Paragon Plus Environment


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However, it is worth emphasizing that MILP – IA model is sensitive to the loop time (LT) definition. In this work, LT values were obtained experimentally, recorded from the moment the search process stops to converge. Future works may contribute in making further analysis in order to find methods to adjust this value. TABLE X. QUANTITATIVE RESULTS TO MILP-IA MODEL

SCENARIO

OF

GAP (%)

LT (s)

T (s)

N

CV (m3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

13.000 40.000 21.394 16.000 22.000 5.450 1.000 31.000 16.000 44.000 9.189 18.000 40.000 41.708 18.000 16.273 2.000 33.000 59.795 37.000

15.4 2.5 53.3 12.5 9.1 8.3 0.0 6.5 18.8 9.1 34.7 16.7 2.5 54.4 22.2 14.0 0.0 6.1 63.2 16.2

500.00 900.00 200.00 120.00 2900.00 300.00 30.00 3500.00 400.00 14000.00 60.00 1700.00 1800.00 5500.00 500.00 2500.00 60.00 6000.00 4200.00 7200.00

1003.76 3614.04 409.78 242.83 5807.53 603.68 0.08 10507.68 802.80 28003.93 123.14 4047.76 5403.80 11009.36 1119.44 5203.65 0.14 12005.07 8806.13 29401.20

2 4 2 2 2 2 1 3 2 2 2 2 3 2 2 2 1 2 2 4

0 0 0 0 0 2267 0 0 0 0 943 0 0 0 0 1366 0 0 0 0

VIOLATIONS TV (h) PV XV DV 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

YV 0 0 6.39 0 0 0 0 0 0 0 0 0 0 13.71 0 0 0 0 26.80 0

ACHIEVABLE NUMBER (FEASIBLE) OF MOVEMENTS PF XF DF YF TF 5 0 0 8 13 15 6 19 0 40 8 0 0 7 15 7 0 1 8 16 3 7 7 5 22 0 3 2 0 5 0 0 1 0 1 13 0 5 13 31 7 0 1 8 16 20 0 3 21 44 5 0 0 4 9 7 0 0 11 18 18 0 14 8 40 15 0 0 13 28 8 0 1 9 18 4 6 6 0 16 1 0 1 0 2 15 0 7 11 33 15 0 1 16 32 16 0 3 18 37

Figure 11 highlights the comparison between some important results in Table VI (MILP model) and in Table X (MILP – IA). This figure indicates the OF value and the T total computational time for each scenario. In fifteen of twenty scenarios, the MILP – IA approach obtained the same OF value given by the MILP model, which shows that the solution quality is indeed maintained. The bigger difference in OF values (14.5%) occurred in scenario 19, only due to variation in time violations (YV). However, the results for the MILP – IA in scenario 19 show that other time (PV, XV, DV) and capacity violations kept null and the minimum number of movements was the same obtained by the MILP model (32). Figure 11 also highlights that the computational time to find solutions with the MILP – IA can be much smaller than the MILP model, as in scenarios 2 and 11. A time reduction in order of 10 hours to 1 hour, for scenario 2, and 8 hours to 2 minutes, in scenario 11, were observed. Even though in scenarios with (LT) loop time higher, so with T total times larger, such as scenarios 10 and 20, a computational time ACS Paragon Plus Environment

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gain is achieved. It is also worth emphasizing that in scenarios 2 and 20, the iterative algorithm performs 4 loops to achieve stop criterion and yet, in both scenarios, the solution is obtained in reduced computational time, when compared to the model without iterative algorithm.

Figure 11. Model MILP x MILP – IA. Objective Function (OF) and Computational Time Comparisons.

N. Tanks’ Scheduling Computation (Inventory Profiles) Figure 12 illustrates the R2 refinery tanks dynamic behavior during the H in the month M1 (scenario 5 of Table I). The scenario has five tanks (T1_C5, T2_C5, T3_C5, T4_C5, and T5_C5) storing PD4 product, each one with opening stocks. The stock tanks evolution computed by the MILP-IA model is shown in Figures 12a-12e. Each figure shows temporal evolution of stock profiles in each tank. The refinery loading and unloading operations for this product consist of receiving and sending through four interfaces (P-X-D-Y). Figure 12a shows the stock evolution at T1_C5, where there were four events, one loading and three unloading operations. The first two events correspond to a product sending to pipeline (Y) and the last one is a sending to demand (D); the third event is a product receiving by pipeline (X). ACS Paragon Plus Environment


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Figure 12b shows the stock evolution of T2_C5 tank, where there were seven loading and unloading events. The figure highlights the occurrence of two events that require a set up time. The loading operation stop is a penalty to the process. It is ideal that as soon as set up time is over, the stored product be shipped because a new receiving implies to a new setup time waiting. This situation is in accordance with 2 and 26 inequalities, which govern the tank operating cycles and the timing and events sequencing, respectively. The relaxation to evaluate tanks’ allocation affects the time issues, since for each product receiving also a tank time out occurs during four hours. However, it is noteworthy that the generated movements’ number is minimized at OF, equation (1), and this fact helps avoiding the observed situation. Figure 12c shows the stock evolution at T4_C5, where there was just an unloading event. The tank kept the stock during most of its scheduling and only near the time instant t = 300h, it was scheduled to send to pipeline. This tank content is used to support a feasible scheduling. The stored product is used to supply the shipment to the pipeline (scheduled by the pipelines’ scheduler) and avoid, for example, a break of a batch coming from another tank. Figure 12d shows the stock evolution in T3_C5, where there are six loading and unloading events. In this case, the tank receives and sends through four interfaces. The first and fifth events are product sending to the demand (D), the second and fourth events are pipeline receiving (X), the third event is a sending to pipeline (Y), and the last event is a receiving at the production (P). In this figure, a loading event that reaches the tank structural capacity limit is highlighted. After this, the tank cannot receive; the set up time during four hours (374 to 378 time instants) is respected before sending the product until the complete tank emptying. Figure 12e shows the stock evolution in T5_C5, where there were four loading and unloading events. As in T3_C5, in T5_C5 also occurs product receiving and shipping through the four interfaces (P-X-DY). A full tank unloading event (until the emptiness) to (Y) pipeline is highlighted. A loading event begins after few hours, corresponding to a receiving from (X) pipeline. However, the operation order established as send and then receive does not require a setup time, and it may be even instantly, without time interval.


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a)


T1_C5 Tank

d) T3_C5 Tank

b) T2_C5 Tank

c)

e)

T4_C5 Tank

T5_C5 Tank

Figure 12. Stock Profile (Scenario 5).

O. Movements Synchronism Checking (Fit of Batches - Scenario 5) This section purpose is to show that the tank farm operation model can indicate loading and unloading at the tanks in a synchronized mode with batch operations imposed by the external pipeline network scheduler. Scenario 5 of Table I was chosen because operations with all interfaces were performed. In this way, the sets are filled as follows: TK={1,...,5}, OPP={1}, OPX={1,...,7}, OPD={1}, OPY={1,...,5}, and BT={1,...,30}. Note that Scenario 5 had interfaces with P-X-D-Y operations, thus the five involved tanks (Table I) can send and receive through any of these fourteen operations (sum of subsets OPP-OPX-OPD-OPY sizes) and each operation is broken into thirty batches. Figures 11-14 illustrate movements’ profiles at interfaces (P-X-D-Y) for R2 refinery during the H of M1 month. By these figures it can be graphically observed that production is a continuous operation and the others are discontinuous operations. Tables XI-XIV show that the tank farm operation model rigorously meets the time imposed by the pipeline scheduler.



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Figure 13 shows the continuous production operation profile with batches’ breaks. Each line represents a product batch that is moved from production to any refinery tank. In this case three different tanks (T5_C5, T2_C5, and T3_C5) are used to receive product from production (P interface). As the product flow is continuous, it is observed that the lines are ordered without interruptions (one after another). Each line represents an internal batch loading a tank. Each batch moves certain product volume, represented by different line segments. However, the segments’ slope is the same, since the flow rate is constant in production operation.

Figure 13. Production Operation Profile (Scenario 5 - Interface P).

Table XI shows the (P) production batches internal details. As in the Figure 13, the batches are also ordered in chronological order resulting in the tank receiving sequence: T5_C5, T2_C5, and T3_C5. According to table, the flow rate is constant for all three batches, as well as the operation are continuous (without time interruption). Each tank receives a different volume, and these three batches’ volumes sum results in total received product through the P interface, during the month. This value checks against the planned value (required value) for monthly production.

TABLE XI. PRODUCTION BATCHES (P INTERFACE - SCENARIO 5) BATCH

1 2 3

TIME (h)

FLOW

DURATION

RATE

(h)

START

END

VOLUME

(m3)

(m3/h) 121.00 121.00 121.00

100 328 292

0 100 428

100 428 720

12100.00 39688.00 35332.00 TOTAL (m3)

REQUIRED VOLUME (m3)

TANK

T5_C5 T2_C5 T3_C5 87120.00 87120.00

Figure 14 shows the demand operation profile. Each line is a product batch that is moved from a tank to the refinery local demand. In this case, four different tanks (T3_C5, T2_C5, T1_C5, and T5_C5) are ACS Paragon Plus Environment

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used to send the product through D interface. Each line is an internal batch, unloading tank to local demand. Different from what occurs in the production, here, besides the line segments size, the line segment slopes may also vary. This variation occurs because each batch may present a different flow rate. Moreover, two tanks, T2_C5 and T3_C5, were used to form more than one batch – three times the T2_C5 tank and twice the tank T3_C5.

Figure 14. Demand Operation Profile (Scenario 5 – D Interface).

Table XII shows (D) internal demand batch details. As in Figure 14, the seven batches are also ordered in chronological mode, generating a product sending by T3_C5, T2_C5, T3_C5, T2_C5, T1_C5, T5_C5, and T2_C5. According to this table, batches 1, 3, 5, 6, and 7 are sent with maximum flow rates of 800m³/h and the batch 2 and 4 have intermediate flow rates of 401.42m³/h and 502.92m³/h, respectively. The planning determines the monthly required demand; however, different flow rates generate a discontinuity in this operation during H. As can be seen in the TIME column, there is a time stop during 278 hours between batches 2 and 3, during 4 hours between batches 3 and 4, and 90 hours between batches 4 and 5. In addition, the batch 7 sending ends before the 720 hours of the H, with a gap of 37 hours. Thus, for a scheduling horizon of 720 hours, any demand sending operation occurs during 409h. This demand free time is a benefit to the refinery operation because the routes are free to be used by other interfaces’ movements. The sum of the seven batches’ volumes results in the monthly total demand sent through the D interface. And this value is slightly higher than the planned value (required value) to the demand, but it does not harm the model formulation, as it was exemplified in highlighted example (*) in Table VII.



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Figure 15 shows the by pipeline receiving operations profile (X interface). As the pipeline operations are discontinuous, the lines are ordered, but temporally spaced apart. The batches correspond to loading tank events, namely from pipeline to the tank. Each receiving operations must occur at defined time (according to the pipelines’ scheduler). This means that in these exactly periods, some tank shall be provided to receive the product. In this case, the four different tanks received product from pipeline (T1_C5, T2_C5, T3_C5, and T5_C5). Some tanks are required in more than one batch receiving. TABLE XII. DEMAND BATCHES (D INTERFACE – SCENARIO 5) BATCH

1 2 3 4 5 6 7

FLOW RATE

(m3/h) 800.00 401.42 800.00 502.92 800.00 800.00 800.00

DURATION

TIME (h)

VOLUME

(h)

START

END

(m3)

22 78 50 79 18 22 42

0 22 378 432 601 619 641

22 100 428 511 619 641 683

17600.00 31310.76 40000.00 39730.68 14400.00 17600.00 33600.00

TOTAL (m3) 3

REQUIRED VOLUME (m

)

TANK

T3_C5 T2_C5 T3_C5 T2_C5 T1_C5 T5_C5 T2_C5 194241.44 193680.00

Figure 15. By Pipeline Receiving Operations Profile (Scenario 5 – X Interface).

Table XIII details internal batches’ operations that occur at the X interface. Seven batches are ordered in chronological mode, corresponding to sending product to tanks T3_C5, T3_C5, T5_C5, T2_C5, T1_C5, T2_C5, and T2_C5. Each of these batches has internal volume, time (duration), and flow rates defined by the pipelines’ scheduler. MILP-IA model just performs the refinery tankage so that these values must be respected, including the sum of all amounts received through pipelines. It is noteworthy that all the values presented in Table XIII are the same required by the pipelines’ scheduler.


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Moreover, the breakage occurring between the batches 4 and 5 is required by the external network scheduling and it is not a necessity of the tank farm operation model.

TABLE XIII. RECEIVING BATCHES FROM PIPELINES (X INTERFACE – SCENARIO 5) BATCH

1 2 3 4 5 6 7

TIME (h)

FLOW

DURATION

RATE

(h)

START

END

VOLUME

(m3)

(m3/h) 1050 600 1000 600 1000 645 900

9 56 18 11 12 18 20

56 318 412 511 522 571 617

65 374 430 522 534 589 637

9450.00 33600.00 18000.00 6600.00 12000.00 11610.00 18000.00

TOTAL (m3) REQUIRED VOLUME (m3)

TANK

T3_C5 T3_C5 T5_C5 T2_C5 T1_C5 T2_C5 T2_C5 109260.00 109260.00

Figure 16 shows the by pipeline sending operations profile (Y interface). Similarly as in X interface, the internal batches are also represented by ordered lines with different sizes and time delayed. Now the internal batches correspond to product unloading events, i.e. from tank to pipeline. As in the previous case, shipping operations should occur in the time set by the pipelines’ scheduler, forcing the tank allocation for these periods. The tanks must contain the product in question, and they must be available to make the shipment. In the scenario presented in Figure 16, four tanks were allocated to send products to pipelines (T1_C5, T3_C5, T4_C5, and T5_C5). Moreover the tank T1_C5 is used by two batches.

Figure 16. By Pipeline Sending Operations Profile (Scenario 5 - Y Interface).

Table XIV details internal batches’ sending to the Y interface. Seven batches are chronologically ordered and sent to tanks T1_C5, T3_C5, T1_C5, T4_C5, and T5_C5. Just as in the previous case, these batches have internal volumes, time (duration), and flow rates defined by the pipelines’ scheduler. Thus MILP-IA model performs the refinery tank farm based on these values.



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TABLE XIV. PIPELINES SENDING BATCHES (Y INTERFACE - SCENARIO 5) BATCH

1 2 3 4 5

TIME (h)

FLOW

DURATION

RATE

(h)

VOLUME

START

END

(m3)

(m3/h) 500 433 455 413 548

10 51 11 12 22

32 101 266 299 381

42 152 277 311 403

5000.00 22083.00 5005.00 4956.00 12056.00

TOTAL (m3) REQUIRED VOLUME (m3)

TANK

T1_C5 T3_C5 T1_C5 T4_C5 T5_C5 49100.00 49100.00

The five tanks (T1_C5, T2_C5, T3_C5, T4_C5, and T5_C5) involved in scenario 5 are shared in operations concerning the four interfaces (P-X-D-Y). It is important to highlight that each tank can perform one operation at time. Therefore, when a tank is allocated to move a product to an interface, this tank is disabled to operate with the other (model assumption in section III). For example, a tank receives product at some time, but for other interval over H, this same tank can load/unload product with other interfaces or it can also be on standby. Cases of sporadic tank capacity violation and even time violation in batches are explored hereinafter. The examples of Figures 12 to 16 and the content of Tables XI to XIV detail the obtained tank farm operation model solution, which had no violations in 14 out of 20 tested scenarios. The MILP-IA model takes into account structural and operational issues from the tank farm and manages the inventory in each scenario tank for attending the refinery production planning and local demand requirements, at the same time that was able to respect hard time-windows imposed by the pipeline scheduler (1). The minimization of movements’ number was another factor addressed by the MILP-IA model, which contributes to feasible procedures involved in the internal refinery alignments of pumps and valves, as hereafter exploited in section Q. P. Time and Capacity Violations Figure 17 shows the stock evolution in a tank scenario 16 (T1_C16), where there are six loading and unloading events. In this case it is highlighted an occurrence of a maximum capacity violation after a production reception. The tank remains overcharged for 8 hours. This is undesirable because, in practice, it requires a resource re-allocation. However, the violation values in figure are small if compared to the tank capacity value and they are even smaller if compared to the tank farm aggregate ACS Paragon Plus Environment

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capacity, as presented in the preliminary Table VI results. Further, according to the MILP-IA model results at Table X, one can observe that capacity violations (CV column) occurred in only three scenarios (6, 11, and 16), and for low values if compared to the tanks’ capacities.

Figure 17. Stock Profile (Scenario 16 - T1_C16 Tank).

The production (P) is a single operation through 720 hours. It can be broken in internal batches without time spacing between them (continuous operation). The same goes for the (D) demand operation with the difference that this is a discontinuous operation, due to the time spacing between internal batches caused by different flow rates. However the MILP-IA model considers the operations involving pipelines in a different way. The interfaces’ movements (X and Y) are generated by the pipelines’ scheduler. Each of these movements corresponds to an operation into the model. So there is the production operation, the demand operation, pipeline receiving operations and pipeline sending operations. Each of X and Y operations does not occur during 720 hours, but it has a time length defined by the pipelines’ scheduler. Figure 18 shows the pipeline sending operations (Y interface) profile for the scenario 3. There are operations corresponding to five external batches that are broken into seven internal batches corresponding to tank unloading operations. As previously illustrated in Figure 8b, the external batch m1 is broken into two internal batches (m1a and m1b). This difference in the number of external and internal batches is due to the break occurred in the operations 3 and 5. In the spotlight, note that the operation 3 has been broken into two uninterrupted internal batches (one after another). The operation 5



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was also broken into two internal batches, but there is a time delay between them. This delay generates a time violation in the operation, as hereafter described.

Figure 18. Pipeline Sending Operations Profile (Scenario 3 - Y Interface).

Table XV details external pipeline batches generated by the pipelines’ scheduler proposed in (1) and the internal batches generated by the proposed model (MILP-IA). For both, the flow rates, duration, start time and end time, and the movements’ volume are presented. It can be observed that this scheduling defines five external batches, or five pipeline sending operations (Y). Thus, the MIN_Y model parameter value is 5 and it represents the minimum internal batches that MILP-IA is expected to generate, as it can be seen in Table V, scenario 3. For these five operations, the MILP-IA model generates seven internal batches chronologically ordered, and discharged from tanks T1_C3, T3_C3, T2_C3, T1_C3, T3_C3, T2_C3, and T1_C3. As already mentioned, the breaks occur in operations 3 and 5, but even with the breaks, the flow rates defined by pipelines’ scheduler should be maintained. This condition requires that, in order to not violate the imposed times, internal batches’ operations be sequenced. This is what happens in the operation 3 (internal batches and 3_A and 3_B), where the flow rate, the moved volume, and the operation start and end times are respected. On the other hand, the operation 5 breaks are not immediately sequenced. This fact generates delays in the operation start time and, therefore, an end time violation. ACS Paragon Plus Environment

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The Table X column YV shows a time violation of 6.39 hours for this scenario 5, corresponding to the difference between the operation 5 end time (687) and internal batch 5_B end time (693.39). It is important to remember that time violations, although possible, do not invalidate the refinery tank farm operation solution but they may represent a real feedback from the production plant to the pipelines’ scheduler. TABLE XV. PIPELINES SENDING BATCHES - SCENARIO 3 PIPELINES’ SCHEDULER (1)

MILP PROPOSED (MILP-IA) TANK

OPERATIONS (EXTERNAL BATCH) 1 2 3 4 5

TIME (h)

FLOW

DURATION

RATE

(h)

START

END

VOLUME

(m3)

(m3/h) 407 500 422

29 24 28

152 357 423

181 381 451

11803 12000 11816

500 500

24 16

613 671

637 687

12000 8000

INTERNAL BATCH 1 2 3_A 3_B 4 5_A 5_B

1 2 3 4 5 6 7

TIME (h)

FLOW

DURATION

(m3/h)

(h)

START

END

VOLUME

(m3)

407 500 422 422 500 500 500

29 24 21 7 24 13.26 2.74

152 357 423 444 613 673.74 690.65

181 381 444 451 637 687 693.39

11803.00 12000.00 8862.00 2954.00 12000.00 6630.00 1370.00

TOTAL (m3) REQUIRED VOLUME

T1_C3 T3_C3 T2_C3 T1_C3 T3_C3 T2_C3 T1_C3

55619.00 55619.00

(m3)

The tankage violations indicated in scenarios 6, 11, and 16 of Table X were relatively small in comparison to the involved volumes. The temporal violations of just three scenarios out of twenty (3, 14, and 19 of Table X) came from time-windows imposed by the pipeline scheduler in an upper layer, and such windows were determined based on aggregate tankage. The pipeline scheduler does not consider operational/temporal issues of each involved tank. Thus, temporal violations can be used as a feedback to the pipeline scheduler. In order to further investigate the storage violation issues, we tested the MILP model of section III. Mathematical Model with some formulation changes. The goal is to verify the feasibility of obtained solutions with respect to storage violations. The concept is to impose storage violation variables set to zero and do not explicitly indicate the model to search for solutions that minimize internal movements of refinery, factor 3 of equation (1). The modified model is herein labeled “MILPT” (T stands for testing model). The modifications made are indicate as follows: the Objective Function (31) of the MILP-T just includes the factor 2 of equation (1) and the additional constraint (32) imposes that no storage violations are allowed. This model was executed within cases of Table X that originally



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presented storage violations (scenarios 6, 11, and 16). The MILP-T just minimizes the temporal violations of time-windows imposed by the pipeline scheduler.

minimize z = − −−− − − +α ⋅ 1−42 43

∑ ∑(tvMin

op,bt

op∈OP bt∈BT 14 4444424444443

factor1

(31)

+tvMaxop,bt ) + − −−− −− 1−42 43 factor3

factor 2

∑ ∑(cvMin

tk ,bt

(32)

+cvMaxtk ,bt ) = 0

tk∈TKbt∈BT

Table XVI follows the same labels presented within the manuscript. The CV column shows the sum of all violations in capacity of tanks, in m3. The columns PV, XV, DV, and YV show the sum of the time violations (TV), in hours, for each interface. The columns PF, XF, DF, YF, and TF show the achievable movement number, i.e., the movements computed by the MILP-T model for each interface. Results for scenarios 6, 11, and 16 are highlighted in Table XVI. No storage violations are observed for these scenarios in relative low computational time. Thus, the model generates solutions that strictly respect storage conditions. A very small temporal violation was observed just for scenario 11, but we remember that temporal violations were not prohibited in MILP-T. However, the number of internal movements (PF, XF, DF, YF, and TF) within the MILP-IA model increased significantly for all tested scenarios. If we just take the TF value we can notice increases from, respectively, 5 to 10, 9 to 14, and 16 to 23 (see Table X). This fact can be a complicating issue to the management of routing procedures. With this additional experiment, we intend to show that the model is able to find solutions with no storage violations, but we allowed some relative small violations to occur as an opportunity for the model to suggest answers that are more suitable for routing purposes. The decision maker can balance the involved capacity/temporal issues and choose the more suitable solution.

TABLE XVI. QUANTITATIVE RESULTS OF MILP-T FOR SCENARIOS 6, 11, AND 16

SCENARIO / MODEL 6 / MILP-T 11 / MILP-T 16 / MILP-T

T (s) 1.09 25.09 39.28

CV (m3) 0 0 0

VIOLATIONS TV (h) PV XV DV 0 0 0 0 0 0 0 0 0

YV 0 0.021 0


PF 0 7 7

NUMBER OF FEASIBLE MOVEMENTS XF DF YF 7 3 0 0 0 7 7 9 0

TF 10 14 23

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Q. Movements Minimization Analysis Figures 19 and 20 show the GANTT charts representing the dynamic behavior of the R3 Refinery tank farm for months M1 and M2. For both figures, GANTT 1 shows the movements in the refinery as computed by the MILP model with changes in OF (without factor 3), the restrictions 17 and 18, and with the exclusion of restrictions 4, 5, 6, 7, and 8. These changes require two conditions: movements are not minimized in OF and the demand conditions are hard (continuous operation and constant flow rate). On the other hand, GANTT 2 shows MILP-IA model results applied to the scenarios. Remember that the model performs each individual scenario. That is, the Gantt of Figure 19 corresponds to results for the scenarios 6, 7, and 8 concatenated into a single chart. The same occurs with the Gantt of Figure 20, showing the results concatenated for the scenarios 17 and 18. Figure 19 shows the refinery R3 tanks (GANTT 1 and GANTT 2) scheduling in month M1. These graphs represent the movements that have occurred in the scenarios 6, 7, and 8 using thirteen tanks to move three product types PD1, PD3, and PD4 (see Table I). Seventy (70) movements (internal batches) occur in GANTT 1. It can be seen that in some cases, as first events in T2_C6 and T3_C6, there is a sequence of short duration batches that move a low amount of volume. Such movements are undesirable from an operational point of view, because they imply in excessive exchange of routes (alignments), underdoing the refinery structural capacity. The GANTT 2 shows another reality; first the internal batches’ number fell sharply to 37 movements in the month. This represents a significant advance from the plant operational point of view, decreasing the need for alignment exchanges and the tanks maximum and minimum capacities are better used. Also, it aids the programmer work, as it reduces the possibility of conflicts between routes in the physical plant. In GANTT 1, T2_C6 and T3_C6 tanks are much requested while in GANTT 2 they are not required. In addition, the GANTT 2 displays a noticeable decrease in movements’ number to tanks in scenario 8. This is not only the model attempt to minimize the movements, but also by the flexibility on demand usage. An exception has occurred to scenario 7: the demand was not relaxed, keeping GANTT 1 and GANTT 2 with the same condition. The PD3 product movement required the T1_C7 tank use throughout the H, and this movement has occurred with nominal flow rate (the lowest). The scheduling for the three different ACS Paragon Plus Environment


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scenarios were run in the MILP-IA approach, and scenario 7 only consists of a single sending demand. As any resource dispute with other interfaces is necessary, the model kept the nominal flow rate.

Figure 19. Month M1 Refinery R3 Tankage GANTT Graphic (Scenarios 6, 7, and 8).

Figure 20 shows the tanks’ scheduling (GANTT 1 and GANTT 2) to the R3 refinery in the month M2. These graphs represent the movements that have occurred in the scenarios 17 and 18 using twelve tanks to move both products PD3 and PD4 (see Table I). Fifty six (56) movements (internal batches) occur in GANTT 1. As in the previous case, the GANTT 1 shows several batches with short duration. These types of batches do not occur in the GANTT 2 dynamics. The GANTT 2 shows only 35 movements in the internal batches number for the month. This fact represents a significant advantage from the operational point of view. For scenario 17, T2_C17 and T3_C17 tanks are allocated throughout the H in the GANTT 1. In GANTT 2, T1_C17 is allocated to receive production and T2_C17 is allocated to send demand, but with a much shorter duration. This advantage is allowed by flexible demand. It can be still seen in scenario 18, GANTT 2, that structural capabilities are better explored by releasing three tanks T1_C18, T2_C18, and T9_C18. It is worth emphasizing that this tanks’ liberation will be effective only from a tank individual analysis, because standing tank (without loading or unloading) does not mean empty tank (free to receive another product). Furthermore, the MILP-IA model considers that the tanks are dedicated by product (assumption A2). Thus, within the proposed model, different products cannot be received in the same tank during the considered scenario.


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Figure 20. Month M2 Refinery R3 Tankage GANTT Graphic (Scenarios 17 and 18).

VII. CONCLUSION This work has addressed the tank farm operation problem (TFOP) in refineries. A MILP iterative model, called MILP-IA, is proposed. This model is developed from a continuous time representation and it takes into account the resources usage in order to make possible the integration between domestic production, local demand, and pipelines’ movements, as illustrated in Figure 3. Real data scenarios are considered, as exemplified in Table 1 to Table 3. The scenarios were obtained from the planning of refineries and external pipeline network scheduling (1). The proposed model looks for a feasible scheduling, which minimizes the movements within the refinery tank farm, in order to respect imposed operational and structural conditions. The results indicate that the proposed model finds solutions in computational times of minutes, taking into account temporal conditions and monthly volume of each of the interfaces: supply from production (P) or from pipeline (X); delivery to local demand (D) or to pipeline (Y). In addition, the focus is to find an integrated solution that, based on information from the pipelines’ scheduler (1), enables to generate the scheduling in tanks. With the proposed MILP-IA model, before considered aggregate tankage, now becomes individual to each tank. This fact makes possible to know loading and unloading events’ details (their times, volumes, origins, and destinations) in each tank during the considered period (720 hours).



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It is noteworthy that the scenarios take into account data such as the operational flow rate values, between minimum and maximum, in the monthly demand planning. The flexible demand solution obtained by MILP-IA model can, in some specific conditions, be difficult to be implemented in the operating level due to, for example, the suggestion of sending operations not respecting turn shifts. More granular information with, for instance, the refinery daily local demand rates, breaking the demand in more than one operation, would allow the tank farm operation solution closest to operational details. Furthermore, it is important to remember that the model fulfils the objective of minimizing the movements’ number to facilitate the plant operational tasks (search for routes - routing). The refinery TS operations make use of routes (paths) formed by pipelines’ segments, valves, and manifolds, among other equipment. These routes between the origin-tank or tank-destination when busy, cannot be shared, causing a neck at the plant. Thereby the demand flexibility and these movements minimization in the MILP-IA solution allow for decreased use of routes, generating routes’ gaps, which contribute to the internal movements operational feasible (lower conflicts possibility) to the refinery. One objective for future works suggests checking the solutions appointed by the tank farm operation model using a software that performs the search for routes (routing of Figure 2). We also suggest the implementation of a discrete-time MILP model to confront the results of this work. To search for more compact and computationally efficient MILP formulations for the proposed problem is also a future goal. According to Table X, some time-windows imposed by (1) are violated. Therefore, an overlapping of operations taking place at refinery tanks can occur. In practice, operators can prevent these situations by applying relocation of products within the set of tanks. So, a possible approach for future developments is the formulation of a model that allows exchange of products in tanks, to permit such operational condition. Finally, we highlight that the proposed iterative algorithm seeks to find applicable solutions for a time horizon of 720 hours in viable computational times. Not necessarily optimal solutions were obtained, but they can contribute to aid the plant activities in operational level.


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ACKNOWLEDGEMENTS This work receives financial support from the ANP/FINEP (PRH-ANP/FINEP, PRH10/UTFPR), PRH-PETROBRAS

(Agreement

6000.0067933.11.4),

CENPES-PETROBRAS

(TC

0050.0049573.09.9) and CNPq (grants 305405/2012-8, 305816/2014-4, and 309119/2015-4). We are also thankful for the suggestions made by the anonymous reviewers, which helped us improving the paper quality.

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MILP Model for the Tank Farm Operation Problem of Finished

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