Crude-Oil Operations under Uncertainty: A Continuous-Time

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Crude Oil Operations under Uncertainty: A Continuous-time Rescheduling Framework and a Simulation Environment for Validation Zihao Wang, Zukui Li, Yiping Feng, and Gang Rong Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01108 • Publication Date (Web): 09 Sep 2016 Downloaded from http://pubs.acs.org on September 29, 2016

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Industrial & Engineering Chemistry Research

Crude Oil Operations under Uncertainty: A Continuous-time Rescheduling Framework and a Simulation Environment for Validation Zihao Wang a, Zukui Lib, Yiping Feng a, Gang Rong a ,* a

State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and

Control, Zhejiang University, Hangzhou, 310027, P.R.China. b

Department of Chemical and Materials Engineering, University of Alberta, Edmonton,

Alberta, T6G2V4, Canada

Corresponding Author *E-mail: [email protected]. Tel: 086-571-87953145. ABSTRACT This work presents a novel rescheduling framework of the crude oil operations based on a continuous-time representation. Abnormal events and uncertainties in the crude oil tank farm area are considered and analyzed in this framework to improve the robustness of the final plan. A rescheduling model is proposed to handle the various uncertainties. Some managerial experiences and consistency rules can be set in the model for different needs and scenarios. A multi-agent based simulator is developed as the validation part with uncertainties to simulate the real-world operations and test the optimization results. The goal of the rescheduling framework is providing a feasible and flexible robust plan and dealing with the disruptive events and uncertainties at the same time. The results of the case studies indicate our framework can support dynamic optimization of crude oil operations under complex real-world environments.

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1. INTRODUCTION Today’s petrochemical enterprises are under highly competitive global markets. These companies are pressurized to use different kinds of technologies to increase the marginal profit, enhance the production efficiency and also keep the production process stable and running continuously. Among these technologies production planning and scheduling can help the plants assign different materials, resources and make production plan to increase the overall operational efficiency and meet the market demands. However, most of the current works in planning and scheduling are made under deterministic conditions where all the parameters are considered known. In practice, uncertainty is an important aspect during scheduling process since many parameters are not known at first. These uncertain situations may cause the delay of material transfer, production oversupply, demand shortage, breakdown of processing facilities. These unstable circumstances will further cause the stopping of production process, increased product cost, lower profit, unqualified products and safety issues. In essence, uncertainty consideration plays the role of validating the use of mathematical models and preserving plant feasibility and viability during operations.1 The scheduling problem under uncertainty will mainly address two key factors i) The generation of initial schedules. ii) The revision of execution reschedule. And these problems can be solved mainly by preventive scheduling and reactive scheduling.1 Preventive scheduling is usually made based on the strategic orders. The scheduling results decide the production and processing targets of different materials, transportation sequences, satisfy the production amount and due time requirements, and optimize the key performance index. The uncertainty parameters are considered beforehand in the preventive scheduling approaches. Thus, the plant will be able to produce a feasible, robust and optimal schedules beforehand to handle the uncertainties which may happen during the execution process. Several approaches are developed for preventive scheduling. These methods include stochastic programming methods, fuzzy programming methods and robust optimization methods.2-4 Stochastic scheduling is most often used for preventive scheduling. The original deterministic model is transformed when the related uncertainties are used as stochastic variables in the new model. And the new model is optimized to satisfy a certain performance

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criterion. These stochastic programming models can be further classified into two categories： two-stage or multi-stage stochastic programming; chance constraint programming based approach. Khor et al proposed a hybrid chance constrained methods to solve the uncertainties in the refinery planning model.5 The two-stage stochastic programming can be also transformed into multi-stage stochastic programming by treating binary variables in the first stage and the continuous variables can serve as a recourse in the second-stage problem.6 The chance-constraint based approach focus on the reliability of the system, which can be summarized as the probability of satisfying certain constraints.7 It was first introduced by Charnes, Cooper and Symonds.7 Li, et al.8 proposed a new chance-constrained method to solve the planning problem of refinery production operation. Mitra, et al.9 also applied the chance-constrained method for a multi-site, multiproduct supply chain planning problem. Nemirovski and Shapiro used the convex approximation to solve the chance constrained problem.10 Robust optimization methods will try to minimize the effects of disruptions on the performance measure, ensure the stability of the executing schedules and achieve a high level of performance in the future operation schedule. Mulvey, et al.11 developed the concept of Robust Optimization, and related early works of El Ghaoui, et al,12 Ben-Tal and Nemirovski13 and Bertsimas and Sim14 extended the framework of robust optimization, using uncertainty sets to describe the uncertain parameters. Lin, et al.15 considered the worst-case values in a bounded form of uncertain parameters with processing times, market demands and prices to address the scheduling problem. Li, et al further extended the robust optimization problem for robust linear optimization and robust mixed integer linear optimization.2 In their later work, they also studied the probabilistic guarantees on constraint satisfaction for robust counterpart optimization and studied the quality of the robust solutions.3, 4 Wang and Rong 16 also proposed a two-stage based model to deal with the preventive scheduling problem with ship arrival and demand fluctuation uncertainty. In their work, the model is based on discrete time formulation. Thus, the arrival time is a discrete value and the distribution of the demand uncertainty should be known at first by using fuzzing programming to approximate the chance constraint. The application of this work is limited. Besides, some disruptive events are still not considered in their work. These inner disruptive events will jeopardize the crude oil daily operations and also 3



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should be considered as well. Reactive scheduling is a process to modify the original schedule during the execution process to deal with different disturbances or changes. These uncertainties in the reactive scheduling process usually include disruptive events, rush order arrivals, order cancellation or machine breakdown.1 The reactive scheduling methods and actions usually rely on simple techniques and aim at giving a quick response to keep the consistency of previous schedules or providing a full scheduling of the tasks to be executed after the disruptions. According to the techniques presented in the literature for reactive scheduling problem, the approaches can be subdivided into Mixed Integer Linear Programming approach and heuristic approach. In the work of Vin and Ierapetritou17, they proposed a rescheduling approach by adding a penalty term in the objective function of a continuous-time scheduling formulation to satisfy the requirement of minimizing the changes from the original scheduling. The rescheduling methods proposed by Mendez and Cerdá18 will reassign the resources for the tasks that haven’t been processed and will reorder the sequence of the processing tasks in the next step. The rescheduling approaches based on the heuristic methods can give a quick response and generate a new order as soon as possible, however, it cannot ensure the optimality of the newly generated tasks. Adhitya, et al.19 studied the crude oil operations in a discrete time formulation. They separated crude oil tank farm area into different blocks and further adopted the related heuristic methods to handle the disruptions in the tank farm area. Furthermore, they proposed a model based rescheduling method which can analyze the status of the crude oil tank farm area and search all the feasible solution.20 Thus, a more robust solution can be acquired. There are two main formulations to model the planning and scheduling problem in a petrochemical plant: continuous-time formulation and discrete-time formulation. The discrete-time formulation can provide a reference grid of time for the operations competing for shared resources.21 But when the time horizon is divided into a number of time intervals of uniform durations and events, it usually leads to very large problem size. For example, to achieve a suitable approximation of crude oil scheduling problem, we use 8 hours as a batch time interval, which will generate 90 scheduling intervals and will lead the problem extremely hard to solve. In continuous-time models, events can potentially occur at any point in the continuous domain of time, thus require much less time intervals to describe the related operations. The resulting mathematical programming models in the continuous-time 4


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formulation usually have smaller size and require less computational efforts. There exists two major categories for the continuous-time formulation: global time model and unit-specific time model. Reddy, et al.22 firstly built a continuous-time mixed integer linear programming (MILP) formulation for the short-term scheduling of crude oil operations in refinery. Moro and Pinto23 developed a continuous model for the crude oil inventory management and used a discretization procedure for the inventory levels of the tank farm to generate a MILP problem. Jia, et al24 also developed a continuous model for the efficient scheduling of oil-refinery operations to take advantage of the relatively smaller number of variables and constraints to the discrete time formulation. Recent works of continuous-time scheduling model of crude oil scheduling can be found in these work of Chen et al25 and Li et al26. The reactive scheduling approaches are mainly focus on the model with discrete time formulation, few works have been reported for the continuous-time based works, especially for those with unit-specific time grid models. Recent work can be found in Zhang and Xu27. They proposed a two-stages rescheduling framework for the crude oil operations with global-time grid model. However, for the unit-specific time model, there are still several difficulties lie on the problem: 1) The schedules in the continuous-time model only provide the starting time status and ending time status in an event for a specific unit. When the uncertain event happens in the middle time of the original order, it is hard to locate the current schedule from the original unit-specific orders and give a quick response. 2) When the disruptive events happen, unlike the discrete-time model with multiple equal time-intervals, the continuous-time model cannot modify the original schedules directly from one interval to the next interval successively and easily keep the completeness and consistency of the original model. 3) When the disruptive events happen, some operational statistic data cannot be monitored or calculated immediately, (e.g. the data of component concentration should be evaluated in Chemical Lab). Moreover, due to the different length of time duration of schedules, the initial scheduling orders only provide the status in the boundary nodes like starting time point and ending time point, while the status like component concentration within the scheduling orders cannot be estimated accurately. Based on the former analysis, in this paper, we propose a novel rescheduling framework with a validation simulator for the continuous-time scheduling problem of crude oil operations in refinery. The initial optimization results are obtained as unit-specific event orders from the 5



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deterministic models. When the disruptive event happens or the uncertain information is obtained, we reevaluate the current status and give an estimation of the uncertain parameters. According to different types of uncertainties, a rescheduling model is developed to incorporate the reactive scheduling constraints and preventive scheduling constraints. Moreover, facing the necessity of keeping the consistency of the scheduling orders for stability issues, we adopt some specific rules and translate them into mathematical constraints. These constraints can be added into the rescheduling model according to user’s choice. To test the robustness and feasibility of the rescheduling framework, a validation platform is developed. The simulation platform will first transform the unit-specific orders into the global time event orders for every device in the crude oil tank farm area. An agent based simulator is developed to simulate the real-world operations and generate disruptive events and uncertainties. Once the disruptive event happens, the information will be gathered and put into the rescheduling model. The new orders generated from the rescheduling model will be executed in the simulation platform continuously until the end of the scheduling horizon. The rest of the paper is organized as follows. In Section 2, we present the scheduling problem with deterministic information and the scheduling problem under uncertainties. In Section 3, the rescheduling model with initial status constraints, consistency constraints, reactive scheduling constraints, preventive scheduling constraints is developed. Section 4 explains the simulation environment and the full rescheduling framework. In Section 5, the proposed framework is investigated through case studies. Section 6 concludes the paper.

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2. PROBLEM STATEMENT The short term scheduling problem of crude oil operation includes the unloading of crude oil from vessels to storage tanks after arrival at the refinery docking station, transferring the crude oil from storage tanks to charging tanks for blending operation, finally charging the mixed crude oil to crude-oil distillation units (CDU). The schedules generated should meet the final demand orders. The key information includes: a) Supply and demand data: estimated vessel arriving date, type and amount of arriving crudes, the specific demand orders from CDU b) Structure data: The number of storage tanks, charging tanks, crude-oil distillation units and the related connections c) Initial status: The initial inventory data, key component concentration in different tanks d) Operational information: The transportation ability between different devices, inventory capability of tanks. We assume the vessels cannot unload the crude oil simultaneously at the dock. The charging tanks cannot have input and output flow at the same time. One charging tank can feed multiple CDUs, while one CDU can only accept one type of mixed crude oil. The crudes are mixed completely and the CDU will process continuously during the scheduling horizon. 2.1 Deterministic scheduling The mathematical model of crude oil scheduling is referred from Furman, et al.28，This model uses the unit-specific continuous-time model and handles the synchronization of time events with material balances. The model is also modified according to the constraints of the scheduling problem in this section, e.g. multiple charging tanks with the same type of mixed oil can feed one CDU simultaneously. The detailed mathematical formulation is presented in the Supporting Information. The objective of the mathematical model aims at minimizing the operational cost during the scheduling horizon. The objective function is presented in eq 1. The first term is the unloading cost, the second term is the vessel waiting cost. Furthermore, the switching of crudes in CDU from one stable operation mode to another operation mode will cause economic loss. Thus, crude oil switching cost measured by the industrial regression data in CDU is punished by the third term. The last two terms represent the inventory cost.

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Crude-Oil Operations under Uncertainty: A Continuous-Time

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