Robust Engineering Strategy for Scheduling Optimization of

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A Robust Engineering Strategy for Scheduling Optimization of Refinery Fuel Gas System Gang Rong, Yi Zhang, Jiandong Zhang, Zuwei Liao, and Hao Zhao Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02894 • Publication Date (Web): 12 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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Industrial & Engineering Chemistry Research

A Robust Engineering Strategy for Scheduling Optimization of Refinery Fuel Gas System Gang Rong,∗,† Yi Zhang,† Jiandong Zhang,† Zuwei Liao,‡ and Hao Zhao† †State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, China ‡State Key Laboratory of Chemical Engineering, Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou, 310027, China E-mail: [email protected]

Abstract As a byproduct of the oil refining process, fuel gas is the primary energy source of refineries. Considering self-generated and purchased fuel gas simultaneously in an optimization model will cut down energy cost and reduce carbon emissions in oil refineries. A mixed-integer linear program (MILP) has been built in our previous work. However, due to the fluctuation in the fuel gas generation and consumption, theoretical scheduling solutions may become infeasible or inaccurate. This paper presents a robust engineering strategy for validating the model to variable conditions in four aspects: model precision, solving performance, optimization effect, and execution. The proposed strategy has been applied to a fuel gas system in one of the largest oil refineries (LRF) in China to ensure model feasibility, necessity, and effectiveness. The implementation results show that the proposed method reduces costs up to 5.63% through the single-period operational optimization and up to 7.76% in the multi-period scheduling.

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Introduction In order to keep business efficiency, oil refineries are increasingly concerned about improving the operational management of their complex processes. Mathematical programming is one of the most popular methods to deal with industrial problems, such as supply chain management (SCM), engineering design, resource procurement and assignment, etc. However, due to the lack of accurate description of processes and equipment, the theoretical optimal solution is sometimes unpractical or infeasible in the real-world production. In fact, as the physical properties and working conditions of equipement are changing, an optimization program cannot integrate all the precious details. Thus the inconsistency between the model-based result and the final executable solution is inevitable, unless we apply proper engineering strategies before implementing the mathematical model. Several theoretical methods have been developed to adjust models to the varying environment, such as data-driven optimization methods, 1–3 stochastic programming, 4,5 adaptive robust optimization, 6,7 etc. Industiral data is collected, filtered, and processed for building implicit and explicit models. For example, input-output regression models for equipment, uncertainty set for endogenous and exdogenous random factors, 8,9 prediction models for quality control and fault diagnosis are popular data-based techniques in industrial applications. All these data-driven models could be integrated to the planning and scheduling programs, resulting in a more robust and accurate solution than the nominal case. Accordingly, the engineering strategy is responsible for determining implementation details, such as the source of industrial data, the proper optimization approach, and suitable adjustment of model parameters. Considering the complex structure of energy network and its coupled relationship with the production system, refineries are desperate to explore the potential benefits from the integrated optimization research. 10–12 Global optimization algorithms for the enterprise-wide planning problems were also studied for accelerating the process of obtaining the optimal solution. 13–15 In the earlier research works, accurate unit models and environmental penalties were included in the mathematical model to improve its applicability. In 1998, Moro et al. 16 2


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developed a nonlinear planning model for refinery production, which was able to represent a general refinery topology and allowed the implementation of nonlinear process models. This framework was later extended to support sequential decisions at the scheduling level by Pinto et al. 17 and Joly et al. 18 Later, Micheletto et al. 19 presented a conceptual modeling framework for operational optimization of utility systems. The mixed-integer linear programming (MILP) model was integrated with the refinery database for the planning of a refinery utility system. This approach effectively optimized the financial performance of the thermoelectric plant without any capital investment. As the primary energy source in refinery, fuel gas is continuously generated and supplied to most of the consumers around the refinery via compressors and pipelines. Furthermore, fuel gas can be converted into other forms of energy, such as steam, electricity, and heat. Therefore, effective operational optimization of the fuel gas system can be very effective for the reduction of emission and energy costs in the refining process. Hasan et al. 20 proposed a design method for the fuel gas system. Zhang and Rong 21 established an MILP model for the multi-period scheduling optimization of fuel gas system, and then gave a marginal value analysis of the system to assist the engineering operation in refinery. Jagannath et al. 22 introduced a multi-period two-stage stochastic method to design and operate the fuel gas system. However, these models did not accurately consider the flow conditions (such as the pressure drop in the branches and loops) in the pipeline, therefore the results are sometimes inefficient and unrealistic. Zhang et al. 23 applied the generalized disjunctive programming (GDP) method to model the branching structure of the pipeline, and developed a simulationbased optimization approach to solve the nonlinear problem. The proposed solving approach was effective, but infeasibility may arise when the simulation platform encounters largescale problems. Therefore, a systematic validation procedure is necessary to be constructed to ensure the mathematical model satisfies the requirement of real-world application. In this context, the objective of this work is to design and implement a robust strategy to LRF, which solves the scheduling optimization problem efficiently and allocates fuels at the

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minimum cost. Meanwhile, we are dedicated to share the improvement and implementation details to engineers and researchers, especially to contribute the ideas about the interaction between models and decision-makers. This is the key for the transformation of planning and scheduling in the current petrochemical plants. The proposed engineering strategy extends the sources of industrial data, where a simulation platform and real-time database are integrated for the implementation and validation of the mathematical model. The main contributions of this works contain: (i) Through iterative updating parameters in pipeline models, the gap between the optimal solution and the exact performance is reduced significantly; (ii) The feasibility, necessity and effectiveness of the optimization model are validated, which ensure the model-driven results are applicable and executable in the real-world production; (iii) Engineering strategy allows the interaction among theoretical models, real-time industrial data and decision-makers; (iv) The optimal solution is implemented on field and reduces the total cost for running the fuel gas system. The rest of the paper is organized as follows: Section 2 describes the problem statement as well as the general features of the fuel gas system in LRF. Section 3 presents the mathematical formulation of the operational optimization problem, and briefly illustrates the simulationbased solving approach. Section 4 elaborates a systematic procedure to implement the model in Section 3 to the LRF. The LRF cases are optimized via the validation procedure in Section 5, and conclusions are given in the last section.

Problem statement Normally, the production process and the utility system are closely coupled, where the energy resources and materials need to be scheduled synchronously. Considering the branching and loop structure of the pipeline network, an MILP model was proposed to obtain the optimal plan of energy assignment and procurement for the fuel gas system in refinery. 23 However, the expected optimal results cannot be achieved by directly utilizing the previous model.

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All the parameters, constraints, and even the structure of the model have to be modified according to the industrial data and records from the real-time database. Thus a systematic engineering strategy deserves to be developed and shared for the industrial application of optimization models. In this work, the detailed implementation process and the strategy are illustrated by a real-world LRF case. At first, the typical fuel gas stream in a simple refinery are shown in Fig.1. 23 The dashed line in Fig.1 represents the gas flow, containing both low-pressure fuel gas (LP gas) and high-pressure fuel gas (HP gas). Most of the LP gas and HP gas will be transported to the LP/HP gas network, LP gas drum, and HP gas vessels. Due to the unsatisfied characteristic of low-pressure gas (LP gas), especially the high percentage of sulfide, no LP gas can be used as fuel directly. Consequently, LP gas is always compressed to higher pressure and then desulfurized in desufuration equipment to compensate the shortage of HP gas, because HP gas can be used as fuel directly by all the heaters and boilers. Before this conversion, LP gas is mostly stored in the gas drum, which is not drawn in both Fig.1 and Fig.2, but it can be regarded as a LP gas source in Fig.2. Like most refineries, HP gas is the primary energy material in LRF. Therefore, operational optimization of the fuel gas system can be focused on HP gas. The optimization problem can be stated as follows: given a set of fuel gas generating/consuming processes and a network of interconnections among the processes, it is desired to determine a scheduling scheme, so that the overall operating cost is minimized, and the processes receive fuel gas of adequate heating value. In the case study (section 5) and the supporting information, the heating value of various fuel types and the heat requirements of equipment are elaborated in detail. The pairing relationships between fuels and equipment are also shown in the supporting information. The simplified flowchart of LRF’s HP gas system is shown in Fig.2, where the pipeline network is represented by the solid lines. Each unit is represented by a polygon with the specific identification. As illustrated in Fig.2, there are 22 main units considered in the optimization problem.

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Figure 1: Schematic representation of a simple refinery process

Figure 2: Simplified flowchart of LRF’s HP gas system

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Among these units, I crude distillation unit (ICDU), II crude distillation unit (IICDU), boiler, I hydrogenator (IHD), II coker (IICK), sulfur plant (SP), II hydrogenator (IIHD), hydrogen plant (HDP), I hydrocracker (I HC), solvent deasphalting (SD), III reformer (III RF), III CDU, IV V hydrogenator (IV V HD), IV reformer (IV RF) and PX (P-Xylene) unit , which only consume but not produce fuel gas, are called as fuel gas consuming unit or fuel gas consumer. These units are denoted by rectangles in Fig.2. Refining units (RU), I coker (ICK), II FCC, III hydrogenator (IIIHD), disproportionation equipment (DE), II hydrocracker (II HC) and hydrocarbon recycle equipment (HR) are the main HP gas producers in LRF. HP gas compressed from low-pressure gas system is desulfurized by RU and ICK, containing desulfuration equipment. Compressor 1 (C1) and Compressor 2 (C2) in LRF are two important equipment to keep the energy balance of the fuel gas system. Load of these compressors will be increased when the capacity of gas drum is large. On the contrary, it will be decreased. Among these HP gas producers, ICK, IIIHD and IIHC not only produce HP gas but also consume HP gas from itself, which are called as self-producing-self-consuming unit. These units are identified by octagons in Fig.2. Heater in IV reformer is required to use fuel gas with high heating value, such as fuel gas from DE, so as to guarantee the quality of its reaction process. As a result, fuel gas from DE is sent to IV reformer directly. At the same time, DE only consumes HP gas from the pipeline network. This kind of unit is called as producing-and-consuming unit. Usually, fuel gas produced during the production process cannot satisfy the energy demand of the whole refinery. The deficit of energy demand is compensated by inputting supplement fuel, such as fuel oil, natural gas, hydrocarbon (C5) and liquefied petroleum gas (LPG). Besides fuel gas, some equipment (ICDU, IICDU, boiler, IIICDU, PX and DE) can consume fuel oil as their additional fuel, while C5 and LPG are alternative fuel for IIIRF, IVRF, PX and DE. According to Fig.1, these alternative fuels are also main products for the refinery, which means consuming these fuels is equivalent to cut down the selling profits. As a result, this LRF established a contract relationship with a nearby hydrogen plant,

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who supply a limited amount of natural gas every day. Thus natural gas becomes the prior alternative fuel, and its transportation and inventory cost can be ignored.

Mathematical model In this section, the scheduling model for the fuel gas system is briefly introduced, and some detailed constraints in our previous work are reviewed in supporting information. Through generalized disjunctive programming (GDP), the complex structure of the pipeline network and the operation of compressors are introduced to the traditional fuel gas optimization model. However, flowrate constraints for the loop pipeline bring nonlinearity to the model. Through applying the simulation-based solving approach in our pervious work, 23 the parameters in a linear relaxation of the nonlinear constraint will be iteratively updated. Thus, the nonlinear formulation was replaced with a sequential MILP problems and the solving efficiency was improved significantly. The details about the simulation model will be illustrated in Section 4.1. The operational optimization model of the fuel gas system in LRF is constructed based on the simplified flowchart of HP gas system in Fig.2. Energy demands, unit capacity bounds and cost coefficients are given in the supporting information. Consequently, the scheduling problem can be formulated as follows: Objective function The objective of the optimization model is to minimize the total operating cost of the fuel gas system, including purchasing and penalty costs. The costs of four kinds of energy materials are considered, containing fuel oil (FO), natural gas (NG), liquefied petroleum gas (LPG), hydrocarbon (C5), which are defined as the first term in Eq.(1). The second term is the conversion cost for LP gas, and the penalty cost for LP gas emission is denoted as the third term. Sometimes a few amount of HP gas flees to LP gas, and these wasted HP gas has to be compressed again before being utilized as fuels. The cost of the transformation

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from HP gas to LP gas is denoted as the last term. M in C =

X k

Ck

T X X t=1

Fk,j,t + CLP 2HP

T X X t=1

j

F Cc,t +Cemi

T X

c

Femi,t + CHP 2LP

t=1

T X

FHP 2LP,t (1)

t=1

Material balance for fuel gas producing units The material balance for the LP gas drum is represented as Eq.(2), which means the amount of fuel gas in the gas drum equals to the sum of inventory at the last period and the newly-produced LP gas. At each period, part of the LP gas will be compressed to HP gas, which is also considered in the balance constraint. Similarly, the material balance for HP gas vessels is illustrated in Eq.(3). The additional material balance constraints for HP gas consumed by equipment are defined as Eqs.(4)-(5). F GG,t = F GG,t−1 + (F PLP,t + FHP 2LP,t − F Cc,t )∆t

F GV,t = F GV,t−1 + (

X

Fi,t + P CN G,t −

i

X

Fj,t −

X

j

Fi,t =

X

FN G,j,t − FHP 2LP,t )∆t

(2)

(3)

j

Fi,j,t

(4)

Fi,j,t

(5)

j

Fj,t =

X i

Through the generalized disjunctive programming approach (GDP), the models of compressors were constructed and presented in supporting information. These models address the material balance of LP gas before and after being converted to HP gas. Energy balance and capacity constraints for fuel gas consuming units According to the complex structure of fuel gas system, every consuming unit is connected to various energy sources. Normally, fuel gas cannot satisfy the overall requirement of heating value for the refinery. Thus all the self-produced energy resources should be utilized at first, and the other purchased materials, such as natural gas and LPG, are introduced to the utility system as the additional energy. Here, all the energy materials flowing indirectly 9



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into the equipment will be regarded as coming from the pipeline network. If the equipment is connected directly to the energy sources, the fuels will be considered as supplied from the sources. Considering different energy sources, the energy balance constraints of fuel gas consumers are shown as Eqs.(6)-(8). ηj (Fk,j,t Hk + Fnet,j,t Hnet ) = Dj,t

(6)

0 ≤ Fk,j,t ≤ zj FfUg,j

(7)

0 ≤ Fk,j,t + Fnet,j,t ≤ FfUg,j

(8)

Here, zj is a binary variable for fuel gas consuming units. If zj equals to zero, the fuel gas system can satisfy the heat requirement of equipment j. Otherwise, the equipment j is driven by the purchased energy resources. Normally, the energy supply condition for equipment j will also influence the value of zj for other devices, which has been discussed in detail in our previous work. 23 The corresponding constraints of the pipeline with energy sources are reviewed in supporting information. Similarly, for self-producing-self-consuming units, the energy balance and capacity constraints are defined as Eqs.(9)-(11). self self ηj Fj,t Hj + Fnet,j,t Hnet = Dj,t

(9)

0 ≤ Fnet,j,t ≤ yj FfUg,j

(10)

self 0 ≤ Fj,t + Fnet,j,t ≤ FfUg,j

(11)

If the self-produced fuel gas can provide enough energy for equipment j, then the binary variable yj equals to zero, which forces Fnet,j,t to be zero. On the contrary, yj = 1 means the running of equipment j need additional support from the pipeline network. When we consider 10


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other equipment connected with self-producing-self-consuming units, some logic constraints are defined and reviewed supporting information. Operational state constraints of each unit Several kinds of operational constraints are built for LP gas drum and HP gas vessels, fuel gas consumers, and compressors. Considering the emission of LP gas and the exhaust of HP gas, the amount of fuel gas should be limited to an acceptable level, indicated by Eqs.(12)-(13). The flowrate limitations for different energy sources (except the natural gas) are represented by Eq.(14). As the total amount of natural gas is determined by the contract with suppliers, the flowrate limitation and purchasing constraints of natural gas are defined as Eqs.(15)-(16). U F GL G ≤ F GG,t ≤ F GG + Femi,t

(12)

U F GL V ≤ F GV,t ≤ F GV + FHP 2LP,t

(13)

U 0 ≤ Fk,j,t ≤ Fk,j , k 6= N G

(14)

0 ≤ P CN G,t ≤ FNU G,t

(15)

X

(16)

FN G,j,t = P CN G,t

j

Model of loop pipelines Since the nonlinear constraints for loop pipelines (reviewed in supporting information) bring nonlinearity to the scheduling model, the flowrate of fuels in the loops is approximately calculated by the linear equation in Eq.(17). bni is defined as the proportion parameter for describing the ratio between flowrates in the related pipelines. Here, bian1,t is introduced to iteratively correct the proportion as Eq.(18). Fl1 = bn1 Fl2

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(17)


Fl1 = (bn1 + bian1,t )Fl2

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(18)

As pointed by Zhang et al., 23 if loops exist in the pipeline, then the above scheduling problem will become an MINLP problem. Because of non-convexity and discontinuity, largesize MINLP problems are difficult to solve within a scheduling period by current techniques. Instead of solving the MINLP problem directly, a simulation based strategy 23 has been introduced to treat the problem by solving a series of MILP problems. In each MILP problem, the flowrate of pipelines in the loop is approximated by adding proportional constraints. In this LRF case, 6 nodes in the pipeline network (n1 to n6 in Fig.2) are selected to compose the flowrate proportion constraints in the MILP model. 1) Node 1 The linear constraint at node 1 is shown as Eq.(19), which denotes the ratio of the fuel gas flowrate in pipeline p1 and p2. Around the node 1, equipment can be classified into two groups, which are Group E1 (containing ICDU, IICDU, Boiler, IHD, IICK, SP, IIHD, IIIHD, HDP, IHC, IIIRF, SD) and Group E2 (containing IIICDU, IVRF, PX&DE). The ratio of the consumed fuel gas by Group E1 and E2 can also be described by Eq.(19). Fp1 = bn1 Fp2

(19)

2) Node 2 Similarly, the linear constraint in Eq.(20) describes the flowrate ratio of fuel gas generated by ICK in pipeline p3 and p4. Only when the flow direction of fuel gas in pipeline p3 is from node 2 to node 3, the constraint in Eq.(20) is valid. Group E3 (containing ICDU, IICDU, Boiler, IHD, IIHD, HDP, IHC, SD) and Group E4 (containing IICK, SP, IIIHD) can be formed by selecting consuming units along the pipeline p3 and p4. Fp3 = bn2 Fp4

3) Node 3-6

12


(20)

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The other linear constraints for nodes 3 ∼ 6 are presented as follows:

Fp5 = bn3 Fp6 ,

Fp7 = bn4 Fp8 ,

Fp9 = bn5 Fp10 ,

Fp11 = bn6 Fp12

Through the above linear constraints, the ratio of consumed fuel gas by different groups of equipment can be calculated. These constraints are able to depict nearly all the linear relationships between the fuel gas flowrate in pipelines. The loop pipeline network can be approximately described by linear constraints, but the proportion parameters may be inaccurate. According to the Kirchhoff’s first and second law, the pressure gradient equation of pipeline could be defined as Eqs.(21)-(23), which are normally more accurate than the above linear constraints. To avoid solving a large-scale MINLP problem, these nonlinear formulas can be approximated by the linear constraints in Eq.(18), but the proportion parameters should be modified. Thus the simulation platform is established by utilizing the nonlinear equations. Through iteratively comparing the output of the simulation model and the optimization model, the proportion parameters are updated. This procedure is developed as the simulation-based solving approach. ∆Pl = − |Fl | Fl

A X

8fl Rg Tabs Cdp Ll M π 2 Dl2 Pl2

(21)

(−1)r Fa,n = 0

(22)

(−1)r ∆Pl = 0

(23)

a L X l

where the symbols are all defined in the nomenclature.

Remark In the real-world implementation, the Kirchhoff’s laws may not be enough for providing accurate pressure drops of all the pipelines. More empirical models and detailed modifications could be included in this part. Probably, industrial data could be utilized 13



for constructing a more accurate model than Eqs.(21-23). No matter what the final model is, the simulation-based approach can hopefully adjust the group of linear approximation constraints.

Robust engineering strategy The above modeling and solving procedures have been partially illustrated through the numerical industrial case in our previous work. 23 However, the optimal solution from the scheduling model is not always feasible and practical for the real-world production. The challenges arise from various reasons, containing the mismatching of model parameters and the poor accuracy of executing decisions, etc. In order to guarantee the performance of the proposed methods in LRF, a systematic procedure is proposed to ensure the feasibility, necessity and effectiveness. As shown in Fig.3, the structure consists of offline and online validations. The model precision and solving performance should be evaluated at first, which can prove whether the model is feasible for the real-world application. After comparing the optimal result with the real-time decision from the database, we can discuss if it is necessary to implement the model to the refinery. This step is called optimization effect validation. At last, based on the former three steps, the effectiveness can be evaluated from the statistics by executing the optimal solution on the real-world fuel gas system. With the assistance of the industrial status and decisions from the real-time database, four aspects of validation can be achieved by the procedures in Section 4.2-4.5.

Definitions of the Basic Concept in the Engineering Strategy Three parts constitute the basis of the implementation procedure, containing the optimization model, the simulation model, and the real-time database. The real-time production data and operation parameters are stored in the database, called as real status. Nonlinear

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Figure 3: Structure of the validation for the operational optimization equations are integrated in the simulation model to calculate the pressure-drop, flowrate and heating values of fuel gas in pipelines and equipment. Through iteratively comparing the output of the simulation model (called as simulated status) and the output of the optimization model (called as model status), the proportion parameters in the linear constraints will be updated until the outputs match.

Remark The simulation model is constructed based on the single-period scheduling model. The only difference between them is that simulation applies the nonlinear models in Eqs.(21)(23) rather than the linear constraints in the optimization model. Once the input (real decision, containing the consumption amount of different energy resources) of the simulation model is determined, the calculation process for this model is the same as solving equations, but not exactly solving optimization programs. It is noteworthy that with the same input, the nonlinear equations in the simulation model should be examined at first to make sure the simulation can generate the same output as the real status. Assuming the accuracy of simulation model can be guaranteed, the optimization model will be updated, and the model status will converge to the simulated status (equals to the real status) in finite steps. Then the scheduling model can be regarded as stable and

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precise. At first, the precision validation procedure is illustrated as follows.

Precision Validation of the Model The first step is the precision validation of the model, which is the foundation of the industrial application of operational optimization. Reliability of the optimal decisions will be guaranteed only when the precision of the model meets the requirement. This step aims to verify if the optimization model can express the real fuel gas system factually. The procedure is illustrated in Fig.4. As shown in Fig.4, the precision validation involves four sub-steps: • Step 1-1: Execute data reconciliation to eliminate measurement error in the initial data, so that the preprocessed data (or called as validation data), will satisfy mass and energy balances. • Step 1-2: Input the real decisions into the single-period MILP model and fix corresponding variables. Then a simplified model will be obtained as the validation model. In this step, the real decision is a non-optimal solution which can be regarded as a feasible solution for the scheduling model. By fixing decision variables at the real decision, if the constraints can approximately describe the exact balance relationship of energy materials, the model status should be similar with the real status. From the real-time database, the consumption amount of all energy resources can be obtained as the real decision, which is only a part of the decision variables in the optimization model. Thus we have to solve the validation model after fixing the real decision. Then the complete model decision will be obtained, containing the solution of purchasing and assigning energy resources. In a word, the model decision is more detailed than the real decision.

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Note: For an efficient validation, only the single-period MILP model is calculated, which is constructed by eliminating the time-related constraints and fixing the index t at one. • Step 1-3: Solve the model by iteratively updating the proportion constraints in the MILP model, where the simulation model could reflect the material and energy balance of the real-world production. The iterative updating process for the proportion parameters in the MILP model will be ended until the model status matches the simulated status. • Step 1-4: Compare the final model status derived from Step 1-3 with the real status. Precision of the model will be satisfied with the application requirement if and only if the deviation between these two statuses is small enough. Then the validation procedure can be ended. If these two status cannot match, the simulated model should be modified until the platform can provide real status when the input for the simulation is the real decision. Finally, when the precision of the model reaches the decision-makers’ demand, the simulation model can be regarded as a digital twin of the real-world process. Moreover, the balance constraints in the scheduling model can accurately describe the real-world transition and transportation process of energy resources. Then the optimal solution can be obtained by solving the multi-period scheduling model.

Performance Validation of the Solving Method The second step is the performance validation of the solving method. The simulation-based iterative approach will be examined by real-time data in this section, so as to explain its value for the industrial application. The procedure of the validation is illustrated in Fig.5, and the detailed method is described as follows.

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Figure 4: Flowsheet of the model’s precision validation • Step 2-1: Develop the multi-period operational optimization model for the fuel gas system and extract the single-period optimization model (the period is one hour) from the multi-period one. • Step 2-2: Input the real decision into the single-period optimization model and solve the MILP model. The proportion parameters are initially calculated based on the real status (flowrate of fuel gas in pipelines). The simulation model has been checked and modified in the precision validation step. • Step 2-3: Employ the optimized result (model status) of the first iteration and the predicted production amount of fuel gas as the initial values of the simulation model. The flowrate and heating values of fuel gas in consumers can be calculated through simulation. • Step 2-4: Calculate the proportion parameters based on the simulated status and update the proportion parameters in the optimization model.

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• Step 2-5: Step into the second iteration and solve the modified scheduling model. • Step 2-6: Comparison analysis of the results in each iteration step to verify the convergence of the solving method, which means to observe whether the model status is approaching the real status. Normally, the above steps can be repeated for more iterations, for example, the singleperiod optimization model can be updated after each iteration. In each iteration, the average relative error will be calculated, and if it meets the requirement, the solving process will be ended. For the fuel gas system in refinery, two kinds of statuses are considered the most, which are the flowrate and heating value of fuel gas in each unit.

Figure 5: Flowsheet of the performance validation for the solving method

Effect Validation of the Operational Optimization To examine whether the optimal solution could bring profits and save operating costs for the refinery, the third step is the effect validation of the model. The procedure of the validation is illustrated in Fig.6. 19



Figure 6: Flowsheet of the optimization effect validation As shown in Fig.6, the optimization effect validation contains four sub-steps: • Step 3-1: Extend the validated single-period optimization model to the multi-period model. • Step 3-2: Input the real status to the multi-period model of step 3-1, where the initial status of units and the predicted demand of energy materials can be set as parameters in the model. • Step 3-3: Solve the multi-period validation model by the simulation-based iterative approach to obtain the optimal decisions. • Step 3-4: Compare the optimal decision with the real decision to analyze the change in the operating cost. As defined at the beginning of this section, some operation parameters for the constraints in the MILP model should be set according to the real status, such as energy demands and the requirement of heating values. Thus the real status is input for fixing partial parameters of the MILP model. After solving the scheduling model, the objective values induced by the optimal solution and the real decision should be compared. If the optimal solution can save

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costs, then the optimization model is proved effective to replace the real decision. Otherwise, the implementation of the model is unnecessary for the real-world fuel gas system.

Execution Validation on Field Despite the above three offline validations have verified the feasibility and necessity of the operational optimization of the fuel gas system in LRF, online validation is essential to guarantee its performance in industrial application. The procedure of the validation is illustrated in Fig.7, involving the following 5 sub-steps: • Step 4-1: Install the optimization model of the fuel gas system on field. • Step 4-2: Obtain the fuel gas production flowrate and energy demand of each unit needed by the optimization model from the real-time database. • Step 4-3: Solve the problem by the proposed simulation-based iterative approach, and save the model status derived during the solving procedure. • Step 4-4: Execute the optimal decisions on field. • Step 4-5: Compare the model status derived from step 4-3 with the real status under the optimal decision, and investigate the effectiveness of implementing the operational optimization in LRF. For better illustrating the proposed engineering strategy, the status and decisions from the LRF’s real-time database are analyzed and discussed in the next section. Thus the feasibility, necessity, effectiveness of the previous scheduling model and the solving method can be verified more clearly.

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Figure 7: Flowsheet of the execution validation

The LRF case study The brief description of the LRF case has been presented in Section 2. The simulation platform of the case study is implemented on Lingo 17.0. The volume unit for fuel gas in this paper is represented by N m3 , which is widely used in industrial applications, meaning Normal Cubic Meter. Here N represents the nominal condition when the volume is measured under a standard atmospheric pressure, the temperature is 0◦ C, and the relative humidity is 0%. Correspondingly, the unit for flowrate of fuel gas is denoted by N m3 /h. The four validation steps are discussed one by one as follows:

Precision Validation It can be seen from Fig.2 that the fluctuations in the supplement of any energy source would directly affect the flowrate of fuel gas in the system. But in this work, natural gas is the main additional energy source for complementing the deficient heating values, which means NG is the prior energy material to be purchased. Since there is an upper limit for the procurement of natural gas, the optimization model should be robust enough to immune against the 22


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mutable demands of heating values. For this reason, two different operational conditions are considered: small complement amount of natural gas (case 1) and large complement amount of natural gas (case 2). Precision validation for case 1 In this case, little natural gas is needed because the self-generated fuel gas is almost sufficient for the total energy demand. The real-time data shows that the complement amount of natural gas is 1361 N m3 /h, while no C5 and LPG are compensated in IIIRF, IVRF, PX&DE. Various amount of fuel oil is consumed as additional energy resources by PX& DE (4.1 ton/h), IIICDU (0.9 ton/h) and I II CDU&B (1.2 ton/h). The flowrate of fuel gas in compressor 1 and compressor 2 are 4,300 N m3 /h and 4,600 N m3 /h. Fuel gas flowrates and heating values of gas producers are shown in Table S1, and the real status of consumers are presented in Table S2. Furthermore, through the pipeline network simulation, the component data of the consumed fuel gas can be obtained. Thus the heating values can be derived accordingly. The heating value of natural gas, hydrocarbon, LPG and fuel oil are 33.092 M J/N m3 , 46000 M J/ton, 53000 M J/ton and 40000 M J/ton, respectively. After configuring the parameters by the above industrial data, the single-period scheduling model can be validated and modified by the simulation-based solving approach. Then the precision of the optimization model is examined through the comparison between model status and real status, which is shown in Table S3. From Table S3, we can see that the average relative error of fuel gas flowrate and heating value in fuel gas consumers are 1.80% and 1.82%. The matching level θco of optimization model is defined as Eq.(24), and δf and δh are the average relative error of the fuel gas flowrate and heating value, which can be calculated through Eq.(25) and Eq.(26). θco = 1 − (δf + δh )/2

(24)

model real SF − SF X j j 1 % δf = |J| SFjreal j∈J

(25)

23



model − SH real SH X j j 1 δh = % |J| SHjreal j∈J

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(26)

where SFjmodel and SFjreal represent the model status and the real status of fuel gas flowrate in the jth consuming unit; SHjmodel and SHjreal denote the model status and the real status of the heating values of fuel gas; J is the set of fuel gas consumers and |J| is the cardinality of the set. Normally 95% is set as the minimum value for the matching level. The result of θco in this case is 98.2%, which meets the requirement of industrial application. Therefore it can be concluded that the proposed optimization model is well defined when the complement amount of natural gas is small. Precision validation for case 2 In this case, a large amount of natural gas is input into the system to complement the great deficit of energy demand. The real-time data shows that the complement amount of natural gas is 8465 N m3 /h. On average, only 1.8 t of C5 is compensated in III RF at each scheduling period, while the consumption amount of fuel oil by PX& DE, III CDU and I IICDU&B are nearly 1.9 t/h, 0.1 t/h, and 2.4 t/h, respectively. The flowrate of fuel gas for compressor 1 and compressor 2 are measured into 4700 N m3 /h and 4200 N m3 /h. Table S1 and S2 show the fuel gas flowrate and its heating value of each fuel gas producers and consumers. The comparison result is presented in Table S4. Compared with the real status, the average relative errors of the flowrate and heating value in fuel gas consumers at this time are 1.48% and 1.15%. The matching level θco of optimization model in this case is calculated as 98.7%, which also meets the requirement of industrial application. The above results show that the optimization model is able to reflect the real-world fuel gas system excellently in two different operational conditions, which verifies the precision of the model.

24


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Performance Validation Solving performance validation for case 1 In case 1, the solving procedure is ended after two iteration steps. Comparison results between model status and real status in the first and the second iteration step are shown in Table 1. It can be concluded that the model status obtained in the second iteration step is much more reliable than the one obtained in the first iteration step. More specifically, the average error and the average relative error of flowrate in fuel gas consumers are reduced by 44.8% and 35.0% after the iteration. At the same time, these two kinds of errors of the heating value in fuel gas consumers are reduced by 44.8% and 42.6%. Solving performance validation for case 2 In case 2, the solving procedure is also ended after two iteration steps. Comparison results are also shown in Table 1. Table 1: Comparison result between the two iteration steps

Case 1

Case 2

Iteration Iteration RIP∗ Iteration Iteration RIP∗

I II I II

Flowrate(N m3 /h) Average error Average relative error 134 2.77% 74 1.80% 44.8% 35.0% 86 1.57% 72 1.48% 16.3% 5.7%

Heating value(M J/N m3 ) Average error Average relative error 1.372 3.17% 0.757 1.82% 44.8% 42.6% 0.571 1.36% 0.466 1.15% 18.4% 15.4%

Note: RIP = (Error in the first step - Error in the second step)/ Error in the first step, representing the rate of improved precision.

From the results, the same conclusion can be drawn that the model status obtained in the second iteration step is more precise. The results also indicated that the similar reduction in the average error and average relative error of flowrate and heating values. In a word, the validation results show that the model status derived by the proposed simulation-based iteration approach will be even more accurate with the iteration going on.

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Effect Validation of operational optimization Cost coefficients in the objective function are listed in Table S5. The capacity bounds of gas drum and HP gas vessel are [6100N m3 , 42000N m3 ] and [700N m3 , 1300N m3 ]. In addition, the contract of natural gas supplement limits the flowrate of natural gas in each operating period to be smaller than 9000 N m3 /h, and the pressure in the natural gas source is given as 0.6 M pa. The single-period MILP model contains 68 continuous variables, 22 binary variables and 175 constraints. It should be noted that the MILP model requires very little computational effort to achieve the optimal solutions. In fact, the optimal solutions are found in less than 5 seconds in an Intel Core 2 Duo 2.2GHz platform with 2GB RAM. Optimization effect validation for case 1 In case 1, the initial capacity of gas drum and HP gas vessel are 16108 N m3 and 953 N m3 . Optimal decisions of compressor 1 and compressor 2 are both 4000 N m3 /h. Results also show that the amount of C5 and LPG compensated in IV RF, III RF and PX&DE are zero, while the amount of fuel oil consumed by PX& DE, IIICDU and I II CDU&B are 3.1 t/h, 0.3 t/h and 1.2 t/h, respectively. As a result, emission phenomena in gas drum and HP gas vessel is totally avoided. It is observed that the complement amount of natural gas in the optimal result is enhanced substantially from 1361 N m3 /h to 3150 N m3 /h, which reduces the complement amount of fuel oil from PX&DE and III CDU as well as the total load of compressors. In fact, the total complement amount of fuel oil is reduced from 6.2 t/h to 4.6 t/h, while the total load of compressors is reduced from 8900 N m3 /h to 8000 N m3 /h. As illustrated in Table 2, the operating cost will be decreased by 3.85% from 22672 yuan/h to 21800 yuan/h if the optimal decisions can be carried out. Optimization effect validation for case 2 In case 2, the initial capacity of gas drum and HP gas vessel are 9065 N m3 and 872 N m3 . Optimal decisions of compressor 1 and compressor 2 in this case are 8000 N m3 /h and 4000 N m3 /h. It is derived that the amount of C5 and LPG compensated in IV RF and PX&DE are zero, while the amount of C5 compensated in III RF is 0.4 t/h. The optimal amount 26


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Table 2: Comparison of operating cost of fuel gas system (yuan/h)

Conversion cost of LP gas to HP gas Cost of fuel oil Cost of natural gas Cost of hydrocarbon Total operating cost Rate of cost reduction

Case 1 Base case Optimal result 4450 4000 15500 11500 2722 6300 0 0 22672 21800 3.85%

Case 2 Base case Optimal result 4450 6000 11000 11750 16930 18000 7200 1600 39580 37350 5.63%

of fuel oil consumed by PX& DE, III CDU and I IICDU&B are 2.9 t/h, 0.4 t/h and 1.4 t/h respectively. Results also indicate that no fuel gas emission as well as no energy source changes in the fuel gas system. It is observed that the complement amount of natural gas in the optimal result is enhanced from 8465 N m3 /h to 9000 N m3 /h, reaching its upper bound. In addition, the total load of compressors is increased from 8900 N m3 /h to 12000 N m3 /h, which transforms much more LP gas to HP gas compared with the base case. Here the base case represents the historical information collected from the database of a real-world enterprise. Consequently, the total complement amount of fuel oil is increased from 4.4 t/h to 4.7 t/h even though a reduction decision of 1 t/h is implemented in I & II CDU. However, the complement amount of hydrocarbon in the optimal result is decreased from 1.8 t/h to 0.4 t/h. As a result, the operating cost of fuel gas system could be ideally decreased by 5.63% from 39,580 yuan/h to 37,350 yuan/h if the operational optimization is executed, as illustrated in Table 2.

Execution validation on field The on field validation involves 24 operating periods with each period 1h. The flowrate of self-produced fuel gas and energy demands are shown in Table S6 and S7. The fuel gas heating values of the fuel gas producers are listed in Table 3. The natural gas contract limits

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the supplement flowrate of natural gas in the whole operating periods below 60000 N m3 , and the pressure in the natural gas source is given as 0.6 M pa. Initial capacities of gas drum and HP gas vessel are 12025 N m3 and 923 N m3 . Table 3: Fuel gas heating value of fuel gas producers

Heating value

(M J/N m3 )

RU 40.775

ICK 42.255

II FCC 30.337

HR 51.658

DE 76.340

II HC 56.653

The multi-period optimization model contains 1611 continuous variables, 720 binary variables and 5137 constraints. Although the number of binary variables, continuous variables, and constraints increase significantly, the computational effort is acceptable (less than 70s in an Intel Core 2 Duo 2.2 GHz platform with 2 GB RAM) when Cplex is chosen as the MILP solver. Optimal decisions of the complement fuels are derived by solving the model. The real status of the fuel gas system is obtained after the execution of the optimal decisions. Comparison of the optimal decisions and the base case is illustrated in Figs.8-11.

Figure 8: Comparison of load decision of compressors

Figure 9: Comparison of complement decision of natural gas

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It is observed that the total load of compressors is increased from 209128 N m3 /day to 226000 N m3 /day, which indicates that much more HP gas is produced by the optimal decision. The complement amount of natural gas is also enhanced from 55804 N m3 /h to the upper bound 60000 N m3 /h. It can also be noted that the total complement amount of fuel oil increases slightly from 178.8 t/day to 180.2 t/day. As a result, the total complement amount of hydrocarbon in the optimal result falls substantially from 23.9 t/day to 4.2 t/day, which is the main cause of the decrease in operating cost. In fact, the operating cost of fuel gas system in the whole operating periods is decreased by 7.76% from 759,228 yuan/day to 700,300 yuan/day if the operational optimization is executed, as illustrated in Table 4.

Figure 10: Comparison of complement decision of fuel oil

Figure 11: Comparison of complement decision of hydrocarbon Through the above validation procedures, the optimization model can be highly adjusted to the real-world production conditions. The property parameters in the unit constraints could be updated by comparing the real status with model status, which guarantees the accuracy of the model. Then the theoretical model provides reasonable and better solutions 29



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Table 4: Comparison between the base case and optimal result Base case Cost (104 yuan/day)

Decision Conversion cost of LP gas to HP gas Cost of fuel oil Cost of natural gas Cost of hydrocarbon Total operating cost (104 yuan/day) Rate of cost reduction

2.091 × 105 (N m3 /day) 178.8 (t/day) 5.580 × 104 (N m3 /day) 23.9 (t/day)

10.456 44.700 11.161 9.600

Optimal result Cost Decision (104 yuan/day) 2.260 × 105 11.300 (N m3 /day) 180.2 (t/day) 45.050 4 6.000 × 10 12.000 (N m3 /day) 4.2 (t/day) 1.680

75.923

70.030 7.76%

for decision makers. Finally the performance of the optimization model is evaluated based on the analysis of separable parts of the objective. In fact, there is always gap between the theoretical model-driven solution and the realworld decision, but the engineering strategy allows the interaction between models and decision-makers. This would definitely improve the applicability of optimization research works and generate more benefits for the production in process industry.

Conclusions This paper introduces a robust engineering strategy for implementing the previous developed optimization method to the fuel gas system in the LRF. Through four kinds of validation procedure, feasibility, necessity, and effectiveness of implementing operational optimization are presented. Cases in the single-period operational optimization show that the optimization achieves up to 3.85-5.63% cost reduction with respect to the base case scenarios. The complex industrial case also indicates a reduction in the operating cost, where a saving of 7.76% is generated. In fact, the proposed method is now developed as a software system and integrated with the refinery database to effectively support the operational optimization of the fuel gas system in the oil refinery. One of our future efforts is to incorporate nonlinear 30


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relationships, such as more precise models of compressor, heater, and boiler, to the proposed formulation so that the work status of the fuel gas system can be expressed much more reasonably.

Supporting Information Available • The detailed constraints for the scheduling optimization of fuel gas optimization in refinery are partially reviewed, containing a) the model for pipeline network with selfproducing-self-consuming unit ; b) the model for pipeline network with consuming unit; c) the model for the compressors with maintenance considered; d) the nonlinear model for the loop pipeline network. • Supporting industrial data; • The convergence of the simulation-based solving method; • The pairing relationship of various fuel types and units.

Author information Corresponding Author *Tel: 086-87953145. Email: [email protected].

Acknowledgement The authors gratefully acknowledge financial support from the National High Technology R&D Program of China (2016YFB0301800) and National Natural Science Foundation of China (61621002).

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Nomenclature Indices a

pipelines connected to nodes

c

compressors

i

fuel gas sources

j

fuel consumers

k

energy sources, containing fuel oil (FO), natural gas (NG), LPG and hydrocarbon (C5)

l

pipelines

n

nodes in the pipeline network

t

period (t = 1, , T )

Sets G

Low-pressure (LP) fuel gas drums

V

High-pressure (HP) fuel gas vessels

Parameters Ck

Unit cost of energy costs, yuan/t for fuel oils (FO) and yuan/N m3 for natural gas, C5 and LPG

CHP 2LP Unit penalty of HP gas exhaust, yuan/N m3 CLP 2HP Unit cost of the conversion from LP gas to HP gas, yuan/N m3 Cdp

Conversion factor for driving force calculation

32


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Cemi Unit penalty of LP gas emission, yuan/N m3 Dl

Diameter of pipeline l, m

F GLG Lower bound of fuel gas amount in the drum, N m3 F GLV Lower bound of fuel gas amount in the HP gas vessel, N m3 Hk

Heating value of energy source k, M J/ton for fuel oil, M J/N m3 for NG, C5, LPG

Hnet

Heating value of fuel gas from the pipeline network, M J/N m3

Ll

Length of pipeline l, m

M

Molecular weight of fuel gas

Pl

Average pressure in pipeline l, KP a

Rg

Gas coefficient

Tabs

Absolute temperature, K

bn

Proportion parameter for node n

bian,t Deviation of the proportion parameter for node n at period t fl

Friction factor in pipeline l

Dj,t

Heat energy demand of equipment j at period t, M J

F GUG Upper bound of fuel gas amount in the drum, N m3 F GUV Upper bound of fuel gas amount in the HP gas vessel, N m3 FNUG,t Upper bound of natural gas flowrate in each scheduling period, N m3 /h FfUg,j Upper bound of the flowrate of fuel gas in equipment j, N m3 /h

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U Fk,j

Upper bound of the flowrate of energy source k in equipment j, t/h for fuel oil, N m3 /h for NG, LPG, C5

Hjself Heating value of self-produced fuel gas in equipment j, M J/N m3 ∆t

Time interval of the scheduling period, h

ηj

Heater efficiency in equipment j

Variables C

Total cost, yuan

F Cc,t Flowrate of fuel gas in compressor c at period t, N m3 /h F PLP,t Flowrate of the produced LP gas at period t, N m3 /h FHP 2LP,t Flowrate of HP gas exhaust at period t, N m3 /h Fa,n

Flowrate of pipeline a connect to node n, N m3 /h

Femi,t Flowrate of LP gas emission at period t, N m3 /h Fi,j,t

Flowrate from fuel gas source i to equipment j at period t, N m3 /h

Fi,t

Flowrate of fuel gas source i at period t, N m3 /h

Fj,t

Flowrate of fuel gas source in equipment j at period t, N m3 /h

self Fj,t Flowrate of self-produced fuel gas in equipment j at period t, N m3 /h

Fk,j,t Flowrate of energy source k in equipment j at period t, t/h for fuel oil, N m3 /h for NG, C5, LPG Fnet,j,t Flowrate of fuel gas from the pipeline network to equipment j at period t, N m3 /h P CN G,t Flowrate of the purchased natural gas at period t, N m3 /h

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∆Pl

Pressure drop in pipeline l, KP a

r

Binary variable representing the flow direction of fuel gas in pipelines

yj

Binary variable that denote if the self-produced fuel gas in equipment j can satisfy its own energy requirement

zj

Binary variable that denote if the fuel gas system can satisfy the heat requirement of equipment j

F GG,t Fuel gas amount in the LP gas drum at period t, N m3 F GV,t Fuel gas amount in the HP gas vessel at period t, N m3 Fl

Flowrate of pipeline l, N m3 /h

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Graphical TOC Entry

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Robust Engineering Strategy for Scheduling Optimization of

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