Three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants

Kexin Bi,Mingyu Yan,Shuyuan Zhang,Tong Qiu,*

1 Department of Chemical Engineering,Tsinghua University,Beijing 100084,China

2 Beijing Key Laboratory of Industrial Big Data System and Application,Beijing 100084,China

3 Fushun Petrochemical Company,PetroChina,Fushun 113008,China

Keywords:Three-scale integrated optimization Cyclic scheduling Supply chain Mixed-integer linear programming Thermal cracking

ABSTRACT In order to explore the potential of profit margin improvement,a novel three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants is proposed and evaluated.A decoupling strategy is proposed for the solution of the three-scale model,which uses our previously proposed reactor scale model for operation optimization and then transfers the obtained results as a parameter table in the joint MILP optimization of plant-supply chain scale for cyclic scheduling.This optimization framework simplifies the fundamental mixed-integer nonlinear programming(MINLP) into several sub-models,and improves the interpretability and extendibility.In the evaluation of an industrial case,a profit increase at a percentage of 3.25% is attained in optimization compared to the practical operations.Further sensitivity analysis is carried out for strategy evolving study when price policy,supply chain,and production requirement parameters are varied.These results could provide useful suggestions for petrochemical enterprises on thermal cracking production.

1.Introduction

The increasing modernization and urbanization in developing countries are enlarging the demand of basic chemical products and therefore stimulate the expanding and development of petrochemical plants,among which the ethylene plants provides one of the most important and profitable industrial chain [1].The rapid expansion in quantity and scale makes the ethylene plants must face the fierce competition and declining profit margin[2].Seeking an optimal operation level,vendor and inventory management strategy or additional profit margin improvement approaches is a necessary task for long-term development of ethylene plants [3].However,the volatile oil prices,unstable upstream supply and downstream demand,and situation-determined production requirements all have significant impacts on three-scale decision making of furnace operation,cyclic scheduling,and supply chain in thermal cracking process [4,5].Therefore,an integrated model was needed for the complex system coordination of multiple production strategy for an acceptable profit to achieve intelligent manufacturing with computer aids [6,7].

It would be a formidable task to directly build an integrated model with no foundation because of the complication and coupling of the thermal cracking process.However,great progresses were achieved in subsystems modeling of the whole process and the combination of these models [8,9].For furnace operation optimization,the goal is to find the profitable product distribution and corresponding operational parameters.Reaction models with high complexity and nonlinearity were usually employed in the related researches,thus intelligent heuristic optimization methods were usually proposed synchronously.Gaoet al.[10]combined the nondominated sorting genetic algorithm (NSGA-II) with SQP (successive quadratic programming) to improve the efficiency of multiobjective optimization and the quality of the Pareto-optimal set.This method was determined to be easily implemented on ethylene plants through an industrial case.Nabaviet al.[11] further improved the NSGA-II with the jumping gene operator,named as NSGA-II-aJG,for the multi-objective operation optimization of an industrial LPG thermal cracker.Wang and Tang [12] presented a multi-objective parallel differential evolution with competitive evolution strategies and illustrated its efficiency in the application of the operation optimization of naphtha pyrolysis simulated by least squares support vector machines(LSSVM)models.As thermal cracking is a batch production process,this type of research could only provide an operational solution within a batch for a specific feedstock and reactor combination.

A further cyclic scheduling model for feedstock allocation and parallel furnaces production arrangement considering coking process is also indispensable for batch production optimization of thermal cracking.In cyclic scheduling and planning,furnace running variables in several batches such as feedstock type,processing time,decoking time are main considerations [13].Jain and Grossmann [14] proposed a fundamental mixed-integer nonlinear programming (MINLP) model to maximize the net profits of a thermal cracking plant per day.Subsequently,several researches were conducted based on this model.Liuet al.[15] considered multiple types of products in the fundamental MINLP model and added time logics to avoid unpractical conditions such as simultaneous shutdown of multiple furnaces.Zhaoet al.[16]improved the MINLP model with the consideration of recycled ethane and the simultaneous identification of the feedstock allocation with quantity,time,and sequence information.Suet al.[17] proposed a hybrid MINLP-generalized disjunctive programming (GDP) formulation and considered the new operating mode of ethylene production process under limitation of raw materials and energy consumption.Although most of these models simplified the furnace yield prediction as exponential decayed function,they were still of great significance to the optimization and production planning on the plant level of thermal cracking.Nevertheless,the depth and comprehensiveness of the current researches are still not enough for a plant manager to coordinate the real production in a thermal cracking plant.A consummate integration of kinetic information in furnace operation optimization and plant information in cyclic scheduling optimization is expected[18].In addition,supply chain information,vendor and inventory strategies are also needed to be considered for the feedstock and product management.

The aim of this work is to help the ethylene plants with intelligent manufacturing strategies formulation from multiple scales.Therefore,a three-scale integrated optimization approach was proposed for optimal profit searching in the plant production.From the reactor scale,we started the whole process with the furnace operation optimization based on our previous proposed integrated transfer learning and intelligent heuristic optimization model[19].From the plant planning scale,we degraded the MINLP model[14]to mixed-integer linear programming(MILP)based on real circumstances,and conducted the cyclic scheduling using GAMS [20] for the solution.From the supply chain scale,we added the vendor and inventory strategy variables into the fundamental model,and made the sensitivity analysis on price,supply chain,and production requirement parameters.An industrial case of thermal cracking production in Northeast of China was exampled and discussed for the evaluation of the whole process.

2.Problem Statement

In order to solve the optimization problems that the enterprises are facing in the reform of thermal cracking intelligent manufacturing,the practical production process is represented as a threescale integrated optimization model as shown in Fig.1.Definitions about a production batch are first provided based on an industrial case of a complex in Northeast of China.Within a single batch,the production is continuous with a subsequence of operations.One type of feedstock is cracked for each batch in a furnace.For various types of feedstock,the processing time during a batch may vary from 30 to 70 days.The flowrate of various combination of feedstock type and furnace type may vary from 500 to 1500 tons per day.From each plant,the processing time and flowrate are predefined and fixed based on actual situations using parameter tables.

With the definition of a batch,an overall production optimization should be carried out when receiving the production task arranged by decision makers of the enterprise.The production strategies should be drawn up with the consideration and coordination of furnace operation parameters,feedstock allocation and supply chain information.To this end,a three-scale integrated optimization framework is designed and displayed in Fig.2.

Fig.1.Mass flow diagram of three-scale integrated optimization model in a specific batch k.

Fig.2.Framework of the three-scale integrated optimization for thermal cracking process.

The framework starts with reactor scale optimization.The optimal operations of each furnace and corresponding product yields are first collected using the yield prediction model and coking model.These outputs are converted together with the supply chain information and then processed in subsequent plant-scale optimization to obtain the feedstock allocation and furnace processing strategies.Compared to the previous model proposed by Jain and Grossmann,there are several modifications of the classic MINLP problem according to the practical scenario:(i) Uses the results of mechanism-based machine learning model instead of exponential decay model for yield prediction and reactor scale optimization,and compile the yield and coking data as tables;(ii) Solve the reactor scale optimization (nonliear problem (NLP) model)and the plant-supply chain scale optimization separately,which could be regarded as a decoupling step;(iii) Considers various sources of feedstock supply and split the bilinear terms into sums of several linear terms,which could help degrade the MINLP model to MILP model.

Using these techniques,the MINLP problem could be decomposed to an NLP problem and an MILP problem.When solving this problem,feedstock sources and supply information data are entered into the MILP model to seek the optimal vendor strategies.After three-scale integrated optimization model is all solved,the total profit could be calculated as the objective function.The detailed models and formulations in three scales are described in the subsequent sections.

3.Models and Methodologies

3.1.Reactor scale model

The reactor scale models in the framework are generated using integrated transfer learning and intelligent heuristic optimization method proposed in our previous research[19].The mathematical formulation is shown in Eq.(1).

wherenis the amount of all types of products;y1,y2,???,ynare the yields of products;w1,w2,???,wnare weight parameters;f1,f2,???,fn+1are prediction models using transfer learning methods;x1,x2,x3are COT curve variables;lb1,lb2,lb3,ub1,ub2,ub3,ub4are the lower and upper bound for the decision variables.The detailed transfer learning modeling process could be referred to our previous research,and the subsequent solving methods for the NLP problem shown in Eq.(1) are set as heuristic optimization using hybrid genetic algorithm-particle swarm optimization (GAPSO) method [21,22].

When promoting this method to the ethylene plants,the demand for models increases dramatically because of the various combination of feedstock type and reactor type[23].For the investigated plant,there are 11 types of feedstock used for cracking,including hydrocracking tail oil (HTO),atmospheric gas oil (AGO),straight-run naphtha (NAP1),naphtha from delay coking (NAP2),naphtha from reforming process (NAP3),raffinate (RAF),light hydrocarbon(LH),topped oil(TO),liquefied natural gas(LNG),Propane (PR),and Ethane (E).There are also 8 cracking furnaces in which only specific types of feedstock could be processed.The 36 possible correlated circumstances between furnaces and feedstocks are listed in Table 1.

Table 1 Correlations between furnaces and feedstocks in a plant of the industrial case

As demonstrated by our previous work,the proposed modelingoptimization framework is applicable to varying types of feedstocks and furnaces due to the generalization of the transfer learning and intelligent heuristic optimization steps.After training step of the model,the optimization results could be obtained for the circumstances using the feedstocks of which the reaction network when thermal cracking is similar or included in the naphtha reaction networks.However,for the heavier liquids like HTO and AGO,the optimal product distribution and the related operations are provided by the petrochemical engineering institute.

The results of the reactor scale under all circumstances are collected and entered into the next scale optimization,including yields of key products (C2H4,C3H6,C4H6,C6H6,C7H8,C8H10,CH4,H2,C2H6,Residue),gas ratio of the products,optimal operations,energy cost of each furnace.

3.2.Problem clarification of plant scale model and supply chain scale model

The further plant scale optimization and supply chain scale optimization could be implemented using necessary inputs,including batch information,inventory conditions,feedstock sources,supply information,and the results collected from the reactor scale optimization.Compared to the MINLP model proposed in previous researches [14,15,17],the framework in this work decouple the furnace reactions from cyclic scheduling and use the numerical results of reactor scale optimization.This step strips out the nonlinear and nonconvex items in the reaction part of the fundamental MINLP model.Besides,we make alterations on nonlinear items in formulations to simplify the formulations in the objective function and decoking process of the plant scheduling,and degrade the MINLP model to MILP model,which is convenient for solving and further analysis.Since the plant scale optimization and supply chain scale optimization are both built by using MILP model,these two problems can consolidate and be solved jointly in a large MILP model.

The joint MILP model on plant scale and supply chain scale is described as follows.The objective is to maximize the net profit over the fixed batches.

Given:

(1) a set of feedstocksi?NTwith initial inventory quantity,

(2) a set of cracking furnacesj?NR,

(3) a set of batchesk?NB,

(4) a set of productsl?NP,

(5) feed rate of feedito furnacej F(i,j),processing time for feediin furnacej tb(i,j),cleaning up time for feediin furnacej dt(i,j),

(6) basic supply ratesFlo(i),upstream feedstock supply time UPST,

(7) the feedstock prices from local refineriesCr(i),feedstock buying cost from vendorsCro(i),feedstock selling priceCrb(i),initial feedstock storageST(i),

(8) energy costCe(j),clean up and start up costCcl(j),cost coefficient of gas separationCgs,cost coefficient of liquid separationCls,

(9) total gas production per batchYG(i,j),total product value per batch for feediin furnacej YP(i,j),which is calculated in the reactor scale model,

(10) operation constraints on total length,coking conditions,starting and ending time logic,

(11) supply chain constraints on inventory,single deal,total deals,production requirements.

Determine:

(1) the number of batches assigned for each furnace,

(2) feed type processed in each batch operation,

(3) starting time and ending time of each batch,

(4) dealing strategy with various suppliers.

In the given term (8),the product value per batchYP(i,j) is calculated using the results of the reactor scale optimization.Given the price of each productP(l)and the optimal product distributionY(i,j,l),theYP(i,j) could be calculated as:

Then the values are fixed in the tableYP(i,j).If reactor optimization problems of all circumstances listed in Table 1 are solved,these results could be directly preprocessed in data conversion model and then used in the MILP model as a parameter table.In this way,the NLP problem of reactor scale model is pre-solved and the solving steps are not necessarily executed simultaneously with the subsequent MILP model.The replacement of yield decaying model and decoupling the fundamental MINLP into MILP and NLP make major contributions to remove nonlinear and nonconvex items in formulations.

3.3.Mathematical formulation of plant scale model and supply chain scale model

3.3.1.Objective function

The objective of the described plant-supply chain joint model is to maximize the net profit for given batches or minimize the minus net profit,as shown in Eq.(2).

In Eq.(3),the first term represents the cost of feedstock from the local refineries under the requirement of the decision maker of the enterprise.The second term represents the cost of feedstock from the dealings with other suppliers for maintain the mass balance of the cracking.The third term represents the total value of the products during the production.The fourth term represents the energy cost of the cracking units.The fifth term represents the separation cost of the products.The sixth term represents the cost of the furnace clean-up.The last term represents the value of the uncracked feedstock in storage tanks after the whole production.

In the objective function,terms about the feedstock flow rates multiplied by processing time are supposed to be bilinear.However,these terms could be split into two parts,including the upstream supply from local refineries and dealings.The upstream supply could be calculated as upstream flowrate,which could be considered as constant because of its stability,multiplied by supplying duration.Thus this item should be linear.The dealings item is the sum of buy and sell.Thus it is also linear.This split method could convert the bilinear terms into a sum of linear terms,which is also more closed to the reality.The split technique is also applied in corresponding bilinear terms in constraints to eliminate the nonlinearity.

3.3.2.Mass balance

3.3.3.Allocation constraints

In the first batch,each furnace should be used to crack one type of feedstock.

In subsequent batches,each furnace should be used to crack less than one type of feedstock.

3.3.4.Timing logics and constraints

The furnace processing time of each batcht（i,j,k）could be calculated from the allocation and processing time of feedstock.

The starting time for each furnace in the first batchS（j,1）is given by plants.

The starting time for each furnaceS（j,k）is the sum of the ending time and decoking time in the subsequent batches.

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The ending time for each furnaceE（j,k）is the sum of the starting time and processing time in each batch.

The starting time and ending time should be less than the total production time.

3.3.5.Inventory constraints

In each batch,storage of the feedstock tank should be in a reasonable range.

3.3.6.Dealing constraints

Buying and selling quantity of each feedstockG1（i,j,k）andG2（i,j,k）should be less than upper bounds.

3.3.7.Supply chain logics

The whole supply chain for thermal cracking is highly intricate.In this work,we preliminarily focus on the major feedstock sources of the investigated plant,including local refineries of the same enterprise,refineries of the same enterprise in other cities,refineries of the different enterprises or imported.Here the values in the parameter vectorFlo(i) could be employed for the judgement of feedstock sources and determination of the significance of variable vectorsG1(i,j,k) andG2(i,j,k).The basic flow rateFlo(i) means the cracking requirements assigned to the plant,and the value of the vector component represents the feedstock supply capacity of the local refineries or refineries in the nearby cities within the same enterprise.If the component is equal to zero,it means that the corresponding feedstock could not be provided from the same enterprise because of the production or transportation capacity.

The source of feedstockicould be given by the significance ofG1(i,j,k) as:

Then the related costCro(i)could be determined using the price list.

The selling logics of feedstockicould be given by the significance of G2(i,j,k) as:

3.4.Solution strategy

The whole three-scale integrated optimization problem is a complex MINLP problem with black box model.However,our framework allows the decoupling of the integrated problem.First,the MINLP model is split into a reactor scale NLP model and a plant-supply chain scale MILP model.Second,the reactor scale NLP model could be first solved by our previously proposed approach [19] using heuristic optimization and run by MATLAB software.Then the total product value per batchYP(i,j) could be set as a parameter table instead of nonlinear regression of the yield decaying process.There are three main advantages of this strategy:(1)transfer learning prediction of the product yields is more accurate,and the integrated transfer learning and intelligent heuristic optimization method is more high-performance compared to the traditional exponential decay fitting [24,25];(2) the decoupling makes the solutions more explicit and understandable for each type of feedstock during one batch;(3)The decomposition of bilinear terms considering various feedstock sources could convert the nonlinear and nonconvex items in formulations into linear ones.After solving the reactor scale model,the MILP model was implemented in GAMS 28.2.0,and the solutions were obtained using CPLEX solver.The three-scale integrated optimization was performed on a personal computer with 64-bit Windows 10 Home,12-core Intel (R) Core (TM) i7-9750H CPU @ 2.60 GHz and 16 GB of RAM.

4.Results and Discussion

4.1.Industrial case

In the investigated thermal cracking plant,all types of feedstock are cracked in Stone &Webster Ultra-Selective Cracking (USC)cracking furnaces.As mentioned above,36 possible circumstances composed of permutations using 11 types of feedstock and 8 furnaces are listed in Table 1 and may occur in each batch of production.Distribution optimization of all 10 products in thermal cracking analyzed in our previous work within reactor scale are implemented on a total of 3 batches.After data collection from the plant and corresponding enterprise,the proposed three-scale integrated optimization could be run on Matlab and GAMS.

4.2.Computational results

The model statistics and performance of the reactor scale model could be referred to our previous work.For the subsequent MILP model,there were 264 discrete (binary) variables,1,105 continuous variables,and 1,500 equations in the industrial case.The MILP model was solved after a total of 84 iterations in CPLEX solver.The optimization results were compared with the practical production in the investigated plant,and the feedstock allocation strategies were listed in Table 2.The COT setting,the yields of ethylene,propylene,butadiene of 8 furnaces during 3 batches were illustrated in Figs.3–6.

As shown in Table 2 and Fig.3,there are differences between optimized and practical production in the feedstock allocation strategies and COT setting.Correspondingly,the yield evolving trends of the three main products(ethylene,propylene,butadiene)were also not the same.Statistics were made on the yield data of each furnace in Figs.4–6,and the overall main product yields were listed in Table 3.

As shown in Table 3,the total yields of the three main products are increased in 8 furnaces after the three-scale integrated optimization.The total profit after optimization is 135,888,342 CNY,which exceeds the practical profit of 131,606,027 CNY at a percentage of 3.25%.The optimized daily profit during production is around 754,935 CNY.

The running time of the three-scale integrated optimization was also recorded for computational performance evaluation.The detailed computation time-consumption of the model is listed in Table 4.

Although the training of the basic model and transfer learning models is time-consuming,this process could be implemented offline before the optimization and then serve as the database of a specific plant.The further training is needed only if new circumstances emerges,such as a new type of feedstock is cracked,the properties of the exist feedstock changes dramatically,or the reactor is replaced.Then for all 36 circumstances,the reactor scale prediction only costs 22.7 seconds,which means the prediction timeconsumption is around 0.6 second per run.Based on this prediction,the reactor scale optimization is accomplished within 1,305 seconds.The subsequent MILP optimization of plant-supply chain scale is accomplished within 3.23 seconds.Thus,the total online optimization time-consumption is 1,308.23 seconds.Despite the higher time-consumption than related researches,the proposed three-scale integrated optimization embedded the mechanisms of the reaction network level into the model,which improved the interpretability and extendibility.

4.3.Sensitivity analysis

Further evaluation of this model was carried out by changing input parameters of the three-scale integrated optimization model for sensitivity analysis.In the first sensitivity case,a production requirement parameter,the total selling limitation of AGO,was changed from 20,000 tons to 0.In another case,a market parameter,the price of ethane,was changed from 4,011 CNY to 4,536 CNY per ton.The feedstock allocation strategy evolving of these two cases was listed in Table 5.

As is shown in Table 5,for sensitivity case 1,if the selling of AGO is limited to 0,all AGO supplied by the basic flowFlo(i)in local refineries should be cracked to prevent the overrun of storage tanks.Therefore,Furnace 2 is used for AGO cracking in the third batch to guarantee the inventory constraints of AGO.However,with this limitation,more profitable HTO cannot be used in this batch,which reduces the total profit.The dealing strategies would also evolve with the growth of net selling of HTO and net buying of AGO.

For sensitivity case 2,if the price of ethane rises dramatically,the cracking of ethane feedstock would be less profitable than that of liquefied natural gas feedstock.Therefore,Furnace 7 is used for LNG cracking instead of ethane in pursuit of higher profits.The net buying of LNG would increase,while the net buying of ethane would decrease.The total profit would decrease because of the price increase of a specific feedstock.The total profit and related dealing strategies evolving of the sensitivity analysis cases is listed in Table 6.

Table 2 Comparison of feedstock allocation strategies between optimized and practical production

Table 3 Comparison of main product yields between optimized and practical production

Table 4 Time-consumption of the three-scale integrated optimization model

Table 5 Sensitivity analysis on feedstock allocation strategies of three cases

Table 6 The total profit and related dealing strategies evolving of the sensitivity analysis cases

5.Conclusions

In this work,a three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain is proposed and applied for industrial thermal cracking cases.The framework and solving strategy of the proposed model effectively searched for profit margin improvement approaches for thermal cracking production.The stability and extendibility of the proposed model were determined by the sensitivity analysis,which also provided strategic evolving of various cases.

Additionally,we should note that with the expansion of plant and supply chain data,this process is expected to be applied for multiple plants within a specific region.The collection and accumulation of reactor scale models are helpful for further speeding of computation.The optimization results could provide production suggestions for plant managers and decision makers on multiplescale,and the whole process has potential to be compiled and developed as an industrial software for digitalization and intelligent manufacturing of petrochemical enterprises.

Fig.3.Comparison of COT setting between optimized and practical production.

Fig.4.Comparison of ethylene yields between optimized and practical production.

Fig.5.Comparison of propylene yields between optimized and practical production.

Fig.6.Comparison of butadiene yields between optimized and practical production.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge the National Natural Science Foundation of China for its financial support (U1462206,21991100,21991104).

Nomenclature

BU（i） buying quantity upper bound for feedstocki

Ccl（j） clean up and startup cost for furnacej

Ce（j） optimized energy cost for furnacej

Cgscost coefficient of gas separation

Clscost coefficient of liquid separation

Cr（i） the price of feedstockifrom local refineries

Crb（i） selling cost of feedstocki

Cro（i） buying cost of feedstockifrom vendors

dt（i,j） cleaning up time for cracking feedstockiin furnacej

E（j,k） ending time ofkth batch in furnacej

F（i,j） feed rate of feedstockito furnacej

Flo（i） basic flow rate from local refineries for feedstocki

G1（i,j,k）buying quantity of feedstockiin batchkof furnacej

G2（i,j,k）selling quantity of feedstockiin batchkof furnacej

IL（i） inventory lower bound for feedstocki

IU（i） inventory upper bound for feedstocki

i=1,???,NTfeedstocks

j,jp=1,???,NRfurnaces

k,kp=1,???,NBbatches

l=1,???,NPproducts

P（l） price of productl

R（i） uncracked quantity of feedstocki

S（j,k） starting time ofkth batch in furnacej

S0（j） initial starting time of the first batch for furnacej

ST（i） initial feedstock storage for feedstocki

SU（i） selling quantity upper bound for feedstocki

tb（i,j） processing time for feedstockiin furnacej

TTtotal processing time

t（i,j,k）running time of batchkto crack feedstockiin furnacej

UPSTupstream feedstock supply time of local refineries

Y（i,j,l）optimal yield of product l to crack feedstockiin furnacej

YG（i,j） total gas production to crack feedstockifor furnacej

YP（i,j） product value per batch to crack feedstockiin furnacej

y（i,j,k）binary variable:1 if feediis cracked in furnacejof batchk,else 0