Di Meng,Cheng Shao,Li Zhu

Institute of Advanced Control Technology,Dalian University of Technology,Dalian 116024,China

Keywords: Ethylene cracking process Energy efficiency scheduling Overall energy efficiency indexes Dual radiation chamber Multiple operation parameters Multiple energy flows

ABSTRACT Ethylene cracking process is the core production process in ethylene industry,and is paid more attention to reduce high energy consumption.Because of the interdependent relationships between multi-flow allocation and multi-parameter setting in cracking process,it is difficult to find the overall energy efficiency scheduling for the purpose of saving energy.The traditional scheduling solutions with optimal economic benefit are not applicable for energy efficiency scheduling issue due to the neglecting of recycle and lost energy,as well as critical operation parameters as coil outlet pressure(COP)and dilution ratio.In addition,the scheduling solutions mostly regard each cracking furnace as an elementary unit,regardless of the coordinated operation of internal dual radiation chambers(DRC).Therefore,to improve energy utilization and production operation,a novel energy efficiency scheduling solution for ethylene cracking process is proposed in this paper.Specifically,steam heat recycle and exhaust heat loss are considered in cracking process based on 6 types of extreme learning machine(ELM)based cracking models incorporating DRC operation and three operation parameters as coil outlet temperature(COT),COP,and dilution ratio according to semi-mechanism analysis.Then to provide long-term decision-making basis for energy efficiency scheduling,overall energy efficiency indexes,including overall output per unit net energy input(OONE),output-input ratio per unit net energy input (ORNE),exhaust gas heat loss ratio (EGHL),are designed based on input–output analysis in terms of material and energy flows.Finally,a multiobjective evolutionary algorithm based on decomposition(MOEA/D)is employed to solve the formulated multi-objective mixed-integer nonlinear programming(MOMINLP)model.The validities of the proposed scheduling solution are illustrated through a case study.The scheduling results demonstrate that an optimal balance between multi-flow allocation,multi-parameter setting,and DRC coordinated operation is reached,which achieves 3.37%and 2.63%decreases in net energy input for same product output and conversion ratio,as well as the 1.56% decrease in energy loss ratio.

1.Introduction

1.1.Energy efficiency scheduling of cracking process

Ethylene industry,providing important base materials for daily life and national economy,is one of the highest energy-consuming process systems [1].According to the Comprehensive Work Plan for Energy Conservation and Emission Reduction during China’s 13th Five-year Plan Period,energy-intensive ethylene industry urgently needs to achieve greater breakthroughs in the application of energy-saving technology [2].As the core section in ethylene production,cracking process accounts for 75%energy consumption of entire plant [3]and dominates the final product yields.Therefore,the energy efficiency scheduling of cracking process becomes an urgent matter for energy conservation and production operation improvement [4].

The ethylene cracking process is associated with assignment of limited resources and coordination of multiple parallel cracking furnaces together over time [5],where each cracking furnace is semi-continuous due to the decoking requirement of furnace tube.Because of multiple energy and material flows in cracking process,how to reasonably evaluate the overall energy efficiency of all cracking furnaces for the long-term scheduling is problematic.Different from traditional economy scheduling,energy efficiency scheduling requires more attention to energy flows,as well as multiple operation parameters associated with energy flows.It is examined that the heat of super high steam(SHS),dilution steam(DS),and exhaust gas respectively account for around 30%,18%,and 6% of fuel combustion heat.It has also been investigated that coil outlet pressure (COP),coil outlet pressure (COT),and dilution ratio are necessary operation parameters for cracking reactions and product yields [6],which directly relate to the energy efficiency of cracking furnace.It is necessary to integrate these energy flows and operation parameters into scheduling to achieve accurate and complete energy efficiency scheduling.In view of the interrelationships between multiple material flows,energy flows,and operation parameters,how to coordinate these flows and parameters in scheduling to maximize energy efficiency is a challenging problem.Moreover,the basic unit of cracking and coking reactions is radiation chamber rather than the entire cracking furnace.In addition to the cracking furnaces,their internal dual radiation chamber (DRC) also needs to be coordinated in scheduling.Actually,not only the DRC of a cracking furnace can handle different feedstocks separately,but also independent operation such as asynchronous batch processing and independent operation parameter setting can be performed between the DRC,which make the scheduling problem even more complicated.

1.2.Literature review of cracking process scheduling

The scheduling problem for multiple feedstocks on parallel cracking furnaces was addressed for an ethylene plant,taking into account exponential decaying performance of furnace with respect to batch time because of coke formation[7].Limet al.[8]exploited a neural network-based input–output model of cracking furnace to represent the decaying productivity of the furnace with coke deposition,such that dynamic data on ethylene and propylene yields could be obtained and used to support scheduling decision.Industrial scheduling strategies for multiple feeds in multiple furnaces were proposed to achieve the best economic performance,where simultaneous shutdown of multiple furnaces is inherently avoided[9].These efforts build the basic scheduling solution for cracking process.

To cope with the occurrence of unforeseen events,Carloset al.[10]presented reactive scheduling of multiproduct batch plants,which can optimally generate updated scheduling schemes and perform multiple rescheduling operations.Zhaoet al.[11]extended the previous scheduling solution by developing a new reactive scheduling strategy,which is capable of smartly generating seamless reschedules and addressing semi-continuous operation for any delivery change of new feed.These studies have provided a better insight for the scheduling under unexpected situations.

Upstream feedstock delivery is a critical link concerned with feedstock allocation in cracking furnaces.A decision-supporting framework for the feeding system considering material delivery,discharge and storage,and material mix was proposed with respect to integrated costs minimization [12].Zhaoet al.[13]proposed a scheduling strategy for cracking process with more consideration of recycle ethane as internal feedstock.Conversely,the operational performance of downstream processes or whole plant is also crucial for cracking process scheduling.Wanget al.[14]integrated the scheduling problem of cracking process with operational plan of downstream units under a synchronized global time scale.Zhaoet al.[15]studied the short-term scheduling problem of both cracking process and downstream process for the purpose of exploring the potential for increasing production margin.The above studies extend scheduling solution by associating cracking process scheduling with upstream or downstream processes.

Most of preceding works mainly focus on feedstock and batch allocations not considering process operation parameter and energy consumption,both of which are critical factors for energy utilization and operation level.Jinet al.simultaneously explored for scheduling and operation decisions by integrating a single operation parameter COT with the product yields and decaying performance of cracking furnace [16].Yuet al.further introduced nonsimultaneous decoking and variable batch-lengths to make the scheduling solution more practical in real-world situations,but assumed COT kept constant during one batch [17].Their work highlights an important fact that the scheduling for cracking process considering operation parameter can enhance the profitability.In addition to COT,fuel consumption was also considered in cracking process based on a linear model incorporating COT and feed property [15].However,the linear fitting model of fuel consumption amount does not very suitable for such a nonlinear ethylene system.Besides,the exhaust gas energy loss and critical operation parameters as COP and dilution ratio are not considered in the scheduling solution.From the perspectives of semimechanism and actual production operation,the current scheduling solutions are not perfect in energy flows and operation parameters,thus resulting in limited optimization space for energy utilization and operation level.

As ethylene industry developed,profit is increasingly not the sole objective for the cracking process scheduling.The MDNSGAII algorithm were applied to multi-objective mixed-integer nonlinear programming (MOMINLP) based cracking process scheduling with three feeds to maximize the average benefits and minimize the average coking amount [18].The environmental sustainability was also concerned in[19].Aiming at causing less adverse environmental impacts,the author wisely allocated furnace decoking emission peaks into time windows,such that the obtained scheduling scheme is responsible for background air-quality.However,the energy efficiency oriented scheduling problem for cracking process is rarely considered,which is the most effective approach for energy saving of cracking process [20,21].Moreover,energy efficiency scheduling is also regarded to be a key measure to achieve economic goals [22].It requires not only a long-term overall decision basis for the energy efficiency of all cracking furnaces,but also the integration of multiple energy flows and associated operation parameters into scheduling.A further problem is that,previous scheduling solutions mostly regard the cracking furnace as a basic unit,ignoring the asynchronous batch processing and independent operation parameter setting of DRC inside each cracking furnace,which limits the energy efficiency improvement space for cracking process scheduling.

1.3.Motivation and main contributions

As mentioned above,although many attempts and studies on scheduling have been proposed and implemented in cracking process,an overall energy efficiency scheduling solution that simultaneously considers multiple energy flows,multiple operation parameters,and DRC coordinated operation is still needed to achieve more comprehensive and effective energy efficiency improvement.The main contributions of this work are as follows:

(a) For the lack of energy efficiency oriented scheduling solution,three process-level energy efficiency scheduling indexes considering energy loss and energy utilization in terms of product output and conversion ratio are designed,which provide a comprehensive long-term decision basis for energy efficiency scheduling of cracking process.

(b) For the neglect of exhaust gas energy loss and operation parameters as COP and dilution ratio in scheduling,a set of cracking models integrating energy recycle,energy loss,and three operation parameters is established.Hence,the optimized multiple operation parameters and energy flows are optimally cooperated with the feedstock and batch allocations after scheduling,which contributes to obtain more complete and efficient scheduling schemes.

(c) For the regardless of DRC coordinated operation in scheduling,asynchronous batch processing (or decoking) and independent operation parameter setting of DRC in each cracking furnace are introduced into the scheduling.All the cracking furnaces and their internal DRC are optimally coordinated after scheduling,which expands the space for energy efficiency enhancement.

2.Methods

2.1.Extreme learning machine

In recent years,neural networks have been widely used in many applications [23].Extreme learning machine (ELM) is an efficient learning algorithm based on single-hidden layer feedforward neural network [24].Different from gradient-based learning algorithms,weights and biases of hidden nodes are initialized and fixed without iteratively tuning.ELM has been applied to data regression,data classification and time series forecasting[25,26].The network architecture of ELM is depicted in Fig.1,wherem,k,nare respectively node numbers of input,hidden,and output layers.

For a given training sample set,supposingxiis theith input data withmdimensions andyiis theith output data withndimensions.β is weight matrix connecting the hidden and output layers,which is the only free matrix that needs to be learned [27].ω is randomly initialized weight matrix connecting input and hidden layers,which does not change during the whole learning phase.bis bias array of the input layer.g（x）denotes non-linear activation function of hidden neuron.All these notations are represented in Eq.(1) [28].

Fig.1.Network architecture of ELM.

The midpoint matrixHof hidden-layer output is described by Eq.2:

wherehiis theith hidden neuron.

Learning procedure equals to obtaining least square solution by solving linear system after a simple generalized inverse operation,as described in Eq.(3):

where Y is output matrix ofNsamples.

2.2.Multi-objective evolutionary algorithm based on decomposition

Multi-objective evolutionary algorithm based on decomposition(MOEA/D),proposed by Zhanget al.[29],works well on a wide range of multi-objective problems with many discrete decision variables and complicated Pareto sets.The essence of MOEA/D is to decompose a multi-objective optimization problem into a number of scalar optimization sub-problems and optimize them simultaneously [30].

Fig.2.Principle diagram of MOEA/D.

3.Problem Statement

A typical cracking process scheduling is shown in Fig.3.After being continuously deposited into charging tanks,multiple feedstocks(i=1，2，···，Nm),fuel,and DS are distributed to the batches(k=1，2，···，Nb) in DRC (u=A，B) of parallel furnaces(j=1，2，···，Nc) under operation parameters as dilution ratio,COP,and COT.Then various products ，（l=1，2，···Np） are formed in cracked gas by cracking reactions.Meanwhile,the boiled feed water (BFW) is respectively allocated to parallel furnaces to recover the heat inside cracked gas and fuel gas,and eventually store the heat in the generated SHS.To maintain normal operation,decoking is requirement for furnace tubes of a radiation chamber after a batch processing because the coke produced in secondary reactions adheres to the inner furnace tube wall.

Fig.4 is an illustrative example for the batch allocation,where the decoking can be separately executed in the DRC of a cracking furnace.Each radiation chamber is only capable of disposing a type of feedstock during one batch,and the duration time of different batches can be different.The concepts are interpreted as follows:

i Batch processing time is duration time starting from the first running of a radiation chamber after the decoking is over until next shutdown for decoking;

Fig.3.An illustration of DRC coordinated cracking process scheduling with multiparameter setting and multi-flow allocation.

Fig.4.Gantt chart for DRC coordinated cracking process scheduling.

ii Decoking time is duration time required to cleanup furnace tubes,equaling to the interval time between two adjacent batches;

iii Batch starts from the first running of a radiation chamber after the decoking is over until the end of next decoking;

iv Total scheduling time is duration time of the scheduling,which contains multiple batches.

Based on the assumptions of traditional scheduling solutions,the proposed scheduling solution introduces an additional assumption (brought by heat loss of exhaust gas): the excess air coefficient is constant.In general,excess air coefficient is calculated by oxygen content of exhaust gas,which is measured by a German Testo XL350 analyzer [32].Nevertheless,the analyzer is not always on line in production,resulting in lacking of oxygen content data.

4.DRC Coordinated Overall Energy Efficiency Scheduling Solution

4.1.Multi-parameter and multi-flow integrated cracking models with respect to DRC operation

The correlations between multiple material flows,energy flows,and operation parameters of cracking furnace need to be quantified to construct the energy efficiency scheduling model.As shown in Fig.5,by absorbing the heat of high-temperature gas produced by fuel combustion,two feedstock flows diluted by two DS flows are respectively cracked in the DRC after being preheated in convection chamber [33],where cracking depth is controlled by adjusting COP,COT,and dilution ratio.The cracked gas is immediately quenched by the BFW in transfer-line exchanger (TLE) after leaving the radiation chamber,where including ethylene,propylene,hydrogen,methane,and pyrolysis carbon 4 (PC4) contained in cracked gas are selected as key products in scheduling solution.The 5 key products can be used to represent the energy efficiency of the pyrolysis process because the sum of key product outputs is about 73% and the energy used to produce these key products accounts for about 94%of the total energy consumption of all products in endothermic cracking reactions.SHS is constantly generated with the quenching of cracking gas.For a cracking furnace,a total of 6 operation parameters,12 material flows,7 energy flows,and 3 temperature parameters is sorted out in Table 1.

Table 1Variables in DRC cracking furnace

The cracking models consist of the following 6 types of models:

①Product output models

Fig.5.Flow diagram of DRC cracking furnace.

According the ubiquitously used Kumar molecular reaction kinetics model described by Eq.(6) [34],the product flows of primary reaction are determined by flow rate,pre-exponential factor and activation energy of feedstock,temperature and pressure of reaction,DS flow,and effective cross-sectional area of furnace tube.The product flows of 21 secondary reactions are determined by exponential factors,activation energy,and flows of primary reaction products,reaction temperature and pressure,DS flow,and effective cross-sectional area of furnace tube.Given that types of primary reaction products are fixed,it can be concluded that flow rate,pre-exponential factor and activation energy of feedstock,temperature and pressure of reaction,DS flow,and effective cross-sectional area of furnace tube are decisive factors for final product flows.

whereNl，Nmrepresent molecular Moore flow rate of componentlorm,mol·s-1;Nis total Moore flow rate mol·s-1;Pis reaction pressure,kPa;Tis reaction temperature,K;dLis length of tube segment,m;Aiis frequency factor;Eiis activation energy,kJ·mol-1;ai，lis stoichiometric coefficient of componentlin reactioni.

Each type of feedstock is separately modeled to cope with different pre-exponential factors and activation energy of different feedstocks.As critical operation parameters,COT and COP mostly represent reaction temperature and pressure.Effective crosssectional area and DS flow can be converted from effective inner tube radius and dilution ratio,respectively.Therefore,feedstock flow,COT,COP,dilution ratio,and effective inner radius are selected as inputs of product model.Because cracking reactions are independently carried out between the DRC,the boundary of product model is consistent with that of a radiation chamber,as shown in Fig.6.Each product model is built for a radiation chamber processing a type of feedstock.

Fig.6.Boundary of product output model.

②Coking rate models A number of coke precursors are contributed in the coke formation [35].Kumar and Kunzru [36]introduced aromatics as coke precursors,whereas other researchers showed that both ethylene and propylene components play a noticeable role as coke precursors[37].Froment[38]believed that a first order kinetic could predict the coking rate precisely based on the concentration of a number of products such as olefins,diolefins,butadiene,and aromatics.One thing is certain that the precursors come from the products of primary and secondary reactions.It can be inferred from[39,40]that the general coking rate formula for any precursor can be expressed as Eq.(8).Thus the decisive factors of coking rate include flow rate,pre-exponential factor and activation energy of feedstock,temperature and pressure of reaction,dilution ratio,and effective inner radius of furnace tube.

whereNcis molecular Moore flow rate of precursor,mol·s-1;Acis precursor frequency factor;Ecis precursor activation energy,kJ·mol-1; β is coking reaction order.

As shown in Fig.7,the boundary of the coking rate model is consistent with radiation chamber,taking into account the independent coking reaction between DRC.

For thekth batch in chamberuofjth cracking furnace that processes theith feedstock,the coking rate model is expressed as Eq.(9).

The coke attached to the inner tube wall reduces circulation areas,such that the effective tube inner radius,defined as the difference between inherent tube inner radius and coke layer thickness,is updated by Eq.(10).

Fig.7.Boundary of coking rate model.

③SHS recycle models

In TLE,preheated BFW is evaporated into SHS by absorbing the heat from cracked gas.According to thermal equilibrium in Eq.(11)[41],the SHS flow is influenced by product flows,COT,and quench temperature,which should be as low as possible to inhibit secondary reactions.Lower limit of quench temperature is dew point of cracked gas,which is influenced by composition of cracked gas.Therefore,decisive factors of SHS flow include pre-exponential factor,activation energy,and flow of feedstock,temperature and pressure of reaction,dilution ratio,and effective tube inner radius.

whereTqis quench temperature,K;Hsis enthalpy of SHS,kJ·kg-1;is DS heat capability,kJ·kg-1·K-1;Cpiis heat capability of producti,kJ·kg-1·K-1.

Considering SHS is generated in TLE,the boundary of SHS recovery model is a radiation chamber with the corresponding TLE,shown in Fig.8.

For thekth batch in chamberuofjth cracking furnace that processes theith feedstock,the SHS recycle model is expressed as Eq.(12).

④Fuel consumption models

As shown in Fig.9,the boundary of fuel consumption model is consistent with radiation chamber,because of independent fuel combustion between DRC.In radiation chamber,the fuel combustion offers heat for endothermic primary and secondary reactions,which is described by Eq.(13) [42].Therefore,fuel flow is determined by flow rate,pre-exponential factor and activation energy of feedstock,temperature and pressure of reaction,dilution ratio,and effective inner radius.Effective inner radius is an essential input of fuel model because more fuel has to be burnt to compensate for the increased heat resistance with the coke accumulated in furnace tube [43].

whereiskth product flow in tube’s inlet,kg;Tciis crossover temperature,K;is standard heat of formation of thekth product,kJ·mol-1.

For the batchkin radiation chamberuof cracking furnacejthat processes feedstocki,the fuel consumption model is expressed as Eq.(14).

Fig.8.Boundary of SHS recycle model.

Fig.9.Boundary of fuel consumption model.

⑤Exhaust gas temperature (EGT) models

The exhaust gas is the major energy loss of cracking furnace due to its higher temperature than external air.According to Fig.5,the high-temperature gas produced by fuel combustion offers the heat for primary and secondary reactions,as well as the heat for BFW preheating and SHS overheating.The residual heat is eventually discharged in the form of low-temperature gas at the top of the convection chamber.Based on the heat balance,the heat loss of exhaust gas is approximately equivalent to the difference between released heat of fuel combustion and total absorbed heat of cracking reactions,BFW preheating,and SHS overheating.From another perspective,the heat loss of exhaust gas depends on EGT and exhaust gas flow,which is influenced by fuel flow when air excess coefficient is constant.Thus it can be inferred that EGT is determined by pre-exponential factor,activation energy,and flow of feedstock,temperature and pressure of reaction,effective tube inner radius,and flows of fuel,BFW,SHS,and DS.The reason for selecting EGT as the model output is that EGT is constrained in production.Given that exhaust gas is initially produced in the DRC and eventually discharged from the convection chamber,the boundary of EGT model is the entire cracking furnace (see Fig.10).

For thejth cracking furnace where batchkAof radiation chamber A processes feedstockij，A，kAand batchkBof radiation chamber B processes feedstockij，B，kB,the EGT model is described by Eq.(15).

⑥Maximum tube temperature (MTT) models

Fig.10.Boundary of EGT model.

The heat transmitted from flue gas to furnace tube wall equals to the heat transferred from tube wall to feedstock and DS when the cracking furnace is under steady state,as described in Eq.16.Thus the MTT can be solved by the following heat equilibrium[41].

where αkis total coefficient of heat transfer,kJ·s-1·m-2·K-1;Cbis radiation coefficient of blackbody,Cb=5˙67 kJ·s-1·m-2·K-1;His effective radiation coefficient;Tgis temperature of fumes,K;nis tube number of each pass;Asis effective area of convective heat transfer,m2.

Apparently,MTT is influenced by the temperature of fuel gas and cracked gas,which is respectively affected by fuel flow and cracking reactions considering cracked gas temperature is constantly changing in the furnace tube from inlet to outlet.It can be inferred that decisive factors of MTT include pre-exponential factor,activation energy,and flow of feedstock,temperature and pressure of reaction,effective tube inner radius,fuel flow,and dilution ratio.Given that the furnace tubes between DRC may have different MTT,the boundary of MTT model is consistent with a single radiation chamber,as shown in Fig.11.

For the batchkin radiation chamberuof cracking furnacejthat processes feedstocki,the MTT model is expressed as Eq.(17).

For intuitive understanding,the variables of the cracking process scheduling are represented in Fig.12,where each variable is distributed in time and space.Due to the tremendous computational load of the cracking models brought by integration of the multiple energy flows,operation parameters,and DRC operation,ELM is employed as a tool of modeling due to its fast learning speed and good generalization performance.

4.2.Overall energy efficiency indexes of cracking process scheduling

According to Fig.13,input side of cracking process includes feedstock and energy input,while output side includes lost energy,product output,and recycle energy.

Input energyEIis the energy sum of fuel,DS,and decoking of all cracking furnaces within scheduling time,as described in Eq.18.

Fig.11.Boundary of MTT models.

Fig.12.An intuitive representation of variables in cracking process scheduling.

where energy conversion factorzrefers to standard GB/T 2589-2008[44];bj，u（τ ）is 1 when radiation chamberuperforms decoking.Otherwise,it is equal to 0.

According to industrial standardization of CNPC Q/SY 66-2002[32],heat of exhaust gas is calculated by fuel energy and EGT when ignoring the changes in ambient temperature and air excess coefficient.The total exhaust gas heat loss of all cracking furnaces within scheduling time is described by Eq.(19).

Fig.13.Input-output of cracking process.

Recycle energy is the difference between the energy of SHS and BFW of all cracking furnaces within scheduling time,as described in Eq.20.

Product output is the weighted quantity sum of all products in all crackingfurnaceswithin scheduling time,where the weight of a product is valued as proportion of market price,as described in Eq.(21).

Given that different batches of a radiation chamber may process different types of feedstocks,feedstock input is the weighted quantity sum of all feedstocks in all batches of all cracking furnaces during total scheduling time (see Eq.(22)),where the weight of a feedstock is measured in terms of its market price.

Net energy input,defined as the difference between input energy and recycle energy,represents the actual energy consumption of cracking process,as described in Eq.(23).

The following three energy efficiency indexes are established by relationships between feedstock,net energy input,lost energy,and product output.

①Overall output per unit net energy input (OONE)

Ethylene industry seeks to produce more products with as little energy consumption as possible.In general,energy consumption would increase with the increase of product output.Therefore,OONE reflects energy utilization level in product output,presented as Eq.(24).

②Output-input ratio per unit net energy input (ORNE)

The conversion from feedstock to product is driven by energy in cracking reactions.Generally,the higher product conversion ratio depends on more energy consumption.Based on OONE,ORNE that reflects the energy utilization level in output-input of material is obtained by introducing feedstock quantity,as described in Eq.(25).

③Exhaust gas heat loss ratio (EGHL)

With the intensification of the energy crisis,energy conservation has become an urgent task for the sustainable development of ethylene industry.For such an energy intensive industry,scientific energy-saving is not to simply pursue energy consumption reduction,but to reduce the energy loss as far as possible.As the major heat loss in cracking furnace,the heat of exhaust gas comes from fuel.Therefore,EGHL that denotes the degree of energy loss is presented,as described in Eq.26.

The bigger OONE and ORNE,and smaller EGHL,the higher overall energy efficiency.Thus scheduling objectives are maximizingM1andM2while minimizingM3(see Eq.27),where decision variables are illustrated in Fig.14.

4.3.Constraints under DRC coordinated operation

Compared with the constraints of traditional scheduling model,the differences of the proposed model are as follows:

①All time variables,flow variables,temperature variables(except EGT),operation variables,and integer variables are constrained in terms of the radiation chamber rather than the entire furnace.

②Constraints of COP,dilution ratio,EGT,and BFW flow are added.

③Decoking constraints are changed.Generally,there should be no overlap of decoking time for batches in all cracking furnaces due to limited resources for decoking and disturbances for downstream processes [17].However,the premise is that DRC of a cracking furnace simultaneously performs decoking.There is an overlap of decoking time for batches in two cracking furnaces where decoking is performed in a single radiation chamber of cracking furnace.Hence,up to any two radiation chambers are able to simultaneously perform decoking,taking DRC coordinated operation into account,which can be described by Eq.28.

4.4.Solution strategy

The proposed scheduling solution is essentially a MOMINLP model with constraints,which is converted into an unconstrained MOMINLP model by penalty function method,as described in Eq.29.

The total quantity constraint for each type of feedstock belongs to point value constraint,which is appropriately relaxed when converting it into domain value constraint for the purpose of avoiding infeasibility due to a large number of constraints,as described in Eq.(30).It is acceptable if total quantity of a type of feedstock has a slight change before and after scheduling.

Then the unconstrained MOMINLP model is transformed into a multi-objective nonlinearity model by mapping integer variables to continuous variables.The point value of the integer variable is mapped to a domain value of a continuous variable (see Eq.(31)),where all domains have identical size to ensure the same search probability between the different domains.Therefore,the same search probability between point values of the integer variable is preserved after mapping.

On this basis,MOEA/D is employed to solve the multi-objective nonlinearity model due to its superior performance for multiobjective optimization.The specific parameter setting is listed in Table 2.All the calculations are performed on the 64 bit MATLAB platform of a Xeon (R) E5-2620 v3 @ 2.4 GHz server with 64 GB RAM.

Fig.14.Decision variables of proposed scheduling model.

5.Results and Discussion: A Practical Case Study

A case study is conducted with a real ethylene plant in northeast China.In the investigated case study,the cracking process contains two heavy cracking furnaces,named as F1 and F2,and three light cracking furnaces(named as F3,F4,and F5).Light feedstocks,including naphtha(NAP)and liquefied petroleum gas(LPG),are disposed by light cracking furnaces,while heavy cracking furnaces process heavy feedstocks such as heavy vacuum gas oil(HVGO),reduction of top oil (RTO),and hydrogenated carbon five fraction (HC5).The case study was presented with 308 time granularity for a total scheduling time of 104 days(each time granularity for half day 12 h).All related parameters are summarized in Table 3,where upper and lower bounds of batch processing time,operation parameters,temperature parameters,feedstocks and energy flows are fixed based on prior operation experience.A MOMINLP model with 3 objectives,150 nonlinear models,and 19,294 constraints was established,where decision variables contain 20,020 continuous variables and 78 integer variables.

As listed in Table 4,the average relative generalization error(ARGE) [45]is used to evaluate the reliability of cracking models between simulation value and actual value of output (see Eq.32),where only part of the models are display due to the space limitation.It is observed that output prediction ARGEs are within industry prediction error threshold (±5%),illustrating the cracking models are reliable.

Table 2Parameter setting on MOEA/D algorithm

After a total of 84.04 hours’ calculation,all energy efficiency indexes have been significantly improved after scheduling (see Fig.15).The OONE increases from 7400 t·kgeo-1to the range between 7650 t·kgeo-1and 7660 t·kgeo-1.ORNE increases from 1˙11×10-8kgeo-1to the range between 1˙14×10-8kgeo-1and 1˙15×10-8kgeo-1.Moreover,EGHL decreases from 5˙78% to the interval between 5˙69% and 5˙70%.

As listed in Table 5,although the product output is decreased by 0.44%after scheduling,the net energy input is decreased by 3.24%and product conversion ratio is increased by 0.69%.Apparently,the major defect of cracking process in energy utilization before scheduling is that excess energy (3˙77×106kgeo) is consumed to produce the extra 3˙85×103ton product output.The 3˙77×106kgeo energy conservation after scheduling mainly comes from the 2˙80×103ton decrease in fuel consumption quantity and 9˙00×103ton increase in SHS generation quantity.Meanwhile,the 1.14% higher production load set for extra 3˙85×103t product output before scheduling also limits the product conversion rate.Additionally,the exhaust gas energy loss is reduced by 3.15% after scheduling,illustrating that most of the extra 3.24%net energy input before scheduling is rarely used effectively,but wasted.It can be seen that key energy links of cracking process,including energy utilization of cracking reactions,energy recycle of SHS,and energy emission of exhaust gas,have been significantly improved after scheduling.

Table 3Related scheduling parameters of cracking process in case study

Table 4ARGEs of testing data of five dynamic simulation models for five cracking furnaces

Table 5Comparison in critical production information of cracking process between before and after scheduling

Throughout the whole cracking furnace group,the net energy input of the two heavy cracking furnaces(F1 and F2)and one light cracking furnace(F5)is significantly reduced after scheduling(see Fig.16).For F1,the reduction in the net energy input is mainly achieved by reducing the fuel consumption quantity of radiation chamber A,while it is mainly the reduction of fuel consumption quantity in radiation chamber B that leads to the reduction of the net energy input of F5.By contrast,the decrease of net energy input in F2 is primarily originated from the increase in SHS generation quantity of radiation chamber A.Quite evidently,the main problems such as high fuel consumption in F1A and F5B,and low steam recycle in F5B are alleviated after scheduling.

The allocations of feedstock and batch before and after scheduling are compared in Fig.17,where the numbers below a batch denote average feedstock flow,fuel flow,COT,COP,dilution ratio,and product output during the batch,respectively.The letter and data inside the batch represent the feedstock type and processing time during the batch.It is interesting that the total batch number is unchanged after scheduling even though batch processing and decoking arrangements are changed,which illustrates that a reasonable balance has been reached between total decoking time and total processing time before scheduling.A remarkable change after scheduling is that RTO is mainly allocated to F1A (radiation chamber A of F1).Compared to the three HVGO-batches in F1A before scheduling,three rearranged RTO-batches in F1A after scheduling have higher product output and lower fuel consumption,illustrating RTO has better cracking performance than HVGO in F1A.Cor111respondingly,two rearranged HVGO-batches of F2A reduce fuel consumption even though there is a decrease in product output after scheduling.However,the product output is reduced and the fuel consumption is increased for a rearrangedHC5-batch of F1B after scheduling.It is reasonable because HC5 has the lowest priority among all feedstocks inferred from the characteristics of high energy consumption and low product conversion ratio.Among three light cracking furnaces,LPG batch number is significantly increased,especially in F4B and F5B.This is because cost of LPG is relatively lower than that of NAP although LPG has no advantages in energy consumption and product conversion ratio.Limited by feedstock flow constraint,LPG is unable to be as the single light feedstock for light cracking furnaces.

Fig.15.Contrast in overall energy efficiency of cracking process between before and after scheduling.

Fig.16.Contrast in equivalent standard oil quantity of energy flow under per unit product output between before and after scheduling.

5.1.Discussion of the proposed scheduling solution

5.1.1.Validation of multi-flow integration in scheduling

As shown in Fig.18,energy flows as fuel,DS,SHS,and exhaust gas are essential in terms of the orders of magnitude of heat.By contrast,the heat of BFW flow can be approximately ignored.

From Table 6,the quantity changes in DS,fuel,SHS,and exhaust gas have significant effects on overall energy efficiency of cracking process.Apparently,these energy flows need to be considered in overall energy efficiency scheduling of cracking process.

Given that fuel and DS are input energy flows,while SHS and exhaust gas are output energy flows,the multi-flow integration in scheduling includes both input and output energy flows.To verify the validity of multi-flow integration in detail,following 4 groups of scheduling experiments are designed: (a) experiment 1 is carried out supposing each energy flow does not changed for every scheduling time granularity,which is used to simulate that all energy flows are not integrated in scheduling; (b) in reverse,to simulate the multi-flow integration in scheduling,all input and output energy flows are variable at every time granularity in the experiment 2; (c) in experiment 3,each input energy flow remains unchanged,while each output energy flow is variable for the aim of simulating the output energy flow integration in scheduling; (d) on the contrary,input energy flows are variable rather than output energy flows in the experiment 4.To prevent the interference of different operation parameter settings on experiments,operation parameters are not included in decision variables of 4 groups of experiments.Dilution ratio is an exception considering DS flow is directly influenced by dilution ratio.Therefore,the 4 groups of experiments have same decision variables,except decision variables of energy flows.The constraints related to energy flows are also different.

The 4 groups of experiments cost 41.07,49.43,41.12 and 49.25 hours’ computation time in turn.Compared to experiment 1,the improvements of the experiment 2 scheduling results lie in the 3˙71×10-5t·kgeo-1increase in OONE,1˙83×10-10kgeo-1increase in ORNE,and 0˙02%decrease in EGHL(see Fig.19),equaling to the 4˙27×104ton increase in product output for same net energy input and the 2˙79×104kgeo decrease in exhaust gas heat loss for same fuel consumption quantity.These crucial improvements indicate that multi-flow integration in scheduling can expand the space of energy efficiency improvement.From Fig.19,the input energy flow integration of experiment 4 makes progress on ORNE and EGHL of scheduling result relative to experiment 1,but shows a decrease in OONE.More than that,the scheduling results of experiment 3 are even worse than that of experiment 4.Apparently,single integration of input or output energy flows is unable to ensure the overall energy efficiency improvement of scheduling result.

From Table 7,the multi-flow integration in scheduling reduces the DS and fuel consumption quantities,and exhaust gas heat loss for same product conversion rate.The net input energy is decreased although SHS recycle quantity has been reduced,leading to the increases in OONE and ORNE.Compared to output energy flow integration scheduling,input energy flow integration scheduling achieves bigger energy efficiency improvement,because allocations of major input energy flows as DS and fuel are optimized.The advantage of multi-flow integration relative to input energy flow integration in scheduling lies in a better balance between DS and fuel consumption quantities,and SHS recycle quantity,such that net energy input of per unit product conversion rate can be further lowered.

5.1.2.Validation of multi-parameter integration in scheduling

Many previous scheduling solutions do not consider process operation parameter,while recent works merely integrate single operation parameter COT into scheduling.As listed in Table 8,COP,COT,and dilution ratio have obvious influence on overall energy efficiency of cracking process,especially on OONE and ORNE.It can be seen that multiple operation parameters are need to be considered in energy efficiency scheduling.To verify the effectiveness of multi-parameter integration,the following 3 groups of scheduling experiments are designed: (a) experiment 1 is conducted supposing COT,COP,and dilution ratio keep constant at every time granularity; (b) by contrast,COT,COP,and dilution ratio are adjustable in scheduling experiment 3; (c) to simulate the integration of single operation parameter,COT is the only adjustable operation parameter in experiment 2.The 3 groups of experiments have identical parameters on MOEA/D algorithm,but with differences on decision variables and constraints of operation parameters due to the integration of different operation parameters.

As shown in Fig.20,overall energy efficiency of each Paretooptimal solution in experiment 2 is bigger than that in experiment 1 after 62.75 and 84.04 hours’ calculation,illustrating that single COT integration in scheduling does expend the overall energy efficiency improvement space of scheduling result.With comparison to experiment 2,A-type Pareto-optimal solutions of experiment 3 perform better in OONE and EGHL,but worse in ORNE.However,it can always find a B-type Pareto-optimal solution with higher overall energy efficiency in experiment 3.On the whole,experiment 3 gives the most efficient scheduling results.Benefited from integration of COP and dilution ratio,product output and revenue of cracking process are increased by 1˙58×104t and 9˙51×106CNY,respectively.Meanwhile,energy loss of exhaust gas is reduced by 5˙63×104kgeo It can be concluded that multiparameter integration is more effective than previous single operation parameter integration for energy efficiency scheduling.

From Table 9,single parameter integration in scheduling reduces DS and fuel consumption quantities of per unit product output,but causes a significant decline in SHS recycle quantity due to the reduction of total energy input.By contrast,the fuel consumption quantity is further decreased in multi-parameter integration scheduling,because the heat absorption of cracking reactions is reduced under same cracking depth by means of optimizing COP and dilution ratio.Although more DS has been consumed,the SHS recycle quantity is increased substantially,resulting in a further decrease in net energy input.

Table 6Change in overall energy efficiency when increasing quantity of an energy flow by 5%

Table 7Contrast in energy statistics under same product conversion rate between scheduling results of 4 groups of experiments

Table 8Change in overall energy efficiency while increasing set value of an operation parameter by 1%

Table 9Contrast in energy statistics of per unit product output between scheduling results of 3 groups of experiments

Fig.17.Contrast in detailed Gantt chart of cracking process between (a) before scheduling and (b) after scheduling.

5.1.3.Validation of DRC coordinated operation in scheduling

The DRC coordinated operation has not been considered in previous scheduling solutions,which is equivalent to adding the following two constraints to the proposed scheduling solution: (1)synchronous batch processing (or decoking) of DRC; (2) identical operation parameter setting of DRC inside each cracking furnace,which are represented by Eq.(33).

Fig.18.Equivalent quantity of standard oil of DS,fuel,SHS,exhaust gas,and BFW during total scheduling time.

Fig.19.Contrast in overall energy efficiency of Pareto-optimal solutions between 4 groups of experiments.

Fig.20.Contrast in overall energy efficiency between Pareto-optimal solutions of 3 groups of experiments.

To validate the effectiveness of DRC coordinated operation in energy efficiency scheduling,the scheduling model without DRC coordinated operation is applied to the same case study.After 62.18 hour’s calculation,Fig.21 shows that all Pareto-optimal solutions solved by scheduling model without DRC coordination are much lower than that solved by DRC coordinated scheduling model in overall energy efficiency.The result suggests that DRC coordinated operation in scheduling greatly expands the space for energy efficiency improvement.

Fig.21.Contrast in overall energy efficiency between Pareto-optimal solutions of DRC coordinated scheduling model,DRC semi-coordinated scheduling model,and scheduling model without DRC coordination.

Fig.22.Contrast in energy flows of per unit product output between Paretooptimal solutions of DRC coordinated scheduling and scheduling without DRC coordination.

From Fig.22,in comparison with the scheduling without DRC coordinated operation,DRC coordinated operation scheduling has decreased the net energy input of per unit product output for almost all radiation chambers,especially F1A,F2A,and F5B.Although DS consumption quantity is increased slightly,fuel consumption quantity is decreased and SHS recycle quantity is increased.Part of the heat inside DS can be recycled in TLE,such that an increase in DS consumption quantity does not necessarily lead to an increase in net energy consumption.Specifically,the decrease in net energy input of F1A and F5B comes from the decrease in fuel consumption,whereas it is the increase in SHS recycle quantity that causes decrease in net input energy of F2A.As there is no DRC synchronous batch processing restriction,batches can be allocated more flexibly in DRC of the cracking furnace,such that cracking performance of LPG,RTO,and HC5 is released in F5B,F1A,and F2A,respectively.

The energy efficiency improvement brought by DRC coordinated operation comes from two perspectives:asynchronous batch processing (or decoking) and independent operation parameter setting of DRC.To analyze their contributions,a DRC semicoordinated scheduling model is designed,where DRC can perform independent operation parameter setting instead of asynchronous batch processing (or decoking).As shown in Fig.21,the red dots are between green and blue dots in terms of the overall energy efficiency after 70.28 hour’s calculation.According to statistics,DRC asynchronous batch processing (or decoking) contributes about 90.65%,94.57%,and 88.57% in the increased OONE,increased ORNE,and reduced EGHL brought by DRC coordinated operation.Cor111respondingly,the contribution of DRC independent operation parameter setting reach 9.35%,5.43%,and 11.43% in the increased OONE,increased ORNE,and reduced EGHL.The results manifest that DRC asynchronous batch processing is crucial to the energy efficiency improvement,while DRC independent operation parameter is limited for energy efficiency enhancement.It is suggested to pay more attention to optimization of batch processing and decoking allocation of DRC in scheduling.

From Fig.23(b),the batches between DRC of any cracking furnace are always asynchronous during scheduling time.There merely exists an overlap between the last decoking of the DRC in F1.This indicates that it is more inclined to select asynchronous batch processing between the DRC of cracking furnace to make efficient scheduling decisions.The DRC asynchronous batch processing brings more flexible batch allocation to cracking process,such that feedstocks and energy sources can be more efficiently distributed.

Fig.23.Contrast in Gantt chart between Pareto-optimal solutions of (a) DRC semi-coordinated scheduling model and (b) DRC coordinated scheduling model.

Fig.24.Contrast in (a) COP,(b) dilution ratio,and (c) COT between DRC of each cracking furnace after DRC semi-coordinated scheduling.

As shown in Fig.24,COP set values between the DRC of each cracking furnace are different during most of the scheduling time even though there are some similarities in trends.The same is true for COT and dilution ratio.It tends to choose different operation parameter settings between DRC in scheduling decisions to maximize the overall energy efficiency of the cracking process when the DRC of cracking furnace processes different types or flows of feedstocks.More appropriate operation parameters can be matched for the radiation chamber processing a specific type and flow of feedstock by means of DRC independent operation parameter setting,resulting in a better overall performance of all feedstocks and radiation chambers.It is suggested increasing production flexibility of cracking process to give full play to the potential of material cracking and energy utilization.

6.Conclusions

This work proposes a novel overall energy efficiency scheduling solution for ethylene cracking process by simultaneously considering multi-flow allocation,multi-parameter setting,and DRC coordinated operation,which achieves energy efficiency improvement comprehensively and scientifically.

The proposed solution reflects several significant features of process operation,for example,the impact of COT,COP,and dilution ratio on product output and energy utilization.Also,SHS recycle energy and exhaust gas energy loss have been taken into account along with the fuel and DS consumption.DRC coordinated operation,including independent parameter setting and asynchronous batch processing,has also been incorporated in scheduling model.Upon comparison with traditional scheduling solutions ignoring multiple parameters,multiple energy flows,or DRC coordination,the proposed solution demonstrates a considerable improvement in overall energy efficiency.

Three conclusions are drawn from this study.Firstly,the scheduling solution considering multiple operation parameters can achieve higher energy efficiency than the previous scheduling with single operation parameter.The cooperation of optimized multiple operation parameters has expanded the space for energy efficiency enhancement.Secondly,the SHS generation,gas exhaust,and DS consumption in cracking process should be simultaneously integrated in the scheduling of feedstocks and fuel consumption to achieve complete and efficient energy efficiency scheduling.Thirdly,DRC coordinated operation,especially asynchronous batch processing,needs to be planned along with the scheduling of parallel furnace groups,which is crucial for the energy efficiency improvement because of the variety of feedstocks.The proposed solution presents a global balance between multiple operation parameters,multiple energy and material flows,multiple furnaces,as well as their internal DRC.The integration of multi-parameter setting,multi-flow allocation,and DRC coordinated operation decrease 2˙28×106kgeo fuel consumption and 1˙65×105kgeo exhaust gas heat loss while increasing 9˙20×105kgeo SHS recycle heat under same product output during 104 days,which are valuable for cracking process even though computational time is increased by 34%,about 21 h.It is also acceptable for the total scheduling period of up to 104 days.The energy efficiency of cracking process is influenced by material and product price change,because the weights of materials and products in OONE and ORNE are affected by the market price.Therefore,the impact of market price changes on the final scheduling scheme should be considered in scheduling.On this point,our research is still insufficient.For further study,we will intend to focus on the dynamic adjustment of scheduling solution with market price changes,so as to improve the feasibility and reliability of the solution in practical application.

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

This work is supported by the High-tech Research and Development Program of China (2014AA041802).

Nomenclatures

bj，u（τ） 0–1 binary variable denotes whether radiation chamberuin furnacejperforms decoking at time τ

Eddecoking energy of cracking process within total scheduling time,kgeo

decoking energy of radiation chamberuin furnacej.every half day,kgeo·d-1

Edstotal DS heat of cracking process within total scheduling time,kgeo

Eegtotal exhaust gas heat loss of cracking process within total scheduling time,kgeo

Eftotal fuel heat of cracking process within total scheduling time,kgeo

EItotal input heat of cracking process within total scheduling time,kgeo

ENItotal net input heat of cracking process within total scheduling time,kgeo

Estotal SHS recycle heat of cracking process within total scheduling time,kgeo

Lpenalty value of constraint

M1OONE of cracking process during total scheduling time,t·kgeo-1

M2ORNE of cracking process during total scheduling time,kgeo-1

M3EGHL of cracking process during total scheduling time

Nbnumber of all batches of a radiation chamber during total scheduling time

Ncnumber of all cracking furnaces

Nmnumber of all feedstock types

Npnumber of all key product types

Nsnumber of all constraints in scheduling model

Oj，uoperation parameter vector of radiation chamberuin furnacej

Subscripts

A index of radiation chamber A

B index of radiation chamber B

iindex of feedstock type

ij，u，kspecific feedstock type during the batchkin the radiation chamberuof cracking furnacej

jindex of cracking furnaces

kindex of batches

lindex of key product type

nindex of constraints

uindex of radiation chambers