Xiaoyong Gao ,Dexian Huang *,Yongheng Jiang Tao Chen

1 Institute for Ocean Engineering,China University of Petroleum,Beijing 102249,China

2 Department of Automation,Tsinghua University,Beijing 100084,China

3 Department of Chemical and Process Engineering,University of Surrey,Guildford GU2 7XH,UK

Keywords:Refinery scheduling Decision tree C4.5 Decomposition method

ABSTRACT Refinery scheduling attracts increasing concerns in both academic and industrial communities in recent years.However,due to the complexity of refinery processes,little has been reported for success use in real world refineries.In academic studies,refinery scheduling is usually treated as an integrated,large-scale optimization problem,though such complex optimization problems are extremely difficult to solve.In this paper,we proposed a way to exploit the prior knowledge existing in refineries,and developed a decision making system to guide the scheduling process.For a real world fuel oil oriented refinery,ten adjusting process scales are predetermined.A C4.5 decision tree works based on the finished oildem and plan to classify the corresponding category(i.e.adjusting scale).Then,a specific sub-scheduling problem with respect to the determined adjusting scale is solved.The proposed strategy is demonstrated with a scheduling case originated from a real world refinery.

1.Introduction

Refinery scheduling has attracted increasing concerns because of increasing environmental standard,intense global competition,and volatile market demand.Fruitful and valuable reports have been published in the last decade.

The dominant research on oil refinery scheduling focus on the integrated model based optimization.The general framework for refinery planning and scheduling were proposed by Pinto and co-workers[1–3].Jia and Ierapetritou proposed a continuous time formulation for refinery scheduling problem and spatially decomposed it into three sub-problems[4,5].In the work of Dogan and Grossmann[6],a decomposition method for simultaneous integrated planning and scheduling problem is proposed.Wu and Ierapetritou[7]proposed a hierarchical approach for production planning and scheduling,in which uncertainty is considered.More recently,Shah and Ierapetritou incorporated logistics into the short term scheduling problem of a large scale refinery and proposed a comprehensive integrated optimization model for the scheduling problem of production units and end-product blending problem[8].Gao et al.considered the impact of variations in crude oil on scheduling for complex reaction processes with a crude classification based multimodal method[9]and also nonlinear characteristics between process model and operating variables for hydro-upgrading processing units using piecewise linear approximation[10],where an integrated model is resulted.Göthe-Lundgren et al.[11]proposed a multi- fixed yield model in terms of several predefined operating states,in which too many binary variables are introduced in the scheduling model,and it is hard to be solved in reasonable time.This method was adopted in Luo and Rong's report[12],in which a hierarchical approach to short-term scheduling is proposed and the binary variables in optimization are significantly reduced.In addition to these specific studies,some excellent reviews have been published in this area,such as Floudas and Lin[13],Bengtsson and Nonås[14],Shah et al.[15],Joly[16],Harjunkoski et al.[17].

However,the formulated integrated large scale mixed integer linear/nonlinear programming problem is really hard-to-solve and seldom successful industrial application report is published.Based on the prior knowledge from field experience,there is no need for plant-wide adjustment in most cases.Moreover,the current scheduling optimization leads to the plant-wide adjustment,which may result in the unreasonable difference between the computed and real yield,due to the existence of process dynamics and long process transition caused by plant-wide arbitrary scheduling adjustments.The arbitrary schedule disturbs the stability of control system,which in turn makes scheduling model inconsistent with the actual process[18].Though some published reports are concentrated on the seamless integration between scheduling and its subside process control system.However,the solution seamlessly mingles these two parts and formulates it as an integrated mathematical programming problem[19,20],which is computationally expensive and hard to obtain a practicable result for a real industrial scale problem in tolerable time.The scheduling task is to stabilize the process as fast as possible and satisfy the demand in most economical way when confronted with the unit break-down or demand changes.

To accelerate the computation of MILP and obtain schedule in reasonable time for real world industrial applications,we propose a decision tree based heuristic decomposition method for refinery scheduling,taking decision tree based upper decision making layer and optimization layer.Decision tree determines the adjusting scale to decrease the process transient time caused by resulted schedule.The lower optimization layer solves a corresponding smaller scale(comparing with the integrated plant-wide scheduling problem)sub-scheduling problem,which not only accelerate the solving speed,but also decrease the schedule's dynamic transition time when carrying out(i.e.the accumulated process dynamic time of all adjusted units for all time periods)and effectively avoid the more complex computation in terms of the model taking schedule dynamics into consideration.

The paper is organized as follows.Decision tree based heuristic decomposition method is proposed in the following Section 2.The mathematical model in terms of decision output is detailed in Section 3.Case study is given in Section 3.1.4 to validate the effectiveness of the proposed strategy and the conclusion is drawn in Section 3.1.5 at the end of the paper.

2.Decision Tree Based Decomposition Method

2.1.Decision tree based decomposition method for refinery scheduling optimization

As aforementioned in the above analysis,refinery scheduling is always formulated as a large scale mixed integer linear or nonlinear programming problem,which is hard to be solved in reasonable time.Moreover,the resulted schedule from the comprehensive model integrating all the plant processes worsen the performance of control because of the existence of process dynamics,which is discarded in the most current dominant researches.In this paper,we proposed a novel decision tree based decomposition method to accelerate the computation and improve the schedule quality.(See Fig.1.)

Fig.1.Schematics of the decision tree based decomposition method.

Based on the field experience,there is no need to adjust all plant wide units for most cases.When confronted with minor changes in finished product oil demand or a unit's small emergence flaw,to adjust part of downstream units may satisfy the target,which is faster to stabilize from the schedule's operation changes.Fast response and quick stability implies that the plant is fast to supply the on-spec components and final product as anticipated in the schedules.Otherwise,the on-spec components and final products are hard to guarantee,because there is no guarantee for the components yields during the dynamic transition process.Moreover,the schedule obtained from this strategy also benefits the MPC and its bottom control system and it makes MPC's operation more stable.

2.2.Decision tree design

The decision tree structure,of which the input attributes variables are most important,is of vital importance to the classification ability.

1)For fuel refinery,the plant productoil conversion rate,defined as the ratio between the final product and the feed crude,has the global influence on the decision,which means that the whole plant,together with the crude oil blending,should be taken in the scheduling optimization if it exceeds the normal value too far.Hence,based on the intrinsic analysis,the plant product oil conversion rate and its delta-value are factors influencing scheduling decision.

2)From the viewpoint of product oil demand quantity,the gasoline diesel demand ratio and its delta-value,delta gasoline diesel ratio,determine the operation of primary processing units(PPU)and secondary processing units(SPU).For example,the PPU and SPU will be driven to the mode benefiting for gasoline component production if there is an increase in gasoline demand during some period.

3)From the quality viewpoint,the demand changes between high quality or premium oil products and regular oil products must have some intrinsic impact on the decision for operation units.The blending components from different operation units have their specific quality characteristics.For gasoline components,research octane number(RON)of straightrun gasoline from crude oil distillation unit is often low,while gasoline components from FCCU or HC are often high with the same high unsaturated olefins content.The reformate from catalytic reforming unit(CRU)is the ideal component for premium and clean gasoline,which has highest RON,low metal and sulfur content.If the premium gasoline demand increases,then units producing high RON and clean gasoline components should be adjusted to increase their processing capacity to yield more premium gasoline components.Then,the ratio between high quality and ordinary oil product and its delta value are impact factors,which should be taken as input variable of decision tree.

To make a summary,the in put variables of decision tree are grouped up in Table 1.One point should be highlighted is the difference between PGR and HGR,PDR and LDR.Some large scale refinery may supply fuels for different regions,where different fuel specification standards are adopted.PGR and PDR denote the ratio between high-spec gasoline and normal-spec gasoline,ratio between high-spec diesel and normalspec diesel respectively.HGR calculates the ratio of high grade gasolinewithout regards of specifications,while LDR gives the ratio of ultra-low freezing diesel among.

Table 1 Schematics of the decision tree based decomposition method

The adjusting scale categories are treated as decision tree output.According to the flow chart of our investigated refinery,the adjusting scale is classified into ten classes,which is listed in Table 2.The detailed classification may be case dependent,and this method is applicable.

Table 2 Tree output

3.Mathematical Model

Under decision tree,the output determines the adjusting scale.Each scale is related with a particular sub-model.According to unittype in refinery, five sub-models are resulted and given as follows.Then,the relationship between decision tree output and the corresponding submodel is given.

3.1.Mathematical sub-models

3.1.1.Sub-scheduling model I(SSM-1)

Only blenders are adjusted in Step I.The objective function to maximize profit is given in SSM-1(1),and SSM-1(2)～SSM-1(5)represent the constraints of blenders,similar to those established for the singlestep decision making approach(Section 3.1).SSM-1(6)and SSM-1(7)are constraints for component oil tanks.In this step,all the upstream units are operated in their steady state.Therefore,the in flow QIuof a specific component oil tank in SSM-1(6),and the property of component oil PROs,u,pin SSM-1(2),are all fixed.

Objective:

Constraints:

In SSM-1,the decision variables are the in flow and out flow of all the tanks and blenders(Qs,u,tand Qs′,u,t),and the blending sequence zu,m,t.

3.1.2.Sub-scheduling model II(SSM-2)

Blenders and HUPUs are scheduled in sub-model SSM-2.The model SSM-2 is summarized as follows.The objective function in SSM-2(1)includes product oils revenues,inventory cost of tanks in step II,and the operating cost of the adjusted HUPUs.

Objective:

Constraints:

The constraints include SSM-1(3–7)because blenders are also considered,and the following:

Since HUPUs are considered for scheduling,the properties of component oils drawn from HUPUs,i.e.PROs,u,p,tin SSM-2(2),are variable.The decision variables are(i)the in flows and out flows of all units(i.e.HUPUs,tanks,blenders)being considered(Qs,u,tand Qs′,u,t),(ii)the blending sequence zu,m,t,and(iii)the operating condition of HUPUs,expressed by ΔPROs′,u,t,p.

3.1.3.Sub-scheduling model III(SSM-3)under Step III

Profit maximization is the objective function,and the only difference compared with SSM-2 is that the operating costs of SPUs are included.

Objective:

Constraints:

The constraints include SSM-1(3–7),SSM-2(2–8),and the following:

In this step,the fractionators of SPUs are also included in schedules,formulated in SSM-3(2–7).The in flows of SPUs(QIu)are fixed in SSM-3(1)and SSM-3(2),because in this step,only main fractionators are considered,while the reactors of SPUs are still in steady state.

The decision variables in this step are(i)the in flows and out flows of HUPUs,tanks and blenders(Qs,u,tand Qs′,u,t),and the out flows Qs′,u,tof SPUs;(ii)the blending sequence zu,m,t;(iii)the operating condition of HUPUs,i.e. ΔPROs′,u,t,p;and(iv)the fractionation mode mfof SPUs

3.1.4.Sub-scheduling model(SSM-4)

In this step,the reactors and main fractionators of SPUs are all adjusted.The variable in flow(QIu,t)for SPUs is formulated in SSM-4(1,2);the reaction mode(mr)and fractionation mode(mf)are adjusted in SSM-4(2,3).The decision variables are(i)the in flows and out flows of the units(SPUs,HUPUs,tanks,blenders)considered in Step IV:Qs,u,tand Qs′,u,t,(ii)the blending sequence zu,m,t,(iii)the operating condition of HUPUs(ΔPROs′,u,t,p),and(iv)the reaction mode mrand fractionation mode mfof SPUs(zu,mr,mf,t).

Objective:

Constraints:

The constraints include SSM-1(3–7),SSM-2(2–8),SSM-3(4–6),and the following:

3.1.5.Sub-scheduling model 5(SSM-5)

In this sub-model,PPUs are also considered in the objective function in SSM-5(1),and the corresponding constraints are formulated in SSM-5(2–6).The decision variables are(i)the in flows and outflows of all units(i.e.PPUs,SPUs,HUPUs,tanks,blenders):Qs,u,tand Qs′,u,t,(ii)the blending sequence(zu,m,t),(iii)the operating condition of HUPUs(Δ PROs′,u,t,p),(iv)the reaction mode mrand fractionation mode mfof SPUs(zu,mr,mf,t),and(v)the operating mode m of PPUs(zu,m,t).

Objective:

Constraints:

SSM-1(3–7),SSM-2(2–8),SSM-3(4–6),SSM-4(2,3)

3.2.Decision tree outputs and sub-models

It is clear that there is a particular sub-model related with every adjusting scale,i.e.the decision tree's output.The detailed relationship between the decision tree outputs and sub-models is listed in Table 3.Clearly,for adjusting scale C1,only blenders are optimized.So,the corresponding sub-model SSM-1 is to be solved.What to be highlighted is that the adjusted unit set is different for tree outputs from C2 to C7 because different HUPUs are included for optimization,though the same sub-model form,i.e.SSM-2 is used.

Table 3Relationship between decision tree outputs and sub-models

4.Case Study

To verify the effectiveness of the proposed decision tree based decomposition method,a scheduling case study is provided here.

4.1.Refinery flowchart

A case refinery originated from a real world refinery in china is provided here,whose flow chart is depicted as in Fig.2.Several crude oils are blended as mixed feed for crude distillation units(i.e.atmospheric and vacuum distillation unit,CDU and VDU in Fig.2).Light gasoline from CDU is further upgraded in CRU to produce reformate for premium and high grade gasoline production.The first side draw,the CDU kerosene,is partly deep processed in DHT and partly distributed as diesel blending component.The second side draw of CDU,the CDU diesel,together with the partly CDU kerosene and light vacuum gas oil(LVGO in Fig.2),is upgraded in DHT to decrease the heavy mental and sulfur content.CDU residue is processed in VDU.High vacuum gas oil(HVGO in Fig.2)is further processed in FCCU,where heavy fraction is cracked into two light fractions,FCC gasoline and diesel.FCC gasoline is upgraded in FCC light gasoline etherification and FCC heavy gasoline desulfurization separately.The gasoline components and diesel components are then blended into the final on-spec gasoline and diesel respectively in blenders.

4.2.Scheduling case study

4.2.1.Decision tree training

Two hundred eighty- five cases are collected to train the decision tree,where 200 cases are used for train and the rest 85 cases are for test.In this research,C4.5 algorithm,is adopted,in which confidence factor is set as 0.25,and ten-fold cross validation method is used to train the tree classifier.The training statistic result is listed in Table 4,which implies that the resulted tree classifier satisfies the accuracy de-mand,because there are only three error cases among 200 cases.The root mean squared error on test cases is 0.026.

Table 4 C4.5 tree training result statistics

The well-trained decision tree is then utilized to make schedule decision determining the optimal schedule adjusting scale and the detailed case study is given in the following section.

Fig.2.The case refinery flowchart.

Fig.3.The Gantt chart of the final oil product demand.

Fig.4.The crude oil supply plan.

4.2.2.Scheduling case study

There is two types fuel demand.Their specifications are quite different,whose details are referred to our previous papers[9,10].In this paper,we can simply take them premium fuel(such as JIV 97,JIV 93,JIV 10 in Fig.3)and regular fuel(i.e.GIII 97,GIII 93,GIII 90,GII 0,GIII 10 in Fig.3).The detailed demand data is depicted as Gantt chart in Fig.3,and the crude supply plan is given in Fig.4.Based on these data,the input attribute variables value can be inferred,which are summarized in Table 5.The obtained value is then input into the well-trained C4.5 decision tree to determine the adjusting class output.Based on this priori knowledge,the scheduling model is fine organized then.Compared with the conventional integrated optimization without these priori knowledge,this method decrease the problem scale and so speed up the optimization,which is meaningful for real world application when confronted with emergency for a timely schedule.

Table 5 The input attribute variable value of case study

The resulted scheduling model based on the discrete time representation is then optimized by LINGO 11.

To further demonstrate the effectiveness of the proposed strategy,the comparison case study is also provided.Two other methods are involved in the comparisons.One is the conventional method,in which an integrated plant-wide model is computed.The other is the heuristic decomposition method,where a from downstream to upstream stepwise trial method is adopted.Clearly,this heuristic method has little knowledge.The comparison results are listed in Table 6.The results reveal that the decomposition strategy largely reduces the computation burden and decreases the problem scale,comparing with the last two columns and the first one,and C4.5 decision tree based method further accelerate the optimization comparing with the heuristic method because it incorporates the knowledge and avoids some meaningless trials.Moreover,the conventional method needs more transient time to reach the schedule goals.Clearly,the longer transition caused by the schedule adjustment results in more profit loss or even the failure to realize theschedule goal in the extreme case if the plant undergoes dynamic transitions during the entire scheduling time horizon.(See Fig.5.)

Table 6 Comparison results

Fig.5.The Gantt chart of the resulted schedule.

5.Conclusions

In this paper,a decision tree based decomposition method is proposed for fuel oriented refinery scheduling optimization to accelerate the computation and improve the decision quality.Based on the deep analysis of mechanism,the decision tree input attributes are well-selected.The trained decision tree is utilized to determine the adjusting scale and guide the scheduling optimization.The case study reveals the effectiveness of the proposed strategy,which speed up the optimization.

Nomenclature

Subscripts