Scheduling of Actual Size Refinery Processes Considering

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Ind. Eng. Chem. Res. 2002, 41, 4794-4806

Scheduling of Actual Size Refinery Processes Considering Environmental Impacts with Multiobjective Optimization Jehoon Song, Hyungjin Park, Dong-Yup Lee, and Sunwon Park* Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea

This paper deals with the scheduling problem of refinery processes considering environmental impacts. To keep abreast of rapidly changing business circumstances, the effective scheduling of the objective of which is to maximize the total profit is absolutely needed for large-scale plants such as refinery processes. In addition, companies cannot avoid making an effort to reduce environmental impacts because now people have a much better understanding of the environment. However, the two objectives mentioned above are conflicting. There is no way to maximize the total profit and minimize environmental impacts simultaneously, but a tradeoff exists. In this case, the best way is to obtain Pareto optimal solutions by multiobjective optimization. Plotting Pareto optimal solutions, decision makers are able to know the correlation between the two objectives. The selection of one of the Pareto optimal solutions depends largely on the decision makers. In this paper, a mixed-integer linear programming model is developed for solving the scheduling problem of actual size refinery processes. Critical Surface-Time 95 (CST95), an impact assessment methodology, is used for considering global environmental impacts. The -constraint method is used in order to implement multiobjective optimization. Finally, this paper proposes Pareto optimal solutions and shows the optimal scheduling of an arbitrary point in Pareto optimal solutions compared with the total profit maximization problem. 1. Introduction Darwin’s1 hypothesis of “survival of the fittest”, which means that nothing can survive unless it adapts itself to perpetually changing circumstances, is applied not only to the world of living things but also to the world of business. Business environments also keep changing. Only the companies that adapt rapidly to these varying circumstances will be prosperous. In particular, the oil refinery industry is not immune to a huge wave of change of business environments. Before the society of knowledge and information, the industrial world of mass production and mass consumption was represented as one of the typical smokestack industries in which the economy of scale plays a key role. However, it has recently faced so many tough problems, which are difficult to cope with by the conventional corporate management system because environmental impacts should be considered, and chemical products are oversupplied. Therefore, an efficient and effective production scheduling is more important than the scheduling for an unconditional increase of products in refinery processes. At the same time, environmental impacts must be considered in the scheduling problem because the concept of pollution prevention is considered in the process integration.2 Many research works have dealt with the scheduling of refinery processes. It was Shah3 who regarded the scheduling problem of refinery processes as an economically important one and applied to it mathematical programming approaches such as mixed-integer linear * To whom all correspondence should be addressed. E-mail: [email protected]. Phone: +82-42-869-3920. Fax: +8242-869-3910.

programming (MILP). Lee et al.4 extended the area of scheduling for refinery processes and developed the MILP model including unloading costs for the crude vessels, costs for vessel waiting in the sea, and inventory costs for storage and blending tanks. Pinto et al.5 developed a mixed-integer nonlinear planning model for refinery production and an MILP scheduling model including transportation of crude oil by an oil pipeline, production of refinery products, and distribution through oil pipelines. Real-world applications were also developed. Park et al.6 proposed a two-level hierarchical method using an optimal control approach to solve the MILP problem for refinery processes. While the global optimum cannot be guaranteed all of the time, computation time was reduced notably. As noted above, environmentally friendly management can be another important issue for large plants such as refinery processes. On the basis of this atmosphere, one of the spotlighted environmental management tools is life cycle assessment (LCA). LCA is a scientific and systematic method to seek measures that can reduce both environmental burden and consumption of energy and resources by means of analyzing environmental pollution effects as well as consumption of energy and resources quantitatively and qualitatively throughout the product life cycle (material, production, transportation, distribution, consumption, and disposal). However, LCA is just a general class of methods. To implement LCA, a specific environmental impact assessment method such as Critical Surface-Time 95 (CST95)7 is needed. CST95 is a new approach to the impact assessment phase in LCA because it introduces the quantitative correlations between pollutants and impacts, impacts and damages, and damages and global impact that is

10.1021/ie010813b CCC: $22.00 © 2002 American Chemical Society Published on Web 08/15/2002

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4795

the key index expressing the total environmental impacts. Research papers on the application of LCA to process industries have been published steadily in the chemical engineering area for the past decade. For example, Azapagic and Clift8 applied a linear programming method to LCA and showed that it was useful to analyze and manage the environmental performance of product systems. A waste reduction algorithm based on the environmental impact balance equation was developed and applied to methyl ethyl ketone processes and synthetic ammonia processes.9,10 Recently, the literature on the application of LCA to chemical processes as a decision-making tool has been reviewed.11-13 Moreover, ecofriendly new methods have been applied to the process systems engineering area using LCA methodology.14,15 If there are two or more optimization objectives, they tend to conflict. A multiobjective optimization technique is used in order to find out Pareto optimal solutions of an optimization problem which includes conflicting objectives. A number of commonly encountered multiobjective optimization problems in chemical engineering have been reviewed by Bhaskar et al.16 recently. Luyben and Floudas17 applied the multiobjective optimization with economic and controllability objectives to binary distillation synthesis. Bhaskar et al.18,19 dealt with multiobjective optimization of an industrial wiped-film poly(ethylene terephthalate) reactor in which the two objectives were the minimization of the acid and vinyl end group concentrations in the product. Furthermore, multiobjective optimizations were implemented in many cases such as membrane separation modules with maximization of alcohol removal from the beer and minimization of removal of the taste chemicals,20 steam reformer with minimization of the methane feed rate and maximization of the flow rate of carbon monoxide in the syngas,21 cyclone separators with maximization of the overall collection efficiency and minimization of the pressure drop,22 and industrial hydrogen plants with maximization of product hydrogen and export steam flow rates.23 The objectives of the above-mentioned multiobjective optimizations were related with just process operations. In other words, they chose conflicting operation conditions as optimization objectives. Besides, other objective functions can be adopted. These are maximization of the total profit in most process optimizations and minimization of the total environmental impacts that are in the spotlight. There are some research papers that are related with the objective functions of economics and environmental impacts. Stefanis et al.24 implemented multiobjective optimization to the dairy industry in order to get optimal design and scheduling considering maximization of the annualized cost and minimization of the global environmental impact in that waste generation is dependent on design and scheduling critically in batch plants. In addition, multiobjective optimization problems between economics and environmental impacts were applied to many design cases such as the synthesis of industrial chemical complexes,25 the production of ethylene glycol,26 the nitric acid plant,27,28 the site location problem,29 the manufacture of methyl chloride process,30 the boron system,31 penicillin production,32 and the methyl ethyl ketone process from secbutyl alcohol.33,34 Recently, Al-Sharrah et al.35 has dealt with the planning problem of an integrated petrochemical industry with an environmental objective.

Figure 1. Graphical overview of a refinery system.

Thus, multiobjective optimization is widely applied to process design problems, but it is rare to implement it to scheduling problems of large processes with considerations of the environmental impacts. In this study, we deal with the scheduling problem of refinery processes on the basis of actual data and propose multiobjective optimization solutions that support environmentfriendly operation considering environmental impacts. This paper is structured as follows. First, the scheduling problem of actual size refinery processes is formulated. Second, CST95, which is a methodology of environmental impact assessment, is introduced.7 Finally, the multiobjective optimization problem is solved by the -constraint method. 2. Scheduling of Actual Size Refinery Processes 2.1. Process Description. Figure 1 shows a graphical overview of an actual refinery system. The system consists of 5 oil fields, namely, 5 kinds of crude oil, 8 oil tankers, 23 storage tanks, 10 blending tanks, 4 crude distillation units (CDUs), and 8 product tanks. In this system, a CDU means a crude oil refinery unit including the secondary treatment processes in a broad sense. The system obeys the operating rules as follows.4 (1) An oil tanker loads one kind of crude oil from a predetermined oil field. (2) An oil tanker cannot unload the crude unless it arrives at the wharf. (3) An oil tanker cannot unload the crude if it leaves the wharf. (4) An oil tanker should arrive and leave the wharf once in the scheduling horizon. (5) Two or more oil tankers cannot stay at the wharf simultaneously. (6) The crude oil cannot be fed into a blending tank while the blending tank is charging CDU. (7) CDU cannot be charged simultaneously by different blended oils. 2.2. Mathematical Model. 2.2.1. Assumptions. For simplicity of the problem, some assumptions are proposed as follows. (1) The process time for the changeover of blends to the CDU is neglected. (2) Perfect mixing occurs in blending tanks. (3) Only specific key components in crude or blended oil fix the property of crude and blended oil. (4) Each oil tanker delivers the specific crude oil from the specific oil field to an assigned storage tank. (5) The proposed scheduling model is based on a uniform discrete time in the given scheduling horizon. (6) The 23 storage tanks are clustered into 8 storage tank groups. (7) The 10 blending tanks are clustered into 5 blending tank groups.

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Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002

Assumptions 1-5 are already introduced by Lee et al.4 A brief explanation is needed for assumptions 6 and 7. Originally, the total capacity of the 23 storage tanks is 2 000 000 m3, that is, ten 120 000 m3 tanks, eight 80 000 m3 tanks, and five 32 000 m3 tanks. The total capacity of 8 oil tankers is 1 500 000 m3, that is, three 300 000 m3 tankers, two 150 000 m3 tankers, and three 100 000 m3 tankers during the scheduling horizon (15 days). When an oil tanker unloads crude oil to storage tanks, it needs two or more storage tanks to unload to because the amount of the crude oil unloaded exceeds the capacity of a storage tank. So, because the total capacity of the storage tanks is limited, it is convenient to make groups of storage tanks considering the initial volume of crude oil in them in order to unload crude oil at a time. The capacities of the storage tank groups are shown in Table 1. In the case of blending tanks, the crude oil from the storage tanks is mixed according to the concentration of sulfur in crude oil. If the concentration reference varies at each blending tank, there are 10 kinds of blended oil. It is more than the number of original crude oils. The role of blending tanks is to keep CDUs running steadily by feeding the crude oils that include the key component within a certain range by mixing several different crude oils from storage tanks. So, many different blending tanks make frequent changeovers of operation conditions and may be obstacles to robust CDU operations. For simplicity of this problem, 10 blending tanks are clustered into 5 blending tank groups. Table 1 shows the capacities of the storage tank groups. The crude oil transfer network for the scheduling problem is shown in Figure 2. 2.2.2. Objective Function. The objective of optimization is to maximize the total profit. The formulation of the objective function is extended from the previous work.6

T

T

XF,v,t ) 1, ∑XL,v,t ) 1 ∑ t)1 t)1 T

TL,v )

tXL,v,t ∑ t)1

∀v

XW,v,t e I

∑XL,v,t′ t′)t

∀v

∀ v, t

∀ v, i, t (8)

V

t

∀v

J

(9)

t

∑ ∑ FVS,v,i,t′ - ∑ ∑ FSB,i,j,t′ v)1t′)1 j)1t′)1

FSB,i,j,min(1 -

∑ PRICEpTOTp/Dprod,p -

C

V

C

L

FSB,i,j,t e FSB,i,j,max(1 -

Dj,l,t) ∑ l)1

∀ i, j, t (11) ∀i

VS,i,min e VS,i,t e VS,i,max

I

VB,j,t ) VB,j,0 +

t

∑ ∑ i)1t′)1

L

FSB,i,j,t′ -

∑ ∑ Ccrude,cVtanker,v - c)1 ∑v)1 ∑ Ccharter,vVtanker,vDcrude,c c)1v)1 V

∑ Cunload,v(TL,v - TF,v + 1) - v)1 ∑ Cstay,v(TF,v v)1

∑ ∑ FBC,j,l,t′ l)1t′)1

I

TARR,v) J

T

∑ ∑ i)1t)1

Cinv_ST,i

T

∑ ∑Cinv_BT,j j)1 t)1 T

J

L

U

J

(

(

)

VS,i,t + VS,i,t-1 2

)

VB,j,t + VB,j,t-1 2

t

∀ j, l, t (15) (16)

∀ j, l, t (17) ∀p

(18)

L

∀ j, k, t (19)

∀ i, j, k

fSB,i,j,k,t ) FSB,i,j,tξS,i,k

(20)

FBC,j,l,tξB,j,k,min e fBC,i,j,k,t e FBC,j,l,tξB,j,k,max ∀ j, k, l, t (21)

-

L

∑ ∑ ∑ Coperate,uOPERj,l,uPROj,lDblend,j j)1 l)1u)1

(14)

fBC,j,l,k,t′) ∑ (∑fSB,i,j,k,t′ - ∑ t′)1 i)1 l)1

-

∑ ∑ ∑ ∑Csetup,j,j′,lZj,j′,l,t t)1 j)1j′)1l)1 J

I

∀ j, t

∀ j, t

PRODUCTp g DEMANDp vB,j,k,t ) vB,j,k,0 +

(13)

t

CFBC,j,l,t ) CFBC,j,l,t-1 + FBC,j,l,t

V

(12)

∀ i, j, t

CFSB,i,j,t ) CFSB,i,j,t-1 + FSB,i,j,t

VB,j,min e VB,j,t e VB,j,max

V

(10)

Dj,l,t) e ∑ l)1

FBC,j,l,minDj,l,t e FBC,j,l,t e FBC,j,l,maxDj,l,t

p)1

∀ i, t

L

P

PROFIT )

(7)

T

∑ ∑FVS,v,i,t ) VV,v,0 i)1t)1 VS,i,t ) VS,i,0 +

(6)

t

∑ ∑ FVS,v,i,t′ i)1t′)1

FVS,v,i,minXW,v,t e FVS,v,i,t e FVS,v,i,maxXW,v,t I

(5)

T

∑ XF,v,t′, t′)1

VV,v,t ) VV,v,0 -

(4)

∀v

TL,v - TF,v + 1 g DURATIONv t

(3)

∀v

TF,v g TARR,v, TF,v+1 g TL,v

XW,v,t e

(2)

T

tXF,v,t, ∑ t)1

TF,v )

∀v

VB,j,tξB,j,k,min e vB,j,k,t e VB,j,tξB,j,k,max L

(1)

2.2.3. Constraints. The constraints are as follows. These equations are from the work of Park et al.5

∀ j, k, t

(22)

J

Dj,l,t e 1, ∑Dj,l,t e 1 ∑ l)1 j)1 Zj,j′,l,t g Dj′,l,t + Dj,l,t-1 - 1

∀ j, l, t

∀ j, j′(j*j′), l, t

(23) (24)

2.2.4. Decision Variables. Decision variables in this model are as follows. (1) Crude oil flow rate from oil

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4797 Table 1. Storage Tank Data storage tank group no.

no. of 120 000 m3 tanks


1 2 3 4 5 6 7 8 total

1 3

1

1 2 3 10


2 1 1 1

1

2 8

1 5

2 1

total capacity (m3)

Angola (Odudu) UAE (Murban) Iran (Iranian Heavy) Saudi Arabia (Arabian Light) Kuwait (Kuwait)

minimal vol. of crude oil (m3)

related blending tank no.

inventory cost [$/(m3 day)]

45000 55000 87000 45000 39000 47000 55000 87000

5000 9000 4800 5000 3600 8800 9000 4800

1 1, 2 2 2, 3 3, 4 4 4, 5 5

0.0069 0.0114 0.0087 0.0069 0.0081 0.0132 0.0114 0.0087

200 000 360 000 192 000 200 000 144 000 352 000 360 000 192 000 2 000 000

Table 2. Crude Oil Data oil-producing countries (crude oil)

initial vol. of crude oil (m3)

Table 3. Oil Tanker Data

vol. of concn of specific price per imports sulfur gravity unit vol. (m3) (wt %) (60 °F/60 °F) ($/m3) 150 000 400 000 250 000 300 000

0.16 0.83 1.74 1.75

0.840 0.823 0.867 0.848

98.00 105.42 99.70 106.62

400 000

2.54

0.873

94.79

tankers to storage tanks, from storage tanks to blending tanks, and from blending tanks to CDUs. (2) Flow rates of key components from blending tank to CDU. (3) Volume of crude oil in each oil tanker, storage tank, and blending tank. (4) Time to start unloading, to complete unloading, and to depart from the wharf. (5) 0-1 binary variables denoting if an oil tanker starts unloading and stops it. (6) 0-1 binary variables denoting if a blending tank charges a CDU. (7) Variables denoting if a changeover of blended oil occurs in a CDU. (8) Key component masses in each blending tank. 2.2.5. Parameters. Parameters in this model are the data of crude oils, oil tankers, storage tanks, blending tanks, production yield in CDUs, utilities consumed in each CDU, utility costs in each CDU, inventory costs, and other costs. These are shown in Tables 2-8. 3. Environmental Impact Assessment In addition to maximization of the total profit, another objective of optimization for the refinery processes is minimization of the total environmental impact. For the assessment of the environmental impact of products, LCA is widely used. It consists of three phases. One is “goal and scope definition”. The aim and the scope of the study are defined here. Another is “life cycle inventory”. In this step, the pollutant emissions and the consumption of resources are listed. The other is “impact assessment”. In this phase, emissions of pollutants are categorized into problem type (classification), the impact and damage of the emissions are weighted and quantified within each category (characterization), and the global impacts are assessed (valuation). Impact assessment plays a key role in LCA. In this study, the CST95 methodology is used for the assessment of environmental impacts.7 3.1. CST95. CST95 provides a systematic and stepby-step methodology with which global environmental impacts are evaluated from inventory pollutants. With this five-step approach, we can obtain not only environmental problems that pollutants give rise to but also damages of the problems. Ultimately, the global impact that is the weighted sum of the damages is obtained as a result. Figure 3 shows the general description of the CST95 impact assessment method.

oil tanker no.

crude oil

1 2 3 4 5 6 7 8

Murban Arabian Light Kuwait Odudu Iranian Heavy Murban Iranian Heavy Kuwait

arrival related capacity charterage day of storage (m3) ($/kg) tankers tank no. 300 000 300 000 300 000 150 000 150 000 100 000 100 000 100 000

0.018 34 0.018 34 0.018 34 0.012 40 0.012 40 0.025 48 0.025 48 0.025 48

1 4 7 10 12 13 14 15

2 6 7 1 4 3 5 8

3.1.1. Impact Classification. The categories of environmental problems used in CST95 are as follows: (1) human toxicity, (2) terrestrial ecotoxicity, (3) aquatic ecotoxicity, (4) photo-oxidant formation, (5) acidification, (6) eutrophication, (7) global warming, (8) depletion of stratospheric ozone, (9) energy and abiotic resources, and (10) land use. 3.1.2. Impact Characterization. A reference substance is selected for each impact category. By multiplication of a characterization factor, emissions of each substance are converted into environmentally equivalent emissions of the reference substance. Therefore, the score of an impact category is the sum of equivalent emissions.

Sq )

∑n CTFq,nMn

(25)

The unit of Sq is kg of the reference substance, MJ, or m2 year. The reference substances and effect scores of each impact category on the basis of eq 25 are shown in Table 9. 3.1.3. Damage Classification. The damages caused by the aforementioned environmental problems are grouped into four classes: human health, aquatic ecosystem health, terrestrial ecosystem health, and indirect damages. The categories of environmental problems related with the damages on the safeguard subjects such as humans, aquatic ecosystems, terrestrial ecosystems, and indirect damages are shown in Figure 3. 3.1.4. Damage Characterization. In the damage characterization step, the damages on the safeguard subjects are quantified with the effect scores of each impact category by multiplying the damage-effect correlations. The general equation is shown in eq 26. The unit of Db is m2 year, which expresses the equivalent polluted or used area for 1 year.

Db )

∑q db,qSq

(26)

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Table 4. Blending Tank Data

blending tank no.


1 2 3 4 5 total

2 2 2 2 8


capacity (m3)

2

160 000 240 000 240 000 240 000 240 000

(m3)

vol. of crude oil initial min 80 000 120 000 120 000 120 000 120 000

4000 6000 6000 6000 6000

mean specific gravity (60 °F/60 °F) 832 838 867 862 873

concn of sulfur (wt %) initial min max 0.49 1.13 1.74 2.01 2.54

0.16 0.81 1.44 1.88 2.28

related CDU no.

inventory cost [$/(m3 day)]

1 1, 2 2, 3 3, 4 4

0.0100 0.0144 0.0144 0.0144 0.0144

0.81 1.44 1.88 2.28 3.00

2

Table 5. Production Yields in CDUs blending tank f CDU

LPG (wt %)

naphtha (wt %)

gasoline (wt %)

kerosene (wt %)

diesel (wt %)

1f1 2f1 2f2 3f2 3f3 4f3 4f4 5f4 aftertax selling price ($/m3) minimal demand (tons/15 days)

1.34 1.46 1.58 1.87 1.73 1.58 1.77 1.93 336 20 000

7.46 11.11 17.04 18.10 18.16 18.22

6.16 4.32

14.24 13.76 13.28 11.30 12.25 13.20 20.77 22.16 283 180 000

18.71 19.54 20.37 22.14 19.79 17.44 14.22 10.23 274 180 000

21.12 33.17 288 150 000

265 100 000

bunker C (wt %)

asphalt (wt %)

fuel gas (wt %)

44.81 46.07 47.33 46.59 48.07 49.56 40.19 30.82 205 480 000

5.99 3.67

0.99 0.07

192 5000

1.93 1.69 256 8000

Table 6. Utilities Consumed in CDU

blending tank f CDU

industrial water (kg)/ feed (kg)

cooling water make-up (kg)/ feed (kg)

fuel (bunker C m3)/ feed (kg)

steam (ESS kg)/ feed (kg)

electricity (W h)/ feed (kg)

1f1 2f1 2f2 3f2 3f3 4f3 4f4 5f4

0.068 14 0.059 21 0.057 65 0.056 09 0.054 61 0.053 12 0.049 07 0.045 02

0.116 17 0.073 20 0.056 23 0.039 25 0.041 06 0.042 88 0.040 55 0.038 21

0.000 018 38 0.000 020 02 0.000 015 64 0.000 011 25 0.000 010 48 0.000 009 71 0.000 013 79 0.000 017 88

0.097 59 0.077 04 0.066 53 0.056 02 0.044 95 0.033 87 0.040 55 0.047 23

7.649 20 7.840 00 5.995 85 4.151 70 3.368 31 2.584 92 7.241 03 11.897 14

Table 7. Utility Costs in CDU fuel ($/ industrial cooling water bunker C steam electricity water ($/kg) make-up ($/kg) m3) ($/ESS kg) ($/Wh) 0.000 641 442 0.000 641 442

410

0.006 414 42 0.003 74

Table 8. Other Costs unloading cost ($/day)

demurrage ($/day)

changeover cost in CDUs ($)

8000

5000

5000

3.1.5. Valuation. The final global impact score for all safeguard subjects is calculated by eq 27.

G)

∑b wbDb

(27)

This value can be a barometer denoting the global environmental impact of the systems. It is assumed that wb would be equal to 1 for all safeguard subjects7 in this paper. Further work is required in order to define the factor in detail. The unit of G is m2 year. 3.2. Pollutants Emission in Refinery Processes. Most of the pollutants are emitted in the course of operating CDU including the secondary treatment processes, which consists of complex equipments and consumes a large amount of energy. Because the operation conditions of CDU are varied according to blended oil fed into CDU from blending tanks, the emission of pollutants varies accordingly. Table 10 shows the emission in CDU per unit mass of blended oil for each pollutant. The characterization factor for pollutant

Figure 2. Crude oil transfer network for the scheduling problem.

substances in an impact category is shown in Table 11. The slope of the damage-effect function for damage characterization is shown in Table 12. 4. Multiobjective Optimization Multiobjective optimization problems can be written as

Minimize U(f1(X),f2(X),...,fM(X)) gy(X) e 0

y ) 1, ..., Y

hz(X) ) 0

z ) 1, ..., Z

X ) [x1, x2, ..., xD]T

(28)


Figure 3. General description of the CST95 impact assessment method. Table 9. Effect Scores of Each Impact Category impact category

total effect score Shumantox )

human toxicity

reference substance (unit)

∑(HTP M + HTP M + HTP ) ∑AEP (f M + M + f M ) ) ∑TEP (M + f M ) ) ∑POCP M ) ∑AP M ) ∑EP NL M ) ∑GWP M ) ∑ODP M ) ∑EIS M ) ∑∆t A a

a

n

w

n

n

w

n

s n

s

Mn )

Pb (kg)

n

ww

Saquaeco

aquatic ecotoxicity

aw

n

n

a

w

n

n

sw

n

s

Zn (kg)

n

n

s

Sterreeco

terrestrial ecotoxicity

s

n

as

n

n

a

Zn (kg)

n

n

photo-oxidant formation

Soxiform

n

ethylene (kg)

n

n

Sacid

acidification

n

SO2 (kg)

n

n

Seutro

eutrophication

n

n

phosphate (kg)

n

n

Sglowarm

global warming

500,n

CO2 (kg)

n

n

depletion of stratospheric ozone

Sozodep

n

CFC11 (kg)

n

n

Sabiores

abiotic resources

n

energy (MJ)

n

n

Sland

land use

n

n

n

Table 10. Pollutants Emitted from CDUs blending tank f CDU

oil (kg)/ feed (kg)

chemical oxygen demand (kg)/ feed (kg)

SOx (kg)/ feed (kg)

NOx (kg)/ feed (kg)

total suspended particles (kg)/ feed (kg)

1f1 2f1 2f2 3f2 3f3 4f3 4f4 5f4

0.000 033 916 0.000 028 613 0.000 021 288 0.000 013 963 0.000 014 973 0.000 015 983 0.000 017 802 0.000 019 620

0.000 014 232 0.000 013 131 0.000 009 769 0.000 006 407 0.000 006 746 0.000 007 084 0.000 008 723 0.000 010 361

0.000 066 930 0.000 077 420 0.000 086 548 0.000 095 675 0.000 133 814 0.000 171 953 0.000 155 278 0.000 138 602

0.000 027 256 0.000 036 957 0.000 044 693 0.000 052 428 0.000 068 600 0.000 084 771 0.000 077 727 0.000 070 683

0.000 002 539 0.000 002 786 0.000 002 957 0.000 003 127 0.000 003 771 0.000 004 414 0.000 005 400 0.000 006 385

If an optimization problem has two or more objective functions, there exist tradeoffs among them instead of a unique solution. Generally, no solution vector X exists that minimizes all of the objective functions simulta-

neously. A feasible vector X is called the Pareto optimal solution if there is no other feasible vector that reduces one objective function without causing an increase in the other objective functions. It is up to the decision

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Table 11. Characterization Factors for Substances in Impact Categories

impact category

oil

HTPa (kg of equivalent Pb emitted to air/ kg of substance emitted to air) AEPww (kg of equivalent Zn emitted to water/ kg of substance emitted to water) AP (kg of equivalent SO2/kg of substance) EP (kg of equivalent phosphate/kg of substance) GWP500 (kg of equivalent CO2/kg of substance)

SOx

NOx

total suspended particles

0.0075

0.0020

0.0075

1

0.7 0.13 0

chemical oxygen demand

0.13 0.022

Table 12. Slope of the Damage-Effect Function damage-effect slope

human toxicity

aquatic ecotoxicity

acidification

eutrophication

global warming

db,q (m2 year/kg of reference substance)

12 100

510 000

830

4800

34

maker to select the best compromising solution among a number of Pareto optimal solutions. There are several methods to obtain Pareto optimal solutions, but one of the most popular methods is the -constraint method. This approach is very useful because it overcomes duality gaps in nonconvex sets.16 In this technique, eq 28 is reformulated as

Minimize U(f1(X)) fm(X) e m

m ) 2, ..., M

gy(X) e 0 y ) 1, ..., Y

X ) [x1, x2, ..., xD]

oil tanker f storage tank 1f2 2f6 3f7 4f1 5f4 6f3 7f5 8f8

time (day) 1

2 3

4

5 6

7

8 9 10 11 12

13

14

15

300 300 300 150 150 100 100 100

Table 14. Crude Oil Flow Rates from Storage Tanks to Blending Tanks for Maximization of the Total Profit (1000 m3/day)

hz(X) ) 0 z ) 1, ..., Z T

Table 13. Crude Oil Flow Rates from Oil Tanker to Storage Tanks for Maximization of the Total Profit (1000 m3/day)

(29)

In other words, a single objective optimization is formulated with one of the objective functions, and the other objective functions become inequality constraints within the bound of the m-constraint level. When m is varied, Pareto optimal solutions can be obtained. The -constraint method is the simplest method to obtain Pareto optimal solutions, but it is not always very practical computationally because it needs to be solved repeatedly whenever the upper bound m varies.36 Especially this method is laborious to treat if the number of m is high. However, if there are only two objectives in this paper such as economics and environmental impacts, Pareto optimal solutions can be obtained easily. 5. Results Refinery process scheduling has been implemented on a refinery with the capacity of 100 000 m3 of crude oil/ day and 1 500 000 m3 of crude oil for the scheduling time horizon, namely, 15 days. The optimization model involves 150 binary variables, 1199 continuous variables, and 2168 constraints. This MILP model was solved with CPLEX in GAMS37 2.50 on a SUN (Ultra 1) workstation. A total of 592 s of CPU time was taken to solve the model. 5.1. Single Objective Optimization: Maximization of the Total Profit or Minimization of Global Environmental Impact. As a result of the single objective optimization without the consideration of the environment, we found the maximum total profit of $171 561 500 per 15 days. Tables 13-15 show the crude oil flow rates from oil tankers to storage tanks, from

storage tank f blending tank 1 2 2f1 2f2 3f2 4f3 5f3 6f4 7f4 7f5 8f5

time (day) 3

4

5

6

7

8 9 10 11 12

13

14 15

70 80 56 10 35.4 55 1

30

80

80 80

45 80

59.8 10 80

80

40

Table 15. Crude Oil Flow Rates from Blending Tanks to CDUs for Maximization of the Total Profit (1000 m3/day) blending tank f CDU 1 1f1 2f1 2f2 3f2 3f3 4f3 4f4 5f4

time (day) 2

3

4

5

10 10 10 10

6

7

8

9 10 11 12 13 14 15

10 10 10 10 10 10 10 10 10 10 10

20 20

20 20

30 30

20 20 20 20 20 20 20 20 20 19.4

20

30 30

30 30 30

30

40 40

30 30 30

40 40 40 40

40 39

30 30 30

40 40 40

30 40

40 40

40

storage tanks to blending tanks, and from blending tanks to CDUs for the total profit maximization. Optimal inventory schedules of storage tanks and blending tanks are illustrated in Figures 4 and 5. The optimal production schedule of CDUs is also shown in Figure 6. Effect scores of each impact category, damage scores of each safeguard subject, and global impact for maximization of the total profit are shown in Table 16. Similarly we can solve the minimization problem of the global environmental impact while satisfying customer’s minimal demand, and Table 17 shows its result. 5.2. Multiobjective Optimization: Pareto Optimum Solutions. The global environmental impacts obtained by the two single optimization cases mentioned


Figure 4. Optimal inventory schedule of storage tanks for maximization of the total profit.

Figure 5. Optimal inventory schedule of blending tanks for maximization of the total profit.

above are regarded as upper and lower bounds of the environmental impact in the multiobjective optimization problem, respectively. Figure 7 shows Pareto optimal solutions of the multiobjective optimization problem. In this plot, the upper and lower bounds of the global impact value are 2 247 011 and 1 976 081 m2 year, respectively. The Pareto optima are plotted between these bounds with 1000 m2 year interval, and 271 Pareto optimal solutions are shown in Figure 7. Point A is the result of maximizing the total profit without considering the environmental effect. Point B is found by minimizing the environmental impact while satisfying minimal customer demand. Point C is the Utopia point. Point D is an arbitrarily selected point among Pareto optimum solutions. The total profit at point D is $155 935 200 per 15 days. It is less than that of point A because it is the result of the optimization problem

with an additional constraint to the optimization problem at point A. However, this value is the maximum within the given environmental impact bound. Tables 18 and 19 show crude oil flow rates from storage tanks to blending tanks and from blending tanks to CDUs for point D. The optimal inventory schedules of storage tanks and blending tanks are illustrated in Figures 8 and 9. The optimal production schedule of CDUs is also shown in Figure 10. The effect score of each impact category, the damage score of each safeguard subject, and the global impact for point D are shown in Table 20. It is reasonable to compare the scheduling of point D, which is one of Pareto optimal solutions, with the scheduling of point A. Point B is not realistic because it is the result of just minimizing the global impact while satisfying the minimal customer demand without eco-

4802


Figure 6. Optimal production schedule of CDU for maximization of the total profit.

Figure 7. Pareto optimal solutions of the multiobjective optimization.

nomic consideration. A sure method to reduce environmental impact is to reduce production. If production is reduced, the revenue from the sales of products also decreases. However, because of the reduction of raw material and energy consumption, pollutant emissions decrease. So, global impact is reduced, but production reduction is limited by customers’ minimal demand that must be satisfied. Therefore, in a refinery it is important to make a scheduling so that CDUs with less global impact are utilized more than CDUs with more global impact. As seen from Tables 11 and 12, it is oil that has the most

influence on the global impact. Table 10 shows that oil emission is the highest from CDU1. This is because CDU1 is the oldest and least efficient and emits oil the most among all CDUs for the same amount of production. Thus, to reduce global environmental impact, CDU1 should be used the least. Comparing Table 19 with Table 15, we can see that the total amount of crude feed to CDUs is less at point D than at point A. Especially, the amount of feed into CDU1 at point D is lower than that at point A. Figures 5 and 9 show that inventories of all blending tanks are almost used up at the end of the scheduling horizon at points A and D


Figure 8. Optimal inventory schedule of storage tanks for point D.

Figure 9. Optimal inventory schedule of blending tanks for point D.

except the inventory of blending tank 1 at point D. Accordingly, the production at point D is less than that at point A, as can be seen in Figures 6 and 10. Figure 7 shows that the maximum total profit increases as the constraint on the global environmental impact (m) increases. The relationship between them is not simply linear. Therefore, it is very important which scheduling a decision maker should choose among the Pareto optimal solutions. In case the restriction on global environmental impact is imposed from the outside, the scheduling is fixed to maximize the total profit while satisfying the global impact constraint. If the restriction on the environmental impact is not imposed from the outside and the decision maker must choose a scheduling from Pareto optimal solutions, there can be many alternatives. In this case, it is desirable to choose

a scheduling so that the total profit decreases relatively less as the global environmental impact decreases. 6. Conclusions Scheduling of actual size refinery processes considering environmental impacts with multiobjective optimization has been addressed in this paper. The scope of scheduling was the whole processes including crude oil purchase from oil fields, oil shipping by tankers, unloading to storage tanks, feeding to blending tanks, and operating CDU and product tanks. The scheduling model was developed as an MILP model. The CST95 method was used for consideration of environmental impact assessment, and the multiobjective method used in this problem was the -constraint method. In this method, first the upper and lower bounds were deter-

4804


Figure 10. Optimal production schedule of CDU for point D. Table 16. Effect Scores of Impact Categories and Damage Scores of Safeguard Subjects for Maximization of Total Profit

impact category

effect score (kg of reference substance)

human toxicity aquatic ecotoxicity acidification eutrophication

1.681 3.824 259.025 12.817

damage score (m2 year)

safeguard subject

human health 20 338 aquatic ecosystems 1 950 158 terrestrial ecosystems 276 514 global impact 2 247 011

Table 17. Effect Scores of Impact Categories and Damage Scores of Safeguard Subjects for Minimization of Global Environmental Impact

impact category



1.530 3.345 235.851 11.685


Table 18. Crude Oil Flow Rates from Storage Tanks to Blending Tanks for Point D (1000 m3/day) storage tank f blending tank 1 2f1 2f2 3f2 4f3 5f3 6f4 7f4 7f5 8f5

time (day) 2

3

4

5

6 7 8 9 10 11 12 13

70 42

14 15

8

48

80 34.5 40 35.4

80 80 36

10 76

80 60

27.2 2.7 80

blending tank f CDU 1 1f1 2f1 2f2 3f2 3f3 4f3 4f4 5f4

8

time (day) 2

3

4

8

8

8

5

8

20 20

24

7

17.4 16 30

14

8

8

8

8

16

30 40

8

15 8 20

24 24 30

40 40 40 40 40

8

20 20 20 20 20 16.5

24

40

9 10 11 12 13

8 20

24 30 30

8

8 8

20 20

6

30 30 30 30

40 40 40

30 40

40 40

40

40

Table 20. Effect Scores of Impact Categories and Damage Scores of Safeguard Subjects for Point D


safeguard subject

Table 19. Crude Oil Flow Rates from Blending Tanks to CDUs for Point D (1000 m3/day)

77.2 2.8

mined by the maximization of the total profit and the minimization of the environmental burden, respectively. Next, varying , we implemented the optimization problem with the objective function of the total profit and the constraint that the global environmental impact should be between its upper and lower bounds. Pareto

impact category



1.624 3.555 250.410 12.413

safeguard subject



optimal solutions can be obtained in this way. One of them is compared with the result of the total profit maximization problem. With these Pareto optimal solutions, decision makers can know how much economic benefit will be reduced when the environmental impact of the processes decreases to some extent. Thus, decision makers can perceive the correlation between the economic profit and environmental impact and can work out a strategy to adapt to changing business circumstances. Acknowledgment This work was partially supported by the Brain Korea 21 project, the Center for Ultramicrochemical Process Systems sponsored by KOSEF, and SK Engineering and Construction Co., Ltd.


Nomenclature An ) area of land required of substance n AEPnww ) aquatic ecotoxicity potential of substance n emitted in water APn ) acidification potential of substance n Ccharter,v ) transporting cost of oil tanker v Ccrude,c ) purchasing cost of crude oil c Cinv_BL,j ) inventory cost of blending tank j per unit interval Cinv_ST,i ) inventory cost of storage tank i per unit interval Coperate,u ) cost of utility u Csetup,j,j′,l ) changeover cost for transition from crude mix j to j′ in CDU l Cstay,v ) sea waiting cost of oil tanker v Cunload,v ) unloading cost of oil tanker v CFBC,j,l,t ) cumulative flow amount from blending tank j to CDU l at time t CFSB,i,j,t ) cumulative flow amount from storage tank i to blending tank j at time t CTFq,n ) characterization factor for substance n in impact category q Db ) weighted damage score for safeguard subject b Dblend,j ) density of mixed oil j Dcrude,c ) density of crude oil c Dj,l,t ) binary variable to denote if crude oil mixed in blending tank j charges CDU l at time t Dprod,p ) density of product p DEMANDp ) total demand of product p during the scheduling horizon DURATIONv ) minimal unloading duration time for oil tanker v EISn ) energy required to bring abiotic resources back to their initial state of substance n EPn ) eutrophication potential of substance n FBC,j,l,max ) maximum mixed oil transfer rate from blending tank j to CDU l FBC,j,l,min ) minimum mixed oil transfer rate from blending tank j to CDU l FBC,j,l,t ) mixed oil transfer rate from blending tank j to CDU l at time t FSB,i,j,max ) maximum crude oil transfer rate from storage tank i to blending tank j FSB,i,j,min ) minimum crude oil transfer rate from storage tank i to blending tank j FSB,i,j,t ) crude oil transfer rate from storage tank i to blending tank j at time t FVS,v,i,max ) maximum crude oil transfer rate from oil tanker v to storage tank i FVS,v,i,min ) minimum crude oil transfer rate from oil tanker v to storage tank i FVS,v,i,t ) crude oil transfer rate from oil tanker v to storage tank i at time t G ) global impact score GWP500,n ) global warming potential of substance n HTPnr ) overall human toxicity potential of substance n emitted in medium r Mn ) inventory emissions of substance n NLn ) nutrient limitation factor of substance n ODPn ) ozone depletion potential of substance n OPERj,l,u ) amount of utiltity u used in CDU l for mixed oil j POCPn ) photochemical ozone creation potential of substance n PRICEp ) turnover produced from product p PROj,l ) total amount of mixed oil j fed into CDU l PRODUCTp ) amount of product p during the scheduling horizon Sq ) effect score of impact category q Shumantox ) effect score of impact category of human toxicity Saquaeco ) effect score of impact category of aquatic ecotoxicity

Sterreeco ) effect score of impact category of terrestrial ecotoxicity Soxiform ) effect score of impact category of photooxidant formation Sacid ) effect score of impact category of acidification Seutro ) effect score of impact category of eutrophication Sglowarm ) effect score of impact category of global warming Sozodep ) effect score of impact category of stratospheric ozone depletion Sabiores ) effect score of impact category of abiotic resources Sland ) effect score of impact category of land use TL,v ) unloading completion time of oil tanker v TOTp ) total amount of product p TF,v ) unloading initiation time of oil tanker v TARR,v ) arrival time of oil tanker v around docking station TEPnw ) terrestrial ecotoxicity potential of substance n emitted in soil VB,j,max ) maximum volume of crude oil in blending tank j VB,j,min ) minimum volume of crude oil in blending tank j VB,j,t ) volume of crude oil in blending tank j at time t VB,j,0 ) initial volume of mixed oil in blending tank j VS,i,max ) maximum crude oil volume of storage tank i VS,i,min ) minimum crude oil volume of storage tank i VS,i,t ) volume of crude oil in storage tank i at time t VS,i,0 ) initial volume of crude oil in storage tank i VV,v,t ) volume of crude oil in oil tanker v at time t VV,v,0 ) initial volume of crude oil in oil tanker v Vtanker,v ) volume of oil tanker v X ) vector of decision variables XF,v,t ) binary variable to denote if oil tanker v starts unloading at time t XL,v,t ) binary variable to denote if oil tanker v completes unloading at time t XW,v,t ) 0-1 continuous variable to denote if oil tanker v is unloading its crude oil at time t Zj,j′,l,t ) 0-1 continuous variable to denote transition from crude mix j to j′ at time t in CDU l db,q ) slope of the damage-effect function on safeguard subject b per unit of the reference substance for impact category q fBC,j,l,k,t ) volumetric flow rate of component k from blending tank j to CDU l at time t fSB,i,j,k,t ) volumetric flow rate of component k from storage tank i to blending tank j at time t vB,j,k,t ) volume of component k in blending tank j at time t wb ) factor expressing the seriousness of the reference damage for each safeguard subject b xD ) decision variable ∆tn ) use duration of substance n Greek Letters ξS,i,k ) concentration of component k in storage tank i ξB,j,k,t ) concentration of component k in blending tank j at time t ξB,j,k,min ) minimum concentration of component k in crude mix of blending tank j ξB,j,k,max ) maximum concentration of component k in crude mix of blending tank j Subscripts b ) safeguard subjects c ) 1, ..., C ) oil field i ) 1, ..., I ) crude oil storage tank j, j′ ) 1, ..., J ) crude oil blending tank k ) 1, ..., K ) key component of crude oil l ) 1, ..., L ) crude distillation unit m ) 2, ..., M ) objective function n ) substance p ) 1, ..., P ) product q ) environmental impact category

4806


t, t′ ) 1, ..., T ) time interval u ) 1, ..., U ) utility v ) 1, ..., V ) oil tanker y ) 1, ..., Y ) inequality constraint z ) 1, ..., Z ) equality constraint Superscripts r ) a, w, s ) medium that substances emitted in a ) air w ) water s ) soil

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Received for review October 2, 2001 Revised manuscript received April 24, 2002 Accepted June 21, 2002 IE010813B

Scheduling of Actual Size Refinery Processes Considering

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