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Optimum Integrated Design of Crude Oil Supply Chain by a Unique Mixed Integer Nonlinear Programming Model Ali Azadeh,* Farideh Shafiee, Reza Yazdanparast, Jafar Heydari, and Ali Keshvarparast School of Industrial and Systems Engineering, Center of Excellence for Intelligent Based Experimental Mechanic and Department of Engineering Optimization Research, College of Engineering, University of Tehran, Tehran, Iran S Supporting Information *

ABSTRACT: In this paper, a mixed integer nonlinear programming model is proposed to concurrently design two segments (i.e., upstream and midstream) of crude1 oil supply chain. The network includes all entities and their connections from oil wells to product depots. Furthermore, a real world example is applied to show the improved model application. Furthermore, a sensitivity analysis in which ±20% deviations at a time were placed on two parameters is presented. Also, model performance is analyzed with GAMS 22.6. The proposed multiperiod and multiproduct model consists of several decisions (i.e., oil field development, transformation, transportation, and distribution). The main contributions of this work are inclusion of all entities related to upstream and midstream segments and both oil field development and transformation planning, simultaneously. Finally, it is shown that a decrease in production cost of refinery products will lead to more net profit given all refinery production capacity are used. Also, increase in refinery production capacity will improve network net profit given new fixed cost investment is not applied (e.g., refineries and transportation modes). This is the first study that simultaneously considers and optimizes upstream and midstream of crude oil supply chain. Second, it presents a unique mathematical model. Third, all features and parameters are included. Fourth, it is practical and may be used for other crude oil supply chain.

1. INTRODUCTION In today’s modern world, the important role of the oil industry is obvious for everyone. Also the oil and petroleum derivations’ consumption market is indubitable. Furthermore, this indiscriminate consumption will be increasing in the near future. As in 2010, the most volume of transportation fuels and total primary energy demand, about 92.6% and 41.2%, have been supplied via the oil industry.1 Crude oil is rare all over the world, so this industry is private by some countries. Also this feature changes the oil industry to a strategic one and is the heart of modern societies. Because of the extension of oil and refinery products consumption all over the world and also the significant role of oil companies on the global economy, optimization of this valuable chain is critical. So the motivations of the authors is obvious. The oil industry has a spread chain that includes a large network of equipment, infrastructures, and complex processes from oil exploration to the refinery products delivery to the final customers. The crude oil industry is often divided into upstream, midstream, and downstream segments. The exploration, oil production, and transportation to customers, i.e., refineries and international markets, done in the upstream segment. The midstream segment includes crude oil transformation into oil derivations through refineries and petrochemicals and transporting the final products to the © 2017 American Chemical Society

depots/customers. The downstream segment includes the storage and distribution of oil products to the final customers. In the current study, we have surveyed just two segments of upstream and midstream. Each segment is formed by several entities that will be mentioned as follows: The upstream segment includes wellhead (WH), Well Platform (WP), Production Platform (PP), and Crude oil Terminal (CT). The midstream segment includes Refinery plant (RF) and Petrochemical plant (PC), and the downstream segment includes Distribution Center/Depot (DC), Market (M), and Customer (C).2 Basically, the supply chain decisions place on strategic, tactical and operational levels that the distinction between them is clear by their planning horizon. The strategic, tactical, and operational levels in the oil industry deal with 5−20 years, 6− 24 months, and only 1 week, respectively. The strategic level covers the decisions such as facility location and capacity determination, facility allocation, investment, facility reallocation, capacity expansion, technology, i.e., selection, upgrading and downgrading, and outsourcing. On other hand, the Received: Revised: Accepted: Published: 5734

July 1, 2016 April 14, 2017 April 19, 2017 April 19, 2017 DOI: 10.1021/acs.iecr.6b02460 Ind. Eng. Chem. Res. 2017, 56, 5734−5746

Article

Industrial & Engineering Chemistry Research Table 1. Main Characteristics of Presented Study versus Previous Ones decisions

study Carneiro et al. (2010) Fernandes et al. (2011) Gupta and Grossmann (2012)20 Oliveira et al. (2013) Sahebi and Nickel (2013) Fernandes et al. (2013)39 Sahebi and Nickel (2014)2 Sahebi et al. (2015)43 Li et al. (2016)44 Boukouvala et al. (2016)45 Guo et al. (2016)46 current study

investment planning

* * * * * * * *

facility location

facility allocation

* * * * * * * * * * * *

* * * * * * *

technology decisions

project planning

oil field production planning *

*

* *

* * * *

*

*

* * *

*

refinery production planning

distribution

* *

* *

*

* * *

* *

* * *

* *

* *

*

* * * *

from refineries to depots. The other one is the final transportation that ships products from depots to final markets and customers. Primary distribution modes are usually pipelines, marine transportation, railcars, and road vehicles. In this study, important decisions in the crude oil supply chain including oil field development, transformation planning, transportation, and primary distribution are surveyed.2 The main contribution of this work is consideration of all related entities in upstream and midstream segments, and also it is the first study that includes both the oil field development and transformation planning, simultaneously. Also, two other features that distinguish this work from the others are that the internal market of crude oil is distinct from the international market and the time value of money is considered more seriously. Actually, the oil supply chain is a spread network, so that it is not possible to consider all the segments in a model and it causes unreal assumptions. On the other hand, considering all segments with all related entities within an integrated model lead to precision and more reliable results. Therefore, this paper considers upstream and midstream segments of the crude oil supply chain simultaneousy. We suggest to survey the downstream segment in a single model because of complications. As mentioned before, there exists a high volume papers in design and planning of the crude oil supply chain. According to Sahebi and Nickel,6 the crude oil supply chain papers are categorized into four main groups as follows. 1.1. Oilfield Development. One of the first attempts in this scope is from Aboudi et al.7 They developed a model in the petroleum fields and transportation network. They emphasized on developing the crude oil transportation system and the selection of new producing oil fields as well. After Aboudi et al.,7 several studies presented models that were not very different from each other.8,9 Generally, they focused on oil production planning, investment planning, and transportation via pipelines. However, lyer et al.10 presented a model in investment planning, facility location-allocation, and production planning that differs from the others. Also the oil rig constraints, surface pressure constraints, and the reservoir performance have been considered in this model. They linearized the nonlinear reservoir performance equations by piecewise linear approximations. After that, several studies attempted to achieve a decrease in solution time by reformulating previous models and upgrading the solving

strategic decisions provide the context in which the tactical and operational decisions should form. The tactical decisions determine the intermediate activities should accrue to meet strategic objectives and in this level, several uncertain factors become clearer. The tactical planning covers decisions (i.e., project planning, production planning, i.e., oil field production planning and refinery production planning, inventory management, and distribution. The strategic and tactical models save about 5−10% of costs. In the current study by focusing on strategic and tactical decisions, we analyzed them in a single model, the 15 years planning horizon discretizes to 6 months periods. For instance, the project planning and production planning are tactical decisions, but the other decisions in this study are strategic ones.2 Among the great percentage of surveys about the oil industry, most of them have reviewed the subject of design and planning. Furthermore, any improvement in the infrastructures and processes of the supply chain should occur in the design phase. Oil industry design and planning optimizes a number of subsystems in this network, i.e., oilfield development, crude oil transportation, refinery planning, and distribution. Oilfield development is an expensive and complex problem for the oil companies. This kind of problem surveys large networks of entities such as wells and platforms in the strategic level and also a large percentage of papers focused on oilfield development. Oil field development problem can be placed in three main categories: investment planning, facility locationallocation, and production planning. An oilfield development model can include one of these three categories or a hybrid of them.3 Furthermore, the transportation has a great importance in the crude oil network. Crude oil transportation starts at the wells and production platforms to the final customers, i.e., refinery, international market. The crude oil usually is transported through pipeline and marine transports, i.e., oil tanker, vessel, and barge.4 Crude oil transportation is reviewed with both oilfield development and transformation planning or alone. Also, the transformation planning is certainly one of the most complex and important chemical processes in the refinery and petrochemical industries. This process contains particular procedures that can be done by several possible designs. The main purpose of this process is to change crude oil into intermediate and final refinery products with a higher value chain.5 There are two kinds of distribution: primary and secondary. Primary distribution consists of shipping products 5735

DOI: 10.1021/acs.iecr.6b02460 Ind. Eng. Chem. Res. 2017, 56, 5734−5746

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Industrial & Engineering Chemistry Research

Figure 1. Structure of the proposed integrated model.

techniques.11,12 After some time, two studies formulated the nonlinear behavior of reservoirs in their models that was not surveyed seriously until that time.13,14 They also attempted to improve solving techniques. Later, uncertainty features were considered in the model by various researchers.15,16,10,17−19 Uncertainty parameters that they considered in their models were demand, crude oil recoverable amounts, crude oil price, and well productivity indices and reservoirs quality. Also Gupta and Grossmann20 surveyed offshore oilfields. Some of the significant features of their strategic-tactical model were consideration of existing facilities, which was surveyed in a few models. Recently Sahebi et al.2 have developed an oilfield design model. They also take into account crude oil transportation. Their model includes decisions, i.e., facility location-allocation, transportation mode selection, and pipeline networks installations. They have used binary variables to study both the available facilities and potential facilities, simultaneously. They have also considered the drilling rig constraint, which is too critical in the oilfield development problems. 1.2. Transformation Planning. One of the first studies in this scope that surveyed the transformation planning in refineries and also presented a linear programming model with uncertainty features in spot selling price, spot supply cost, and product demand is presented by Escudero et al.21 After that, several stochastic linear models were proposed that differ only in uncertainty features.22,23 Dempster et al.22 and Escudero et al.21 considered uncertain demand and spot supply cost. Later, the study of Li et al.23 proposed a model to plan refineries. Their model was included in the uncertain demand and raw material. Some studies surveyed nonlinearity blending and processing operations.24−27 For instance, study of AlQahtani et al.27 considered nonlinearity formulations of risk components (i.e., projected benefits and forecasted demand). 1.3. Transportation. Generally, the studies in this scope are divided into three subgroups. The first group takes into account both the crude oil transportation and oil field

development. This group usually considers pipeline connections, but Sahebi2 considered the crude oil tanker planning. Some researchers considered the possibility of pipeline network capacity selection.7,16,9 The second group considered transportation coupled with transformation planning. Their model includes transportation costs and transportation modes. Also Rocha28 has taken transportation, transformation planning, and distribution into account. There are other important studies in this regard.24,29−34 The third group has focused only on crude oil transportation. The most important papers in this group are refs 35−37. 1.4. Distribution. The distribution papers fall into two groups. The first group considers pure distribution. It deals with distribution facilities and only takes downstream segment into account.35,36,38,39 The second group includes production planning and distribution. Various studies have considered transformation planning, oilfield development, and distribution in this context.21,24,29,39−42 It is clear in the literature that no study has ever been conducted to include all decision parameters of design and planning process. However, in the current study, all the stated parameters are considered. Table 1 surveys several papers in detail and confirms our significant and unique contributions. Several studies have been involved with crude oil supply chain in the past decades due to the important role of the oil industry. Although researchers have considered various objective functions and assumptions in analyzing the crude oil supply chain, it seems certain gaps remain unchanged. This is the first study that considers and integrates the upstream and midstream segments of the crude oil supply chain simultaneously. Most studies in this area have considered only the upstream segment, while the others have considered the midstream and downstream segments simultaneously. Considering the midstream and downstream segments together lead to unreal assumptions due to the complexity and extensive 5736


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Industrial & Engineering Chemistry Research distribution network. It is also notable that all strategic and tactical decisions are made in the upstream and midstream segments. Moreover, modeling and analyzing both segments can lead to enhanced precision and efficiency.6 Therefore, it is reasonable to consider the downstream segment of the crude oil supply chain with all its entities separately, while analyzing upstream and midstream segments simultaneously, which is the main significance of the present study. This paper evaluates and optimizes the upstream and midstream segments of the crude oil supply chain with all related entities simultaneously through a real world case study in the Persian Gulf. The proposed multiperiod and multiproduct model consists of several decisions, i.e., oil field development, transformation, transportation, and distribution. Moreover, this is the first study that considers limitations of crude oil exports in order to maximize the market share. Crude oil export has significant importance in the world. Moreover, it is important to maximize the share of crude oil exports. Therefore, it is important to consider upstream and midstream segments of crude oil supply chain with all related entities, long-term and short-term decision variables simultaneously.

Table 2. List of Sets Used in This Study w pp f m c t pl P g g̅ g̿

wells production platforms refineries external markets depots time horizon transportation modes products oil extraction technologies oil production technologies in wells oil storing technologies in production platforms

≡

production technologies of products in refineries

g

3. MATHEMATICAL FORMULATION This section presents a multiperiod and multiproduct mathematical model for optimizing upstream and midstream segments of crude oil supply chain simultaneously. The proposed model includes all entities and their connections from oil wells to product depots. Also, several decisions including oil field development, transformation, transportation, and distribution are considered in the model. Table 2 shows the list of sets used in this study. Furthermore, the notations used for parameters, binary variables, and continuous variables are presented in Tables S1, S2, and S3 of the Supporting Information, respectively. 3.1. Objective Function. The objective function maximizes the net present value of the total cash flow summation in all time periods as stated in eq 1. TCFt max: NPV = ∑ (1 + i)t − 1 (1) t

2. PROBLEM DEFINITION As described before, in the current study, an offshore oil field design and planning, transportation system planning, crude oil transformation planning, and distribution planning are considered. First, the general assumptions are specified. In some specific scopes in the world, there are several oil fields that include certain reservoirs. Every reservoir consists of a number of potential wells. The extracted oil from wells is mixture of crude oil and water. The liquid is pumped to production platforms via pipelines. At production platforms, crude oil and water will be separated by various technologies, so crude oil is obtained. Then, the crude oil will be transferred to the refineries and international markets via pipelines/oil tankers. The crude oil will be transformed to the oil derivations by various technologies, in refineries. Then refinery products, i.e., gasoline engine, kerosene, fuel oil, and gas oil will be carried to the depots via pipelines or oil tankers. The problem deals with several decisions: (1) Investment decisions: Facilities and the time that they should be established. Decisions deal with facility locationallocation and project planning as well. (2) Transportation decisions: Pipelines capacity selection the number of oil tankers and the amount of oil that should be transferred between production platforms to refineries and international markets as well. (3) Transformation planning decisions: How much raw material (crude oil) should be processed and which products should be produced. (4) Distribution decisions: determining the pipeline capacities, number of oil tankers and amount of refinery products that should be delivered to the depots. (5) Operation decisions: determining the pipelines capacity, number of oil tankers and amount of refinery products that should be delivered to the depots. In the following section, we will explain the objective function and constraints of the presented mathematical model. Figure 1 shows the structure of the proposed integrated model.

Equations and models 2a−9 will facilitate the calculation of objective function. Total cash flow in each period is calculated by difference between the fraction of total depreciable capital (FTDCt) and net earnings, in regards to the salvage value of capital is last period. It is shown by eqs 2a and 2b. t = 1, 2, ..., T − 1

TCFt = NEt − FTDCt

t=T

TCFt = NEt − FTDCt + (sv) ·TFCI

(2a) (2b)

Net earnings in each period are calculated by subtracting total variable cost from sale revenues with regard to tax rate (α) and capital invested depreciation as shown by eq 3. NEt = (1 − α)(SRevt − TVCt ) + α Dept

∀t

(3)

Sale revenues are calculated by crude oil sales to the export markets and refinery product sales to the depots. Furthermore, pft, pmt , pp,c t state crude oil price in refinery f, crude oil price in external market m, and price of final product p in depot c, respectively. It is shown by model 4. SRevt =

∑ ∑ ∑ pt f ·Q plpp,t,f f

+

pp

pl

∑ ∑ ∑ ptm ·Q plpp,t,m m

pp

+∑ ∑ ∑ ∑ Q plf ,,ct , p·ptp , c − p

c

f

pl

∀t

pl

∑ ∑ ∑ pt f ·Q plpp,t,f t f

pp

pl

(4) 5737


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Industrial & Engineering Chemistry Research The total variable cost coming from the drilling cost associated with selected potential wells, cost of technology (i.e., extraction technologies (g) at wells, producing technologies (g)̅ at production platforms, storing technologies (g)̿ at platforms, ≡ producing technologies ( g ) at refinery), transporting cost of material (crude oil between the production platforms) and refinery/export market and also between refineries and depots via pipelines and/or oil tanker are calculated using eq 5. The nonlinearity of the model arises from eq 5 in which refers to multiplication of variables or existence of binary variables

FCl t =

w

pp

g

w

+

pp

g

+

+

g

pp

∑ ∑ βtg ,f ·XFt f ,g

w

g

w

pl

PP

+

pp

pp

+

g

p

f

g

pl

∀t

c

∑ ∑ ∑ γt pl·δ w ,pp·Q plw ,,ppt

+

w

+

pp

m

PP

f

f

pl

C

(5)

In eq 5, ⌀wt represents the drilling operation cost of potential g,pp g,pp ̅ ̿ denote the operating well w in period t. Also vg,w t , vt , and πt cost of extracting technology g in well w, producing technology g ̅ in production platform pp and storing technology g ̿ at production platform pp for per unit of liquid in period t, ≡

respectively. Also pc͠ t g , p states operation cost of producing

w

∑ t

pp

(6)

(8)

∀t (9)

f

pl

+

∑ ∑ Q plpp,t,m m

pl

pl

(10)

≥

cep ∑ ∑ Q plf ,,ct ,p·∼ c

pl

∀p (11)

3.2.2. Capacity Constraints. Constraint 12 expresses the budget upper bound for fixed cost investment FCIt in each period. Constraints 13−16 show the upper and lower bound for capacity transportation modes. Constraint 17 expresses the upper bound of extraction capacity for wells. Constraints 18 −20 express the upper bound and lower bound of technology capacity. Constraint 21 shows the upper bound and lower bound of oil demand for international markets. Constraint 22 expresses the upper bound and lower bound of product demand for depots. Constraint 23 shows the upper bound and lower bound for producing capacity in refinery. Constraint 24

FCIt (1 + i)t − 1

p

pl

∑ ∑ Q plpp,t,f ∀t

pl

∀ pp , t

The total fixed capital investment is calculated by the summation of fixed cost investment that is discounted with interest rate i as shown by eq 7. TFCI =

c

∑ ∑ Q plw ,,ppt ·owr tw ≥ ∑ ∑ Q plpp,t,f

≡

technology g for per unit of product p in period t. Furthermore, γplt denotes the transportation cost of mode pl for per unit of liquid in period t. The depreciation of capital invested (Dept) is calculated by the straight-line method as shown by eq 6 (1 − sv)TFCI Dept = T

pl

3.2. Constraints. We divide all the constraints in three broad categories. They are classified as mass balance constraints, capacity constraints, and logical constraints. They are discussed next. 3.2.1. Mass Balance Constraints. The mass balance constraints ensure a positive flow in our supply chain network. Constraint 10 states that the input flow from wells to production platforms must be more than the output flow to international markets and refineries. Also, constraint 11 expresses that input flow from production platforms to refineries must be more than the output flow to depots.

pl

∑ ∑ ∑ ∑ δ fc·γt pl·Q plf ,,ct ,p p

f

⎡ i(1 + i)t ⎤ FTDCt = (TFCI)⎢ ⎥ ⎣ (1 + i)t − 1 ⎦

pl

∑ ∑ ∑ γt pl·δ pp,f ·Q plpp,t,f

+ +

pl

∑ ∑ ∑ γt pl·δ pp,m·Q plpp,t,m PP

pl

In eq 8, βg,w t shows fixed investment of extracting technology g w,pp in well w, and also βpl,t shows fixed investment of transportation mode pl between well (w) and platform (pp) in period t. The other similar parameters will be clear by the same analysis. Fraction of the total depreciable capital is calculated by the summation of total fixed capital investment that is discounted by interest rate i as shown by eq 9

g

∑ ∑ ∑ ∑ ∑ pctg ,p ·YFt f , g ·Q plf ,,ct ,p

m

∑ ∑ ∑ ∑ ass plf ,,ct, p·βplf ,,tc , p f

ctg ̅ ·πtg ̅ , pp·YPPtpp , g ̅ g ̿

pl

∑ ∑ ∑ βplpp,t,f ·ass pppl ,,tf +

g

∑∑∑

+

pp

∑ ∑ ∑ βplpp,t,m ·ass pppl ,,tm

+

g

pl

∀t

g

∑ ∑ ∑ βplw,,tpp ·asswpl,,ppt

+

⌀tw ·XWtw , g

∑ ∑ ∑ ∑ ∑ vtg ̅ ,pp··YWtpp,g ̅ g ̿ ·Q plw ,,ppt pp

g

f

∑ ∑ ∑ ∑ vtg ,w·Q plw ,,ppt ·YWtw ,g w

g

∑ ∑ ∑ βtg ̅ ,pp ·XPPtpp,g ̅ g ̿

+

≡

∑∑

g

∑ ∑ ∑ βtg ̅ ,pp ·XPPtpp,g ̅ g ̿

+

w,g pp,g,g ̅ Q ̿ w,pp and YF f , g Q f , c , p ) (Qw,pp pl,t YWt , YPPt pl,t t pl , t

TVCt =

∑ ∑ βtw ·XWtw ,g

(7)

Fixed cost investment in period t comes from the cost of technology establishments and transportation cost of pipeline installations as shown by eq 8. 5738


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each entity should form at only one time. Constraint 35−41 express when the material transfer between entities that entities be established. Constraint 43−46 express when the material transfer between entities via modes that the modes be established between entities.

expresses the upper bound of refinery capacity for acceptance the crude oil. Constraint 25 shows the upper bound of platform capacity for acceptance of the liquid. ∀t

FCIt ≤ TFCI

(12)

w , pp w , pp pl ctpl·ass wpl,,pp t ≤ Q pl , t ≤ ct · ass pl , t

XWtw , g ≥ YWtw , g − YWtw−,1g

∀ pp , w , pl , t (13)

,f ctpl·ass pp pl , t

≤

Q plpp, t, f

,f ctpl·ass pp pl , t

≤

,g ̅ ,g ̿ XPPtpp , g ̅ , g ̿ ≥ YPPtpp , g ̅ , g ̿ − YPPtpp −1

Q plpp, t, m

≤

,m c t̅ ·ass pp pl , t pl

≤

(27) ≡

∀ pp , m , pl , t (15)

ctpl·ass plf ,,ct, p ≤ Q plf ,,ct , p ≤ ctpl·ass plf ,,ct, p

∑∑ pp

ctw·YWtw , g

≤

≤

∑∑ pl

Q plw ,,pp t

≤

Ytw , g · ctg

XFt f , g ≥ YFt f , g − YFt −f ,1g

∀ f , t, g

(28)

XM tm ≥ YM tm − YM tm− 1

∀ m, t

(29)

∀ w, g , t

(31)

∀ pp , g ̿ , t (32)

∑ YPPtpp,g ̅ ,g ̿ ≤ 1

∀ pp , g ̅ , t

=

+

∑∑ m

Q plpp, t, m

≡

f

≤ YPPt

∑ YFt f ,g ≤ 1 · ctg

∀ pp , t , g ̅ , g ̿

pl

f

∑ ∑ Q plpp,t,m) m

pl =

≤ YPPtpp , g ̅ , g ̿ · ctg

∀ pp , t , g ̅ , g ̿ (20)

dtm·YM tm

≤

∑∑ pp

Q plpp, t, m

≤

dtm·YM tm

∀ m, t

pl

(21)

DtP , C ·YCtc ≤

∑ ∑ Q plf ,,ct ,p ≤ f

DtP , C , YCtc

pl

∀ p, c , t ≡

(22) ≡

YFt f , g · cap gf ,, pt ≤

≡

∑ ∑ Q plf ,,ct ,p ≤ YFt f ,g · c

(34)

There are two type of binary variables for establishment of entities in the presented model. The first group of these binary variables which are X variables are explaining the establishment of an entity in period t while the second group of binary variables, namely, Y variables are representing the establishment of entities until period t. This dual presentation of binary variables in the model ensures that the establishment cost of an entity is considered only one time in the model, at most. For instance consider XWw,g t which represents the drilling of well w via technology g in period t in the model. This variable takes value equal to 1 in only one period in the model while YWw,g t takes value equal to 1 for period t and next periods that the well is processing in the model. So if the drilling of a well w via technology g start from the beginning until period T, means that XWw,g t is equal to 1 for t = 1 and is equal to 0 for t ≠1 while YWw,g t is equal to 1 for t = 1,2,3..., T. This technique is used for ensuring that establishment of each entity is not considered more than one time in the model while the entity is online and processing in more than one period of time.

YPPtpp , g ̅ , g ̿ · ctg ≤ εpp(∑ ∑ Q plpp, t, f pl

∀ f, t

≡

g

(19)

+

(33)

g

∑ ∑ Q plpp,t,f pp , g ̅ , g ̿

(30)

g

(18)

pl

∀ c, t

∀ w, t

∑ YPPtpp,g ̅ ,g ̿ ≤ 1

pp

YPPtpp , g ̅ , g ̿ · ctg ≤

≡

g

(17)

ctg

≡

∑ YWtw ,g ≤ 1

∀ w, t

pl

Ytw , g ·

≡

XCtc ≥ YCtc − YCtc− 1

∀ f , c , pl , p , t (16)

Q plw ,,pp t

(26)

∀ pp , g ̅ , g ̿ , t

∀ pp , f , pl , t (14)

,m ctpl·ass pp pl , t

∀ w, g , t

≡

cap gf ,, pt

ass wpl,,pp t ≤

pl

∑ YWtw ,g

∀ w , pp , pl , t (35)

g

≡

∀ f , p, t , g

∑∑ pl

f

≤ ct ·YFt

≡

f ,g

w

ass wpl,,pp t ≤

≡

(24)

Q plw ,,pp t

≤

ctpp·YPPtpp , g ̅ , g ̿

∑ ∑ YPPtpp,g ̅ ,g ̿ g

∀ f, g, t

pp

∑∑ pl

Q plpp, t, f

(23)

,f ass pp pl , t ≤

(25)

,f ass pp pl , t ≤

3.2.3. Logical Constraints. Constraints 26−46 express logical relationships that are creating our supply chain network. Constraints 26−30 express when an entity form in a time that it is not form in previous times. Constraints 31−34 express that

(36)

∑ ∑ YPPtpp,g ̅ ,g ̿ g

∀ pp , t , g ̅ , g ̿

∀ w , pp , pl , t

=

g

∀ pp , f , pl , t

=

(37)

g

≡

∑ YFtf ,g

∀ pp , f , pl , t

≡

(38)

g

ass plf ,,ct ≤ YCtc 5739

∀ f , c , pl , t

(39)


Article


Figure 2. Schematic view of the proposed network.

ass plf ,,ct ≤

≡

∑ YFtf ,g

∀ pp , f , pl , t

≡

(40)

g ,m ass pp pl , t

≤

∑∑ g

=

YPPtpp , g ̅ , g ̿

(41)

,m m ass pp pl , t ≤ YM t

∀ pp , m , pl , t

(42)

w , pp ass wpl,,pp t ≤ p1pl , t

∀ w , pp , pl , t

(43)

∀ f , pp , pl , t

(44)

,f pp , f ass pp pl , t ≤ p2pl , t

,m ass pp pl , t

ass plf ,,ct, p

≤

,m p3 pp pl , t

∀ m , pp , pl , t

≤

p4 plf ,,ct, p

∀ f , c , pl , t

(51)

β − BigM(1 − α) ≤ γ

(52)

In order to show the linearization method, related steps for linearizing eq 5 is presented as follows. Furthermore, eq 5 is replaced with eq 55, and then eqs 56, 57, and 58 are added to the model. Other nonlinear equations are transformed in a similar way.

∀ pp , m , pl , t

g

γ≤β

TVCt =

∑ ∑ ∑ ∑ vtg ,w·Q plw ,,ppt ·YWtw ,g + ... w

(45) (46)

(47)

β≥0

(48)

α×β=γ

(49)

γ = BigM × α

(50)

pp

(5)

pl

YWtw , g ∈ {0, 1}

(53)

Q plw ,,pp t

(54)

≥0

YWtw , g × Q plw ,,pp = γ, t

Considering the nonlinear constraints, number of constraints, and existence of continuous and integer variables in the model, we are facing a NP-hard problem. Thus, to solve the problem, the nonlinear constraints and equations should be transformed into linear equivalences. The following approach is presented for the linearization process since all nonlinear equations are formed based on multiplication of continuous and binary variables. Consider α as a binary variable, β as a continuous variable, and γ as a multiplication of α and β. For linearizing the model, γ is used instead of the multiplication of α and β and then, Equations 50, 51, and 52 are added to the model. α ∈ {0, 1}

g

TVCt =

∑ ∑ ∑ ∑ vtg ,w·γ + ... w

g

pp

(55)

pl

γ = BigM × YWtw , g

(56)

γ ≤ Q plw ,,pp t

(57)

Q plw ,,pp − BigM(1 − YWtw , g ) ≤ γ t

(58)

4. CASE STUDY In this study, a mixed integer nonlinear programming model is developed to maximize the net present value of upstream and midstream segments of crude oil supply chain in an oil company in the Persian Gulf. In the considered network, there are two wells (1) and (2) with the extraction technology of (3) and (1), respectively. There are two alternative spots for new wells at (3) and (7). The available wells are connected to 5740


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Industrial & Engineering Chemistry Research Table 3. Description of Wells and Their Alternatives

Table 7. Distance Matrix (km) between Production Platforms and External Terminals

oil well

capacity (MB/Y)a

oil-to-water rate

drill cost (1 × 106 USD)

W1 W2 W3 W4 W5 W6 W7 period rate

4.731 4.715 4.457 4.907 4.627 4.908 4.904 3−%b

0.805 0.924 0.805 0.839 0.836 0.895 0.897 2−%

0 (drilled) 0 (drilled) 13.45 12.89 13.21 13.34 13.87 3+%

pp(1) pp(2) pp(3) pp(4)

MB/Y = million barrels per year. bIncrease/decrease rate in each period.

f(1) f(2) f(3)

Table 4. Description of Technologies and Related Costs capacity (MB/Y) upper bound

lower bound

2.6 5.2 15

m(1) m(2) m(3) m(4) period rate

7.7 12.8 23

1393.6 1397.5 1299.9 1245.4

c(1)

c(2)

c(3)

c(4)

10.3 8.4 8.5

8.9 7.9 10.7

7.8 10.1 8.8

9.5 10.3 9.6

upper bound

lower bound

crude oil price (USD)

7.6 8.3 8.6 8.3 %+3

3.06 3.3 3.2 3.3 %+1

60 61 61.5 59.9 %+5

Table 10. Oil Price and Demand of Refineries 1.5 2.6 5.8

demand (MB/Y) f(1) f(2) f(3) period rate

25 19 %+3

upper bound

lower bound

crude oil price (USD)

8.091 8.41 8.05 %+3

3.236 3.11 2.98 %+1

58 56.9 55.2 %+5

Table 11. Production Cost of Each Product Based on Each Production Technology

PP1

PP2

PP3

PP4

85.4 74.1 67.7 71.6 109.0 63.1 112.8

97.6 66.8 64.5 53.0 99.5 60.5 44.7

89.9 83.0 75.7 103.4 82.3 78.6 109.3

68.6 99.5 40.3 71.6 77.1 56.2 49.0

pc͠ t g ̿ , p

g (1)

g (2)

g (3)

g (4)

p(1) p(2) p(3) p(4) p(5) period rate

65 61 54 58 58

64 62 52 57 57

64 62 52 57 57

64 62 52 57 57

3%

Table 12. Capacity Production for Each Production Technology in f(1)

Table 6. Distance Matrix (km) between Production Platforms and Refineries pp(1) pp(2) pp(3) pp(4)

m(4)

942.7 1147.1 998.2 885.4

demand (MB/Y)

Table 5. Distance Matrix (km) between Wells and Production Platforms W1 W2 W3 W4 W5 W6 W7

m(3)

Table 9. Oil Price and Demand of External Terminals

capital cost (1 × 105 USD)24

potential oil extracting technologies T1 5.9 1.8 T2 5.1 1.6 T3 2.1 0.6 potential crude oil producing technologies T4 11.1 4.3 T5 7.8 3.2 T6 4.5 1.6 potential storing technologies T7 1.53 0.6 T8 1.3 0.5 T9 0.9 0.4 potential refinery producing technologies T10 19.8 10.4 T11 18.7 9.8 period rate %−2 %−2

m(2) 315.7 363.2 330.7 403.0

Table 8. Distance Matrix (km) between Refineries and Reservoirs

a

technology

m(1) 907.5 814.0 913.8 797.6

f(3)

f(2)

f(1)

cap ͠ fg,̿ ,tp

132.4 125.9 135.8 134.7

120.1 133.6 120.6 120.4

118.6 149.9 132.9 123.8

P(1) P(2) P(3) P(4) P(5) period rate

platform (3) using high capacity pipelines. There are also three alternative spots including (1), (2), and (4) for new platforms. Platform (2) is now dedicated to India. It uses pipelines and high capacity tankers. Considering the growth in oil demand, platforms (1), (3), and (4) will be allocated to Singapore, Malaysia, and other parts of India. Refinery (1) represents Bandar Abbas Oil Refining Company, which is constructed

g (1)

g (2)

g (3)

g (4)

54276 14870 109874 8900 8900

0 0 0 0 0

54276 0 0 0 0

0 0 0 0 0

−2%

using technology (1). Alternative spots (1) and (2) are dedicated to under construction refineries including Hormoz Heavy Oil Refinery and Setare Khalij Fars Refinery. Reservoir (1) is considered for productions storage of refinery (1) using two transportation modes including pipelines and tankers. Also, 5741


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technology in each refinery (1), (2), and (3) are presented in Tables 12, 13, and 14, respectively. The production capacity and cost is different for each technology. Table 11 presents the production cost of each product based on each production technology.

Table 13. Capacity Production for Each Production Technology in f(2) cap ͠ fg,̿ ,tp P(1) P(2) P(3) P(4) P(5) period rate

g (1)

g (2)

g (3)

g (4)

0 0 0 0 0

36168 10907 78436 0 0

0 0 0 0 0

0 0 0 0 0

5. COMPUTATIONAL EXPERIMENTS A real world example of Iranian National Oil Company (NIOC) in the Persian Gulf has been chosen to illustrate the applicability and superiority of the unique mathematical model of this study. Several features of the actual case study are as follows. (i) Problem dimension: It includes the number of potential wells, production platforms, and periods in the time horizon, refineries, international markets, and depots. (ii) Drilling, establishment, and installing costs: The drilling costs of wells, establishment costs of platforms, refineries, and depots, and also installation costs of pipelines have been estimated and then are matched by the actual case study. (iii) Distances and transportation: By identifying the placement of entities on the map, the process of calculating all the distances will be straightforward. The transportation costs have been estimated for different kinds of modes. (iv) Production capacity of refineries and production cost of refinery products: These parameters are quite critical. They are surveyed by the sensitivity analysis of this study. (v) All other parameters are generated so that they can be verified by actual data. Furthermore, the differences between simulated data and actual data are negligible. For solving the presented model, a computer with core-i 5 processor (2.4 GHz) is used. GAMS 22.6 solved the stated problem. The obtained results of MOEAD indicate that alternative well (5) should be constructed based on extraction technology

−2%

Table 14. Capacity Production for Each Production Technology in f(3) cap ͠ fg,̿ ,tp P(1) P(2) P(3) P(4) P(5) period rate

g (1)

g (2)

g (3)

g (4)

0 0 0 0 0

36168 10907 78436 0 0

0 0 0 0 0

0 0 0 0 0

−2%

three alternative spots are considered for production storage. The tax rate, the minimum rate absorbers, and salvage value rate are equal to 14%, 8%, and 25%, respectively. Figure 2 presents the schematic view of the proposed network. We have 15 years that are discrete in 30 time horizons. The time horizon is 6 months. The description of wells are presented in Table 3. The description of technologies are presented in Table 4. The distance matrices between units are presented in Tables 5−8. Tables 9 and 10 present the information on external terminals and refineries demand and price, respectively. The capacity production for each production

Figure 3. Designed network based on initial obtained results. 5742


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Figure 4. Designed network based on considered economic changes.

portation mode should be used in the entire network. Also, the new construction is not allowed in the stated periods except for the first period. This may be the result of considered values for interest rate (i) and tax rate (α) in the solved problem. Since the cost parameters’ rates are considered constant in the solved problem, the results of the model will not change in the considered 14 periods and no new construction will be done. The designed network based on the obtained results are presented in Figure 3. In order to evaluate the responds of the model based on possible changes in economic conditions, the cost parameters’ rate is considered −5% until the fifth period and 5% for the next periods. The obtained results for the new problem indicate that there are no new construction in the first period, similar to the original problem’s results. However, in the fifth period, the model constructs two new wells, a platform and a refinery. The construction of two wells instead of one indicates that the model intends to use the maximum production capacity of refineries which indicate the improving economic conditions for production. The obtained results also indicate that most of the crude oil will be exported in the first five periods. Figure 4 presents the obtained results for considered economic changes in the model.

Table 15. Description of Test Problems and Related Results index problem

w*g *g ̅ *g ̿ *pp*f *m*pl*g *p*c*t

objective function (NPV)

required time (Min)

1 2 3 4 5 6 7 8 9 10 11 12

1*2*2*1*2*5*2*2*2*2*2*2 1*2*2*2*2*5*2*2*2*3*3*2 2*2*2*2*2*6*2*2*2*3*3*2 2*2*2*2*6*5*2*2*2*4*4*2 2*3*3*2*3*7*2*2*2*4*4*3 3*3*3*2*3*7*2*2*2*4*4*3 3*3*3*2*3*7*2*3*3*4*4*4 4*3*3*2*3*8*2*3*3*4*4*4 4*3*3*3*4*8*2*4*3*4*4*4 5*3*3*3*4*8*2*4*3*5*5*4 5*3*3*3*5*10*4*4*3*5*5*4 6*3*3*3*5*10*4*4*3*5*5*4

2434177 3595042 3810153 4085985 4905675 5152387 6613237 7186032 8995828 9339361 9849352 10028995

17.2 21.3 26.1 29.9 32.4 35.9 38.1 42.8 48.4 56.6 59.9 68.1

(2). This well is connected to platform (2) which should use production technology and storage (1), using the highest capacity pipelines. Also, transportation mode (2) should be used for transporting crude oil to external terminal (4). Refinery (3) with production technology (2) should be constructed. It is important to note that pipelines trans-

Table 16. Performance of NPV Encountering Two Parameters Variation at a Time production cost of products limit of production

0.8

0.9

1

1.1

1.2

0.8 0.9 1 1.1 1.2

11860131 12345631 12896542 14863019 16544387

1128943 11937619 12400765 1406531 1457653

1076543 1146548 12014079 1258649 1347421

1046736 11054371 11387621 1196538 1203671

11253419 10754313 10976321 11476439 11745328

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of production does not exceed from production capacity and FCI is fixed. However, as soon as it exceeds from production capacity, the network will establish more platforms. In addition, more transportation modes are established to increase more transferred crude oil to refineries. Consequently, FCI will be increased. The trend of network will not be changed when the cost of production increases as long as it does not lead to noneconomic production. However, severe increase in cost of production and also decrease in production capacity will lead to noneconomic performance of refinery. Therefore, the network prefers to work with fewer number of refineries. When production capacity increases and cost of production is constant, NPV and TVCt will have an increasing trend but FCI remains constant up to point 1.2 variations. Moreover, the network prefers to use more transportation modes and construction of new facilities. When the production cost of refinery products increases, TVC increases which leads to lower NPV. Logically, in this situation the model decides to decrease the production rates in refineries which leads to lower crude oil demand which makes the model to decrease the diameter of pipes and stoppage to the refineries. This continues until the model decides to omit one of the refineries due to economic aspects, which leads to lower FCI and higher NPV in the model. This issue is happened in the model for limit of production of 0.8 in Tables 16−18.

The objective function of various test problems and required processing times are presented in Table 15. As shown in Table 15, the required time for solving the presented model considering various test problems is acceptable, and the considered case study can be optimized within an hour. The obtained results in Table 15 also indicate that expanding the network and increasing the number of entities in the model is acceptable based on economic aspects.

6. SENSITIVITY ANALYSIS Decision makers are aware of the importance of sensitivity analysis to interpret the model performance. It also identifies Table 17. Performance of TVCt Encountering Two Parameters Variation at a Time production cost of products limit of production

0.8

0.9

1

1.1

1.2

0.8 0.9 1 1.1 1.2

3465174 3706542 4276541 4753812 5265100

3556812 3865623 4399521 4964685 5499431

3675912 4056822 4563551 5186461 5652091

3807162 4269313 4763782 5368213 5981439

1364983 4567832 4968231 5537926 6173725

the optimum values of parameters.47 The one-factor-at-a-time (OAT) is the earliest sensitivity analysis dealing with analyzing parameter variation effects while other parameters are constant.48 Also, analyzing the variation effects of several factors at a time is a complex problem. Moreover, it is closer to actual situations. In order to attain exact solution of the model via the numerical data, GAMS 22.6 is used. Then, two-factors-at-a-time sensitivity analysis of two parameters (production capacity of refineries and production cost of refinery products) will be presented next. Moreover, the case study will be analyzed under variation values of two stated parameters. Also, the performance of net present value (NPV), total variable cost (TVCt), and fixed cost investment (FCIt) encountering just one parameter variation at a time is considered. It is obvious from Tables 16, 17, and 18 when the cost of refinery products decreases the network will be headed for more production. Thus, total variable cost (TVCt) and net present value (NPV) will be increased. This result is expected because increasing production volume will lead to increased variable cost and net earnings. Also, NPV will be changed in the same direction via net earnings (the investigated product is kerosene) It is noteworthy to foresee if FCI may increase? When two stated parameters have their primary values, all production capacity is not used. Therefore, decreasing cost of production will lead to increasing volume of production as long as volume

7. CONCLUSION The importance of oil industry is undeniable in today’s new world, and the distribution of crude oil has become a strategic issue. Therefore, there is a need to oversee the strategic and tactical decisions in the oil industry. A unique mixed integer nonlinear programming model is introduced with the purpose of optimizing decision making process in investment, transformation, distribution, transportation, and operation decisions in the oil industry. The objective function maximizes the net present value of the project. In order to plan the strategic and tactical decisions in a single model, the 15 years planning horizon discretizes to 6 month periods. In the modeling approach of this study, the international crude oil market is separated from the internal crude oil demand. A complete sensitivity is conducted to identify the strength and weakness of the stated parameters. An actual case study is used to show the robustness and practicability of the mathematical model. All results are shown in several tables and figures. It is shown that reducing cost of production and increasing production capacity have nearly the same effects on NPV. However, increasing production capacity is easier and less costly than reducing the cost of production. This is the first study that includes all entities of upstream and midstream segments, simultaneously. Future studies may consider extending the prescribed model of

Table 18. Performance of FCIt Encountering Two Parameters Variation at a Time production cost of products limit of production

0.8

0.9

1

1.1

1.2

0.8 0.9 1 1.1 1.2

15654182 15654182 15900643 15900643 16165381

15654182 15654182 15654182 15900643 15976391

15654182 15654182 15654182 15654182 15900643

14962531 15379312 15654182 15654182 15654182

9655437 14962531 14962531 15379312 15379312

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(11) Carvalho, M.; Pinto, J. A bilevel decomposition technique for the optimal planning of offshore platforms. Braz. J. Chem. Eng. 2006, 23 (1), 67−82. (12) Tsarbopoulou, C. Optimisation of Oil Facilities and Oil Production. M.Sc. Dissertation, University College London (UCL), London, U.K., 2000 (13) Van Den Heever, S. A.; Grossmann, I. E. An iterative aggregation/disaggregation approach for the solution of a mixedinteger nonlinear oilfield infrastructure planning model. Ind. Eng. Chem. Res. 2000, 39 (6), 1955−1971. (14) van den Heever, S. A.; Grossmann, I. E.; Vasantharajan, S.; Edwards, K. A Lagrangean decomposition heuristic for the design and planning of offshore hydrocarbon field infrastructures with complex economic objectives. Ind. Eng. Chem. Res. 2001, 40 (13), 2857−2875. (15) Haugen, K. K. A stochastic dynamic programming model for scheduling of offshore petroleum fields with resource uncertainty. European Journal of Operational Research 1996, 88 (1), 88−100. (16) Jørnsten, K. O. Sequencing offshore oil and gas fields under uncertainty. European Journal of Operational Research 1992, 58 (2), 191−201. (17) Goel, V.; Grossmann, I. E. A stochastic programming approach to planning of offshore gas field developments under uncertainty in reserves. Comput. Chem. Eng. 2004, 28 (8), 1409−1429. (18) Goel, V.; Grossmann, I. E.; El-Bakry, A. S.; Mulkay, E. L. A novel branch and bound algorithm for optimal development of gas fields under uncertainty in reserves. Comput. Chem. Eng. 2006, 30 (6), 1076−1092. (19) Tarhan, B.; Grossmann, I. E.; Goel, V. Stochastic programming approach for the planning of offshore oil or gas field infrastructure under decision-dependent uncertainty. Ind. Eng. Chem. Res. 2009, 48 (6), 3078−3097. (20) Gupta, V.; Grossmann, I. E. An efficient multiperiod MINLP model for optimal planning of offshore oil and gas field infrastructure. Ind. Eng. Chem. Res. 2012, 51 (19), 6823−6840. (21) Escudero, L. F.; Quintana, F. J.; Salmerón, J. CORO, a modeling and an algorithmic framework for oil supply, transformation and distribution optimization under uncertainty. European Journal of Operational Research 1999, 114 (3), 638−656. (22) Dempster, M.; Pedron, N. H.; Medova, E.; Scott, J.; Sembos, A. Planning logistics operations in the oil industry. Journal of the Operational Research Society 2000, 51, 1271−1288. (23) Li, W.; Hui, C.-W.; Li, P.; Li, A.-X. Refinery planning under uncertainty. Ind. Eng. Chem. Res. 2004, 43 (21), 6742−6755. (24) Neiro, S. M.; Pinto, J. M. A general modeling framework for the operational planning of petroleum supply chains. Comput. Chem. Eng. 2004, 28 (6), 871−896. (25) Elkamel, A.; Ba-Shammakh, M.; Douglas, P.; Croiset, E. An optimization approach for integrating planning and CO2 emission reduction in the petroleum refining industry. Ind. Eng. Chem. Res. 2008, 47 (3), 760−776. (26) Kim, Y.; Yun, C.; Park, S. B.; Park, S.; Fan, L. An integrated model of supply network and production planning for multiple fuel products of multi-site refineries. Comput. Chem. Eng. 2008, 32 (11), 2529−2535. (27) Al-Qahtani, K.; Elkamel, A.; Ponnambalam, K. Robust optimization for petrochemical network design under uncertainty. Ind. Eng. Chem. Res. 2008, 47 (11), 3912−3919. (28) Rocha, R.; Grossmann, I. E.; de Aragão, M. V. P. Petroleum allocation at PETROBRAS: Mathematical model and a solution algorithm. Comput. Chem. Eng. 2009, 33 (12), 2123−2133. (29) Kuo, T.-H.; Chang, C.-T. Application of a mathematic programming model for integrated planning and scheduling of petroleum supply networks. Ind. Eng. Chem. Res. 2008, 47 (6), 1935−1954. (30) Alabi, A.; Castro, J. Dantzig−Wolfe and block coordinatedescent decomposition in large-scale integrated refinery-planning. Computers & Operations Research 2009, 36 (8), 2472−2483. (31) Ghatee, M.; Hashemi, S. M. Optimal network design and storage management in petroleum distribution network under

this study by considering demands for products and risk management issues.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b02460. List of parameters (Table S1); list of binary variables (Table S2); and list of continuous variables (Table S3) (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or [email protected]. Phone: +982182084162. Fax: +982188013102. ORCID

Ali Azadeh: 0000-0002-1685-3257 Reza Yazdanparast: 0000-0002-8656-7192 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors are grateful for the valuable comments and suggestions from the respected reviewers. They have enhanced the strength and significance of our paper. This study was supported by grants from the University of Tehran (Grant No. 8106013/1/17 and 29917-01-01). The authors are grateful for the support provided by the College of Engineering, University of Tehran, Iran.

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REFERENCES

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