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Optimal Infrastructure of the Upgrading Operations in the Oil Sands under Uncertainty: A Multiscenario MINLP Approach Ubirajara Gomes,† Bhushan Patil,† Alberto Betancourt-Torcat,‡ and Luis Ricardez-Sandoval*,† †

Department of Chemical Engineering, University of Waterloo, 200 University Ave. West, Waterloo, ON, Canada N2L 3G1 Department of Chemical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

‡

ABSTRACT: The upgrading operations in the Oil Sands are a key asset to Canada’s economy since they currently process more than 60% of the crude bitumen extracted from this region. Despite their significance and relevance, mathematical tools that can evaluate the infrastructure and economy of the upgraders’ operations under fluctuations and variability in key operational and economic factors are limited. It is the purpose of this study to present a stochastic optimization model that has been developed to specify the optimal infrastructure that may be required by the Oil Sands’ upgraders to satisfy the projected production demands at minimum cost in the presence of uncertainty in key economic and operational parameters. A multiscenario approach, describing the potential realizations in the uncertain parameters affecting the upgrading operations, is employed in this work to identify the upgraders’ infrastructure that can simultaneously accommodate the projected production demands and the uncertainty in the system’s parameters. A case study featuring the upgrading operations for year 2035 under uncertainty in key economic and operational factors is presented. The results show significant variability in the upgraders’ infrastructure, and their corresponding energy costs, when this system is evaluated under different uncertain scenarios.

1. INTRODUCTION Canada has approximately 173 billion of barrels of proven oil reserves that can be economically recovered using today’s oil and gas technologies; almost 97% of these oil reserves are in the Canadian Oil Sands.1 This makes Canada the third largest country with proven global oil reserves in the World next to Saudi Arabia (266 billion of barrels) and Venezuela (298 billion of barrels). The Canadian Oil Sands is a region located in the Province of Alberta and parts of Saskatchewan that includes three large deposits, i.e., the Athabasca, Peace River, and Cold Lake. The oil extracted from the Oil Sands, also known as bitumen, is heavy oil mixed with sand, water, and clay. It is estimated that the Canadian Oil Sands contain 1.84 trillion of barrels of crude bitumen; approximately 9% of this volume, i.e., 168.7 billion of barrels, can be processed using the current technology.2 Almost 20% of the crude bitumen can be extracted using surface mining technologies, i.e., Oil Sands within 70 m below the surface, whereas the remaining 80% of the Oil Sands, which are located deeper underground, can be reached using in situ methods. Due to the chemical properties of bitumen, i.e., it is too thick that cannot be transported to the downstream refineries for further processing; this oil is typically mixed with Naphtha to be sold as commercial diluted bitumen. Alternatively, bitumen can be upgraded and sold as a synthetic crude oil (SCO), which is a mix of different light oil grades of high value for different processing applications. This transformation of crude bitumen into SCO occurs in the upgrading processing plants installed in the Oil Sands. These plants processed in 2012 almost 1.1 million of barrels per day, which represents almost 60% of crude bitumen extracted from the Oil Sands in that year (1.8 million of barrels per day).2 Nevertheless, the production from the Oil Sands’ upgrading operations is expected to increase due to the mediumterm future global demands in terms of energy.3 Therefore, there is great interest to develop the Oil Sands’ upgrading operations © 2014 American Chemical Society

since they have the potential to increase Canadian oil production and business with the United States of America and abroad in the nearby future. The development of the Keystone XL pipeline project,4 which is expected to further increase the Oil Sands’ business in North America, is one key potential investment that can boost the Oil Sands operations, and therefore Canada’s economy, in the future. The projected expansion of the Canadian Oil Sands operations requires accurate mathematical models that can assist in the decision-making process. However, the development of reliable and accurate models that can be used to provide an overview on the Oil Sands operations in the upcoming years has been very limited. Very recently, energy models aiming to describe the Oil Sands operations have started to emerge in the literature.5−9 However, those studies have only considered in the analysis the overall production process of SCO and bitumen. That is, specific details regarding the upgrading processes in the Oil Sands, which produce the different types of oil grades, were not explicitly considered in those modeling studies. Similarly, those studies have assumed perfect knowledge of the processes describing the Oil Sands operations, i.e., deterministic optimization models, which do not explicitly account for uncertainty in the model parameters. In practical process systems applications, the assumption of a perfectly known model is unrealistic because sudden and unpredictable changes can occur in the system; this translates into parameter uncertainty in the model of the system, i.e., model uncertainty. Although extensive research has been devoted to evaluate the effects of model uncertainty for various energy Received: Revised: Accepted: Published: 16406

April 29, 2014 September 21, 2014 September 30, 2014 September 30, 2014 dx.doi.org/10.1021/ie501772j | Ind. Eng. Chem. Res. 2014, 53, 16406−16424

Industrial & Engineering Chemistry Research

Article

Figure 1. Upgrading plants configuration employed in the Oil Sands industry.

systems,10−19 most of those studies have not analyzed the uncertain effects in the Oil Sands operations. To the authors’ knowledge, the only study that considered uncertainty in the Oil Sands operations is that developed by Betancourt-Torcat et al.20 In that work, uncertainty in the natural gas prices and steam-tooil ratio (SOR) were taken into account to determine the future production of SCO and bitumen from the Oil Sands. Details regarding the production of the different oil grades (i.e., that make up the SCO) under uncertainty were not considered since that study did not include a model that explicitly describes the upgrading operations. Like many other large-scale energy systems, the Oil Sands are also surrounded by uncertainty since the day-to-day operations in this sector are often subject to sudden and unpredictable changes in the environmental, economic, and operational regulations that have a deep impact in the profits of the different oil producers operating in this sector. Although the Oil Sands activities are expected to continue growing in the upcoming years, the large variability in price differential for heavy crude bitumen has slowed down investments in this sector since mid2012.3 Moreover, the projected estimates of the key oil grades produced in the Oil Sands, i.e., naphtha (NA), vacuum gas oil (VGO), light gas oil (LGO), and heavy gas oil (HGO), are continuously changing due to new investments in the market and

the current offer and demand for oil abroad. To date, the energy projections on the future growth in the Oil Sands operations have been based on studies that rely on historical data and current trends in the oil and gas sector. A key assumption made in those studies is that the infrastructure needed to accommodate the Oil Sands production demands in the upcoming years will be sufficient.3,21 Otherwise, the Canadian oil production may reduce their exports thus producing a negative effect on the Canadian crude oil prices and in general in the future growth of the oil sector in Canada. Therefore, there is a critical need to develop models that can provide a realistic overview on the infrastructure that will be potentially required by the Oil Sands’ upgrader producers to satisfy the projected oil production demands under uncertainty in key internal and external factors affecting this industry. To date, a study that analyzes the infrastructure needed for the upgrading plants operating in the Oil Sands under uncertainty is not available. The aim of this study is to present a stochastic optimization model that estimates the infrastructure that is expected to be required by the upgraders’ operators in the Oil Sands. The key novelty of this study is to present, for the first time, a stochastic optimization model for the Oil Sands’ upgrading operations that explicitly specifies the optimal infrastructure needed under uncertainty in key economic and operational factors affecting this 16407

dx.doi.org/10.1021/ie501772j | Ind. Eng. Chem. Res. 2014, 53, 16406−16424


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sector. To the authors’ knowledge, this is the first work that models the Oil Sands’ upgrading operations in this fashion. In order to provide a realistic overview of the optimal infrastructure of the upgrading operations, the present analysis assumed probabilistic-based descriptions for the uncertain parameters. Therefore, the proposed optimization model can be casted as a stochastic-based mixed-integer nonlinear optimization model, since number of integer and continuous variables are involved, which will be discussed throughout the manuscript. Stochastic optimization problems have been addressed using several approaches.22−25 Studies reported in the literature have reviewed in detail the approaches to handle the stochastic optimization problems.26−28 The approaches consist of programming with recourse, where the problem is considered in stages. This includes integer stochastic programming, linear and nonlinear stochastic programming and robust stochastic approach. Another approach is the probabilistic or chance-constrained programming where the focus is on the ability of the system to meet feasibility in uncertainty, while the approach relies on the minimization of the expected value of the objective function. Multiscenario approach is also one of the widely used methods to solve the stochastic problem, especially in the cases where complete adherence to the process constraints is necessary. The approach involves discrete sampling, and therefore, higher accuracy can be achieved at higher computational cost. Although recent methods have been developed to address stochastic optimization problems,29−32 the present analysis used the multiscenario approach because it is a widely used technique that has been successfully applied to problems that involve integer decisions. The proposed stochastic optimization model was used to evaluate the infrastructure that is expected to be required by the Oil Sands’ upgraders in 2035 under uncertainty in the projections. The infrastructure specified by the developed model was evaluated under different scenarios involving uncertainty in different economic and operational factors affecting this energy sector. A deterministic energy model for the upgrading operations that was recently published by two of the coauthors of this work has been adopted to develop the present stochastic optimization model.33 Although that study provided a first glance at the upgrading operations for the Oil Sands, it has been widely demonstrated that the application of deterministic models under uncertainty often returns either suboptimal or even infeasible solutions.10,26 Therefore, the considerations of uncertainty in the Oil Sands’ key economic and operational factors provides with a more realistic description of the upgrading operations in terms of its infrastructure, especially when significant fluctuations in the oil production demands and energy commodity prices are soaring. Moreover, the present stochastic model can take into account the effect of single and multiple uncertain parameters in the calculations, which has never been considered for the Oil Sands operations. Thus, the present stochastic-based optimization tool can be used in the decision-making process since it can identify the potential new developments and investments that are expected to be required to accommodate the multiple uncertainties surrounding the Oil Sands’ upgrading operations. This paper is organized as follows: the problem statement is presented next. Section 2 presents the mathematical model used in this work to describe the upgrading operations in the Oil Sands. Section 3 introduces the stochastic optimization algorithm developed in this study to search for the optimal upgraders’ infrastructure under uncertainty. Section 4 illustrates the application of the present stochastic optimization model to

describe the operations of the upgrading process under uncertainty in year 2035. Four scenarios involving uncertainty in different internal and external factors affecting the upgrading operations are presented in this section. Concluding remarks are stated at the end of this article. Problem Statement. The problem under consideration can be stated as follows: Given a set of upgraders’ configurations, each with different production characteristics and energy requirements, and specific oil production demands for each of the products obtained from the upgraders plants, determine the optimal configuration (infrastructure) of the upgraders that minimizes the total energy costs in the presence of production demand constraints and uncertainty in key economic and operational parameters affecting this sector. Figure 1 presents the model superstructure considered in this study. As shown in this figure, crude bitumen enters the system and is processed (refined) to obtain different type of oil grades or petroleum fractions. The system consists of six upgrading plants that include different types of processes and sections as shown in Figure 1. The oil products obtained from these plants are NA, LGO, HGO and VGO. To produce such oil products, the upgrading operations require of significant amounts of energy that varies depending on the section or process of each of the upgrading configurations considered, i.e., hydrogen (H2), heat (H), electricity or power (P), and steam (ST). The model built for the optimization of the upgrading operations is presented next followed by the mathematical formulation of the stochastic MINLP model.

2. UPGRADING OPERATIONS MODEL This section presents the mathematical model that is used to describe the upgraders operations in the Oil Sands. The key objective of the upgraders is to upgrade the crude bitumen extracted from the Oil Sands into SCO with different levels of quality, also known as petroleum fractions. As shown in Figure 1, the present model considers six upgrading plants configurations (RP1−RP6), which represent the typical plant configurations employed by companies in the Oil Sands to produce SCO. Although new technologies are under development to improve the efficiency of the current upgrading plants, the viability of these technologies to become fully operational is still under analysis. Each upgrading configuration has specific efficiencies and operating conditions thus requiring different forms of energy to process the crude bitumen coming from the mining or in situ operations. Note that the upgraders’ plant configurations mostly differ from each other on the cracking process used to transform crude bitumen into SCO, i.e., hydrocraking or thermocracking. In the hydrocracking process, hydrogen is added during the cracking process to promote the production of light petroleum fractions, e.g., NA or LGO. The current leading technology for hydrocracking is LC-fining (LC). On the other hand, the thermocracking process uses thermal energy (i.e., heat) and power to break down the heavy compounds into lighter fractions. Thus, this method is energy intensive requiring significant amounts of fossil fuels such as natural gas and coal to transform bitumen into different petroleum fractions. The current leading thermocracking technology in the Oil Sands is delayed cooking (DC). Each of the processes involved in the upgrading processes, and their corresponding energy requirements, are described next. Due to the large number of algebraic equations involved in the modeling of the different plant configurations in the upgrading operations, the notation in Table 1 is introduced first to ease the presentation of the model, where AD, VD, LC, DC, HT, and SO 16408



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where ERu,j,n represents the energy of form u required per unit of hydrocarbon fraction processed while using the atmospheric distillation unit of the upgraders with infrastructure j. As shown in Figure 1, the ATB fractions obtained from the atmospheric distillation section are further processed in a vacuum distillation unit, which extracts light compounds from the ATB using trains of distillation columns operating at low pressures. The outcome of this operation produces sour fuel gas and VGO as light components whereas the bottoms product in the vacuum distillation section (VTB) is mostly heavy oil that needs to be processed in the cracking sections of the upgrading plants. The flow rate of the stream of VTB per plant is calculated as follows:

Table 1 j = 1, ..., 6 i = {NA, LGO, VGO, HGO} m = {AD, VD, LC, DC, HT, SO} t = {H, H2, P, ST}

index used to denote the configuration of an upgrader. index that denotes the petroleum fractions considered in the model. index that denotes the sections (stages) in an upgrading plant configuration. index used to denote the form of energy required in the sections of a plant.

denote atmospheric distillation, vacuum distillation, LC-fining, delayed coking, hydrotreatment and storage, respectively. In this study, the term output variable is used to denote those variables that appear in the model equations and that need to be calculated to evaluate the present model, and therefore are different from the decision variables, which values are obtained from optimization. Hence, the key model parameters and output variables used in the present model are in Table 2.

VTBj = yDj ATBj(BSFj − SFGj −

k

j = 1, 2, ..., 6;

EDt,j,m PFi,j,m RPj

k = {VGO};

model parameter that represents the yield of the ith petroleum fraction obtained in the mth section of the jth upgrading plant configuration. output variable that determines the requirements of energy of type t in the mth section of the jth upgrading plant configuration. output variable that denotes the production of the ith petroleum fraction obtained from the mth section in the jth upgrading plant configuration. configuration of the jth upgrading plant as shown in Figure 1.

EDu , j , n = yDj ATBjER u , j , n u = {H, P};

The complete set of decision variables and model parameters used in the present model are defined below and in the nomenclature section of this article. Atmospheric distillation (AD) is the first process considered in the upgrading operations. The crude bitumen coming from the diluent recovery units is passed through a train of distillation columns that separates the heavy and light compounds mixed in the bitumen. Most of the light petroleum fractions recovered from this unit, e.g., NA, LGO, are sent back to the diluent recovery units so that they can be used for the transportation of the bitumen via pipelines. The heavy compounds, also known as the atmospheric tower bottoms (ATB), are sent to the vacuum distillation unit in the upgraders for further processing. The flow rate of ATB stream obtained as a bottom product in the atmospheric distillation process for the jth upgrader shown in Figure 1 are calculated as follows: ATBj = zjCapBj(1 −

∑ Yk ,j ,n)

u = {H, P};

n = {AD}

n = {VD}

k = {NA, LGO, HGO}; (1)

(4)

u = {H 2 , H, P};

j = 1, 2, ..., 6;

n = {LC}

EDu , j , n = yPj VTBjER u , j , n

where zj is a binary decision variable that represents the number of upgrading plants with configuration j whereas CapBj is a model parameter denotes the bitumen processing capacity of upgrader j. Atmospheric distillation requires thermal energy (heat) and power to perform the separation required in this section of the upgrading plants. The total energy demands in the atmospheric distillation section per each plant configuration can be calculated as follows: EDu , j , n = zjCapBjER u , j , n

j = 1, 2, ..., 6;

PFk , j , n = yPj Yk , j , nVTBj(1 + HRLCj)

j = 1, 2, ..., 6;

n = {AD}

(3)

The vacuum bottoms product obtained from the vacuum distillation section are further purified through the implementation of cracking technologies. The most widely used cracking methods in the Oil Sands upgrading operations are LC-fining and DC. Upgrading plant configurations with LC-fining (i.e., RP1, RP2, and RP3 in Figure 1) requires large amounts of hydrogen to break down (crack) the heavy oil compounds coming from the vacuum distillation units into lighter petroleum fractions. In addition, this section of the upgraders also requires power and heat to process the vacuum distillation bottoms, i.e., VTBj. The petroleum fractions obtained in the LC-fining section of the jth plant, and the corresponding energy requirements, can be estimated as follows:

k

k = {NA, LGO};

n = {VD}

where yDj is a binary decision variable used to determine if the jth plant configuration includes or not vacuum distillation; BSFj represents the bitumen split factor in the vacuum distillation unit; SFGj denotes the sour fuel gas yield in the jth plant and Yk,j,n represents the yield of the kth petroleum fraction of the light species obtained in the vacuum distillation section, i.e., n = {VD}. As in the case of the atmospheric distillation section, vacuum distillation requires heat and power to support their operations. These energy requirements can be calculated as follows:

Table 2 Yi,j,m

∑ Yk ,j ,n)

j = 1, 2, ..., 6;

n = {LC} (5)

where HRLCj is a model parameter that determines the hydrogen requirements in the LC-Fining process of the jth upgrading plant; yPj is a binary decision variable used to determine whether or not the jth upgrader uses LC-Fining as the cracking process, i.e., ⎧1 yPj = ⎨ ⎩0

j = 1, 2, ..., 6;

⎪

⎪

(2) 16409

if upgrading plant j includes LC‐fining if upgrading plant j includes DC

(6)



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The leading thermocracking technology used to recover light compounds from heavy oil in the upgrading processing plants is delayed coking. As mentioned above, this method cracks the heavy oil using large amounts of heat and power. The petroleum fractions produced by the upgraders that use this cracking technology are obtained from the following expressions: PFk , j , n = (1 − yPj)Yk , j , nATBj k = {NA, LGO, HGO};

EDu , j , n =

i = {NA, LGO, HGO, VGO};

u = {H, P};

EDu , j , n =

i = {NA, LGO, VGO, HGO};

(8)

i

n = {HT} (10)

j = 1, ..., 6; i = {NA, LGO, VGO, HGO}; n = {HT}; n1 = {AD} ⎧1 if i = {NA, LGO} z Fi = ⎨ ⎩ 0 otherwise

1

n = {HT}; (11)

j = 1, ..., 6;

n1

k = {HGO};

n = {HT};

HCk , j , n = BVDj ATBjHR k , j , nYk , j , n1 k = {VGO};

n = {HT};

n1 = {LC, DC}

(12)

j = 1, ..., 6; n1 = {VD}

(17)

Equations 1−17 represent the model used in the current work to describe the upgraders’ operations in the Oil Sands. This model was validated using historical data reported in the literature for the Oil Sands upgrading operations in 2003.34−37 In that year, only upgrading configurations RP3 and RP4 were operating in the Oil Sands; thus, these configurations were the infrastructures considered for model validation. The energy cost per barrel of upgraded product obtained from the present model ($8.3/bbl) is in a reasonable agreement with the data reported for 2003 for upgraders RP3 and RP4 ($6−12/bbl). Similarly, the historical hydrogen consumption rate per barrel of upgraded product reported for upgraders RP3 and RP4 for 2003 is 0.0045 t/ bbl and 0.0027 t/bbl, which are in good agreement with those obtained by the present model, i.e., 0.0042 t/bbl and 0.0027 t/bbl for upgraders RP3 and RP4, respectively. Therefore, the proposed model captures the key characteristics of the upgrading operations in the Oil Sands. More details about this model and its validation are described in Charry-Sanchez et al.33 Additional historical data that can be used to further validate the present model was not available. Most of the information on the upgrading operations that can be used for model validation is

∑ Yk ,j ,n ) n1

HCk , j , n = HR k , j , n ∑ Yk , j , n1

(16)

TPFi , j = PFi , j , n + z FizjCapBjYi , j , n1

where HRi,j,n is a model parameter that associates the amount of hydrogen per unit mass of petroleum fraction i that is needed to remove the impurities in the hydrotreatment section (i.e., n = {HT}) of the upgrader plant of type j. Moreover, HCk,j,n denotes the actual hydrogen demands needed to sweet the petroleum fraction k in the hydrotreatment section of the jth upgrading plant. This variable is calculated as follows:

j = 1, ..., 6; k = {NA, LGO}; n1 = {LC, DC}; n2 = {AD}

n = {HT};

where HERi,j,n and PRi,j,n represent heat and power consumption requirements per unit mass of the ith petroleum fraction that are processed in the hydrotreatment section of upgrading plant type j, respectively. The products obtained from the hydrotreatment section, together with the rest of the products produced from the different sections of the upgraders, are collected and stored for their corresponding transportation to the downstream processes, i.e., refineries. The storage of these products represents the last section or stage considered in the upgraders. Thus, the total production of each of the petroleum fractions i obtained from each upgrading plant j is estimated as follows:

j = 1, 2, ..., 6;

HCk , j , n = HR k , j , n(yj zjCapBjYk , j , n2 +

j = 1, ..., 6;

u = {P}

Following the upgrading plant configurations shown in Figure 1, the products obtained from the cracking processes, together with the VGO fractions recovered in the vacuum distillation section, are hydrotreated to remove traces of impurities such as sulfurs thus producing sweet light oil compounds. The petroleum fractions from this section per upgrading plant configuration are calculated from the following expressions:


⎛ HCi , j , n ⎞ ⎟⎟PR i , j , n ⎝ HR i , j , n ⎠


(9)

⎛ 1 ⎞⎟ PFi , j , n = HCi , j , n⎜⎜1 + Yi , j , n HR i , j , n ⎟⎠ ⎝

n = {HT}; (15)

∑ ⎜⎜

j = 1, 2, ..., 6;

n = {DC}

j = 1, ..., 6;

u = {H} EDu , j , n =

u = {ST};

⎛ HCi , j , n ⎞ ⎟⎟HER i , j , n ⎝ HR i , j , n ⎠

∑ ⎜⎜ i

j = 1, 2, ..., 6;

EDu , j , n = (1 − yPj)CapBjER u , j , n

(14)

Likewise, the heat and power consumption requirements in the hydrotreatment section are calculated as follows:

(7)

n = {DC}

n = {HT};

u = {H 2}

Similarly, the energy requirements for delayed coking are calculated as follows: EDu , j , n = (1 − yPj)ATBjER u , j , n

j = 1, ..., 6;

i

j = 1, 2, ..., 6; n = {DC}

∑ HCi ,j ,n

(13)

where yj is a binary decision variable that denotes whether or not the jth upgrader sends products directly from atmospheric distillation to the hydrotreatment section. Based on the above, the total hydrogen demands for the hydrotreatment section per plant configuration can be estimated as follows: 16410



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model parameters is approximated into a set of discrete (finitedimensional) scenarios, each having a specific probability of occurrence or weight. Therefore, problem 18 can be reformulated (discretized) as follows:

protected by companies operating in this sector and therefore cannot be accessed. Accordingly, a full model validation cannot be performed at this time given the limited amount of data available in the open literature. However, the sensitivity analysis performed in a previous study33 shows that the proposed model makes reasonable predictions for the upgrading operations and therefore can be used to analyze the expected behavior of this sector and identify potential areas of improvement that can further enhance the productivity of this sector under different (uncertain) scenarios. The next section describes the optimization problem considered to estimate the optimal infrastructure for the upgraders under uncertainty.

NS (s) (s) (s) min ∑ wJ s (d , x , h , θ ) d

s. t.

3. STOCHASTIC OPTIMIZATION MODEL This section presents the mathematical framework developed in this work to determine the optimal infrastructure of the upgrading processes for the Canadian Oil Sands. The key novelty introduced in this work is the computation of the optimal infrastructure for the upgrading processes in the presence of uncertainty in key operational and economic parameters affecting the Oil Sands operations. Therefore, the optimization problem under consideration can be formulated as follows:

f(d, x(s), h(s), θ(s)) = 0

s∈S

g(d, x(s), h(s), θ(s)) ≤ 0

s∈S

S = {1, 2, ..., s , ..., NS}

(19)

where S represents the set of discrete realizations or scenarios considered for the uncertain model parameters; the superscript in brackets (s) denotes the index set for the scenarios whereas ws represents the set of discrete probabilities or weights assigned for each uncertain scenario, i.e., ∑sNS = 1ws = 1. Note that expectation term has been replaced in problem 19 by the evaluation of the performance index function J at each discrete scenario s weighted with the corresponding discrete probability weight ws. Also note that the f in 19 are solved for each discrete point s. Accordingly, the set of eqs 1-17 are solved for each realization (s) considered for the uncertain parameters θ. Similarly, d are integer decision variables for this problem representing the number of upgrading plants with a specific configuration (see Figure 1). Moreover, each of the constraints included in the g in 19 are evaluated for each discrete realization (s). The discretization approximation described above allows the transformation of the stochastic infinite-dimensional shown in eq 18 into its deterministic equivalent problem. Accordingly, problem 19 represents a multiscenario MINLP problem that can be solved using standard optimization techniques, which is the key feature offered by the multiscenario method. On the other hand, the multiscenario MINLP approach requires sampling of the uncertain parameters’ space. Thus, the mathematical descriptions specified for the uncertain parameters are relaxed and constrained to a set of realizations (scenarios) in these parameters; this is the key approximation made by this method. While increasing the number of scenarios will improve the quality of the solution, this also increases the optimization problem’s size and therefore the computational costs since additional discrete scenarios need to be added into the analysis. Nevertheless, the multiscenario is a valid method that is widely used when full compliance of the constraints is needed under uncertainty. While the multiscenario MINLP formulation presented in 19 has been extensively used for optimization of systems under uncertainty,38−42 the implementation of such formulations to address the optimal operation of the upgrading processes in the Oil Sands under uncertainty has not been addressed in the open literature. The uncertainty descriptions θ, the constraints g, and the cost function used in the present analysis are described next. Uncertainty Description. It has been widely recognized that models will deviate from the actual plant behavior due to the lack of perfect knowledge in the model parameters. In the case of the Oil Sands, the industries and processes operating in this sector are surrounded by uncertainty due to different internal and external factors such as changes in governmental policies, market demands for oil and the stock market. For example, the natural gas prices and hydrogen production costs are sensitive to changes in economic and technical factors, which can be affected by

min EθJ(d, x, h, θ) d

s. t. f(d, x , h, θ) = 0 g (d , x , h , θ ) ≤ 0 θ low ≤ θ ≤ θ up

s=1

(18)

where x represents the vector of output variables, e.g., EDt,j,m, PFi,j,m, whereas h represent the model parameters that are assumed constant in the analysis, e.g., CapBj, SFGj; d represents the decision variables that cannot be adjusted while running the upgrading operations, e.g., yj, zj. Likewise, f is a vector function that includes the algebraic model equations that describe the behavior of the system under analysis. Thus, f represents the set of eqs 1−17 described in the previous section for the upgrading processes in the Oil Sands. Also, g is a vector function that denotes the constraints that need to be satisfied by the decision variables, e.g., demand constraints on a particular petroleum fraction. Moreover, θ represents the set of uncertain parameters considered in the analysis, i.e., the true values of these parameters are not known a priori but assumed to vary within an uncertain range space limited by predefined lower and upper bounds, θlow and θup, respectively. Following 18, J represents an index that measures the performance of the system; J usually takes the form of an economic index, e.g., the total annualized energy costs of the upgrading operations. Note that the expectation term Eθ in the problem’s objective function J is considered so that it accounts for all the possible realizations of the uncertain model parameters θ. Also, the formulation presented in problem 18 ensures that the constraints g must be satisfied for every potential realization in the uncertain model parameters θ. Therefore, problem 18 can be casted as a stochastic infinite dimensional mixed-integer optimization problem, which is a challenging problem to solve and may even become prohibitive for largescale systems such as that considered in the present study. This is because each parameter θ can take an infinite set of values given by their corresponding upper and lower limits. To make problem 18 tractable, the present analysis adopted the multiscenario approach, i.e., the infinite-dimensional space of the uncertain 16411



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operations is defined in terms of the energy costs required by the different plant configurations. Therefore, the total expected annual energy consumption cost required by the upgrading operations represents the cost function (CF) for the present optimization formulation and is defined as follows:

investments made by the oil and gas companies, new governmental and environmental policies, the discovery of new oil and gas fields or natural phenomena (e.g., hurricanes). Therefore, it is critical to take these uncertain effects into account in the design of an optimal infrastructure for the upgrading processes that can maintain the production of the different petroleum fractions on target while meeting the process constraints in the presence of uncertainty in key economic and operational parameters affecting this sector. In the present analysis, a probabilistic-based description has been used to describe the behavior of the uncertain parameters affecting the upgraders’ processes. Each uncertain parameter is assumed to follow a user-defined probability distribution function with specific model parameters, i.e., θ ≈ PDF(α). This mathematical description for the uncertain parameters is then used to generate a discrete set of scenarios or critical points for the uncertain parameters that can then be used to estimate the optimal infrastructure using the formulation presented in eq 19, i.e.,

NS

CF =

s=1

η(θ ) =

m

t = {H, P, H 2 , ST} (22)

where ct is a model parameter that represents the cost assigned to the energy demands of type t. In the case of the heat and steam costs, these are assumed to be directly related to the natural gas prices (NGprice) as follows: ⎧ NGprice t = {H} ⎪ ct = ⎨ NG (λ price steam − λ feed ) ⎪ t = {ST} ⎩ κ

(23)

where λsteam and λfeed represent the enthalpies of the steam and the boiler’s feedwater used to generate such steam, respectively; κ denotes the boiler’s efficiency. That is, the present analysis assumes that natural gas is the key fuel used to generate the heat and steam required by the different sections of the upgraders shown in Figure 1. The constraints g considered in the present study represent the key production demands that need to be satisfied to ensure feasible operation of the upgrading processes. These constraints are as follows:

(20)

where the subscript ns (ns ∈ NS) indicates the number of discrete points used to represent the uncertain parameter θ whereas wθ represents the set of probabilities of occurrence or weights assigned to each discrete scenario of the uncertain parameter θ that are obtained from the uncertain parameter’s probability distribution function. Accordingly, wθ,ns represents the probability that the realization of the uncertain parameter θ is θ(ns). In most of the engineering applications, the Gaussian probability distribution is perhaps the most widely used description employed to define the probability distribution of an uncertain (random) variable. Due to the central limit approximation theorem,43 Gaussian probability distributions are typically expected when large volumes of samples are taken from a random variable, i.e., the random variable will have an expected (mean) value centered on a distribution with a specific variance. In addition, the Gaussian distribution can represent other types of probability distributions, e.g., binomial or poisson.43 Based on the above, the present study assumes that the actual behavior of the uncertain parameter (θ) can be accurately represented using a Gaussian probability distribution function η(θ) with a specific mean (μθ) and variance (σθ2), i.e., ⎛ (θ − μ )2 ⎞ θ ⎟ exp⎜⎜ − ⎟ 2σθ 2 ⎠ ⎝ σθ 2 2π

j

m = {AD, VD, LC, DC, HT};

θ ≈ PDF(α) → θdisc = {θ (1), ..., θ (s), ..., θ (ns)} wθ = {wθ ,1 , ..., wθ , s , ..., wθ , ns}

∑ ∑ ∑ wcs t ED(t s,)j ,m

∑∑ j

i

TPF(i ,sj) ρj

≥ SCO*(s)


j = 1, ..., 6;

s∈S (24)

∑ TPF(i ,sj) ≥ PF*i (s)

j = 1, ..., 6;

s∈S (25)

j

z jlow ≤ zj ≤ z jup

j = 1, ..., 6

(26)

(s)

where SCO* represent the total equivalent synthetic crude oil production target whereas PFi*(s) denotes the production demand specification of a petroleum fraction of type i for a particular realization s in the uncertain parameters. In addition, ρj represents an averaged density of the equivalent SCO product obtained from upgrader j. As shown in 24 and 25, these constraints ensure that the total equivalent SCO production, and the corresponding production of the petroleum fractions, obtained from the upgrading processes operating in the Oil Sands is satisfied to meet the demands from the downstream processes, e.g., refineries. These two parameters represent an input to the present formulation; estimates for these parameters are reported in the literature. Constraint 26 ensures that the number of plants selected by the present optimization model remains within feasible limits. Note that constraints 24 and 25 must be evaluated, and satisfied at the optimal solution, for each one of the s realizations considered for the uncertain parameters. Based on the above developments, the multiscenario MINLP formulation used in the present analysis is as follows:

1

(21)

Thus, Gaussian distribution function η(θ) is used to generate a set of discrete realizations for the uncertain parameter θ (θdisc) and their corresponding set of probabilities of occurrence or weights (wθ) as shown in 20. Since the actual Gaussian probability distribution function is an unbounded function, i.e., θ can take values approaching infinity that may lead to infeasibilities, the present analysis truncated the function to consider only realizations in the uncertain parameters that are bounded between ±3 σθ to avoid infeasibilities in the analysis. The discrete sets θdisc and wθ can be easily generated using standard subroutines included on commercial off-the-shelf software, e.g., the randn and normpdf built-in functions available in MATLAB. Index Performance Function and Constraints. The index performance function considered for the upgraders’ 16412



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Table 3. Model Parameters for the Upgrading Operations34−37,49−57 upgrader configurations petroleum fractions Yi,j,m

RP1

RP2

RP3

RP4

RP5

RP6

YNA,j,AD YLGO,j,AD YVGO,j,VD YHGO,j,LC YLGO,j,LC YNA,j,LC YLGO,j,DC YNA,j,DC YHGO,j,DC YHGO,j,HT YLGO,j,HT YNA,j,HT YVGO,j,HT energy requirements ERt,j,m ERP,j,AD (kWh/t) ERH,j,AD (MJ/t) ERP,j,VD (kWh/t) ERH,j,VD (MJ/t) ERH,j,LC (MJ/t) ERP,j,LC (kWh/bbl) ERH2,j,LC (t H2/t VTBj) ERP,j,DC (kWh/t) ERH,j,DC (MJ/t) additional model parameters BSFj SFGj HRNA,j,HT (t H2/t) HRLGO,j,HT (t H2/t) HCHGO,j,HT (t H2/h) HCVGO,j,HT (t H2/h) HERHGO,j,HT (MJ/t) HERLGO,j,HT (MJ/t) HERNA,j,HT (MJ/t) HERVGO,j,HT (MJ/t) PRHGO,j,HT (kWh/t) PRLGO,j,HT (kWh/t) PRNA,j,HT (kWh/t) PRVGO,j,HT (kWh/t)

0.0970 0.1370 0.4400 0.3000 0.3800 0.1200 0.0000 0.0000 0.0000 0.8950 0.9820 0.9580 0.8950

0.0000 0.1830 0.2700 0.3900 0.1800 0.0580 0.0000 0.0000 0.0000 0.8950 0.9820 0.9580 0.9550

0.1000 0.1400 0.4400 0.3000 0.3800 0.1200 0.0000 0.0000 0.0000 0.8950 0.9820 0.9580 0.8950

0.0000 0.1400 0.0000 0.0000 0.0000 0.0000 0.2400 0.1700 0.3200 0.8950 0.9820 0.9580 0.0000

0.0000 0.1700 0.0000 0.0000 0.0000 0.0000 0.1600 0.2400 0.2900 0.9000 0.9820 0.9580 0.0000

0.0000 0.1200 0.0000 0.0000 0.0000 0.0000 0.1600 0.1300 0.3800 0.9450 0.9740 0.9830 0.0000

4.1 85 0 257 269 16.5 7154 0 0

4.1 157 1.6 474 269 16.5 18 511 0 0

4.1 84 1.6 252 269 16.5 7154 0 0

4.1 52 0 156 0 0 0 19.8 880

4.5 90 0 271 0 0 0 57.8 1,117

4.1 68 0 207 0 0 0 19.8 1,568

1 0.26 280 280 280 420 306 324 178 306 36.8 12.8 12.5 36.8

1 0.26 829 1264 1835 1135 802 802 802 802 36.8 12.8 12.5 36.8

1 0.26 930 1150 1150 1725 169 150 115 169 36.8 12.8 12.5 36.8

0 0 864 1280 1280 0 306 324 178 0 12.8 12.8 12.5 0

0 0 798 1590 2127 0 169 150 115 0 36.8 36.8 12.7 0

0 0 826 923 2099 0 322 748 96 0 12.8 12.8 12.5 0

min CF

eqs 1, 2, and 9. Similarly, zj, which denotes the number of plants with configuration j, is explicitly included in the model as per eqs 1, 2, 11 and 17 and directly affects the constraints and cost function considered in the analysis. The formulation presented in 27 is a multiscenario MINLP problem that was implemented on GAMS46 and solved using Dicopt, which is an MINLP solver based on the outer approximation algorithm.47 Minos and CPLEX were employed to solve the corresponding NLP and MILP subproblems, respectively.

d

s. t. Reforming model: eqs (1) − (17) Constraints: eqs (24) − (26) S = {1, 2, ..., s , ..., NS}

s∈S

s∈S (27)

As shown in problem 27, the resulting set of discrete constraints specified for a set of scenarios (or realizations) in the uncertain parameters (S) is shown in eqs 24−26 whereas the probability of occurrence of each uncertain scenario (ws) is accounted for in the problem’s objective function as shown in eq 22. This approach ensures that the resulting upgrading configuration complies with the required constraint specifications under uncertainty while minimizing the problem’s cost function. Note that the structure of this multiscenario MINLP problem is similar to that presented in previous multiscenario studies.44,45 The capacities of each upgrading plant configuration j (CapBj) have been taken into account in the model as shown in

4. CASE STUDY: UPGRADING OPERATIONS IN 2035 The stochastic optimization model presented in section 2 has been used to estimate the projected infrastructure for the Oil Sands’ upgraders under uncertainty in key economic and operational parameters. In order to provide insight on the upgrading operations, the number of the different upgrading plant configurations that are able to meet the Oil Sands demands for year 2035 was estimated. Tables 3 and 4 list the model parameters and projections for the Oil sands’ upgraders in 2035 in terms of energy demands, production capacity and infra16413



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for 2035. The uncertainty on each model parameter was quantified using the forecasting information available in the open literature for year 2035 or assumed to follow reasonable estimates based on the current information available for the upgrading operations. While the later represents an approximation, the outcomes of this analysis will provide, for the first time, an outlook on the upgraders’ infrastructure that may be required to meet the Oil Sands demands under uncertainty. The scenarios analyzed in this study are presented next. Problems in all the scenarios were solved using an Intel Core i7 CPU @3.4 GHz (8 GB in RAM). Scenario 1: Uncertainty in Natural Gas and Hydrogen Prices. The upgrading processes in the Oil Sands heavily rely on natural gas and hydrogen. Natural gas is mainly used as fuel to supply the heat required by the different sections in the upgraders. In addition, natural gas can also be used to generate power and steam. On the other hand, hydrogen is the key energy resource used by the plant configurations that include LC-Fining to crack and transform the heavy oil into lighter petroleum fractions. The prices of these two fuels are continuously fluctuating and therefore subject to uncertainty. Market demands and new explorations and drillings of Canada’s tight gas and shale gas resources are the current key factors affecting the price in those fuels.3,21 Over the past decade, large swings in natural gas and hydrogen prices have been observed in both directions, e.g., the natural gas price reached a maximum in 2003 and 2005 whereas the current price of this fuel is about half of the price in 2008.21 These price swings affect the company’s revenues thus making it difficult to assess their ability to make investments in this sector, e.g., the development of new infrastructure, aimed to increase the fleet of upgrading plants in the Oil Sands, will be affected by the natural gas and hydrogen prices. The objective of this scenario is to analyze the upgraders’ infrastructure in 2035 under uncertainty in the natural gas and hydrogen prices, respectively. The multiscenario MINLP formulation presented in eq 27 was used to analyze the energy costs and the upgraders’ infrastructure in the presence of uncertainty in those parameters. Both NGprice and ct (t = {H2}) were assumed to follow a Gaussian probability distribution as shown in 21 with nominal (mean) values (μθ) 11.69 ($/GJ) and 1700 ($/t of H2) and variance (σθ2) 0.6502 ($/GJ) and 1612 ($/t of H2), respectively. The mean prices correspond to the reference (most likely) prices projections expected for these fuels for 203521 whereas the variance was determined based on the most attractive and conservative estimates for these parameters for

Table 4. Projected Estimates for the Upgrading Operations for 203521,58−62 model inputs

specifications

natural gas cost μ = $0.01169/MJ, σ2 = 0.6502 hydrogen production cost μ = $1700/t H2, σ2 = 1612 process steam cost $64.728/t electricity cost $0.076356/kWh annual operating hours 8760 h/yr total upgraded product 1 900 000 bbl/d minimum naphtha production demand μ = 399 180 (bbl/d), σ2 = 39 9182 minimum VGO production demand μ = 357 840 (bbl/d), σ2 = 35 7842 minimum HGO production demand 401 890 (bbl/d) minimum LGO production demand 726 200 (bbl/d) upgrading plant nominal crude bitumen minimum/maximum configurations processing capacities (CapBj) no. of plants RP1 RP2 RP3 RP4 RP5 RP6

641 t/h 493 t/h 641 t/h 576 t/h 1282 t/h 641 t/h

1/10 1/10 1/10 1/10 1/10 1/10

structure. This year was selected because it represents a key time frame to evaluate the Oil Sands operations given the following factors: upcoming in situ dominated oil operations, expected new environmental regulations as a result of a global GHG emission framework agreement, and uncertain effects of the oil and shale gas developments in North America.3,21 Additionally, sufficient data was available in the literature. The expectations for the Oil Sands industry in the medium-term future are subject to various internal and external factors that may significantly impact their growth thus motivating the need to account for uncertainty in the upgrading operations. The multiscenario MINLP model shown in 27 can be considered as a large-scale model since it includes hundreds of models parameters (h) and output variables (x). Analyzing the uncertainty effects of all the elements in h and x (including potential combinations between these variables) is a formidable task that will require extensive time-consuming simulations and long postprocessing that may become prohibitive, especially when multiple sources of uncertainty are considered. Therefore, the optimal infrastructure was evaluated under scenarios that involve uncertainty in key economic and operational parameters that are expected to affect the Oil Sands upgrading operations for 2035. As it will be shown later in this section, the effect of the uncertain economic and operational parameters are significant and affect the upgraders’ configuration

Figure 2. Natural gas prices: predictions and spot prices. 16414



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Table 5. Optimal Upgraders Infrastructure base case upgraders’ infrastructure RP1 RP2 RP3 RP4 RP5 RP6 production levels naphtha (bbl/d) HGO (bbl/da) LGO (bbl/d) VGO (bbl/d) expected energy costs hydrogen ($/yr) power ($/yr) heat ($/yr) steam ($/yr) total energy costs ($/yr)

Sc1-NG

Sc1-H2

Sc2-naphtha

Sc3-VGO

Sc4-LC

9 1 1 9 1 1

9 1 1 9 1 1

9 1 1 9 1 1

9 1 1 3 6 1

10 3 3 4 1 2

9 1 1 9 1 1

4.16 × 1005 4.24 × 1005 7.60 × 1005 3.58 × 1005

4.16 × 1005 4.24 × 1005 7.60 × 1005 3.58 × 1005

4.16 × 1005 4.24 × 1005 7.60 × 1005 3.58 × 1005

5.70 × 1005 5.13 × 1005 8.92 × 1005 3.58 × 1005

4.15 × 1005 4.08 × 1005 7.75 × 1005 4.62 × 1005

4.25 × 1005 4.34 × 1005 7.60 × 1005 3.58 × 1005

4.18 × 1009 4.98 × 1008 1.52 × 1009 9.11 × 1008 7.13 × 1009

4.18 × 1009 4.98 × 1008 1.52 × 1009 9.11 × 1008 7.13 × 1009

4.18 × 1009 4.98 × 1008 1.52 × 1009 9.11 × 1008 7.13 × 1009

4.25 × 1009 5.18 × 1008 1.54 × 1009 9.11 × 1008 7.22 × 1009

4.24 × 1009 5.08 × 1008 1.50 × 1009 9.30 × 1008 7.18 × 1009

4.16 × 1009 4.97 × 1008 1.50 × 1009 8.87 × 1008 7.05 × 1009

2035,21 i.e., μθ + 3σθ (μθ − 3σθ) corresponds to the most conservative (attractive) prices for each of these fuels. To test the accuracy of the prediction, the actual Henry Hub spot price data was compared against the prediction of prices for natural gas. As shown in Figure 2, for the year of 2011, most of the spot price data falls within the range of average low, high and reference predicted price21 (avg. low predicted price = 4.005, avg. actual spot price = 3.9961). For the year of 2012, the prediction has been on the higher side overall, i.e., most of the actual spot price data falls below the average low of predicted price in that year (avg. low predicted price = 4.205, avg. actual spot price = 2.75), however, the year 2012 witnessed the lowest price over the decade, which shows unusual behavior of the market demand conditions and production.48 One of the reasons that triggered the situation was the warm winter experienced in USA, which reduced the demand for natural gas for heating, while the productions stayed at higher level with the recent technology to extract gas from shale rock.48 An improvement in the prediction can be observed in 2013 (avg. low predicted price = 4.4, avg. actual spot price = 3.73), while in 2014 the prediction ranges cover a large part of the actual spot prices (avg. low predicted price = 4.5, avg. actual spot price = 4.63). Thus, the prediction data can be assumed to represent the larger part of the actual spot prices with an exception of 2012 (due to the unusual behavior in the production and market) and its subsequent effects in 2013. The forecasting data, thus, is reliable up to certain extent and therefore, has been used in the analysis presented in this study. The uncertainty descriptions given above for the natural gas and hydrogen prices were then used to generate a set of 100 critical scenarios for each uncertain variable, i.e., the set θdisc for each uncertain parameter is composed of 100 elements (S = 100 in problem 27), each value corresponds to a particular realization of either the natural gas price or the hydrogen costs. These scenarios cover the uncertain space of interest for these parameters, i.e., μθ + 3σθ, μθ − 3σθ. The probability or weights (wθ) assigned to each of these scenarios were estimated by evaluating the Gaussian probability distribution function 21 for each realization of the uncertain parameters considered in the set θdisc. The set realizations in the uncertain parameters used to solve the multiscenario MINLP problem was obtained from sampling the uncertain parameter’s space given the mathematical

uncertainty description specified for that parameter, e.g., the uncertain realizations in NGprice were selected from a normal distribution with μθ= 11.69 and σθ2 = 0.6502. The Monte Carlo sampling method was employed here to obtain the set of scenarios considered for the uncertain parameters. A preprocessing analysis was performed and determined that 100 realizations in these uncertain parameters provide a suitable representation of the uncertain parameters’ space and therefore can be used to generate the set of uncertain realizations considered in the multiscenario approach. Increasing the number of realizations in the uncertain parameters does not improve the solution, but it does increases the computational costs due to the additional number of uncertain scenarios that need to be considered in the optimization formulation. To ensure that the selection of the realizations in the uncertain parameter accurately describes the uncertain parameter description, the solution obtained from that analysis was validated using a new set of realizations in the uncertain parameters, which was obtained using Monte Carlo sampling techniques and that is different from that used in the solution of the multiscenario optimization problem. Note that the present validation method using Monte Carlo sampling is the traditional method used to validate results obtained from stochastic optimization formulations.29−32,63,64 The other scenarios presented in this study have been validated in the same fashion. The uncertainty descriptions provided for NGprice and ct (t = {H2}) together with the model parameters shown in Tables 3 and 4 were used to determine the infrastructure that minimizes the energy costs that are expected to be required for the upgrading operations in the Oil Sands. For comparison purposes, the optimization formulation shown in 27 was solved under the assumption that the estimates for the natural gas and hydrogen prices for year 2035 are perfectly known a priori and equal to their corresponding reference case projections shown in Table 4. The multiscenario MINLP for this scenario consists of 679 constraints, 783 continuous variables, 120 binary variables, and 705 model parameters. The CPU time required by Dicopt to solve this problem was approximately 1.8 s. Table 5 presents the results obtained for the case that all the projections for 2035 are perfectly known (Base case) and the cases when there is uncertainty in the natural gas prices (Sc1-NG) and in the 16415



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hydrogen costs (Sc1−H2), respectively. The results indicate that the expected optimal infrastructure for the upgraders’ plants includes 9 plants with configuration RP 1 , 9 plants of configuration type RP4 and 1 plant for the rest of the plant configurations considered in the present analysis. This result suggests that plants with configurations RP1 and RP4 are the most energy efficient plants. While RP1 used LC-fining as the cracking method, the plant with configuration RP4 uses delayed coking to break down the heavy oil into lighter components. Plants of type RP1 have the lowest heat consumption (therefore consuming low natural gas resources) whereas RP4 plants have low hydrogen consumptions and averaged heat consumption. This result shows that both cracking technologies are needed to satisfy the demands of the different oil grades required by the downstream processes (i.e., oil refineries). Therefore, upgraders with both cracking technologies are needed to satisfy the oil production demands. While RP1 (an LC-Fining-based technology) produces most of the VGO, RP4 produces most of the HGO and LGO needed to satisfy the oil grades mix. Hence, both cracking technologies are expected to coexist in the Oil Sands’ upgrading sector to satisfy the oil refineries requirements. Figure 3a,b shows the variability in the expected annualized energy costs in the upgrading operations due to changes in the natural gas prices and the hydrogen prices that follow the uncertainty description considered for these parameters, respectively. These figures were obtained by evaluating the cost function for each discrete scenario considered for the natural gas price and the hydrogen costs in the analysis, respectively, while maintaining the optimal upgraders’ infrastructure obtained from optimization (see Table 5). As shown in Table 5 (Sc1-NG and Sc1−H2), the hydrogen and heat consumption costs dominate the annual energy costs for the upgraders with nearly 60% and 21% of the total energy costs, respectively. Table 5 also shows that the power and steam costs are not significant when compared to the hydrogen and heat. As shown in Figure 3a, the total annual energy costs fluctuate between 6700 and 7500 $MM/yr due to uncertainty in the natural gas prices. Those critical (extreme) scenarios correspond to a probability of occurrence of 0.001, respectively. This represents a change in the total energy costs of approximately 6% with respect to the base case (7127 $MM/yr). On the other hand, Figure 3b shows that the expected annualized energy costs for the upgrading operations in 2035 may be subjected to an even larger variability due to the uncertainty in the hydrogen costs (almost 17% with respect to the base case). This result was expected based on the infrastructure obtained from the present scenario. As shown in Table 5, 9 plants of type RP1 are expected to be required to satisfy the demands for the upgrading operations in 2035. RP1 plants are required to satisfy the VGO demands for the upgraders since they can produce this oil grade using less hydrogen than RP2 and RP3, which are the other two upgrader configurations that can produce this type of oil grade, respectively. Nevertheless, this type of plant requires significant amounts of hydrogen since its cracking method is based on LC-Fining. Consequently, small changes or fluctuations in the hydrogen costs will result in significant changes in the energy costs for the 9 RP1 upgrading plants. Hence, the uncertainty in the hydrogen prices will play a key role in the Canadian Oil Sands upgrading industry in the upcoming years. Moreover, plants with configuration RP4 operate based on heat and power, which are energy commodities that are not as expensive and hydrogen, and can achieve yields for LGO and HGO higher than the other DC-based plants, i.e., RP5 and RP6.

Figure 3. Total annualized energy costs due to uncertainty in natural gas and hydrogen costs in 2035: (a) natural gas prices and (b) hydrogen costs.

As shown in Table 5, the expected values for the upgrading plants in the infrastructure for the Base Case, Sc1-NG and Sc1− H2 are comparable. This is because, for the moderate price variability ranges considered for the energy commodities (i.e., as a result of including uncertainty in the analysis), the overall energy efficiency associated with this type of plants makes them more economical than the remaining options for every uncertain realization s considered in the analysis. That is, the uncertain space considered for NGprice and ct (t={H2}) is not sufficiently large so that it can produce a migration of petroleum fractions production to other upgraders’ plants. In addition, the Gaussian distribution function, which has been used to describe the uncertainty in the natural gas and hydrogen prices, is a symmetric probability distribution centered on its nominal value. Hence, the expected energy costs also remained at similar levels. Nevertheless, the present results based on the multiscenario analysis have revealed the importance of the hydrogen costs and natural gas prices for the entire Oil Sands operations. Scenario 2: Uncertainty in Production Demands of Naphtha. This scenario aims to specify the projected (robust) infrastructure that is needed for the upgraders at minimum energy cost in the presence of uncertainty in the naphtha production demands. Naphtha is an important petroleum 16416



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The results obtained for the present scenario were validated employing the same approach used for scenario 1. The results for this scenario are shown in Table 5 (Sc2-Naphtha). As shown in Figure 4a, the total annualized energy costs for this scenario has a

fraction in the oil and gas sector that is widely used in the transportation of crude bitumen via pipelines and in the refineries to produce high-value products. The expected production demands for this oil grade are highly uncertain due to social, political, and environmental factors including the potential development of Keystone XL pipeline project, which may allow Canadian crude bitumen to be processed in U.S. refineries.4 Thus, a significant increase in the naphtha production demands from the Oil Sands operations may be expected so that crude bitumen can be transported from the Canadian Oil Sands to the U.S. Gulf Coast. To ensure such demands, new projects involving the development of infrastructure for the upgrading operations may be required to ensure that the Oil Sands can accommodate the fluctuations in the naphtha production demands. As shown in Table 4, the naphtha minimum production demands were assumed to be an uncertain parameter that follows a Gaussian probability distribution with mean and variance of 399 180 (bbl/d) and 39 9182, respectively. The mean value for this uncertain parameter corresponds to the projected reference case demands for this oil grade in year 2035 in the Oil Sands.21 The Gaussian probability distribution function described above was used to generate 100 realizations for this uncertain parameter, i.e., S = 100 in eq 27. The resulting 100 scenarios for the naphtha production demands were used to solve the multiscenario MINLP problem shown in eq 27. For the present scenario, the model’s constrains, binary variables and continuous variables are 479, 120 and 583, respectively. The CPU time needed to solve this problem was approximately 1.3 s. As shown in Table 5 (Sc2-Naphtha), the expected infrastructure needed to accommodate the uncertainty in the minimum Naphtha production demand is significantly different from that obtained for Sc1-NG and Sc1-H2, respectively. Although the expected annualized energy costs for this scenario is 2% higher than that obtained for the Base Case, Sc1-NG and Sc1-H2, the projected upgraders’ infrastructure that is needed to maintain the naphtha demand requirements on target is significantly different. Since hydrogen is the most expensive energy commodity considered in the present analysis, i.e., it accounts for almost 60% of the total annualized energy costs, the number of upgrading plants that uses LC-Fining (RP1−RP3) remained the same as in the previous scenarios. On the other hand, upgrading plants based on delayed coking are energy intensive units in terms of heat and power; however, the total costs for these energy commodities represent only 21% and 7% of the total annualized energy costs. Consequently, 3 and 6 upgrading plants of type RP4 and RP5, which use delayed coking (DC) as the cracking method, were selected to accommodate the uncertainty in the naphtha production demands, respectively. Upgrading plants with configuration RP5 are more prone to produce Naphtha over the other two DC-based upgrading plants (i.e., RP4, RP6). This is produced by the combination of a few factors. On the one hand, the yield obtained for naphtha from RP5 plants is at least 7% higher than the production that can be obtained from the other DC-based upgrading plants (see Table 3). Also, the heat consumption in RP5 is not as intensive as in upgrading plants with configuration RP6. Similarly, RP5 is the most energy intensive plant configuration in terms of power; however, this energy commodity is the least expensive (see Table 4). Therefore, upgrading plants with configuration RP5 are attractive to maintain the energy costs of the upgrading processes at minimum cost in the presence of uncertainty in the naphtha production demands.

Figure 4. Sc2-naphtha (validation): (a) Frequency histogram of the annual expected energy cost in 2035 and (b) evaluation of the production demand constraints under uncertainty.

non-Gaussian (nonsymmetric) distribution, which suggests that there exist a strong nonlinear correlation between the minimum naphtha production demand constraint and the total energy costs for the upgrading operations. Moreover, Figure 4b shows the normalized production levels obtained for the petroleum fractions and their corresponding minimum demands. This graph was obtained as follows: the minimum production demands, i.e., PFi*(s), i = {NA, LGO, HGO, VGO} in eq 25 were normalized to the unity whereas the actual production levels estimated by the optimization model 27 for each scenario considered in the validation test of the present scenario were normalized by computing the ratio between actual production levels and the minimum production demand for each petroleum fraction. Note that the uncertain parameter considered for this scenario is PFi*(s), i = {NA} in eq 25. As shown in Figure 4b, the projected production levels for the petroleum fractions satisfied their corresponding minimum production demands for each of the scenarios considered in the validation test. The results shown in Figure 4b also indicate that the projected production levels for VGO remained close to its minimum 16417



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realizations in the VGO production demands (i.e., S = 100 in 27), which were selected from the Gaussian probability distribution assigned to this uncertain parameter. Scenario 3′s problem consists of 479, 120, and 583 constrains, binary variables, and continuous variables, respectively. The CPU time needed to solve this problem was approximately 1.28 s. As shown in Table 5 (Sc3-VGO), a different projected infrastructure to that obtained for the previous scenarios is required to accommodate the uncertainty in the VGO production demands at minimum energy costs. The results show that the uncertainty in this parameter produces a mix in the upgraders’ plant infrastructure, which is a clear indication of the effect of this uncertain parameter in the upgrading operations in the Oil Sands. As shown in Table 5 (Sc3-VGO), the number of upgrading plants with configuration RP1 represents almost 43% of the total plants required for the upgrading operations. Although the upgraders’ plants RP1 and RP3 have the same yield for VGO in the VD section of those plants, i.e., 44% (see Table 3), RP1 is preferred over RP3 because the hydrogen requirements for RP3 to produce VGO are four times higher than those needed by RP1 in the hydrotreatment section of these upgraders plants (see HCVGO,j,HT ; j = {1,2,3} in Table 3). Therefore, the upgrading plant RP1 is one of the most economically attractive configurations to satisfy the VGO productions demands for the Oil Sands operations. The upgrader plant with configuration RP4 represents the second highest infrastructure used to accommodate the uncertainty in the VGO production demands. This plant was selected because it produces naphtha, LGO and HGO using power and heat, which are less expensive energy commodities than hydrogen. Although upgraders RP2 and RP3 are relatively expensive, these upgrading plants are projected to be required to accommodate the VGO demands under the critical (worst-case) scenario, i.e., when the realizations in the VGO demands are set to high (extreme) levels. As in the previous scenario, the results were validated using the approach described in scenario 1. The upgrading configuration obtained for this scenario is presented in Table 5 (Sc3-VGO). As shown in Figure 6a, there is a high nonlinear correlation between the expected annualized energy costs and the minimum VGO production demands, i.e., the expected annualized energy costs is only 3.25% (233.8 $MM/yr) higher than the most economically attractive scenario evaluated for the VGO demands whereas the worst-case (most expensive) scenario indicates that the total energy costs would be 12.2% (995 $MM/yr) higher than the expected annualized energy costs reported in Table 5 (Sc3VGO). Note that the nonlinear frequency distributions obtained for the expected annualized energy costs due to uncertainty in naphtha and VGO production demands shown in Figures 3a and 5a are different, which is also reflected on the different infrastructures specified for both scenarios, respectively. For example, note that the most economically attractive scenario for Sc2-Naphtha is typically the most frequent; thus, it also corresponds to its expected annualized costs. However, the most critical scenario found for Sc2-Naphtha is 23% higher than the expected annualized costs estimated for that scenario (see Figure 4a). Due to these highly nonlinear behavior, the present analysis found that the expected annualized energy costs for Sc3VGO are approximately 32.52 $MM/yr lower than that obtained for Sc2-Naphtha. Figure 6b shows the normalized production levels obtained under uncertainty in the VGO production demands. As shown in that figure, the production levels for the different oil grades remained above their minimum specifications for each of the realizations considered for the VGO production demands. This figure also shows that the HGO production levels

production demand limit for the different realizations considered for the naphtha production demands. VGO is only produced by upgrading plants RP1−RP3, which require large amounts of hydrogen to operate. Therefore, the production of VGO in the upgrading plants is costly since hydrogen is the most expensive energy commodity considered in the present analysis. Accordingly, it is expected that the constraint on the minimum demands for VGO will play a key role for the upgrading operations in 2035. Figure 5 shows the yield of the different oil grades (produced from each plant configuration) using the most critical (worst-

Figure 5. Production levels of the petroleum fractions at the critical scenario, Sc2-naphtha.

case) realization evaluated for the minimum naphtha demand. As shown in the figure, the upgrading plants RP1 and RP5 are expected to deliver almost 85% of the naphtha required to satisfy the worst-case production demands for this oil grade with RP5 being the lead producer, i.e., almost 54% of the total naphtha demands are projected to be produced from this type of upgrading plants. In addition, RP5 is expected to produce most of the LGO and HGO production requirements for the year 2035. The results in this figure also show that RP1 will be the lead producer of VGO. These results suggest that the upgrading plant with configuration RP5 will likely become a key producer of naphtha, LGO and HGO whereas VGO will be much likely be produced from upgrading plants with relatively low hydrogen requirements such as RP1. Scenario 3: Uncertainty in the VGO Production Demands. The objective of this scenario is to determine the projected infrastructure that will accommodate the uncertainty in the VGO’s minimum production requirements for the Oil sands operations in 2035. As it was discussed in the previous scenario, it is expected that the production demands for VGO will dominate the economics of the upgrading operations due to the limited availability of configurations that can produce VGO, i.e., RP1− RP3, and the fact that these upgrading plants require hydrogen, which is the most expensive energy commodity considered in the present model. To evaluate the present scenario, the VGO minimum production demand constraint shown in eq 25, i.e., PF*i (s), i = {VGO}, was considered to be an uncertain parameter in the optimization problem 27. As in the previous scenario, a Gaussian probability distribution function with mean 357 840 bbl/d and variance 35 7842 was considered to describe the uncertainty in the demands for this petroleum fraction for year 2035. The nominal value corresponds to the Base Case production demands projected for this oil fraction for year 2035.21 Problem 27 was solved for this scenario using 100 16418



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Figure 7. Production levels of the petroleum fractions at the critical scenario, Sc3-VGO.

present scenario aims to evaluate the uncertainty of these model parameters on the projected infrastructure and energy costs of the upgrading operations in the Oil Sands in 2035. Due to the large number of petroleum yield fraction parameters included in the present stochastic optimization model (see Table 3), the present scenario only considered uncertainty in the petroleum fraction parameters affecting the LC-fining operations, i.e., Yi,j,m, i = {NA, LGO, HGO}, j = {1,2,3}, m = {LC}; accordingly, the present scenario aims to determine the optimal infrastructure that can accommodate (at minimum energy cost) the uncertainty in petroleum fraction yields in the LC-fining section of the plants with configuration RP1-RP3 while meeting the projected demands for naphtha, VGO, LGO, and HGO for 2035. The stochastic optimization model shown in 27 was used to analyze the present scenario (Sc4-LC). In this case, however, nine uncertain parameters representing the different petroleum fraction yields obtained from the LC-fining sections were considered in the analysis. Therefore, a multivariate normal probability distribution was used to describe the uncertainty in the petroleum yield fractions, i.e.

Figure 6. Sc3-VGO (Validation): (a) Frequency histogram of the total expected energy cost in 2035 and (b) evaluation of the production demand constraints under uncertainty.

remain close to its corresponding production demands (see Table 4) under uncertainty in the VGO production demands. Furthermore, Figure 7 presents the yields obtained for the petroleum fractions when the uncertainty in the VGO production demand was set to its corresponding worst-case (critical) realization. This figure shows that the upgrader plant RP1 is the lead producer of all the oil fractions under these worstcase conditions. RP1 produces almost 80% of the total VGO production and almost 50% of the total naphtha production required. This figure also shows that upgrading plants with configuration RP4 are mainly used to accommodate the demands in LGO that cannot be produced by RP1. Therefore, it is expected that the upgrading plants with configuration RP1 will likely become the lead producers of the different oil fractions in the Oil Sands. Scenario 4: Uncertainty in Yield Petroleum Fractions, LC-Fining. One of the key factors considered in the present analysis is the petroleum yield fractions, i.e., Yi,j,m. As shown in section 2, these parameters are used to estimate the production of the oil grades from the different sections included in the upgraders. These parameters are typically estimated based on averaged (expected) projected production demands. As such, a single mean value for this parameter may not reflect a realistic description of the potential oil production levels that can be attained by the different upgrading operations. Therefore, the

ϑ(θ1 , ..., θK ) =

⎛ 1 exp⎜ − (θ − μθ )T Ξ−1 ⎝ 2 (2π ) |Ξ| 1

K

⎞ (θ − μθ )⎟ ⎠

(28)

where K represent the number of uncertain parameters considered in the multivariate normal probability distribution function (K = 9 for the present scenario); μθ represents the nominal (mean) values of the uncertain parameters whereas Ξ is the covariance matrix describing the dispersion or variance of the uncertain parameter set. For the present scenario, the mean values of the uncertain parameters were set to their corresponding projected estimates reported in Table 3. Similarly, the standard deviation of each uncertain parameter was set to 0.05Yi,j,m, i.e., 5% of the parameters’ projected nominal estimates. The variances of each of the uncertain parameters, i.e., 0.05Yi,j,m2, were used as the diagonal elements of the covariance matrix whereas the off diagonal elements were set to zero. To the authors’ knowledge, this is the first study that evaluates the Oil Sands operations under the effect of multiple uncertain parameters. 16419



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Figure 8. Sc4-LC: Annual expected costs for the energy commodities in 2035 under uncertainty in the petroleum fraction yields in LC-fining.

Figure 9. Production levels per type of upgrader plant at the critical scenario identified for 2035, Sc4-LC.

However, the expected annualized energy costs for the present scenario is approximately 2% lower (77.76 MM$/yr) than that obtained for the base case. Although these results may indicate that the effect of these uncertain parameters is not relevant, the validation test shows that there is significant variability in the results. The validation of this scenario was performed using the same approach used for scenario 1. The results for this scenario are shown in Table 5 (Sc4-LC). Figure 8 shows that there is a significant variability in the total annualized energy costs since the distribution obtained for the expected annualized costs are highly nonlinear and cannot be accurately represented by any known probability distribution function, e.g., Gaussian distribu-

Problem 27 was solved under the uncertainty specifications described above, 200 realizations in the uncertain parameters were generated from the multivariate normal probability distribution defined for this scenario; the rest of the parameters were set to their corresponding nominal values shown in Tables 3 and 4, respectively. This multiscenario MINLP problem consists of 26 846 equations, 26 950 continuous variables, 120 binary variables, and 12 196 model parameters. The CPU time required to solve this problem was approximately 67.5 s. As shown in Table 5 (Sc4-LC), the optimal infrastructure that satisfies the oil grades production demands under uncertainty in the LC-Fining petroleum fractions is similar to that obtained for the base case. 16420



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5. CONCLUSIONS

tion. Figure 8 also shows the costs of each individual energy commodity; the frequency distribution obtained for the different energy commodity costs indicates that hydrogen costs represent between 57 and 60% of the costs, whereas the heat costs fluctuate between 20 and 22% of the expected annualized energy costs. Note that the frequency distributions of each energy commodity are also nonsymmetric, indicating a strong nonlinear correlation between these costs and the uncertain parameters. As shown in Figure 9a, the naphtha, LGO, and VGO production levels remained above their minimum specification whereas the VGO production level only met its minimum demand requirement. VGO can only be produced in upgrading plants with configurations RP1−RP3, which are the only plants in the analysis that consider LC-Fining. Since these plants also require significant amounts of hydrogen, which is the most expensive energy form as shown in Figure 8, only the minimum number of RP1-RP3 plants required to satisfy the minimum VGO production demands has been specified. As mentioned above, RP1 is preferred over RP2 and RP3 because of its efficiency to produce VGO at low hydrogen consumption costs. Figure 9b shows the production levels obtained from each plant configuration using the worst-case (critical) realizations in the uncertain parameters identified from the validation test. As shown in this figure, plants with configuration RP1 produce about 91% and 44% of the total VGO and naphtha production demands projected for 2035, respectively. On the other hand, upgrading plants with configuration RP4 are the lead producers of LGO and HGO accounting for 41% and 48% of the total projected demands for these oil grades in year 2035, respectively. These results indicate that the upgrading plants with schemes RP1 and RP4, which are based on different cracking methods, are expected to produce nearly 80% of the total projected SCO demands for the Oil Sands operations in 2035. Therefore, these two upgraders schemes are expected to play a key role in the future of the Canadian Oil Sands. The different upgraders’ configurations obtained for each of the scenarios considered here is an indication of the effect of key uncertain economic and operational parameters on the Oil Sands upgrading operations (see Table 5). While a worst-case (pessimistic) approach can be used to select the upgrading plants needed for 2035, i.e., by selecting the highest number of plants obtained for each upgrading configuration RPj, this approach is expected to return overly an conservative upgrading configuration that may not be economically viable. On the other hand, selecting the lowest number of upgrading plants may also result in upgrading operations unable to meet the Oil Sands demands. Therefore, the present analysis provides with an outlook on the potential plants needed for each configuration under different uncertain scenarios. Note that other model parameters affecting these operations and that were not considered in the analysis may also return different upgrading configurations. Also note that the uncertainty quantification method described above can be readily modified to make more realistic assumptions if new reliable historical or forecasting data for the Oil Sands upgrading sector becomes available in the near future. In all the case studies presented here, the optimization solver (Dicopt) used to solve the present optimization problems converged (stopped) when the nonlinear optimization subproblems (NLP) stopped improving the cost function, i.e., the total expected energy costs obtained from that NLP subproblem started to deteriorate.

A stochastic optimization model that identifies the optimal upgraders’ infrastructure that is expected to be required for the Oil Sands operations under uncertainty has been presented. The multiscenario approach, which discretizes the domain of the uncertain parameters to a fixed set of realizations, has been applied to solve the proposed stochastic mixed-integer nonlinear optimization model. The set of uncertain realizations, i.e., multiscenarios, are used to identify the upgraders infrastructure that satisfies the different oil grades’ production demands at minimum energy costs in the presence of uncertain realizations in the model parameters. Thus, the present model specifies a robust upgraders’ infrastructure since it meets the upgraders’ production demands in the presence of critical (worst-case) realizations in key uncertain economic and operational factors affecting the upgrading plants. The uncertain parameters considered in the analysis were described using Gaussian probability distribution functions. However, the present model is not restricted to this type of distribution and can be readily implemented using other probabilistic-based uncertainty descriptions, e.g., log-normal or exponential. The developed stochastic optimization model was used to determine the optimal (robust) infrastructure for the Oil Sands’ upgrading operations that is projected to be required to minimize the energy cost in year 2035. Four scenarios that explicitly account for uncertainty in key economic and operational factors affecting this industry were studied. The results show that the upgrading plants with configurations RP1 and RP4 are the most energy efficient plants. Plants of type RP1 have the lowest heat consumption (therefore consuming low natural gas resources) whereas RP4 plants have low hydrogen consumptions and averaged heat consumption. Additionally, among DC-based upgraders, i.e., RP4−RP6, upgrading plants with configuration RP5 are more prone to produce naphtha. The projected production of VGO will have a significant effect on the infrastructure that is expected to be required for the upgrading operations in the upcoming years. This is, VGO is only produced by upgrading plants including LC-Fining (RP1−RP3), which require large amounts of hydrogen to operate. However, a significant number of upgrading plants with configuration RP1 have been projected due to their relatively low hydrogen consumption and high efficiency to produce VGO, these types of plants are expected to produce most of the projected VGO demands from the upgraders. Accordingly, it is expected that the minimum demands for VGO may drive the investments and developments of LC-fining-based upgrading configurations in 2035. Furthermore, hydrogen and heat consumption costs are expected to dominate the energy costs for the Oil Sands’ upgrading operations. While hydrogen is essential in LC-fining technologies, which produced most of the VGO production demands, delayed coking is a heat intensive process that is mainly used to meet the LGO and HGO production demands. Therefore, it is expected that these two types of upgraders’ technologies will need to coexist in the future to satisfy the domestic and international SCO demands from the Oil Sands. These results highlight the importance to develop uncertainty analyses for the Oil Sands’ upgrading operations to make robust informative decisions on the projected future developments for this sector. 16421



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AUTHOR INFORMATION

yj

Corresponding Author

*Tel: +1-519-888-4567 ext. 38667. Fax: 1-519-888-4347. E-mail: [email protected].

zFi

Notes

The authors declare no competing financial interest.

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BSFj yDj

ACKNOWLEDGMENTS The financial support provided by Brazilian National Counsel of Technological and Scientific Development (CNPq) and the program Science without Borders (SWB) and the Natural Sciences and Engineering Research Council of Canada (NSERC) are gratefully acknowledged.

CapBj CF yPj

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ct d zj

ABBREVIATIONS AD atmospheric distillation ATB atmospheric tower bottoms DC delayed coking H heat H2 hydrogen HGO heavy gas oil HT hydrotreatment LC LC-fining LGO light gas oil NA naphtha P power SCO synthetic crude oil SO storage ST steam VD vacuum distillation VGO vacuum gas oil

EDt,j,m ERt,j,m Eθ f g h HCi,j,m HERi,j,n

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INDEXES i = {NA, LGO, VGO, HGO}

HRi,j,n

index that denotes the petroleum fractions considered in the model j = 1,2,...,6 index used to denote the configuration of an upgrader m = {AD, VD, LC, DC, HT, SO} index that denotes the sections (stages) in the upgraders s index used to denote a particular realization in the uncertain parameters θ t = {H, H2, P, ST} index used to denote the form of energy required in the sections of a plant j = 1,2,...,6 index used to denote the configuration of an upgrader k index used to denote the subset of the petroleum fractions n index used to denote the subset of the section in the upgraders u index used to denote the subset of the form of energy required

J NGprice NS ns PFi,j,m PF*i PRi,j,n RPj S SCO* SFGj TPFi,j

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VTBj ws

MODEL PARAMETERS AND VARIABLES ATBj amount of ATB produced in the jth upgrading plant (t/h)

x 16422

binary decision variable that specifies if whether or not the jth upgrader configuration sends products directly from atmospheric distillation to the hydrotreatment section binary decision variable that specifies if NA and LGO are considered or not in the path bitumen split factor in the jth upgrading plant (%) binary decision variable used to determine if upgrader j includes VD in its configuration nominal bitumen capacity of the jth upgrading plant (t/h) annualized cost function ($/yr) binary decision variable used to determine if the jth upgrader uses LC-fining or not cost assigned to the energy commodity of type t set of decision variables number of upgrading plants with configuration j (binary decision variable) output variable that determines the energy requirements for energy of type t in the mth section of the jth upgrading plant configuration energy commodity of form t required per unit of hydrocarbon fraction processed in the mth section of upgrader j (units of energy/h) expectation term in the cost function model equations model constraints model parameters hydrogen required to sweet the petroleum fraction i in the mth section of upgrader j heat consumption per unit mass of the ith petroleum fraction that are treated in the hydrotreatment section (MJ/t of fraction i) hydrogen consumption per unit mass of petroleum fraction i required to remove impurities in the hydrotreament section (t H2/t Yi,j,n) economic index performance function natural gas price ($/t of Natural Gas) number of scenarios considered in the set S number of scenarios considered for a single uncertain parameter θ variable that denotes the production of the ith petroleum fraction obtained from the mth section in the jth upgrading plant configuration production demands of petroleum fraction i for a particular realization s in the uncertain parameters (bbl/d) power consumption per unit mass of the ith petroleum fraction that are treated in the hydrotreatment section (kWh/t of fraction i) upgrader with configuration j set of scenarios considered for the uncertain parameters θ total equivalent synthetic crude oil production target for a particular realization s in the uncertain parameters θ (bbl/d) sour fuel gas yield (%) production of petroleum fraction i produced from upgrader j (bbl/d) heavy oil extracted from vacuum distillation (t/h) probability of occurrence or weight assigned to scenario s output variables dx.doi.org/10.1021/ie501772j | Ind. Eng. Chem. Res. 2014, 53, 16406−16424


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model parameter that represents the yield of the ith petroleum fraction obtained in the mth section of the jth upgrading plant configuration α set of parameters the specifies the probability distribution function of the uncertain parameters η(θ) normal probability distribution function of an uncertain parameter θ θ uncertain parameters θdisc discrete set of realizations of the uncertain parameter θ κ boiler’s efficiency μθ mean value of the uncertain parameter θ σθ2 variance of the uncertain parameter θ ρj averaged density of the equivalent SCO product obtained from upgrader j (t/bbl) λfeed enthalpy of the feedwater used to generate steam in the boilers λsteam enthalpy of the steam used to generate steam in the boilers ϑ(θ1,...,θK) multivariate normal probability distribution of K uncertain parameters Ξ covariance matrix of a multivariate normal probability distribution function Yi,j,m

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