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Stochastic Modeling of the Oil Sands Operations under Greenhouse Gas Emission Restrictions and Water Management Alberto Betancourt-Torcat,† Ali Almansoori,† Ali Elkamel,*,‡ and Luis Ricardez-Sandoval‡ †

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

‡

ABSTRACT: There exist several inherent uncertainties in the energy optimization modeling of Oil Sands operations. In this work, the deterministic model proposed by Betancourt-Torcat et al. in 2011 has been extended to account for parameter uncertainty in the natural gas price and steam-to-oil ratio (SOR). The new extended steady-state model considers freshwater withdrawal constraints and a new methodology to account for greenhouse gas (GHG) emissions. The problem was formulated as a single-period stochastic (MINLP). The application of the stochastic energy optimization model includes results reflecting all uncertain outcomes simultaneously and enabling optimal arrangement of the energy supply and oil producer infrastructures. The model’s capabilities have been shown in the present work through two new case studies accounting for uncertainty while the deterministic case is presented as a reference. The case studies under uncertainty consider the forecasted oil production scenario for the year 2035 in an uncertain environment where the price of natural gas is volatile and the SOR unknown. The results of the stochastic model were compared with those of the deterministic model by studying the expected values of the stochastic approach and those of the deterministic solution. The results presented in this study were discussed regarding the characteristics of uncertainty of the varied fuel price and SOR parameter. The key findings of this study are that oil producers considering hydrocracking are favored over thermocracking-based schemes, and the GHG emission constraint cannot be met for SOR values higher than 2.48.

1. INTRODUCTION Alberta’s Oil Sands represent the third-largest proven oil reserves in the world, behind only Saudi Arabia and Venezuela. Alberta’s oil reserves amount to 170.8 billion barrels, which consists of 169.3 billion barrels of bitumen and 1.5 billion barrels of conventional oil.1 Moreover, half of the Canadian crude oil production (i.e., 1.6 million barrels of oil per day) comes from the Oil Sands. The Oil Sands consist of a natural mixture of sand, water, clay and a form of heavy oil called bitumen; they are commonly referred as the tar sands, because bitumen has a consistency similar to that of tar, which is a human-made product. The bitumen first must be removed from the sand and water in order to be processed into commercial petroleum products. Bitumen can be sold directly as commercial diluted bitumen that consists of the extracted heavy oil mixed with a solvent (typically naphtha). The solvent decreases the bitumen viscosity enabling its transportation via pipeline for further processing in downstream refineries. Also, bitumen can be sold as a higher value product usually known as synthetic crude oil (SCO), which requires the prior processing and upgrading of the crude bitumen. The bitumen can be converted to SCO using two different production schemes: (i) integrated in situ/upgrading and (ii) integrated mining/upgrading. Recent advances have been made toward the development of alternative energy systems to replace the existing carbon-based systems. However, those technologies have not reached the maturity to overcome the current carbon-based systems. Moreover, carbon-based fuels are expected to continue to play an important economic role in the foreseeable future.1 Accordingly, Alberta’s vast oil reserves, enough to meet Canada’s current energy demands for ∼400 years, are a very © 2013 American Chemical Society

important asset for the world energy security. Two important strategic aspects to consider about the Oil Sands are (i) almost 13% of the world’s proven oil reserves are accessible to private investment (the remainder is controlled by national governments) and Alberta’s Oil Sands account for 51% of this accessible reserves, and (ii) Alberta provides more crude oil to the United States than any other country in the world, including Saudi Arabia, Mexico, or Venezuela. Therefore, Alberta must help meet the U.S. and global energy demands in the forthcoming future. Despite the latest technological advances in the Oil Sands sector, the operations still rely heavily on natural gas. For example, mined bitumen extraction requires, on average, 0.5 thousand cubic feet (mcf) of natural gas per barrel of crude bitumen produced, whereas in situ (steam-assisted gravity drainage (SAGD)) extraction methods demand over 1.0 mcf of natural gas.2 The fossil fuel pricesin particular, that of crude oil and natural gashave had a historical volatile tendency promoted by geopolitical instability in oil producer countries, growing demands, and unforeseen global economic events. For example, in the year 2008, during the development of the recent global economy crisis, the price of oil initially experienced a historical high of $147/barrel, only to fall drastically in the coming weeks to $60/barrel.3 Moreover, the expected significant role that in situ SAGD extraction should play in the upcoming future of the Oil Sands industry is promoting technical developments in this area. Oil Sands developers Received: March 5, 2013 Revised: July 6, 2013 Published: July 8, 2013 5559

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with those obtained from the simultaneous optimization of the energy supply and oil production infrastructures under deterministic conditions and uncertainty considerations. The considerations of uncertainty in these parameters provide a more accurate and practical analysis of the problem, especially at a time when fluctuations in energy commodity prices/ demands are soaring and improvements in the oil sector are constant. This paper is organized as follows: Section 2 presents the uncertainty in the price of natural gas and SOR values. Section 3 presents the main features of the energy model under deterministic conditions and stochastic optimization. Section 4 presents two case studies that were used to predict the Canadian Oil Sands operations for the year 2035, using the proposed stochastic approach and the deterministic base case. Also, comparisons between the results obtained by the present stochastic model and the deterministic approach are presented in this section. Concluding remarks and future work are presented in Section 5.

currently operate with a steam-to-oil ratio (SOR) that ranges from 2.9 to 3.1 units of SAGD steam per unit of crude bitumen produced (2.9−3.1:1). However, SAGD projects are presently seeking to achieve a SOR target of 1.8:1 in their operations for the medium-term future.4 A lower SOR would bring several benefits to the Oil Sands sector, e.g., reduce capital and operating costs, reduce water use and energy consumption, and lower air emissions including greenhouse gases (GHG). As a result of this energy price context (where change is the only constant) and the expected improvements on the SOR value, it is necessary to incorporate the assumption of unpredictable changes into the energy models that are used to analyze energy-related scenarios. The development of energy models is a widely extended practice for evaluating the designs, strategies, configurations, and supply chains in the energy sector, especially for the analysis of optimal resources allocation. Energy models with a bottom-up structure are used to identify the optimal mix of technologies that would lead to the minimum present value of total costs.5 Some deterministic energy models that describe the operations of the Oil Sands industry have been reported in the literature. For example, Ordorica-Garcia et al.6 presented a nonlinear mathematical tool that estimates the energy demands and GHG emissions associated with the Oil Sands industry. Another study by Ordorica-Garcia et al.7 presents a mixed-integer linear programming (MILP) energy model that determines the optimal configuration of energy plants to minimize the energy costs related to the Oil Sands operations. Their model only considers a case study of the historical Oil Sands operations in the year 2003. Moreover, Betancourt-Torcat et al.8 developed a mixed-integer nonlinear programming (MINLP) model that simultaneously determines the most suitable infrastructures of oil producer and energy plant to minimize the total annual energy cost of the Oil Sands industry. The model includes a CO2 emission target as environmental constraint and was used to forecast the industry operations for the year 2020. Similarly, in a recent study conducted by Betancourt-Torcat et al.,9 the authors analyze the effect of key environmental and operational factors on the Canadian Oil Sands sector using a MINLP model that considers GHG emissions constraints. The deterministic energy models typically evaluate the uncertainties in their parameters by analyzing multiple deterministic scenarios (sensitivity analysis). However, when a deterministic energy model is applied under uncertainty, it is relatively difficult to achieve robust results.5 Alternatively, stochastic energy models consider the uncertainties within the problem’s formulation and they cover different aspects of the systems that they represent. For example, the stochastic energy systems models usually consider uncertainties associated with future investment costs for technologies or restrictions such as demands and emissions.10−12 On the other hand, supply-oriented models occasionally consider explicitly uncertainties on energy price, such as optimization of the product portfolio of utilities.13 However, to the author’s knowledge, a stochastic energy optimization model that can be used to study the Oil Sands operations is not currently available in the open literature. In the present work, the steady-state deterministic model proposed by Betancourt-Torcat et al.8 is extended to consider uncertainty in the natural gas price and SOR. In addition, the model accounts for a new GHG emission quantification approach, as well as water management. The problem is formulated as a single-period stochastic MINLP. The results obtained by the present stochastic formulation are compared

2. UNCERTAINTY IN PRIMARY ENERGY PRICES AND SOR The mathematical representation of energy systems considers external parameters subject to uncertainty. A few of these parameters are typically denoted by the price of primary energy resources (e.g., coal, natural gas) in the international market and operational parameters (e.g., SOR). In order to account for uncertainty, the variation in the price of natural gas and SOR will be discussed in this section. The existing uncertainty in the natural gas price is mainly due to the volatility of crude oil prices, which influence the price of related carbon-based fuels in the market. In addition, variables such as climate and economic changes may play an important role in the price of natural gas.14,15 The Oil Sands industry heavily relies on natural gas as a primary energy resource, because of its use as feedstock for the production of steam, electricity, and hydrogen. Thus, the volatility in the price of natural gas creates uncertainty and concern in this sector, which may lead to decision changes from oil companies over new investments and expansion planning. Such changes may result in lost market opportunities and inefficient long-run resource allocations. However, it is also very important to recognize that energy prices play a necessary role in the operations of free-market energy systems. The price of energy resources transferred essential information on the energy supply/demand balance, both on a short and long-term investment planning perspective.15 In addition, the continuous improvement on the amount of SAGD steam used per barrel of oil produced in Alberta, and the efforts of the Oil Sands sector to achieve lower SOR values in their operations, generates uncertainty on the SOR value to be used in the upcoming future. The further improvement of the SOR could potentially boost the development of in situ SAGDbased oil developments in the Oil Sands industry, thus affecting the projected pace of expansion of this industrial sector. Under the existing energy price and SOR uncertain scenarios, the use of stochastic mathematical modeling can be used as a practical tool to help the energy sector in the decision making process.14,15 In this work, the fluctuations in the natural gas price and SOR were assumed to follow a normal probability distribution. This type of statistic distribution approximates well naturally occurring phenomena (e.g., height, intelligence, error measurements), with few members at the high and low ends and many in the middle region. This type of distribution is the 5560

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Figure 1. Oil Sands energy costs with their corresponding demands sources.

3. MODEL FORMULATION 3.1. Deterministic Model. The deterministic model developed by Betancourt et al.8 aimed to minimize the annual energy costs of the Oil Sands operations, assuming that the main fuel feedstock prices (e.g., natural gas) and operational parameters (e.g., SOR value) are known a priori. Accordingly, the deterministic model objective function is defined as follows:

most widely known and the standard reference for many probability problems. Moreover, random variables with unknown distributions are often assumed to be normal, this assumption is justified by the Central Limit Theorem.16 Therefore, the methods developed using normal theory applied well in many practical cases, even when the distribution is not normal. Furthermore, the use of data samples following normal distribution in stochastic models to handle uncertainty in the price of natural gas has been reported in recent works.17 The probability density function for the normal distribution is given by P(X ) =

1

2

2πσ 2

e−(x − μ)

min CF = PTC + HTC + STC + SSETC + HWTC η

+ PFTC + DTC + CTC + CSC

/(2σ 2)

(1)

where CF represents the objective annualized cost function of the deterministic model, and the rest of the terms of the equation (eq 3) are the single energy costs of the operation. These energy costs are the following: power generation (PTC), hydrogen production (HTC), process steam production (STC), SAGD steam production (SSETC), hot water production (HWTC), process fuel (PFTC), diesel (DTC), CO2 transport (CTC), and CO2 storage (CSC). These single energy costs are annual costs and they are a function of the total energy demands of the oil operations (see Figure 1 for energy costs details). The energy demands are defined in terms of mass and energy balances and depend on the processing stages involved in the production of commercial diluted bitumen and SCO, as well as the carbon capture and storage (CCS) systems (see previous work for details8). Furthermore, the deterministic model considers environmental metrics to account for a CO2 emission constraint. This constraint plays a key role in determining the most suitable infrastructure of oil and energy producers in the Oil Sands industry. The environmental constraint can be set according to data obtained from environmental regulators or green policy projections.18−20 The deterministic model proposed by Betancourt et al.8 assumes that the natural gas market price and SOR value are perfectly known a priori. This assumption will be relaxed in the following section, and uncertainty will be accounted for using a single-period stochastic programming modeling approach.

where μ is the mean value of the distribution, σ2 is the variance and P(X) represents a normal distribution in a variate X (random variable) with mean μ and variance σ2. The parameters μ and σ determine the shape of the distribution. Moreover, the most commonly used distribution is the standard normal distribution, the standard normal distribution function (Φ(z)) provides the probability that a standard normal variate assumes a value in the interval [0,z]. Φ(z) =

1 2π

∫0

z

e −x

2

/2

dx =

1 ⎛ z ⎞ ⎟ erf⎜ 2 ⎝ 2⎠

(3)

(2)

where erf is a function commonly known as the error function. Both functions Φ(z) and erf cannot be expressed in terms of finite arithmetical procedures (i.e., additions, subtractions, multiplications, and root extractions). Hence, both functions must be either computated numerically or otherwise approximated. Uncertainty is considered in the model through a discrete distribution of the random parameter (i.e., natural gas price and SOR value) with a finite number “S” of possible outcomes (scenarios). In order to generate the discrete probabilistic scenarios, a Matlab pseudo-random number generator was used to withdraw values from the standard normal distribution. 5561

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S

min CF = η

S

S

s=1

s=1

S

+

S

S

∑ SSETCs + ∑ HWTCs + ∑ PFTCs s=1

s=1

s=1

+ DTC + CTC + csc

f = {ME, SE, C , H , DBE, U , CCSS}

(4)

(commercial diluted bitumen and SCO production schemes)

Total Energy Demands (power, hydrogen, process steam, SAGD steam, hot water, process fuel, diesel) Production Capacities

(capacities of the oil schemes)

Energy Plants

(hydrogen plants, power plants, and boilers)

PD =

∑ Pf ,

f = SE, H , DBE, U , CCS (6)

f

where PD is the total demand of power from the Oil Sands operations and Pf represents the power consumption by stage f. The total process steam demand (SD) can be calculated as follows:

Energy Plants Installed Capacities Environmental Constraints (CO2 emission target) Water Management

(5)

where ME denotes the mining extraction stage, SE SAGD extraction, C conditioning, H hydrotransport, DBE diluted bitumen extraction, U upgrading, and CCSS CO2 capture and storage systems. Accordingly, the total power demand in the oil operations can be formulated as follows:

subject to Oil Schemes

oil schemes oil schemes capacities

where the new objective function in problem (4) is formulated in terms of the single energy costs involved in the Oil Sands operations due to a specific realization (scenario) “s” in the uncertain model parameters. Accordingly, the terms PTCs, HTCs, STCs, SSETCs, HWTCs, and PFTCs represent the power, hydrogen, process steam, SAGD steam, hot water, and process fuel costs, respectively. These energy costs are defined in terms of the discrete values in the natural gas price distribution and their corresponding probability ps (which are introduced later in this section). Likewise, the discrete values obtained from the SOR normal distribution also affect the SAGD steam production costs. Furthermore, the terms DTC, CTC, and CSC are not affected by the variation in the natural gas price or SOR value, because they are not a function of these parameters. Figure 3 illustrates the general layout of the stochastic energy model used in this work. It shows the key model inputs and outputs considered for the present modeling approach. The single energy costs of the objective function are defined next in the following subsection. Following problem (4), η represents the set of decision variables of the problem. The model is formulated in terms of different energy plant’s technologies (see Table 1) and oil production schemes (i.e., integrated in situ (SAGD)/upgrading and integrated mining/upgrading) with their corresponding processing stages (see Figure 2). In addition, SAGD commercial diluted bitumen is included in the model. Energy Demands. The total energy demands of the Oil Sands operations are a function of the energy requirements of the stages involved in the production of commercial diluted bitumen and SCO (see Figures 1 and 2), as well as the carbon capture and storage (CCS) systems. The set of oil processing stages and CCS systems involved in the Oil Sands operation ( f) is described as follows:

∑ PTCs + ∑ HTCs + ∑ STCs s=1

⎫ ⎪ ⎪ ⎪ number of SAGD steam boilers available ⎪ ⎪ number of process steam/hot water boilers ⎪ ⎬ available ⎪ type and number of hydrogen plants available ⎪ ⎪ type and number of power plants available ⎪ ⎪ ⎪ energy plants operating capacities ⎭

⎧1: ⎪ ⎪ 2: ⎪ ⎪ 3: ⎪ ⎪ 4: η=⎨ ⎪ ⎪ 5: ⎪ ⎪ 6: ⎪ ⎪ 7: ⎩

3.2. Stochastic Model Formulation. The mathematical formulation of the single-period stochastic problem seeks for the optimal integration of energy plants and oil production schemes in the Oil Sands industry operations that minimize the annual energy production costs. The model considers two products: (1) commercial diluted bitumen produced at in situ (SAGD) projects and (2) SCO (SOi) produced at mining and in situ (SAGD) extractions-based projects through oil scheme i. Each oil scheme consists of different production stages where the bitumen is either recovered from the sand for its direct commercialization as diluted bitumen or further processed into SCO (see Figure 2 for processing stage details). The most suitable configuration of oil schemes that are needed to meet the expected production levels of commercial diluted bitumen and SCO is required to plan and schedule the future Oil Sands operations (see Figure 2 for details of the oil schemes). The energy demands of the oil schemes are: power (PD), hydrogen (HU), process steam (SD), SAGD steam (SSE), hot water (HWD), process fuel (PFU), and diesel (D). Furthermore, the optimal infrastructure of energy plants, e.g., hydrogen (j), power (m), and boilers (SB and SSEB), are required to meet the energy demands of the oil schemes (see Table 1 for energy plant details21−28). The model objective is to minimize the annualized energy costs associated with the Oil Sands operations at a given time horizon, by means of simultaneously determining the optimal infrastructure of energy plants and oil schemes under CO2 emissions constraint and water management. In the present work, after acknowledging the limitations of the deterministic energy models, uncertainty is considered in the natural gas price and SOR value, which is considered through a discrete normal distribution of the random parameter with a finite number S of possible outcomes (scenarios) corresponding to a probability ps. The formulation of the stochastic optimization model is as follows:

SD =

(freshwater withdrawal limits)

∑ Sf , f

5562

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Figure 2. Oil Sands producers with their processing stages and corresponding energy demands.

where Sf represents the process steam requirements by stage f. Similarly, the total hot water demand is estimated as follows: HWD =

∑ HWf ,

where the subindex s represents the natural gas price scenario, m represents the type of power plant technology (see Table 1), M is the total number of power plant technologies, NPPm is an integer variable denoting the number of type m power plants, ACCm is the capital cost of type m plant, OMCm is the annual operating and maintenance cost, ps is the probability of scenario s for the natural gas price, t is the total annual operating hours of the plant, PGm the power generated by the plant, HRm the heat rate by plant, FCm,s is the unit fuel cost (natural gas/coal) that for natural gas depends on scenario s, and EC is an energy conversion factor. The hydrogen production costs (HTCs) can be estimated as follows:

f = C , H , DBE (8)

f

where HWD is the total demand of hot water in the oil operations and HWf denotes the hot water requirements by stage f. Furthermore, the remaining total energy demands involved in the oil operations are (1) hydrogen (HU) that depends on the amount used in the upgrading stage (U ∈ f); (2) SAGD steam (SSE), which is determined by the amount consumed in the SAGD extraction stage (SE ∈ f), for both the production of commercial diluted bitumen and SAGD SCO; (3) process fuel (PFU) which depends on the fuel requirements for upgrading (U ∈ f); and 4) diesel (D) that represents the consumption of fuel in the mining stage (ME ∈ f). Energy Costs. The overall annual energy cost of the Oil Sands operations (problem’s objective function) is defined as a function of single energy costs. In general, these single energy costs are defined in terms of the fuel, capital, and operating costs associated to the energy plants and supply infrastructure required to meet the energy demands of the oil operations. Accordingly, the power generation costs (PTCs) in the present stochastic model are calculated as follows:

J

HTCs =

j=1

∑ NPPm(ACCm + OMCm) ps t PGm HR m FCm , s EC

EC

where the subindex j represents the type of hydrogen plant technology (see Table 1), J is the total number of hydrogen plant technologies, NHPj is an integer variable indicating the number of type j plants, ACCj is the annual capital cost of the type j hydrogen plant, OMCj is the annual operating and maintenance cost for the plants, Fj represents the amount of fuel consumed by hydrogen plant (natural gas/coal), FHVj is the heating value of the fuel, and FCj,s is the unit fuel cost that, for type j hydrogen plants using natural gas, is determined by the scenario s.

m=1

+

ps t Fj FHVj FCj , s (10)

M

PTCs =

∑ NHP(ACC j j + OMCj ) +

(9) 5563

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Table 1. Energy Production Technologiesa energy producerb

installed capacity

capital costc

emission factor

NG, at 6300 kPa and 500 °C steam, w/o CO2 capture (SB) NG, 80% steam at 8000 kPa, w/o CO2 capture (SSEB)

340 tonne/h

NGCC w/o CO2 capture (PP1) supercritical coal w/o CO2 capture (PP2) IGCC w/o CO2 capture (PP3) IGCC with 88% CO2 capture via Selexol (PP4)

507 000 524 000 539 000 448 000

NGCC with 90% CO2 capture via MEA (PP5)

432 000 kW

$930/kW

0.000043 tonne CO2/kWh

supercritical coal with 90% CO2 capture via MEA (PP6) NG oxyfuel with CO2 capture (PP7)

492 000 kW

$1980/kW

0.000107 tonne CO2/kWh

440 000 kW

$1250/kW

0.000012 tonne CO2/kWh

coal oxyfuel with CO2 capture (PP8)

532 000 kW

$1950/kW

0.000084 tonne CO2/kWh

SMR w/o CO2 capture (HP1)

6.25 tonne/h 32.09 tonne/h 6.25 tonne/h 32.09 tonne/h

Hydrogen Plants 11 130 MM$ 8.992 tonne CO2/tonne H2 h/tonne H2 23 780 MM$ 18.732 tonne CO2/tonne h/tonne H2 H2 17 760 MM$ 1.050 tonne CO2/tonne H2 h/tonne H2 1.502 tonne CO2/tonne H2 25 070 MM$ h/tonne H2

coal gasification w/o CO2 capture (HP2) SMR with 90% CO2 capture via MEA (HP3) coal gasification with 90% CO2 capture via Selexol (HP4)

340 tonne/h

kW kW kW kW

CCS factor

Boilers NI 0.00179 tonne CO2/Nm3 NG NI 0.00179 tonne CO2/Nm3 NG Power Plants $570/kW 0.000367 tonne CO2/kWh $1230/kW 0.000811 tonne CO2/kWh $1760/kW 0.000800 tonne CO2/kWh $2400/kW 0.000131 tonne CO2/kWh

source

0 tonne CO2/Nm3 NG

Harrel21

0 tonne CO2/Nm3 NG

Harrel21

0 tonne CO2/kWh 0 tonne CO2/kWh 0 tonne CO2/kWh 0.000911 tonne CO2/kWh 0.000387 tonne CO2/kWh 0.000959 tonne CO2/kWh 0.000403 tonne CO2/kWh 0.000831 tonne CO2/kWh

Rubin et al.22 Rubin et al.22 Ordorica-Garcia et al.23 Ordorica-Garcia et al.23

0 tonne CO2/tonne H2

Simbeck et al.,25 Simbeck26 Chiesa et al.,27 Kreutz et al.28 Simbeck et al.,25 Simbeck26 Chiesa et al.,27 Kreutz et al.28

0 tonne CO2/tonne H2 9.446 tonne CO2/tonne H2 17.262 tonne CO2/ tonne H2

Rubin et al.22 Rubin et al.22 Davison24 Davison24

a

Note: HP2, HP4, and HP6 co-generate 2240, 1210, and 1210 kWh/tonne H2, respectively. bNG = natural gas, NGCC = natural gas combined cycle, IGCC = integrated gasification combined cycle, SMR = steam methane reforming, MEA = monoethanolamine. cNI = Not included. The capital costs of the boilers were not included in the model because they do not contribute meaningfully to the total production costs of process steam, hot water, and SAGD steam.

the steam demands involved in the production of commercial diluted bitumen and SAGD SCO. The SAGD steam demands are defined in terms of the SOR, which is one of the parameters subject to uncertainty in the stochastic model. The SAGD steam demand (SSE) can be estimated as follows:

The process steam production costs are calculated as follows: ⎡ 1 ⎤ STCs = t ⎢ (p NSB NGSB CS HVNG PNGs) + SD CFW⎥ ⎣ EC s ⎦ (11)

where STCs represents the production costs of process steam in the boilers (SB), NSB is an integer variable that represents the number of boilers (SB) producing process steam, NGSB is the average consumption of natural gas per boiler, CS denotes the percentage of the boiler capacity used to produce steam, HVNG is the assumed natural gas heating value, PNGs is the unit price of the natural gas for scenario s, SD is the total amount of process steam generated in the boilers, and CFW is the cost of the boilers feedwater. Similarly, the production costs of SAGD steam can be calculated as

S

SSE =

N

∑ [ps SOR s(DBR + ∑ PSi BIT)] i s=1

(13)

i=1

where the subindex i represents an oil production scheme (see Figure 2) and N the total number of oil schemes considered in the model. SORs is a model parameter that represents the steam-to-oil ratio, in terms of the scenario s, DBR is the commercial diluted bitumen production rate, and PSi is a binary variable (PSi = 1 if the oil producer follows an integrated SAGD/upgrading scheme, or PSi = 0 otherwise. BITi is the bitumen production rate via SAGD extraction for SCO production by oil scheme i. The costs of the hot water consumed in the oil operations can be estimated as follows:

⎛ 1 ⎞ SSETCs = t ⎜ (p NSEB NGSEB HVNG PNGs) + SSE CFW⎟ ⎝ EC s ⎠ (12)

where SSETCs denotes the SAGD steam generation costs for natural gas fired-boilers (SSEB) producing SAGD steam for in situ bitumen extraction operations, NSEB is an integer variable representing the number of boilers (SSEB) that produce SAGD steam, NGSEB is the average consumption of natural gas per SAGD boiler, and SSE is the amount of SAGD steam produced in the boilers. The capital cost of the boilers is not taken into account in the model, because it can be neglected, when compared to its annual fuel consumption cost. Moreover, the amount of SAGD steam produced in the boilers should meet

{ EC1 [p NSB NGSB (1 − CS) HVNG PNG ] + HWD CFW}

HWTCs = t

s

s

(14)

where HWTCs represents the hot water costs and HWD is the amount of hot water produced in the boilers (SB). 5564

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Figure 3. General layout of the stochastic energy model.

is the unit CO2 transport cost, and PL is the total length of the pipeline used to transport the CO2 from the operation site to nearby depleted oil fields. The CO2 storage cost (CSC) is estimated from the following expression:

The costs of process fuel are given as ps t PFU HVNG PNGs

PFTCs =

EC

(15)

where PFTCs specifies the costs of the process fuel involved in the upgrading stage operations, and PFU is the total amount of process fuel required in the upgrading stages. The total diesel cost (DTC) is calculated as follows: DTC = D CD t

⎛ J csc = t UCSC⎜⎜∑ HPCj CCHj + ⎝ j=1

where UCSC represents the unit CO2 underground injection cost. The last three equations that define the total diesel cost (DTC), the CO2 transport cost (CTC), and CO2 storage costs (CSC) are not dependent on the natural gas price or SOR value. Carbon Dioxide Emission Constraint. The stochastic model considers the carbon dioxide emissions restriction as a key environmental constraint in the problem’s formulation. All forms of oil and gas developments represent environmental challenges and risks to human society. However, the environmental concerns about the Oil Sands industry are distinctive and serious compared with conventional oil operations. There are several objections to Oil Sands developments, because of the relatively high energy and GHG emissions intensity of their extraction and processing stages. For example, the well-towheel GHG emissions are typically higher for the oil produced from the Oil Sands than the oil produced through conventional methods.29 For example, on a well-to-wheel life cycle GHG emission basis, Oil Sands blends were reported to generate, on average, 107 g CO2 equiv/MJ, whereas EU conventional refinery feedstocks generate, on average, 87 g CO2 equiv/MJ.30

J

CTC = (∑ HPCj CCHj j=1 M

∑ PPCm CCPm)(t UCTC PL) m=1

(18)

(16)

where D is the demand of diesel in the Oil Sands mining operations and CD is the unit cost of the diesel. In addition, the energy optimization model considers energy plants with and without CO2 capture technologies, which enables mitigating GHG emissions and aiming for specific CO2 emissions target in the Oil Sands operations. As a result, the cost related to the transport of the CO2 captured (CTC) in the power and hydrogen plants is formulated as follows:

+

⎞ ⎟ PPC CCP ∑ m m⎟ ⎠ m=1 M

(17)

where HPCj is a binary variable equal to 1 if the hydrogen plant j captures CO2, 0 otherwise. Similarly, PPCm represents a binary variable equal to 1 if power plant m captures CO2, 0 otherwise. CCHj and CCPm are the total amounts of CO2 captured in the hydrogen and power plants respectively, UCTC 5565

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generated by power plant. The amount of carbon dioxide emissions produced by the hydrogen plants is given as

That is, the Oil Sands blends generate, on average, 23% more CO2 equiv than EU conventional refinery feedstock. Moreover, the continued expansion of Oil Sands developments to meet growing global energy demand is increasing the overall emissions of the industry. The total GHG emissions of Canada grew by 103 Mt between 1990 (589 Mt CO2 equiv) and 2010 (692 Mt CO2 equiv); the Oil Sands industry were responsible for 32% of this increase. Furthermore, Oil Sands GHG emissions accounted for 21% of Albertan emissions and 7% of Canadian emissions in the year 2010.31 However, Alberta is currently the only North American jurisdiction regulating GHG emissions; this province imposes mandatory reduction targets for large GHG industrial emitters across all sectors producing over 100 000 tonnes of GHG per year. The large industrial emitters of Alberta are now required to comply with mandatory emission reduction targets. Accordingly, emitters unable to meet the GHG emission targets either must pay $15 per additional tonne of GHG emitted into a clean energy technology fund (this fund is worth $312 million, as of April 2012), or purchase Alberta offset carbon credits.18 Among the large GHG industrial emitters of the region, the Oil Sands industry takes up an important part. The present stochastic energy model includes power and hydrogen production plants with and without carbon capture and storage (CCS) methods. The energy plants including CCS methods help to comply with the CO2 emissions restrictions imposed by governmental entities or environmental regulating agencies. The stochastic programming model also considers a new approach to account for the CO2 emissions constraint into the problem’s formulation. Accordingly, the CO2 emission constraint is formulated as follows: M

J

B

CO2 Ej = EFj HPj

where CO2Ej is the amount of CO2 emissions produced by the hydrogen plant j, EFj represents the emission factor of the hydrogen plant j (see Table 1), and HPj is the amount of hydrogen produced by hydrogen plant. The amount of carbon dioxide emitted by the process steam boilers (CO2Eb) can be calculated as follows: CO2 Eb = NGb EFNG

j=1

b=1

+ CO2 E PF + CO2 ED ≤ TCO2 E

CO2 Ee = NGe EFNG

(23)

where the subindex e represents the boilers used to meet the SAGD steam demands of the oil operations, and NGe denotes the natural gas consumed in boiler e. The CO2 emission of the process fuel (CO2EPF) is calculated as follows:

CO2 E PF = PFU EFNG

(24)

where PFU is the natural gas consumed as upgrading process fuel in the oil operations. The emission associated with the fuel diesel (CO2ED) is estimated as follows:

E

CO2 ED = D EFD

e=1

(25)

where EFD is the CO2 emission factor of the diesel fuel. The mathematical model also considers energy plants with carbon capture methods. Accordingly, the amount of CO2 captured (CO2Cm) through power plants can be calculated as

(19)

where TCO2E represents the CO2 emission constraint in the problem that must be specified by the user according to the government environmental regulations, industrial targets, or global policies such as the Durban Platform.20 The total CO2 emission from the Oil Sands industry is defined in terms of the individual carbon dioxide emissions from the energy plants that comprise the energy infrastructure (i.e., power and hydrogen plants, process steam, and SAGD steam boilers) and carbonbased fuels used in the oil operations (i.e., process fuel and diesel). Accordingly, the variables CO2Em, CO2Ej, CO2Eb, and CO2Ee denote the carbon dioxide emissions from power plant m, hydrogen plant j, process steam boiler b, and SAGD steam boiler e. The indexes M, J, B, and E represent the total number of power plants, hydrogen plants, process steam boilers, and SAGD steam boilers, respectively. These energy plants are used to meet the energy demands of the oil operations. Furthermore, the overall CO2 emissions from the process fuel used in the upgrading stages is denoted by CO2EPF and the amount of emissions from the diesel consumed by the fleet of trucks and shovels used in the mining operations is denoted as CO2ED. Moreover, the amount of CO2 emissions produced in the power plants (CO2Em) is calculated as follows: CO2 Em = EFm PGm

(22)

where the subindex b represents the process steam natural gasfired boilers, NGb is the amount of natural gas consumed in process steam boilers, and EFNG is the CO2 emission factor of natural gas (see Table 1). The carbon dioxide emissions of boilers producing SAGD steam (CO2Ee) for in situ bitumen extraction is estimated as follows:

∑ CO2Em + ∑ CO2Ej + ∑ CO2Eb + ∑ CO2Ei m=1

(21)

CO2 Cm = CCFm PGm

(26)

where CCFm is the carbon dioxide capture factor by power plant type m (see Table 1). The carbon dioxide captured through hydrogen plant j can be estimated as CO2 Cj = CCFj HPj

(27)

where CO2Cj is the amount of CO2 captured by the type j hydrogen plant and CCFj is the carbon dioxide capture factor of the hydrogen plant (see Table 1). The CO2 emission constraint considered in the present stochastic model (see eq 19), which is denoted by the CO2 emission target, plays a key role in the selection of the type of energy plants (e.g., plants with and without CCS technologies). Also, this environmental restriction plays an important part in the selection of the most suitable oil production schemes to comply with the GHG emissions regulation. Water Management Constraint. The stochastic model presented in this work considers as a key feature freshwater consumption and water recycling constraints. According to Allen,32 the decline of the river flow during winter represents a constraint for future Oil Sands developments. Thus, there is a need to include a plan for the optimal use of water resources in the Athabasca region. The province of Alberta has enacted strict

(20)

where EFm is the CO2 emission factor associated with the type m power plant (see Table 1) and PGm is the amount of power 5566

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The amount of freshwater that can be withdrawn from the Athabasca River in a given time period to be used in the Oil Sands operations is limited through the following constraint:

restrictions on the amount of freshwater that Oil Sands companies can withdraw from the Athabasca River for their operations. The water conservation regulations were established by the provincial government through the Water Management Framework for the Lower Athabasca River.33 The framework specifies strict limits on the amount of freshwater that Oil Sands operators can withdraw from the river during environmentally sensitive periods (e.g., winter); these periods are classified as green, yellow, and red conditions, according to the river’s flow rate. The objective is to guarantee low impact to the river ecosystem and preserve water resources. Under this framework, the flow of the Athabasca River is constantly being monitored and evaluated. When the river flow condition is denoted as green, the oil companies can withdraw freshwater according to their standard operating allowances. On the other hand, when the river flow condition is indicated as yellow, the oil sand companies are required to proceed with caution and may be required to limit their freshwater withdrawal allowances. Furthermore, when the river flow indicates a red condition (i.e., most environmentally sensitive period), the oil companies are required to limit freshwater withdrawal from the Athabasca River.34 Green condition occurs during most years; it is characterized by enough flow in the river to meet environmental and human needs. This condition allows water withdrawals up to 15% of the flow in the river. On the other hand, during yellow condition the river experiences natural low flows. According to the records, this condition has occurred ∼14% of the time. Whereas in red flow condition periods, the river experiences natural low flows, which records show have occurred ∼4% of the time.33 This framework intends to prevent ecological risks and damages to the river rather than react to them after they arise. The Oil Sands companies are currently complying with Phase One of the framework. The total water withdrawn by Oil Sands operators from the Athabasca River for the year 2010 was ∼104 million cubic meters, or an average of 3.3 m3 per second, this represents