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Multiperiod Stochastic Optimization Model for Carbon Capture and Storage Infrastructure under Uncertainty in CO2 Emissions, Product Prices, and Operating Costs Jee-Hoon Han and In-Beum Lee* Department of Chemical Engineering, POSTECH, Pohang, Korea S Supporting Information *

ABSTRACT: A multiperiod stochastic programming model is developed for planning a carbon capture and storage (CCS) infrastructure including CO2 utilization and disposal in an uncertain environment and with a time-varying investment environment. An inexact two-stage stochastic programming approach is used to analyze the effect of possible uncertainties in product prices, operating costs, and CO2 emissions. The proposed model determines where and how much CO2 to capture, store, transport, utilize, or sequester for the purpose of maximizing the total profit of handling the uncertainty while meeting the CO2 mitigation target during each time period of a given planning interval. The capability of the proposed model to provide correct decisions despite a changing uncertain environment is tested by applying it to designing and operating the future CCS infrastructure on the eastern coast of Korea over a 20-year planning interval (2011−2030).

1. INTRODUCTION Carbon capture and storage (CCS) is a key method to reduce greenhouse gas (GHG) emissions that contribute to climate change.1 CCS is an integrated infrastructure which consists of utilization, capture, storage, sequestration, and transportation technologies that are mutually connected. Considerable research, typically based on the net present value (NPV), has focused on the technoeconomic assessment (TEA) of CCS infrastructure.2 TEAs of CCS infrastructure can be classified into two categories: those which minimize its cost3−8 and those which maximize its profit.9,10 Relatively few studies have considered the objective function of maximizing profit, because recent research work increasingly considers the value added by utilization of CO2, such as acquisition of carbon credit from CO2 reduction, and sale of products (e.g., biofuel or “green” polymer) made from CO2. These studies address static deterministic NPV approaches assuming that all problem parameters are invariant over a given planning interval. However, uncertainties may exist in various factors that affect the CCS infrastructure; these include GHG emissions inventory, GHG reduction costs, and product prices. Moreover, the CCS infrastructure design can be modified to satisfy a given CO2 reduction variation over a long time interval which is divided into several subintervals to account for variations in CO2 emissions, prices, and costs. To obtain realistic results, these considerations may affect the way in which the design and operation of a CCS infrastructure are modeled. Thus, the TEA of CCS infrastructure can also be performed using methods and decision criteria that are more advanced than those used in the static deterministic NPV approach. Four different valuation models are available, which differ in their treatment of uncertainty (stochastic vs deterministic) and decision structure (multiperiod vs stable)11 (Figure 1). Stochastic models consider uncertain parameters whose values cannot be forecast precisely and, therefore, can obtain more realistic results than deterministic models. Our previous research12,13 was conducted to evaluate the effects of various uncertainties in the © 2012 American Chemical Society

Figure 1. Economic assessment matrix.11

CCS infrastructure. However, the uncertainties in the study were divided into variation of CO2 emissions in a two-stage stochastic programming approach12 and variation in product prices and operating costs in a multiscenario stochastic programming approach.13 Here we develop a model in which all of these uncertainties are considered, and we compare its results to those of the previous work. However, multiperiod models can be more appropriate than deterministic models when the timing of the investment is flexible, e.g., when investing today precludes investing tomorrow and vice versa.11 Hence multiperiod models consider Received: Revised: Accepted: Published: 11445

February 25, 2012 July 24, 2012 August 8, 2012 August 8, 2012 dx.doi.org/10.1021/ie3004754 | Ind. Eng. Chem. Res. 2012, 51, 11445−11457

Industrial & Engineering Chemistry Research

Article

Figure 2. Superstructure of the multiperiod stochastic model.

infrastructure. This study is based on the infrastructure model and expanded to a multiperiod stochastic model considering possible uncertainties of parameters. The superstructure (Figure 2) used in the previous research14 which is relevant to this part of the paper is summarized below. It includes five main components associated with each technology option (Figure 3): utilization, capture, storage, sequestration facilities, and transport modes. There are regions gn enclosing different types cn and sizes jn of CO2 capture technologies, regions enclosing different types sn and sizes jn of CO2 sequestration technologies, and different types pn and sizes jn of CO2 utilization technologies. The CO2 captured by the capture technologies established in various emission sources sin and spn within regions should be matched by disposal activities such as sequestration or utilization activities such as production of biobutanol and green polymers. In other words, it is possible to link from one capture technology to either sequestration technology or utilization technology, and CO2 leaving one capture technology can also split between two or more possible sequestration technologies and utilization technologies. If the regions containing the capture technologies do not contain sequestration or utilization technologies, these regions rn must be connected to the sequestration or utilization technology in other regions rn′ by different potential transportation modes ln (truck, railcar, or ship). Regions containing different types mn and sizes jn of intermediate storage technologies only exist to collect CO2 captured from emission sources within a particular region, to load CO2 for delivery by different transport modes. Capture technology regions are directly connected to the sequestration or utilization technology regions by pipeline-based transportation without intermediate storage technologies. The decision-making problem of the CCS infrastructure model is to determine the following considerations with the overall goal of maximizing the expected profit: (1) the number,

that decisionmaking is multiperiod, including operational or investment decisions at one time that depend on decisions at another time. Our previous research14 was conducted to consider variance in CO2 emission and change in emission reduction targets over a long time interval, as well as the possibility of selecting different scales of utilization, capture, storage, sequestration, and transportation technologies. Therefore, to obtain realistic results, CCS infrastructure models must use multiperiod decision tree analysis to consider possible uncertainties. This study addresses the problem of designing a multiperiod stochastic model for CCS infrastructure that considers the effects of (1) future uncertain product prices, operating costs, and CO2 emissions, (2) different sizes of utilization, capture, storage, and sequestration facilities, and (3) change in the CO2 reduction target over a long-term planning interval. The proposed mathematical model is formulated as a mixed-integer linear programming (MILP) problem and can help determine where and how to utilize, capture, store, transport, and sequester CO2 to maximize the total net profit and to satisfy the mandated reduction of CO2 emissions. To incorporate uncertainty in the model, we employ an inexact two-stage stochastic programming approach;15 this approach compares a multiperiod stochastic model and a multiperiod deterministic model to assess the variation of product prices, operating costs, and CO2 emissions for CCS infrastructure. This study then uses the proposed models to examine various configurations to treat CO2 on the east coast of Korea over a 20-year planning interval (2011−2030). The proposed model in this study helps decision makers to establish an optimal strategy to time the investment decision; this strategy balances cost efficiency against stability in an uncertain future CCS infrastructure.

2. PROBLEM STATEMENT Our previous research14 has addressed the design and operation problem of a multiperiod deterministic model for CCS 11446

dx.doi.org/10.1021/ie3004754 | Ind. Eng. Chem. Res. 2012, 51, 11445−11457


Article

Figure 3. CCS technology options.

In this study, we develop a multiperiod stochastic model of CCS infrastructure and compare its predictions to those of a previously developed multiperiod deterministic model.

location, size, and type of CO2 capture, storage, sequestration, and utilization facilities in each region considered; (2) the number, size, and type of CO2 transport modes among regions considered; (3) the total amount of capture, storage, sequestration, utilization, and transportation of CO2 under the given conditions, which include CO2 reduction target, capacity limitations of CCS technologies, and uncertain parameters (i.e., CO2 emissions, prices, and operating costs). This model is based upon the following assumptions: • The goal is to produce a network capable of satisfying a given CO2 reduction pattern. • The network design is multiperiod and covers a fixed time interval divided into several subintervals to allow accounting for variation in CO2 emissions, prices, and costs. • The CO2 emissions, product prices, and operating costs of the network are uncertain. • All other parameters involved are deterministic. This model structure is adopted allow analysis of the effects of different sources of uncertainty separately. However, the model can be easily extended to account for other parameter uncertainties. Economies of scale and capacity expansions must be considered. To avoid nonlinearities in the problem formulation, the six-tenths factor rule16 is used to approximate the effect of the economies of scale,17 and capacity expansions are introduced to adapt the network design to variation in CO2 reduction target.

3. MODEL FORMULATION In the previous work,14 a multiperiod deterministic model was used to determine the optimal design and operation of a CCS infrastructure over a given planning horizon. The deterministic model assumes that all parameters present in the model are invariant for a given planning horizon (section 3.1). This assumption is very restrictive; we make the model more realistic by allowing the parameters to be stochastic (section 3.2). The presented model uses a multiscenario stochastic programming approach13 to account for the uncertainty of the coefficients of the objective function (i.e., product prices and operating costs, section 3.2.1), and uses a two-stage stochastic programming approach12 to account for the uncertainty of the right-hand-side constraint (i.e., CO2 emissions; section 3.2.2). With a given scenario for each of the uncertain parameters in the annual utilization and disposal of CO2, the multiperiod stochastic model is given by an inexact two-stage stochastic programming approach15 (section 3.2.3). The CO2 emissions, product prices, and operating costs associated with the design and operation of the CCS infrastructure are uncertain and stochastic variables that follow a set of 11447



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capital cost TCCt, facility operating cost FOCt, and transport operating cost TOCt:

scenarios, each with a given probability of occurrence. In fact, the model uses a finite set of scenarios to maximize the expected value of the profit distribution over a given planning horizon. 3.1. Multiperiod Deterministic Model. In this section, a multiperiod deterministic model to determine the optimal reduction policy for a given planning horizon is briefly described; this model is based on ref 14. 3.1.1. Objective Function. The objective function is to maximize the average annual profit TAP of the CCS infrastructure over a long-term planning interval; TAP is the difference between the total annual benefit TAB and the total annual cost TAC: 1 max TAPave = ∑ (TABt − TACt ) δ t (1)

∀t

TACt = FCCt + TCCt + FOCt + TOCt

(3)

FCCt is determined from the capacity expansions made in the utilization, capture, storage, and sequestration facilities during that period. It is the product of the capital cost (PCCe,p,j, CCCi,c,si,j, MCCi,m,j, SCCi,s,j) of each facility and the associated total number of facilities (IPe,p,j,g,t, ICi,c,si,j,sp,g,t, IMi,m,j,g,t, ISi,s,j,g,t, respectively): FCCt =

⎡

⎛

⎣

LR ⎝

∑ ⎢⎢ CCRf ⎜⎜∑ ∑ ∑ PCCe , p ,jIPe ,p ,j ,g , t g

e

p

j

⎛ + ∑ ⎜⎜∑ ∑ ∑ (CCCi , c ,si, jICi , c ,si, j ,sp , g , t ) i ⎝ c si sp

To find the average profit of the network over the entire planning interval, the right-hand side of eq 1 is divided by the number of time periods δ. 3.1.1.1. Total Annual Benefit. The total annual benefit TABt obtained in period t is the income from selling products made by utilizing CO2 in utilization facilities:

⎞⎞⎤

+

∑ ∑ MCCi , m, jIMi , m, j , g , t + ∑ ∑ SCCi ,s ,jISi ,s ,j , g , t ⎟⎟⎟⎟⎥⎥ m

j

s

∀t

⎠⎠⎦

j

(4)

∑

TABt =

∑ ∑ USBe ,p,t Pe ,p,g , t

e ∈ {green polymer,biobutanol}

p

∀t

where CCRf is the capital charge rate of facilities and LR is the learning rate.9 TCCt is obtained by multiplying the number of transport units, i.e., truck, railcar, ship or pipeline, by the cost of each respective form and then summing.

g

(2)

3.1.1.2. Total Annual Cost. The total annual cost TACt,r spent in period t is the sum of the facility capital cost FCCt, transport TCCt =

∑ i

⎛ CCR l ⎞ ⎜ (NTUoni , l , t TMCi , l )⎟ + ⎝ ⎠ LR l ∈ {railcar,truck}

∑

⎛ CCR l ⎞ (NTUoffi , l , tTMCi , l )⎟ ⎝ ⎠ LR l ∈ {ship}

∑ ∑ i

⎜

⎛ CCR l ⎞ INTPoni , l , g , g ′ , d , t Long , g ′TPIConi , l , d + INTPoffi , l , g , g ′ , d , tLoffg , g ′TPICoffi , l , d ⎟ + ∑ ∑ ∑∑∑⎜ ⎝ LR ⎠ i l ∈ {pipe} g g′ d

(

)

FOCt is obtained by multiplying the unit utilization, capture, storage, and sequestration costs by the corresponding amounts of utilization, capture, storage, and sequestration:

TOCt = TOCEPt + TOCPt

⎛ ⎝

c

si

sp

⎞⎞

+

∑ UMCi ,m,j ,t Mi ,m,j ,g ,t + ∑ USCi ,s ,j ,t Si ,s ,j ,g ,t ⎟⎟⎟⎟ m

FCt =

LCt =

∑

∑

i

l ∈ {railcar,truck}

∑

∑

i


g′

⎡Q

∑ ∑ DWl , t⎢⎢ g

g′

(6)

⎛ 2Long , g ′Q ⎞ i,l ,g ,g′,t ⎟+ ⎟ ⎝ FElTcapi , l ⎠

i , l , g , g ′ , t ⎛ 2Long , g ′

⎜ ⎣ Tcapi , l ⎝

SPl

∀t

(8)

where

∑ ∑ FPl ,t ⎜⎜ g

(7)

TOCEPt = FCt + LCt + MCt + GCt

∀t

⎠⎠

s

∀t

where TOCEPt is the operating costs associated with road, railway, and ship transportation technologies excluding pipelines and TOCPt is the operating costs associated with pipelines. The first term includes the fuel (FCt), labor (LCt), maintenance (MCt), and general costs (GCt) in period t:

∑ ⎜⎜∑ ∑ ∑ UCCi ,c ,si,j ,t Ci ,c ,si,j ,sp ,g ,t i

(5)

TOCt is determined from eq 7:

⎛ FOCt = ∑ ∑ ⎜∑ ∑ UPCe , p , j , t Pe , p , j , g , t ⎜ j g ⎝ e p +

∀t

⎞⎤ + LUTl⎟⎥ + ⎠⎥⎦

⎛ 2Loffg , g ′Q ⎞ i,l ,g ,g′,t ⎟ ⎟ ⎝ FElTcapi , l ⎠

∑ ∑ ∑ ∑ FPl ,t ⎜⎜ i

l ∈ {ship}

g

g′

⎡Q

∑ ∑ ∑ ∑ DWl , t⎢⎢ i

l ∈ {ship}

g

g′

i , l , g , g ′ , t ⎛ 2Loffg , g ′

⎜ ⎣ Tcapi , l ⎝

SPl

∀t

⎞⎤ + LUTl⎟⎥ ⎠⎥⎦

(9)

∀t (10)

11448


Industrial & Engineering Chemistry Research MCt =

∑

∑

i


⎛ 2Long , g ′Q ⎞ i,l ,g ,g′,t ⎟ ⎟ Tcapi , l ⎝ ⎠

g

g′

⎛ 2Loffg , g ′Q

i

l ∈ {ship}

g

Q i,l ,g ,g′,t =

∑ ∑ MEl ,t ⎜⎜

∑ ∑ ∑ ∑ MEl ,t ⎜⎜

+

Article

⎝

g′

i,l ,g ,g′,t

Tcapi , l

⎞ ⎟ ⎟ ⎠

∑ QPi ,l ,g ,g ′ ,d ,t

∀ i , l , g , g ′, t ; g ≠ g ′, l ∈ {pipe}

d

(17)

As the network evolves over time, new CCS facilities will be constructed to meet the increased mandated reduction of CO2 emissions. The time evolution constraints are expressed by the following constraints:

∀t (11)

NPe , p , j , g , t = NPe , p , j , g , t − 1 + IPe , p , j , g , t

and

(18)

⎡ Q ⎛ 2Long , g ′ ⎞⎤ ∑ ∑ ∑ GEl ,t ⎢ i ,l ,g ,g ′,t ⎜ + LUTl⎟⎥ GCt = ∑ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {railcar,truck} g g′ +

⎡ Q ⎞⎤ i , l , g , g ′ , t ⎛ 2Loffg , g ′ ⎜ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦

l ∈ {ship}

g

g′

NCi , c ,si, j ,sp , g , t = NCi , c ,si, j ,sp , g , t − 1 + ICi , c ,si, j ,sp , g , t ∀ i , c , si, j , sp , g , t

∑ ∑ ∑ ∑ GEl ,t ⎢ i

(20)

+

g

g′

l ∈ {pipe}

g

g′

∀ i , l , g , g ′, d , t ∀t

i

si

sp

∑ ∑ ∑ (∑ Si ,s ,j ,g ,t + ∑ Ui ,p,j ,g ,t ) ≥ Tt i

l

p

g′

s

∀ i , c , si, j , sp , g , t

The inventory rate Mi,m,j,g,t in period t is also bounded by the min minimum storage capacity Mcapi,m,j and the maximum storage capacity Mcapmax : i,m,j

j

∀ i, g , t

Mcapimin NMi , m , j , g , t ≤ Mi , m , j , g , t ≤ Mcapimax NMi , m , j , g , t ,m,j ,m,j

(15)

j

∑ ∑ Mi ,m,j ,g ,t = SSF( j

(24)

(25)

where ηc is the CO2 capture efficiency for a type of capture facility.14 Moreover, the total inventory Mi,m,j,g,t of CO2 in physical form i of all storage facilities in region g is a function of the total flow rate Qi,l,g,g′,t of CO2 in physical form i leaving region g multiplied by a safety stock factor SSF: m

∀t

p

sp

∑ ∑ Ui ,p,j ,g ,t

+

s

≤ Ccapimax NCi , c ,si, j ,sp , g , t , c ,si, j

∑ ∑ (Q i ,l ,g ,g ′ ,t − Q i ,l ,g ′ ,g ,t ) + ∑ ∑ Si ,s ,j ,g ,t

=

g

Ccapimin NCi , c ,si, j ,sp , g , t ≤ Ci , c ,si, j ,sp , g , t , c ,si, j

∑ ∑ ∑ ∑ ηcCi ,c ,si,j ,sp ,g ,t j

j

All facilities and transportation modes must be constrained by upper and lower boundaries. Therefore, the capture rate Ci,c,si,j,sp,g,t in period t is bounded by the minimum capture max capacity Ccapmin i,c,si,j and the maximum capture capacity Ccapi,c,si,j of all facilities established in a particular region:

∀t

g

Mass balances of individual regions should consider rates of total annual capture Ci,c,si,j,sp,g,t, transport Qi,l,g,g′,t, utilization Ui,p,j,g,t, and sequestration Si,s,j,g,t: si

(23)

3.1.2.2. Capacity Constraints. The total amount of CO2 sequestered Si,s,j,g,t and used Ui,p,j,g,t in all regions cannot be less than Tt:

(14)

c

(22)

∀ i , l , g , g ′, d , t

3.1.2. Constraints. 3.1.2.1. Mass balance constraints. The target amount Tt of CO2 to be reduced by CCS facilities in period t is the product of the mandated reduction of CO2 emissions LMRi,t, the utilization UCCSi,t of CCS as CO2 reduction technology, and the total amount Ei,si,sp,g,t of CO2 emissions, summed over all sources:

∑ ∑ ∑ ∑ LMR i ,tUCCSi ,t Ei ,si,sp ,g ,t

(21)

NTPoffi , l , g , g ′ , d , t = NTPoffi , l , g , g ′ , d , t − 1 + INTPoffi , l , g , g ′ , d , t

d

(13)

Tt =

∀ i, s, j, g , t

NTPoni , l , g , g ′ , d , t = NTPoni , l , g , g ′ , d , t − 1 + INTPoni , l , g , g ′ , d , t

d

∑ ∑ ∑ ∑ ∑ UPOCoffi ,l ,d ,tQPi ,l ,g ,g ′ ,d ,t i

NSi , s , j , g , t = NSi , s , j , g , t − 1 + ISi , s , j , g , t

∑ ∑ ∑ ∑ ∑ UPOConi ,l ,d ,tQPi ,l ,g ,g ′ ,d ,t l ∈ {pipe}

∀ i , m, j , g , t

NMi , m , j , g , t = NMi , m , j , g , t − 1 + IMi , m , j , g , t

Finally, eq 13 calculates the pipeline operating costs from the unit operating costs of the pipelines (UPOConi,l,d,t and UPOCoffi,l,d,t) and the freight to be delivered: i

(19)

∀t

(12)

TOCPt =

∀ e , p, j , g , t

∑

∑ Q i ,l ,g ,g′,t)

∀ i , m, j , g , t

(26)

The sequestration rate Si,s,j,g,t in period t is bounded by the minimum sequestration capacity Scapmin i,s,j and the maximum max sequestration capacity Scapi,s,j : Scapimin NSi , s , j , g , t ≤ Si , s , j , g , t ≤ Scapimax NSi , s , j , g , t ,s,j ,s,j

∀ i, g , t

∀ i, s, j, g , t (27)

l ∈ {railcar,truck,ship} g ′

The utilization rate Ui,p,j,g,t in period t is bounded by the minimum and maximum utilization capacities, which are calculated by multiplying the CO2 use factor CUFi,e,p of product form e by the minimum production capacity Pcapmin e,p,j and the maximum production capacity Pcapmax e,p,j , respectively:

(16)

Also, the total flow of CO2 in physical form i by pipeline between different regions is equal to the sum of the flow rates of all pipelines of type d that are established: 11449



∑

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The transportation of CO2 in physical form i must occur only from a source to a sequestration facility or utilization facility:

CUFi , e , pPcapemin NPe , p , j , g , t ≤ Ui , p , j , g , t ,p,j


∑

≤

CUFi , e , pPcapemax NPe , p , j , g , t ,p,j

ug ′ − ug + nXi , l , g , g ′ , t ≤ n − 1


∀ i , l , g , g ′, t ;g = 2, ..., n , g ′ = 2, ..., n;g ≠ g ′

∀ i , p, g , t

(30)

(28)

Moreover, a minimum flow rate Qmin i,l and a maximum flow rate of CO2 Qmax are needed to justify the establishment of a i,l transportation mode between two regions:

∑ ∑ Xi , l , g , g ′ , t ≤ 1 i

∑ ∑ Xi , l , g ′ , g , t ≤ 1

Q imin Xi , l , g , g ′ , t ≤ Q i , l , g , g ′ , t ≤ Q imax Xi , l , g , g ′ , t ,l ,l ∀ i , l , g , g ′, t , r ; g ≠ g ′

NTUoni , l , t ≥

∑∑ g

NTUoffi , l , t ≥

i

(29)

g′

∑∑ g

g′

∀ g , g ′, t ;g ≠ g ′ (31)

l

∀ g , g ′, t ;g ≠ g ′ (32)

l

The number of transport units excluding pipelines is

Q i , l , g , g ′ , t ⎛ 2Long , g ′ ⎞ + LUTl⎟ ∀ i , l , t ; l ∈ {railcar, truck} ⎜ TMA lTcapi , l ⎝ SPl ⎠ (33)

Q i , l , g , g ′ , t ⎛ 2Loffg , g ′ ⎞ + LUTl⎟ ∀ i , l , t ; l ∈ {ship} ⎜ TMA lTcapi , l ⎝ SPl ⎠

The flow rate of CO2 in physical form i by pipeline with a type of diameter d is QPi , l , g , g ′ , d , t ≤ TPcapi , l , d NTPoni , l , g , g ′ , d , t ∀ i , l , d , g , g ′, t ; g ≠ g ′, l ∈ {pipe} (34)

QPi , l , g , g ′ , d , t ≤ TPcapi , l , d NTPoffi , l , g , g ′ , d , t ∀ i , l , d , g , g ′, t ; g ≠ g ′, l ∈ {pipe}

3.2. Multiperiod Stochastic Model. This paper aims to use an inexact two-stage stochastic programming approach15 because it is possible to create a multiperiod stochastic model that can analyze most realistically. It compares the other approaches such as a multiscenario stochastic programming approach13 and a twostage stochastic programming approach12 as described sequentially in section 3.2.1. 3.2.1. Changes in the Coefficients of the Objective Function: Uncertain Product Prices and Operating Costs with Scenario-Based Approach. To formulate the multiperiod stochastic model under uncertain product prices and operating costs, we employ a multiscenario stochastic programming approach.13 The model presented considers that the coefficients of the objective function (e.g., total annual benefit, total annual cost) are uncertain and that their variability can be described using a set of scenarios with given probabilities of occurrence. As a result, the coefficients of the objective function associated with the establishment and operation of the CCS infrastructure are variable values as stochastic parameters, but they do not directly affect the decision variables of the objective function and constraints. In principle, the network for CCS infrastructure described by the model is demand-driven, which means that the establishment and operation of capture facilities, storage facilities, sequestration facilities, utilization facilities, and transport links depend mainly on CO2 emissions.9 Because the model in this section assumes a steady-state operation in which CO2 emissions are constant in a given period, quantities such as the number and annual operating amount of facilities and transport modes cannot change suddenly, but the benefits and costs depend on the expected scenarios with each having a given probability of occurrence. In fact, this model aims to use a finite set of scenarios to maximize the expected value of the profit distribution over a given planning

horizon. The previous multiperiod deterministic model is reformulated as a multiperiod stochastic model which maximizes the expected total profit: max E[TAP] =

∑ probr TAPave r

(35)

r

where r represents a particular scenario and probr is its probability of occurrence. Similarly, eqs 2, 3, and 6−13 associated with the uncertain parameters are each modified to multiperiod stochastic model formulations eqs 36−46. 1 ∀r TAPave ∑ (TABt ,r − TACt ,r ) r = δ t (36)

∑

TABt , r =


∑ ∑ USBe ,p ,t ,r Pe ,p,g ,t p

∀ t, r

g

(37)

TACt , r = FCCt + TCCt + FOCt , r + TOCt , r

∀ t, r (38)

FOCt , r

⎛ = ∑ ∑ ⎜∑ ∑ UPCe , p , j , t , r Pe , p , j , g , t ⎜ j g ⎝ e p ⎛

+

∑ ⎜⎜∑ ∑ ∑ UCCi ,c ,si,j ,t ,r Ci ,c ,si,j ,sp ,g ,t i

⎝

c

si

sp

⎞⎞

+

∑ UMCi ,m,j ,t ,r Mi ,m,j ,g ,t + ∑ USCi ,s ,j ,t ,r Si ,s ,j ,g ,t ⎟⎟⎟⎟ m

s

⎠⎠

∀ t, r

(39) 11450



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∀ t, r

TOCt , r = TOCEPt , r + TOCPt , r

scenarios r that represent changes in the values of one of the right-hand-side constraints.

(40)

∀ t, r

TOCEPt , r = FCt , r + LCt , r + MCt , r + GCt , r

FCt , r =

+

⎛ 2Long , g ′Q

∑

∑

i


∑ ∑ FPl ,t ,r ⎜⎜ g

⎝

g′

i,l ,g ,g′,t

FElTcapi , l

⎛ 2Loffg , g ′Q ⎞ i,l ,g ,g′,t ⎟ ⎟ ⎝ FElTcapi , l ⎠

∑ ∑ ∑ ∑ FPl , t , r ⎜⎜ i

l ∈ {ship}

g

g′

i

⎞ ⎟ ⎟ ⎠

⎡Q

∑ ∑ DWl ,t ,r⎢

∑

∑

i


g

g′

SPl

∑

∑

i


⎛ 2Loffg , g ′Q ⎞ i ,l ,g ,g′,t ⎟ + ∑ ∑ ∑ ∑ MEl , t , r ⎜⎜ ⎟ Tcapi , l ⎝ ⎠ i l ∈ {ship} g g′

∀ t, r

∑ ∑ ⎜⎜∑ ∑ UPCe ,p,j , t Pe ,p,j , g , t , r j

g

⎝

e

p

⎛ + ∑ ⎜⎜ ∑ ∑ ∑ UCCi , c ,si, j , t Ci , c ,si, j ,sp , g , t , r i ⎝ c si sp ⎞⎞

+

∑ UMCi ,m,j , t Mi ,m,j , g , t , r + ∑ USCi ,s ,j , t Si ,s ,j , g , t , r ⎟⎟⎟⎟ m

∀ t, r

⎠⎠

s

+

⎡ Q ⎞⎤ ⎛ 2Long , g ′ =∑ ∑ ∑ ∑ GEl ,t ,r⎢ i ,l ,g ,g ′ ,t ⎜ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {railcar,truck} g g′ ⎡ Q ⎞⎤ i , l , g , g ′ , t ⎛ 2Loffg , g ′ ⎜ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦

∑ ∑ ∑ ∑ GEl ,t ,r⎢ i

l ∈ {ship}

g

g′

∀ t, r (49)

(44) GCt , r

∀ t, r

g

⎛

FOCt , r =

⎛ 2Long , g ′Q ⎞ i ,l ,g ,g′,t ⎟ ⎟ Tcapi , l ⎝ ⎠

g′

p

(48)

∑ ∑ MEl ,t ,r⎜⎜ g

∑ ∑ USBe , p,t Pe ,p,g , t , r


(43) MCt , r =

∑

TABt , r =

⎞⎤ + LUTl⎟⎥ ⎠⎥⎦

⎡Q ⎞⎤ i , l , g , g ′ , t ⎛ 2Loffg , g ′ ⎜ + ∑ ∑ ∑ ∑ DWl , t , r⎢ + LUTl⎟⎥ ⎢⎣ Tcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {ship} g g′

∀ t, r

g

sp

Thus, the objective function, mass balance and capacity constraints must be represented by all second-stage decision variables Ui,p,g,t,r, Ci,c,si,sp,g,t,r, Mi,m,g,t,r, Si,s,g,t,r, and Qi,l,g,g′,t,r associated with CO2 emissions in period t and scenario r (Ei,si,sp,g,t,r).

∀ t, r

i , l , g , g ′ , t ⎛ 2Long , g ′

⎜ ⎢⎣ Tcapi , l ⎝

si

(47)

(42) LCt , r =

∑ ∑ ∑ ∑ LMR i ,tUCCSi ,t Ei ,si,sp ,g ,t ,r

Tt , r =

(41)

FCt , r =

∑

∑

i


⎛ 2Long , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ ⎟ FE Tcap l ⎝ ⎠ i,l

∑ ∑ FPl ,t ⎜⎜ g

g′

⎛ 2Loffg , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ + ∑ ∑ ∑ ∑ FPl , t ⎜⎜ ⎟ FElTcapi , l ⎝ ⎠ i l ∈ {ship} g g′

∀ t, r

∀ t, r

(45)

TOCPt , r =

∑ ∑ ∑ ∑ ∑ UPOConi ,l ,d ,t ,rQPi ,l ,g ,g ′ ,d ,t i

+

l ∈ {pipe}

g

g′

d

∑ ∑ ∑ ∑ ∑ UPOCoffi ,l ,d ,t ,rQPi ,l ,g ,g ′ ,d ,t i

(50)

l ∈ {pipe}

g

g′

LCt , r =

∀ t, r

⎡Q

∑ ∑ DWl ,t⎢

∑

∑

i


g

i , l , g , g ′ , t , r ⎛ 2Long , g ′

⎢⎣ Tcapi , l

g′

⎜ ⎝

SPl

⎞⎤ + LUTl⎟⎥ ⎠⎥⎦

⎡Q ⎞⎤ i , l , g , g ′ , t , r ⎛ 2Loffg , g ′ ⎜ + ∑ ∑ ∑ ∑ DWl , t⎢ + LUTl⎟⎥ ⎢⎣ Tcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {ship} g g′

d

(46)

∀ t, r

(51)

The main sources of uncertainty here are the unit selling benefit (USBe,p,t,r), unit production cost (UPCe,p,j,t,r), unit capture cost (UCCi,c,si,j,t,r), unit intermediate storage cost (UMCi,m,j,t,r), unit sequestration cost (USCi,s,j,t,r), fuel price (FPl,t,r), driver wage (DWl,t,r), maintenance expense (MEl,t,r), general expense (GEl,t,r), and unit operating costs for pipeline transportation onshore (UPOConi,l,d,t,r) and offshore (UPOCoffi,l,d,t,r), because none of these quantities can be perfectly known in advance during the design stage. 3.2.2. Changes in the Values of One of the Right-Hand-Side Constraints: Uncertain CO2 Emissions with Scenario-Based Approach. Unlike section 3.2.1, the network for CCS infrastructure described by the model considers the variability of CO2 emissions in a given period. To formulate the multiperiod stochastic model under uncertain CO2 emissions, a two-stage stochastic model using the expected scenario approach12 is employed in this paper. In this model, first-stage quantities such as the number of facilities and transport modes cannot change suddenly, but second-stage quantities such as the operating amount of facilities and transport modes depend on the expected scenarios. To represent the uncertainty in CO2 emissions, the mass balance (eq 14) must be rewritten by separating all CO2 emissions in period t into one for each of the CO2 emission

MCt , r =

∑

∑

i


⎛ 2Long , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ ⎟ Tcap ⎝ ⎠ i,l

∑ ∑ MEl ,t ⎜⎜ g

g′

⎛ 2Loffg , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ + ∑ ∑ ∑ ∑ MEl , t ⎜⎜ ⎟ Tcapi , l ⎝ ⎠ i l ∈ {ship} g g′

∀ t, r (52)

GCt , r =

⎡ Q ⎞⎤ i , l , g , g ′ , t , r ⎛ 2Long , g ′ + LUTl⎟⎥ ⎜ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦

∑ ∑ GEl ,t ⎢

∑

∑

i


g

g′

⎡ Q ⎞⎤ i , l , g , g ′ , t , r ⎛ 2Loffg , g ′ ⎜ + ∑ ∑ ∑ ∑ GEl , t ⎢ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {ship} g g′

∀ t, r

(53)

TOCPt , r =

∑ ∑ ∑ ∑ ∑ UPOConi ,l ,d ,tQPi ,l ,g ,g ′ ,d ,t ,r i

+

l ∈ {pipe}

g

g′

d

∑ ∑ ∑ ∑ ∑ UPOCoffi ,l ,d ,tQPi ,l ,g ,g ′ ,d ,t ,r i

l ∈ {pipe}

g

g′

∀ t, r

d

(54) 11451



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∑ ∑ ∑ (∑ Si ,s ,j ,g ,t ,r + ∑ Ui ,p,j ,g ,t ,r) ≥ Tt ,r i

j

g

s

∀ t, r

FCt , r =

p

∑

i


(55)

∑ ∑ ∑ ∑ ηcCi ,c ,si,j ,sp ,g ,t ,r = ∑ ∑ (Q i ,l ,g ,g ′ ,t ,r − Q i ,l ,g ′ ,g ,t ,r) c

j

si

l

sp

s

j

p

m

j

i

l ∈ {ship}

g

∑ Q i ,l ,g ,g′,t ,r)

∀ t, r

⎞⎤ i , l , g , g ′ , t , r ⎛ 2Long , g ′ + LUTl⎟⎥ ⎜ ⎢⎣ Tcapi , l ⎝ SPl ⎠⎥⎦ ⎡Q

∑ ∑ DWl ,t ,r⎢

∑

∑

i


∀ i, g , t , r

g

g′

⎡Q

l ∈ {railcar,truck,ship} g ′

+

(57)

∑ ∑ ∑ ∑ DWl ,t ,r⎢ i

l ∈ {ship}

g

i , l , g , g ′ , t , r ⎛ 2Loffg , g ′

⎢⎣ Tcapi , l

g′

Ccapimin NCi , c ,si, j ,sp , g , t ≤ Ci , c ,si, j ,sp , g , t , r , c ,si, j

⎜ ⎝

SPl

⎞⎤ + LUTl⎟⎥ ⎠⎥⎦

∀ t, r

(66)

∀ i , c , si, j , sp , g , t , r

MCt , r =

(58)

∀ i , m, j , g , t , r

∑

∑

i


⎛ 2Long , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ ⎟ Tcapi , l ⎝ ⎠

∑ ∑ MEl , t , r⎜⎜ g

g′

⎛ 2Loffg , g ′Q ⎞ i,l ,g ,g′,t ,r ⎟ + ∑ ∑ ∑ ∑ MEl , t , r ⎜⎜ ⎟ Tcapi , l ⎝ ⎠ i l ∈ {ship} g g′

Mcapimin NMi , m , j , g , t ≤ Mi , m , j , g , t , r ≤ Mcapimax NMi , m , j , g , t ,m,j ,m,j

∀ t, r

(59)

(67)

Scapimin NSi , s , j , g , t ≤ Si , s , j , g , t , r ≤ Scapimax NSi , s , j , g , t ,s,j ,s,j

GCt , r

∀ i, s, j, g , t , r

(60) +

CUFi , e , pPcapemin NPe , p , j , g , t ≤ Ui , p , j , g , t , r ,p,j

∑

⎞ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎠

(65) (56)

≤ Ccapimax NCi , c ,si, j ,sp , g , t , c ,si, j

i ,l ,g ,g′,t ,r

FElTcapi , l

⎝

g′

FElTcapi , l

⎝

g′

i ,l ,g ,g′,t ,r

∀ i, g , t , r

j

∑

g

⎛ 2Loffg , g ′Q

LCt , r =

∑ ∑ Mi ,m,j ,g ,t ,r = SSF(

∑ ∑ FPl ,t ,r ⎜⎜

∑ ∑ ∑ ∑ FPl ,t ,r ⎜⎜

+

g′

∑ ∑ Si ,s ,j ,g ,t ,r + ∑ ∑ Ui ,p,j ,g ,t ,r

+

⎛ 2Long , g ′Q

∑

⎡ Q ⎞⎤ ⎛ 2Long , g ′ =∑ ∑ ∑ ∑ GEl ,t ,r⎢ i ,l ,g ,g ′ ,t ,r ⎜ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦ i l ∈ {railcar,truck} g g′ ⎡ Q ⎞⎤ i , l , g , g ′ , t , r ⎛ 2Loffg , g ′ ⎜ + LUTl⎟⎥ ⎢⎣ TMA lTcapi , l ⎝ SPl ⎠⎥⎦

∑ ∑ ∑ ∑ GEl ,t ,r⎢ i

l ∈ {ship}

g

g′

∀ t, r

(68)


CUFi , e , pPcapemax NPe , p , j , g , t ,p,j

∑

≤

∀ i , p, g , t , r

TOCPt , r =


i

(61)

+

Q imin Xi , l , g , g ′ , t ≤ Q i , l , g , g ′ , t , r ≤ Q imax Xi , l , g , g ′ , t ,l ,l

∑

∑ ∑ USBe ,p,t ,r Pe ,p,g ,t ,r p

∀ t, r

g

∑ ∑ ⎜⎜∑ ∑ UPCe ,p,j ,t ,r Pe ,p,j ,g ,t ,r

j g ⎝ e p ⎛ + ∑ ⎜⎜∑ ∑ ∑ UCCi , c ,si, j , t , r Ci , c ,si, j ,sp , g , t , r i ⎝ c si sp

⎞⎞

∑ UMCi ,m,j ,t ,r Mi ,m,j ,g ,t ,r + ∑ USCi ,s ,j ,t ,r Si ,s ,j ,g ,t ,r ⎟⎟⎟⎟ m

d

l ∈ {pipe}

g

g′

∀ t, r

d

4. CASE STUDIES To illustrate the capabilities of the proposed model, the case study in ref 14 is adopted as a benchmark (Figure 4). This case study considers the following: (1) the CCS infrastructure is planned from 2011 to 2030; (2) the levels of mandated reduction of CO2 emissions are 10, 30, 32, and 35% from the first period to the final period and assume that utilization of CCS as the CO2 reduction technology is 5, 12.5, 20, and 30% from the first period to the final period, respectively; (3) CO2 is emitted from the four different industrial sources of power, steel, oil refinery, and petrochemical plants in four regions; (4) several CCS technologies are used, such as CO2 capture, storage, transportation, utilization, and sequestration technologies (Table 1). Also, upper and lower boundary capacities, capital costs, and unit operation cost of each component for CCS are obtained from ref 14. This study especially examines CO2 emissions, product prices, and operating costs for design and operation of the CCS infrastructure. The versatility of the proposed model derived (section 3) is examined using four case studies that vary according to uncertainty types and model types: case 1 is the baseline deterministic model from ref 14; case 2 considers uncertain CO2 emissions; case 3 considers uncertain prices and costs; case 4 considers uncertain CO2 emissions, uncertain prices, and costs (Table 1). For the model, this study used data and parameters from ref 14. However, the addition of three uncertainties, i.e., in CO2

⎛

+

g′

(69)

(63) FOCt , r =

g

(62)

However, the constraints associated with first-stage variables will not change with the scenarios. 3.2.3. Uncertain CO2 Emissions, Product Prices, and Operating Costs with Scenario-Based Approach. To formulate the multiperiod stochastic model under all uncertainties such as CO2 emissions, product prices, and operating costs, an inexact two-stage stochastic programming approach15 is employed in this paper. This approach combines a multiscenario stochastic programming approach and a two-stage stochastic programming approach. Thus, eqs 48−54 associated with the uncertain parameters described in section 3.2.1 are each modified to multiperiod stochastic model formulations, eqs 63−69. e ∈ {green polymer,biobutanol}

l ∈ {pipe}

∑ ∑ ∑ ∑ ∑ UPOCoffi ,l ,d ,t ,rQPi ,l ,g ,g ′ ,d ,t ,r i

∀ i , l , g , g ′, t , r ;g ≠ g ′

TABt , r =

∑ ∑ ∑ ∑ ∑ UPOConi ,l ,d ,t ,rQPi ,l ,g ,g ′ ,d ,t ,r

s

⎠⎠

∀ t, r

(64) 11452



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Figure 4. Configuration of all possible CCS technologies used in the case study.9

Table 1. Analysis Conditions Selected for the Case Studya,b case 1

2 3 4 a

uncertainty no

CO2 emissions prices and costs CO2 emissions, prices and costs

model multiperiod deterministic

multiperiod stochastic multiperiod stochastic multiperiod stochastic

description • utilization of liquid CO2 (LCO2) via different sizes j of biobutanol p1 and “green” polymer plants p2 • capture of liquid CO2 (LCO2) using monoethanolamine (MEA) c1 in different sizes j of capture facilities • liquid CO2, or LCO2 held in semipressurized cylindrical tanks m1 • sequestration of liquid CO2 (LCO2) via different sizes j of depleted gas reservoir (DGR) s1 and saline aquifer storage (SAS) s2 • delivery of liquid CO2 (LCO2) via different sizes j of railcar l1, pipeline l2 onshore, and tanker ship l3, pipeline l4 offshore the same as above the same as above the same as above

Case 1 was described in ref 14. bDifferent sizes j ∈ j1, j2, j3 {small, medium, large}.

Considering the variation in CO2 emissions resulted in a 0.004% decrease in total network profit, considering the variation in product prices and operating costs resulted in a 0.023% increase, and considering all uncertainties resulted in a 0.028% increase. The decrease in total network profit is a result of decrease of the income from selling products made by utilizing CO2, which occurs because the uncertain CO2 emissions enforce less utilization of CO2 to satisfy the mandated reduction of CO2 emissions, just in case the CO2 emissions are below average in a specific scenario. In contrast, the total network profit of case 3 increased when variation of product prices and operating costs was considered. The major reason for this is a decrease in operating costs, particularly the facility operating cost. This means that the design of case 3 has a lower financial loss under all scenarios, even though it causes variability in profit over the different scenarios. Similar trends are also observable in case 4, which considered variation of product prices, operating costs, and CO2 emissions. However, a definite difference of optimal design and operation for CCS infrastructure occurs between

emissions, product prices, and operating costs, to the model presented in ref 14 makes the process of collecting data even more complicated. Because the parameters of product price, operating cost, and CO2 emissions are inexact, the uncertainties can be expressed as probability density functions and discrete interval values. Thus, the uncertain parameters are described by 50 scenarios using Monte Carlo sampling considering a normal distribution with a mean14 and variance1,18,19 (Table 2). Appendix A in the Supporting Information includes additional tables regarding parametric analyses and cost estimates.14

5. RESULTS AND DISCUSSION The proposed model was computed using CPLEX 9.0 (GAMS) on a computer equipped with a Pentium 4 chip, operating at 3.16 GHz. The relatively short times required to solve the four different case studies and the low optimality gaps (Table 3) are satisfactory. The difference of total network profit, i.e., multiperiod deterministic model minus multiperiod stochastic model, of each case ranged from −0.004 to +0.028% (Table 4). 11453



Article

caused changes in the location and number of CO2 capture facilities among cases, but did not affect the location and number of CO2 storage, sequestration, and utilization facilities and transportation modes (Figures B.1−B.16 in the Supporting Information). For example, variation in product prices, operating costs, and CO2 emissions had a significant effect on the location of capture facilities during the introductory stage of the CCS infrastructure: one small-scale monoethanolamine (MEA) capture facility was built in the Pohang region (in POSCO no. 4 unit) to satisfy the CO2 reduction target for case 1, whereas one small scale MEA capture facility was built in POSCO no. 5 unit for cases 2−4, which considered the uncertainties. As time progressed and CO2 was increasingly reduced, the variation of CO2 emissions had a significant effect on the number of capture facilities, whereas the variation of product prices and operating costs affected the location of capture facilities. This means that the mandated reduction of uncertain CO2 emissions was satisfied by installing additional facilities, in case the CO2 emissions exceeded the average in a specific scenario. On the contrary, the reduction target did not vary according to uncertain product prices and operating costs, so the mandated reduction of invariant CO2 emissions was satisfied without installing additional facilities. Unlike the number of facilities or transportation modes, the average total amount that each of them processed per year varied according to the variation of CO2 emissions, but was relatively independent of variation in product prices and operating costs (Figure B.17 in the Supporting Information). Case 4 was very sensitive to all uncertainties. In overall value, case 2, which considered variation of CO2 emissions, resulted in 0.11% decrease at most in total operating amount compared to case 1, whereas case 4, which considered all uncertainties, decreased more than case 2, reaching 0.21% at most. In particular, the annual average amount of CO2 capture by the steel industry was more sensitive than that of the power industry to change in product prices, operating costs, or CO2 emission uncertainty in during the entire simulation interval, even though the magnitude of variation of CO2 emission was lower in the steel industry than in the power industry (Table 2). The reason for this result is the relatively low cost per unit of capture for the steel industry in the Pohang region, compared with other industries.9 The required number of capture facilities varied with the mandated CO2 reduction amount. When the reduction target rate was low, a few capture facilities in steel plants fulfilled the required reduction demand. Thus, the annual average amounts of CO2 storage, transportation, sequestration, and utilization operation, which is associated with CO2 capture, vary greatly according to uncertain CO2 emissions during the introductory stage of the CCS infrastructure. As the reduction target increased, the difference in those operating amounts for CCS infrastructure among the cases increased. In particular, the difference of the total operating amount in CO2 disposal facilities increased greatly, but the difference of the total operating amount

cases 3 and 4 because the uncertain CO2 emissions affect directly the decision variables of both of them. The relative elasticity of uncertain product prices, operating costs, and CO2 emissions of each case was also compared (Figures B.1−B.17 in the Supporting Information) for the optimal CCS network structures during the four time periods of the planning interval. These figures encapsulate the number and location of CCS technologies, as well as their technology types and sizes. For example, the numbers above the triangles, diamonds and boxes at each node and arrows between nodes denote the number of their technology types and sizes. The figures also depict the relative difference between the corresponding flow rates of CO2 operated in their technologies, indicated by the skewed and enlarged shapes. Particularly, variation of product prices, operating costs, and CO2 emissions Table 2. Parameters Used for Estimating Uncertain Prices and Operating Costs parameters CO2 emissions

activity b

product pricesc

mean valuea variance (%)

type

emission

utilization

operating costsd capture storage sequestration transportation

power steel oil refinery petrochemical biobutanol green polymer MEA liquid CO2 DGR SAS onshore pipeline railcar offshore pipeline ship

7.9 6.5 7.5 7.5 20.0 40.9 29.0 10.0 36.1 43.7 25.0 10.0 12.0 13.5

a

The average value of each uncertain parameter is offered from Appendix A in the Supporting Information.14 bThe variance of each uncertain CO2 emission was based on the economic analysis of ref 18. c The variance of each uncertain product price was considered based on historic data provided by ref 19. dThe variance of each uncertain operating cost was based on the economic analysis of ref 1.

Table 3. Summary of Computational Results for the Examined Model case quantity

1

2

3

4

no. of constraints no. of integer variables no. of continuous variables optimality gap (%) CPU time (s)

39 332 52 060 94 042 0.0 71.42

155 707 52 060 1 414 837 0.0 90 958.40

41 243 52 060 97 325 0.0 75.75

155 707 52 060 1 414 837 0.0 82 662.43

Table 4. Benefits, Costs, and Profit of CO2 Infrastructure in Four Different Case Studies (million $·year−1) facilities

transportation modes

case

uncertainty

model

selling benefit

capital cost

operating cost

capital cost

operating cost

total profit

% change

1 2 3 4

no CO2 emissions prices and costs CO2 emissions, prices and costs

multiperiod deterministic multiperiod stochastic multiperiod stochastic multiperiod stochastic

7,120.9 7,120.6 7,120.9 7,121.1

227.3 227.4 227.3 227.4

3,502.6 3,502.4 3,501.8 3,501.8

8.3 8.3 8.3 8.3

10.8 10.8 10.9 10.8

3,371.9 3,371.7 3,372.6 3,372.8

−0.004 +0.023 +0.028

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suggests a mathematical modeling framework which could be extended to similar applications such as the existing petroleum supply chain and the promising renewable energy network with more data.

in CO2 utilization facilities decreased dramatically. This difference is due to the limitation in total production capacity of the utilization facilities (Table A.3 in the Supporting Information). When planning the additional construction of utilization facilities as the reduction target increases, the gap of the total operating amount for the CCS infrastructure will continue to increase. Therefore, this result suggested that investment strategies that consider only an uncertain environment for CO2 emissions may be as good as those that consider all uncertainties (e.g., product prices, operating costs, and CO2 emissions). In view of stability under an uncertain environment for CO2 emissions, CO2 can be reduced during the introductory phase by establishing one smallscale capture facility in a steel plant and one in a medium-scale “green” polymer utilization facility. As the reduction target rate increases, the vast demand of CO2 reduction can be met by dispersed small- to large-scale CCS facilities. Especially, disposal facilities such as depleted gas reservoir sequestration would be utilized to reduce CO2. Also, the models suggest that, in Korea, a multitransportation mode network is more favorable than a single-mode network: pipelines, which are profitable for transportation across large distances, are used in conjunction with railcars which are profitable for transportation of CO2 across short distances.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables A.1−A.8 listing CO2 emissions of each plant and time period, sequestration planned and time period, production capacities and costs of CO2 utilization facilities, capture capacities and costs of CO2 capture facilities, liquid CO2 storage capacities and costs of intermediate storage facilities, sequestration capacities and costs of sequestration facilities, capital costs and unit transport costs of pipeline with diameter, and costs and sizes of sites for CO2 utilization facilities; Figures B.1−B.17 showing optimal solutions of CCS infrastructure design during the first through fourth time periods for cases 1−4 and the optimal solution of CCS infrastructure operation (annual average treated CO2). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-54-279-2274. Fax: +82-54-279-5528. E-mail: iblee@ postech.ac.kr.

6. CONCLUSIONS To propose an optimal strategy for utilizing and disposing of CO2, we developed a multiperiod stochastic model to design and operate a future CCS infrastructure for Korea. This study applied an inexact two-stage stochastic programming approach to analyze the effect of possible uncertainties in product prices, operating costs, and CO2 emissions. The proposed model was formulated as an MILP problem. During each time period of a given long-term planning interval, the proposed model determined where and how much CO2 to capture, store, transport, sequester, and utilize. It is an ambitious attempt to include a large set of integrated decisions within a single mathematical modeling framework that considers uncertainties. The proposed model was used to examine its ability to establish and operate optimal CCS infrastructures despite uncertain product prices, operating costs, and CO2 emissions in Korea over a 20-year planning interval from 2011 to 2030. Simulation results showed that the optimal CCS network configuration that considers only uncertain CO2 emissions is as good as the configuration that considers all uncertainties (e.g., product prices, operating costs, and CO2 emissions). In view of stability under an uncertain environment for CO2 emissions, investment strategies for CO2 capture technology in the steel industry must be planned first and carefully because they are very sensitive to variation in CO2 emissions. On the contrary, the optimal allocation of CO2 storage, sequestration, and utilization facilities and transportation modes was relatively independent of variation in CO2 emissions. Since all of the design decisions in simulation results are based on real existing or potential data, the model can help policy makers compare and combine to find the most profitable way to meet CO2 reduction demands. We can also propose the optimal design and operation planning on the independent companies which would be affected, as well as the government’s policyoriented ones under uncertainty. These characteristics of the model can improve the knowledge of how to design and operate optimal CCS infrastructures that can be adjusted to compensate for uncertainties in realistic problems. Moreover, this study

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This paper was supported by a Korea Research Foundation Grant funded by the Korea Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-313-D00178).

■

NOMENCLATURE

Indices

c = type of capture facility d = pipeline diameter e = product form g = geographical region g′ = geographical region (g′ ≠ g) i = physical form of CO2 j = size of utilization, capture, storage, and sequestration facilities l = type of transport mode m = type of intermediate storage facility p = type of utilization facility or production facility r = scenario s = type of sequestration facility si = type of source industry sp = source plant name t = time period of the planning interval Parameters

ALg = available land sizes on each region g, km2 max Ccapi,c,si,j = maximum CO2 capture capacity of facility type c and size j of industry type si, t of CO2 year−1 min Ccapi,c,si,j = minimum CO2 capture capacity of facility type c and size j of industry type si, t of CO2 year−1 CCCi,c,si,j = capital cost of building CO2-capture facility type c and size j of industry type si, $ CCRf = capital charge rate of facilities; rate or return required on invested capital cost, 0 ≤ CCRfacility ≤ 1 11455



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CCRl = capital charge rate of transport mode l; rate or return required on invested capital cost, 0 ≤ CCRpipeline ≤ 1 CUFi,e,p = CO2 use factor of product form e in utilization facility type p, t of CO2·t−1 or t of CO2·L−1 DWl = driver wage of transport mode l, $ h−1 Ei,si,sp,g,t = amount of CO2 emitted from source plant sp of industry type si in region g during time period t, t of CO2·year−1 FEl = fuel economy of transport mode l, km·L−1 FPl = fuel price of transport mode l, $ L−1 GEl = general expenses of transport mode l including transportation insurance, license and registration, and outstanding finances, $ year−1 GScapi,s,g,t = available geological capacity for CO2 in physical form i sequestered by sequestration facility type s in region g during time period t, t of CO2·year−1 LMRi,t = level of mandated requirement of reducing CO2 emissions during time period t, 0 ≤ LMRi,t ≤ 1 Long,g′ = average delivery distance between regions g and g′ onshore, km·trip−1 Loffg,g′ = average delivery distance from harbor region g onshore to sequestration region g′ offshore, km·trip−1 LR = learning rate; cost reduction as technology manufacturers accumulate experience, 0 ≤ LR ≤ 1 LSFp,j = land size factor for utilization facility type p and size j, km2 LUTl = load/unload time of transport mode l, h·trip−1 Mcapmax i,m,j = maximum storage capacity of facility type m and size j to store CO2 in physical form i, t of CO2·year−1 Mcapmin i,m,j = minimum storage capacity of facility type m and size j to store CO2 in physical form i, t of CO2·year−1 MCCi,m,j = capital cost of establishing intermediate storage facility type m and size j storing CO2 in physical form i, $ MEl = maintenance expenses of transport mode l, $·km−1 Pcapmax e,p,j = maximum CO2 production capacity of facility type p and size j, t·year−1 or L·year−1 Pcapmin e,p,j = minimum CO2 production capacity of facility type p and size j, t·year−1 or L·year−1 PCCe,p,j = capital cost of establishing utilization facility type p and size j producing product form e, $ probr = probability of occurrence of scenario r Qi,lmax = maximum flow rate of CO2 in physical form i transported by transport mode l, t of CO2·year−1 Qi,lmin = minimum flow rate of CO2 in physical form i transported by transport mode l, t of CO2·year−1 Scapmax i,s,j = maximum CO2 sequestration capacity of facility type s and size j, t of CO2·year−1 Scapmin i,s,j = minimum CO2 sequestration capacity of facility type s and size j, t of CO2·year−1 SCCi,s,j = capital cost of establishing CO2 sequestration facility type s and size j, $ SPl = average speed of transport mode l, km·h−1 SSF = safety stock factor of CO2 inventory within a intermediate storage facility, % Tcapi,l = capacity of transport mode l to transport CO2 in physical form i, t of CO2·trip−1 Tt = target amount of CO2 to be reduced by CCS facilities during time period t, t of CO2·year−1 TMAl = availability of transport mode l, h·year−1 TMCi,l = cost of establishing transport mode l to transport CO2 in physical form i, $ TPcapi,l,d = capacity of pipeline with diameter d to transport CO2 in physical form i, t of CO2·year−1

TPICoffi,l,d = total capital cost of installing pipeline transport mode l with diameter d offshore transporting CO2 in physical form i, $·km−1 TPIConi,l,d = total capital cost of installing pipeline transport mode l with diameter d onshore transporting CO2 in physical form i, $·km−1 UPOCoffi,l,d = total operating cost of pipeline transport mode l with pipe diameter d offshore transporting CO2 in physical form i, $·km−1·(t of CO2)−1 UPOConi,l,d = total operating cost of pipeline transport mode l with pipe diameter d onshore transporting CO2 in physical form i, $ km−1·(t of CO2)−1 UCCi,c,si,j = unit capture cost for CO2 captured by capture facility type c and size j in source industry si, $·(t of CO2)−1 UCCSi,t = utilization of CCS as CO2 reduction technology during time period t, 0 ≤ UCCSi,t ≤ 1 UMCi,m,j = unit storage cost for CO2 in physical form i stored by intermediate storage facility type m and size j, $·(t of CO2)−1 UPCe,p,j = unit production cost for product form e produced by utilization facility type p and size j, $·t−1 or $·L−1 USBe,p = unit selling benefit of product form e produced by utilization facility p, $·t−1 or $·L−1 USCi,s,j = unit sequestration cost for CO2 sequestered by sequestration facility type s and size j, $·(t of CO2)−1 α = a small number to limit the number of pipelines δ = number of time periods ηc = CO2 capture efficiency of capture facility c, 0 ≤ ηc ≤ 1 Binary Variables

Xi,l,g,g′,t = 1 if CO2 in physical form i is to be transported from region g to g′ by transport mode l during time period t, 0 otherwise Continuous Variables

Ci,c,si,j,sp,g,t = amount of CO2 in physical form i captured by capture facility type c and size j in source plant sp of industry type si in region g during time period t, t of CO2·year−1 E[TAP] = expected total annual profit FC = fuel cost for CO2 transportation, $·year−1 FCC = facility capital cost, $·year−1 FOC = facility operating cost, $·year−1 GC = general cost for CO2 transportation, $·year−1 LC = labor cost for CO2 transportation, $·year−1 MC = maintenance cost for CO2 transportation, $·year−1 Mi,m,j,g,t = inventory of CO2 in physical form i stored by intermediate storage facility type m and size j in region g during time period t, t of CO2·year−1 Pe,p,g,t = amount of product form e produced by utilization facility p in region g during time period t, t·year−1 or L·year−1 Qi,l,g,g′,t = flow rate of CO2 in physical form i transported by transport mode l between regions g and g′ during time period t, t of CO2·year−1 QPi,l,g,g′,d,t = flow rate of CO2 in physical form i transported by pipelines with diameter d between regions g and g′ during time period t, t of CO2·year−1 Si,s,j,g,t = amount of CO2 in physical form i sequestered by sequestration facility type s and size j in region g during time period t, t of CO2·year−1 TAB = total annual benefit, $·year−1 TAC = total annual cost, $·year−1 TAPave = total average profit of the network over the entire planning interval, $·year−1 TCC = transport capital cost, $·year−1 11456



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TOC = transport operating cost, $·year−1 TOCEP = total transportation operating cost excluding pipeline, $·year−1 TOCP = total transportation operating cost of pipeline, $·year−1 ug = number of regions visited after visiting region g Ui,p,j,g,t = amount of CO2 used by utilization facility p with size j in region g during time period t, t of CO2·year−1

(9) Han, J. H.; Lee, I. B. Development of a scalable and comprehensive infrastructure model for carbon dioxide utilization and disposal. Ind. Eng. Chem. Res. 2011, 50 (10), 6297−6315. (10) Han, J.-H.; Lee, I.-B. Development of a scalable infrastructure model for planning electricity generation and CO2 mitigation strategies under mandated reduction of GHG emission. Appl. Energy 2011, 88 (12), 5056−5068. (11) Jakobsen, J. P.; Brunsvold, A.; Husebye, J.; Hognes, E. S.; Myrhvold, T.; Friis-Hansen, P.; Hektor, E. A. Comprehensive assessment of CCS chainsConsistent and transparent methodology. Energy Procedia 2011, 4, 2377−2384. (12) Han, J.-H.; Lee, I.-B. Two-Stage Stochastic Programming Model for Planning CO2 Utilization and Disposal Infrastructure Considering the Uncertainty in the CO2 Emission. Ind. Eng. Chem. Res. 2011, 50 (23), 13435−13443. (13) Han, J.-H.; Ahn, Y.-C.; Lee, I.-B. A multi-objective optimization model for sustainable electricity generation and CO2 mitigation (EGCM) infrastructure design considering economic profit and financial risk. Appl. Energy 2012, 95, 186−195. (14) Han, J.-H.; Lee, J.-U.; Lee, I.-B. Development of a multi-period model for planning CO2 disposal and utilization infrastructure. Ind. Eng. Chem. Res. 2012, 51 (7), 2983−2996. (15) Liu, Y.; Huang, G.; Cai, Y.; Dong, C. An Inexact Mix-Integer TwoStage Linear Programming Model for Supporting the Management of a Low-Carbon Energy System in China. Energies (Basel, Switz.) 2011, 4 (10), 1657−1686. (16) Williams, R. Six-tenths factor aids in approximating costs. Chem. Eng. 1947, 54 (12), 124−125. (17) Sabio, N.; et al. Strategic planning with risk control of hydrogen supply chains for vehicle use under uncertainty in operating costs: A case study of Spain. Int. J. Hydrogen Energy 2010, 35 (13), 6836−6852. (18) Presidental Committee on GreenGrowth. A blueprint for the national greenhouse gas emissions reduction; 2011. (19) Ministry of Knowledge Economy. The price trend of petrochemical products; 2011.

Integer Variables

ICi,c,si,j,sp,g,t = investment of capture facility type c and size j capturing CO2 in physical form i in source plant sp of industry type si in region g during time period t IMi,m,j,g,t = investment of storing facility type m and size j storing CO2 in physical form i in region g during time period t INTPoffi,l,g,g′,d,t = investment of pipelines offshore during time period t INTPoni,l,g,g′,d,t = investment of pipelines onshore during time period t IPe,p,j,g,t = investment of plants of type p and size j producing product form e in region g during time period t ISi,s,j,g,t = investment of sequestration facility type s and size j sequestrating CO2 in physical form i in region g during time period t NCi,c,si,j,sp,g,t = number of capture facilities type c and size j capturing CO2 in physical form i in source plant sp of industry type si in region g during time period t NMi,m,j,g,t = number of intermediate storage facilities of type m and size j storing CO2 in physical form i in region g during time period t NPe,p,j,g,t = number of utilization facilities type p and size j of product for e in region g during time period t NSi,s,j,g,t = number of well or injection facilities of type s and size j sequestering CO2 in region g during time period t NTPoffi,l,g,g′,d,t = number of pipelines offshore NTPoni,l,g,g′,d,t = number of pipelines onshore NTUoffi,l,t = number of transport units offshore excluding pipeline NTUoni,l,t = number of transport units onshore excluding pipeline

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REFERENCES

(1) Carbon Dioxide Capture and Storage; Metz, B., Davidson, O., de Coninck, H., Loos, M., Meyer, L., Eds.; IPCC Special Report; Cambridge University Press: Cambridge, U.K., 2005. (2) Bey, R. B.; Doersch, R. H.; Patterson, J. H. The net present value criterion: Its impact on project scheduling. Proj. Manage. Q. 1981, 12 (2), 35−45. (3) Svensson, R.; et al. Transportation systems for CO2Application to carbon capture and storage. Energy Convers. Manage. 2004, 45 (15− 16), 2343−2353. (4) Middleton, R. S.; Bielicki, J. M. A scalable infrastructure model for carbon capture and storage: SimCCS. Energy Policy 2009, 37 (3), 1052− 1060. (5) Johnson, N.; Ogden, J. Detailed Spatial Modeling of Carbon Capture and Storage (CCS) Infrastructure Deployment in the Southwestern United States. Energy Procedia 2011, 4, 2693−2699. (6) Kuby, M. J.; Bielicki, J. M.; Middleton, R. S. Optimal spatial deployment of CO2 capture and storage given a price on carbon. Int. Reg. Sci. Rev. 2011, 34 (3), 285−305. (7) Morbee, J.; Serpa, J.; Tzimas, E. Optimal planning of CO2 transmission infrastructure: The JRC InfraCCS tool. Energy Procedia 2011, 4, 2772−2777. (8) Han, J.-H.; Ryu, J.-H.; Lee, I.-B. Developing A Mathematical Modeling Framework of Carbon Dioxide Capture, Transport and Storage Networks. J. Chem. Eng. Jpn. 2012, 45 (7), 504−527. 11457


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