Developing a Two-Stage Stochastic Programming Model for CO2

Article pubs.acs.org/IECR

Developing a Two-Stage Stochastic Programming Model for CO2 Disposal Planning under Uncertainty Jee-Hoon Han,† Jun-Hyung Ryu,‡ and In-Beum Lee† †

Department of Chemical Engineering, POSTECH, Pohang, Korea Department of Nuclear and Energy System, Dongguk University, Gyeongju, Korea

‡

ABSTRACT: It is difficult to clearly estimate CO2 emissions because CO2 is emitted from various sources according to changing environments. Any approach relating to CO2 disposal has to deal with the presence of such uncertainty in CO2 disposal demand. A two-stage stochastic programming model is developed for planning CO2 emissions disposal networks by taking into account this uncertainty. The proposed CO2 disposal network model allows us to determine where and how much captured CO2 can be held for storage, and where to sequester the given amount of CO2 among multiple potential candidates for the purpose of minimizing the total cost of handling in the face of uncertainty in CO2 sequestration demand. The proposed model is applied to a case study that examines the robustness of the model in terms of handling changing environments in the context of CO2 emissions and disposal targets in Korea. The results gained aid in determining policy to plan the budget for the disposal of CO2.

1. INTRODUCTION The emission of CO2 is known to be one of the primary causes of the recent dramatic climate change. Global attention has been given to reducing CO2 emissions to minimize its impact on global climate change. However, this way does not give us the optimal solution because it is almost impossible to reduce CO2 emission completely at present. It is a prominent issue to develop an economic and cost-effective capture and storage technology of CO2, often called CCS (carbon capture and storage). Some research has been conducted to address this issue. Bakken and Velken have studied linear models of the most common components in the value chain for CO2 capture and storage.1 Middleton and Bielicki introduce a scalable infrastructure model for CCS (simCCS) that generates a fully integrated, costminimizing CCS system.2 Some studies have addressed the design problem of the CO2 disposal network including various activities such as capture, storage, transportation, and sequestration. In particular, Han et al. attempted to evaluate the possibility of a CO2 disposal infrastructure according to various configurations by taking into account the above remarks.3 On the other hand, the CO2 emissions in the future cannot be estimated accurately because of unobservable data and insufficient assumptions. Therefore, we need to take into account the presence of uncertainty with focusing particularly on the variation of CO2 emissions to obtain more realistic results in constructing CO2 infrastructure models. There are some research papers that deal with uncertainty from a similar viewpoint. Kim et al. have studied a stochastic model that covers the impact of a hydrogen supply chain under hydrogen demand uncertainty.4 Chen et al. have considered a two-stage inexact stochastic programming method developed for planning CO2 emission trading taking uncertainty into account.5 However, the previous studies did not consider the variation of CO2 emission within CCS for CO2 disposal. Moreover, few studies have examined the design and operation of all available configurations for the future CCS infrastructure based on all physical forms of CO2. © 2012 American Chemical Society

Therefore, this study addresses the design problem of the CO2 disposal network considering the effect of uncertainty. The proposed CO2 disposal network model allows us to determine where and how to capture, store, transport, and sequestrate CO2 in order to minimize the total net cost and satisfy its disposal demand. This study especially considers the effect of the demand uncertainty in CO2 activities using scenario approach based on a two-stage stochastic programming. The proposed stochastic model also considers CO2 physical types, such as gas or liquid CO2, simultaneously according to the disposal target. The model can compare the variation of CCS infrastructure with respect to CO2 physical types by comparing the deterministic and stochastic models.

2. PROBLEM STATEMENT This work is based upon the following assumptions: (1) All CO2 emission sources are known in terms of their locations and amounts. (2) Candidate regions for CO2 storage and sequestration are specified. (3) Operation at steady state, namely CO2 emission amount, is invariant over time.6 (4) Capital charge factors are associated with the depreciated present value per year over the lifetime of the system: capture, intermediate storage, and sequestration facilities: 10 years; tube trailer and tanker truck transport modes, 5 years; ship, 10 years; pipeline, 20 years.6 The key objectives of the proposed model are summarized as follows: (1) Create a robust model to incorporate various CO2 disposal activities such as capture, storage, transport and sequestration. (2) Apply uncertainty effects to the proposed model which rationalize changing environments. (3) Assess the impact of the configuration of the CO2 disposal infrastructure according to changes in the disposal target. (4) Determine the optimal disposing policy across the CO2 disposal network and propose the investment strategy. Received: Revised: Accepted: Published: 3368

May 29, 2011 January 18, 2012 January 21, 2012 January 21, 2012 dx.doi.org/10.1021/ie201148x | Ind. Eng. Chem. Res. 2012, 51, 3368−3380

Industrial & Engineering Chemistry Research

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Figure 1. Schematic diagram of CO2 disposal network.

but will serve as the basis for a more complex extension, which is described in the next section. This extension replaces some of the uncertain parameters through a finite set of scenarios in the model formulation. In the model, the knowledge of dynamic demand is crucial because the model represents the future state of CO2 disposal in terms of a present state. Assuming a given scenario for all the parameters in the annual disposal of CO2, the deterministic model uses the notation shown at the end of this paper. The proposed deterministic model is given by the following optimization problem:

On the basis of these objectives, the infrastructure of overall CO2 disposal activities is constructed as shown in Figure 1. The corresponding specific network design problem is formulated into an MILP problem as shown in the next section.

3. THE DETERMINISTIC MODEL In this section, a deterministic model used to determine the optimal disposal policy for a given planning horizon is briefly described. The deterministic model assumes that we know with certainty all the parameters present in the model. This assumption is very restrictive Minimize TACd = FCC − VOC

⎛ ⎜ ∑s CCCs , iBCi , s , g + ∑m (MCCm , i + CSMg , m)NMi , m , g + ∑r RCCr , iBR i , r , g FCC = ∑ ⎜ ⎜ FCCF i,g ⎝ +

⎛ FTEPConi , lNTEPoni , l , g , g ′ + FTEPCoff NTEPoff i,l i,l ,g ,g′ ) TEPCCF ⎝

∑ ∑ ⎜⎜ l

g′

FTPConi , l , dLonl , g , g ′NTPoni , l , g , g ′ , d + FTPCoffi , l , d Loffl , g , g ′ NTPoffi , l , g , g ′ , d ⎞⎞ ⎟⎟ +∑ ⎟⎟⎟ TPCCF ⎠⎠ d

⎛ ⎜ VOC = ∑ ⎜ ∑ UCCs , iCiL, s , g + ∑ UMCm , iMi , m , g ⎜ i,g ⎝ s m +

subject to CiT, g =

∑ ∑ (Q i , l , g , g ′ − Q i , l , g ′ , g ) + R iT, g l

∑ URCr , iR i , r , g

g′ (2)

r

+

∑ ∑ (UTEPConi , l , g , g ′ + UTEPCoffi , l , g , g ′ l

∀ i, g ∈ S

CT i , g =

g′

∑ CsL, i , g

∀ i, g ∈ S (3)

s

⎞ ⎟ + ∑ (UTPConi , l , d + UTPCoffi , l , d ))Q i , l , g , g ′⎟ ⎟ d ⎠

R iT, g =

∑ Ri,r ,g r

(1) 3369

∀ i, g ∈ R (4)

dx.doi.org/10.1021/ie201148x | Ind. Eng. Chem. Res. 2012, 51, 3368−3380


∑ MiT, m , g = ∑ ∑ Q i , l , g , g ′ m

l

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⎛ ⎞ DWlLUTl GElLUTl ⎟ UTEPConi , l , g , g ′ = ⎜⎜ + ⎟ SP TCap SP TMA TCap l l l ⎝ i,l i,l ⎠

∀ i, g ∈ M

g′

(5)

L max Ccapsmin , g BCs , i , g ≤ Cs , i , g ≤ Ccaps , g BCs , i , g

⎛ FPl DWl MEl + ⎜⎜ + + FE TCap SP TCap TCap l ⎝ l i,l i,l i,l ⎞ GEl ⎟Lon + l , g , g ′ ∀ i , l , g , g ′; SPlTMAl TCapi , l ⎟⎠

∀ s, i, g ∈ S (6)

T max ∑ Ccapsmin , g BCs , i , g ≤ Ci , g ≤ ∑ Ccaps , g BCs , i , g s

s

∀ i, g ∈ S

(7)

l ∈ {tank, tube}, g ∈ C , g ′ ∈ M , g ≠ g ′

T max Mcapmmin , i NMi , m , g ≤ Mi , m , g ≤ Mcapm , i NMi , m , g

∀ i , m, g ∈ M

⎛ ⎞ DWlLUTl GElLUTl ⎟ UTEPCoffi , l , g , g ′ = ⎜⎜ + SPlTMAl TCapi , l ⎟⎠ ⎝ SPlTCapi , l

(8)

⎛ FPl DWl MEl + ⎜⎜ + + SPlTCapi , l TCapi , l ⎝ FElTCapi , l ⎞ GEl ⎟Loff + ∀ i , l , g , g ′; SPlTMAl TCapi , l ⎟⎠ l , g , g ′

max Rcaprmin , i , g BR r , i , g ≤ R i , r , g ≤ Rcapr , i , g BR r , i , g

∀ i, r , g ∈ R

(9)

T max ∑ Rcaprmin , i , g BR r , i , g ≤R i , g ≤ ∑ Rcapr , i , g BR r , i , g r

r

∀ i, g ∈ R

(10)

max Q imin , l Xi , l , g , g ′ ≤ Q i , l , g , g ′ ≤ Q i , l Xi , l , g , g ′

∀ i , l , g , g ′;

l ∈ {ship}, g ∈ M , g ′ ∈ R , g ≠ g ′

T≤

∑∑

∀ s, i, g ∈ S

(12)

R iT, g

i g∈R

(13)

∑ ∑ Xi , l , g , g ′ ≤ 1 i

g ≠ g′ (14)

∑ ∑ Xi , l , g ′ , g ≤ 1 i

∀ g , g ′;

l

∀ g , g ′;

g ≠ g′ (15)

l

ug − ug ′ + nXi , l , g , g ′ ≤ n − 1 g = 2, ···, n , g ′ = 2, ···, n; NTEPoni , l , g , g ′ = ∀ i , l , g , g ′;

NTEPoffi , l , g , g ′ = ∀ i , l , g , g ′;

∀ i , l , g , g ′; g ≠ g′

(16)

⎛ 2Lonl , g , g ′ ⎞ + LUT1⎟ ⎜ TMA1TCapi , l ⎝ SP1 ⎠ Q i,l ,g ,g′

g ≠ g ′, l ∈ {tank, tube}

(17)

⎞ ⎛ 2Loffl , g , g ′ ⎜ + LUT 1⎟⎟ TMA1TCapi , l ⎜⎝ SP1 ⎠ Q i,l ,g ,g′

g ≠ g ′, l ∈ {ship}

(18)

max TAPimin , l , dNTPi , l , g , g ′ , d ≤ Q i , l , g , g ′ ≤ TAPi , l , d NTPi , l , g , g ′ , d

∀ i , l , d , g , g ′, d ;

g ≠ g ′, l ∈ {pipe}

∑ ∑ NMi , m , g LSFMm ≤ PREFg LSg i

m

(22)

The objective function in 1 represents the minimization of the TAC (total annual cost) of the CO2 disposal network. TAC consists of FCC (fixed capital cost) and VOC (variable operating costs). The FCC (fixed capital cost) is calculated by multiplying the required number of facilities, transportation modes, and the establishment cost with the occupied site cost. This value is then divided by FCCF, TEPCCF, and TPCCF, which indicates the capital charge factors or depreciated present value per year over the lifetime of the system. The VOC (variable operating cost) denotes the total charge generated when the CO2 from all regions is disposed of using the CO2 disposal facilities. This is calculated by multiplying the unit cost of the facilities, transportation modes, and the amounts captured, stored, and transported. Constraints 2−4 describe the requirement that the mass balance must be satisfied in each region of the CO2 disposal network. More specifically, constraint 2 represents that CTig, the total CO2 amount captured in the region, plus Qi,l,g′,g, the total flow rates of each individual product from i imported to region g, must be equal to the sum of Qi,l,g,g′, the total flow rate leaving this region, and RTig, the total sequestration amount in this region. Constraint 5 refers to the requirement that the storage facilities should be built to allow for changes in the means of transportation and should be capable of storing Qi,l,g,g′, the total flow rate leaving this region. Constraints 6−11 represent the limitation that all facilities and transportation modes must be bound within certain limits. Constraint 12 denotes how much CO2 can be captured from the source region with maximum limits. Constraint 13 specifies the target system-wide CO2 disposal amounts. CO2 is moving from an emission source to a final sequestration region to meet the disposal demand. Thereby the overall flow of a product form i is in one direction from a source to a sequestration site. Constraints 14−16 refer to the Miller, Tucker, and Zemlin (MTZ) formulation in order to formulate this network feature.7 Constraints 17−19 determine the number of transportation modes. Constraint 20 refers to the limit in the number of sites

g ≠ g′

(11)

CsL, i , g ≤ CEsL, i , g CCE

(21)

(19)

∀g∈M (20) 3370



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able to construct storage facilities in the region. Constraints 21−22 determine the unit operating costs of the transport modes via tube trailer and tanker trucks onshore.

section, the first-stage decisions are CO2 capture, storage, sequestration, and transportation through pipeline quantities of FCCs. All other decision variables are considered to be secondstage decisions. As we assume steady state operation, first-term quantities such as the number of facilities cannot change suddenly, while second-term quantities depend on random events. The role of the random event is to average the costs incurred in the CO2 activities. The scenarios emerging from the assumption that they are random events are indicated using a superscript w = 1, 2, and 3 are +10%, above average, 0%, average, and −10%, below the average CO2 demand, respectively.4 This assumption also implies that the three scenarios have an equal probability. The previous deterministic model is reformulated as a stochastic model which minimizes the expected cost of the network. To consider additional sets and indexes to those given in the previous section, the formulas become as follows:

4. STOCHASTIC PROGRAMMING MODEL The proposed model introduced in the previous section includes some parameters often associated with uncertainty. Despite often considering the uncertainty by replacing the stochastic parameters with their expected values in a deterministic model, this method does not give us the optimal solution due to insufficient reality and variability of these parameters concerning their expected value. Thus, among the different methodologies with respect to uncertainty, we focus on the two-stage stochastic model with the expected scenario approach. To to fulfill this method, a distinction must be made between the first-stage and the second-stage. In the previous

Minimize TACs = FCC − VOC ⎛ ⎜ ∑s CCCs , iBCi , s , g + ∑m (MCCm , i + CSMg , m)NMi , m , g + ∑r RCCr , iBR i , r , g FCC = ∑ ⎜ ⎜ FCCF i,g ⎝ FTPConi , l , dLonl , g , g ′NTPoni , l , g , g ′ , d + FTPCoffi , l , d Loffl , g , g ′ NTPoffi , l , g , g ′ , d + ∑∑∑ TPCCF l

1 + 3

g′ d

w ⎛ FTEPConi , lNTEPon w ⎞⎞ i , l , g , g ′ + FTEPCoffi , l NTEPoffi , l , g , g ′ ⎟⎟ ⎜ ∑ ∑∑⎜ ⎟⎟⎟ TEPCCF ⎠⎠ w = 1,2,3 l g ′ ⎝

⎛ ⎜1 VOC = ∑ ⎜ ∑ ∑ UCCs , iCiL, s,,wg ⎜3 i , g ⎝ w = 1,2,3 s 1 ∑ ∑ UMCm , iMiw, m , g + 3

CiT, g, w =

1 3

1 + 3

w ∈ {1, 2, 3} (25)

R iT, g, w =

∑ R iw, r , g

∀ i, g ;

g ∈ R;

w ∈ {1, 2, 3}

∑ ∑ URCr , iR iw, r , g

(26)

w = 1,2,3 r

∑ MiT, m, w, g = ∑ ∑ Q iw, l , g , g ′

∑ ∑ ∑ (UTEPConi , l , g , g ′ w = 1,2,3 l

m

g′

⎞ ⎟ w + UTPCoffi , l , d ))Q i , l , g , g ′⎟ ⎟ ⎠

l

g′

g ∈ S;

(27)

(23)

∀ s, i, g ;

w ∈ {1, 2, 3}

(28)

max T ,w ∑ Ccapsmin , g BCs , i , g ≤ Ci , g ≤ ∑ Ccaps , g BCs , i , g s

s

∀ i, g ;

w ∈ {1, 2, 3}

g ∈ M;

max L,w Ccapsmin , g BCs , i , g ≤ Cs , i , g ≤ Ccaps , g BCs , i , g

subject to

∑ ∑ (Q iw, l , g , g ′ − Q iw, l , g , g ′) + R igT , w l g′

∀ i, g ;

w ∈ {1, 2, 3}

∑ (UTPConi , l , d d

g ∈ S;

g ∈ S;

r

+ UTEPCoffi , l , g , g ′ +

CiT, g , w =

∀ i, g ;

s

w = 1,2,3 m

+

∑ CsL, i , g

∀ i, g ;

g ∈ S;

w ∈ {1, 2, 3}

(29)

max T ,w Mcapmmin , i NMi , m , g ≤ Mi , m , g ≤ Mcapm , i NMi , m , g

∀ i , m, g ;

(24) 3371

g ∈ M , w ∈ {1, 2, 3}

(30)


Industrial & Engineering Chemistry Research w max Rcaprmin , i , g BR r , i , g ≤ R i , r , g ≤ Rcapr , i , g BR r , i , g

g ∈ R;

Article

⎛ ⎞ DWlLUTl GElLUTl ⎟ UTEPConi , l , g , g ′ = ⎜⎜ + ⎟ SP TCap SP TMA TCap l l l ⎝ i,l i,l ⎠

∀ i, r , g ;

w ∈ {1, 2, 3}

(31)

⎛ FPl DWl MEl + ⎜⎜ + + FE TCap SP TCap TCap l ⎝ l i,l i,l i,l ⎞ GEl ⎟Lon + l , g , g ′ ∀ i , l , g , g ′; SPlTMAl TCapi , l ⎟⎠

max T ,w ∑ Rcaprmin , i , g BR r , i , g ≤ R i , g ≤ ∑ Rcapr , i , g BR r , i , g r

r

∀ i, g ;

g ∈ R , w ∈ {1, 2, 3}

(32)

w max w w Q imin , l Xi , l , g , g ′ ≤ Q i , l , g , g ′ ≤ Q i , l Xi , l , g , g ′

g ≠ g ′;

∀ i , l , g , g ′;

w ∈ {1, 2, 3}

CsL, i,,wg ≤ CEsL, i,,wg CCE

(33)

∀ s, i, g ;

∑∑

R iT, g, ww ∈ {1, 2, 3} (35)

∑ ∑ Xiw, l , g , g ′ ≤ 1 i

⎛ FPl DWl MEl + ⎜⎜ + + FE TCap SP TCap TCap l ⎝ l i,l i,l i,l ⎞ GEl ⎟Loff + ∀ i , l , g , g ′; SPlTMAl TCapi , l ⎟⎠ l , g , g ′

(34)

i g∈R

∀ g , g ′;

g ≠ g ′;

l ∈ {ship}, g ≠ g ′

w ∈ {1, 2, 3}

l

i

∀ g , g ′;

g ≠ g ′;

w ∈ {1, 2, 3}

l (37)

ugw − ugw′ + nXiw, l , g , g ′ ≤ n − 1 g = 2, ···, n , g ′ = 2, ···, n;

∀ i , l , g , g ′; g ≠ g ′;

w ∈ {1, 2, 3} (38)

Q iw, l , g , g ′ ⎛ 2Lonl , g , g ′ ⎞ w NTEPoni , l , g , g ′ = + LUT1⎟ ⎜ TMA1TCapi , l ⎝ SP1 ⎠ ∀ i , l , g , g ′;

g ≠ g ′;

l ∈ {tank, tube};

w ∈ {1, 2, 3}

5. CASE STUDY (39)

The CO2 disposal network of Korea in 20303 is selected as a benchmark to evaluate the applicability of the proposed model. To use the model, upper and lower boundary capacity, and the capital and operating cost and benefit of each CCS technology are required. This study used data and parameters from ref 3, in which the authors collected the data from previous studies and national reports and applied a number of engineering-oriented methods such as cost estimation. Also, the CO2 disposal demand map of Korea in 2030 is depicted by using a detailed economic analysis from ref 3, and shown in Figure 2. The corresponding CO2 disposal demand should be fulfilled by using CO2 methodologies such as capture, sequestration, transportation, and storage. Specific disposal activities used in this case study are summarized in Table 1. To evaluate the impact according to different CO2 disposal network configurations, four case studies are examined according to distinctive disposal amount targets and model types as shown in Table 2.

⎞ Q iw, l , g , g ′ ⎛ 2Loffl , g , g ′ w ⎜ NTEPoffi , l , g , g ′ = + LUT 1⎟⎟ TMA1TCapi , l ⎜⎝ SP1 ⎠ ∀ i , l , g , g ′;

g ≠ g ′;

l ∈ {ship};

w ∈ {1, 2, 3} (40)

w max TAPimin , l , dNTPi , l , g , g ′ , d ≤ Q i , l , g , g ′ ≤ TAPi , l , d NTPi , l , g , g ′ , d

∀ i , l , d , g , g ′;

g ≠ g ′;

l ∈ {pipe};

w ∈ {1, 2, 3} (41)

∑ ∑ NMi , m , g LSFMm ≤ PREFg LSg i

m

(44)

The objective function in eq 23 represents the minimization of the expected costs. In this model, variables considered in the first-stage such as BCs,i,g, BRr,i,g, NMi,m,g, and NTPi,l,g,g′,d will not change according to the scenario examined. However, all second-stage variables are replaced by the corresponding variables applied for the three scenarios. Because constraints 28−32, 41, and 42 concerned with FCC are considered as first-stage decision variables excluding NTEPonwi,l,g,g′ and NTEPof f wi,l,g,g′, they need no modification, and are used in the stochastic model formulation. Otherwise, in order to represent uncertainty, all other constraints 24−27 and 33−40 concerned with second-stage decision variables need to be separated into three parts, one for each of the CO2 demand scenarios. More specifically, CEs,i,gL.w in eq 34 refers to the uncertainty in demand defined in terms of the three scenarios.

(36)

∑ ∑ Xiw, l , g , g ′ ≤ 1

(43)

⎛ ⎞ DWlLUTl GElLUTl ⎟ UTEPCoffi , l , g , g ′ = ⎜⎜ + SPlTMAl TCapi , l ⎟⎠ ⎝ SPlTCapi , l

g ∈ S;

w ∈ {1, 2, 3}

T≤

l ∈ {tank, tube}, g ≠ g ′

∀g∈M (42) 3372



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Figure 2. CO2 disposal demand forecast in Korea 2030 based on the core sectors of power, steel, cement, and petrochemical industries.

disposal alternatives is compressed gaseous CO2 (CCO2) capture or storage, transport via pipeline (onshore, offshore) and depleted gas reservoir (DGR), saline aquifer storage (SAS), or ocean storage via pipeline (OSP) sequestration. CO2 is captured from seven different source regions onshore to meet the required CO2 sequestration target. Almost all of the CO2 is captured from steel and power plants in regions 11, 13, 14, and 15. This can be traced back to the highest CO2 emission density of the source plants in these harbor regions. The other reason is cheaper transport costs owing to their being near the final sequestration site. This affects the installation of a considerably large number of intermediate storage facilities (35, 49, and 94 facilities) in regions 7, 14, and 15. It also has an effect on the installation of the pipeline surrounding the CCS facilities. A specific feature is the 21.6 in. diameter pipelines established largely because of the relative merits of the transport operating costs compared to pipes with smaller diameters. The final sequestration sites are presented evenly in g14, g17, g18, g19, and g20. A considerable amount of CO2 is sequestrated with DGR type in regions 17 and 18. The major cause of this is that the operating costs of the DGR type are cheaper than others and the capacity is larger. The result of the other case, for an annual sequestration target of 300 M ton, is shown in Figures 5 and 6. This case corresponds with previous cases in terms of optimal disposal activities which consist of compressed gaseous CO2 (CCO2) capture or storage, transport via pipeline and depleted gas reservoir (DGR), saline aquifer storage (SAS), or ocean storage via pipeline (OSP) sequestration. On the other hand, there is some difference in the numbers and operating amounts of the CCS facilities. Specifically, the number of intermediate storage facilities in regions 7 and 14 increases considerably. The amount of CO2 captured from power plants in regions 4 and 11 also increases. According to the increase in the annual sequestration target, the CO2 transported to region 7 or region 14 grows onshore, and the deviation in the amount of CO2 is delivered to candidate sites 17 and 18 offshore. It also affects

Table 1. Summary of the Capture, Storage, Sequestration, And Transportation Technologies Considered in the Case Study8 activity

type

capture technology

the absorption and desorption of carbon dioxide in aqueous monoethanolamine (MEA) liquid CO2, or LCO2 held in semipressurized cylindrical tanks compressed gaseous CO2, or CCO2 held in steel tanks depleted gas reservoir, or DGR saline aquifer storage, or SAS ocean storage via pipeline, or OSP ocean storage via tanker, or OST liquid CO2, or LCO2 via tanker truck liquid CO2, or LCO2 via tanker ship compressed gaseous CO2, or CCO2 via tube trailer compressed gaseous CO2, or CCO2 via pipeline

intermediate storage technology sequestration method

transportation mode

Table 2. Analysis Conditions Selected for the Case Study case

target of disposal amount

1

200MtCO2/yr

2

300MtCO2/yr

3 4

200MtCO2/yr 300MtCO2/yr

description deterministic model including all CO2 activities deterministic model including all CO2 activities stochastic model including all CO2 activities stochastic model including all CO2 activities

6. RESULTS AND DISCUSSION To examine the case studies, the model is implemented in GAMS and solved using the MILP solver of CPLEX 9.0 in Pentium 4, 3.16 GHz. 6.1. The Optimal CO2 Infrastructure: Deterministic Model. To illustrate the suitability of the proposed deterministic model eq 1−22, two case studies are presented. The first result concerns the optimal CO2 infrastructure for the annual sequestration target of 200 M ton as shown in Figure 3 and 4. The optimal network configuration concerning all available 3373



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Figure 3. Case 1 deterministic model. CO2 capture, storage, and sequestration activities for an annual sequestration target of 200 M ton.

Figure 4. Case 1 deterministic model. CO2 transport activities for an annual sequestration target of 200 M ton.

much more the installation of 21.6 in. diameter pipelines surrounding the CCS facilities in these regions. 6.2. Effects of Demand Uncertainty: Stochastic Model. To illustrate and assess the suitability of the stochastic approach, three scenarios were defined in this example and applied in the previous cases. At first, the result of case 3 is depicted in Figures 7 and 8. It represents the difference in the CCS infrastructure between the deterministic model of case 1 and the stochastic model of case 3 for an annual sequestration

target of 200 M ton. The optimal disposal activities are likewise compressed gaseous CO2 (CCO2) capture or storage, transport via pipeline and depleted gas reservoir (DGR), saline aquifer storage (SAS), or ocean storage via pipeline (OSP) sequestration. There is little difference between cases 1 and 3 in terms of the number of or operating amounts of CCS facilities. The number of intermediate storage facilities in region 14 is larger than in case 1. The amount of CO2 captured from power plants in region 11 represents great gaps according to 3374



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Figure 5. Case 2 deterministic model. CO2 capture, storage, and sequestration activities for an annual sequestration target of 300 M ton.

Figure 6. Case 2 deterministic model. CO2 transport activities for an annual sequestration target of 300 M ton.

using the deterministic model. All optimal disposal activities have been presented in the previous cases, as have those representing liquid CO2-based activities of CCS facilities. This feature is present especially in regions 14 and 18. The number of intermediate storage facilities with respect to the amount of compressed gaseous CO2 in region 14 reduces and increases with respect to liquid CO2 levels. Liquid CO2 captured from the steel plant in region 14 also increases, while compressed

three scenarios. CO2 sequestrated with OSP type in region 18 has been removed and enlarged in region 17. The diameter of the pipeline transported to region 17 has also been made larger. Additionally, it appears that CO2 captured from region 11 is transported to region 14 since region 11 has a higher amount captured according to the w 3 scenarios. On the other hand, case 4, using the stochastic model as depicted in Figures 9 and 10, is distinctly different from case 2 3375



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Figure 7. Case 3 stochastic model. CO2 capture, storage, and sequestration activities for an annual sequestration target of 200 M ton.

Figure 8. Case 3 stochastic model. CO2 transport activities for an annual sequestration target of 200 M ton.

appearance of transport via ship between harbor region 14 and sequestration region 18. The total network costs of the examined cases are shown in Figure 11. We can compare the cost difference between the deterministic and stochastic model by using the change of percentage. In overall, we can see that the total cost according

gaseous CO2 captured from power plants in regions 4 and 9 reduces. These items mean that less 21.6 in. diameter pipeline is needed surrounding the CCS facilities in outward regions 4, 9, and 14. Compressed gaseous CO2 sequestrated with OSP type in region 17 has been reduced and liquid CO2 sequestrated with OSP type in region 18 appears. It also affects the 3376



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Figure 9. Case 4 stochastic model. CO2 capture, storage, and sequestration activities for an annual sequestration target of 300 M ton.

Figure 10. Case 4 stochastic model. CO2 transport activities for an annual sequestration target of 300 M ton.

facilities, and, more specially, the fixed capital cost of the transport modes. The facts are clearly represented in Figure 11. The fixed capital costs are sensitively changed by the variation of CO2 demand as shown in Figure 11. In particular, the change rates in the fixed capital cost of the transport modes are more sensitive to demand uncertainty than

to the stochastic model is generally higher than that of the deterministic model. The total network cost in case 3 increases by about 0.4% according to the variation of CO2 demand when compared to case 1. Case 4 also shows a slightly greater increase of nearly 0.7%. Most of this increased cost is derived from the fixed capital cost of CCS facilities, the variable operating costs of CCS 3377



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Figure 11. Comparison of costs between the deterministic model and the stochastic model.

The results from the stochastic model can provide more valuable insights on making investment strategies for the CO2 disposal network, such as cost efficiency versus stability under an uncertain environment for CO2 emissions. Only the variation in the CO2 emission has been considered here, but other more important multiple variations (e.g., carbon taxes, costs of CCS) need to be included to make the paper more meaningful. As a future work, it would be worthwhile to extend the proposed modeling approach for developing refined scenarios in terms of addressing other types of uncertainties as well as evaluating the effects of demand uncertainty over the planning time horizon.

CCS facilities. It can be found out by reviewing that the change rates in the fixed capital cost of transport modes is +6.5% and 29.3%, while those of the CCS facilities is +1.5% and 5.1% in cases 3 and 4, respectively. From this result, we may say that establishing new transport modes is a more economically feasible option than establishing new CCS facilities. Unlike the fixed capital cost, Figure 11 shows that variations in CO2 demand can have both positive and negative influences on each cost components of CCS facilities and transport modes. In case 4, we see that the change rates in the variable operating costs of the CCS facilities is +0.3%, while the change rates of the transport modes is −4.9%. Figure 11 also shows that the variable operating cost of the CCS facilities is a dominant factor in the total network cost to satisfy the required CO2 demand. For example, the total network cost of case 1 is 12.23 billion dollars and the variable operating cost of the CCS facilities in case 1 is 10.47 billion dollars. The construction of the CO2 infrastructure should focus on operating CCS facilities. That is to say, establishing new transport modes is preferable to any other means with a view to stabilizing in uncertain environments.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-54-770-2859. Fax.: +82-54-770-2874. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (KRF-2008-313-D00178, 2010-0023678).

7. CONCLUSIONS This study has developed a stochastic model to design the CO2 infrastructure in order to propose a strategy for disposing a future CO2. This study analyzed the effect of demand uncertainty by constructing a two-stage stochastic model. The proposed model is utilized to examine the robustness in terms of handling changing environments in the context of CO2 emissions and disposal targets in Korea in 2030. From the results, it was proven that the optimal network configuration is to employ compressed gaseous CO2 (CCO2) capture or storage, transport via pipeline (onshore, offshore) and depleted gas reservoir (DGR), saline aquifer storage (SAS), or ocean storage via pipeline (OSP) sequestration. To address the effects of demand uncertainty, liquid CO2 activities should be also implemented additionally. The model also compares the network costs between the deterministic and stochastic models.

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NOTATION i product physical form g region g′ region such that g′ ≠ g s source plant type m intermediate storage facility type with different storage technologies r sequestration type with different sequestration technologies l type of transportation mode d pipeline diameters

Parameters

CCCs,i = capital cost for capturing product form i from source plant type s, $ 3378



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UTEPConi,l,g,g′ = unit cost of transporting product form i by transportation mode l, excluding pipeline transportation, between regions g and g′ onshore, $ UTEPCof f i,l,g,g′ = unit cost of transporting product form i by transportation mode l, excluding pipeline transportation, between regions g and g′ offshore, $ FTPConi,l,d = fixed cost of establishing pipeline l, transporting product form I, onshore with pipe diameter d, $ km−1 FTPCof f i,l,d = fixed cost of establishing pipeline l, transporting product form I, offshore with pipe diameter d, $ km−1 UTPConi,l,d = unit cost of onshore pipeline with pipe diameter d, $ km−1 ton−1 UTPCoff i,l,d = unit cost of offshore pipeline with pipe diameter d, $ km−1 ton−1 FCCF = facility capital charge factorpayback period of capital investment, year TEPCCF = transportation modes excluding pipeline capital charge factorpayback period of capital investment, year TPCCF = transportation modes for pipeline capital charge factorpayback period of capital investment, year T = target amount of CO2 to be sequestered, ton year−1

MCCm,i = capital cost of establishing storage type m storing product form i, $ RCCr,i = capital cost of establishing sequestration type r sequestrating product form i, $ UCCs,i = unit capture cost for product form i captured in plant type s, $ ton−1 UMCm,i = unit storage cost for product form i at intermediate storage facility type m, $ ton−1 URCr,i = unit sequestration cost for product form i at sequestration type r, $ ton−1 CELs,i,g = amount of product form i emitted by source plant type s in source region g, ton year−1 Lonl,g,g′ = average delivery distance between regions g and g′ by transport mode l onshore, km trip−1 Lof f l,g,g′ = average delivery distance between regions g and g′ by transport mode l offshore, km trip−1 CCapmini,s,g = minimum capture capacity of facility type s for product form i on source region g, ton year−1 CCapmaxi,s,g = maximum capture capacity of facility type s for product form i on source region g, ton year−1 MCapminm,i = minimum intermediate storage capacity of facility type m for product form i, ton year−1 MCapmaxm,i = maximum intermediate storage capacity of facility type m for product form i, ton year−1 RCapminr,i,g = minimum sequestration capacity of type r for product form i on disposal region g, ton year−1 RCapmaxr,i,g = maximum sequestration capacity of type r for product form i on disposal region g, ton year−1 Qmini,l = mininum flow rate of product form i by transportation mode l, ton year−1 Qmaxi,l = maximum flow rate of product form i by transportation mode l, ton year−1 TAPmini,l,d = mininum capacity of transportation mode l on including pipeline with diameter d transporting product form i, ton year−1 TAPmaxi,l,d = maximum capacity of transportation mode l on including pipeline with diameter d transporting product form i, ton year−1 TMCi,l = cost of establishing transportation mode l transporting product form i, $ TCapi,l = capacity of transportation mode l transporting product form i, ton trip−1 FEl = fuel economy of transportation mode l, km L−1 SPl = average speed of transportation mode l, km h−1 TMAl = transportation mode availability of transportation mode l, h year−1 LUTl = load−unload time of transportation mode l, h trip−1 DWl = driver wage of transportation mode l, $ h−1 FPl = fuel price of transportation mode l, $ L−1 MEl = maintenance expenses of transportation mode l, $ km−1 GEl = general expenses of transportation mode l, $ y−1 CCE = CO2 capture efficiency CSMgm = the cost of sites g for intermediate storage facility type m, $ LSg = the land size for each region g, m2 LSFMm = the land size factor for intermediate storage facilities of type m, m2 PREFg = the possible rate to establish facilities at each region g, % FTEPConi,l = fixed cost of establishing transportation mode l, excluding pipeline transportation, of product form i onshore, $ FTEPCof f i,l = fixed cost of establishing transportation mode l, excluding pipeline transportation, of product form i offshore, $

Binary Variables

Xi,l,g,g′ = 1, if product form i is to be transported from region g to g′ by transportation mode l, 0 otherwise BCi,s,g = 1, if source plant type s with product form i on region g is opened, 0 otherwise BRi,r,g = 1, if sequestration type r with product form i on region g is opened, 0 otherwise Continuous Variables

TAC = total annual cost, $ year−1 FCC = fixed capital cost, $ year−1 VOC = variable operating cost, $ year−1 ug = the number of regions visited after visiting region g Qi,l,g,g′ = flow rate of product form i by transportation mode l between regions g and g′, ton year−1 CLs,i,g = the amount of product form i captured from source plant type s in source region g, ton year−1 CTi,g = the total amount of product form i captured in source region g, ton year−1 MTi,g = total average inventory of product form i in region g, ton year−1 RTi,g = total average sequestered amount of product form i in region g, ton year−1 Ri,r,g = average sequestered amount of product form i in region g with sequestration type r, ton year−1 Integer Variables

NMm,i,g = number of intermediate storage facilities of type m for product form i in region g NTEPoni,l,g,g′ = number of transport units onshore for product physical form i transported from region g to g′ by transport mode l, excluding pipeline NTEPof f i,l,g,g′ = number of transport units offshore for product physical form i transported from region g to g′ by transport mode l, excluding pipeline NTPoni,l,g,g′,d = number of transport units onshore for product physical form i transported from region g to g′ by transport mode l, only including pipelines with diameter d NTPof f i,l,g,g′,d = number of transport units offshore for product physical form i transported from region g to g′ by transport mode l, only including pipelines with diameter d 3379



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Developing a Two-Stage Stochastic Programming Model for CO2

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