ARTICLE pubs.acs.org/IECR
Two-Stage Stochastic Programming Model for Planning CO2 Utilization and Disposal Infrastructure Considering the Uncertainty in the CO2 Emission Jee-Hoon Han† and In-Beum Lee*,† †
Department of Chemical Engineering, POSTECH, Pohang 790784, Korea ABSTRACT: Numerous research works have been undertaken to plan carbon capture and storage (CCS) infrastructures for CO2 utilization and disposal. CO2 emissions are difficult to estimate precisely, because CO2 is emitted from various sources at varying rates. In this study, a two-stage stochastic programming model is developed for planning CCS infrastructure including CO2 utilization and disposal under stochastic CO2 emissions. The proposed model considers uncertainties in the variation of CO2 emissions. It can help determine where and how much CO2 to capture, store, transport, utilize, or sequester for the purpose of maximizing the total profit of handling uncertain CO2 emissions while meeting the CO2 mitigation target. The capability of the proposed model to provide correct decisions despite changing CO2 emissions is tested by applying it to an industrial complex on the eastern coast of Korea in 2020. The results will help to determine planning of, and budgeting for, development of a CCS infrastructure.
1. INTRODUCTION Increased emission of CO2 since the industrial revolution is associated with, and probably contributes to, recent climate change.1 Thus, reducing CO2 emission to minimize its influence on global climate change has become a global goal. Rapid carbon capture and storage (CCS) technologies will be a major part of the solution to reduce CO2 emissions.2 Research has been conducted to assess CCS technologies. Bakken and Velken have studied a linear model of the most common components in the value chain for CCS.3 Middleton and Bielicki introduced a scalable infrastructure model for CCS that generates a fully integrated, cost-minimizing CCS system.4 Other studies have addressed the problem of designing a CCS infrastructure for CO2 disposal that includes various activities such as capture, storage, transportation, and sequestration.57 Han and Lee evaluated the possibility of developing a CCS infrastructure that utilizes CO2 as a fuel, a chemical, or a nutrient for bioreactors.8 Development of CCS models and strategies is complicated by the fact that CO2 emissions in the future cannot be estimated precisely, because of incomplete data and inability to forecast future emissions. Therefore, to obtain more realistic results, CCS infrastructure models must consider the uncertainty in future CO2 emissions. This study addresses the problem of designing a CCS infrastructure model that considers the effect of uncertain future CO2 emissions. The proposed mathematical model can help determine where and how to utilize, capture, store, transport, and sequester CO2 to maximize the total net profit and satisfy the mandated reduction of CO2 emissions. To formulate a model that considers uncertainty in CO2 emissions mathematically, we apply twostage stochastic programming based on a scenario approach;9 this approach compares a stochastic model and a deterministic model to assess the variation of 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 in 2020. The rigorous model proposed in this study helps r 2011 American Chemical Society
decision makers to establish an investment strategy that balances cost efficiency against stability in an uncertain future CCS infrastructure.
2. PROBLEM STATEMENT The key objectives of the proposed model are to (1) create a robust model to incorporate a scalable and comprehensive CCS infrastructure model. for CO2 utilization and disposal, which consists of capture facilities, transport modes, storage facilities, sequestration facilities, and utilization facilities, (2) assess the effect of the configuration of CCS infrastructure according to technology alternatives, (3) apply uncertainty effect to the proposed model which rationalizes changing environments of CO2 emissions, and (4) determine the optimal policy for utilizing and disposing of CO2 across the CCS infrastructure and propose the optimal investment strategy. Developing a CCS infrastructure model to address these objectives requires knowledge of relevant features of supply chain management. Therefore, this study represents the CCS infrastructure as a network (Figure 1) which consists of a CO2 utilization component and a CO2 disposal component. Design of the network is formulated as a mixed-integer linear programming problem. The model is used to establish and investigate three strategic decisions that must be made to fulfill the mandated reduction of CO2 emissions, i.e., to determine the ideal: (1) the number, location, type, and capacity of CO2 capture, storage, sequestration, and utilization facilities; (2) the total amount of capture, storage, sequestration, and utilization of CO2 in each region considered; (3) the size and type of CO2 transport. The model also maximizes the total annual profit of the CCS infrastructure while considering these decisions. Received: February 22, 2011 Accepted: October 12, 2011 Revised: October 7, 2011 Published: October 13, 2011 13435
dx.doi.org/10.1021/ie200362y | Ind. Eng. Chem. Res. 2011, 50, 13435–13443
Industrial & Engineering Chemistry Research
ARTICLE
FCC is the total cost of establishing utilization, capture, storage, and sequestration facilities. It is calculated by multiplying the required number of CCS facilities and their capital costs and then summing: " CCRf ð PCCe;p BPe;p;g FCC ¼ LR g e p
∑
∑∑
∑i ð ∑c ∑si ∑sp CCCi;c;si;sp;g BCi;c;si;sp;g
þ
∑m MCCi;m NMi;m;g
þ
þ
∑s SCCi;s NSi;s;g ÞÞ
ð4Þ
Figure 1. Schematic diagram of CO2 infrastructure.
This model is based upon the following assumptions: (1) The locations of all CO2 emission sources, and the amounts of CO2 that they emit, are known. (2) Candidate regions for CO2 storage and sequestration are specified. (3) The CO2 emission amount is in steady state, i.e., invariant over time.8 (4) Capital charge factors associated with depreciated present value per year over the lifetime of the system8 are as follows: capture, intermediate storage, and sequestration facilities (0.148 with a 30 year plant lifetime and a 14.8% discount rate); tanker truck and tanker railcar transport modes (0.163 with a 10 year lifetime and a 10.0% discount rate); pipeline and tanker ship transport modes (0.148 with a 20 year lifetime and a 13.9% discount rate).In this study we develop a stochastic model of CCS infrastructure and compare its to those produced by a previously developed deterministic model. We describe the deterministic model first.
3. DETERMINISTIC MODEL In this section, a deterministic model to determine the optimal reduction policy for a given planning horizon is briefly described; this model is based on ref 8. The deterministic model assumes that all parameters in the model are known with certainty. This assumption is very restrictive but will serve as a base for a more complex extension (section 4) that replaces some of the uncertain parameters by using a finite set of scenarios. In the model, the knowledge of dynamic CO2 emission is crucial because the model represents the future state of CO2 utilization and disposal in terms of a present state. With a given scenario for all of the parameters in the annual utilization and disposal of CO2, the deterministic model is given by the following optimization problem. 3.1. Objective Function. The objective function is to maximize the total annual profit TAP of the CCS infrastructure; TAP is the difference between the total annual benefit TAB and the total annual cost TAC: maximize TAP ¼ TAB TAC
TCC is the sum of the cost of building transport links, which is calculated by multiplying the number of transport units and their capital cost:
TCC ¼
∑
∑ ∑g USBe;p Pe, p, g
ð2Þ
TAC is the sum of facility capital cost FCC, transport capital cost TCC, facility operating cost FOC, and transport operating cost TOC: TAC ¼ FCC þ TCC þ FOC þ TOC
ð3Þ
∑i ∑ ∑ ∑ ∑
> > > > :
∑i
9 CCR l > ðTPICd Ll;g, g 0 NTPi;l;g, g 0 , d Þ > > > = LR d g0 l ∈ fpipeg g CCR l > > > ðNTUi;l TMCi;l Þ > ; LR l ∈ frailcar;truck;shipg
∑
FOC is the total cost of operating utilization, capture, storage, and sequestration facilities. It is calculated by multiplying the annual amount needed for CCS facilities and their unit cost: FOC ¼
∑g ð ∑e ∑p UPCe;p Pe;p;g þ
∑i ð ∑c ∑si ∑sp UCCi;c;si;sp;g Ci;c;si;sp;g
þ
∑m UMCi;m Mi;m;g
þ
∑s USCi;s Si;s;g ÞÞ
ð6Þ
TOC is the sum of the annual cost of operating transport links:
TOC ¼
8 > > < > > :
9
> ∑i l ∈ ∑ ∑ ∑g ∑d TPOCd Qi;l;g, g > = fpipeg g ðFCil þ LCil þ MCil þ GCil Þ > ∑i l ∈ frailcar;truck;shipg ∑ > ; 0
0
ð7Þ 3.2. Constraints. 3.2.1. Mass Balance Constraints. The target amount T of CO2 to be reduced by CCS facilities is the product of the mandated reduction of CO2 emissions LMRi, the utilization UCCSi of CCS as CO2 reduction technology, and the total amount Ei,si,sp,g of CO2 emissions from all sources:
ð1Þ
e ∈ fgreen polymer;biobutanolg p
8 > > > >
