Article pubs.acs.org/IECR
Continuous-Time Optimization Model for Source−Sink Matching in Carbon Capture and Storage Systems Raymond R. Tan,†,* Kathleen B. Aviso,† Santanu Bandyopadhyay,‡ and Denny K. S. Ng§ †
Chemical Engineering Department/Center for Engineering and Sustainable Development Research, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines ‡ Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India § Department of Chemical and Environmental Engineering/Centre of Excellence for Green Technologies, University of Nottingham, Malaysia, Selangor 43500, Malaysia ABSTRACT: Carbon capture and storage (CCS) is widely considered to be an essential technology for reducing carbon dioxide (CO2) emissions from sources such as power plants. It involves isolating CO2 from exhaust gases and then storing it in an appropriate natural reservoir that acts as a sink. Therefore, CCS is able to prevent CO2 from entering the atmosphere. In this work, a continuous-time mixed integer nonlinear programming (MINLP) model for CO2 source−sink matching in CCS systems is developed; the initial model is then converted into an equivalent mixed integer linear program (MILP). It is assumed that in CCS systems, CO2 sources have fixed flow rates and operating lives, while CO2 sinks have an earliest time of availability and a maximum CO2 storage capacity. Thus, the resulting optimization model focuses on important physical and temporal aspects of planning CCS. The usefulness of the model is illustrated using two case studies.
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INTRODUCTION Climate change as a result of emissions of greenhouse gases, particularly carbon dioxide (CO2), is widely considered to be the most critical environmental issue facing the world today. CO2 emissions from combustion processes in energy systems are a significant part of the problem, particularly because of the strong link between energy use and economic development. Thus, effective climate change mitigation can only be achieved through the wide deployment of low-carbon energy systems based on such strategies as energy management (e.g., energy efficiency enhancement), fuel substitution (e.g., biomass cofiring), utilization of noncombustion technologies (e.g., solar, wind, or nuclear energy), and use of carbon capture and storage (CCS).1 The latter option is unique among these technologies since it potentially allows the continued use of fossil fuels (coal, oil, and natural gas) while resulting in CO2 emission levels that are dramatically lower than those of conventional fossil-fired systems without CCS.2 CCS involves capturing relatively pure CO2 from the gaseous combustion products of industrial sites that act as sources and storing it in various reservoirs (e.g., inaccessible coal seams, saline aquifers, depleted oil wells, and geological reservoirs) that act as sinks. Carbon capture techniques include postcombustion capture through flue gas scrubbing, precombustion capture in integrated gasification combined cycle (IGCC) plants, oxy-fuel combustion, and chemical looping combustion. The latter two options involve burning fuel in the absence of atmospheric nitrogen to produce flue gas comprised mainly of CO2 and water vapor. The captured CO2 may then be transported offsite and stored in various sinks. It is estimated that CCS will be commercially viable by the end of the decade.2,3 Commercial employment of CCS requires rigorous decision support due to various technical, environmental, and economic issues that arise from its use. One of the major issues is the energy penalty when plants are retrofitted for CO2 capture. © 2012 American Chemical Society
This power loss makes it necessary to generate electricity from new plants to maintain the grid-wide power output prior to CCS deployment. The emissions from compensatory power generation have been shown to be significant from a life cycle standpoint.4 Systematic approaches such as pinch analysis5,6 and mathematical programming6−8 have thus been developed to plan CCS deployment while accounting for these energy penalties. Integration of CCS within a larger energy planning framework has also been demonstrated by Koo et al.9 Meanwhile, the design of CO2 transportation infrastructure to match stream sources with appropriate sinks or storage sites is now also recognized as an important prerequisite to successful CCS commercialization.10 Turk et al.11 proposed the earliest model for allocating CO2 to depleted wells for enhanced oil recovery (EOR) operations. Their work made use of a pure integer linear programming (ILP) model with stream pooling. A similar nonlinear programming (NLP) model for designing a minimum cost pipeline network was later developed by Benson and Ogden.12 One major improvement in the latter model is that it takes into account both the dynamic changes in the network as well as the effect of parameter uncertainties. Later, the SimCCS model was developed13,14 using a mixed integer linear programming (MILP) formulation that incorporates decisions about infrastructure characteristics such as pipeline size. The main disadvantage of SimCCS is that it is a static optimization model which implicitly assumes that all sources and sinks are present simultaneously. CO2 network design based on NLP Special Issue: APCChE 2012 Received: Revised: Accepted: Published: 10015
December 2, 2011 February 5, 2012 February 10, 2012 February 10, 2012 dx.doi.org/10.1021/ie202821r | Ind. Eng. Chem. Res. 2012, 51, 10015−10020
Industrial & Engineering Chemistry Research
Article
and genetic algorithm (GA) has also been demonstrated,15 even though in general GA and similar stochastic algorithms do not ensure strict convergence to optimal solutions. In addition to optimization techniques, an alternative heuristic algorithm for the design of a CCS pipeline network has also been proposed.16 The algorithm allows for gradual evolution of network topology over time but does not perform any direct optimization. In our previous work,17 a discrete-time MILP model for source− sink matching with temporal, storage capacity and injection rate constraints was proposed. The main disadvantage of this alternative formulation is that increased precision of the model can be achieved only by using shorter time intervals, which in turn results in a rapid increase in the number of model variables. This paper presents a continuous-time MILP model for matching CO2 sources and sinks under temporal and storage capacity constraints. Injection rates are neglected since capacity is considered to be the most significant physical characteristic of CO2 sinks.18 Furthermore, this new model also accounts for CO2 emission penalties that result from generating extra electricity to compensate for grid-wide CCS power losses.5−8 The model developed in this work does not explicitly account for economic aspects of CCS infrastructure investment, as it is assumed that all the sources and sinks in a given system are in sufficiently close geographic proximity to make all possible matches economically viable. The rest of the paper is organized as follows. First, a formal problem statement is given in the section that follows. An initial mixed integer nonlinear programming (MINLP) model is then developed; however, due to the potential computational difficulties that may be encountered in solving such models, an equivalent MILP formulation is then proposed in the next section. The usefulness of the linearized model is then demonstrated through two illustrative case studies. Finally, conclusions and prospects for future work are given at the end of the paper.
CCS connectivity is defined for the system (i.e., CO2 capture from a given source i is only considered economically worthwhile if the total period of connection to a sink j exceeds this threshold value). Hence, for any given source−sink pair, the latest allowable time to begin CO2 capture in source i must be compatible with the earliest available time of sink j. In other words, the sink must be ready to store CO2 once a decision is made to begin capturing CO2 in a corresponding source. Furthermore, once a source is connected to a sink, it is assumed to remain connected until it ceases to operate. • The objective is to determine the maximum amount of CO2 emissions reduction by matching CO2 sources and sinks, given these specified temporal and physical constraints. The superstructure of such a CO2 network is shown schematically in Figure 1. Additional CO2 emissions
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Figure 1. Superstructure for a CO2 network.
PROBLEM STATEMENT The formal problem statement addressed in this work is as follows: • The CCS system is assumed to be comprised of m CO2 sources and n CO2 sinks. • The planning horizon spans the operating lives of all CO2 sources in the system and ranges from t = 0 to t = tmax. • Each CO2 source i (i = 1, 2, ..., m) is characterized by fixed captured CO2 flow rate that corresponds to the maximum removal from the plant’s flue gas. Furthermore, the start and end of the operating life of each source i is also defined. • Each CO2 sink j (j = 1, 2, ..., n) is characterized by an upper limit for CO2 storage capacity, as determined by geological characteristics of the storage site. The earliest time of availability of each sink j is also specified; however, the time at which storage capacity limit is reached is a variable which depends on the rate at which CO2 is actually injected into it. • It is assumed that any given CO2 source i may be connected to only one CO2 sink j (i.e., no outward branching is allowed); however, a CO2 sink j may be linked to multiple CO2 sources. • Temporal issues arise in planning CCS systems since the operating lives of CO2 sources and sinks may not completely coincide; thus, source−sink matches need to be made during periods of overlap. A minimum duration of
arising from the need to generate more electricity to compensate for CCS power losses are also taken into account.
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MINLP OPTIMIZATION MODEL The objective is to maximize reduction of CO2 emissions, accounting for both CO2 captured and the penalties from CO2 emissions of compensatory power generation: max ∑ ∑ (Ti end − Tij start)SiBij i
−
j
∑ ∑ (Tiend − Tijstart)PiBijC i
j
(1)
where variable Tijstart is the time at which source i links to sink j; parameter Tiend is the time at which source i ceases to operate; parameter Si is the CO2 capture rate from source i; binary variable Bij signifies the connection of source i to sink j; parameter Pi is the power loss from source i if CO2 is captured; and C is the CO2 intensity (or carbon footprint) of compensatory power to make up for CCS energy losses. Thus, the first term of eq 1 gives the amount of CO2 captured, while the second term gives the additional CO2 emissions as a consequence of the need to make up for power losses. Note that the bilinear product of variables Tijstart and Bij makes eq 1 nonlinear. Then, each CO2 sink is subject to the constraint
∑ (Tiend − Tijstart)SiBij ≤ Dj i 10016
∀j (2)
dx.doi.org/10.1021/ie202821r | Ind. Eng. Chem. Res. 2012, 51, 10015−10020
Industrial & Engineering Chemistry Research
Article
Bij = 1 and to be 0 when Bij = 0. Substituting eq 8 into eq 1 gives
where parameter Dj is the CO2 storage capacity of sink j. It can be seen that this constraint contains the same bilinear term as eq 1. Also, each CO2 source can be connected to only one sink (i.e., no branching is allowed):
max ∑ ∑ (Ti endBij − Zij)Si − i
∑ Bij ≤ 1
j
(12) (3)
Likewise, substituting eq 8 into eq 2 gives
The starting time at which source i is connected to sink j must not come before the availability of both the source i and the sink j. The starting time of the connection between a source and a sink must be higher than the maximum of Ti and Tj, that is, Tijstart ≥ max{Ti, Tj}, where parameter Ti is the time at which source i begins to operate and parameter Tj is the earliest time of availability of sink j. Mathematically, this constraint can be expressed as Tij start ≥ Tj
∀ i,j
(4)
Tij start ≥ Ti
∀ i,j
(5)
∑ (TiendBij − Zij)Si ≤ Dj
(Ti end − Tij start) ≥ T minBij
∀ i,j
∀ i,j
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(6)
CASE STUDY 1 This case study involves planning for CCS over a time horizon of 40 years given five hypothetical power plants as CO2 sources and two geological reservoirs as sinks, whose main characteristics are shown in Tables 1 and 2, respectively. In this case
(7)
Table 1. CO2 Source Data for Case Study 1
while non-negativity constraints for continuous variables in the system are redundant by virtue of eqs 4 and 5. Note that this is a MINLP model due to the bilinear terms that occur in eqs 1 and 2. Given m sources and n sinks, the model has (m × n) binary variables and (m × n) continuous variables. Due to the computational difficulties that arise in solving MINLP problems, this preliminary model is linearized to yield a MILP model in the next section.
capacity source (MW) 1 2 3 4 5 total
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LINEARIZATION TO MILP MODEL To ensure that globally optimal solutions can be found efficiently, the MINLP model in the previous section needs to be rigorously linearized by eliminating bilinear terms.19,20 First, a new variable, Zij, is introduced to replace the bilinear product: start
Bij
Zij ≤ Tij start
∀ i,j
Zij ≥ Tij start − (1 − Bij )M
(10)
∀ i,j
coal coal coal coal natural gas n/a
3 4 2 7 4 20
100 100 70 200 220 690
0 to 30 0 to 40 5 to 30 10 to 40 0 to 40 n/a
maximum capture (Mt) 90 160 50 210 160 670
sink
start time, Tj (y)
maximum storage, Dj (Mt)
A B total
0 10 n/a
200 400 600
study, the minimum viable duration of connectivity is assumed to be 20 years and the average carbon footprint of compensatory power generation is assumed to be C = 0.001 Mt/y/MW. The latter figure is equivalent to 0.11 t/MWh, which is about an order of magnitude lower than emissions from power generation using coal; thus, in this case study, the compensatory generation makes use of a relatively clean power mix dominated by low-carbon sources such as renewable. The planning horizon is 40 years, which corresponds to the end of life of Source 5. The total potential CO2 capture during this period is 670 Mt;
(9)
∀ i,j
400 500 250 800 1000 2950
fuel
time of flow power operation, rate, Si loss, Pi Ti and Tiend (Mt/y) (MW) (y)
Table 2. CO2 Sink Data for Case Study 1
(8)
∀ i,j
(13)
Equations 12 and 13 are the linearized forms of eqs 1 and 2. Note that although Tijstart takes on an arbitrary value when Bij = 0, the arbitrariness presents no real problems for decision-making purposes, since whatever value it does assume becomes irrelevant if the model solution specifies that no link should be made in the first place. It can be seen that this formulation results in a MILP model for which any solution found is globally optimal. Even though the linearization is achieved at the expense of adding another (m × n) continuous variable to the model, no significant computational difficulties are expected in real applications of this model for cases of typical size. In the case studies that follow, the model is implemented using the commercial modeling software Lingo 12.021 using a PC with a 2.53 GHz processor and 3 MB of RAM. In both cases, solutions were found with negligible processing time (
