A Graphical Approach for Pinch-Based Source–Sink Matching and

Article pubs.acs.org/IECR

A Graphical Approach for Pinch-Based Source−Sink Matching and Sensitivity Analysis in Carbon Capture and Storage Systems Joseph Angelo R. Diamante,† Raymond R. Tan,*,† Dominic C. Y. Foo,‡ Denny K. S. Ng,‡ Kathleen B. Aviso,† and Santanu Bandyopadhyay§ †

Chemical Engineering Department/Center for Engineering and Sustainable Development Research, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines ‡ Department of Chemical & Environmental Engineering/Centre of Excellence for Green Technologies, University of Nottingham, Malaysia, 43500 Semenyih, Selangor, Malaysia § Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India ABSTRACT: Carbon capture and storage (CCS) is regarded as an important interim technology for the reduction of carbon dioxide (CO2) emissions from large industrial facilities such as power plants and refineries. CCS involves capture of concentrated CO2 streams from point sources (industrial flue gases), followed by subsequent secure storage in an appropriate natural reservoir. Such reservoirs include various geological formations such as depleted oil or gas wells, inaccessible coal seams, and saline aquifers. In practice, such storage sites will have limitations on both CO2 storage capacity and injection rate, subject to geological characteristics. In this work, a graphical approach is proposed for matching multiple CO2 sources and storage sites (sinks) optimally within a predefined geographical region. The technique is developed on the basis of analogies with existing graphical pinch analysis approaches for the synthesis of industrial resource conservation networks (RCNs). Generalized principles for optimal CO2 source−sink matching based on pinch analysis insights are discussed in this work. In addition, sensitivity of the system to the uncertainties that occur in CCS planning (e.g., variation of actual injectivity and capacity as well as options for increase or decrease of source lifetime) is considered. Realistic case studies are shown to illustrate these various aspects of the methodology.

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pipeline infrastructure.9,10 MILP models have also been used for multiperiod CO2 allocation with discrete10,11 or continuous time,12,13 while approaches based on mixed-integer nonlinear programming (MINLP) combined with metaheuristic algorithms14 have been proposed. Other models focused on the grid implications of retrofitting power plants.15,16 Geological reservoirs in which the captured CO2 will be stored are evaluated through geological surveys. These techniques contain an inherent uncertainty based on the scale of the survey as well as the type of the site to be surveyed.17,18 The injectivity and capacity of a certain geological sink is characterized by parameters such as its porosity (i.e., the fraction of a formation volume that can be occupied by injected fluid) and permeability (i.e., the extent of connectivity of pore space that allows transport of the injected fluid within the formation) of the structure. Geological sinks are expected to be heterogeneous; properties such as permeability and porosity vary significantly across the storage reservoir.19 The properties across the geological sinks may, in fact, be much different from the initial estimates given in the geological surveys. This may affect the design and planning of the overall CCS system. Additional information regarding the uncertainties associated

INTRODUCTION In addition to strategies involving energy efficiency enhancement and increased use of low-carbon energy sources, carbon capture and storage (CCS) is widely considered as an essential technology for mitigating climate change by reducing industrial greenhouse gas emissions. The International Energy Agency (IEA) has projected that in order to achieve a desired emissions level of 14 Gt/y by 2050 at the lowest cost, 19% of the total reduction in emissions must come from CCS.1 Worldwide evaluation of geological reservoirs has estimated that over 236 Gt of CO2 can be captured and stored by 2050.2 On the basis of the proposed reduction of carbon dioxide (CO2) emissions set by the IEA (i.e., approximately 9 GT/y from CCS out of a total reduction of 48 Gt/y by 2050),1 the reservoirs will last approximately three decades. CCS entails capturing relatively pure CO2 streams from point sources through techniques such as flue gas scrubbing, precombustion capture through gasification-based combined cycles, and oxy-fuel combustion. CO2 may then be stored in various reservoirs such as depleted oil and gas wells, inaccessible coal seams, saline aquifers, and other geological structures.3 Various process systems engineering techniques have been proposed for the planning of the deployment of CCS on a large scale, including insight-based analysis,4,5 rule-based algorithms,6 and various mathematical programming models.7−16 For the specific problem of source/sink matching, there are early works on enhanced oil recovery application,7 a nonlinear programming (NLP) model with stream pooling,8 and mixed integer linear programming (MILP) models for © 2012 American Chemical Society

Special Issue: PSE-2012 Received: Revised: Accepted: Published: 7211

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retrofit; alternatively, this stream is merely released to the atmosphere if CO2 capture is not implemented. Furthermore, the operating life of each source i is also defined. (iii) Each CO2 sink j (j = 1, 2, ..., n) is characterized by an upper limit for CO2 storage capacity which is the total amount of CO2 that can be stored in the sink over its lifetime; as well as the injectivity or the maximum rate at which CO2 may be injected into each sink. Both of which are based on the geological characteristics of the storage site, as determined by site surveys. (iv) The main objective is to determine thetarget, i.e., the minimum amount of unutilized CO2 storage capacity by matching CO2 sources and sinks, given these specified temporal and physical constraints. This is equivalent to the maximization of CO2 storage capacity utilization in various sinks. (v) The appropriate source−sink matching of the CCS system will then be determined based on the pinch target. (vi) Furthermore, pinch-based sensitivity analysis will be done to determine the influence of changes in the sink injectivity, sink capacity, and source life on the system target.

with a CCS system will be presented later, along with case studies to illustrate the target changes that may occur. A summary of the sources of uncertainty in CCS systems is given in Table 1. Table 1. Typical Sources of Uncertainty in CCS17−19 uncertainty

description and examples

sink injectivity

• porosity and permeability of geological formations vary within the same system • injection of CO2 in geological formations may cause swelling in coal formations leading to reduced permeability and injectivity • options to add injection wells within the same geological formation will increase the overall injectivity

sink storage capacity

• initial estimates from geological surveys are never completely accurate and different survey methods may give different results • the operating capacity may be less than the estimated capacity due to increase in well pressures constraining the injectivity • initial estimates may not show a complete geography and a portion of the geological sink may not be accessible for storage

source life

• the life of a given power plant may be cut short or extended depending on economic considerations • the lives of power plants are often extended due to increases in energy demand.

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TARGETING AND SOURCE−SINK MATCHING METHODOLOGY The targeting procedure used in this work is based on the MRPD approach,22,23 and is hereby referred to as the CO2 capture and storage pinch diagram (CCSPD). As with all pinchbased techniques, it requires that each source and sink be characterized in terms of “quantity” (amount of CO2 associated with the source or sink, typically measured in megatons or Mt) and “quality” (the reciprocal of the lifespan of the source or sink, measured in 1/year or y−1). For the latter parameter, a sink/source with longer lifespan is of better quality, as compared to that of shorter lifespan, because a longer lifespan for any given CO2 load places less demand on the reservoir injection rate limits. Note that an alternative or dual formulation may also be used, where the flow rate is used as the “quantity” index and the lifespan is used as the “quality” index. However, such a formulation minimizes the surplus injectivity of the sinks in the system, and not the unused CO2 storage capacity, and thus its direct interpretation is not as useful for purposes of maximizing the amount of CO2 captured and stored. The approach that is used here allows for direct minimization of unused storage capacity and subsequent maximization of total stored CO2, which is more relevant to CCS objectives. The corresponding linear programming model is shown in the appendix. The main steps for targeting using CCSPD and source−sink matching are given as follows: (1) The sources are first ranked in order of ascending numerical value of their quality indices. Since the quality index is simply the inverse of duration, the CO2 source with the longest lifespan is ranked first, and the rest are listed based on progressively shorter operating lives. (2) The “load” for each source is calculated by multiplying the “quantity” and “quality” index. Note that the resulting value is measured in megatons per year (Mt/y), and is thus actually the CO2 flow rate of the source. (3) The source composite curve is drawn using the cumulative “quantity” index as the horizontal axis and the cumulative “load” index as the vertical axis. Each segment of this composite curve corresponds to one source. The sources are plotted end to end, in the same manner as with graphical summation of vector quantities.

From a systems standpoint, one key problem in planning the deployment of CCS is matching CO2 sources with the appropriate sinks. This problem is structurally analogous to the synthesis of resource conservation networks (RCNs)20 as well as carbon-constrained energy planning.21 The specific graphical procedure used in this work is based on the material recovery pinch diagram (MRPD)22,23 which was developed for targeting minimum fresh resource consumption in an RCN. However, there are various pinch techniques described in a recent review24 which are equivalent to MRPD, and may thus be used as alternative solution techniques. Such insight-based approaches have been shown to be an effective complement to mathematical programming based strategies, especially for decomposing difficult problems into computationally tractable subproblems. The rest of the paper is organized as follows. A formal problem statement is given, followed by a description of the methodology and an illustrative case study. Subsequent examples then illustrate the use of pinch-based insights to determine the effects of uncertainties in system parameters on CCS planning. Note that the approach used is based on the analysis of process changes in RCNs.25,26 Finally, conclusions and future work are given.

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PROBLEM STATEMENT The formal problem statement addressed in this work is as follows: (i) The CCS system is assumed to be composed of m CO2 sources, and n CO2 sinks; all of which are available at the start of the planning horizon. The latter period extends up to the end of life of the last CO2 source. (ii) Each CO2 source i (i = 1, 2, ..., m) is characterized by fixed potential captured CO2 flow rate that corresponds to the maximum annual removal from the plant’s flue gas. This potential flow rate represents the maximum amount of CO2 that can be captured from the source if the decision is made to 7212

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this region above the pinch point. Figure 1b illustrates the orientation of an optimal CCSPD. (6) The CO2 allocation network showing matches between sources and sinks may be determined using the pinch “golden rule” combined with systematic techniques such as the nearest neighbor algorithm (NNA).23 If necessary, the resulting allocation may be modified using various source shift methods to give an improved network.27−30 These steps will be illustrated in Example 1 which is discussed in the following section. Example 1: Four Sources and Two Sinks Problem. In this example, there are four CO2 sources and two CO2 sinks, with relevant data as shown in Table 2. Note that the sources

(4) The previous three steps are repeated for the sinks, to generate the sink composite curve. Note that the “load” for the sink represents its maximum injectivity limit. (5) The relative positions of the two composite curves then provide the basis to determine the system target. The source composite curve must stay below and to the right of the sink composite curve. If this geometric condition is not met, as in Figure 1a, then the current solution is infeasible. The region

Table 2. Quantity and Quality Indices and CO2 Loads for Sources and Sinks in Example 1 amount of CO2 (Mt)

lifespan (y)

1/lifespan (y−1)

CO2 flow rate (Mt/y)

40 30 25 20

0.025 0.033 0.04 0.05

5 10 8 5

sinks

200 300 200 100 800 amount of CO2 (Mt)

1 2 total

750 250 1000

source 1 2 3 4 total

lifespan (y)

1/lifespan (y−1)

CO2 injectivity limit (Mt/y)

50 10

0.02 0.1

15 25

generate a combined 800 Mt of CO2 throughout the entire planning period, while the combined storage capacity of the sinks is 1000 Mt. Thus, it may seem at first that it will be possible to capture and store all of the CO2 in the system. An optimal solution may be found by plotting the CCSPD in Figure 2. The distance by which the source composite curve shifted to the right gives the targeted unutilized storage capacity as 250 Mt (see Figure 2). As the sinks have a combined 1000 Mt of storage capacity, this solution implies that 750 Mt of CO2 can be captured and stored, which is the horizontal span of the overlap of the source and sink composite curves. Note that this targeted amount of CO2 is 93.75% of the 800 Mt of CO2 from the sources. Thus, there is 50 Mt of CO2 which may not be stored in these available sinks, indicated by the opening of the source composite curve on the right (see Figure 2). The source−sink matching can be solved by treating the above-pinch and below-pinch regions separately, either by inspection or through the NNA23 (for more complicated cases). First, the pinch location allows the problem to be decomposed into two smaller subproblems; in this case, there is one sink below the pinch and another above the pinch. The unused capacity below the pinch is then treated as a fictitious stream that is analogous to a pure, fresh source in RCN applications.20 Note that, because cross-pinch transfer of CO2 is forbidden, it can immediately be deduced that the blank cells in the source−sink matching matrix20 (Table 3) should have zero allocation. Starting from the sink of longest potential operating life, the quantity and load requirements are met by mixing streams from its “nearest neighbors” (i.e., those with quality levels just above and just below the source requirement). The proportions are established via linear mixing rules. For example, we find that all 200 Mt of Source 1 can be accommodated in Sink 1. Following a similar procedure we can then find the

Figure 1. Generic CCSPD showing (a) infeasible and (b) optimal solutions.

where the source composite curve overlaps the sink composite curve indicates that the flow rate from the source is higher than the injection rate that can be handled by the sink. The target may be determined by shifting the source composite curve horizontally to the right, until the condition is just met, where the two composite curves just meet each other. As a result, the two composite curves will be tangent to each other at the pinch point (note that in some instances, there may be multiple pinch points). The distance by which the source composite curve was shifted is the minimum unutilized CO2 storage capacity (in Mt). The overlapping region between the two composite curves indicates the amount of CO2 that can be stored in the sinks. The opening of the source composite curve on the right indicates that the current CO2 storage capacity is insufficient for use for the given CCS planning problem, and hence more storage capacity is needed. This may be satisfied by developing more CO2 storage, or the captured CO2 may be sent to external storage. Alternatively, this deficit may be interpreted by making a decision not to capture the CO2 from the affected plants in 7213

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Figure 2. CCSPD showing optimal solution for Example 1.

predicated on the possibility of finding a second storage site once the current one is fully utilized. On the other hand, the authority may want to explore opportunity to store a CO2 load in a nearby geographical region (e.g., a different country). The third alternative interpretation is that source 4 will be linked to sink 2 for the last 10 years of its operating life. Thus, the plant is only retrofitted for capture after the first ten years. This scenario means that emissions during the first 10 years are released to the atmosphere, and will allow for flexibility if more stringent emissions targets are required in the future. It should be noted that similar ambiguity exists above the pinch point in conventional applications such as RCNs; in the case of this approach, the principal objective is to determine system targets. Subsequent detailed planning of CCS systems is best done with mathematical programming to be able to consider other factors (e.g., detailed pipeline network topology and discounting of CO2 emissions).11,12,31

Table 3. Source−Sink Matching Matrix for Example 1 sink 1 (Mt) source 1 source 2 source 3 source 4 surplus capacity

sink 2 (Mt)

storage deficit (Mt)

200 50 0

0 50

200 300

250

source−sink allocation for all the other sinks. Details are omitted here due to space limitations, but a full description of the methodology can be found elsewhere.20,23 The resulting optimal allocation for this system is given in Table 3. This result illustrates that, below the pinch point (with sink 1, sources 1 and 2), there is surplus storage capacity, and the main bottleneck for CCS is the injection rate limit into the sinks in this region. On the other hand, there is surplus injectivity above the pinch point (with sink 2, sources 3 and 4); however, this region has insufficient storage capacity such that only half of the CO2 from source 4 can be stored. Different interpretations of the solution are as follows: The first interpretation is that only half of the CO2 from source 4 will be captured throughout its 20 years of operation. The injection will only handle 2.5 Mt/y (= 50 Mt/20 years). If the planning is done at the early stage, we will have to refine the planning target, in order not to capture the remaining 50 Mt CO2 load. Such an option is possible since many power plants actually comprise multiple identical power generation units at the same site. Thus, partial capture means retrofitting only half of the units within the plant for CO2 capture. An alternative interpretation is that source 4 will be linked to sink 2 during the first 10 years of operation while, and alternative storage site is developed for the remaining 50 Mt of CO2 that will be stored in the final 10 years of the life of source 4. This may be considered as a high-risk interpretation that is

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PINCH-BASED SENSITIVITY ANALYSIS TO PROCESS CHANGES As discussed previously, the planning of CCS systems is characterized by high levels of inherent uncertainty in the characteristics of both sinks and sources. Thus, a pinch-based sensitivity analysis procedure is developed in this work to determine the effect of such uncertainties on the system targets. There are two main steps: (1) A variant of the plus/minus principle for RCNs26 may be used to assess the effects of uncertainties of source and sink characteristics on the overall target, as potential adjustments are made in response to events which occur during the planning horizon. (2) Note that the adjustment in the system using the plus/minus principle may change the order of the sources and sinks in the composite curve. In such cases, the composite curves will have to be reconstructed following the steps described above. The order will still be based on the quality measure. 7214

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point, while the region above the pinch refers to the portion above the highest pinch point. It is important to note that CCS planning involves long time horizons spanning multiple decades, and that significant uncertainties arise for both sinks and sources as mentioned previously. Illustration of the effects of changing sink characteristics will be demonstrated next. For ease of discussion, the current scenario is termed as the base case. Scenario 1: Increase of Sink Capacity. The planning of CCS systems assumes that the geological survey of the sink determines its maximum storage capacity. Estimates for any given site may vary depending on the specific survey technique used.17,18 Note that further surveys may be done, at additional expense, to obtain more precise estimates (and hence possible increases) of a sink’s storage capacity. In this scenario, it is first assumed that additional data leads to a revised estimate of the storage capacity of sink 1, which is below the lowest pinch point, by an additional 50 Mt. The CCSPD for this scenario is replotted in Figure 4. Note that all sinks and sources data remain the same, with the exception for sink 1 with a capacity of 300 Mt instead of 250 Mt as before. In Figure 4, it can be seen that the total captured CO2 that can be sent to storage remains at 750 Mt, which is identical to that in the base case. In other words, the increase of storage capacity has no effect on the amount of CO2 that can be stored. As discussed in Example 1, in the region below the pinch, the storage is limited by the injectivity of the sink, and not the capacity. Thus, any additional storage capacity remains unutilized. Next, we assume that there is a revised estimate increasing the storage capacity of sink 3, which is above the pinch point, by 50 Mt. The CCSPD is replotted in Figure 5 using the same data in Table 4, except that the capacity of sink 3 is assumed as 200 Mt instead of 150 Mt. In Figure 5, it is noted that the total captured CO2 that can be stored has now increased to 800 Mt

The pinch-based sensitivity analysis will be illustrated in Example 2. Example 2: Effects of Changes in Sink Characteristics. In this example, a CCS system consisting of four sinks and four sources is analyzed. The source and sink baseline data are given in Table 4. Note that in this example the sources generate a Table 4. Quantity and Quality Indices and CO2 Loads for Sources and Sinks in Example 2 source 1 2 3 4 total

amount of CO2 (Mt)

sinks

150 250 200 400 1000 amount of CO2 (Mt)

1 2 3 4 total

250 250 150 200 850

1/lifespan (y−1)

CO2 flow rate (Mt/y)

0.033 0.04 0.05 0.05

5 10 10 20

1/lifespan (y−1)

CO2 injectivity limit (Mt/ y)

0.02 0.04 0.1 0.1

5 10 15 20

total load of 1000 Mt of CO2; while the total capacity of the storage sink is only 850 Mt of CO2. Using the CCSPD, it is determined that a total of 750 Mt of the captured CO2 will be sent to to storage (see Figure 3). There is an unutilized capacity of 100 Mt, and a deficit of 250 Mt of CO2 which may be captured and sent to external storage; alternatively, a decision may be made not to capture this amount of CO2 from the sources (see Figure 3). Note that double pinch points exist for this case, represented by the both ends of the sink 2 segment. For this kind of multiple pinch case, the region below the pinch refers to the portion of the CCSPD below the lowest pinch

Figure 3. CCSPD for example 2 (base case). 7215

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Figure 4. Effect of increase in sink capacity below the pinch for example 2 (scenario 1).

Figure 5. Effect of increase in sink capacity above the pinch for example 2 (scenario 1).

(from 750 Mt in the base case), indicated by the overlapping horizontal distance of the source and sink composite curves. This increased capture amount is equal to the increased capacity of sink 3. This result shows that, above the pinch point, the main physical limitation is the storage capacity of the sink, and not the sink injectivity. From a practical CCS planning standpoint, these results show that investment in additional geological surveys to determine a possible increase of the storage size should be

concentrated on the sinks above the pinch rather than those below the pinch point. In general, similar results can be expected for decreases in sink storage capacity (i.e., decrease in storage capacity of sinks above the pinch will have a corresponding decrease in the total capture of the system). However, such a scenario is not discussed here, as the CCS planning process will generally use conservative data (i.e., the lower bound of the storage capacity estimates). Thus, 7216

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Figure 6. Effect of increased injectivity above the pinch for example 2 (scenario 2).

Figure 7. Effect of increased injectivity below the pinch for example 2 (scenario 2).

characteristics of the rock strata (i.e., porosity and permeability). Note that the former can be controlled through engineering interventions (the injectivity can be increased through addition of injection wells at the storage site), while the latter cannot. The sink injectivity limits the rate of injection of CO2. Besides, further geological surveys of the formation may determine that the sinks possess different porosity and permeability from the initial estimate. In this scenario, we

additional information from site surveys is more likely to indicate increases in formation size. Scenario 2: Increase in Sink Injectivity. Other than sink capacity, the injectivity of a sink is also another important parameter in CCS planning. Therefore, in this scenario, the effect of sink injectivity on CCS planning is studied. The injectivity of a certain geological sink is determined by factors such as the number of CO2 injection wells and the inherent 7217

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Figure 8. Effect of decreased injectivity above the pinch for example 2 (scenario 3).

Figure 9. Effect of decreased injectivity below the pinch for example 2 (scenario 3).

point, the limiting factor is the sink storage capacity and not the injectivity. Next, the injectivity of sink 1, which is located below the pinch point, is analyzed. Suppose that the injectivity of sink 1 has been increased to 10 Mt/y from 5 Mt/y by the addition of injection sites of the sink. The corresponding CCSPD for this scenario is replotted in Figure 7. As shown, the total emissions captured by the system have increased to 850 Mt from 750 Mt. It can also be seen that multiple pinch points still exist for this

assume that process changes have increased the injectivity of sink 4, which is above the pinch point, by 5 Mt/y through the addition of an appropriate number of injection wells. CCSPD for this scenario is generated in Figure 6, with the same data, but with an increase in the injectivity of sink 4 by 5 Mt/y. In Figure 6, it can be seen that the total captured CO2 that may be stored remains at 750 Mt, which is identical to that in the base case. This result illustrates that above the pinch 7218

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Figure 10. Effect of extended life of source below the pinch for example 2 (scenario 4).

case; however one of the original pinch points has now moved to the origin, resulting in a threshold problem without any unutilized capacity that resembles the RCN cases.20 This revised result clearly shows that in the region below the pinch, the physical limitation is the injectivity of the sink, and not the storage capacity. The results show that any efforts to increase the injectivity of the sinks through the addition of injection wells and other methods should be prioritized in the sinks which fall below the pinch point. Such efforts will not significantly impact the system when applied to sinks above the pinch point. Scenario 3: Decrease in Sink Injectivity. The inherent injectivity of geological sinks may change over time due to physical and chemical reactions brought about by the introduction of CO2. These changes may cause a decrease in the injectivity of the sink over time. The effects of decreased injectivity above and below the pinch point will be illustrated here. In this scenario, the initial assessment of the reservoir injectivity of sink 3 of 15 Mt/y proves to be overestimated and the actual injectivity is found to be only 10 Mt/y. On the basis of the additional information, CCSPD is constructed and shown in Figure 8. It is noted that a decrease of the injectivity of sinks above the pinch point does not affect the total capture of the system, which remains at 750 Mt. This is because there is a surplus of injectivity above the pinch, as seen in Figure 8. Note that the decrease in the injectivity above the pinch point is still limited by the characteristics of the system. In the next scenario, the overestimation of the injectivity occurs in a sink located below the pinch point. To analyze the problem, the injectivity of sink 1, which was initially 5 Mt/y was found to be overestimated and that the actual injectivity is only 2 Mt/y. Using the new data for the injectivity of sink 1, CCSPD is constructed as shown in Figure 9. Note that there is now only a single pinch point. Figure 9 also illustrates that a decrease in

the injectivity of sink 1 has decreased the total stored CO2 to 650 Mt. This can be seen from the reduced horizontal overlap of the sink and source composite curve. This reduction again shows that the main physical limitation of capture below the pinch is the injectivity of the sinks, so that any reduction manifests through decrease of the amount of CO2 captured. These results show that, in actual CCS planning problems, efforts should be taken to ensure that the injectivity of sinks below the pinch point do not fall to maintain the optimum capture of the system. Geological surveys should focus on sinks falling below the pinch point so that better injectivity estimates are obtained. Furthermore, the applicability of putting additional injection wells at the site should also be determined, in order to compensate for the reduction of inherent injectivity. Scenario 4: Increase in Source Operating Life. The initial economic life expectancy of a certain CO2 source such as power plants is determined during the construction of the plant. Such operating lives are typical of any given set of technologies, and generally spans several decades in the case of thermal systems. However, during the course of operations, the actual life of a plant may be altered based on the energy demand or the environmental concerns of emissions. A plant may be refurbished to extend its operating life in order to meet growing electricity demand in a geographical region; alternatively, a plant may be shut down earlier than originally planned due to environmental issues from emissions. On the other hand, inclusion of a fossil fuel-fired power plant in a CCS program may actually serve to increase its service life because of the reduced CO2 emissions that result from retrofits. We will analyze the effect of increasing the operating life of a source both above and below the pinch. In the following scenario, we extend the life expectancy of source 1, which is below the pinch, by 10 years and study the effects on the system. Figure 10 shows the revised CCSPD, with an increase of total load of source 1 by 50 Mt. This value is the total CO2 generated 7219

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Figure 11. Effect of extended life of source above the pinch for example 2 (scenario 4).

by source 1 over the 10 year extension. Figure 10 shows that for the increased source lifetime, we have increased the total stored CO2 to 800 Mt from the original 750 Mt. This outcome shows that, for sources below the pinch, there is an opportunity for increasing the life expectancy of power plants while allowing emissions to be captured and stored. In the next scenario, we will examine the effect of increasing the life of a source above the pinch point. Here, the lifetime of source 3 is increased by 5 years in order to meet the energy demand. Figure 11 shows the revised CCSPD that is generated with an increased load of source 3 of 300 Mt (from 250 Mt). The increase of 50 Mt in the load of source 3 corresponds to the CO2 generated by source 3 over the lifespan extension of 5 years. Figure 11 shows no change in the total stored CO2 (i.e., remains as 750 Mt), with an increase of storage deficit to 300 Mt (from 250 Mt in the base case). This is because above the pinch point, the physical limitation for storage is the total capacity of the sinks. The results show that for sources above the pinch, extending the life expectancy is not recommended, as it incurs a penalty of increased external storage requirement. Cutting short the life of sources above the pinch may also be considered to possibly reduce the CO2 emissions. The results show that from an energy planning standpoint, to meet the energy demand through extending the operating life of power plants, recommendations should be made to increase the life of power plants that fall below the pinch point whenever conditions allow. A similar conclusion can be drawn for cutting short the operating life of a power plant. For sources falling below the pinch point a longer operating life is preferred while above the pinch point shorter operating lifetimes are preferred. Summary of Pinch-Based Insights for CCS Planning. As with other pinch analysis applications, some key insights can be drawn from the CCSPD. General planning principles can be drawn from the case studies: (i) Storage sinks below the pinch

point are limited by the injectivity and not the storage capacity. Improved capture will be achieved by increasing injectivity, for instance through the addition of injection wells. Further geological surveys should be conducted on the sinks to ensure the proper assessment of reservoir properties to allow CO2 to be introduced more rapidly. (ii) Storage sinks above the pinch point are limited by the storage capacity of the sinks, rather than injectivity. Additional geological surveys should thus focus on determining if a higher storage capacity may be realized in the sink. (iii) Increasing the operating life of power plants is recommended for sources below the pinch point. Above the pinch point, extending the operating lives will result in additional external storage requirement. Conversely, cutting short the lifetime of power plants may help in reducing the storage requirement. These three planning principles will help to improve the total captured CO2 of the system and reduce the CO2 emissions of the sources. However, there may be situations in which one of the three principles may not be applied, depending on the characteristics case-specific to a given scenario. For example, some sinks may not allow for additional injection sites due to the stability or risk issues. However, these general principles founded on well-established pinch analysis concepts provide simple but effective guidelines for managing uncertainties in CCS planning.

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CONCLUSION A graphical pinch analysis approach to optimal matching of CO2 sources and sinks in CCS systems has been developed. This technique is based on pinch analysis methods developed for resource conservation networks (RCNs), and as with such insight-based strategies, allows system targets to be determined based on the physical characteristics of the sources and the sinks. Furthermore, pinch-based insights can be used for problem decomposition to determine general guidelines for the 7220

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ACKNOWLEDGMENTS J. A. R. Diamante would like to thank the Philippine Department of Science and Technology (DOST) for providing research funding for the project through the ERDT schlarship program. We also wish to acknowledge additional support from the University Research Coordination Office of De La Salle University (Grant No. 04 RPW AY11-12) and the Commission on Higher Education (CHED) with the PHERNet program on sustainability studies.

synthesis of the CO2 allocation network, and also to facilitate pinch-based sensitivity analysis which is necessary in real-life applications. In particular, the pinch point determines whether or not it is justifiable to invest in additional effort to determine more precise estimates of the capacities and injectivities of potential CO2 storage reservoirs. The pinch point also helps to determine which sources are recommended for extension or reduction of the total lifespan. Examples have been used to demonstrate the methodology. Note that this methodology may also be implemented using various equivalent graphical or algebraic pinch techniques for source−sink problems.20,24,25 In this paper, all sources and sinks are assumed to be in close geographical proximity, that is, pipeline costs between various sources and sinks are neglected. Future research work may be directed to address this issue in conjunction with mathematical programming models. Extensions of the methodology developed here will also address issues on determination of appropriate power source to be built as well as problems on multiperiod planning of CCS systems. The latter problem may also take into account discounting rates to account for the manner in which time affects the amount of damage associated with CO2 emissions.

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Dj = storage capacity of sink j (Mt) Qi = quality index of source i (y−1) Qmax = quality index limit of sink j (y−1) j Si = total amount of emissions from source i (Mt) Variables

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APPENDIXEQUIVALENT LINEAR PROGRAMMING MODEL The equivalent linear programming (LP) formulation of the graphical pinch approach is shown here. It is structurally similar to LP models for RCN22,23 and carbon-constrained energy networks:21 (A-1)

∀i

Fj + ΣiR ij = Dj

(A-2)

∀j

ΣiQ iR ij ≤ Q jmax Dj Fj ≥ 0 R ij ≥ 0

∀j

∀j ∀ i, j

(A-3) (A-4) (A-5) (A-6)

The objective function is to minimize the unutilized storage capacity in Mt (eq A-1). The carbon load balance (in Mt) for sources and sinks are given by eq A-2 and eq A-3, respectively. The slack in eq A-2 indicates the CO2 that cannot be captured in available sinks. The carbon flow rate balance at the sinks (in Mt/y) is given by eq A-4, where the right-hand side of the constraint (Qmax j Dj) is the sink injectivity. Note that no separate flow rate balances are needed for the sinks, as these equations are made redundant by eq A-2. All system variables are nonnegative (eq A-5 and A-6).

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Fj = unutilized storage capacity of sink j (Mt) Rij = CO2 emissions stored from source i to sink j (Mt)

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subject to: ΣjR ij ≤ Si

NOTATION i = source index j = sink index

Parameters

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minimise ΣjFj

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: (R.R.T.) [email protected]; (J.A.R.D.) [email protected]; (D.C.Y.F.) dominic.foo@nottingham. edu.my; (D.K.S.N.) [email protected]; (K.B.A.) [email protected]; (S.B.) [email protected]. Notes

The authors declare no competing financial interest. 7221

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