Uvsccsce 2012 Chem_Eng_Sci Targeting Carbon Capture and Storage

Author's personal copy

Targeting and design of energy allocation networks with carbon captureand storage

Akshay U. Shenoy a, Uday V. Shenoy b,n

a Narsee Monjee Institute of Management Studies, NMIMS, V.L. Mehta Road, Vile Parle (W), Mumbai 400056, Indiab Synew Technologies, A 502, Galleria, Hiranandani Gardens, Powai, Mumbai 400076, India

a r t i c l e i n f o

Article history:

Received 22 July 2011

Accepted 20 September 2011Available online 29 September 2011

Keywords:

Design

Energy

Optimization

Systems engineering

Environmental emissions

Carbon footprint

a b s t r a c t

The mathematical formulation for targeting during energy allocation with carbon capture and storage

(CCS) is formally developed. For operating-cost optimization with zero excess, it is shown that CCS

sources may be regarded as resources with their cost taken as the increment over the non-CCS option.

CCS sources along with clean-carbon resources may then be targeted by profile matching with the

limiting composite to establish optimal primary cases. The limiting composite curve is itself sacrosanct

and obtained by a single computation of the composite table algorithm (CTA) including only non-CCS

sources. Carbon emission networks (CENs) are designed by the nearest neighbors algorithm (NNA).

A cost criterion is established to determine cost-factor ranges for optimality of the primary cases, and

results validated by solving linear programming (LP) and mixed integer linear programming (MILP)

formulations. The methodology essentially comprises four distinct stages – targeting, network design,

cost analysis, and optimization – with the first two stages not requiring any cost data.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Optimal planning of energy systems subject to carbon foot-print constraints aimed at reducing climate change effects hasbeen the focus of recent research (Tan and Foo, 2007; Foo et al.,2008; Lee et al., 2009; Pekala et al., 2010; Shenoy, 2010). This is indirect response to policies on sustainable development, includingthe Kyoto Protocol, that attempt to balance the expected increasein energy demand and the desirable decrease in greenhouse gases(GHGs) emissions. For instance, emissions targeting and planninghas been done by Atkins et al. (2008, 2009a, 2009b) for the NewZealand electricity industry, and by Crilly and Zhelev (2008, 2009)for the Irish electricity generation sector.

Carbon capture and storage (CCS), alternatively referred to ascarbon capture and sequestration, is a technology for mitigatingthe contribution of carbon emissions to global warming, bycapturing carbon dioxide (CO2) from large point sources such asfossil-fired power plants and storing it in a manner to prevent itfrom entering the atmosphere. Some CCS techniques (Steeneveldtet al., 2006; Wall, 2007; Yang et al., 2008) with capability forminimally 80% CO2 removal include post-combustion capture(PCC where CO2 is absorbed from flue gases using chemicalagents), oxyfuel combustion (Oxyf where pure oxygen rather

than air is used for combustion), and integrated gasificationcombined cycle (IGCC where self-generated hydrogen is utilizedfor combustion).

The objective of this work is to develop an algorithmicprocedure with a graphical representation for the carbon-con-strained energy planning problem with CCS that will identify anoptimum strategy for integrating sources and demands to mini-mize operating cost. CCS may be simply viewed as a means topurify fossil-fuel energy sources; then, from the standpoint ofprocess integration (Shenoy, 1995; El-Halwagi, 1997, 2006;Smith, 2005; Kemp, 2007), CCS is analogous to the concept ofregeneration or interception in resource conservation networkssuch as those for water and hydrogen (Agrawal and Shenoy, 2006)but with some differences. One basic difference is the possibilityof multiple CCS sources in carbon emission networks (CENs),which is in contrast to typically a single regeneration stream inwater and hydrogen networks. The problem of targeting multipleresources has been studied earlier in the context of heat exchan-ger networks (Shenoy et al., 1998; Shethna et al., 1999), massexchanger networks (Fraser et al., 2005) and resource allocationnetworks (Shenoy and Bandyopadhyay, 2007). Here, the unifiedconceptual approach (Agrawal and Shenoy, 2006; Prakash andShenoy, 2005a), which essentially depends on the composite tablealgorithm (CTA) for targeting and the nearest neighbors algorithm(NNA) for network design, is adapted to handle multiple CCSsources as demonstrated below. The unified conceptual approach(with the CTA and NNA) has been successfully used by Deng and

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Chemical Engineering Science

0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2011.09.041

n Corresponding author. Tel.: þ91 22 40104615.

E-mail address: [email protected] (U.V. Shenoy).

Chemical Engineering Science 68 (2012) 313–327


Feng (2009) for an optimal water network with regeneration/recycle in an alumina plant to obtain zero wastewater dischargeand significant freshwater savings.

The proposed algorithmic procedure for CENs is associatedwith a graphical representation called the limiting compositecurve, in which net deficit/surplus may be conveniently repre-sented on an emission factor versus emission load diagram(Shenoy, 2010) similar to the temperature versus enthalpydiagram in heat exchanger network synthesis (Shenoy, 1995) orthe concentration-mass diagram in mass exchanger networksynthesis (El-Halwagi and Manousiouthakis, 1990) or the waterpurity versus contaminant load diagram in the design of waternetworks (Wang and Smith, 1994; Hallale and Fraser, 1998). Theconcepts and algorithms are illustrated below through a casestudy based on the data given by Pekala et al. (2010), who studiedCCS options to retrofit fossil-fuel power plants.

2. Problem statement and mathematical formulation

Based on the problem statement for carbon-constrainedenergy planning (Tan and Foo, 2007; Pekala et al., 2010), adetailed mathematical formulation for the targeting problem ofenergy allocation with carbon capture and storage (CCS) isdeveloped below. A set of ND demands (regions) and a set of NS

sources are given. Each demand Dj has an energy requirement FDj

and a carbon footprint or emission load that must not exceed aspecified maximum limit MDj. Each source has a known avail-ability FSi,total. Without CCS, each source Si has a specified carbonintensity/emission factor CSi and a cost per energy unit cSi. WithCCS (denoted by single prime), each source Si

0 has a specifiedemission factor C0Si and a cost per energy unit c0Si. A set of (NRþ1)clean-carbon resources (zero-carbon R0 and/or low-carbon Rk) is

available. Each resource has a specified carbon intensity/emissionfactor CRk and a cost per energy unit cRk. The excess (or unused)energy (denoted by subscript E) may be treated as an externaldemand or waste (Shenoy and Bandyopadhyay, 2007) withoutany restrictions.

The network for the energy allocation problem with CCS isrepresented in the form of a matching matrix (Prakash andShenoy, 2005b; Das et al., 2009; Shenoy, 2010) in Fig. 1. Thevalues of emission load M, energy F, and emission factor C arenon-negative real numbers. The three quantities are related by

M¼ FC ð1Þ

In general, the following conservation balance equations andlinear mixing rules fundamentally hold for energy and emissionload, when sources S1 and S2 are mixed to satisfy demand D.

FS1þFS2 ¼ FD ð2aÞ

FS1CS1þFS2CS2 ¼ FDCD ð2bÞ

The objective is to match sources (after appropriate mixing, ifnecessary, as per Eqs. (2a,b)) and demands, so as to minimize theoperating cost OC given by the following expression:

OC ¼XNR

k ¼ 0

cRkFRkþXNS

i ¼ 1

c0SiF0Siþ

XNS

i ¼ 1

cSiðFSi�f iEÞ ð3aÞ

In Eq. (3a), the three terms signify clean-carbon resources, thesources with CCS, and the sources without CCS (excluding theexcess or unused energy fiE), respectively. On noting that the CCSand non-CCS portions of each source total the known availability(i.e., FSi

0 þFSi¼FSi,total), Eq. (3a) may be rewritten as

OC ¼XNR

k ¼ 0

cRkFRkþXNS

i ¼ 1

ðc0Si�cSiÞF0Siþ

XNS

i ¼ 1

cSiFSi,total�XNS

i ¼ 1

cSif iE ð3bÞ

Fig. 1. General representation of an energy allocation problem with CCS as a matching matrix.

A.U. Shenoy, U.V. Shenoy / Chemical Engineering Science 68 (2012) 313–327314


In Eq. (3b), the four terms signify the cost of clean-carbonresources, the additional cost of sources with CCS (with referenceto the non-CCS option), the cost of total available sources (whichis a constant), and the cost of excess or unused energy, respec-tively. Since the third term is constant and the fourth term is zerofor the case of CCS with no excess energy, the objective functionto be minimized consists of the first two terms in Eq. (3b). For thecase of CCS with zero excess, Eq. (3b) importantly indicates thatCCS sources may be regarded as clean-carbon resources with theircost per energy unit taken as (c0Si�cSi).

Let fij denote the energy allocated from non-CCS source i todemand j, and f 0ij denote the energy allocated from CCS source i todemand j. Further, let fkj represent the energy allocated fromclean-carbon resource k to demand j, and fiE designate the excessenergy from non-CCS source i. Thus, f symbolizes the energyallocations for the cell matches of the matching matrix in Fig. 1.Due to the energy conservation in Eq. (2a), the energy balance foreach demand and each non-CCS source is given by

XNR

k ¼ 0

f kjþXNS

i ¼ 1

f 0ijþXNS

i ¼ 1

f ij ¼ FDj for every demand jAND ð4aÞ

XND

j ¼ 1

f ijþ f iE ¼ FSi for every non-CCS source iANS ð4bÞ

The total requirement of each CCS source and each resource iscalculated from

XND

j ¼ 1

f 0ij ¼ F 0Si for every CCS source iANS ð5aÞ

XND

j ¼ 1

f kj ¼ FRk for every resource kANRþ1 ð5bÞ

Eq. (4a) corresponds to the column sum, whereas Eqs (4b),(5a), and (5b) correspond to the row sum for the energy values inthe matching matrix (Fig. 1). As mentioned earlier, the CCS andnon-CCS amounts of each source total the specified availabilityaccording to

F 0SiþFSi ¼ FSi,total for every source iANS ð5cÞ

The total excess energy and the total resource requirement(using Eq. (5b)) may be expressed as

FE ¼XNS

i ¼ 1

f iE ð6aÞ

FR ¼XNR

k ¼ 0

FRk ¼XNR

k ¼ 0

XND

j ¼ 1

f kj ð6bÞ

On taking the summation over all demands and all non-CCSsources (using Eqs. (4a) and (4b), respectively), the followingoverall energy balance over the system is established.

XNR

k ¼ 0

XND

j ¼ 1

f kjþXNS

i ¼ 1

XND

j ¼ 1

f 0ijþXNS

i ¼ 1

FSi ¼XND

j ¼ 1

FDjþXNS

i ¼ 1

f iE ð7aÞ

Using Eqs. (5a),(6a) and (6b), the above overall system energybalance may be compactly rewritten as

FR�FE ¼D1 where D1 �XND

j ¼ 1

FDj�XNS

i ¼ 1

ðF 0SiþFSiÞ ð7bÞ

In an analogous manner, the overall system emission loadbalance (as per Eq (2b)) may be written as

FRCR�FECE ¼D2 where D2 �XND

j ¼ 1

FDjCDj�XNS

i ¼ 1

ðF 0SiC0

SiþFSiCSiÞ

ð7cÞ

As per Eqs. (7b) and (7c), the net system energy deficit (D1)and the net system emission load deficit (D2) are obtained bysubtracting the sum of all sources (CCS and non-CCS) from thesum of all demands. Defining such net system quantities, whichare constant for a given problem, is useful (Bandyopadhyay et al.,1999, 2004; Shenoy, 2010) in process systems engineering.

On using the emission load conservation in Eq. (2b), the carbonfootprint or emission load limit for each demand may beexpressed as

XNR

k ¼ 0

f kjCRkþXNS

i ¼ 1

f 0ijC0Siþ

XNS

i ¼ 1

f ijCSirFDjCDj

for every demand jAND ð8aÞ

An alternative (Pekala et al., 2010) to Eq. (8a) would be anaggregated emission limit (i.e., total emissions of all demandsmust not be exceeded), which is obtained by summing over alldemands. Further, if the availability of clean-carbon resources isrestricted, then each resource may be limited in general to aspecified maximum FRk,max as

FRkrFRk,max for every resource kANRþ1 ð8bÞ

The objective is to minimize the operating cost OC in Eq. (3)subject to the constraints given by Eqs. (4), (5), and (8). As theobjective function and all the constraints are linear, this is a linearprogramming (LP) formulation.

Besides, note that the problem formulation for targetingmultiple resources (Shenoy and Bandyopadhyay, 2007) becomesa special case of the above formulation wherein CCS sources arenot present.

The above LP formulation is solved below through an algebraicprocedure and validated using optimization software. The pro-posed algebraic procedure is based on the limiting compositecurve for carbon emission networks (Shenoy, 2010), whose dataare readily obtained through the Composite Table Algorithm(CTA), first proposed by Agrawal and Shenoy (2006).

3. Representation of CCS sources

The starting point for the Composite Table Algorithm (CTA) isthe representation of sources (and demands) by vertical arrows toconveniently determine their populations in the different emis-sion-factor intervals. For each source (and demand), the arrowbegins at its specified emission factor. All arrows end at anarbitrarily chosen large value of the emission factor. Fig. 2a showsthe representation used in the CTA in terms of separate arrows fora CCS source (with emission factor CSi

0 and energy availability FSi0)

and its corresponding non-CCS source (with emission factor CSi

and energy availability FSi).Fig. 2b shows an equivalent composite representation

obtained by appropriately adding the energy values in the twoemission-factor intervals. Combining gives the energy value as F 0Si

for C0SioCrCSi, and the energy value as F 0SiþFSi¼FSi,total for C4CSi.Thus, in the equivalent composite representation, the non-CCSsource is represented by an arrow with a known constant energyvalue of FSi,total (rather than an unknown variable FSi). Further, inthe equivalent composite representation, the CCS source isrepresented by a line-segment between C0Si and CSi (rather thanan arrow from CSi

0 to an arbitrary large emission-factor value).

A.U. Shenoy, U.V. Shenoy / Chemical Engineering Science 68 (2012) 313–327 315


The equivalent composite representation has two importantimplications. First, the implementation of the CTA from Shenoy(2010) remains unchanged requiring the demands and only thenon-CCS sources (with energy values of FSi,total) to be considered.Second, the CCS sources (represented as line segments) can beregarded as resources and targeted by profile matching with thelimiting composite curve. Note that the limiting composite forcarbon emission networks developed by Shenoy (2010) is thussacrosanct: it remains unchanged for targeting with and withoutCCS because it itself does not include the CCS sources. Further-more, the number of targeting variables associated with sources ishalved because only CCS sources are targeted whereas non-CCSsources (with their total energy availability) are included in theCTA. Both the CTA implementation and the profile matching areillustrated in the next section through a case study.

4. Targeting by profile matching with limiting composite

To illustrate the methodology, the case study from Pekala et al.(2010), which is itself adapted from Tan and Foo (2007), isconsidered. The data for the three demands (three regions withtheir expected energy consumptions FDj in TJ and emission loadlimits MDj in t CO2) and the three sources (natural gas, oil and coalwith their emission factors CSi in t CO2/TJ and total energyavailabilities FSi,total in TJ) are given in Table 1. The values for CDj

in t CO2/TJ and MSi in t CO2 (in parenthesis) in Table 1 are readilycalculated using Eq. (1). The emission factors C 0Si in t CO2/TJ for thethree sources with CCS (S10, S20 and S30) are also provided. Theonly clean-carbon resource is a zero-carbon resource (R0). Oper-ating cost factors for all sources (zero-carbon resource, three CCSsources, and three non-CCS sources) are given in unspecified costunits (Pekala et al., 2010) per TJ of energy (relative to baselinepower generation costs).

The implementation of the CTA (with details available in Shenoy,2010) for this case study is shown in Table 2. The data in Table 2may also be readily generated by the Unified Targeting Algorithm(UTA), which is a generalized CTA recently proposed by Shenoy(2011). The emission-factor C (in the first column) is plotted againstthe cumulative emission load M (in the fourth column) to obtain thelimiting composite curve (dashed line in Fig. 3). The limitingcomposite provides the net deficit (as a function of emission factor)after considering all demands and non-CCS sources with their totalenergy availabilities FSi,total. The clean resource(s) and the CCSsources are excluded because the aim is to target their minimumrequirements as demonstrated next.

4.1. Clean-carbon resource with No CCS source

For the case of zero-carbon (or completely CO2-neutral)resource (i.e., CR¼CR0¼0), referred to as Case A henceforth,targeting may be graphically done by rotating the horizontal axiswith the origin as pivot until it just touches the limitingcomposite curve. The reciprocal of the slope of this rotatedresource target line gives the minimum zero-carbon resourcerequirement. The point where the target profile touches thelimiting composite defines the pinch (Fig. 3). This graphicalprocedure (Shenoy, 2010) is identical in principle to that sug-gested by Wang and Smith (1994) for the determination of theminimum freshwater target.

The mathematical alternative is to use the following equationbased on an emission load balance over the below-pinch region:

MP ¼ FRðCP2CRÞ ð9Þ

where MP is the cumulative emission load of the pinch point on thelimiting composite, CP is the pinch emission factor, and FR is theenergy requirement target for resource R with emission factor CR.

Since the pinch point is not known a priori, the followingprocedure is adopted (Agrawal and Shenoy, 2006; Shenoy, 2010).In accordance with Eq. (9), the possible amount of resourcerequired is calculated on dividing the cumulative emission loadM by (C�CR) in Table 2 and tabulated in the last column. Thepossible resource requirement corresponds to the reciprocal ofthe slope of a line originating from CR on the vertical axis to apoint on the limiting composite curve. Since the resource line can

Table 1Data for case study.

Demands/sources Emission factor C Energy F Emission M Cost factor c

Demand dataD1 (region I) (20) 100 20

D2 (region II) (50) 40 20

D3 (region III) (100) 60 60

Total 200 100

Source dataR0 (zero-C resource) 0 0.045

S10 (CCS—natural gas) 10 0.042

S20 (CCS—oil) 15 0.034

S30 (CCS—coal) 20 0.032

S1 (natural gas) 55 20 (11) 0.025

S2 (oil) 75 80 (60) 0.022

S3 (coal) 105 60 (63) 0.020

Total 160 134

Units: emission factor C in t CO2/TJ, energy F in 104 TJ, emission load M in

106 t CO2, cost factor c in 1/TJ.

C’Si

CSi

CCS Source Si’ non-CCS Source Si

F’Si

FSi,total

C’Si

CSi

CCS Source Si’ non-CCS Source Si

F’Si

F’Si FSi

Fig. 2. Arrow representation of CCS source and corresponding non-CCS source in CTA (a) separately and (b) as equivalent composite.



never be above the limiting composite, the minimum slope isrequired; so, the maximum value in the last column of Table 2gives the minimum resource target. Thus, the zero-carbonresource target FR is 813,333 TJ (as per Table 2) and the corre-sponding emission factor specifies the pinch (75 t CO2/TJ).

From Eqs. (7b) and (7c), D1¼(200–160)�104¼400,000 TJ and

D2¼(100–134)�106¼�34�106 t CO2 on using Table 1 and not

considering CCS sources. Since FR¼813,333 TJ and CR¼0, Eqs. (7b)and (7c) yield FE¼413,333 TJ and CE¼82.258 t CO2/TJ (which isthe minimum emission factor possible for the excess energy whendemands are met at the maximum emission load—the limit ofmaximum environmental cost and minimum economic/operatingcost). In essence, the minimum targets for zero-carbon resourceand excess energy are 813,333 and 413,333 TJ, respectively. Thesetargets and the carbon emission networks that satisfy the targetsare discussed in detail by Shenoy (2010).

4.2. Single CCS source

The zero-carbon resource requirement can be reduced byusing a less expensive CCS source. The absolute minimum zero-carbon resource can be targeted in a manner similar to that usedfor regeneration with recycle for water networks (Wang andSmith, 1994; Agrawal and Shenoy, 2006; Deng and Feng, 2009)as illustrated next. The slope of the limiting composite below C0Si

sets the minimum FR or FE target in accordance with Eq. (7b). Forthis case study, the limiting composite starts at 20 t CO2/TJ(Table 2) and the values of C0Si are 10, 15 and 20 t CO2/TJ(Table 1). Therefore, the slope of the limiting composite belowCSi0 is infinite, and its reciprocal sets the minimum FR or FE as

zero. Since D1¼400,000 TJ, Eq. (7b) gives the absolute minimum

zero-carbon resource requirement (with FE¼0, i.e., zero excess) asFR¼FR0¼400,000 TJ.

For the case of clean-carbon resource with no CCS sources, thetarget profile is a single straight line of constant slope (as in Fig. 3)starting from CR0. When a single CCS source is used along with theclean-carbon resource, the target profile is the composite of twolines: one for the clean-carbon resource starting from CR0, andanother for the CCS source starting from CSi

0 and terminating atCSi. In general, the target profile will comprise three sections,whose arrow representation is shown in Fig. 4a and whoseequations based on emission load balances are as follows:

M¼ FR0ðC2CR0Þ for CrC0Si ð10aÞ

M¼ FR0ðC2CR0ÞþF 0SiðC2C0SiÞ for C0SirCrCSi ð10bÞ

M¼ FR0ðC2CR0ÞþF 0SiðCSi2C 0SiÞ for CZCSi ð10cÞ

As before, the target profile must just touch the limitingcomposite curve (at the pinch) and must always be below it.

Since the pinch is not known a priori, a procedure similar tothat adopted earlier with Eq. (9) is used. With FR0¼400,000 TJ(the absolute minimum zero-carbon resource requirement in thiscase), F 0Si is the only unknown variable and may be readilycalculated from Eqs. (10b) or (10c) for the different points(M, C) of the limiting composite as shown in Table 3. With CR0¼0(for zero-carbon resource), substitution in Eqs. (10b) and (10c)yields the values in Table 3 for F 0S1 (third column with C 0S1¼10 andCS1¼55), F 0S2 (fourth column with C0S2¼15 and CS2¼75), and F 0S3

(fifth column with C0S3¼20 and CS3¼105). As before, the highestvalue in each of these three columns gives the target asF 0S1¼755,556 TJ (with pinch at 105 t CO2/TJ), F 0S2¼566,667 TJ(with pinch at 105 t CO2/TJ) and F 0S3¼563,636 TJ (with pinch at75 t CO2/TJ). For the target to be feasible, it must not be greaterthan the total available FSi,total. Although the target is feasible forS2 (566,667 TJo800,000 TJ) and S3 (563,636 TJo600,000 TJ), it isnot for S1 (755,556 TJ4200,000 TJ). Since it is not possible to usethe absolute minimum zero-carbon resource (FR0¼400,000 TJ),the target for S1 is reworked. On setting F 0S1¼200,000 TJ (max-imum possible based on availability), Eqs. (10b) and (10c) yieldthe values in the last column of Table 3 for FR0 with the highestvalue providing the target as FR0¼693,333 TJ (with pinch at75 t CO2/TJ).

Target profiles using Eqs. (10a)–(10c) are plotted in Fig. 5 foreach one of the three CCS sources (S10, S20, and S30) along with thezero-carbon resource R0. The pinch, where the target profiletouches the limiting composite, is expectedly observed at105 t CO2/TJ (in Fig. 5b for S20, referred to as Case B2 hereafter)and at 75 t CO2/TJ (in Fig. 5c for S30 (Case B3) and in Fig. 5d for thereworked feasible case of S10 (Case B1)). The infeasible case of S10

(with F 0S1¼755,5564200,000 TJ) is shown in Fig. 5a.

0

25

50

75

100

125

150

0

Em

issi

on F

acto

r (t

CO

2/TJ)

Emission Load or Carbon Footprint (106 t CO2)

Limiting CompositePinch

Target Profile

1/FR0

908070605040302010

Fig. 3. Target profile for zero-carbon resource with no CCS source. (Case A with

FR0¼813,333 TJ).

Table 2Limiting composite curve by Composite Table Algorithm (CTA).



4.3. Two CCS sources

On considering two CCS sources along with the zero-carbonresource R0, three cases exist: Case C1 with (R0, S10, S20); Case C2with (R0, S10, S30); and Case C3 with (R0, S20, S30). Targeting foreach of these cases is discussed next.

When two CCS sources are used along with the clean-carbonresource, the target profile is the composite of three lines: one forthe clean-carbon resource R0 starting from CR0, second for the CCSsource Si starting from C0Si and terminating at CSi, and third for theCCS source S(iþ1) starting from CS(iþ1)

0 and terminating at CS(iþ1).Here, the notation i and (iþ1) is used for convenience to denoteany two sources, which may not actually be consecutive. Ingeneral, the target profile will comprise five sections, whosearrow representation is shown in Fig. 4b and whose equationsbased on emission load balances are as follows:

M¼ FR0ðC2CR0Þ for CrC0Si ð11aÞ

M¼ FR0ðC2CR0ÞþF 0SiðC2C0SiÞ for C0SirCrC0Sðiþ1Þ ð11bÞ

M¼ FR0ðC2CR0ÞþF 0SiðC2C0SiÞþF 0Sðiþ1ÞðC2C0Sðiþ1ÞÞ

for C0Sðiþ1ÞrCrCSi ð11cÞ

M¼ FR0ðC2CR0ÞþF 0SiðCSi2C0SiÞþF 0Sðiþ1ÞðC2C0Sðiþ1ÞÞ

for CSirCrCSðiþ1Þ ð11dÞ

M¼ FR0ðC2CR0ÞþF 0SiðCSi2C0SiÞþF 0Sðiþ1ÞðCSðiþ1Þ2C0Sðiþ1ÞÞ

for CZCSðiþ1Þ ð11eÞ

With FR0¼400,000 TJ (the absolute minimum zero-carbonresource requirement) and F 0Si¼F 0S1¼200,000 TJ (the maximumavailability of S10), FS(iþ1)

0 is the only unknown variable and maybe easily calculated from Eqs. (11c),(11d) or (11e) for the differentpoints (M, C) of the limiting composite in Table 4. With CR0¼0 (forzero-carbon resource), C0Si¼C0S1¼10 and CSi¼CS1¼55, substitutionin Eqs. (11c),(11d) and (11e) gives the values in Table 4 for F 0S2

(third column with C0S2¼15 and CS2¼75), and F 0S3 (fourth columnwith C 0S3¼20 and CS3¼105). The highest value in each columngives the target as F 0S2¼416,667 TJ (with pinch at 105 t CO2/TJ)and F 0S3¼400,000 TJ (with pinch at 75 t CO2/TJ). The targets, beingless than the total available FSi,total, are feasible for S2(416,667o800,000) as well as S3 (400,000o600,000). Profiles,based on these targets and Eqs. (11a)–(11e), are plotted in Fig. 6aand b for Case C1 with (R0, S10, S20) and Case C2 with (R0, S10, S30),respectively. The pinch, as expected, is seen at 105 t CO2/TJ (inFig. 6a) and at 75 t CO2/TJ (in Fig. 6b).

Table 3Targeting for single CCS source.

Units: emission factor C in t CO2/TJ, energy F in 104 TJ, emission load M in 106 t CO2.

Eq. (11a)

Eq. (11c)

Eq. (11d)

Eq. (11e)

Eq. (11b) C’Si

CSi

R0

F’Si

FR0

C’S(i+1)

CS(i+1)

CR0

F’S(i+1)

S(i+1)’

C’Si

CSi

R0 Si’

F’Si

FR0CR0Eq. (10a)

Eq. (10b)

Eq. (10c)

Si’

Fig. 4. Arrow representation of target profile for clean-carbon resource R0 with (a) single CCS source and (b) two CCS sources.



The third case of (R0, S20, S30), referred to as Case C3, is nowexplored. With FR0¼400,000 TJ (the absolute minimum zero-carbonresource requirement), Eqs. (11b)–(11e) have two unknown variables

(F 0Si and FS(iþ1)0 ). Two unknown variables imply the existence of two

pinch points. The approach thus far suggests the simultaneoussolution of two equations from Eqs. (11b)–(11e) for every possiblepair of points (M, C) on the limiting composite. However, a simplerapproach fruitfully utilizes the fact that all points on the limitingcomposite are not candidate pinch points. A point on the limitingcomposite is a candidate pinch only if the slope of the curve increasesafter the point and consequently the point ‘protrudes toward’ thetarget profile. Thus, the net energy deficit in an interval (Fnet as givenby the second column in Table 2), which corresponds to the reciprocalof the slope of a segment on the limiting composite, must decrease atcandidate pinch points. In this case study, the candidate pinches areat emission factors of 55 t CO2/TJ (where Fnet decreases from 140 to120 TJ), 75 t CO2/TJ (where Fnet decreases from 120 to 40 TJ), and105 t CO2/TJ (where Fnet decreases from 100 to 40 TJ). However, thepinch at 55 t CO2/TJ is possibly not a candidate (because of therelatively small change in the Fnet value and the slope/shape of thelimiting composite curve).

With the two pinch points at 75 t CO2/TJ and 105 t CO2/TJ (asobserved in all the six cases analyzed so far), Eqs. (11c) and (11d) give

61� 106¼ FR0ð7520ÞþF 0S2ð75215ÞþF 0S3ð75220Þ ð12aÞ

76� 106¼ FR0ð10520ÞþF 0S2ð75215ÞþF 0S3ð105220Þ ð12bÞ

Subtracting Eq. (12a) from Eq. (12b) yields

ð76261Þ � 106¼ ðFR0þF 0S3Þð105275Þ ð12cÞ

Table 4Targeting for Two CCS Sources.

Units: emission factor C in t CO2/TJ, energy F in 104 TJ, emission load M in 106 t CO2.

0

25

50

75

100

125

150

0

25

50

75

100

125

150

Limiting Composite

Pinch

Target Profile

Limiting Composite

Pinch

Target Profile

0

25

50

75

100

125

150

Emis

sion

Fac

tor (

tCO

2/TJ)

Emis

sion

Fac

tor (

tCO

2/TJ)

0

25

50

75

100

125

150

0Emission Load or Carbon Footprint (106 t CO2) Emission Load or Carbon Footprint (106 t CO2)

Emission Load or Carbon Footprint (106 t CO2) Emission Load or Carbon Footprint (106 t CO2)

1/(FR0 +F’S3) 1/(FR0 +F’S1)

1/(FR0 +F’S2)

1/FR0

1/FR0

1/FR0

1/FR0

1/FR0

Limiting Composite

Pinch

Target Profile

1/(FR0 + F’S1)

1/FR0

1/FR0

Pinch

Target Profile

Emis

sion

Fac

tor (

t O2/T

J)

Emis

sion

Fac

tor (

tCO

2/TJ)

9080706050403020100 908070605040302010

0 9080706050403020100 908070605040302010

Limiting Composite

Fig. 5. Target profile for single CCS source (a) infeasible case with F 0S1¼755556 TJ and FR0¼400,000 TJ, (b) Case B2 with F 0S2¼566,667 TJ and FR0¼400,000 TJ, (c) Case B3

with FS30 ¼563,636 TJ and FR0¼400,000 TJ, and (d) Case B1 with F 0S1¼200,000 TJ and FR0¼693,333 TJ.



Eq. (12c) is simply an emission load balance between the twopinches (whereas Eq. (12a) is a balance below the pinch at75 t CO2/TJ, and Eq. (12b) is a balance below the pinch at105 t CO2/TJ) and provides a direct way to calculate the F 0S3 target.If CSi and CS(iþ1) denote the two pinch points (with the corre-sponding emission loads on the limiting composite given by MSi

and MS(iþ1)), then Eq. (12c) in generalized form may be written as

FR0þF 0Sðiþ1Þ ¼ ðMSðiþ1Þ2MSiÞ=ðCSðiþ1Þ2CSiÞ ð12dÞ

Equations (similar to Eq. (12d)) for the emission load balancebetween two pinches can be written for any of the sections in Fig. 4and readily used to establish targets in some multi-pinch cases.

For Case C3 with (R0, S20, S30), Eq. (12c) gives the target asF 0S3¼100,000 TJ and then Eq. (12a) or (12b) give F 0S2¼425,000 TJon substituting FR0¼400,000 TJ. The targets, being less than thetotal available FSi,total, are feasible for both S2 (425,000o800,000)and S3 (100,000o600,000). The profile for Case C3 with (R0, S20,S30), based on these targets and Eqs. (11a)–(11e), is plotted inFig. 6c and expectedly shows two pinches (at 75 and 105 t CO2/TJ).

4.4. Three CCS sources

The last case (Case D) considers all three CCS sources alongwith the zero-carbon resource R0.

When three CCS sources are used along with the clean-carbonresource, the target profile is the composite of four lines: one forthe clean-carbon resource R0 starting from CR0, second for the CCSsource Si starting from C0Si and terminating at CSi, third for the CCS

source S(iþ1) starting from C0Sðiþ1Þ and terminating at CS(iþ1), andfourth for the CCS source S(iþ2) starting from C0Sðiþ2Þ andterminating at CS(iþ2). In general, the target profile will compriseseven sections [CrC0Si; C0SirCrC0Sðiþ1Þ; C0Sðiþ1ÞrCrC0Sðiþ2Þ;C0Sðiþ2ÞrCrCSi; CSirCrCS(iþ1); CS(iþ1)rCrCS(iþ2); andCZCS(iþ2)], whose arrow representation can be shown in a formsimilar to Fig. 4 (omitted for brevity) and whose emission loadbalance equations can be written in a manner similar to Eqs. (10)and (11) (not shown).

With FR0¼400,000 TJ (the absolute minimum zero-carbonresource requirement) and F 0Si¼F 0S1¼200,000 TJ (the maximumavailability of S10), there remain two unknown variables (F 0S2 andF 0S3). As before, this suggests the existence of two pinch points (at75 and 105 t CO2/TJ). An emission load balance between the twopinches yields Eq. (12c) and the target as F 0S3¼100,000 TJ (same asin the earlier case). Now, balances below the pinches at 75 t CO2/TJ and 105 t CO2/TJ give the following equations (which are theanalogs of Eqs. (12a) and (12b)):

61� 106¼ FR0ð7520ÞþF 0S1ð55210ÞþF 0S2ð75215ÞþF 0S3ð75220Þ

ð13aÞ

76� 106¼ FR0ð10520ÞþF 0S1ð55210ÞþF 0S2ð75215ÞþF 0S3ð105220Þ

ð13bÞ

On substituting FR0¼400,000 TJ, F 0S1¼200,000 TJ and F 0S3¼

100,000 TJ, the target is obtained from Eq. (13a) or (13b) as

0

25

50

75

100

125

150

Emis

sion

Fac

tor (

t CO

2/TJ

)

0

25

50

75

100

125

150

Emis

sion

Fac

tor (

t CO

2/TJ

)

1/(FR0 + F’S1+F’S3)

1/FR0

1/FR0

Limiting Composite

Pinch

Target Profile

1/(FR0 + F’S3)

1/(FR0 + F’S1)

1/(FR0 + F’S1+F’S2)

1/FR0

1/FR0Limiting Composite

Pinch

Target Profile

1/(FR0 + F’S2)

1/(FR0 + F’S1)

0

25

50

75

100

125

150

0

Emis

sion

Fac

tor (

t CO

2/TJ

)

Emission Load or Carbon Footprint (106t CO2)



1/(FR0 + F’S2+F’S3)

1/FR0

1/FR0

Limiting Composite

Pinches

Target Profile

1/(FR0 + F’S3)

1/(FR0 + F’S2)

10 20 30 40 50 60 70 80 90

0 10 20 30 40 50 60 70 80 90

0 10 20 30 40 50 60 70 80 90

Fig. 6. Target profile with FR0¼400,000 TJ for two CCS sources (a) Case C1 with F 0S1¼200,000 TJ and F 0S2¼416,667 TJ, (b) Case C2 with F 0S1¼200,000 TJ, and F 0S3¼400,000 TJ

(c) Case C3 with F 0S2¼425,000 TJ and F 0S3¼100,000 TJ.



F 0S2¼275,000 TJ. The targets, being less than the total availability,are feasible for S2 (275,000o800000) and S3 (100,000o600,000). The profile for Case D with (R0, S10, S20, S30) based onthese targets is plotted in Fig. 7 and expectedly shows twopinches (at 75 and 105 t CO2/TJ) as well as seven sections.

The targets for all eight primary cases (only R0 with no CCS,three cases with single CCS source, three cases with two CCSsources, and a final case with all three CCS sources) are summar-ized in Table 5 (first six rows). The target for the operating cost(seventh row) as per Eq. (3) can be established a priori in six cases(where the excess energy is zero, i.e., when FR0¼400,000 TJ) withthe exception of Case A and Case B1.

5. Network design by Nearest Neighbors Algorithm (NNA)

In this section, networks are synthesized to meet the targetsestablished. The Nearest Neighbors Algorithm (NNA), proposed byPrakash and Shenoy (2005a) for water networks and discussed byAgrwal and Shenoy (2006) for water/hydrogen networks as wellas by Shenoy (2010) for carbon emission networks (CENs), is usedfor this purpose. In the context of CENs, the basic principle behindthe NNA may be stated as follows: ‘To satisfy a particular demand,

the sources to be chosen are the nearest available neighbors tothe demand in terms of emission factor.’ Details of the NNA areavailable in these works and are not discussed here.

The NNA, which is a network design tool and should be appliedonly after targets are established, is conveniently implemented interms of the matching matrix representation (Prakash and Shenoy,2005b; Das et al., 2009; Shenoy, 2010). All CENs (Figs. 8, 9, and 10)in this work are presented in the form of matching matrices.A matching matrix provides a superstructure with a placeholderfor every possible match in the allocation network. The emissionloads or carbon footprints [shown in square brackets in thebottom half of each relevant cell of the matching matrix for readyreference] are calculated by simple multiplication using Eq. (1)only after completing the design. These values are not required tobe calculated during the actual design of the network by the NNA.In the matching matrix, it is convenient to arrange sources in orderof increasing (or decreasing) emission factor to promptly identifythe nearest neighbors; however, it is not essential (although oftenconvenient) to arrange demands because they can be met in anyorder. Arranging demands in order of emission factor nonethelessallows easy identification of the cross-pinch regions (gray cells inthe matching matrices that follow). To achieve the targets usingthe NNA, there should be no cross-pinch energy transfer, which is

Table 5Summary of results for case study.

No CCS Single CCS Two CCS Three CCS

S10 S20 S30 (S10 , S20) (S10 , S30) (S20 , S30) (S10 , S20 , S30)

Case A Case B1 Case B2 Case B3 Case C1 Case C2 Case C3 Case D

FR0 (104 TJ) 81.3333 69.3333 40 40 40 40 40 40

F 0S1 (104 TJ) – 20 – – 20 20 – 20

F 0S2 (104 TJ) – – 56.6667 – 41.6667 – 42.5 27.5

F 0S3 (104 TJ) – – – 56.3636 – 40 10 10

Pinch CP (t CO2/TJ) 75 75 105 75 105 75 75, 105 75, 105

Limiting composite Fig. 3 Fig. 5d Fig. 5b Fig. 5c Fig. 6a Fig. 6b Fig. 6c Fig. 7

Operating cost target – – 59,400 59,364 61,000 60,800 58,900 60,500

Networks by NNA Shenoy (2010) Fig. 8a Fig. 8b Fig. 8c Fig. 9a Fig. 9b Fig. 9c Fig. 10

Operating cost 62,307 62,947 59,400 59,364 61,000 60,800 58,900 60,500

Fixed cost 0 1000 800 700 1800 1700 1500 2500

Total cost 62,307 63,947 60,200 60,064 62,800 62,500 60,400 63,000

0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90

Emis

sion

Fac

tor (

t CO

2/TJ)


1/(FR0 + F’S1 + F’S2 + F’S3)

1/FR0

Limiting Composite

Pinches

Target Profile

1/(FR0 + F’S1)1/(FR0 + F’S1 + F’S2)

1/(FR0 + F’S2 + F’S3)

1/(FR0 + F’S3)

1/FR0

Fig. 7. Target profile with FR0¼400,000 TJ for three CCS sources: Case D with F 0S1¼200,000 TJ, F 0S2¼275,000 TJ and F 0S3¼100,000 TJ.



ensured by designing separately in the non-grayed below-pinchand above-pinch regions.

Many different networks, all satisfying the targets, may ingeneral be designed by the NNA depending on the order in whichthe demands are met (Agrawal and Shenoy, 2006; Shenoy, 2010).Here, one promising network synthesized by the NNA ispresented for each primary case taking into consideration thatthe number of CCS matches must be minimized to keep the fixedcost low. In all the networks below, the NNA is applied to satisfythe demands D1, D2 and D3 in that order. Three possible net-works using only a single CCS source are shown in Fig. 8a (forCase B1), Fig. 8b (for Case B2) and Fig. 8c (for Case B3). Another

three networks using two CCS sources are shown in Fig. 9a (forCase C1), Fig. 9b (for Case C2) and Fig. 9c (for Case C3). Finally,a network using all three CCS sources is shown in Fig. 10 for CaseD. Of these seven networks, two networks (Figs. 8b and 9c) matchthose reported by Pekala et al. (2010), who obtained them bysolving a mixed integer linear programming (MILP) formulationusing optimization software and varying the fixed cost factors forCCS sources. The network for Case A of only zero-carbon resourceR0 (with no CCS sources) is not presented here because it hasbeen dealt with in detail by Shenoy (2010).

In all the networks except those in Figs. 8c and 9b, the demandsare met at the maximum emission load limits or equivalently

Fig. 8. Carbon emission networks with single CCS source using (a) S10 (Case B1), (b) S20 (Case B2), and (c) S30 (Case B3).



maximum emission factors. In Figs. 8c and 9b, demand D3 (which isthe only demand above the pinch at 75 t CO2/TJ in this case) issatisfied with a carbon footprint below its specified maximum limitof 60�106 t CO2. This is consistent with an important observationin this regard made by Prakash and Shenoy (2005a) for waternetworks and Shenoy (2010) for carbon emission networks. In thecontext of CENs, the observation may be stated as: ‘to meet theminimum resource target, all demands below the pinch must besatisfied at emission factors equal to their maximum allowablevalues, whereas demands above the pinch can be satisfied atemission factors less than their maximum allowable values’.

6. Cost analysis

The costs for the networks synthesized in the previous sectionmay now be evaluated as shown in Table 5 (last three rows). Theoperating costs (third last row in Table 5) exactly match withtheir respective targets (seventh row). In addition to the operatingcost factors given in the last column of Table 1, Pekala et al.(2010) have specified the fixed cost factors (in unspecified costunits) for matches using the three CCS sources (1000 forCCS—Natural Gas match; 800 for CCS—Oil match; and 700 forCCS—Coal match). Using these factors (of 1000, 800, and 700), thefixed cost (second last row in Table 5) can be calculated andadded to the respective operating cost to obtain the total cost (lastrow). Note that the operating costs as well as the total costs forthe various cases are within about 7% of the minimum. Further,the operating costs are expectedly higher for cases using S10

(because of the relatively high operating cost factor of 0.042 forS10, being close to 0.045 for R0).

From Table 5, the network with the minimum operating cost(58,900) is found to use one CCS—Oil match and one CCS—Coalmatch (Fig. 9c). It has a total cost of 60,400, which is reported tobe the globally optimal total cost solution by Pekala et al. (2010)based on an MILP formulation. However, this is not consistentwith Table 5, which shows the network using only one CCS—Coalmatch (Fig. 8c) to have the minimum total cost (60,064). Thenetwork in Fig. 8c, in addition to being optimal in terms of totalcost, satisfies demand D3 with a carbon footprint of just46.091�106 t CO2 (which is below its specified maximum limitof 60�106 t CO2). Thus, the network in Fig. 8c provides a superiorsolution to that reported by Pekala et al. (2010) (Fig. 9c) because ithas a lower total cost (60,064 instead of 60,400), a lower carbonfootprint (46.091�106 rather than 60�106 t CO2 for demand D3)and one fewer match (8 instead of 9 matches).

In Table 5, the targeting results (in the first six rows) includeeight primary cases (in the columns) because there are three CCSsources in this case study. In general, 2NS primary cases are expectedif there are NS CCS sources. Note that the primary cases have beenfundamentally established by profile matching with the limitingcomposite curve, without using any specific cost data. Generally,when actual cost data are unavailable or uncertain, it may beassumed that the unit operating cost (i.e., the operating cost perenergy unit) reduces with decrease in quality (i.e., increase incarbon intensity/emission factor) of the resource or source. In what

Fig. 9. Carbon emission networks with two CCS sources using (a) S10 , S20 (Case C1)

(b) S10 , S30 (Case C2), and (c) S20 , S30 (Case C3).

Fig. 10. Carbon emission networks with three CCS sources using S10 , S20 , and S30

(Case D).



follows, a better approach is presented wherein a cost criterion isestablished for the applicability of the (eight) primary cases.

Consider for concreteness the introduction of S10 as a partialreplacement for S20 (specifically, for the optimal solution tochange from Case C3 to Case D). Given the relatively highoperating cost factor (0.042) of S10 (in Table 1), this is currentlynot optimal. However, a condition in terms of the operating costfactor may be derived for the use of S10 to be optimal by usingEq. (13) as a starting point. On substituting FR0¼400,000 TJ andF 0S3¼100,000 TJ, Eqs. (13a) and (13b) both give F 0S1(55–10)þF 0S2(75–15)¼25.5�106. This equation includes Case C3(F 0S2¼425,000 if F 0S1¼0) as well as Case D (F 0S2¼275,000 ifF 0S1¼200,000). On substituting for F 0S2 from Eqs. (13a) and (13b)into Eq. (3b), the operating cost may be expressed as

OC ¼XNS

i ¼ 1

DcSiF0SiþK1 ð14aÞ

OC ¼DcS1F 0S1þDcS2F 0S2þK2 ð14bÞ

OC ¼ ½DcS1�DcS2ð55�10Þ=ð75�15Þ�F 0S1þK3 ð14cÞ

where DcSi�c0Si�cSi (i.e., DcSi signifies the additional cost of CCSsource Si0 with reference to its non-CCS option Si) with K1, K2, andK3 denoting constants. Eq. (14a) is obtained because of theconstancy of the first term (noting FR0¼400,000 TJ), the thirdterm (which is the cost of total available sources) and the fourthterm (which is zero for no excess energy) in Eq. (3b). Eq. (14a)gives Eq. (14b) on expanding the summation and absorbing theDcS3F 0S3 term into the constant, whereas Eq. (14b) finally yieldsEq. (14c) on substituting for F 0S2 from Eqs. (13a) and (13b). For theintroduction of S10 (F 0S140) to be advantageous, the operatingcost must decrease. This requires the term in square brackets inEq. (14c) be negative, giving the following simple condition:

DcS1oRCDcS2 where RC ¼ ð55210Þ=ð75215Þ ð14dÞ

Eq. (14d) specifies the condition where it is optimal tointroduce S10 to partially replace S20. In other words, the optimalsolution is Case C3 for a positive deviation (i.e., DcS1¼RCDcS2þd)and it is Case D for a negative deviation (i.e., DcS1¼RCDcS2�d),where d is a small deviation (say, 10�6) of DcS1 from RCDcS2. Theabove result is given in the last row of Table 6, where severalother results are tabulated based on a generalization of Eq. (14d)as given next in Eq. (15a).

For the optimal introduction of CCS source Si0 as a partialreplacement for CCS source S(iþ1)0, the general cost criterion may

be elegantly expressed as

DcSioRCDcSðiþ1Þ where RC � ðCEi2C0SiÞ=ðCEðiþ1Þ2C0Sðiþ1ÞÞ ð15aÞ

Here, CE is appropriately taken as the emission factor of eitherthe corresponding non-CCS source or the pinch, whichever islower in value. Note that the line segments (see Table 4) for bothS10 and S20 terminate at or before the pinches (at 75 and105 t CO2/TJ) and therefore CE is taken as the emission factor ofthe corresponding non-CCS source (55 for S1 and 75 for S2) inEq. (14d), which may not always be case. As discussed earlier, theoptimal solution does not use any Si0 for a positive deviation (i.e.,DcSi¼RCDcS(iþ1)þd), whereas it is does use Si0 (in place of S(iþ1)0)for a negative deviation (i.e., DcSi¼RCDcS(iþ1)�d), where d is asmall deviation of DcSi from RC DcS(iþ1).

The RC cost criterion in Eq. (15a) is validated by solving the linearprogram (LP) formulated in Section 2 for 28 runs (considering bothpositive and negative deviations of the 14 rows tabulated in Table 6).The LP runs may be taken using Eq. (3) with base cost factors asgiven in the last column of Table 1, i.e., cR0¼0.045, c0S1¼0.042,c0S2¼0.034, c0S3¼0.032, cS1¼0.025, cS2¼0.022, and cS3¼0.020. Analternative is to use cR0¼0.045, c0S1¼DcS1¼0.042�0.025¼0.017,c0S2¼DcS2¼0.034�0.022¼0.012, c0S3¼DcS3¼0.032�0.020¼0.012,cS1¼0.0, cS2¼0.0 and cS3¼0.0. These modified cost factors alloweasier validation during the 28 LP runs (for positive and negativedeviations of the 14 rows in Table 6) for the optimal cases listed inthe last two columns of Table 6 (although the actual objectivefunction value will differ from that obtained on using base costfactors). Note that two new sub-cases (in addition to the eightprimary cases in Table 5) are discovered during the LP runs, andtabulated as Case B2S and Case C1S at the bottom of Table 6. Thesesub-cases are variations of Case B2 (Fig. 5b) and Case C1 (Fig. 6a) dueto the pinch point jumping from 105 to 75 t CO2/TJ. Such pinchjumps have been observed earlier and are discussed by Shenoy andBandyopadhyay (2007).

The cost criterion in Eq. (15a) may be rewritten as

ðc0Si2cSiÞ=ðCEi2C0SiÞo ðc0Sðiþ1Þ2cSðiþ1ÞÞ=ðCEðiþ1Þ2C 0Sðiþ1ÞÞ ð15bÞ

In this slightly different version of the cost criterion, thequantity (c0Si�cSi)/(CEi�C0Si) may be called the prioritized cost(Fraser et al., 2005; Shenoy and Bandyopadhyay, 2007) of theith CCS source. Note that it is not necessary to maximize the usageof the CCS source with the minimum unit cost (i.e., cost perenergy unit) in order to minimize the overall operating cost. Theprioritized cost, in a sense, is a ratio of the economic/operatingcost change to the environmental benefit change when the CCS

Table 6Optimality analysis for minimum operating cost based on the RC cost criterion.

Replace RC DcS1 DcS2 DcS3 Forbidden Optimal for

þve deviation

Optimal for

�ve deviation

R0 by S10 (55�10)/(75�0) RC DcR07d S20 , S30 Case A Case B1

R0 by S20 pinch at 105 (75�15)/(105�0) RC DcR07d S10 , S30 Case B2S Case B2

R0 by S20 pinch at 75 (75�15)/(75�0) RC DcR07d S10 , S30 Case A Case B2S

R0 by S30 (75�20)/(75�0) RC DcR07d S10 , S20 Case A Case B3

R0 by S20 pinch at 105 (75�15)/(105�0) RC DcR07d S30 Case C1S Case C1

R0 by S20 pinch at 75 (75�15)/(75�0) RC DcR07d S30 Case B1 Case C1S

R0 by S30 (75�20)/(75�0) RC DcR07d S20 Case B1 Case C2

S20 by S10 (55�10)/(75�15) RC DcS27d S30 Case B2 Case C1




S20 by S30 (105�20)/(75�15) 0.009�d RC DcS27d Case C1 Case D

S30 by S20 (75�15)/(75�20) 0.009�d RC DcS37d Case C2 Case D

S20 by S10 (55�10)/(75�15) RC DcS27d Case C3 Case D

Note: DcR0¼0.045, DcS1¼0.017, DcS2¼0.012, DcS3¼0.012; d¼10�6.

Case B2S: FR0¼500,000 TJ, F 0S1¼0, F 0S2¼391,667 TJ, F 0S3¼0.

Case C1S: FR0¼500,000 TJ, F 0S1¼200,000 TJ, F 0S2¼241,667 TJ, F 0S3¼0.



option is used over the non-CCS one. The prioritized costs providean order in which the CCS sources may be used; however, theymay be difficult to calculate a priori in some multi-pinch andpinch-jump cases.

7. MILP formulation and validation for total cost optimization

The LP formulation discussed so far focuses on the optimiza-tion of only the operating cost. In this section, the formulation isextended to a mixed integer linear program (MILP) for theoptimization of the total cost given by the following expression:

TC ¼XNR

k ¼ 0

cRkFRkþXNS

i ¼ 1

c0SiF0Siþ

XNS

i ¼ 1

cSiðFSi�f iEÞþXNS

i ¼ 1

XND

j ¼ 1

c0FSiy0ij ð16aÞ

In Eq. (16a), the first three terms are identical to those inEq. (3a). The last (additional fourth) term corresponds to the fixedcost with y0ij denoting the binary variables (1 if demand j is met byCCS source i, and 0 otherwise) and c0FSi

denoting the associatedfixed cost factors. The binary variable associated with each CCSmatch requires the following big-M disjunctive constraint:

f 0ij�My0ijr0 ð16bÞ

where M is a very large constant value (providing the upper limitof fij

0). Depending on whether the binary variable is zero or unity,Eq. (16b) ensures that the associated continuous variable is eitherzero or positive.

The objective is to minimize the total cost TC in Eq. (16a) subjectto the constraints given by Eqs. (4), (5), (8), and (16b). The MILPformulation can be solved using optimization software such as GAMS.On using the cost data in Table 1 along with the earlier-specified fixedcost factors of 1000, 800, and 700 (originally from Pekala et al., 2010),the optimum for minimum total cost corresponds to the values ofFR0¼400,000 TJ and F 0S3¼563,636 TJ. This validates the resultobtained earlier in Table 5 and reported as Case B3.

Furthermore, the MILP may be used to validate other cases inTable 5 by simply varying the cost data as demonstrated below.Based on Eq. (16a), the expression for the operating cost in Eq. (14a)may be extended to obtain the following equation for the total cost:

TC ¼XNS

i ¼ 1

DcSiF0SiþK1þ

XNS

i ¼ 1

XND

j ¼ 1

c0FSiy0ij ð17aÞ

Applying Eq. (17a) for Cases B2 and B3 (using values for F 0Si

from Table 5 along with fixed cost factors of 800 for CCS—Oilmatch and 700 for CCS—Coal match) gives

TCB2 ¼ 566667 DcS2þK1þ800 for Case B2 ð17bÞ

TCB3 ¼ 563636 DcS3þK1þ700 for Case B3 ð17cÞ

The optimum is Case B3 for the cost data in Table 1 becauseTCB3 yields the minimum value. For Case B2 to be the optimum, itis necessary (though not sufficient) that TCB2oTCB3. On substitut-ing from Eqs. (17b) and (17c)

566667DcS2þ800o563636DcS3þ700 ð17dÞ

Note that Eq. (17d) is an extension of the Rc cost criterion(Eqs. (14d) and (15) considering only operating cost) to the case oftotal cost. Eq. (17d) yields two possibilities for Case B2 to beoptimum: DcS2o(563,636 DcS3�100)/566,667 (i.e., DcS2o0.01176or C0S2o0.03376 on substituting DcS3¼0.012 and cS2¼0.022); andDcS34(566,667 DcS2þ100)/563,636 (i.e., DcS340.01224 orc0S340.03224 on substituting DcS2¼0.012 and cS3¼0.020). Bothpossibilities are readily verified by solving an MILP to yield Case B2as the optimum (FR0¼400,000 TJ and F0S2¼566,667 TJ) on choosingdifferent values for the cost factors (c0S2o0.03376 or c0S340.03224).

Based on the preceding discussion, Table 7 summarizes theMILP validation for six cases (corresponding to zero excess, i.e.,FR0¼400,000 TJ) in Table 5 by varying the cost data. Case B3 is theoptimum for the base-case cost data in Table 1 (when c0S2¼0.034),whereas Case B2 is the optimum when c0S2¼0.0337 (i.e.,c0S2o0.03376 in accordance with Eq. (17d)). The last four columnsin Table 7 show possibilities where Cases C1, C2, C3 and D areoptimum when cost data are varied (with changed values high-lighted in bold).

8. Conclusions

A detailed mathematical formulation has been developed forthe targeting of the energy allocation problem with CCS. For thecase of CCS with zero excess, it has been shown that CCS sourcescan be treated as resources with their cost per energy unit takenas the increment over the non-CCS option. The limiting compositeis a valuable, unique curve for targeting with and without CCS. Itis readily obtained using a single computation of the compositetable algorithm (CTA) by considering demands and only non-CCSsources with their total energy availabilities.

In this work, the recent methodology (Shenoy, 2010) fortargeting and design of carbon emission networks has beenextended by the inclusion of carbon capture and storage (CCS)of the fossil fuel sources. As in the earlier work (Shenoy, 2010),the CTA is applied to generate the limiting composite and theNNA is used to design the network. However, the earlier work waslimited to targeting of clean-carbon resources with no CCSsources, whereas the present work focuses on targeting ofclean-carbon resources with multiple (specifically, one, two orthree) CCS sources. Further, the earlier work did not consider anycost data nor discuss any cost analysis. This work develops aformal mathematical formulation, discusses detailed cost optimi-zation, and considers the effects of varying cost data. Broadly, thecontribution takes a systems engineering approach to energyutilization with regeneration through carbon sequestration forsustainable development. The contribution is inspired by the keyrepresentation in Fig. 2 of a CCS source and its corresponding non-CCS source in terms of an equivalent composite. The equivalentcomposite representation has two important implications: onlynon-CCS sources (with energy values given in terms of theirspecified totals) are first considered to establish a unique limitingcomposite; and only CCS sources (depicted as line segmentsbetween CSi

0 and CSi) are then regarded as resources for targetingby profile matching. The approach is novel because it allows

Table 7MILP validation by varying cost data.

Input cost data

cR0 0.045 0.045 0.045 0.045 0.045 0.045

c0S1 0.042 0.042 0.036 0.036 0.042 0.036

c0S2 0.0337 0.034 0.034 0.034 0.034 0.034

c0S3 0.032 0.032 0.033 0.032 0.032 0.032

cS1 0.025 0.025 0.032 0.0315 0.025 0.0315cS2 0.022 0.022 0.022 0.022 0.0164 0.0196cS3 0.020 0.020 0.020 0.020 0.0141 0.016c0FS1

1000 1000 1000 1000 1000 1000

c0FS2800 800 800 800 800 800

c0FS3700 700 700 700 700 400

Optimum solution from MILPFR0 (104 TJ) 40 40 40 40 40 40

F 0S1 (104 TJ) – – 20 20 – 20

F 0S2 (104 TJ) 56.6667 – 41.6667 – 42.5 27.5

F 0S3 (104 TJ) – 56.3636 – 40 10 10

Case B2 B3 C1 C2 C3 D



targets to be set and networks to be synthesized even when costdata are unavailable or uncertain. The results have been validatedthrough an LP formulation for minimum operating cost and anMILP formulation for minimum total cost considering the sensi-tivity of varying cost data.

The presented approach differs from earlier established methodsin the following ways. Firstly, the presented approach for carbonemission networks requires handling of multiple CCS sources andconsequently determination of Ns unknown variables correspondingto the optimum requirements of Ns CCS sources. In contrast,established methods for water and hydrogen networks typicallyhandle a single regeneration stream and consequently are a specialcase of the presented approach for Ns¼1. Secondly, in carbonemission networks, the operating cost in the objective functiondepends on the clean resources, the sources with CCS, and thesources without CCS (excluding the excess or unused energy). Inwater and hydrogen networks, the operating cost depends on theresources (freshwater usage and hydrogen makeup, respectively)and the regeneration, but not on the sources (which are internal).Thirdly, in carbon emission networks, there is a constraint on theCCS and non-CCS portions of each source totaling the specifiedavailability. In water and hydrogen networks, no such constraintexists except that the regeneration flowrate must not exceed theclean resource flowrate. Finally, in carbon emission networks, the‘equivalent concentration’ for inlet regeneration is known because itis given by the specified non-CCS source emission factor Csi. In waterand hydrogen networks, the inlet regeneration concentration is notknown and must be determined.

In this work, multiple CCS sources along with clean-carbonresources are simultaneously targeted by profile matching withthe limiting composite. It may be noted that Figs. 3, 5, 6, and 7show ‘utility pinches’ where the target profile touches the limit-ing composite. The problem of targeting CCS sources is a challen-ging one and its solution by profile matching is non-trivial. Forthis purpose, fundamental carbon emission load balance equa-tions may be utilized where clean-carbon resources are repre-sented by arrows and CCS sources by line segments. Targetingtypically results in 2NS optimal primary cases for NS CCS sourcesand does not require cost data.

Design of carbon emission networks (CENs) that achieve thealready-established targets may be next done by systematicallyusing the nearest neighbors algorithm (NNA) along with thematching matrix representation. It must be emphasized that theNNA, by merely varying the order of satisfaction of demands,allows synthesis of many optimum CENs (all meeting the targetsand the specified emission load limits) for each primary case.

Cost analysis may be now performed in terms of both operat-ing cost as well as total cost, if cost data are available. The costranges in which the different primary cases are optimal may bedetermined using the RC cost criterion.

Optimization may be finally done by solving a linear program-ming (LP) formulation for minimum operating cost. The solutionsby mathematical programming permit validation of the earliertargeting results and network designs. They also help in identi-fication of unusual new sub-cases (of pinch jumps, for instance)and additional networks.

To summarize, the methodology in this work comprises fourdistinct stages: targeting using the CTA/UTA along with funda-mental balances for profile matching with the limiting compositecurve; designing networks for each of the optimal primary casesusing the NNA; analyzing costs using the RC cost criterion; andfinally optimizing solutions using mathematical programmingformulations. This work therefore proposes a hybrid approachbased on the CTA/NNA as well as mathematical programming(LP/MILP). The methodology using the CTA/NNA provides deeperinsights into the problem, its pinch points and its network

structure. A significant advantage of the CTA/NNA methodologyis that targets may be set and networks synthesized based onprimary cases even in the absence of cost data.

Nomenclature

C emission factor or carbon intensity, t CO2/TJc operating cost (factor) per energy unit, cost unit/TJcF fixed cost factorCCS carbon capture and storage/sequestrationCEN carbon emission networkCTA composite table algorithmD demand for energy in a region/sectorE excess (or unused) energy, TJF energy, TJf energy allocation for cell matches in matching matrix, TJi index denoting number of source (CCS or non-CCS)j index denoting number of demandK1, K2, K3 constants in Eq. (14)k index denoting number of clean-carbon resourceLP linear programmingMILP mixed integer linear programmingM emission load or carbon footprint, t CO2 or constant in

big-M constraintNNA nearest neighbors algorithmN total numberOC operating costR resource (zero-carbon or low-carbon)R0 resource (zero-carbon)RC ratio of emission-factor differences defined in eq 15aS source for energy (conventional fossil fuel such as coal,

oil, or natural gas)UTA unified targeting algorithmy binary variable associated with total cost termD1 net system energy deficit, TJD2 net system emission load deficit, t CO2

Dc additional cost of CCS source with reference to its non-CCS option

Subscripts

D demandE excess (or unused) energyi index for source (CCS or non-CCS)j index for demandk index for clean-carbon resourcemax maximum (specified availability of clean-carbon

resource)R clean-carbon resource (zero-carbon or low-carbon)R0 resource (zero-carbon)P pinchS source (CCS or non-CCS)total total (availability of source)

Superscript

0 prime to denote CCS source

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