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Energy 32 (2007) 540–548

www.elsevier.com/locate/energy

Efficiency of Carbon storage with leakage:Physical and economical approaches

Fei Tenga,b,�, Daniel Tondeura

aLaboratoire des Sciences du Genie Chimique-CNRS, ENSIC-INPl, BP 451, 54001 Nancy Cedex, FrancebInstitute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, PR China

Received 13 October 2005

Abstract

In this paper, two methods are proposed to assess the efficiency of carbon capture and storage (CCS) involving back-leakage of CO2

from geological storage reservoirs to the atmosphere. The first method is a physical approach based on radiative forcing. It leads to a

criterion that assesses whether a given technology of CCS is physically beneficial compared to a reference technology without CCS. The

second method is an economic approach based on the classical framework of net present value (NPV). It leads to an economic feasibility

condition that assesses whether a given CCS technology is economically beneficial compared to a reference technology. The two models

are compared with respect to their parametric dependence. In particular, a maximum leakage rate may be defined, above which neither of

the feasibility criteria is satisfied. The two approaches are also discussed with respect to the type of decision they may generate. Under

general assumptions, the economic criterion is stricter than the physical criterion when the leakage coefficient is small, and the opposite is

true when the leakage coefficient is large.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Carbon sequestration; Carbon dioxide; Greenhouse control; Efficiency assessment; Leakage

1. Introduction

There is currently a great interest in carbon sequestrationas a complemental option for carbon mitigation. TheIntergovernmental Panel on Climate Change (IPCC)defines sequestration as an increase in carbon stock insome reservoir other than the atmosphere. Several kinds ofreservoirs have been considered for carbon sequestration,such as biological carbon sinks including forests and soil;onshore geological reservoirs such as deep coal seams,depleted hydrocarbon reservoirs, deep saline aquifers; anddeep ocean.

For biological carbon sinks, one can grow plants andmanage forest so as to remove greenhouse gas fromatmosphere; such kinds of activities are called Land use,land-use change and forestry (LULUCF). Under the

e front matter r 2006 Elsevier Ltd. All rights reserved.

ergy.2006.07.027

ing author. Institute of Nuclear and New Energy Technol-

niversity, Beijing 100084, PR China. Tel.: +861062784805;

71150.

ess: tengfei@tsinghua.edu.cn (F. Teng).

framework of the Kyoto Protocol [1], the parties havedecided that emission caused by afforestation, reforestationand deforestation will be included as a part of nationalcommitment. For geological reservoirs, greenhouse gas willbe captured at the places of fossil fuel combustion and thentransported and injected into these reservoirs. Suchactivities are often called carbon capture and storage(CCS). There is still no clear conclusion whether CCS canbe used as an approach for mitigation though mostscientists consider it to be a potential long-term strategy,which could help make a smooth transition towards newenergy infrastructures.A particular feature of carbon sequestration is that the

carbon sequestered (stored in plantation or underground)is always at risk of leaking back to the atmosphere. Incontrast, carbon mitigation caused by a reduction of fossilfuel consumption will result in a risk-free reduction inatmospheric CO2 level. This is the issue of permanence,which has been hotly debated in the literature of LULUCF[2,3]. Researchers have sought to analyze this problem inthe CCS area through an economical approach [4–6],

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Nomenclature

ag radiative efficiency due to a unit increase inatmospheric abundance of gas g, W/m2/kg

CR capture rate of CCS technologyEF emission factor of fuel employed, tCO2/GJEFc emission factor of generation in capture plant,

tCO2/kWheEFr emission factor of generation in reference plant,

tCO2/kWhefC (t) time-dependant decay function of CO2

fg (t) time-dependent decay function of gas gGWP (Z) global warming potential of carbon storage

with a constant leakage coefficient Z

HRc heat rate of captured plant, GJ/kWheHRr heat rate of reference plant, GJ/kWheL(t) leakage rate, tCO2/yearl(t) specific leakage rate, year�1

PC carbon price at time 0, $/tCO2

Pe electricity price in wholesale market, $/kWhePF fuel price at time 0, $/GJr discount rateS(t) carbon stock in reservoir at time t, tCO2

S0 amount of carbon sequestered at time 0, tCO2

b expectation of increase of carbon priceZ leakage coefficientl energy penalty of Capture technology

F. Teng, D. Tondeur / Energy 32 (2007) 540–548 541

where a net present value (NPV) model has often been usedfor assessment of CCS projects. Differing from thesestudies, the present paper concerns the permanence issue inthe CCS area through two different approaches: the firstone is a physical approach, comparing the cumulativeradiative forcing of the CCS plant with its reference plant;the second one is an economic approach focusing on theeconomic efficiency, using a more detailed NPV model forthe same comparison. At last, these two approaches arecompared and conclusions are given.

1Radiative forcing is defined as the change in net irradiance at the

tropopause (in W/m2) due to a change in greenhouse gas concentrations

(in ppm).2The Kyoto Protocol uses 100 years as selected time scale, but it is based

on a political negotiation rather than a scientific argument.

2. Background

The core problem of the permanence issue is thefollowing: compared with carbon avoided from fossil fuelusage, what is the value of temporary sequestered carbon?As Chomitz [7] suggested, two possible approaches can beused to address this issue: (1) To assess the environmentaland economic benefit of commitments to limited-termsequestration agreements. (2) To devise mechanisms thatprovide reasonable assurance of indefinite sequestration.

The first approach leads to researches for a numericalindex comparing the contribution to global warming oftemporary sequestration and permanent fossil fuel avoided.From an environmental point of view, as Smith and Wigley[8] discussed, there is the question of what component ofclimate change should be used for such comparison. Thecausal chain of climate change can be represented asfollows [8]:

Emissions changes! concentrations!

radiative forcing! climate changes!

climate impacts! human welfare

Though climate impacts and their damage to humanwelfare are direct motivations for greenhouse gases(GHGs) mitigation, radiative forcing or concentration areoften used as proxy for comparison [9] because they can bespecified with better accuracy, and most global carbonmodels (GCMs) [9] suggest that global mean surface

temperature response is related to radiative forcing by alinear relation.

2.1. Radiative forcing and global warming potential

When comparison is needed between ‘the contributions ofvarious ‘‘GHGs’’ to global warming’ [10], the natural choiceis to express these contributions in terms of radiativeforcing.1 The impact of GHGs upon the atmosphere is notonly related to radiative properties, but also to their lifetime,which controls the time-scale of their influence on thethermal budget. That means the radiative property shouldbe integrated over a selected time period while accountingfor the cumulative effects of the gas during that period.Then, an absolute global warming potential (AGWP) of agiven GHG symbolized by ‘‘g’’ can be defined as

AGWPðgÞ ¼

Z TH

0

agfgðtÞdt, (1)

where TH is the time scale selected for the calculation2, ag is theradiative efficiency due to a unit increase in atmosphericabundance of the substance in question (i.e., Wm�2kg�1), fg(t)is the time-dependent decay function (sometimes called impulseresponse function). fg(t) is equal to the fraction of the initiallyadded carbon at time t ¼ 0 which is still found in theatmosphere at any later time t. For the purpose of comparingvarious GHGs, a relative rather than absolute index is preferred,and CO2 is often selected as a reference gas. Then GWP can bedefined as the ratio of the time-integrated radiative forcing frominstantaneous release of 1kg of a given GHG relative to that of1kg of CO2 (reference gas). This definition can be presented by

GWPgC ¼

AGWPðgÞ

AGWPðCO2Þ¼

R TH

0 agfgðtÞdtR TH

0 aCf CðtÞdt

. (2)

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Table 1

GWP of several typical GHGs

Radiative Efficiency

(W/m2/ppb)

Global warming potential

20 years 100 years 500 years

CO2 1.55� 10�5 1 1 1

CH4 3.7� 10�4 62 23 7

N2O 3.1� 10�3 275 296 156

HFCs 0.02–0.40 40–9400 12–12,000 4–10,000

SF6 0.52 15,100 22,200 32,400 0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

f c (x)

Year

Fig. 1. Impulse response function of CO2 over 100-years duration.

F. Teng, D. Tondeur / Energy 32 (2007) 540–548542

The GWPs of various GHGs can be easily compared todetermine which will cause the greater integrated radiativeforcing over the given time period. GWP of some typicalGHGs are listed in Table 1.

Currently the best-known CO2 impulse response func-tion is the function described in Bern’s carbon cycle model[11]. In the literature, a simplified parameter version isoften used [11], which does not take into account theconcentration level, and is represented by the empirical Eq.(3) and Fig. 1:

f CðtÞ ¼ 0:30036� e�t=6:6993 þ 0:34278� e�t=71:109

þ 0:3568� e�t=815:727. ð3Þ

3. Efficiency of CCS

Based on the first approach suggested by Chomitz [7],two possible ways have been identified in the precedingcontext to evaluate the efficiency of temporary storage: onefrom an environmental point of view and the other from aneconomical point of view.

3.1. Radiative forcing efficiency of CCS

The impact of CO2 leakage from storage depends onvolumes stored and leakage rate. However, it is difficult toknow how much carbon will be sequestered in the futurebecause it will depend on the trade off among differentmitigation options. To account for this problem, we take amarginal point of view where only an additional unit ofsequestered carbon is considered. In addition, there is stillnot sufficient experience to estimate leakage rate.3

The processes and pathways for release of CO2 fromgeological storage site are very complex including throughthe pore system, openings in the caprock and someanthropomorphic pathways [12]. Several numerical simula-tion models have been developed to study the long-termstorage performance in operating CCS project andthe complex hydrogeological–geochemical–geomechanicaltrapping mechanism: for example, [13] for Sleipner, [14,15]for Weyburn. Unfortunately, there is at present no model

3Some models have been developed for evaluating direct injection CO2

into the ocean, for example [16].

able to predict or estimate the release across a sample ofstorage site. We shall, therefore, introduce a simple modelassuming the leakage rate is proportional to the stock.Although this assumption lacks experimental validation, itis probably conservative because the storage security willactually increase with time due to the trapping mechanisms[12]. This model involves only one parameter. Suchsimplification permits us to focus only on the efficiencycomparison of CCS and will not harm our majorconclusions.We start from a conservation equation of CO2 over the

storage, assuming the leakage rate L(t) (with unit of tonsper year) is proportional to the stock S (tons):

LðtÞ ¼ �dSðtÞ

dt¼ ZSðtÞ, (4)

the proportionality coefficient Z (year�1) is called theleakage coefficient and assumed constant in the followingdiscussion. Eq. (4) is integrated over time into Eq. (5):

SðtÞ ¼ S0e�Zt, (5)

where S0 is the amount of carbon sequestered at time 0.Substituting Eq. (5) into Eq. (4) and dividing by the initialvalue S0, we get a non-dimensional expression for theinstantaneous leakage rate:

lðtÞ ¼LðtÞ

S0¼ Ze�Zt. (6)

This function is illustrated in Fig. 2 for different leakagecoefficients Z.The leaked carbon will get into the atmosphere and then

the carbon cycle, so the cumulative decay function causedby the former leakage curve can be expressed from thefollowing integral:

f SðtÞ ¼

Z t

0

f Cðt� tÞlðtÞdt, (7)

that is illustrated in Fig. 3:If we treat sequestered carbon with leakage as a kind of

‘‘GHG’’, the corresponding ‘‘GWP’’ can be calculatedfrom the above-defined formulation, where the radiativeefficiency is that of CO2. Hence, the ‘‘GWP’’ of thesequestered carbon with leakage is calculated by the

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0 20 40 60 80 1000.00

0.01

0.02

0.03

0.04

0.05

Car

bon

Lea

kage

Rat

e, l

(t),

(Y

ear-1

)

Time (Years)

�=0.05

�=0.01

�=0.005

Fig. 2. Leakage curve of CCS under different leakage coefficient.

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

f S (

t)

Time (Years)

�=0.005

�=0.01

�=0.05

f C (t)

Fig. 3. Decay function corresponding to different leakage coefficient.

Table 2

‘‘GWP’’ and efficiency factors of sequestered carbon under different

leakage coefficient

Leakage coefficient (Z) 0.001 0.005 0.01 0.02 0.04 0.05

GWP 0.054 0.237 0.404 0.613 0.796 0.839

Efficiency (1-GWP) 0.946 0.763 0.596 0.387 0.204 0.161

0.00 0.01 0.02 0.03 0.04 0.050.0

0.2

0.4

0.6

0.8

1.0

Eff

icie

ncy

Fact

or, 1

-GW

P (�

)Leakage Coefficient, �

Fig. 4. Function relationship between leakage coefficient and efficiency

factors.

4The energy used for carbon transportation and injection was not

included here.5This figure and corresponding data came from Herzog [17] Fig. 2.

F. Teng, D. Tondeur / Energy 32 (2007) 540–548 543

following formula:

GWPSTH ¼

R TH

0aCf SðtÞdtR TH

0 aCf CðtÞdt

. (8)

Assuming a constant radiative efficiency, we get asimplified version as follows:

GWPSTH ¼

R TH

0f SðtÞdtR TH

0f CðtÞdt

¼

R TH

0

R TH

0f Cðt� tÞlðtÞdt dtR TH

0f CðtÞdt

. (9)

Using a standard numerical method, we can calculate the‘‘GWP’’ of sequestered carbon when the leakage curve fC isgiven. Table 2 gives some results for a series of constantleakage coefficients when the time scale TH is fixed to 100years.

Though it is difficult to give a close form relationbetween leakage rate and corresponding efficiency factor,Fig. 4 gives an illustration of this function.

The quantity of 1-GWP can be considered as an index of‘‘efficiency’’ which translates one unit of sequesteredcarbon with leakage into some unit of carbon reductionwithout leakage risk. For example, given Z ¼ 0.01, oneadditional ton of sequestered carbon has the samecumulated radiative forcing effect as 0.404 ton (Table 2)of carbon emitted at the same time (time 0). Thus it may beconsidered to be equivalent to 0.596-ton carbon avoided.

Based on a 5% level, a sequestration with a leakagecoefficient of 0.001 can be regarded as efficient.

3.2. Energy penalty issue and carbon accounting

Even if there is no leak risk for carbon storage, it is stillwrong to account all of the captured and sequesteredcarbon as carbon credits. We still have to compare to theamount of carbon to be emitted into the atmosphere in theabsence of sequestration activities. A benchmark needs tobe defined for calculating how much carbon is offsetcompared with a business-as-usual scenario.In the literature, a reference plant is often defined as a

power plant without carbon capture facilities, while othercharacteristics are the same as a plant with capture.Because more energy is needed to capture and compressthe carbon dioxide from the flue gas4, a plant with capturewill consume more fuel than a reference plant whengenerating the same output (e.g. 1 kWh). That is, not allof the carbon captured and sequestered should beconsidered as carbon reduction, because the additionalenergy needed for carbon capture and compressing willalso cause CO2 emission but has no contribution to energyoutput, and such emission should be removed from carboncredit. The difference between CO2 captured and CO2 non-permanent avoided has been noticed by many researchers[17]. Fig. 55 is often used in literature for illustrating suchdifference.

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0.0 0.2 0.4 0.6 0.8 1.0

Direct EmissionCaptured CO2

CO2 captured

CO2 avoided (non permanent)

ReferencePlant

Plantwith Capture

CO2 Produced (kg/kWhe)

Fig. 5. Difference between CO2 ‘‘avoided’’ and CO2 captured.

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.0

0.2

0.4

0.6

0.8

1.0

� /C

R

�m

Membrane

PSATSA

AbsorptionMembrane+MEA

Infeasible Region

Feasible Region

Fig. 6. Different capture technologies and corresponding Zm.

Table 3

l/CR of different capture technology with different reference plant

PC+FGDa NGCCb IGCCc CO2/O2d IGCC

selexol

Absorption 0.31 0.22 0.37 0.09 0.17

Adsorption (PSA) 0.32 0.39 0.40 0.13 —

Adsorption (TSA) 0.29 0.26 0.33 — —

Cryogenic — — 0.16 0.21 —

Membranes 0.29 0.50 0.48 0.08 —

Membranes+MEA 0.31 0.13 0.30 0.11 —

aPulverised coal power plant+flue gas desulphurisation.bNatural gas-fired combined cycle.cIntegrated gasification combined cycle.dCarbon dioxide recycle power plant.

F. Teng, D. Tondeur / Energy 32 (2007) 540–548544

Energy penalty l is defined as the reduction in net poweroutput of the capture plant compared to the reference plantfor equal fuel inputs, thus:

l ¼ð1=HRrÞ � ð1=HRcÞ

ð1=HRrÞ¼ 1�

HRr

HRc(10)

or

HRc ¼HRr

1� l, (11)

where HR is the so-called ‘‘heat rate’’, a measure of apower plant thermal efficiency.

For the reference plant, the CO2 emission factor ofelectricity generation (in kg CO2/kWhe) is

EFr ¼ HRrdEF, (12)

while the emission factor of electricity generation in theplant with capture may be defined as:

EFc ¼ HRcdEFdð1� CRÞ þHRcdEFdCRdGWPðZÞ.

(13)

The first term of Eq. (13) is related to direct emission ofnon-captured CO2, and the second term is related to thecaptured and sequestered carbon with a leakage coefficientZ. Recall that one unit of CO2 sequestered is equivalent toGWP(Z) unit of CO2 emission based on cumulativeradiative forcing. If we use Eq. (11) to rewrite Eq. (13),we get:

EFc ¼ ð1� CRÞ þ CRdGWPðZÞ½ �dHRrdEF

1� l. (14)

From Eqs. (12) and (14), it can be understood that theemission of the plant with capture is smaller than that ofthe reference plant if and only if EFcoEFr, which isequivalent to the condition in Eq. (15).

1�GWPðZÞ4l=CR. (15)

This formulation means that CCS in a power plant may

cause a larger global warming effect than in a referenceplant, if the capture rate is too low, energy penalty is too

high or leakage coefficient is too large. Generally speaking,if the criterion (15) is not satisfied, the CCS project shouldbe rejected because it will increase cumulative radiativeforcing instead of decreasing it. For this reason, Eq. (15)can be considered as an efficiency criterion for a CCSproject in the power sector.The ratio l/capture ratio (CR) can be regarded as an

index representing characteristics of different capturetechnologies, while the characteristics of geological reser-voir are represented by Z. When a specific capturetechnology is given (that is l/CR is given), a maximum

allowable leakage coefficient gm can be defined as thesolution of the following equation:

1�GWPðZmÞ ¼ l=CR. (16)

Eq. (16) is illustrated in Fig. 6 and shows the relationshipbetween different capture technologies, characterized bytheir index l/CR, and the corresponding maximumallowable leakage rate. Characteristics of different capturetechnologies are collected in Table 3 with original datafrom International Energy Agency (IEA) [18]; a morecomprehensive calculation is listed in the Appendix.Note that the graph of Fig. 6 is identical to that of Fig. 4,

but they have different interpretations.For example, a typical pulverized coal (PC) capture

plant has an energy penalty l of about 27%, while the CR

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6For simplicity, we use an infinite time scale here instead of a finite one.

This simplicity will not do harm to our subsequent conclusion because

Profitc4Profitr is a sufficient condition (but not necessary) for Profit-

cTH4Profitr with any given finite time scale.7If this condition fails, then the sum of Eq. (19) is firmly negative so that

the CCS project is financially unbeneficial.8Note that a40 and r+Z�b40.

F. Teng, D. Tondeur / Energy 32 (2007) 540–548 545

is assumed as 90% for most research works [14]. Accordingto condition (15), 1�GWP(Z), the efficiency of sequesteredcarbon should be larger than 0.30, which requires that theleakage coefficient Z be smaller than 0.027. As anotherexample, an energy penalty of 35% and a capture ratio of80% require that the corresponding efficiency of seques-tered carbon be larger than 0.44, which is equivalent to aleakage coefficient smaller than 0.017.

The preceding simple analytical model shows that thetrade-off between capture plant and non-capture plant isaffected by two factors: (1) the capture technologycharacteristics defined as energy penalty divided by thecapture ratio; (2) the leakage of stored carbon.

As a conclusion of the physical approach, it appears thatCCS does not always prevent us from global warming.Under certain conditions of high-energy penalty and/orlow capture ratio and/or high leakage, CCS can beineffective and even worsen the warming effect.

3.3. Economic efficiency of CCS

Differing from the above approach, some researcherssuggested to treat emissions and removal separately [6], thusthe sequestration will not be different from permanent carbonavoided. In other words, when one removes a ton of carbon,one gets credits for its removal; when the sequestered carbonleaks back to the atmosphere, one must buy credits fromsomewhere for offsetting its ‘‘emission’’, we call it ‘‘pay whenleak’’. The essential feature of this approach is thatsequestered carbon implies a permanent liability for the‘‘owner’’. With this permanent liability, a potential investor ina sequestration project will face an investment decisionproblem based on a cash flow caused by leakage fromreservoirs and carbon credits price in the future. The classicalapproach for such decision problems is the so-called NPV[19], which calculates the discounted present value of projectcash flow. It can be expressed as follows:

NPV ¼

Z 10

pðtÞAðtÞe�rt dt, (17)

where t is the time, p(t) is the carbon price or carbon tax attime t, A(t) is the carbon credits acquired (positive) or needed(negative) at time t, r is the discount rate. This framework iswidely employed for discussion of economic efficiency ofsequestration [4–6]. But the definition of economic efficiencyin literature is not consistent. Some researchers define it froma point of view of potential investors [4,6], framing it as anindustrial economics problem, while others define it on thebasis of carbon tax path [5]. The second definition is a moremacroscopic measure for CCS because carbon tax is often ashadow price of carbon emission coming from a complexeconomy-environment model.

The difference between these two definitions is clear: theformer is based on expectation about future carbon priceand discount rate of specific investors, and can be used forexplaining decision making of an individual; the latter isbased on carbon tax path and social discount rate, and can

be used for a collective analysis, concerning for examplepublic policies. For the latter way, it can be considered as apartial equilibrium model if carbon tax path and socialdiscount rate are exogenously given; it can also beintegrated with some economy-environment model tomake the carbon tax path determined endogenously.As Keller et al. [5] argued, in a simple NPV framework,

the tradeoff between CO2 abatement and CO2 sequestra-tion is affected by four factors: (1) energy penalty; (2)leakage rate; (3) future carbon tax path; (4) discount rate.We follow this simple analytical framework, from theviewpoint of an investor, to determine whether or not CCSshould be employed in a power plant. For linking thissection and former discussion, a fifth factor, capture ratio,is added into this framework.For the reference plant, the marginal benefit from 1kWh

electricity output is

Profitr ¼ Pe � EF �HRr � Pc � PF �HRr. (18)

While for the plant with capture, the marginal benefitfrom 1kWh electricity output6 is

Profitc ¼ Pe � EF �HRc � ð1� CRÞ � Pc

�

Z 10

EF �HRc � CR � Ze�Zt|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}AðtÞ

�Pc � ebt|fflfflffl{zfflfflffl}

PðtÞ

�e�rt dt

� PF �HRc. ð19Þ

The integral of the preceding equation can be calculatedanalytically, assuming r+Z�b407 and the solution can bewritten as follows:

Profitc ¼ Pe � EF �HRc � ð1� CRÞ � Pc

�EF �HRc � CR � Pc � Z

rþ Z� b

� PF �HRc. ð20Þ

The criterion for the plant with capture to be preferredover a reference plant is Profitc4Profitr. Using Eqs. (11),(18) and (20), this condition can be expressed as

1þPF

EF � Pc

� �lCR

o1�Z

rþ Z� b. (21)

Letting

a ¼ 1þPF

EF � Pc

� �lCR

, (22)

Eq. (21) is equivalent to the following condition:8

Zoð1� aÞðr� bÞ

a. (23)

A necessary condition (but not sufficient) for Eq. (23) to

ARTICLE IN PRESS

Feasible Region

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.0

0.2

0.4

0.6

0.8

1.0

� /CR

�m

Pc=93$/tC

Pc=14$/tC

Pc=50$/tC

r-�= 3.5%

Pc=5$/tC

Infeasible Region

Fig. 7. Physically and economically maximal permissible leakage coeffi-

cient under different carbon price.

F. Teng, D. Tondeur / Energy 32 (2007) 540–548546

hold is ao1, otherwise the emission of capture plant will behigher than that of the reference plant no matter how smallis the leakage rate (keeping in mind that it cannot benegative). We call this condition economical feasibility

condition.When the economical feasibility condition stands, a

maximum allowable leakage coefficient can be given by

Zm ¼ð1� aÞðr� bÞ

a. (24)

For illustration, the following parameters set areselected:

PF ¼ 1.5$/GJ9, PC ¼ 24$/tCO210, EF ¼ 90 kg CO2/GJ11

for coal burning.With the above parameter set for coal, the economic

feasibility condition is: l/CRo0.59. For a CR of 90%; theabove condition is equivalent to lo0.53. Almost all thecapture technology listed in Table 3 is economicallyfeasible.

4. Comparison among different Factors

As we have discussed earlier, for a physical analysisbased on a cumulative radiative forcing calculation, themaximum allowable leakage coefficient Zm is only relatedto the technological characteristics of capture technology,which is qualified by l/CR. For an economical analysis, Zmis affected not only by technological characteristics, butalso by economical term (1+PF/(EF*PC)) and by theexpectation term (r�b). The expectation term gives theexpectation about future carbon price path and discountrate of a specific investor. The economical term determineswhether or not a capture technology is economicallyfeasible (not considering the leakage issue).

1�GWPðZÞ4l=CR; (15)

Zoð1� aÞðr� bÞ

a. (23)

As the criterion Eq. (15) coming from a radiative forcingapproach, formulation Eq. (23) gives a criterion based on afinancial analysis. If the latter criterion fails to hold, a CCSproject should be rejected economically, but it may still beacceptable physically, that means the criterion Eq. (15) stillstands, and vice versa. In other words, the radiative forcingcriterion Eq. (15) is inconsistent with the economical oneEq. (23). In addition, the criterion based on radiativeforcing is an objective criterion which does not vary withany subjective expectation while the economical criterionwill vary with different subjective expectation and econom-ical variables (e.g. fossil fuel price and initial carbon price).

9Data came fromWorld Energy Outlook [20]; The price of fuel reported

in WEO is fuel price without carbon tax. When a carbon tax regime is

employed, the fuel price should also change to reflect a new equilibrium.10Data from [21], the carbon tax adopted by Norway government in

1999 for coal burning.11Data came from Emission Factor Database, http://www.ipcc-nggip.i-

ges.or.jp/EFDB/main.php.

These differences between radiative forcing criterion andeconomical criterion are illustrated in Fig. 712 and Fig. 8under different expectation and different carbon price13.The relationship between physical criterion and econom-

ic criterion is complex; none of them is simply dominatedby the other. Generally speaking, for lower leakagecoefficient, the economic criterion is stronger than thephysical one while for higher leakage coefficient, it is justthe opposite. As we discussed above, the economiccriterion relaxes further and further when carbon priceand/or expectation term become higher and higher, whilethe physical one remains. Under high carbon price andhigh expectation, some CCS technologies will be economic-ally worthwhile but physically non-beneficial.When using the economic approach, as Herzog argued

[4–6], the potential investor must carefully estimate thefuture carbon price and calculate the rate of return of asequestration project, which will be compared with that ofother alternatives. Once he decides to implement suchproject, he must cover the leakage when it happens. The‘‘pay when leak’’ approach relies on individual expectationterm (r�b), not on social aggregate one. If an individualinvestor overestimates the expectation term and uses aphysically inefficient storage site, the whole society has tosuffer from the wrong decision because the permanentliability cannot be really unlimited [22]: at one point theinvestor will chose bankruptcy to avoid further losses.Most important, if such overestimation for the expectationterm was commonly done by investors, the pertinence ofpursuing the CCS option would be questionable unless astrong regulation for reservoir selection is set up. Just asBaer argued [22] ‘‘If we are to proceed with the use ofsequestration, we need to regulate it in a way thatestablishes a precautionary limit on storage today basedon the long-term rate of leakage and the plausible failure ofliability’’.

12(r�b) ¼ 3.5% is based on estimation of [5] They used a RICE model

[24] as a starting point which is a optimal growth model.13But the fuel price is assumed fixed here.

ARTICLE IN PRESS

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.100.0

0.2

0.4

0.6

0.8

1.0

� /CR

�m

Pc=50$/tC

r-�=5%

r-�=3.5%

r-�=2%r-�=1%

Feasible Region

Infeasible Region

Fig. 8. Physically and economically maximal permissible leakage coefficient under different future expectation.

Table A.1

Details of the calculation of l/CR for different capture technology with

different reference planta

PF+FGD GTCC IGCC CO2/O2 IGCC

selexol

Reference plant efficiency

(100/HRr)

40% 52% 42% 33% 42%

Absorption

Efficiency After Capture 29% 42% 28% 30% 36%

Energy penalty 0.28 0.19 0.33 0.09 0.14

Capture rate 90% 85% 90% 99% 82%

l/CR 0.31 0.22 0.37 0.09 0.17

Adsorption (PSA)

Efficiency after capture 28% 33% 26% 29% —

Energy penalty 0.30 0.37 0.38 0.12 —

Capture rate 95% 95% 95% 95% —

l/CR 0.32 0.39 0.40 0.13

Adsorption (TSA)

Efficiency after capture 29% 39% 29% — —

Energy penalty 0.28 0.25 0.31 — —

Capture rate 95% 95% 95% — —

l/CR 0.29 0.26 0.33 — —

Cryogenic

Efficiency after capture — — 36% 27% —

Energy penalty — — 0.14 0.18 —

Capture rate — — 85% 85% —

l/CR — — 0.16 0.21 —

Membranes

Efficiency after capture 31% 31% 26% 31% —

Energy penalty 0.23 0.40 0.38 0.06 —

Capture rate 80% 80% 80% 80% —

l/CR 0.29 0.50 0.48 0.08 —

Membranes+MEA

Efficiency after capture 30% 47% 32% 30% —

Energy penalty 0.25 0.10 0.24 0.09 —

Capture rate 80% 80% 80% 80% —

l/CR 0.31 0.13 0.30 0.11 —

aData collected from [18].

F. Teng, D. Tondeur / Energy 32 (2007) 540–548 547

When they underestimate the ‘‘expectation term’’, somephysically feasible CCS project will be pending because ofeconomical consideration, some other mitigation strategywith higher cost will be employed. There will be anefficiency loss.

5. Conclusion

This paper examined carbon capture and storagetechnology with leakage under different aspects: a physicalaspect based on radiative forcing, and an economicalaspect based on discounted NPV. The former approachcan be interpreted as a systemic point of view, while thelatter can be interpreted as a cost-benefit assessment fromthe viewpoint of individual investors.

The analysis based on the GWP concept confirms that aleakage coefficient of 0.001 (i.e., a 0.1% loss of the stockper year) is nearly the same as perfect storage, meaningstorage without any leakage or carbon avoided. The sameconclusion has been reached by several other researchersthrough different approaches [23]. A comparison analysisshows that for high leakage rates CCS may cause largerglobal warming effect than a reference plant, at least forCCS in power plants. The impact of such project uponcumulative radiative forcing is determined by the interac-tion between energy penalty, capture ratio and leakagerate. Careful technology choices, project design, plantoperation and reservoir selection are essential for prevent-ing project failure.

Although the economical approach is straightforwardfor CCS, it is strongly affected by ‘‘individual expectation’’about the future carbon price path. When the carbon pricepath is overestimated, some high leakage reservoirs may beemployed and cause higher radiative forcing in the future.When it is underestimated, some CCS project that ought tobe good will be rejected, thus an efficiency loss.

Of course the radiative forcing approach also has someshortcomings. Firstly, it does not take the economic termsinto consideration and gives no idea on cost considerationsand investor’s incentives. Secondly, the marginal treatmentwe used in this paper only gives an insight for comparativestatic analysis. But it is useful for being a benchmark case.

There is no simple relationship between the physicalcriterion and the economic criterion. Generally speaking,the economic criterion is more selective than the physicalone when the leakage coefficient of the reservoir is small,

ARTICLE IN PRESSF. Teng, D. Tondeur / Energy 32 (2007) 540–548548

but it is just the opposite when this coefficient is large. Notealso that the two criteria cannot be the elements of acompromise or a multi-criterion optimization: they shouldboth be satisfied for a project to make any sense.

Finally, our models are based on a set of assumptions,some of which are strong and restrictive. The resultsshould, therefore, be used carefully and checked undersome more realistic assumptions. A fully comprehensiveanalysis requires more realistic numerical models to bedeveloped in the future.

Acknowledgements

This work has been carried out in Nancy in theframework of the CEFCEET (Sino-French Center forEnergy and Environment of Tsinghua University). Theauthors gratefully acknowledge the financial support of theFrench Ministry of Research. Dr. Fei Teng would like tothank Mr. Weizhong Wang for outstanding researchassistance.

Appendix A

For details of the calculation of l/CR see Table A.1.

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