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Climate strategy with CO2 capture from the air

David W. Keith∗ Minh Ha-Duong Joshuah K. Stolaroff

March 31, 2005

Abstract

It is physically possible to capture CO2 directly from the air and immobilize it

in geological structures. Air capture differs from conventional mitigation in three

key aspects. First, it removes emissions from any part of the economy with equal

ease or difficulty, so its cost provides an absolute cap on the cost of mitigation.

Second, it permits reduction in concentrations faster than the natural carbon cycle:

the effects of irreversibility are thus partly alleviated. Third, because it is weakly

coupled to existing energy infrastructure, air capture may offer stronger economies

of scale and smaller adjustment costs than the more conventional mitigation tech-

nologies.

We assess the ultimate physical limits on the amount of energy and land re-

quired for air capture and describe two systems that might achieve air capture at

prices under 200 and 500 $/tC using current technology.

Like geoengineering, air capture limits the cost of a worst-case climate sce-

nario. In an optimal sequential decision framework with uncertainty, existence

of air capture decreases the need for near-term precautionary abatement. The

long-term effect is the opposite; assuming that marginal costs of mitigation de-

crease with time while marginal climate change damages increase, then air capture

∗Corresponding author. Department of Chemical and Petroleum Engineering, University of Calgary,

2500 University Drive NW, Calgary, AB, Canada T2N 1N4, [email protected]

increases long-run abatement. Air capture produces an environmental Kuznets

curve, in which concentrations are returned to preindustrial levels.

1 Introduction

It is physically possible to capture CO2 directly from air and immobilize it in geolog-

ical structures. Today, there are no large-scale technologies that achieve air capture

at reasonable cost. Yet, several strong arguments suggest that it will be possible to

develop practical air capture technologies on the timescales relevant to climate policy

[Elliott et al., 2001, Zeman and Lackner, 2004]. Moreover, we argue that air capture

has important structural advantages over more conventional mitigation technologies

which suggest that, in the long-run, air capture may play a significant role in mitigating

CO2 emissions.

Air capture may be viewed as a hybrid of two related mitigation technologies. Like

carbon sequestration in ecosystems, air capture removes CO2 from the atmosphere,

but it is based on large-scale industrial processes rather than on changes in land-use,

and it offers the possibility of near-permanent sequestration of carbon. It is also pos-

sible to use fossil fuels with minimal atmospheric emissions of CO2 by capturing the

carbon content of fossil fuels while generating carbon-free energy products, such as

electricity and hydrogen, and sequestering the resulting carbon. Like CO2 Capture

and Storage (CCS), air capture involves long-term storage of CO2, but unlike CCS air

capture removes the CO2 directly from the atmosphere and so manipulates the global

atmospheric concentration rather than the exhaust stream of large fixed-point sources

such as power plants.

This paper hangs on the long-run performance of air capture, a technology that

does not now exist at commercial scale. Predicting the performance of technologies

a century or more in the future might appear to be a fool’s errand. We embark on it

nevertheless because near-term climate policy does depend on long-run estimates of

the cost of mitigating CO2 emissions, whether or not such dependence is considered

explicitly.

We don’t believe we can estimate the costs of air capture late in this century with an

accuracy of better than perhaps a factor of three. Moreover, we are similarly pessimistic

about anyone’s ability to make predictions about any large-scale energy technologies

a century in the future. If near-term decisions were strongly contingent on long-run

technology forecasts, then the task would be hopeless. As we shall demonstrate in the

latter half of the paper, however, the sensitivity of near-term decisions to assumptions

about the distant future is sufficiently weak that estimates with this level of uncertainty

can provide a meaningful guide to near-term decisions.

We suggest that the two most important factors in estimating the long-run perfor-

mance of energy technologies are, first, the basic physical and thermodynamic con-

straints and, second, the technology’s near-term performance. Section 2 addresses the

first factor, the ultimate physical and economic constraints that may determine the long-

run performance of air capture technologies. The second factor is addressed in Section

3, which presents two examples of how air capture might be achieved using current

technology. Our view is that air capture could plausibly be achieved at roughly 500

$/tC (dollars per ton carbon) using currently available technologies, and that the com-

bination of biomass with CCS could remove carbon from the air at about half that cost.

While these technologies are not competitive with near-term mitigation options such

as the use of CCS in electric power generation, they may be competitive with other

prominent mitigation technologies such as the use of hydrogen fuel-cell cars [Keith

and Farrell, 2003].

In the second half of the paper we examine the implications of air capture for the

long-run policy and economics of climate change using a global integrated assessment

model. The Dynamics of Inertia and Adaptability Model (DIAM) is described in Sec-

tion 4. Section 5 explores the economic consequences of air capture for global climate

policy, by examining how air capture affects optimal CO2 emission strategies.

2 Ultimate physical and economic limits on the perfor-

mance of air capture technologies

An air capture system (as we define it) removes CO2 from the air and delivers a pure

CO2 stream for sequestration. In general, air capture systems will use some sorbent

material that selectively captures CO2. The sorbent is then regenerated to yield con-

centrated CO2 and fresh sorbent ready to be used for capture. A contacting system is

necessary to expose the sorbent to fresh air. At the simplest, a pool of sorbent open to

the air might serve as a contactor. Active contacting systems might look like water-air

heat exchangers that are associated with power plants in which fans blow air past a

system of flowing sorbent. Energy is required for regeneration, to pump sorbet and air

through the contacting system, and to compress the CO2 stream for pipeline transport

or sequestration. The energy could be supplied by any source: fossil, solar, or nuclear

systems are all plausible.

Extraction of pure gases from air is more than theory: oxygen, nitrogen, and argon

are commercially produced by capture from air. The crucial questions about air capture

are the cost and energy inputs. In this section we assess some of the ultimate physical

limits on the amount of energy and land required to capture CO2 from the air. While

there are no detailed engineering-economic estimates of performance of air capture

technologies, there is a wealth of analysis on the capture of CO2 from centralized power

plants (although we do not expect that the performance of air capture technologies will

approach these limits for many decades). We therefore assess the basic physical and

economic factors that influence relationship between the cost of direct CO2 capture

from air and the more familiar process of capture from centralized power plants. The

relationship between these ultimate limits and nearer term costs is addressed in the

following section.

These thermodynamic arguments do not, of course, prove that practical air capture

systems can be realized, nor is the performance of air capture technologies likely to

approach thermodynamic limits in the near future. The ultimate thermodynamic limits

are nevertheless an important basis for suggesting that air capture can be achieved

at comparatively low cost. From the liberation of pure metals from their oxides to

the performance of internal combustion engines, electric motors and heat pumps, the

historical record strongly supports the view that thermodynamic and other physical

limits serve as an important guide to the long run performance of energy technologies.

2.1 Physical limits to the use of energy and land

Thermodynamics provides a lower-bound on the energy required for air capture. The

minimum energy needed to extract CO2 from a mixture of gases in which the CO2

has an partial pressure p0 and to deliver it as a pure CO2 stream at final pressure p

is set by the enthalpy of mixing, k T ln (p/p0), where k is the Boltzmann constant

(8.3 J mol−1 K−1) and T is the working temperature. At typical ambient temperatures,

k T is about 2.5 kJ/mol. The minimum energy required to capture CO2 from the air at

a partial pressure of 4 × 10−4 atm and deliver it at one atmosphere is therefore about

20 kJ/mol or 1.6 GJ/tC (gigajoules per ton carbon). If we add the energy required for

compressing the CO2 to the 100 atm pressure required for geological storage (assuming

a 50% efficiency for converting primary energy to compressor work) the overall energy

requirement for air capture with geologic sequestration is about 4 GJ/tC.

The ∼4 GJ/tC minimum may be compared to the carbon-specific energy content

of fossil fuels: coal, oil, and natural gas have about 40, 50, and 70 GJ/tC respectively.

Thus if the energy for air capture is provided by fossil fuels then the amount of carbon

captured from the air can—in principle—be much larger than the carbon content of

the fuel used to capture it. The fuel carbon can, of course, be captured as part of the

process rather than being emitted to the air.

Now consider the requirement for land. Land-use is an important constraint for

energy technologies in general, and is a particularly important constraint for biological

methods of manipulating atmospheric carbon that may compete with air capture. An air

capture system will be limited by the flux of CO2 that is transported to the absorber by

atmospheric motions; even a perfect absorber can only remove CO2 at the rate at which

it is carried to the device by large-scale atmospheric motion and turbulent diffusion. At

large scales (100’s of km), CO2 transport in the atmospheric boundary layer limits the

air capture flux to roughly 400 tC/ha-yr [Elliott et al., 2001].

If air capture is used to offset emissions from fossil fuels as a means to provide

energy with zero net CO2 emissions, then we can divide the power provided by the

fossil fuels by the land area required to capture the CO2 emission resulting from the

fuel combustion in order to compute a power density. If coal is used as the fuel, then an

air-capture/coal system can provide a CO2-neutral energy flux of 50 W m−2 (the value

would be almost twice this for an air-capture/natural-gas system).

This result is the effective density at which fossil fuels with air capture provide

power with zero net emissions. It may be directly compared with the power densities of

alternative CO2-neutral energy systems. Both wind power and biomass based systems

can produce roughly 1 W m−2, and even solar power which is constrained much more

strongly by cost than by land-use can deliver only ∼20 Wm−2.

There is a strong analogy between the land requirements for air capture and for

wind power. Both depend on the rate of turbulent diffusion in the atmospheric boundary

layer: diffusion of CO2 for air capture and diffusion of momentum for wind power. In

each case, large scale processes limit the average flux. Large wind farms, for example,

must space their turbines about 5–10 rotor-diameters apart to avoid “wind shadowing”

by allowing space for momentum to diffuse downward from the fast moving air above.

Similarly for an air capture system, the individual units must be spaced far enough apart

to ensure that each receives air with near-ambient CO2-concentration. In each case the

footprint of the actual hardware can be limited to only a tiny fraction of the required

land because the footprint of an individual wind turbine or air capture system can be

small, and the land between the units can be preserved for other uses. If computed

using only the footprints of the individual air capture units, CO2-neutral flux can be

many 100’s of W m−2.

The large effective power densities of air capture, however computed, make it im-

plausible that land-use could be a significant constraint on the deployment of air cap-

ture.

2.2 Capture from the air compared with capture from power plants

Almost all the literature on industrial CO2 capture and sequestration has addressed the

problem of capturing CO2 from large centralized facilities such as electric power plants

[Reimer et al., 1999, Willams et al., 2001]. It is therefore instructive to compare the

cost of air capture with the cost of capture from these sources.

First, a technical point. One might expect that the energy required to capture CO2

from the air, where its concentration is 0.04% would be much larger than the energy

required for capture from combustion streams which have CO2 concentrations of 10%.

The enthalpy of mixing is logarithmic, however, so the theoretical energy required to

capture atmospheric CO2 is only ∼3.4 times the theoretical requirement for capture

from a 10% source at atmospheric pressure.

The energy requirement computed from the enthalpy of mixing assumes that the

capture system removes only an infinitesimal fraction of the CO2 stream (in economist’s

terms it’s the value for marginal removals). For real capture systems removing a sig-

nificant fraction of the CO2, the energy requirement will be driven by the energy cost

integrated up to the last unit of CO2 captured. The overall energy requirement increases

when the concentration in the discharge air exiting a capture system decreases.

This matters because air capture and power plant capture differ significantly on out-

put concentration. The need to make deep reductions in CO2 emissions will probably

make it desirable to capture most of the CO2 from a fossil plant. Indeed most existing

design studies have aimed at capturing more the 90% of the CO2 in the exhaust gases.

Whereas, in optimizing the overall cost of an air capture system one can freely adjust

the faction of CO2 which is captured from each unit of air, trading off the energy cost

of capture against the cost of moving air through the system. Practical capture systems

might capture less than a quarter of the CO2 in the air.

Thus it is sensible to compare air capture with CO2 removed from a fossil plant at a

partial pressure of 10−2 (1%) with removal from the air at a partial pressure of 3×10−4.

On these grounds the intrinsic total energy penalty of air capture for delivering CO2 at

1 atm is 1.8 rather than the 3.4 derived previously by considering the marginal energy

costs of capture 1.

Put simply, thermodynamic arguments suggest that capturing CO2 from air requires

(at minimum) only about twice as much energy as capturing 90% of the CO2 from a

power plant exhaust. In addition, several economic arguments suggest that the overall

difference in costs may well be much smaller because air capture has several practical

advantages over CCS.

First, siting issues are less acute for air capture facilities. The location of a CCS

power plant is constrained by three transportation requirements: fuel must be trans-

ported to the plant, CO2 from the plant to a suitable storage site, and finally the carbon-

free energy products—electricity or hydrogen—to users. The location of an air capture

plant is less constrained: there is no final energy product, and the energy inputs per

unit of CO2-output may be as little as 10% (Section 2.1) of that needed for an CCS

plant. Moreover, air capture plants will likely be located at CO2 sequestration sites,

eliminating the CO2 transport cost.

While the cost of transportation is hard to quantify, there is little doubt that reduc-

tion in transportation requirements lowers the cost of air capture compared to CCS.

Perhaps more importantly, it lowers the barriers posed by the siting of new energy

1That is ln(1/10−2)/ ln(1/3 × 10−4) = 1.8 rather than ln(1/10−1)/ ln(1/4 × 10−4) = 3.4. Note

that this argument is strictly true only for a one-step capture process.

infrastructure. Public resistance to the construction of new energy transportation in-

frastructure such as gas and electric transmission systems is already a serious problem;

the development of CCS would only increase these difficulties. It is plausible that the

reduction of these barriers is one of the most important attributes of air capture.

Second, air capture systems can be built big, taking maximum advantage of returns-

to-scale, because air capture need not be tightly integrated into existing energy infras-

tructures. One of the features that makes CCS so appealing is its compatibility with

existing fossil energy systems: CO2 capture may be though of as a retrofit of the energy

system. But this feature also limits the rate of its implementation and the scale of the

individual CCS facilities. An power plant with CO2 capture may need to be located

and sized to replace and existing power plant. Too rapid implementation of CCS will

raise adjustment costs. Air capture, in contrast, is more loosely coupled to the existing

system: it is not an intermediate but a final energy use. This implies that the air capture

facilities can be optimally sized to suit geology and technology, and can be constructed

rapidly if required. In this respect air capture is more like geoengineering than it is like

conventional mitigation [Keith, 2000].

Finally, air capture differs from CCS because it effectively removes CO2 with equal

ease or difficulty from all parts of the economy. This is its most important feature. In

this section we have argued that the long-run cost of air capture may be quite close

to the cost of capture from power plants. But even if the cost of abatement with air

capture is considerably more than the cost of abatement at large centralized facilities,

air capture still has the unique ability to provide abatement across all economic sectors

at fixed marginal cost. Air capture operates on the heterogeneous and diffuse emis-

sion sources in the transportation and building sectors where the cost of achieving deep

emissions reductions by conventional means are much higher than they are for central-

ized facilities.

3 Two examples

We now describe two systems that could demonstrate air capture using existing tech-

nology. The first is biomass energy with CCS, and the second is a direct capture system

using aqueous sodium hydroxide. We argue that air capture could likely be achieved

at costs under 200 $/tC using biomass-CCS or at costs under 500 $/tC with direct air

capture.

We say could be achieved because technological developments are driven, in part,

by investments in research, development and deployment (RD&D). The development

of air capture, or other carbon management technologies, is strongly contingent on

the level of RD&D investment. The cost estimates presented below implicitly assume

a significant RD&D effort involving the construction of a handful of industrial-scale

pilot projects sustained over a couple of decades prior to the large-scale deployment of

the technology at a total cost of several billion dollars. We do not assess the likelihood

of this assumption, but we do note that similar assumptions underlie many statements

about the cost and performance of future energy technologies although they are often

unstated.

3.1 Biomass with capture and sequestration

There are many ways in which terrestrial biotic productivity may be harnessed to retard

the increase in atmospheric CO2. Biomass may be, (i) sequestered in situ in soil or

standing vegetation; (ii) used as an almost CO2-neutral substitute for fossil fuels; (iii)

sequestered away from the atmosphere by burial [Metzger and Benford, 2001]; or (iv)

used as a substitute for fossil fuels with capture and sequestration of the resulting CO2

[Keith, 2001, Obersteiner et al., 2001]. The latter two options remove carbon from the

active biosphere and transfer it to long lived reservoirs.

Biomass with capture provides an energy product—electricity, hydrogen, or ethanol—

while simultaneously achieving the capture of CO2 from the air. This may allow it to

0 50 100 150 200 250 300 Carbon price ($/tC)

C os

to fe

le ct

ric ity

(c /k

W h)

Coal

Natural gas

Cost of air capture at current electricity prices

Biomass with capture competitive with coal

Biomass with CO capture2

Figure 1: Cost of electricity as a function of carbon price. The cost and performance

of these technologies is uncertain; the robust result is that the cost of electricity from

biomass-with-capture declines with carbon price, so that at very high carbon prices it

will tend to dominate other options. Similar graphs can be made for the production of

hydrogen or ethanol. The following assumptions were used: for natural gas, coal, and

biomass with capture, capital costs in $/kW were respectively 500, 1000, and 2000;

operating costs were 0.3, 0.8, and 1.0 c/kWhr; efficiencies were, 50%, 40%, and 30%

on an HHV basis; and finally, fuel costs were 3.5, 1, and 3 $/GJ respectively. For

simplicity, values were adjusted to make the cost of electricity equal for coal and natural

gas at a carbon price of zero.

nearly double the effective CO2 mitigation in comparison to conventional biomass en-

ergy systems. Unlike pure air capture systems, biomass with capture is limited by the

availability of biomass. It cannot take advantage of the flexibility that arises from air

capture’s decoupling from the energy infrastructure. Nevertheless, biomass with cap-

ture provides an important middle ground between conventional mitigation and pure

air capture.

Biomass-with-capture systems can be built with existing technology [M’ollerstena

et al., 2003, Rhodes and Keith, 2005, Audus, 2004]. Capture is most easily achieved

for ethanol production, where a pure CO2 stream containing about a third of the carbon

in the feedstock is naturally produced from the fermentation step. Existing designs for

the production of electricity or hydrogen using biomass gasification technologies can

readily be adapted to achieve CO2 capture by the addition of water-gas-shift reactors

and CO2 capture from the syngas stream. While the cost and performance of such tech-

nologies is uncertain, all the required component technologies have been demonstrated

commercially.

To derive a carbon price for this technology, consider electricity production. We

estimate that a biomass gasification combined cycle power plant with CO2 capture

from the syngas using physical absorption in glycol would produce electricity at about

8 c/kWhr while effectively capturing CO2 at a rate of 0.29 kg-C/kWhr [Rhodes and

Keith, 2005]. If the electricity were valued at the current producer cost of about

3.5 c/kWhr, then the cost of CO2 capture is about 160 $/tC. If nuclear, wind or CCS

technologies set the cost of electricity in a CO2 constrained electric market at 5–7

c/kWhr, then the cost of CO2 removal using biomass is about half this value (Figure 1).

Unlike fossil-based technologies, the cost of electricity from biomass with capture

decreases when the carbon price increases. At a sufficiently high carbon price, biomass

with capture becomes relatively cheaper. As can be seen from Figure 1, this occurs

well before 160 $/tC. It competes with coal-based electricity (without CCS) at around

100 $/tC.

3.2 Air capture with sodium hydroxide

To illustrate a direct air capture system that could be built with available technology

we describe a system based on sodium and calcium oxides that uses technology very

closely related to that used in integrated paper mills and the cement industry. We

choose this system for ease of analysis and because of its close relationship to cur-

rent commercial technologies although we doubt is the best or most likely means of

achieving air capture. Put bluntly, our objective is to describe a system most likely to

convince skeptics that air capture could be realized with current technologies.

The following description provides an overview of the system; technical details

are included in Appendix B. Carbon dioxide is captured in an NaOH solution sprayed

through the air in a cooling-tower-like structure, where it absorbs CO2 from air and

forms a solution of sodium carbonate (Na2CO3). The Na2CO3 is regenerated to NaOH

by addition of lime (CaO), forming calcium carbonate (CaCO3). The CaCO3 in turn is

regenerated to CaO by addition of heat in a process called calcining.

The appeal of this system is that the chemicals involved are all inexpensive, abun-

dant, and relatively benign, and that almost all the processes are well-understood as

current industrial-scale practices. Given a well-funded R&D program, such a system

could be built at large scale within a decade. The energy and monetary costs of the sys-

tem are dominated by the calcining portion. This owes to the large amount of chemical

energy needed to convert CaCO3 to CaO and the energy required to heat and separate

the water from the CaCO3 mud entering the caliner. The primary drawback of this

system is indeed this large energy requirement.

As a lower bound on the cost of the system, one can consider the current cost of

calcining dry CaCO3 without CO2 capture. This is precisely what the lime produc-

tion industry does, so we can base this bound on the market price of lime, which gives

$240/t-C. To estimate an upper bound, we consider a complete system built from com-

ponents from today’s industries. With a minimum of new design, we can assemble

component costs from analogous operations in industry. As described in Appendix B,

we find the total cost by this method is roughly $500/t-C.

An optimized system, with a modest amount of new design and novel technology,

could be substantially cheaper than $500/t-C, but could not substantially reduce the

energy and capital costs of calcining. Still, the NaOH capture scheme is a feasible and

scalable near-term option for carbon capture from air.

4 Air capture changes optimal climate policy

The two previous examples suggest that air capture is possible, and that it may be

achieved at costs of a few hundred dollars per ton carbon. The cost of air capture is

uncertain, but not necessarily much more uncertain than the cost of more conventional

emissions abatement technologies half a century in the future. In the remainder of this

paper we assume that air capture is available at this cost and explore the consequences

for climate policy

It is generally agreed that deep cuts in greenhouse gases emissions will be required

to avert dangerous climate change. The debate has often been framed as a problem

of defining an appropriate target at which to stabilize atmospheric CO2 concentration.

This long-term problem can not be solved today, and consequently debates on the op-

timal timing for climate policy have failed to converge on a definitive answer to the

near-term policy question “how fast should we get there?” [IPCC, 2001, chapters 8.4

and 10.4.3]. Introducing the possibility of air capture casts the discussion in a new light

by implying that stabilization is irrelevant, as results presented below will explain.

In this study a stylized integrated assessment model, DIAM, first described by Ha-

Duong et al. [1997], is used to compare optimal global CO2 strategy with and with-

out air capture. DIAM does not represent explicit individual technologies or capital

turnover, but instead the inertia related to induced technical change. The inertia of

the worldwide energy system induces adjustment costs, related to the rate of change

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Unlucky Lucky

Lucky (p=0.8) Unlucky (p=0.2)

Expected impact

Figure 2: The cost of climate change. The fraction of global wealth lost as a function

of carbon dioxide concentration. Damage is assumed to be zero in 2000.

of abatement. The model maximizes the expected discounted inter-temporal sum of

utility under the risk of abrupt adverse climate-change impact.

We acknowledge that this cost-benefit optimization framework lacks a special claim

to universality, and that it obscures many of the distributional issues that drive climate

politics. We adopt it nevertheless, to explore the effect of removing the irreversibility of

CO2 emissions accumulation via air capture, because of its importance as a reference

for considering long-term climate policy.

4.1 Climate change impacts

DIAM represents the uncertainty in the benefits of avoiding climate change, or al-

ternatively the cost of climate impact, using one of two non-linear damage functions

represented Figure 2. This frames optimal climate policy as a problem of precaution

against a risk of abrupt climate change, as discussed by NAS [2002]. The stochastic

impact function represents several defining characteristics of the climate problem: un-

certainty regarding climate and ecosystems sensitivity; nonlinearities in the physical

and political system; and expected growth in the degree of environmental concern with

increasing wealth.

Figure 2’s vertical scale represents a fraction f of global wealth lost. Because of

the inertia found in ecosystems and climate system, the impact at date t depends on the

lagged concentration, so that (omitting mitigation costs) wealth at date t in the model

is W (t) = W ref (t)(1 − f(pCO2 (t − 20))). The order of magnitude of the impact

compares with a few years of economic stagnation, since impact costs in the 4–8%

range represents a few times the world’s rate of economic growth.

The impact is a function of atmospheric carbon dioxide concentration. While it is

measured in monetary units, it represents a global willingness to pay to avoid the given

level of climate change, including non-market values. The impact at any date is defined

as a fraction of wealth at this date. Therefore it scales over time with the size of the

economy. The assumption is that, even though a richer economy is structurally better

insulated against climate variations than an poorer economy, the overall desire to limit

interference with the biosphere increases linearly with wealth.

Our representation of impacts is consistent with the literature. For example, IPCC

[1997, section 3.1.3] reports that for a +2.5 ˚ C warming, economic losses around 1.5 to

2 % of the Gross World Product are commonly used. Because the impacts are expressed

as a function of CO2 concentrations they implicitly include uncertainty in the climate’s

response to radiative forcing as well as uncertainty in climate change impacts.

These uncertainties are summarized as a binary risk in the model. There are two

cases, Lucky or Unlucky. If ‘Unlucky’ (p = 0.2) then a 550 ppmv concentration level

leads to approximately a 4% impact. If ‘Lucky’ (p = 0.8) then this impact is not re-

alized until 650 ppmv. Uncertainty is resolved only in 2040, so that a precautionary

policy has to be found for the period 2000–2040. Expected impact, the weighted aver-

age of the two cases, is shown Figure 2 in solid line. Because there is little available

evidence to quantify uncertainty further, probabilities are purely subjective.

The impacts are nonlinear; in both cases there is a step in the damage function. As

shown in the figure, the main difference is that the step starts at about 600 ppmv in the

Lucky case, and 500 ppmv in the Unlucky case.

Rather than imposing a fixed stabilization target, this formulation allows a cost-

benefit trade-off. But the kink in the damage function serves as a soft concentration

ceiling, and the location of the kink is therefore a critical parameter.

4.2 Abatement cost

The model represents emissions abatement occurring by three processes, called activi-

ties X, Y and Z hereafter, each with its own cost function. Activity X represents emis-

sions abatement through conventional existing energy technologies; its marginal cost

increases with mitigation. Activity Y represents a conventional backstop technology,

for example producing power and hydrogen from solar energy. It reduces emissions at

a marginal cost independent of the amount of mitigation. Activity Z represents air cap-

ture. The cost of each activity depends on both the scale and rate of its implementation

(see Table 1 and Figure 3).

Ignoring adjustment costs, activity X incurs quadratic abatement costs up to full

abatement. With adjustment costs, assuming that abatement increases at rate of 2% per

year, then the abatement cost function is 4.9X2 per cent of global production. This

was calibrated following the DICE-98 model by Nordhaus [2002]. This is represented

in Figure 3 by curve X. It says, for example, that if implemented over 50 years, a 100 $

tax per ton of carbon would produce a 40% reduction in emissions.

Activity Y , the conventional backstop, and activity Z, representing carbon capture

and sequestration from the air, look alike with constant marginal costs. But there are

two important differences. First, the potential for conventional and backstop abatement

is limited to the baseline, so that X + Y ≤ 1, whereas air capture allows negative net

emissions, so Z is not bounded above (see Figure 3, curve XYZ).

The second difference has to do with adjustment costs. Using quadratic adjustment

costs to represent the dynamics of inertia and adaptability is the distinguishing feature

of DIAM. Section 2.2 argued that air capture is less coupled with the energy system

than CCS. This is why adjustment costs for Z depend only on Ż, while adjustment

costs for the other two activities depend on their joint growth rate Ẋ + Ẏ .

The scale of adjustment costs in the model is determined by the characteristic time

constant for change in the global energy system. We adopt a time constant, τ, of 50

years—roughly in accord with the historical rate of diffusion for new primary fuels

[Grübler et al., 1999]. This leads to the plausible result that on typical optimal trajec-

tories, the rate-dependent and -independent terms in the cost function are comparable.

The previous section provided rough engineering estimates of the near-term cost

of air capture, and suggested values in the range 200-500 $/tC. These estimates cannot

be easily compared with the cost of various mitigation activities in DIAM for three

reasons: (1) because of the use of adjustment costs in DIAM, (2) because of the well

known incompatibilities between bottom-up engineering estimates and the top-down

economic estimates against which DIAM is calibrated [IPCC, 2001], and (3) because,

as we will see below, air capture is not used by the model until after the middle of this

century and the long-term costs of air capture likely fall between the near-term cost

estimates described in Section 3 and the long-run limits described in Section 2.

As a base case we assume that air capture costs 150 $/tC in the model if it is im-

plemented over 50 years (the adjustment time constant). This cost is equivalent to

the marginal carbon price that would (if implemented over 50 years) produce a 60%

reduction in emissions given our baseline abatement cost curve (Activity ’X’, Figure

3). Although the capture cost used in DIAM is less than half that derived from our

engineering estimates the values are comparable. This is roughly consistent with our

Activity Total cost = Base cost × Scale × Multiplier

Conventional

abatement CX = 2.45% GWP(t0)

Eref

Eref (t0) X2 + (τ(Ẋ + Ẏ ))

Clean energy

backstop CY = 75 $/tC Y Eref 1 + (τ(Ẋ + Ẏ ))

Air capture CZ = 75 $/tC ZEref 1 + (τŻ) 2

Table 1: The cost of reducing carbon emissions in DIAM for each activity. Gross World

Production (GWP) was about 18 × 1012 $ for the base year. All base costs decline at

an autonomous technical progress rate of 1 per cent per year. The τ = 50 yr inertia

parameter in adjustment costs is the characteristic time of the world’s energy system.

engineering cost estimates given that (i) air capture is not used for more than half a

century, and (ii) its cost lies in the upper 40% of the mitigation supply curve, above the

cost of mitigation for many large-scale point sources, but comparable to, or below, cur-

rent engineering cost estimates for mitigating dispersed sources such as transportation

where costs can exceed 1000 $/tC Keith and Farrell [2003].

The costs are scaled in time according to the scale of the future energy demand

Eref (t), shown in Figure 4, top panel. Reference emissions grow slower than GDP,

and then are left constant at 20 GtC/yr after 2100. This baseline is necessarily arbitrary.

An important assumption is that the decoupling between GNP and energy consumption

observed in industrialized countries after the oil shocks is a persistent general effect.

5 Optimal climate strategies with air capture

The model was used to compare three scenarios X, XY and XY Z by changing the

availability of carbon management activities in the cost function, as Figure 3 illustrates.

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2

$ / t

Fraction of emissions abated

XYZ

quadratic abatement cost X X + clean backstop XY

XY + air capture XYZ

Figure 3: Marginal abatement cost functions, assuming that adjustment costs double

the long-run permanent costs. Backstop technology allows clean energy without carbon

emissions at a constant marginal cost. Air capture allows abatement beyond 100%.

-5

2000 2050 2100 2150 2200 2250

G tC

Year

quadratic abatement cost X with clean backstop XY

with cb + air capture XYZ reference

300

350

400

450

500

550

600

650

700

2000 2050 2100 2150 2200 2250

pp m

v C

O 2

Year

Unlucky

Lucky

quadratic abatement cost X with clean backstop XY

with cb + air capture XYZ reference

Figure 4: Optimal CO2 trajectories. Top panel, emissions for the ‘Lucky’ case. Bottom

panel, CO2 concentration for both cases.

In scenario X, the backstop Y and air capture Z technologies are not available. Con-

sequently, the marginal cost curve is a simple ramp culminating at 250 $ per tC for

complete emission abatement. In scenario XY , backstop is available but not direct

capture, so that the marginal cost ramp is capped at 150 $ per tC. Finally, scenario

XY Z allows all three abatement activities.

Results are displayed Figure 4. The top panel displays the optimal CO2 emissions

trajectory, where for clarity only the ‘Lucky’ branch (smaller impact) of the contingent

strategy is drawn. As acknowledged in previous literature, even in this case emissions

have to be deeply reduced in the long run. When air capture is not available, emissions

are reduced to zero around 2150. When it is available, air capture kicks-in after 2060

and grows large enough to drive net emissions negative by around 2140.

The first result is that the backstop technology (activity Y ) has almost no effect

on the emission trajectory. There are two reasons. First, nonlinearity in the impact

function serves as a soft constraint on concentration, as discussed above. The optimum

is at the intersection of marginal cost and benefit curves, where the marginal benefit of

abatement is steep so the optimal abatement quantity is relatively insensitive to changes

in cost.

Another explanation for this result is that the changes in cost are actually relatively

small. The carbon value stays below 150 $/tC for a long time, where the backstop

makes no difference. Although the backstop’s (Y ) marginal cost is lower than marginal

cost of activity X by up to forty percent, this is only relevant in the twenty-second

century when the overall costs are a small fraction of global wealth.

The results are similarly insensitive to the cost of air capture. Even if the cost of

air capture is doubled to 300 $/tC (including the 50-year adjustment cost), the optimal

concentration trajectories are qualitatively similar to those shown here (Appendix A).

The second result is that the concentration overshoots its final level in all cases

(Figure 4, bottom panel). Given that the model assumes constant economic growth,

this can be called an environmental Kuznets curve. Most published scenarios have

concentrations and climate change increasing monotonically. Even in intervention sce-

narios, concentration generally increases asymptotically to a stabilization ceiling. Yet

the idea that managed atmospheric pollutants first increase and then decrease with time

has been heavily discussed in the environmental economics literature; see, for example,

Anderson and Cavendish [2001] or the survey by Borghesi [1999].

Carbon dioxide is a long-lived stock pollutant. Technical progress, the decreasing

energy intensity of the economy and the effect of adjustment costs make it comparably

cheaper to reduce emissions in the future. These factors explain why the optimal tra-

jectory overshoots. Also, an inverted Malthus effect is at play. On one hand, climate

change impact is a fraction of wealth. Therefore the willingness to pay to solve the

problem grows exponentially. On the other hand, the costs of abatement are propor-

tional to the amounts of pollution generated in the business-as-usual scenario, where

reference emissions are assumed to grow only up to 2100 and linearly.

The third result elaborates on the previous one: When air capture is available con-

centration declines rapidly toward preindustrial levels. Without air capture the dynam-

ics that dictate a return toward a low concentration target remain as described above,

but the rate of CO2 concentration decline is determined by natural removal. With air

capture, the rate is determined by the trade-off between its costs and the benefits of

reducing climate change.

This idea is overlooked in the existing literature. Admittedly, the decrease is mostly

happening in the twenty-second century, while most scenario studies reasonably focus

on this one. Yet the factors driving the return toward preindustrial concentration—

the inverted Malthus effect—are general, as is the environmental Kuznets curve. This

result suggest that if technology exists to reverse climate damage it will be employed.

The rate at which concentrations return to pre-industrial levels depends on the cost

of air capture, but for reasons mentioned in our discussion of the first result above, the

Optimal % abatement in 2030

Decision framework → Certain Stochastic Certain

↓ Abatement cost function Lucky Unlucky

Quadratic abatement cost X 7.3 9.8 16.9

Clean backstop XY 7.3 9.8 16.9

Air capture XY Z 5.9 7.4 12.1

Table 2: Abatement (%) of global CO2 emissions, in 2030, for the three different abate-

ment cost function X, XY and XY Z defined Figure 3. The first column shows the

optimal abatement if one were certain from the start that climate impact is low. Con-

versely, the third column shows optimal abatement if one knew that climate impact on

Figure 2’s higher curve. Central column shows the optimal abatement on a precaution-

ary path in a stochastic world, as displayed on Figure 4.

rate is only weakly dependent on cost. The ultimate return to pre-industrial concentra-

tions and the rate of return also depend on the role of adaptation in reducing, or pos-

sibly eliminating, climate impacts over the long run. We speculate that, if reasonable

estimates of long-run adaption were included in the model’s climate-damage function

we would still see a prominent concentration peak and subsequent decline (i.e., the

Kuznets curve) but that the decline would be slower and, depending on assumptions

about adaptation, the concentrations might not return to pre-industrial levels.

The fourth result highlights a short-term implication of air capture. The model com-

putes an optimal contingent strategy, given that uncertainty is resolved in 2040. Table 2

shows the optimal emission abatement in 2030 under various uncertainty (columns) and

technology availability (rows) scenarios.

The optimal contingent strategy is in the middle ‘Stochastic’ column. The left col-

umn, ‘Lucky’ applies when it is known from the start that damages are relatively low.

As can be seen, precaution is a middle-of-the road approach, leaning on the optimist

side towards the ‘Lucky’ outcome, which is expected (p = 0.8).

Air capture reduces initial abatement. Abatement is 9.8 percent below business as

usual in the X case, but only 7.4 percent with air capture XY Z (Table 2). Because the

total costs are initially quadratic, this difference in abatement corresponds to a much

larger difference in spending on abatement: $13 billion per year with air capture, and

$24 billion without. This effect arises even though air capture is not until long after

2030 and is due to the possibility of moderating future impacts in the ‘Unlucky’ case.

The result can be understood as the reduction of the environmental irreversibility:

it is optimal to pollute more when it is possible to cleanup afterward than when it is

not.

This fourth result suggests that air capture reduces an important irreversibility from

the decision problem. Note however that the irreversibility in impacts themselves was

not modeled. This aspect does have significant policy implications, as we discuss next.

While air capture may reduce our vulnerability to extreme climate responses, it

does not necessarily allow us to eliminate consequences. The time-scale for abrupt

climate change may be as short as a few decades. If an abrupt change occurred—

suppose a rapid shutdown of the thermohaline circulation—a large scale air capture

program might conceivably be built in a comparable time frame, but it would need

to operate continuously for several decades to significantly decrease the atmospheric

concentration of CO2. Air capture is therefore unable to eliminate vulnerability to such

rapid changes.

More generally, air capture eliminates only the irreversibility of atmospheric carbon

dioxide accumulation in the long run. It does not address irreversibilities in climate

change damages. This distinction is critical because of many remaining unknown time

constants in the links between CO2 concentration, global warming, earth climate, and

human activities. Further research is needed to model explicitly abrupt climate damage

with hysteresis.

6 Conclusion

No air capture systems exist today, yet we argued that one could be readily built with-

out any new technology, and that in the long run, the ability to capture CO2 from

the air fundamentally alters the dynamics of climate policy (even if it is more expen-

sive than any conventional mitigation available in the economy). Air capture differs

from conventional mitigation in three key aspects. First, it removes emissions from

any part of the economy with equal ease or difficulty. Consequently, its price caps the

cost of mitigation with a scope unmatched by any other kind of abatement technology.

Second, because air capture allows the removal of CO2 after emission it permits reduc-

tion in concentrations more quickly than can be achieved by the natural carbon cycle.

Third, because it is weakly coupled to the energy system, air capture may offer stronger

returns-to-scale and lower adjustment costs than conventional mitigation options.

This is not to claim that air capture systems are trivial to build today, nor that

they will play a quantitative role in the next decade. With regard to the technology, we

advanced three arguments. First, that both thermodynamics and economic reasons sug-

gest that in the long run, the cost of large-scale air capture will be roughly comparable

to the cost of capturing CO2 from large fixed sources. Second, we have described two

systems that could plausibly achieve air capture a costs from 200 to 500 $/tC within

the next few decades. Finally, while their costs are large compared to near term carbon

prices, they are competitive with, or significantly cheaper than, the cost of abatement

from diffuse sources found in the transportation sector. While both costs will likely

decline with technological improvement, air capture is likely to be competitive with

conventional mitigation when the time comes to achieve very deep reductions in emis-

sions.

Several research groups [McFarland et al., 2004, Herzog et al., 2003, Keller et al.,

2003, for example], have begun to explore the implications of carbon management

technologies and the leakage of sequestered carbon using integrated assessment mod-

els. Our paper extends this work by exploring the role of direct air capture.

The most obvious impact of carbon management technologies is in altering the cost

of mitigation. The model used here, DIAM, is designed to explore climate policy over

century-long time-scales and contains a very simplistic representations of the energy

sector. From such a perspective, including CCS is achieved by a rather minor adjust-

ment to the aggregate abatement cost function. Consequently, while mitigation using

CCS may differ in many important dimensions from mitigation achieved using non-

fossil renewables, the outcomes in terms of cost-benefit optimal emission strategy was

very similar.

Absent air capture or the possibility of unlimited biological sequestration, leak-

age of sequestered carbon presents novel problems with respect to the inter-temporal

distribution of abatement costs and benefits. If industrial carbon management plays a

dominant role in mitigating emissions, then as much as 500 GtC could be stored by

2100. Even if the average leak rate is only 0.2 percent annually, there would be a 1 GtC

per year source undermining CO2 stabilization. As [Keller et al., 2003, Figure 4] has

shown, absent air capture the leakage issue has significant consequences on optimal

long-term climate policy.

This problem may be compounded by the CCS energy cost, which is likely to result

in somewhat faster mobilization of the fossil carbon reserves than in a business-as-usual

scenario: the 500 Gt of fossil carbon would be burned sooner with CCS than without.

Air capture, or any similar means of engineering a near-permanent carbon sink,

reduces the leakage problem to a relatively minor perturbation in the distribution of

abatement cost over time.

Previous research suggested that when carbon dioxide accumulation is irreversible,

the ultimate concentration target is the most important parameter for the timing of

abatement. For example, if it is assumed that CO2 concentration will be stabilized at

600 ppmv or over, then there is little cause for action before 2020. The opposite holds if

the ultimate ceiling is 450 ppmv, or if one wishes to keep open the option of remaining

below that ceiling.

But this stock irreversibility is less relevant when capture from the air is possi-

ble. Our simulations demonstrate that air capture can fundamentally alter the temporal

dynamics of global warming mitigation.

Air capture is a form of geoengineering because it directly modifies the biosphere

and would be implemented with the aim of counterbalancing other human actions

[Keith, 2000]. Like geoengineering, its availability reduces our vulnerability to some

high-consequence low-probability events. In an optimal sequential decision frame-

work, we have shown that the consequence is a decrease in the need for precautionary

short-term abatement. Because air capture may provide some insurance against cli-

mate damages, it presents a risk for public policy: the mere expectation that air capture

or similar technologies can be achieved reduces the incentive to invest in mitigation.

Yet, while air capture removes irreversibility in CO2 concentration increase, it does not

protects against irreversibilities in the climate system’s response to forcing.

While air capture may reduce the amount of mitigation in the short run, it can in-

crease it on longer time-scales. If air capture is possible, even at comparatively high

cost, and if the willingness to pay for climate change mitigation grows with the econ-

omy, then the optimal trajectory follows an environmental Kuznets curve. At some

point the optimal target will be to return atmospheric greenhouse gases concentration

to lower levels. These may be even lower than present-day levels. Air capture changes

the temporal dynamics of mitigation by making this response possible.

Acknowledgments

Research supported by the Centre National de la Recherche Scientifique, France and by

the Center for Integrated Assessment of Human Dimensions of Global Change, Pitts-

burgh PA. This Center has been created through a cooperative agreement between the

National Science Foundation (SBR-9521914) and Carnegie Mellon University, and has

been generously supported by additional grants from the Electric Power Research In-

stitute, the ExxonMobil Corporation, and the American Petroleum Institute. We thank

Hadi Dowlatabadi, Granger Morgan, Ted Parson, Hans Ziock, Klaus Keller and Alex

Farell for their useful comments.

References

Dennis Anderson and William Cavendish. Dynamic simulation and environmental

policy analysis: Beyond comparative statistics and the environmental Kuznets curve.

Oxford Economic Papers, 53(4):721–746, October 2001.

Harry Audus. Climate change mitigation by biomass gasification combined with CO2

capture and storage. In Proceedings of 7th International Conference on Greenhouse

Gas Control Technologies, volume Volume 1: Peer-Reviewed Papers and Plenary

Presentations, Cheltenham, UK, 2004. IEA Greenhouse Gas Programme.

Simone Borghesi. The environmental Kuznets curve: a survey of the literature. Tech-

nical Report Nota do lavoro 85.99, Fondazione Eni Enrico Mattei, November 1999.

URL http://www.feem.it/web/resun/wp/85-99.html.

S. Elliott, K. S. Lackner, H. J. Ziock, M. K. Dubey, H. P. Hanson, S. Barr, N. A.

Ciszkowski, and D. R. Blake. Compensation of atmospheric CO2 buildup through

engineered chemical sinkage. Geophysical Research Letters, 28(7):1235–1238,

2001.

Peter Flanagan. Email conversation. Associated with Groupe Laperrire and Verreault,

May 2004.

K. Greenwood and M. Pearce. The removal of carbon dioxide from atmospheric air

by scrubbing with caustic soda in packed towers. Transactions of the Institution of

Chemical Engineers, 31:201–207, 1953.

Arnulf Grübler, Nebojša Nakićenović, and David G. Victor. Dynamics of energy tech-

nology and global change. Energy Policy, 27:247–280, 1999.

Minh Ha-Duong, Michael J. Grubb, and Jean-Charles Hourcade. Influ-

ence of socioeconomic inertia and uncertainty on optimal CO2-emission

abatement. Nature, 390:270–274, 1997. URL file://HaDuong.

ea-1997-InfluenceInertiaUncertaintyAbatement.pdf.

H. Herzog, K. Caldeira, and J. Reilly. An issue of permanence: Assessing the effec-

tiveness of temporary carbon storage. Climatic Change, 59, 2003.

P.J. Hoftyzer and D.W. van Krevelen. Applicability of the results of small-scale exper-

iments to the design of technical apparatus for gas absorption. Transactions of the

Institution of Chemical Engineers, Supplement (Proceedings of the Symposium on

Gas Absorption, 32:S60–S67, 1954.

IPCC. Stabilisation of Atmospheric Greenhouse Gases: Physical, Biological and

Socio-economic Implications (IPCC Technical paper III). UNEP/WMO, 1997.

Working Group I.

IPCC. Climate Change 2001: Mitigation. Cambridge University Press, 2001.

N.A.C. Johnston, D.R. Blake, F.S. Rowland, S. Elliott, K.S. Lackner, H.J. Ziock, M.K.

Dubey, H.P. Hanson, and S. Barr. Chemical transport modeling of potential atmo-

spheric CO2 sinks. Energy Conversion and Management, 44(5):683–691, 2003.

David W. Keith. Geoengineering the climate: History and prospect. Annual Review of

Energy and the Environment, 25:245–84, 2000.

David W. Keith. Sinks, energy crops, and land use: Coherent climate policy demands

an integrated analysis of biomass. Climatic Change, 49:1–10, 2001.

David W. Keith and Alexander E. Farrell. Rethinking hydrogen cars. Science, pages

315–316, 2003.

Klaus Keller, Zili Yang, and Matt Hall. Carbon dioxide sequestration: When and how

much? Working Paper Series 84, Princeton University, Center for Economic Policy

Studies, 2003. In revision for Climate Change.

J.R. McFarland, J.M. Reilly, and H.J. Herzog. Representing energy technologies in

top-down economic models using bottom-up information. Energy Economics, 26:

685–707, 2004.

R. A. Metzger and G. Benford. Sequestering of atmospheric carbon through permanent

disposal of crop residue. Climatic Change, 49:11–19, 2001.

Kenneth M’ollerstena, Jinyue Yana, and Jose R. Moreirab. Potential market niches

for biomass energy with CO2 capture and storage—opportunities for energy supply

with negative CO2 emissions. Biomass and Bioenergy, 25:273–285, 2003.

National Academy of Science NAS. Abrupt climate change: inevitable surprises. Na-

tional Academy Press, Washington, D.C., 2002. ISBN 0-309-07434-7.

William D. Nordhaus. Modeling induced innovation in climate-change policy. In Ar-

nulf Grübler, Nebojsa nakicenovic, and William D. Nordhaus, editors, Technological

change and the environment, chapter 8, pages 182–209. Resources For the Future,

2002.

M. Obersteiner, C. Azar, P. Kauppi, K. Möllersten, J. Moreira, S. Nilsson, P. Read,

K. Riahi, B. Schlamadinger, Y. Yamagata, J. Yan, and J.-P. van Ypersele. Managing

climate risk. Science, 294(5543):786–787, October26 2001.

Anand B. Rao. Personal communication. June, October 2004.

Anand B. Rao and E. S. Rubin. A technical, economic, and environmental assessment

of amine-based CO2 capture technology for power plant greenhouse gas control.

Environmental Science and Technology, 36(20):4467–4475, 2002.

P. Reimer, B. Eliassed, et al., editors. Greenhouse gas control technologies: Proceed-

ings of the 4th international conference, Interlaken, Switzerland, 1999. Pergamon.

J. S. Rhodes and D. W. Keith. Engineering-economic analysis of biomass IGCC with

carbon capture and storage. Biomass and Bioenergy, (submitted), 2005.

J. K. Stolaroff, G. V. Lowry, and D. W. Keith. Using CaO- and MgO-rich industrial

waste streams for carbon sequestration. Energy Conversion and Management, 46

(5):687–699, 2005.

Robert C. Weast, editor. CRC Handbook of Chemistry and Physics. CRC Press, Boca

Raton, FL, 2003.

D. Willams, B. Durie, P. McMullan, C. Paulson, and A. Smith, editors. Greenhouse gas

control technologies: Proceedings of the 5th international conference on greenhouse

gas control technologies, Collingwood, Australia, 2001. CSIRO Publishing.

Frank S. Zeman and Klaus S. Lackner. Capturing carbon dioxide directly from the

atmosphere. World Resources Review, 16:62–68, 2004.

A Sensitivity analysis

Abatement 2030 Maximum Year 2200

fraction BAU ppmv CO2 ppmv CO2

L or U L U L U

X = Quadratic abatement cost 0.10 604 524 563 482

XY = X+ Clean backstop 0.10 603 524 562 478

XYZ = XY+ Air capture 0.07 596 514 467 350

D = XYZ+ Air capture 300$/tC 0.09 604 521 518 410

E = XYZ+ No lag in damage 0.09 583 506 401 337

F = XYZ+ Better lucky case 0.06 678 515 527 349

GX = X+ Bad surprise close 0.10 603 505 562 437

GXYZ= XYZ+ Bad surprise close 0.07 596 485 470 337

I = XYZ+ Air capture ≤ 2GtC yr−1 0.09 600 520 538 443

Optimal strategies are characterized by five key numbers. First, the optimal percentage

of global CO2 emissions abatement in 2030 shows how much precaution is incorpo-

rated in the strategy, before uncertainty resolution. The second and third characteristics

are the magnitude of the atmospheric CO2 concentration peak, in ppmv, for the Lucky,

‘L’, and Unlucky, ‘U’ states of the world. Columns four and five display the maximum

concentration and concentration in 2200, respectively, for the U and L states.

Runs X, XY and XYZ explore different cost abatement functions as discussed in

the body of the text. Runs D and F each use the XYZ damage function, but Run D

doubles the cost of air capture while Run E removes the lag in the damage function.

Run F has abrupt climate damage in the ‘Lucky’ case kicking in at 705 ppmv instead

of 605.

Conversely, runs GX and GXYZ have abrupt climate damage in the ‘Unlucky’ case

kicking in at 450 ppmv instead of 511, with a probability 5 percent instead of 20.

Finally, in Run I the use of air capture is restricted to 2 GtC/yr, to explore the role of

Figure 5: Top level process diagram of an example direct air capture system. Closed

chemical loops of NaOH and CaO extract CO2 from air convert it to a pure, compressed

form for sequestration.

biomass capture alone under the assumption that biomass supply would be limited.

Runs GX and GXYZ combine this damage with the cost function from run X and

run XYZ, respectively. They represent the risk of early abrupt climate damage without

capture.

Table B.1: Chemistry of Na/Ca capture system

Reaction Enthalpy of reactiona, ∆HO

kJ/mol-C GJ/tC

(1) CO2(g) + 2Na+ + 2OH− → CO2−3 + Na+ + H2O -110 -9

(2) CO2−3 + Ca 2+ → CaCO3(s) 12 1

(3) CaO(s) + H2O(l) → Ca2+ + 2 OH− -82 -7

(4) CaCO3(s) → CaO(s) + CO2(g) 179 15

a Derived from Weast [2003].

B Example direct air capture scheme

B.1 Overview

The example system proposed here uses an aqueous solution of sodium hydroxide

(NaOH) to capture CO2 from the air and then regenerates this solution. A top-level

process diagram was presented in Figure B.1. The chemistry of the system is summa-

rized by the reactions in Table B.1.

In the Contactor, the NaOH is brought into contact with atmospheric air and ab-

sorbs CO2, forming sodium carbonate (Na2CO3). This carbonate-containing solution

is then sent to the Causticizer. In the Causticizer, lime (CaO) is added to the solution,

producing solid calcium carbonate (CaCO3) and NaOH. The CaCO3 is collected and

sent to the Calciner while the NaOH is sent back to the Contactor. The Calciner heats

the CaCO3 until the CO2 is driven off and CaO is re-formed. The CO2 is collected

and compressed for sequestration. Each of these components – Contactor, Causticizer,

Calciner, is discussed in detain below.

B.2 Contacting

Extraction of CO2 from air with NaOH solution has been an established, well-known

process for many decades [Greenwood and Pearce, 1953, Hoftyzer and van Krevelen,

1954]. Even at ambient concentrations, CO2 is absorbed efficiently by solutions with

high pH [Johnston et al., 2003]. The most common industrial method of absorbing a

gas into solution is to drip the solution through a tower filled with packing material

while blowing the gas up through the tower (a “packed tower” design). Indeed, if we

choose a capture efficiency of 50%, which is suitable for our application2, the combined

gas and liquid pumping energy requirements of running such a unit are rather small –

1.2 GJ/tC, as shown in Table B.3. This is an empirical result based on towers which

were designed for high capture efficiency; a tower with this dense packing need only

be 1.5 m tall to achieve 50% capture efficiency. Furthermore, the low flow rate of CO2

(because it is so dilute in air) requires the “tower” to be very wide – perhaps hundreds

of meters in diameter. A contactor of these dimensions would be very different from

conventional packed towers and might look like a trickle-bed filter used in wastewater

treatment plants: a wide cylindrical basin, drafted from underneath, with a rotating

distributor arm. The properties of this type of design are likely dictated by ”edge

effects” – the nature of the system at the top and bottom of the bed – and by the

engineering of the distribution mechanism for air and water. While not intractable,

these issues make it hard to estimate the cost and operating parameters of this system.

An alternate strategy is to use a lighter packing and taller tower. In the limit, this

becomes an empty tower with the solution sprayed through, much like a power plant

evaporative cooling tower or an SO2-scrubbing tower for combustion flue gas. For

the purposes of this paper, this strategy has the advantage that the costs are easier to

estimate because of the simplicity of the design and the analogy to industrial cooling

towers.

The key parameters of our example capture unit are presented in Table B.2. A

cooling tower of equal dimensions can be built today for about US$8 million which

2Taller towers and therefor higher pumping energies are required for higher capture efficiencies of the

CO2 passing through the system. Because atmospheric air is so abundant there is no compelling reason to

capture most of the CO2 from any given parcel.

includes mechanisms for spraying and collecting liquid. The major difference in our

design is the addition of fans to force air through co-currently. More sophisticated

infrastructure for handling and moving the working solution may also be required. For

the cost presented in Table B.3, we assume that these additions increase the capital cost

of the tower by 50%, to US$12 million. Moreover, as we will see, the total system

cost is insensitive to the capital cost of the tower. Physically-based modeling of the

operating parameters gives the energy requirements presented in Table B.3.

A theoretical investigation of evaporative water loss indicates that the water re-

quirements may be substantial – on the order of 5 tons of water per ton CO2 captured

in a temperate climate with a dilute NaOH solution [Stolaroff et al., 2005]. However,

the NaOH solution becomes hydrophilic for high concentrations of NaOH (about 4-6

mol/l, depending on ambient humidity). By adjusting the concentration of NaOH in

the working solution, we expect that evaporative loss can be reduced as needed.

B.3 Causticization

In this step, the Na2CO3 solution from the capture unit is mixed with CaO from the

Calciner (Reactions 2 and 3 from Table B.1). A near-perfect analogy can be drawn be-

tween this and the causticizing step in the kraft recovery process used in the pulp and

paper industry. The kraft process takes spent pulping chemicals, primarily Na2CO3

and Na2S, and regenerates them to NaOH and Na2S with the same chemical reac-

tions as above. The substantive differences between the kraft process and the proposed

Causticization process for air capture are as follows.

B.3.1 Sulfur content

The presence of sulfide aids the preparation of wood pulp, and so must be carried

through the kraft recovery process. The process has been tested, however, without the

addition of Na2S, and the primary result is an improvement in the conversion efficiency

Table B.2: NaOH spray tower air capture unit: key parameters

Parameter value motivation

Tower diameter 110 m equal to cooling tower

Tower height 120 m equal to cooling tower

Air velocity 2 m/s reasonable valuea

CO2 capture efficiency from air 50% reasonable valueb

Mean drop diameter 0.7 mm spray distribution from a hollow-

cone spray nozzle

NaOH concentration in Solution 3–6 mol/l adjusted to minimize evaporative

loss based on local climate.

Carbonate captured per passb 0.2 mol/l based on numerical model of

falling drops

Solution flow rate 1 m3/s fixed by above parameters

Pressure drop accross towerb 22 Pa based on numerical model of

falling drops; excludes wall fric-

tion.

Electricity use 1.4 MW based on 75% fan and 85% pump

efficiency

Carbon capture rate 76000 tC/yr fixed by above parameters

Capital costc $12 million (cooling tower cost)×1.5c

Operation and maintenence cost 400,000 $/yr conservative guess

a The air velocity trades off higher CO2 throughput, i.e. lower capital cost, with in-

creased fan energy (since fan energy goes as the square of velocity). While this value

is not optimized, it falls in the likely range of the optimal value since capital costs

baloon for air speeds much below this, and fan electricity costs dominate for values

much above this.

b The capture efficiency trades off higher CO2 throughput, i.e. lower capital cost, with

increased solution pumping. Because higher efficiencies require exponentially more

energy to achieve, but low efficiencies drive up capital costs, 50% is in the likely

optimal range.

c The contactor has additional cost over a cooling tower of fans and some liquid-

handling components.

of Na2CO3 to NaOH by a few percent, and in general the sulfur only complicates the

process. Since our proposed system doesn’t require any sulfide, we expect it to run a

bit more efficiently than the kraft equivalent.

B.3.2 Temperature

In the kraft process, the slaking and causticizing steps are typically performed with

a solution temperature in the range of 70-100oC. However, the solution entering this

step in the proposed system will be at ambient temperature or cooler. The solution is

heated by the slaking reaction; assuming a (typical) concentration of about 2 mol/l CaO

added, the slaking reaction will increase the solution temperature by about 20Co, but

that would only bring the solution to, perhaps, 40oC. While the equilibrium conversion

efficiency of Na2CO3 to NaOH is higher at lower temperatures, the kinetics become

prohibitively slow. Without changing the process design to accommodate significantly

longer residence times, we will have to add additional heat to the solution. Another

30Co would bring us into the industrial range. We can do so with a liquid-to-liquid

heat exchanger and a low grade heat input of (assuming the exchanger is 80% efficient)

14 kJ/mol-CO2, or about 1 GJ/ton-C.

B.3.3 Solids content

In the kraft process, the initial Na2CO3 solution contains organic particles and insol-

uble minerals (“dregs”) in the part-per-thousand range. The dregs impair the perfor-

mance of the process and so most must be removed in a clarifier. For the proposed

system, the entire dreg-removal subsystem can probably be eliminated. The source

of contamination most analogous to the dregs in the proposed system is fine particles

captured from the air along with the CO2. Assuming a particle concentration of 100

µg/m3 and equal absorption efficiency with CO2, the particle concentration in solution

will be in the range of 10 parts per million.

Given the small and favorable differences between the kraft process and our adap-

tation of it, a conservative estimate of the monetary and energy costs of running this

component can be lifted directly from the pulp and paper industry. Such an estimate is

presented in Table B.3.

B.4 Calcination

Calcination is the process where CaCO3 is heated to make CaO. It is practiced at very

large scale in the production of lime, cement, and in pulp and paper mills. Modern

calciners are frequently comprised of a fluidized bed fired with natural gas. Such a

calciner for lime production can operate with an energy input of 17 GJ/tC – close to

the thermodynamic limit of 15 GJ/tC. Calciners in the pulp and paper industry require

more energy because they start with CaCO3 mud instead of dry CaCO3, and must drive

off the water. A typical energy requirement for a paper-industry calciner is shown in

Table B.3.

The calciner in our example system is a close analogy with that paper industry since

it is also starting with CaCO3 mud produced during caustization. It is certainly possible

to remove more of the water in the CaCO3 mud before calcination. The pulp and

paper industry has presumably optimized the trade-off between capital expenditure and

mechanical energy for dewatering and energy cost for calcining for their circumstances.

However, with the higher energy costs we have assumed would probably elicit a more

energy-efficient design.

In contrast to current industrial systems, the proposed system must, of course, cap-

ture CO2 from the calciner. The most straightforward method for doing this would be

to use a conventional high-efficiency fluid bed calciner followed by an amine-based

CO2 capture system. If the calciner was fired by natural gas, the CO2 concentration

in the exhaust gases would approach 20% (dry basis) lowering the capital and energy

costs of amine capture compared to existing estimates for capture from coal-fired power

plants ( 14% CO2). Furthermore the water in the lime mud becomes high-temperature

steam in the calciner. This steam can be used as a heat source for regeneration of the

amines. Preliminary analysis suggests that there is sufficient steam to supply much

of the needed regeneration heat in the amine capture unit [Rao and Rubin, 2002, Rao,

2004].

The capture of CO2 from calcination might alternatively be achieved using oxygen

blown combustion in a fluidized bed. Such a system would be a hybrid of existing

fluid bed calciners and oxygen-fired coal combustion with CO2 capture which has been

studied (but not implemented) as a method for achieving CO2 capture at electric power

plants. Such a system might offer significant energy savings over the amine system but

because it introduces significantly more new engineering we do not consider it here.

B.5 Integrated system

One could assemble an air capture system with technology available today. It could

consist of components listed in Table B.3: a causticizer and calciner nearly identical to

those widely in use, an amine capture and compression system nearly identical to those

currently in use, and a spray tower capture unit very much like a power plant cooling

tower. The sole novelties would be efficient heat integration allowing low-grade waste

heat from the calcination and slaking system to be used for regeneration of the amines,

and the addition of a heat exchanger to allow the contactor and causticizer to operate at

different temperatures. The sum of costs of the several components is about 500 $/tC.

Of the 500 $/tC, about a third is capital and maintenance costs. These could be

brought down with optimizations and economies of scale (the capacity of the contactor

and calciner presented is an order of magnitude less than the output of a large coal

power plant). The other two thirds of the cost are those of natural gas and carbon-

neutral electricity. The thermodynamic energy requirement for calcination and the

energy of CO2 compression (together accounting for 40% of energy cost) might be

Table B.3: Example air capture system: estimated and analogous costs and energy requirements

System Mechanical Thermal Cost [$/tC]a

Energy [GJ/tC] Energy [GJ/tC]

Calcination

Calcination in lime production 0.3 17 230b

Calcination in Kraft process (small) 32 ?

Calcination + caustization in Kraft Process (small) 40 373c

CO2 capture and compression

Amine capture 0.4d 14d,e 49d,f

CO2 compression 1.6d 0 43d

Contacting

Spray tower 1.0 0 41f

Packed tower 1.2g 0 ?

a All capital costs are annualized with 10%/yr discount rate and 20 year plant life. The fol-

lowing prices for energy were used: 4 $/GJ for natural gas and 0.07 $/kW-hr for carbon-

neutral electricity. Natural gas was chosen for simplicity, but other fuels may be used. Also,

stranded natural gas, which is available at significantly lower cost than 4 $/GJ, would be a

good canidate for use in an air capture system.

b Based on the current market price of lime (CaO), adjusted to remove the cost of limestone

input (CaCO3)

c Approximate estimate, based on Flanagan [2004].

d From Rao [2004], applying the model developed for Rao and Rubin [2002].

e This heat requirement is assumed to be satisfied by steam from the calciner and is not included

in the cost estimate.

f Engineering cost estimate, including capital, operation, and maintenance.

g Extrapolated from Greenwood and Pearce [1953] and Hoftyzer and van Krevelen [1954]

seen as a hard lower limit for the energy requirements of this type of system, but that

leaves significant room for improvements in efficiency. The figures given are with

none of the components optimized for the purpose of air capture, and so are meant to

be conservative estimates.

It should be noted that the large energy use of the system results in significant

added burden on fossil fuel supply, especially if the electricity is generated by fossil

fuel plants with carbon capture. This includes all the upstream impacts of additional

fossil fuel extraction. Also, compared with point-source sequestration costs, the cost

of sequestration (after the compression step) will be higher per unit of CO2 captured,

since the air capture system must also sequester carbon from the fuel, sequestering

1.5–2 tons carbon for every ton captured. However, we do not expect this subtlety to

significantly change the cost of the total system.

We doubt that the system just described is the lowest cost design, even in the near

term. One obvious improvement is to engineer a separate unit to carry out the slaking

reaction, Reaction 3, at elevated pressure and temperature and use the energy for elec-

tricity production. No doubt other significant improvements could be made with only

moderate development of new technology.