Technical communication: Optimum CO2 management of the atmosphere

ht. J. Hydrogen Energy, Vol. 20, No. 6, pp. 501-505, 1995 International Association for Hydrogen Energy Elsevier Science Ltd Printed in Great Britain 036&3199/95 $9.50 + 0.00

0360-319

TECHNICAL

COMMUNICATION: OPTIMUM OF THE ATMOSPHERE

CO, MANAGEMENT

WALTER SEIFRITZ Chapfstr. 4, CH-5200 Windisch, Switzerland

(Received for publication

24 June 1994)

Abstract-Optimum CO, managementof the atmosphereis proposedto stabilizeits anthropogenicCO, inventory at a tolerableconstantlevel, In order to achievesuch a situation while burning fossil fuels further on a massive worldwide scale, a temporal decoupling of useful energy production and the emission of CO, has to be achieved. The genesis of such possible processesis discussedand presented generically.

with a being a constant (=0.131), meaning that about 13.1% of all of the CO1 massemitted into the atmosphere In order to mitigate the greenhouse effect in the atmos- remains there forever due to a new equilibrium of the phere, mainly due to carbon dioxide (CO,) from the main C reservoirs on the Earth; b = 0.869is the amplitude burning of fossil fuels, we can postulate the following of the exponential recovery function possessinga mean optimization principle: find the time-dependent CO, decay time of ? = 117.2 yr Cl]. Equation (1) is an emission rate function I(t) into the atmosphere in such a abbreviated form of Green’s function recommended by way that (after a transient) the allowable maximum the ICPP with five exponential functions. inventory of CO, in the atmosphere Q,,, given by Equation (1) can be solved by making use of the meteorologists, remains constant forever. In this casethe convolution theorem when applying the Laplace transmean temperature increase of the Earth will increaseafter form on both sides and converting Z(s)back to the time the transient to a tolerable level and thereafter remains domain [Z]. After a lengthy calculation, which will not constant. If we allow an additional anthropogenic mass be repeated here, we obtain as the result of CO, in the atmosphere corresponding to, for instance, half of the pre-industrial level (620 Gt C), then a-l -’r’-p.e ?/A - 1 -l/A Q,,,., = 0.5 x 620 Gt x 44/12 = 1,137 Gt CO,, giving -.e Z(t) = + (3) rise to a 50% higher CO, concentration compared with ah/? 1 aAl7 - 1 [ the pre-industrial time. Mathematically, the problem is formulated in the form with of an integral equation of the first kind as follows: INTRODUCTION

1

Q,,,(l - e-‘jA) =

* G(t -

s0

7).1(7)

dz,

where A is the time constant with which the equilibrium in the atmosphere will be reached and G(t) is the so-called dimensionless Green’s function of the atmosphere,i.e. the response to a &like input function, given here in the simplified form of G(t) = a + be+‘,

a - 7lA Q,., Z(O)=------.

(1)

(2) 501

al\/?-- 1 ?

Independent of the totally emittable amount of CO, is m I(t).dt = + s0 which is a rather high figure.

= 7.63 Q,.,,

(5)

502

W. SEIFRITZ

emission rate of CO, into the atmosphere I(t) is principally proportional to the useful power production rate P(t) given by Z(t) = &P(t),

0

I

I

5

10

Time (t/Y) Fig. 1.Optimum CO, emission rates for three different transients to meet the requirements of equation (1).

For A = 7, equation (3) reduces to 0.131 I@)+yT’

and in Fig. 1 two further casesof 1(t) for a slow (A = 27) and a fast (A = 0.5 ?)transient are shown. Asymptotically, all curves Z(t) approach the exponentially decaying function exp (at/?) which is the result of the true integrating fraction a for CO, in the atmosphere. The faster the transient assumed (A > 7) the smaller Z(0)and the lower the time t,,, for the maximum of Z(t),

(8)

where E (in units of the mass of CO, emitted per unit of energy produced) is the CO, intensity factor. Historically and on a worldwide basis, the energy consumption density p in kW per km2 of civilization area the related population density D in cap/km2 increased with a power of about 513,which means for equation (8) that P(t) increased much faster than the number of people Z, namely P(t) cc Z513[3]. Energy saving measureswould now have the task of reducing &P(t)with a power larger than 5/3 of the (still increasing) world population to make 1(t) a monotonically decaying function. In other words, it is hardly imaginable that CO, emissions can be reduced due to energy saving measures alone, although they possessthe highest positive political acceptability at present. Contrary to energy saving measures, a temporal decoupling of the useful energy production and the CO, emissions can be realized basically by the following two techniques when using fossil fuels. These processesallow the “filling up” of the atmosphere with CO, later than the actual production of energy and are useful tools to approach the CO, management schemeof equation (1). THE HYDROCARB PROCESS [4]

1 - ?/A t mx = a(1 - a)(1 + &” However, due to the actual situation, the curves with A < 7 are more important. For instance, if we assume a realistic figure ofA = 0.5 i then in a time span of about 3A = 6 decadesthe atmosphere would be “filled up” and reach its equilibrium CO, inventory Q,.,. The question now is how to realize a chosen worldwide emission rate I(t) with a given Q,.,? Using fossil fuels alone in future there are the following possibilities. ENERGY SAVING Energy saving means, however, that in the cumulative sense,no fossil energy will be saved, but only the rate of its use is slowed down by measureslike the switch to less CO,-intensive fossil fuels like natural gas, conservation of energy by better thermal insulation, combined processesusing low temperature waste heat for heating purposes, increasing the thermal efficiencies of power plants, etc. However, the real disadvantage in the energy saving philosophy, which has been overlooked so far, is the fact that there is an inherently prompt coupling between useful energy production and the associated CO, emission into the atmosphere. This means that the

In this process methane is decomosed autothermally to carbon and hydrogen in a methane pyrolyser reactor (MPR) at about 100&1100”C according to CH, + XC + (1 - x)CH, + 2xH,,

(9)

where 0 < x < 1 is the decomposition efficiency of the MPR. The hydrogen gasstripped (and in the casewhere x # 1 the non-decomposed CHJ can be burnt with oxygen from air to produce promptly useful energy. The corres-ponding stoichiometric chemical equation is (1 - x)CH, + 2xH, + (2 - x)0, (from air) + (1 - x)CO, + 2H,O

(10)

resulting in the overall equation [equations (9) and (lo)] being CH, + (2 - x)0, (from air) + XC + (1 - x)CO, + 2H,O - (192 - 94x) kcal. (11) The amount of carbon separated, XC, in the form of carbon black, can be stored relatively easily under

TECHNICAL

ambient conditions due to its low chemical affinity to oxygen in the air and due to the fact that it is a solid. The energy hidden in the carbon atom can either be sacrificed by storing the carbon atom forever or it can be regained after an arbitrary time span T by burning it according to

N

1.00

8

XC + x0, (from air) -+ xC0, - 94x kcal.

t

(12)

This latter possibility is of special interest in relation to equation (1). The latter fraction of CO, releasedto the atmosphere, z&O,, as well as the corresponding fraction of energy, - 94 kcal, are delayed in time and are an inherent feature of the Hydrocarb process. The total released energy in equations (11) and (12) is - 194 kcal per mole of CH, originally used. In the ideal case of the energy/CO, decoupling phenomenon in the Hydrocarb process, characterized by x = 1, there are no immediate CO, emissions at all, although 51% (98 kcal) of the energy is gained immediately. After a time delay T, the rest of the energy, i.e. 49 % (94 kcal), is gained but is associated with 100% (1 mole) of the CO, emissions if the calculation is based on one mole of CH,. Present decomposition efficiencies x of MPRs on the basis of a once-through flow schemefor CH, are in the reahn of x x 0.5. This means that 76% (145 kcal) of the energy is gained immediately with an immediate emission of CO, being 50% (half a mole) of the total emission. After time T, when the carbon is burnt, 24% (94 kcal) of the total energy will be available accompanied by the other 50% (half a mole) of CO, emission. All these calculations are baaed on ideal conditions in order to show the energy/CO, emission decoupling phenomenon in a simplified way. Figure 2 visualizes the decoupling mentioned for three different values of x in units. of fractional energy release (E) and in units of fractional CO, emission (CO,) into the atmosphere. It is obvious that the generally valid agreement between I(t) and P(t) in equation (8) is given only in the special case of x = 0, i.e. in the case of the classical use of natural gas without any decomposition before its use. Two further improvements are of theoretical interest. (i) If the energy hidden in the C atom is sacrificed by storing it for an infinitely long time there is no delayed CO, emission. Again for one mole of CH, used, the extractable immediate energy is (1 - 0.49x) x 192 kcal and the associated prompt CO, emission is (1 - x) in units of moles of CO,, yielding a CO, intensity factor of

0.197(1 - x) in kg COJkW h. = (1 - 0.49x)

503

COMMUNICATION

(13)

I ----------------_-----

m

x = 0.5 0.24 4 0.5

g oso 5---------------------x= crl

1.0

0.49

051 t ;

r-4 ::

I T

0

Time (t) Fig. 2. Fractionsof the energygain (E) and the CO, emission different values of the MPR decomposition efficiencyin the Hydrocarg process.The decouplingbetween energyand CO, emissionis clearly borne out. (CO?) for three

For x = 1 (classical burning of CH,), cp results in the well known value of 0.197 kg COJkW h. In the other extreme case,if all the C is separated, x = 1, ap is zero, meaning a completely CO,-free burning of CH,. For the present once-through decomposition efficiency of MPRs, x = 0.5, ap results in 0.13 kg COJkW h, which is only two-thirds of the above value for x = 1. The lower sp (x + I), the higher the fraction of energy hidden in one mole of CH, (1 - 0.49x) we have to sacrifice. For instance, if x = 0.5 only 76%, i.e. 145 kcal, can be extracted from one mole of CH,. (ii) A further possibility to get a delay time higher than T for the delayed CO, emission in Fig. 1, but to recover the energy hidden in the stored C atoms at time T, is to remove the CO, from the burning process of equation (12) and to store it in one of the schemeswhich will be describedin the next section. Then in the ideal casex = 1 and 100% removal efhciency (for instance, if the carbon is burnt with pure oxygen), the total delay time is T + T under the assumption that the storage time in the CO, storage site is T This latter example, which may be called a C-CO, storage chain, shows that, in principle, it is now possible to extract the energy from fossil fuels and to emit the CO, much later, thus fttlglllng the requirements in equation (1).

504

W. SEIFRITZ m

CO, STORAGE

t -S(t). dt.

T=

Whilst the Hydrocarb processis best suited for natural gas,becausethe H/C ratio is the highest of the fossil fuels, the CO, storage techniques can be applied for practically all hydrocarbons C,H, including coal (CH, s), representing the largest fossil fuel reserve we can dispose of. Burning fossil fuels according to

If in equation (15), one mole of C,,,H, is burnt at time t = 0, i.e. if N(t) = 1.6(t) then the prompt and delayed CO, emission fractions are given by f, = (1 - Y)m.W, f&) = ym’S(t)

0, + mCO,+;H1O,

(14)

the CO, produced can be removed from the burning processin two ways: (a) in a pre-combustion manner by gasifying the hydrocarbons into a synthesis gas (mainly H, and CO), shifting the CO into CO, by the water shift reaction and separating the CO, from the hydrogen rich gas by a physical or chemical washing process; or (b) after combustion, e.g. by burning with pure oxygen and condensing the steam of the RHS of equation (14) by cooling the flue gas sufficiently. At present, an extended effoit in this direction is under way by the IEA Greenhouse Gas R&D Programme, which is lead by the British. In this programme, all possibilities of storing the CO, are investigated thoroughly. Such possible storage sites are: empty gas and oil wells which will be re-filled with supercritical CO,; disposal of liquid and solid CO, in the deep ocean; storage of CO, in aquifers by dissolving CO, gas in water under pressure; and the terrestrial storage of solid CO, in dry ice repositories [S] exhibiting only a very slow sublimation rate. The details of these techniques will not be discussed here, but from the principal point of view the prompt and delayed emission rates of CO, into the atmosphere, 1,(t) and la(t), respectively, are given by Z,(t) = (1 - y)m . N(t) and

(17)

I 0

(18)

in units of moles of CO, per time unit and per mole of C,H, used. The total time integrated CO, emission fraction f is f=

m [f,(t) + f-(t)] dt = 1. s0

(19)

It is important to note here that it is not necessarythat a CO, storage site must be absolutely tight. Also, with a leaky storage site with a mean storage time T>> ?, i.e. 7 in the range of only a few hundred years, the possibility exists of decoupling energy production from the emission of CO, to fulfil the requirements of equation (1) and Fig. 1, respectively. For instance, the mean delay time 7 in the dry-ice repository mentioned is about 800 [S] and T for the ocean disposal method is in the realm of a few hundred years to a millenium, depending on the depth where the injection of CO, took place. T in the case of CO, storage in empty gas and oil fields and in aquifers is practically infinity, i.e. milleniary to millions of years depending on the ground water flow conditions. In order to achieve the decoupling effect when storing CO, in one or the other form, one has to sacrifice a certain fraction of useful energy to meet the energy requirements for the necessaryCO, removal and disposal processes. CONCLUSIONS

The main messageof this Technical Communication is that both the C storage technique, described by the Hydrocarb process using natural gas, and the CO, in units of moles of CO, per unit of time if one mole of storage techniques, applicable to all kinds of fossil fuels, C,H, is used in equation (14). y is the CO, separation may be instrumental in shifting CO, emissions in the efficiency in the removal process.The presently discussed future in order to synthesize CO, emission rates which y-values for the pre-combustion techniques are y x 0.9, approach the ideal rate shown in Fig. 1. whereas in the case of burning C,H, with pure oxygen The fact is that in the next century mankind needs the y approaches unity. N(t) is the rate at which C,H, is energy from the fossil fuels but the hitherto intimate burnt and S(t) is the characteristic or Green’s function coupling with the associatedCO, emissions would result of the actual CO, storage site chosen in units of reciprocal in a strong greenhouse effect. More emphasis should time. An ideal CO, storage site is characterized by S = 0, therefore be given to the practical performance of the meaning that no CO, at all can escapeinto the atmos- CO, delay techniques which are discussed in this Techphere. If the storage site is leaky, then nical Communication. m S(t) dt = 1 (16) REFERENCES s0 MO = ym ’ W - t).W).dt s0

(15)

holds and the mean delay time 7 for the escaperate of CO, is defined to be the first moment of S(t), being

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TECHNICAL COMMUNICATION 2. Bronstein-Semedjajew, Tascbenbuchakr Muthematik, p. 637, 25. B.G. Teubner, Stuttgart (1991). 3. W. Sassin,Assessingclimate responsestrategies.Contribution to IPCC WGI. Data by B. Fritsch and A. Grilbler (March 1994).

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4. M. Steinber& et al., The coprocessing of fossil fuels and biomass for CO, emission reduction in the transportation sector. Energy Cowers. Mgmt 34,1015-1022 (1993). 5. B. Fritsch, S. Schmidheiny and W. Se&k, Towards an EcologicalIy Sustainable Growth Sociery. Springer, Berlin (1994).