CARBON DIOXIDE

ATMOSPHERIC CONCENTRATION

By Charles Rhodes, Xylene Power Ltd.

GLOSSARY OF TERMS

INTRODUCTION:
This web page presents a quantitative analysis of the atmospheric carbon dioxide (CO2) concentration, the rate of change of this atmospheric CO2 concentration and the projected final value of this atmospheric CO2 concentration. This analysis is based on conservation of energy and basic physics.

In this analysis there is an implicit assumption that the the total mass of carbon trapped in biomatter is nearly constant over time and hence plants normally do not cause a significant net change in the atmospheric CO2 concentration. This assumption is justified because the average rate of absorption of CO2 from the atmosphere by living plants must be approximately equal to the average rate of release of CO2 to the atmosphere by biomatter decay and combustion. If this CO2 balance did not exist, over millions of years plants would have either accumulated the entire world supply of carbon on dry land or totally depleted carbon from dry land.

Conversion of forests into farm land releases net CO2 to the atmosphere and conversion of farm land into forests absorbs net CO2 from the atmosphere, but this contribution to the change in atmospheric CO2 concentration is quite small as compared to the increase in atmospheric CO2 concentration that has been caused by combustion of fossil fuels.

The rate of absorption of atmospheric CO2 by plants to form carbohydrates is constrained by the availability of sunlight, water and suitable temperature. Hence the measured increase in atmospheric CO2 concentration has little effect on plant growth rate.

Carbon dioxide in the atmosphere dissolves in water and then combines with limestone to form a calcium bicarbonate solution. This calcium bicarbonate solution accumulates in the oceans. The relevant chemical equations are:
 
CO2(gas) + H2O(liquid) => H2CO3(weak acid)
H2CO3(weak acid) + CaCO3(limestone) => Ca(HCO3)2(calcium bicarbonate solution)

On the surface of the ocean wind and tide cause waves and chop which are accompanied by fine spray and foam. Most of the solar radiation incident upon the ocean causes evaporation of this fine spray and foam. When ocean water fine spray or foam evaporate the contained calcium bicarbonate solution decomposes and releases carbon dioxide gas to the atmosphere. The relevant chemical equations are:
 
(solar radiation) => heat
heat => latent heat + direct IR radiation
latent heat + Ca(HCO3)2(solution) => CaCO3(limestone) + CO2(gas) + H2O(vapor)
H2O(vapor) => H2O(liquid) + IR radiation(latent heat release)

A similar sequence of chemical reactions causes formation of stalactites and stalagmites in limestone caves.

Some CO2 gas is also released to the atmosphere via volcanos on land. The chemical reaction is:
CaCO3 + SiO2 + heat = CaSiO3 + CO2 (gas)
This reaction is only significant at locations where there is active volcanic activity to supply the required high temperature heat. Elsewhere on the Earth's surface where it is cooler this reaction proceeds in reverse and slowly absorbs CO2 from the Earth's atmosphere.

Antarctic Ice Core Data indicates that prior to the industrial revolution the equilibrium atmospheric carbon dioxide concentration was stable at 275 ppmv +/- 5%, at which concentration the mass flow rate of carbon dioxide entering the atmosphere via evaporation of sea water fine spray or foam was equal to the mass flow rate of carbon dioxide dissolving in the oceans and other exposed water.

Since the beginning of the industrial revolution mankind has burned fossil fuels to obtain energy and heat. Combustion of fossil fuels releases additional carbon dioxide gas to the atmosphere. It is shown herein that the rate of release of carbon dioxide by mankind is now comparable to the natural rate of release of carbon dioxide by evaporation of ocean water. In order for the rate of dissolving of carbon dioxide in the oceans to balance the rate of release of carbon dioxide from combustion of fossil fuels, the average atmospheric carbon dioxide concentration must increase.

It is shown herein that, in order to return the atmospheric carbon dioxide concentration to its 1990 level of 354 ppmv, it is necessary to reduce the world wide fossil carbon dioxide emission rate to the atmosphere to less than 47.8% of the 2004 world wide fossil carbon dioxide emission rate.

It is shown herein that, in order to prevent the ultimate atmospheric carbon dioxide concentration exceeding 550 ppmv, it is necessary to prevent the world wide fossil carbon dioxide emission rate to the atmosphere exceeding 166.7% of the 2004 world wide fossil carbon dioxide emission rate.

It is shown herein that sequestration of carbon dioxide, beyond the level that naturally occurs, is only practical in very restricted circumstances, and is unlikely to have a significant impact on world wide fossil carbon dioxide emission rate to the atmosphere.

It is concluded that the only practical solution to the problem of increasing atmospheric carbon dioxide concentration is for mankind to cease using combustion of fossil carbon as a primary energy and heat source.

It is shown that in the year 2004 the half life of excess carbon dioxide in the atmosphere was about 25 years. Failure to act immediately to sufficiently reduce carbon dioxide emissions will have substantial adverse effects for at least the next 100 years (4 half lives). The resulting increased carbon dioxide concentration will reduce the Earth's ability to cool itself by emitting infrared radiation, and hence will cause increased temperatures.

The absorption of excess atmospheric CO2 by the oceans relies on the presence of sufficient exposed carbonate radical (CO3-- in limestone and sea shells) in the ocean water. However, CO3-- is relatively insoluble. The supply of exposed CO3-- is diminishing due to the huge mass of excess CO2 that is been converted to HCO3-. As the available inventory of exposed CO3-- diminishes, the ocean will cease absorbing CO2 gas and the half-life of excess atmospheric CO2 will greatly increase. The atmospheric CO2 concentration will then continue rising until solar driven biological processes convert the excess CO2 back into coal (C), oil (CH2), methane (CH4) and carbonate radical (CO3--). In the mean time there will be a massive extinction of higher mammals such as ourselves due to starvation and related conflict and disease.

Unfortunately there is no political appreciation of the immensity of this problem, its rate of onset and what must be done to solve it.

Abandonment of fossil fuels for primary energy and heat production in Ontario requires construction of several major new nuclear plants as well as major transmission lines: to northern Ontario to access wind power, to Manitoba and Quebec to access Hydro Power and to down town Toronto to deliver transportation and building heating power. It may also be necessary to build further nuclear facilities in downtown Toronto for district heating and absorption cooling. These are engineering realities that governments (federal, provincial and municipal) and environmental organizations are presently unwilling to face.

Once the public understands these issues the remedy lies in teaching others and at the ballot box.

In Canada the worst offenders with respect to carbon dioxide emissions are electricity generators and heavy oil producers that burn fossil fuels when they have non-fossil fuel alternatives available. The organizations and executives responsible for the construction, approval and ongoing operation of fossil fuelled electricity generators and fossil fuelled steam plants for heavy oil extraction must be held both personally and corporately responsible for the financial costs and consequences of their negligence. The financial costs include increased air conditioning costs world wide that will continue for about a century after these fossil fuelled plants are taken out of service.

SURFACE AREA OF THE EARTH:
The distance along the earth's surface from the equator to the pole is 10,000,000 metres. Thus, since the earth is approximately spherical, the circumference of this sphere is 4 times the distance from the equator to the pole, or 40,000,000 m = 40,000 km.

Let R be the radius of the earth. Then:
Circumference = 2 Pi R
or
R = Circumference / 2 Pi = 40,000 km / 6.28 = 6369.4 km

The surface area As of a sphere of radius R is:
As = 4 Pi R^2.
Hence the surface area As of the earth is:
As = 4 Pi R^2
= 4 X 3.14 X (6369.4)^2 km^2
= 509.55 X 10^6 km^2
= 509.55 X 10^12 m^2

MASS OF THE ATMOSPHERE:
The average atmospheric pressure P at sea level is about:
P = 101,324 Pascals
= 101,324 newtons / m^2
= 1.01324 X 10^5 newtons / m^2.

The acceleration G of gravity near the earth's surface is:
9.80665 m / s^2.

Let M be the total mass of the earth's atmosphere. From Newton's law:
Force = Mass X Acceleration.
Hence the total weight (force) of the atmosphere on the earth's surface is:
M X G.
This weight is evenly distributed over the spherical surface area As.
Thus the atmospheric pressure P at sea level is given by:
P = (M X G) / As
Rearranging this equation gives:
M = (P X As) / G

Numerical evaluation of the mass M of the atmosphere gives: M = (P X As) / G
= (1.01324 X 10^5 newtons /m^2 X 509.55 X 10^12 m^2)/ 9.80665 m-s^-2
= [(1.01324 X 5.0955) / 9.80665] X 10^19 kg
= .5265 X 10^19 kg

HISTORIC MASS OF CARBON DIOXIDE IN THE ATMOSPHERE:
The preindustrial fraction of carbon dioxide in the atmosphere, as indicated by analysis of ice cores, was about 275 ppmv (parts per million by volume). Air is about 21% oxygen and 79% nitrogen. Oxygen and nitrogen both occur as diatomic molecules. The molecular weight of oxygen is 32 and the molecular weight of nitrogen is 28. Thus the average molecular weight of air is about:
.21(32) + .79(28) = 6.72 + 22.12 = 28.84.
The molecular weight of carbon dioxide is about 44. In preindustrial times when carbon dioxide was approximately uniformly distributed around the Earth, the total mass of carbon dioxide in the atmosphere was about:
(275 /1,000,000) X (44 / 28.84) X .5265 X 10^19 kg
= 220.89 x 10^13 kg
= 220.89 X 10^10 tonnes

HISTORIC MASS OF CARBON IN THE ATMOSPHERE:
Carbon has an atomic weight of 12 and oxygen has an atomic weight of 16. Hence the weight fraction of carbon in carbon dioxide is:
(12 /(12 + 16 + 16))= .273
Thus, if carbon dioxide was uniformly distributed through the atmosphere at 275 ppmv the mass of carbon in the atmosphere was:
.273 X 220.89 X 10^10 tonnes = 60.24 X 10^10 tonnes.

FOSSIL CARBON RELEASE RATE:
Our modern society presently relies on energy obtained primarily from the fossil fuels coal, oil and natural gas. Coal is almost 100% carbon by weight.
Oil, which consists of carbon chains, each carbon atom having about 2 hydrogen atoms attached, is about:
(12/14) X 100% = 86% carbon by weight.
Natural gas (mostly methane) has about 4 hydrogen atoms per carbon atom. Hence natural gas is about:
(12 / 16) X 100% = 75% carbon by weight.
The rate of release of fossil carbon can be calculated simply by summing the carbon contributions from coal, oil and natural gas production.

WORLD COAL PRODUCTION:
During the year 2004 the total world coal production, obtained by summing the productions from the major producers as listed at:
World Coal Production was 6079 million short tons. Converting this figure into metric tonnes gives:
6079 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 5521 X 10^6 tonnes/year
= .5521 X 10^10 tonnes/year
Almost all of this carbon mass enters the atmosphere.

WORLD OIL PRODUCTION:
The world oil production in 2004 as obtained by summing producers outputs listed at:
World Oil Production, was about 72,224,000 barrels per day. The corresponding annual carbon output is:
72,224,000 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= .3105 X 10^10 tonne / year
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt and resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unreported coal.

WORLD NATURAL GAS PRODUCTION:
The world dry natural gas production during 2004, as obtained by summing the producers outputs listed at:
World Natural Gas Production, was:
98,620 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
98,620 X 10^9 ft^3/year X 28.328 m^3 / 1000 ft^3 X 1000 lit / m^3 X 1 mole / 22.4 lit X 273/288 X 16 gm / mole X 1 tonne/10^6 gm X .75
= 9.8620 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes / year
= 141.87 X 10^7 tonnes / year
=.14187 X 10^10 tonnes / year
Almost all of this carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE RATE:
Thus the total release rate of fossil carbon obtained by summing the 2004 contributions from coal, oil and natural gas is:
(.5521 + .3105 + .14187) X 10^10 tonnes / year = 1.00447 X 10^10 tonnes /year

The corresponding rate of production of fossil carbon dioxide in 2004 was:
(44 / 12) X 1.00447 X 10^10 tonnes / year = 3.683 X 10^10 tonnes / year

The corresponding per capita annual production of fossil carbon dioxide in 2004 for the entire world was:
(3.683 X 10^10 tonnes / year) / (6.479 X 10^9 persons) = 5.68 tonnes / person-year

The corresponding per capita annual production of greenhouse gases in Canada during 2004 was:
(758 X 10^6 tonnes / year) / (32,299,496 persons) = 23.47 tonnes / person-year
Thus in 2004 the Canadian per capita greenhouse gas production rate was more than four times the per capita average for the entire world.

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
Direct atmospheric carbon dioxide concentration measurements were conducted at Mauna Loa during the period 1958 to 2004. The data is reported at:
Mauna Loa. In 1959 the atmospheric carbon dioxide concentration at Mauna Loa was 316.00 ppmv.
During the three year period from 1959 to 1962 the atmospheric carbon dioxide concentration at Mauna Loa increased from 316.00 ppmv to 318.46 ppmv. This is an annual atmospheric carbon increase of:
(318.46 - 316.00) / (3 years X 316.00) = .00259 / year
= .259% / annum
During the three year period from 2001 to 2004 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 371.04 ppmv to 377.43 ppmv. This is an annual atmospheric carbon increase of:
(377.43 - 371.04) / (3 years X 371.04) = .00574 / year
= .574% / annum

Thus in the 42 year period between 1959 and 2001 the measured rate of increase in the atmospheric carbon dioxide concentration over Mauna Loa increased by a factor of .574 / .259 = 2.2. This pattern of an increase in the rate of increase of carbon dioxide in the atmosphere is being further driven by industrialization of populous emerging nations such as China, due to production of electricity by combustion of coal. Any attempt by the USA to achieve energy independence based on synthesis of automotive fuel from coal will further aggravate the problem. Even if today all nations take the strongest possible action to replace fossil fuel energy by other forms of energy, industrialization of the third world will likely cause the carbon dioxide concentration in the atmosphere measured at Mauna Loa, Hawaii to exceed 550 ppmv.

It must be emphasized that the atmospheric carbon dioxide concentration measurements at Mauna Loa are indicative of the lowest atmospheric carbon dioxide concentrations on earth, not the average atmospheric carbon dioxide concentration. The atmospheric carbon dioxide concentration near fossil fuelled power stations and over cities is much higher than at Mauna Loa.

RATE OF INCREASE IN ATMOSPHERIC CARBON DIOXIDE CONCENTRATION:
The atmospheric carbon dioxide concentration measurements at Mauna Loa show a compounding .574% per annum increase in the atmospheric carbon dioxide concentration. This increase corresponds to a 5.89% increase compounding every ten years or a 12.1% increase compounding every 20 years. In 40 years the increase is 25.67%. In 60 years the increase is 40.9%. This Simple extrapolation indicates an atmospheric carbon dioxide concentration at Mauna Loa of about 541 ppmv 60 years hence.

The more immediate problem is that the atmospheric carbon dioxide concentration over many major cities is already above 450 ppmv and is continuing to increase.

NATURAL CARBON DIOXIDE CONCENTRATION CONTROL PROCESS:
Antarctic ice core samples going back 420,000 years show that prior to the advent of mankind the carbon dioxide concentration in the atmosphere slowly oscillated in the range 180 ppmv to 300 ppmv. For the 10,000 years prior to the industrial revolution the carbon dioxide concentration was stable at about 275 ppmv +/- 5%. In order to calculate the future carbon dioxide concentration it is necessary to understand the natural carbon dioxide concentration control process.

Solar radiation shines on the Earth. About 30% of this solar radiation is reflected back into space by the planetary albedo (reflectance). A small portion of the remaining solar radiation is absorbed by the atmosphere. Most of the remaining solar radiation is absorbed by the oceans. The ocean has an albedo of about .035, so about 96.5% of the solar radiation directly incident upon the ocean is absorbed by the ocean and becomes heat. Almost none of this heat leaves the ocean surface directly via infrared radiation. Instead most of the heat evaporates ocean water. It is the later condensation of water vapour that emits infrared radiation.

Water evaporates from the ocean in two ways. There is direct evaporation from the ocean surface and there is the evaporation of wind borne fine spray and wave foam. When the ocean is dead calm and there is no wind almost all the evaporation comes from the surface of the ocean. When there is a high wind and strong wave action almost all of the evaporation comes from wind borne fine spray and wave foam. The difference between these two evaporation mechanisms is of great importance.

When water evaporates directly from the ocean surface, the bicarbonate ion remains in solution in the liquid ocean. However, when wind borne fine spray or wave foam evaporates the bicarbonate ion in solution in the fine spray or wave foam is released to the atmisphere. The released bicarbonate immediately breaks down into carbonate dust and carbon dioxide gas. The carbonate dust settles back into the ocean and the carbon dioxide gas mixes with the atmosphere.

The fraction of total net ocean evaporation that releases bicarbonate from solution is defined as Fs. If all the oceans were dead calm everywhere all the time then Fs would be close to zero. However, most of the time most of the ocean surface has waves and wind, so generally Fs is close to unity.

During daylight hours water vapor rises carrying latent heat of vaporization. At some altitude or during the evening the water vapor cools enough that the water vapor changes phase to liquid droplets and releases its latent heat of vaporization as infrared radiation.

The infrared radiation from the condensing water vapor can be measured by a thermal emission spectrometer mounted on a spacecraft.

The condensed liquid water droplets fall either as dew or precipitation. The evaporation-condensation cycle is a continuous process that at any particular longitude repeats itself daily. The average rate of precipitation indicates the average net ocean evaporation rate. Hence, the natural carbon dioxide release rate can be approximately determined by measurement of average rainfall, subject to a correction for Fs.

In preindustrial times the natural rate of release of carbon dioxide to the atmosphere was balanced by the rate of gaseous carbon dioxide disolving in the exposed water. This balance held the atmospheric carbon dioxide concentration at about 275 ppmv for many thousands of years.

The excess carbon dioxide gas from combustion of fossil fuels mixes with the naturally occurring carbon dioxide in the atmosphere. The carbon dioxide then dissolves in rain water, lake water or sea water. This carbon dioxide in water forms a weak carbonic acid that reacts with insoluble calcium carbonate (limestone) to produce calcium bicarbonate solution. This calcium bicarbonate solution accumulates in the oceans.

The process that dissolves carbon dioxide in water is independent of the source of the carbon dioxide. In order for this process to remove the extra carbon dioxide released by fossil fuels, the carbon dioxide concentration in the atmosphere must increase.

SEASONAL CHANGES:
Superimposed on the aforementined processes are small (< 2% peak to peak) annual oscillations in the atmospheric CO2 concentration due to the 23.5 digree inclination of the Earths rotation axis with respect to a normal to the plane of the Earth's orbit. This inclination causes the summer and winter seasons. There is also the fact that the area of the ocean in the southern hemisphere is much greater than the area of the ocean in the northern hemisphere and conversely the land area in the northern hemisphere is much greater than the land area in the southern hemisphere.

Consider what happens when it is winter in the northern hemisphere and summer in the southern hemisphere. Most of the land mass is in the northern hemisphere. In the northern winter there is very little photosynthesis by land based plants, so that absorption of CO2 from the atmosphere by living plants almost stops. Decaying plants liberate more CO2 to the atmosphere. Meanwhile in the southern hemisphere, which is mostly ocean, it is summer. Evaporation increases releasing yet more CO2. Hence when it is winter in the northern hemisphere there is a net increase in atmospheric CO2 concentration.

Consider what happens when it is summer in the northern hemisphere and winter in the southern hemisphere. The plant life in the northern hemisphere flourishes and absorbs CO2. The ocean evaporation decreases reducing the rate of release of CO2. Hence when it is summer in the northern hemisphere there is a net decrease in atmospheric CO2 concentration.

These two effects lead to a small seasonal oscillation in the atmospheric CO2 concentration. However, these seasonal effects have been in play for many millions of years, so the Earth has reached a steady state condition where these effects cause no net increase or decrease in the annual average atmospheric CO2 concentration.

NET CHANGE:
The change in the annual average atmospheric CO2 concentration is almost entirely due to ongoing combustion of fossil carbon. A relatively small component of the net change in atmospheric CO2 concentration is due to conversion of forests into farm land.

OCEAN VOLUME:
The surface area of the oceans is about 361 X 10^6 km^2. The average ocean depth is about 3711 m. Hence the ocean volume is about:
361 X 10^6 km^2 X 10^6 m^2 / km^2 X 3.711 X 10^3 m
= 1339.67 X 10^15 m^3

DISSOLVED CARBON DIOXIDE GAS:
The temperature and salt concentration dependent solubility coefficient X 10^2 of carbon dioxide gas in sea water is given by the following table from:
NIST CO2 Solubility in Sea Water. The units are mol kg-1 atm-1

TEMPERATURE	No Salt	3.4%	3.5%	3.6%	3.8%
273.15 K	7.758	6.325	6.287	6.249	6.175
283.15 K	5.367	4.413	4.328	4.363	4.313
293.15 K	3.916	3.258	3.241	3.223	3.189
303.15 K	2.995	2.530	2.517	2.505	2.480
313.15 K	2.389	2.054	2.045	2.036	2.018

The 2006 partial pressure of atmospheric carbon dioxide gas over the pacific ocean is about 384 X 10^-6 atmospheres. The above table indicates that for sea water at 10.0 degrees C (283.15 K), 3.5% salinity at equilibrium the amount of carbon dioxide gas in solution is given by:
.04328 moles/kg-atmosphere X 384 X 10^-6 atmospheres
= 16.62 X 10^-6 moles / kg
The corresponding maximum density of carbon dioxide gas dissolved in sea water near the ocean surface is:
(16.62 X 10^-6 moles / kg water) X (1000kg water / m^3) X (44 g CO2/ mole) X (1 kg CO2 / 1000 g CO2)
= 731.25 X 10^-6 kg CO2/ m^3

GREAT LAKES BICARBONATE CONCENTRATION:
Various cities such as Chicago, Detroit and Cleveland obtain their fresh water from the Great Lakes. As part of the water treatment for these cities the concentration of dissolved bicarbonate ion is monitored. This concentration is typically measured as .07295 kg / m^3 as reported at:
Drinking Water Analysis.

GREAT LAKES STORED CARBON DIOXIDE CONCENTRATION IN BICARBONATE SOLUTION:
Two bicarbonate ions effectively store one molecule of carbon dioxide. Hence the density of stored carbon dioxide in the great lakes that can be released by evaporation is:
[Molecular weight of carbon dioxide / 2(molecular weight of bicarbonate ion)] X .07295 kg / m^3
= 44 /2(61) X .07295 kg / m^3
= .0263 kg / m^3

OCEAN BICARBONATE CONCENTRATION:
Near the ocean surface the concentration of carbon dioxide as a gas and as dissolved carbonic acid total to about.025 X 10^-3 moles / kg of sea water. However, in the ocean the dominant form of inorganic carbon storage is the bicarbonate ion. Various authors have reported ocean bicarbonate concentrations in the range 142 gm / m^3 to 152.5 gm / m^3. Reference: The Chemical Composition of Seawater, Seawater Composition. For the purposes of the calculations herein we will assume that near the ocean surface the concentration of the bicarbonate ion is about .0025 moles / kg water as set out at:
Ocean Bicarbonate Concentration. Two bicarbonate ions store one molecule of carbon dioxide that can be released by evaporating the water. Hence the amount Kc of stored carbon dioxide that can potentially be released by evaporation of sea water is:
Kc = 1 mole CO2 / 2 moles HCO3 X .0025 moles HCO3 / kg water
= .00125 mole CO2 / kg water
= 1.25 mole CO2 / m^3 water
= 1.25 X 44 gms CO2 / m^3 water
= .055 kg CO2 / m^3 water
This value is confirmed by measurements in a paper titled "The Adsorption of Ions from Sea-Water by Sand" by F. P. Stowell:
The adsorption of ions from sea water by sand. This paper reports a sea water bicarbonate mass concentration of .15 X 10^-3. This amount corresponds to a carbon dioxide mass concentration that can be released by evaporation of:
(44/122) X .15 X 10^-3
= .0541 X 10^-3 tonne / m^3
= .0541 kg / m^3

Thus there is good agreement amongst the reference data sources relating to the dissolved bicarbonate ion concentration in ocean water.

RELEASE OF CARBON DIOXIDE:
As sea water containing dissolved carbon dioxide warms from 0 degrees C to 30 degrees C the solubility of the dissolved carbon dioxide gas decreases by a factor of:
6.287 / 2.517 = 2.50
causing part of the dissolved carbon dioxide gas to come out of solution and re-enter the atmosphere.

Most people have observed the temperature dependence of a carbon dioxide solution in water with soda drinks. Open a cold soda container and it fizzes slightly. Open a warm soda container and it fizzes a great deal. The fizz is carbon dioxide coming out of solution.

When ocean water in the form of spray or foam evaporates both the dissolved carbon dioxide gas and the the carbon dioxide in bicarbonate solution are released to the atmosphere.

The ratio of the concentration of evaporation releaseable carbon dioxide stored in calcium bicarbonate solution in the oceans to the maximum concentration of carbon dioxide gas in solution in the ocean is about:
(.055 kg / m^3) / (731.25 X 10^-6 kg / m^3) = 75.2 at an ocean surface temperature of 10 degrees C. Generally the dissolved carbon dioxide concentration is even smaller due to the presence of calcium carbonate (limestone) that combines with the carbon dioxide to form calcium bicarbonate. Thus the natural carbon dioxide release rate from the ocean is proportional to the the bicarbonate ion concentration in the ocean and is not significantly affected by the atmospheric carbon dioxide concentration.

WORLD WIDE CARBON DIOXIDE STORED IN OCEANS:
The corresponding total mass of releaseable carbon dioxide stored in the oceans is about:
.055 kg / m^3 X 1339.67 X 10^15 m^3
= 73.68 X 10^15 kg
= 73.68 X 10^12 tonnes.

Recall that the historic mass of carbon dioxide in the atmosphere was:
220.89 X 10^10 tonnes. Hence the mass of releaseable carbon dioxide in the oceans is much larger than the mass of carbon dioxide in the atmosphere.

CARBON DIOXIDE FROM FOSSIL FUELS:
Since the industrial revolution combustion of fossil fuels has added a new flow of carbon dioxide into the atmosphere. Part of this flow has accumulated in the atmosphere causing an increase in the concentration and hence the partial pressure of carbon dioxide. The increased partial pressure of carbon dioxide increases the rate at which carbon dioxide dissolves in open water. This increased rate of dissolving carbon dioxide accounts for the portion of the carbon dioxide flow coming from combustion of fossil fuels that does not accumulate in the atmosphere.

QUANTIFICATION OF THE ATMOSPHERIC CARBON DIOXIDE CONCENTRATION:
Conservation of mass requires that the mass M of carbon dioxide in the atmosphere follow the general differential equation:
dM / dT = F + Fv + Ev Kc Fs - Kd M
where:
T = time
F = mass flow of carbon dioxide to the atmosphere from combustion of fossil fuels
Fv = net mass flow of carbon dioxide to the atmosphere from land based volcanic action
Ev = ocean evaporation rate in m^3 / year
Kc = mass of carbon dioxide per m^3 of ocean water stored in calcium bicarbonate solution and released to the atmosphere as the ocean water evaporates
Fs = fraction of net ocean evaporation that releases bicarbonate
Kd = proportionality constant relating the rate of dissolving of carbon dioxide gas in open water to the mass of carbon dioxide in the atmosphere

If the sea water temperature is constant Ev is proportional to the absorbed solar energy flux.

PRIOR TO THE INDUSTRIAL REVOLUTION:
dM / dT = Fa + Fv + Ev Kc Fs - Kd M
dM / dT = 0
Fa = 0
M = Ma
Fv = constant Hence:
Fv + Ev Kc Fs = Kd Ma
or
Kd = (Fv + Ev Kc Fs) / Ma
This equation can potentially be evaluated to find Kd.

AT THE PRESENT:
dM / dT = Fb + Fv + Ev Kc Fs - Kd M
F = Fb
M = Mb
or
(1 / Ma)(dM / dT) = Kd [(Fb + Fv + Ev Kc Fs) / (Kd Ma)] - (M / Ma)]
or
d(M / Ma)/ dT = Kd [(Fb / Kd Ma) + 1 - (M / Ma)]
If Fb is held constant between times Ta and Tb the solution to this differential equation is:
(Mb / Ma) = [(Fb / Kd Ma) + 1] - [(Fb / Kd Ma) EXP [-Kd (Tb - Ta)]

The important issue with this equation is its exponential time constant
To = (1 / Kd)
Note that a time of about (3 X To) is required for (Mb / Ma) to come within 5% of its ultimate value.

Recall that:
d(M / Ma)/ dT = Kd [(Fb / Kd Ma) + 1 - (M / Ma)]
Rearranging this equation gives:
d(M / Ma) / dT - (Fb / Ma) = Kd [1 - (M / Ma)]
or
(1 / Kd)
=To = [1 - (M / Ma)] / [d(M / Ma) / dT - (Fb / Ma)]
or
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]

Numerical Evaluation of To:
Recall that in 2004:
Fb = 3.683 X 10^10 tonnes CO2 / year
Ma = 220.89 X 10^10 tonnes CO2
From Mauna Loa data for 2004:
M / Ma = 377.38 / 275 = 1.37229
d(M / Ma) / dT = (377.38 - 375.64) / 275 = .0063272 / year
Hence:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [1.37229 - 1] / [.0166734 year^-1 - .0063272 year^-1]
= .37229 year / [.010346]
= 35.984 years ~ 36 years
Note that this experimental determination of To is valid independent of assumptions regarding the mechanism of natural CO2 transport into and out of the Earth's atmosphere.

The corresponding half life Th of the excess carbon dioxide is given by:
EXP(-Th / To) = 0.5
or
Th = (-To) Ln(0.5)
= (35.984 years) X .693
= 24.94 years ~ 25 years

IN THE FUTURE:
Assume that Fc is held constant. Then the differential equation solution gives the ultimate value of (Mc / Ma) as:
(Mc / Ma) = [(Fc / Kd Ma) + 1]
or
(Mc / Ma) = [((Fc To) / Ma) + 1]

Numerical evaluation of (Mc / Ma) for Fc = Fb gives:
(Mc / Ma) = [((Fb To) / Ma) + 1]
= [(3.683 year^-1 / 220.89) X 35.984 years + 1]
= 1.59998
Thus if CO2 emissions were held at the 2004 level, the global CO2 concentration would stabilize at:
1.59998 X 275 ppmv = 440.0 ppmv.

Unfortuantely the reality is that in Canada, USA, China, India and elsewhere CO2 emissions are already substantially above the 2004 level and are further increasing.

Recall that:
(Mc / Ma) = [(Fc To/ Ma) + 1]
Rearranging this equation gives:
Fc = (Ma/ To) [(Mc/Ma)-1]
or
(Fc / Fb) = (Ma / (To Fb))[(Mc/Ma)-1]

The term (Ma /(To Fb)) is given by:
(Ma /To Fb) = (220.89 X 10^10 tonnes) /(35.984 years X 3.683 X 10^10 tonnes/year)
= 1.6667

If the atmospheric carbon dioxide concentration is to be stabilized at 550 ppmv:
(Mc / Ma) = 550 ppmv / 275 ppmv = 2
and
(Fc / Fb) = (Ma / (To Fb))[(Mc/Ma)-1]
= 1.6667
It has been shown that in order to prevent the atmospheric carbon dioxide concentration measured at Mauna Loa exceeding 550 ppmv the world wide total rate of emissions of fossil carbon to the atmosphere must be kept below 1.6667 times the 2004 world wide carbon emission rate.

If the atmospheric carbon dioxide concentration is to converge to its 1990 concentration of 354 ppmv, then:
(Mc / Ma) = 354 / 275 = 1.287
and
(Fc / Fb) = (Ma / (To Fb))[(Mc/Ma)-1]
= 1.6667 (1.287 - 1)
= .478

The corresponding world wide fossil CO2 emission rate is given by:
Fc = .478 Fb = .478 X 3.683 X 10^10 tonnes / annum = 1.76 X 10^10 tonnes / annum
On a per capita basis the corresponding fossil CO2 emission rate is:
1.76 X 10^10 tonnes / 6.6 X 10^9 persons = 2.66 tonnes CO2 / person - year

It has been shown that in order to cause the atmospheric carbon dioxide concentration measured at Mauna Loa to converge to its 1990 value of 354 ppmv the world wide fossil carbon dioxide emission rate must be reduced to 47.8% of the 2004 world wide fossil carbon dioxide emission rate. Most of this reduction must come from high CO2 per capita emitters such as Canada and the USA. In order to do their share towards reaching 1990 atmospheric CO2 concentration levels Canadians and Americans will have to reduce their per capita CO2 emissions from 24 tonnes / annum - person to about 2.66 tonnes / annum - person (9 fold).

THE PHYSICAL ORIGIN OF To:
The value of To of 35.984 years was obtained by analysis of the experimentally measured atmospheric carbon dioxide concentration as a function of time. It is helpful to investigate the physical origin of the exponential time constant To.
Recall that:
To = (1 / Kd)
= [Ma / (Fv + Ev Kc Fs)]

Recall that Ev is the ocean evaporation rate in m^3 / year. Assume that the average evaporation rate over water is much greater than the average evaporation rate over dry land because over land there is relatively little exposed water to evaporate.
Let the area of the earth's oceans be Ao.
Let the surface area of the entire Earth be As. Then the fraction of the earth's surface covered by ocean is:
Ao / As = 361 X 10^12 m^2 / 509.55 X 10^12 m^2 = .708

DEFINITION OF Fp:
Define Fp as the fraction of the absorbed solar power that evaporates ocean water. Satelite infared spectral observations indicate that almost all of the infrared radiation apparently emitted by the oceans actually comes from water vapor above the ocean surface. Hence, at radiation balance, 100% of the solar radiation absorbed by the oceans causes evaporation of ocean water. Hence, since about .708 of the earth's surface is covered by oceans:
Fp = .708

OCEAN SURFACE EVAPORATION:
Assume that almost all the evaporation from the surface of the ocean is due to evaporation of wind borne fine spray or wave foam. Then:
Fs = 1.0
There is some scientific debate regarding the value of Fs. However, as Fs decreases the calculated value of Fv increases, so the experimentally determined value of To remains unchanged.

CROSS SECTIONAL AREA OF THE EARTH:
The cross sectional area Ac of the earth is a disc of radius R. Thus:
Ac = Pi R^2
= 127.39 X 10^12 m^2

SOLAR POWER ABSORBED BY THE ENTIRE EARTH:
The solar power absorbed by cross sectional area Ac is:
Ho (1 - Fr) Ac
= 1367 watts / m^2 X .703 X 127.39 X 10^12 m^2
= 122.42 X 10^15 watts
= 1.2242 X 10^17 J / s X 1 cal / 4.18 J X 1 gm C /cal X 1.8 F / C X 1 lb / 454 gm X 1 BTU / lb F X 3600 s / h X 8766 h /year
= 3.664 X 10^21 BTU / year
In this calculation Fr = .297 = planetary albedo.

NET VOLUME OF OCEAN WATER EVAPORATED PER YEAR:
At 60 degrees F (15.55 C) the latent heat of vaporization of water Hv is:
Hv = 1200 BTU/lb
Hence the net amount of ocean water evaporated annually Ev is given by:
Ev = Ho (1 - Fr) Ac Fp / Hv
[(Fp X 3.664 X 10^21 Btu / year) / (1200 BTU / lb)] X .454 kg / lb X 1 tonne / 1000 kg
= Fp X 1.386 X 10^15 tonnes / year
= Fp X 1.386 X 10^15 m^3 water / year
Thus:
Ev = Fp X 1.386 X 10^15 m^3 water / year

FIND RATE OF EMISSION OF CO2 DUE TO EVAPORATION OF SEA WATER:
Rate of CO2 emission due to evaporation of sea water is:
Ev Kc Fs
Recall that:
Ev = Fp X 1.386 X 10^15 m^3 water / year
Hence:
Ev Kc Fs = Kc Fs Fp X 1.386 X 10^15 m^3 water / year
For the assumed Fs and Fp values of:
Fs = 1.0
Fp = .708
Ev Kc Fs = Kc X .708 X 1.386 X 10^15 m^3 water / year
= (.055 kg CO2 / m^3 H2O X 1 tonne CO2 / 1000 kg CO2 X .708 X 1.386 X 10^15 m^3 water / year)
= 5.397 X 10^10 tonne CO2 / year

FIND RATE OF EMISSION OF CO2 DUE TO VOLCANIC ACTION Fv:
Recall that:
To = Ma / (Fv + Ev Kc Fs)
Rearrange this equation to get:
Fv + Ev Kc Fs = Ma / To
or
Fv = (Ma / To) - (Ev Kc Fs)
Numerical evaluation of Fv gives:
Fv = (220.89 X 10^10 tonnes CO2 / 35.984 years) - (5.397 X 10^10 tonne CO2 / year)
= 6.1385 X 10^10 tonnes CO2 / year - 5.397 X 10^10 tonnes CO2 / year
= .7415 X 10^10 tonnes CO2 / year

Thus the physical process that determines To is well understood. We have great certainty regarding the value of To. The exact value of Fv could be affected by the assumptions relating to Fb, Fp and Fs. However, for the purposes of the calculations herein the small errors related to these assumptions are not material.

AVERAGE PRECIPITATION:
Conservation of water mass requires that:
Ev = Rf As
where:
Rf = the average world wide annual (rainfall + dew + condensation) in m / year
As = surface area of the spherical Earth = 509.55 X 10^12 m^2

Rearranging the above equation gives:
Rf = Ev / As
= (Fp X 1.386 X 10^15 m^3 / year) / (509.55 X 10^12 m^2)
= (.708 X 1.386 m) / (.50955 year)
= 1.926 m / year
This value compares with typical annual rainfall measurements of about 1 m / year on dry land. However, rainfall measurements on dry land do not take into consideration low altitude condensation that occurs over the oceans.

SEQUESTERING CARBON DIOXIDE:
There is a possible method of sequestering carbon dioxide in the ocean by dissolving the carbon dioxide in ocean water in the presence of an excess of limestone. However, the amount of energy required to perform this function per kg of CO2 sequestered is presently unknown.

If we want a higher level of fossil fuel combustion without increasing the atmospheric carbon dioxide concentration, we must devise engineering techniques for increasing the rate of carbon dioxide sequestration in the oceans. The sequestration process involves the following steps:
1. Gaseous products of combustion of fossil fuels must be cooled to room temperature;
2. Toxic pollutants such as mercury and sulphur must be removed;
3. The carbon dioxide must be dissolved in cold water to form weak carbonic acid and the non-dissolveable gases such as nitrogen and excess oxygen must be vented to the atmosphere;
4. The weak carbonic acid must be reacted with limestone to form calcium bicarbonate solution;
5. The newly formed calcium bicarbonate solution must be mixed with the larger ocean.

There are serious questions relating to whether the energy required to perform these five steps is so large as to make the net energy available for end use too small to justify the use of fossil fuels.

Step 1 can be done by passing the combustion exhaust gas through a series of water cooled stainless steel heat exchangers. The fan electrical load, the water pumping energy and the water consumption (if evaporative cooling is used) must be considered.

Step 2 is comparable to existing exhaust gas scrubbers and will not be further considered here.

Step 3 involves pumping the exhaust gas through a head of at least one atmosphere, piping it to an ocean front location and then bubbling the gas upwards through a large counter current cold sea water flow to dissolve the carbon dioxide gas and then release the other gases to the atmosphere. Both the required gas pumping power and the water circulation power must be considered.

Step 4 involves passing the discharge water from Step 3 through a large limestone gravel bed. Since sequestering each atom of carbon (atomic weight = 12) involves one molecule of calcium carbonate (molecular weight = 100):
100 / 12 = 8.3 tonnes of limestone / tonne carbon
are required. Quarrying, crushing and transporting all this limestone may by itself make the sequestration process prohibitively expensive.

Step 5 involves piping the resulting calcium bicarbonate solution sufficiently far out to sea that it will mix with a major ocean current. The cost of this pipe and the related pumps is not small.

In summary, ocean sequestration of carbon dioxide, if it is practical at all, is restricted to locations that have an abundance of limestone and that are close to a cold ocean with a strong cross current.

PROHIBITION OF LAND BASED CARBON DIOXIDE SEQUESTRATION:
All proposals for land based sequestration of carbon dioxide are inherently dangerous. If concentrated carbon dioxide gas escapes to the atmosphere it is locally toxic. If the geology is favourable, carbon dioxide injected deep underground will react with a mineral metal oxide to form a stable carbonate compound. However, excess carbon dioxide will dissolve into ground water. This ground water forms weak carbonic acid that will react with the metal carbonate to form water soluble metal bicarbonate. Sooner or later the water containing metal bicarbonate solution will make its way to the surface where it will evaporate, releasing the carbon dioxide.

For example, farmers draw ground water from deep wells for irrigation. If the water in these deep wells contains bicarbonate solution, the contained carbon dioxide will be released to the atmosphere when the water is used for irrigation. Hence all land based sequestration of carbon dioxide should be prohibited.

Natural anaerobic decomposition of biomass usually yields about 50% CH4 (methane) and about 50% CO2 (carbon dioxide). However, most natural gas deposits are >90% methane, indicating that over time the carbon dioxide leaks out many times faster than the methane. This observation confirms that at best underground CO2 sequestration is a time delay mechanism rather than a permanent storage mechanism and that long term storage of CO2 under dry land is virtually impossible due to diffusion of dissolved calcium bicarbonate through ground water.

The practical constraints on carbon dioxide sequestration limit its application. It is not anticipated that carbon dioxide sequestration will significantly reduce world wide carbon dioxide emissions to the atmosphere.

SEQUESTERING FREE CARBON:
Free carbon sequestration is essentially coal mining in reverse. Instead of digging free carbon (coal) out of the ground, free carbon sequestration involves putting free carbon back into the ground. Free carbon sequestration works. Coal seams have existed underground and under the sea for many thousands if not millions of years.

In order to make free carbon sequestration improve the Earth's atmosphere it is necessary to use plants and solar energy to capture carbon dioxide from the atmosphere and turn it into carbohydrates. Then, before rotting, the carbon rich plant material must be buried deep enough that oxygen cannot get at it. In many places this objective can be met by burying the plant material below the summer water table. Over time anerobic bacteria break down the buried plant material into non-volatile and volatile components. The volatile gases may eventually diffuse to the surface leaving the non-volatile material underground.

Obviously, intentional free carbon sequestration will not improve the atmosphere until combustion of fossil fuels for primary energy generation is stopped. Combustion of coal is the exact opposite of free carbon sequestration.

Municipal Land Fills:
A simple example of free carbon sequestration is a municipal waste land fill. The waste, which is primarily a mix of various hydrocarbons, is placed underground where oxygen cannot get to it. Over time anerobic bacteria break down the waste into volatile gases such as methane and heavier carbon rich material. Municipal land fills have been in existence for many years.

Pyrolysis:
A method of accelerating natural free carbon sequestration, known as pyrolysis, is to first heat the plant material in an oxygen free atmosphere. The volatile components outgas from the plant material and can be burned as an energy source. The remaining carbon rich material is then buried or is used for agricultural soil enhancement. The major problem with this process is that the value of the energy recovered may not be sufficient to pay the costs of operating the process. There are tremendous costs involved in growing, harvesting, collecting, transporting and drying plant material. The costs of burying the remaining carbon rich material are additional.

A variation on this same concept is to apply the same pyrolysis acceleration process to municipal waste. The chief advantage of using municipal waste is that disposal of municipal waste earns a tipping fee which improves the economics of the whole process. The chief disadvantages of municipal waste are that the waste stream contains plastics that are made from chlorinated hydrocarbons and contains toxic metals. When the chlorinated hydrocarbons are heated they form a variety of carcinogenic compounds. The pyrolysis process must be very carefully controlled to ensure that these carcinogens are fully destroyed before the gaseous products are released to the atmosphere. Another important economic issue is that the remaining carbon rich material, which still contains toxic metals, must be buried. Municipal politicians tend to want to burn this carbon rich material to recover more energy value. However, burning the carbon rich material defeats the free carbon sequestration objective of the process. A rural population, that relies on well water for drinking, understandably opposes the location of toxic waste dumps anywhere near aquifer recharge zones that provide drinking water. Hence, many plans to obtain energy from municipal waste, other than by anerobic digestion, have been vigerously opposed by those who live in proximity to the required companion toxic waste dumps.

Hydrothermal Carbonization:
Another method of obtaining free carbon from plant carbohydrate is hydrothermal carbonization. In hydrothermal carbonization biomatter is heated for 12 to 24 hours at 180 to 200 degrees C in slightly acidic water. The corresponding vapor pressure of water is about 20 atmospheres. This process is exothermic and the resulting carbohydrate decomposition yields free carbon plus water. Various parties are investigating scaling up this process. In order to make this process economic the heat released must serve a useful purpose such as district heating or concentration of ethanol. A major advantage of hydrothermal carbonization is that there is no release of carbon dioxide. Another advantage is that the left over solids can be used for agricultural soil enhancement.

Summary:
In summary, free carbon sequestration is a potentially practical long term means of removing carbon dioxide from the atmosphere. However, free carbon sequestration will not be financially viable as long as combustion of fossil fuels for primary energy generation is permitted. In order to achieve net free carbon sequestration, fossil fuels must be left buried in the ground.

CONCLUSION:
Fossil carbon is no longer a viable fuel for primary power generation. Like it or not, the world is going to have to rapidly convert to non-fossil fuel energy sources. The longer this conversion process is delayed the more expensive this conversion process will become, because in the mean time carbon dioxide will continue to accumulate in the atmosphere, causing increased extra air conditioning load and decreased agricultural production for at least another century.

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This web page last updated January 17, 2011.