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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 the atmospheric CO2 concentration and the projected future value of the atmospheric CO2 concentration. In this analysis it is assumed that there is sufficient exposed metal carbonate rock in the ocean to fully absorb all the available fossil CO2.

This analysis will become invalid in the future when the supply of exposed metal carbonate rock in the ocean is exhausted.

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 do not cause a significant net change in the atmospheric CO2 concentration except via long term formation of fossil fuels.

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 these contributions to the change in atmospheric CO2 concentration are 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 both rain water and open ocean water.

Initially rain water droplets are very pure H2O and have a very high ratio of surface area to volume, so the rate of carbon dioxide removal from the atmosphere via rain water is set via Henry's law by the total average evaporation of sea water, the partial pressure of CO2 in the atmosphere, and the temperature of the lower atmosphere.

Carbon dioxide in the atmosphere also directly dissolves in sea water. At present, the CO2 in solution near the ocean surface immediately becomes H2CO3 which then diffuses into the deep ocean where it combines with insoluble exposed metal carbonates such as limestone (CaCO3) to form a water soluble metal bicarbonate solution. The metal bicarbonate solution due to fossil CO2 will accumulate in the oceans until the supply of exposed marine metal carbonate is exhausted. For the metal calcium the relevant chemical equations are:
 
CO2(gas) + H2O(liquid) => H2CO3(weak acid)
H2CO3(weak acid) + CaCO3(limestone) => Ca(HCO3)2(calcium bicarbonate solution)

Note that as long as the deep ocean remains cold and as long as there is a supply of exposed CaCO3 the rapid conversion of H2CO3 into Ca(HCO3)2 prevents H2CO3 directly liberating CO2 to the atmosphere.

The metal bicarbonate solution diffuses everywhere in the ocean, including to the ocean surface.

On the ocean surface 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 metal bicarbonate solution decomposes and releases carbon dioxide gas to the atmosphere. The relevant chemical equations for the metal calcium are:
 
(solar radiation) => absorbed heat
absorbed heat => latent heat + direct IR radiation
latent heat + Ca(HCO3)2(solution) => CaCO3(limestone) + CO2(gas) + H2O(vapor)

At some height above the ocean surface:
H2O(vapor) => H2O (liquid rain or dew) + 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 volcanic action 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 and where there is an existing supply of metal carbonate. 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 for several thousand years 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 rain water, rivers, lakes and the oceans.

Note that the atmospheric CO2 concentration is not govered by Henry's Law because the atmosphere is in a steady state rather than a thermal equilibrium situation. As long as there is a surplus of metal carbonate in the oceans the partial pressure of CO2 in the ocean will be much smaller than the partial pressure of CO2 in the atmosphere. Non-equilibrium solar heat driven evaporation of sea water foam and droplets injects CO2 into the atmosphere at a nearly constant rate. This rate is balanced by diffusion of CO2 back into the oceans due to the partial pressure difference between the atmosphere and the oceans.

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 both solar driven evaporation and combustion of fossil fuels, the 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 44.2% 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 154.1% 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 30.3 years. Failure to act immediately to sufficiently reduce carbon dioxide emissions will have substantial adverse effects for at least the next 121 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 on dry land and net heat absorption by the oceans.

The ongoing absorption of excess atmospheric CO2 by the oceans relies on the presence of sufficient exposed carbonate radical (CO3-- in limestone and sea shells) in cold deep ocean water. However, CO3-- is relatively insoluble. The supply of exposed (CO3)-- is rapidly diminishing due to the huge mass of excess atmospheric CO2 that is been converted to (HCO3)-. As the available inventory of exposed (CO3)-- decreases and as the average ocean temperature increases, the ocean will no longer readily absorb CO2 gas and the apparent half-life of excess atmospheric CO2 will greatly increase. Due to the rising water temperature the oceans will then become a net CO2 source rather than a net CO2 sink. The atmospheric CO2 concentration will then continue rising until the concentration of (HCO3)- ions in solution significantly decreases and solar driven biological processes convert the excess atmospheric 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 rising sea level, 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. 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 on average is about 80% 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 was 6221.398 million short tons. Converting this figure into metric tonnes gives:
6221.398 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 5650.68 X 10^6 tonnes/year
= .56507 X 10^10 tonnes/year
The corresponding carbon mass that entered the atmosphere in 2004 was about:
0.8 X .56507 X 10^10 tonnes / year = .45205 X 10^10 tonnes / year.

WORLD OIL PRODUCTION:
The world oil production in 2004 as obtained by summing producers outputs was about 70,557,100 barrels per day. The corresponding annual carbon output is:
70,557,100 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= .3034 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. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unreported coal.

WORLD NATURAL GAS LIQUIDS PRODUCTION:
The world natural gas liquids production in 2004 as obtained by summing producers outputs was about 7,393,210 barrels per day. The corresponding annual carbon output is:
7,393,210 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .03179 X 10^10 tonne / year
Not all of this carbon goes into the atmosphere because part of the carbon related to NG liquid production is used to produce 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 was:
95,637.77 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
95,637.77 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
= 9.563777 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes / year
= 137.578 X 10^7 tonnes / year
=.137578 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:
(.45205 + .3034 + .03179 + .13758) X 10^10 tonnes / year = 0.92482 X 10^10 tonnes /year

The corresponding rate of production of fossil carbon dioxide in 2004 was:
Fb = (44 / 12) X 0.92482 X 10^10 tonnes / year
= 3.391 X 10^10 tonnes / year

The corresponding per capita annual production of fossil carbon dioxide in 2004 for the entire world was:
(3.391 X 10^10 tonnes / year) / (6.479 X 10^9 persons) = 5.23 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 about 4.5 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 from 1958 onwards. The data is reported at:
Mauna Loa. In 1959 the average atmospheric carbon dioxide concentration at Mauna Loa was 315.97 ppmv.
In 1961 the average atmospheric carbon dioxide concentration at Mauna Loa was 317.64 ppmv. This is an annual atmospheric carbon dioxide concentration increase of:
(317.64 ppmv - 315.97 ppmv) / (2 years) = .835 ppmv / year

During the period from 2003 to 2005 the average atmospheric carbon dioxide concentration measured at Mauna Loa increased from 375.77 ppmv to 379.80 ppmv. This is an annual atmospheric carbon increase of:
(379.80 - 375.77) / (2 years) = 2.015 ppm / year

Hence during 2004 the increase in CO2 mass in the atmosphere was:
(2.015 / 275) X 220.89 X 10^10 tonnes = 1.6185 X 10^10 tonnes / year

Thus in the 44 year period between 1960 and 2004 the measured rate of increase in the atmospheric carbon dioxide concentration over Mauna Loa increased by a factor of:
2.015 / .835 = 2.41
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.

In 2010 the atmospheric CO2 concentration measured at Mauna Loa reached 389.78 ppmv. The average annual increase in atmospheric CO2 mass between 2001 and 2010 was:
((389.78 ppmv - 371.13 ppmv) / 275 ppmv) X (220.89 X 10^10 tonnes) / 9 years
= 1.6645 X 10^10 tonnes CO2 / year

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.

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. As indicated by satellite borne infra red spectrometers, 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 this water vapour at a high altitude 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 atmosphere. The released bicarbonate immediately breaks down into carbonate dust and carbon dioxide gas. The microscopic 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 is determined by the known ocean evaporation rate. Hence, subject to a correction for Fs, the natural carbon dioxide release rate due to ocean evaporation can be approximately determined from the known ocean bicarbonate concentration, the incident solar energy flux and the latent heat of vaporization of water.

Similarly the approximate rate of washout of carbon dioxide from the Earth's atmosphere via rain water can be determined from the known ocean evaporation rate and from the known solubility of CO2 in distilled water as a function of temperature and CO2 partial pressure.

In preindustrial times the natural rate of release of carbon dioxide to the atmosphere was balanced by the rate of gaseous carbon dioxide dissolving in rain water and open sea 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 gas then dissolves in rain water and sea water. This dissolved carbon dioxide forms a weak carbonic acid (H2CO3) that in cold water reacts with insoluble metal carbonate rock such as calcium carbonate (CaCO3 or limestone) to produce water soluble metal bicarbonates such as calcium bicarbonate (Ca(HCO3)2. The metal bicarbonate ions accumulate in the oceans.

In the presence of an excess of metal carbonate this chemical reaction greatly reduces the partial pressure of CO2 in the oceans, especially in cold water.

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 flux of fossil carbon dioxide, the carbon dioxide concentration in the atmosphere must increase from its long term steady state value of 275 ppmv.

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 in the southern hemisphere 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 on an annual average basis these effects cause no net increase or decrease in the annual average atmospheric CO2 concentration.

NET CHANGE:
As long as the ocean temperature remains constant the net year over year change in the annual average atmospheric CO2 concentration is almost entirely due to 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.

DANGER:
An increase in atmospheric CO2 concentration caused by combustion of fossil carbon will cause global warming that leads to net heat absorption by the ocean. This net heat absorption will gradually increase the average ocean temperature and hence reduce the solubility of (HCO3)- ions in the ocean. The consequent reduction of stored CO2 in the ocean will liberate CO2 gas from the ocean to the atmosphere which will cause a further increase in atmospheric CO2 concentration.

This feedback process could easily lead to complete melting of all land borne glaciers, including the Greenland and the Antarctic glaciers. The result would be a 80 m sea level rise and a corresponding reduction of animal life on Earth. Eventually after millions of years plant photosynthesis and related carbon sequestration would reduce the atmospheric CO2 concentration but in the mean time many larger animals would become extinct.

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:
381.9 X 10^-6 X (44/ 28.84) = 582.65 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 582.65 X 10^-6 atmospheres
= 25.217 X 10^-6 moles / kg
The corresponding maximum density of carbon dioxide gas dissolved in sea water near the ocean surface and hence forming H2CO3 is:
(25.217 X 10^-6 moles / kg water) X (1000kg water / m^3) X (44 g CO2/ mole) X (1 kg CO2 / 1000 g CO2)
= 1109.5 X 10^-6 kg CO2/ m^3
= 0.0011095 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 releasable molecule of carbon dioxide. Hence the mass 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 CO2 / 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 (3.5% salt) containing dissolved carbon dioxide as (HCO3)- ions warms from 0 degrees C to 20 degrees C the solubility of the dissolved carbon dioxide gas decreases by a factor of:
3.241 / 6.287 = .5155
causing almost half 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 hard 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. If you warm up cold ocean water it will release CO2 gas.

When ocean water in the form of spray or foam evaporates due to solar energy absorption both the dissolved carbon dioxide gas and the the carbon dioxide in bicarbonate solution are released to the atmosphere. At steady state conditions the solar driven 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.

Similarly, since the CO2 partial pressure in the ocean is very low the CO2 absorption rate by the ocean is proportional to the atmospheric CO2 concentration and is not significantly affected by the ocean bicarbonate ion concentration.

The ratio of the concentration of evaporation releaseable carbon dioxide stored in calcium bicarbonate (Ca(HCO3)2) solution in the oceans to the theoretical maximum concentration of carbon dioxide in carbonic acid solution (H2CO3) in the ocean is about:
(.055 kg / m^3) / (.001115.65 kg / m^3) = 49.3 at an ocean temperature of 10 degrees C. However, generally the H2CO3 concentration in the ocean is much smaller than its theoretical maximum value due to the presence of calcium carbonate (limestone) that rapidly combines with the H2CO3 to form calcium bicarbonate solution.

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 ratio of mass of releaseable carbon dioxide in the oceans to mass of carbon dioxide in the Earth's atmosphere is:
73.68 X 10^12 tonnes / 220.89 X 10^10 tonnes = 33.35
Hence a relatively small increase in average ocean temperature that changes the dissolved bicarbonate ion concentration by only 3% will double the Earth's atmospheric CO2 concentration. Such an increase in average ocean temperature is a real near term threat to mankind.

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 rain water and sea 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:
As long as the partial pressure of CO2 in the atmosphere is much greater than the partial pressure of CO2 in the ocean 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 borne 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 and hence concentration of carbon dioxide in the atmosphere. Note that Kd is proportional to the open ocean area.

Let subscript 'a' denote a time prior to the industrial revolution when the atmospheric concentration of carbon dioxide was about 275 ppmv;
Let subscript 'b' denote the present time
Let subscript 'c' denote a future time when the average carbon dioxide concentration in the atmosphere reaches its maximum value.

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

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

MEANING OF To:
Define To by:
To = (1 / Kd)
= Ma / (Fva + Ev Kc Fs)
= Average residency time of a CO2 molecule in the Earth's atmosphere.

AT THE PRESENT:
dM / dT = Fb + Fvb + Ev Kc Fs - Kd M
F = Fb
M = Mb
or
(1 / Ma)(dM / dT) = [(Fb + Fvb + Ev Kc Fs) / Ma] - Kd (M / Ma)]
or
d(M / Ma)/ dT = [(Fb + Fvb - Fva) / Ma) + ((Fva + Ev Kc Fs) / Ma) - Kd (M / Ma)]
= [(Fb + Fvb - Fva) / Ma) + Kd - Kd (M / Ma)]
= [(Fb + Fvb - Fva) / Ma) + Kd(1 - (M / Ma))]

If (Fb + Fvb - Fva) is held constant between times Ta and Tb the solution to this differential equation is:
(Mb / Ma) = [((Fb + Fvb - Fva) / Kd Ma) + 1]
- [((Fb + Fvb - Fva) / Kd Ma) EXP [-Kd (Tb - Ta)]

The important issue with this equation is its exponential time constant To, the average CO2 molecule residency time in the Earth's atmosphere, which is given by:
To = (1 / Kd)

The corresponding half life Th of the excess carbon dioxide in the earth's atmosphere is given by:
EXP(-Th / To) = 0.5
or
Th = (-To) Ln(0.5)
= .693 To

Note that a time of about:
(Tb - Ta) = (3 X To) is required after a step change in (Fb + Fvb - Fva) for (Mb / Ma) to come within 5% of its ultimate value.

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

For the near term case of Fvb = Fva:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]

This equation for To can be numerically evaluated using published data for the period 1980 to 2010. The Ma values correspond to an atmospheric CO2 concentration of 275 ppmv. Then (M / Ma) values are easily obtained from measured atmospheric CO2 concentration data as a fuction of time for Mauna Loa. The world fossil carbon emissions as a function of time can easily be derived from World Fossil Fuel Production By Type

Since fossil fuel consumption has a substantial seasonal component and the various corporate and government fiscal years do not align with the calendar years for the Mauna Loa data it is helpful to use five year blocks of data to average out short term variations. For simplicity of analysis we have arbitrarily chosen the time intervals:
1980-1984,1985-1989,1990-1994,1995-1999,2000-2004,and 2005-2009 for fossil fuel production and 1980-1985, 1985-1990, 1990-1995, 1995-2000, 2000-2005 and 2005-2010 for CO2 concentration.

Numerical Evaluation of To:
Assume that Fvb = Fva
Recall that in 2004:
Fb = 3.391 X 10^10 tonnes CO2 / year
Ma = 220.89 X 10^10 tonnes CO2
From Mauna Loa data for 2004:
M / Ma = 377.49 / 275 = 1.37269
d(M / Ma) / dT = (379.80 - 375.77) / 2 X 275) = .00732727 / year
Hence:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [1.37269 - 1] / [.0153515 year^-1 - .00732727 year^-1]
= .37269 year / [.00802426]
=46.44 years

IN THE NEAR FUTURE:
Assume that Fb is held constant and Fvb = Fva. Then the differential equation solution gives the ultimate value of (Mc / Ma) as:
(Mc / Ma) = [(Fb / Kd Ma) + 1]
or
(Mc / Ma) = [((Fb To) / Ma) + 1]
Note that the product (Fb To) determines the ultimate atmospheric CO2 concentration. Hence To is of huge importance in terms of determining the average surface temperature on Earth. The problem is that To is increasing due to depletion of exposed metal carbonates in the ocean and due to a gradual increase in deep ocean temperature.

Numerical evaluation of (Mc / Ma) in 2004 gives:
(Mc / Ma) = [((Fb To) / Ma) + 1]
= [((3.391 X 10^10 tonnes CO2 year^-1 / 220.89 X 10^10 tonnes CO2) X 46.44 years) + 1]
= 1.7129
Thus if CO2 emissions were held at the 2004 level, and if To remained constant, the global CO2 concentration would stabilize at:
1.7129 X 275 ppmv = 471.05 ppmv.

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

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

The term (Ma /To) is given by:
(Ma / To) = (220.89 X 10^10 tonnes) /(46.44 years)
= 4.756 X 10^10 tonnes / year

If the atmospheric carbon dioxide concentration is to be stabilized at 550 ppmv:
(Mc / Ma) = 550 ppmv / 275 ppmv = 2
and
Fb = (Ma / To)
= 4.756 X 10^10 tonnes / year

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 4.756 X 10^10 tonnes CO2 per year, which is:
(4.756 X 10^10 tonnes / year) / (3.391 X 10^10 tonnes CO2 / year)
= 1.40 times the 2004 world wide fossil 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
Fb = (Ma / To)[(Mc/Ma)-1]
= 4.756 X 10^10 tonnes/ year X (1.287 - 1)
=1.36 X 10^10 tonnes / year

As a fraction of the 2004 emissions this amount is:
(1.36 X 10^10 tonnes CO2) / (3.391 X 10^10 tonnes CO2) = .401 = 40.1%

On a per capita basis the corresponding fossil CO2 emission rate is:
1.36 X 10^10 tonnes / 6.6 X 10^9 persons = 2.06 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 40.1% 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 2.06 tonnes / annum - person (12 fold).

THE PHYSICAL ORIGIN OF To:
The value of To = 46.44 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 To.
Recall that before the industrial revolution:
To = (1 / Kd)
= [Ma / (Fva + 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. Satellite 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

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:
Let Fp = fraction of the incident solar power absorbed by the oceans.
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
= .708 X 1.386 X 10^15 m^3 water / year
= .981 X 10^15 m^3 / year

FIND Fs:
Recall that:
To = Ma / (Fva + Ev Kc Fs)
Due to prior long term steady state conditions:
Fva = 0
Hence:
Fs = Ma / (To Ev Kc)
Numerical evaluation of Fs gives:
Fs = (220.89 X 10^10 tonnes CO2 / (46.44 years)(5.397 X 10^10 tonne CO2 / year)
= 0.881
Note that we expected to find that Fs would be a bit less than unity.

FIND RATE OF EMISSION OF CO2 FROM THE OCEANS 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 Fp and Fs values of:
Fp = .708
Fs = .881
Ev Kc Fs = Kc X .708 X 1.386 X 10^15 m^3 water X .881 / year
= [(.055 kg CO2 / m^3 H2O) X (1 tonne CO2 / 1000 kg CO2) X (.981 X 10^15 m^3 water/ year) X .881]
= 4.75 X 10^10 tonne CO2 / year

FIND THE RATE OF ABSORPTION OF CO2 FROM THE ATMOSPHERE BY RAIN WATER:
Rate of CO2 absorption by rain water at 15 degrees C is:
Ev X (density of water) X (rain water gms CO2 / kg H2O)
= (.981 X 10^15 tonne water / year) X (1000 kg H2O / tonne H2O)
X (2.2 g CO2 X (585.85 X 10^-6) / kg H2O) X (1 tonne CO2/ 10^6 g CO2)
= 1264.4 x 10^6 tonne CO2 / year
= 0.1264 X 10^10 tonne CO2 / year

The above calculation indicates that most of the CO2 exchange from the atmosphere to the oceans is by direct contact with the ocean surface. Rain water will only absorb a small fraction of the known fossil carbon and sea water evaporation related CO2 emissions to the atmosphere.

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 dew and low altitude condensation that occurs over the oceans.

COMMON DATA

FOSSIL CARBON RELEASE RATE:
Our modern society presently relies on energy obtained primarily from the fossil fuels coal, oil and natural gas. Coal on average is about 80% 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.

1980 DATA

WORLD COAL PRODUCTION:
During the year 1980 the total world coal production was 3796.862 million short tons. Converting this figure into metric tonnes gives:
3796.862 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 3448.557 X 10^6 tonnes coal /year
= .3448557 X 10^10 tonnes coal /year
The corresponding fossil carbon mass that entered the atmosphere in 1980 was about:
(0.8 tonne carbon / tonne coal) X (.3448557 X 10^10 tonnes coal / year)
= .2758846 X 10^10 tonnes carbon / year.

WORLD OIL PRODUCTION:
The world crude oil production in 1980 was about 59,420,560 barrels per day. The corresponding annual carbon output is:
59,420,560 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= .2555339588 X 10^10 tonne carbon / year
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unreported coal.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 1980 was about 3,446,130 barrels per day. The corresponding annual carbon output is:
3,446,130 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .01481984 X 10^10 tonne carbon / year
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unreported coal.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 1980, as obtained by summing the producers outputs was:
52,669.96 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
52,669.96 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
= 5.266996 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes / year
= 75.767 X 10^7 tonnes carbon / year
=.075767 X 10^10 tonnes carbon / year
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE RATE:
Thus the total release rate of fossil carbon obtained by summing the 1980 contributions from coal, oil, natural gas liquids and natural gas is:
(.2758846 + .2555339588 +.01481984 + .075767) X 10^10 tonnes carbon / year
= .6220053988 X 10^10 tonnes carbon / year

The corresponding rate of production of fossil carbon dioxide in 1980 was:
Fb = (44 / 12) X .6220053988 X 10^10 tonnes carbon / year
= 2.280686462 X 10^10 tonnes CO2 / year

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the two year period from 1979 to 1981 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 336.78 ppmv to 340.10 ppmv. This is an annual atmospheric carbon increase as compared to the historic value of:
(340.10 - 336.78) / (2 years X 275) = .0060363636 / year
= .60363636 % / annum

The corresponding number of tonnes of CO2 retained by the atmosphere per annum is:
.0060363636 / year X 220.89 X 10^10 tonnes CO2
= 1.333372364 X 10^10 tonnes CO2 / year

The exponential decay time constant To for 1980 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(338.68 / 275) - 1] / [(2.280686462 / 220.89) year^-1 - .0060363636 year^-1]
= [.2315636364] / [.0042886238 year^-1]
= 53.99 years in 1980
This calculated value of To is too large because the Fb input data is too low due to nonreporting of substantial amounts of combusted fossil fuels (eg unmetered natural gas that is flared).

The year 1990 is typically used as a reference year because it is believed to have more reliable data for Fb. The market for natural gas was more developed, so much less natural gas was flared than during the 1980s.

1980 to 1985 DATA

WORLD COAL PRODUCTION:
During 1980 to 1984 inclusive the total world coal production was 19,957.877 million short tons. Converting this figure into metric tonnes gives:
19,957.877 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 18,127.0545 X 10^6 tonnes
= 1.81270545 X 10^10 tonnes
The corresponding carbon mass that entered the atmosphere in 1985 to 1989 inclusive was about:
(0.8 tonne carbon / tonne coal) X (1.81270545 X 10^10 tonnes coal)
= 1.45016436 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 1980 to 1984 inclusive was 276,155,560 / 5 barrels per day. The corresponding carbon output is:
276,155,560 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.188401071 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unmetered flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 1980 to 1984 inclusive was about 18,230,260 / 5 barrels per day. The corresponding carbon output was:
18,230,260 barrels / 5 day X 365.25 days/year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .0784516542 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 1980 to 1984 inclusive, as obtained by summing the producers outputs was:
274,431.63 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
274,431.63 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
= 27.443163 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes
= 394.7784757 X 10^7 tonnes carbon
= .3947784757 X 10^10 tonnes carbon
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release rate of fossil carbon obtained by summing the 1980 to 1984 inclusive contributions from coal, oil, natural gas liquids and natural gas is:
(1.45016436 + 1.188401071 +.0784516542 + .3947784757) X 10^10 tonnes carbon
= 3.111795561 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1985 to 1989 inclusive was:
(44 / 12) X 3.111795561 X 10^10 tonnes carbon
= 11.40991706 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the 5 year period from 1980 to 1985 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 338.68 ppmv to 346.04 ppmv. This atmospheric carbon increase as compared to the historic value was:
(346.04 - 338.68) / (275) = .0267636364

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0267636364 X 220.89 X 10^10 tonnes CO2
= 5.911819636 X 10^10 tonnes CO2

The value of To for 1982 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(341.44 / 275) - 1] X 5 / [(11.40991706 / 220.89) year^-1 - .0267636364 year^-1]
= [.2416]X 5 / [.0248906579 year^-1]
= 48.53226479 years in 1982

1985 to 1990 DATA

WORLD COAL PRODUCTION:
During 1985 to 1989 inclusive the total world coal production was 23,789.606 million short tons. Converting this figure into metric tonnes gives:
23,789.606 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 21,607.27157 X 10^6 tonnes
= 2.160727157 X 10^10 tonnes
The corresponding carbon mass that entered the atmosphere in 1985 to 1989 inclusive was about:
(0.8 tonne carbon / tonne coal) X (2.160727157 X 10^10 tonnes coal)
= 1.728581726 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 1985 to 1989 inclusive was 284,705,660 / 5 barrels per day. The corresponding carbon output is:
284,705,660 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.225195362 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unmetered flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 1985 to 1989 inclusive was about 21,406,910 / 5 barrels per day. The corresponding carbon output was:
21,406,910 barrels / 5 day X 365.25 days/year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .092121972 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 1985 to 1989 inclusive, as obtained by summing the producers outputs was:
331,327.73 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
331,327.73 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
= 33.132773 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes
= 476.6252936 X 10^7 tonnes carbon
=.4766252936 X 10^10 tonnes carbon
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release rate of fossil carbon obtained by summing the 1985 to 1989 inclusive contributions from coal, oil, natural gas liquids and natural gas is:
(1.728581726 + 1.225195362 +.092121972 + .4766252936) X 10^10 tonnes carbon
= 3.522524354 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1985 to 1989 inclusive was:
(44 / 12) X 3.522524354 X 10^10 tonnes carbon
= 12.91592263 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the 5 year period from 1985 to 1990 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 346.04 ppmv to 354.35 ppmv. This atmospheric carbon increase as compared to the historic value was:
(354.35 - 346.04) / (275) = .0302181818

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0302181818 X 220.89 X 10^10 tonnes CO2
= 6.67894182 X 10^10 tonnes CO2

The value of To for 1987 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(349.16 / 275) - 1] X 5 / [(12.91592263 / 220.89) year^-1 - .0302181818 year^-1]
= [.2696772727]X 5 / [.0282540108 year^-1]
= 47.72291077 years in 1987

1990 to 1995 DATA

WORLD COAL PRODUCTION:
During 1990 to 1994 inclusive the total world coal production was 24,574.859 million short tons. Converting this figure into metric tonnes gives:
24,574.859 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 22,320.48955 X 10^6 tonnes
= 2.232048955 X 10^10 tonnes
The corresponding carbon mass that entered the atmosphere in 1990 to 1994 inclusive was about:
(0.8 tonne carbon / tonne coal) X (2.232048955 X 10^10 tonnes coal)
= 1.785639164 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 1990 to 1994 inclusive was 299,662,330 / 5 barrels per day. The corresponding carbon output is:
299,662,330 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.289559529 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 1990 to 1994 inclusive was about 24,824,040 / 5 barrels per day. The corresponding carbon output was:
24,824,040 barrels / 5 day X 365.25 days/year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .1068271655 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 1990 to 1994 inclusive, as obtained by summing the producers outputs was:
376,805.39 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
376,805.39 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
= 37.680539 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes
= 542.0463287 X 10^7 tonnes carbon
=.5420463287 X 10^10 tonnes carbon
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release rate of fossil carbon obtained by summing the 1990 to 1994 inclusive contributions from coal, oil, natural gas liquids and natural gas is:
(1.785639164 + 1.289559529 +.106271655 + .5420463287) X 10^10 tonnes carbon
= 3.723516677 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1995 to 1999 inclusive was:
(44 / 12) X 3.723516677 X 10^10 tonnes carbon
= 13.65289448 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the 5 year period from 1990 to 1995 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 354.35 ppmv to 360.80 ppmv. This is an annual atmospheric carbon increase as compared to the historic value was:
(360.80 - 354.35) / (275) = .0234545455

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0234545455 X 220.89 X 10^10 tonnes CO2
= 5.180874545 X 10^10 tonnes CO2

The value of To for 1992 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(356.38 / 275) - 1] X 5 / [(13.65289448 / 220.89) year^-1 - .0234545455 year^-1]
= [.295927]X 5 / [.038354022 year^-1]
= 38.57838856 years in 1992

1995 t0 2000 DATA

WORLD COAL PRODUCTION:
During 1995 to 1999 inclusive the total world coal production was 25,231.039 million short tons. Converting this figure into metric tonnes gives:
25,231.039 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 22,916.475 X 10^6 tonnes
= 2.2916475 X 10^10 tonnes
The corresponding carbon mass that entered the atmosphere in 1995 to 1999 inclusive was about:
(0.8 tonne carbon / tonne coal) X (2.2916475 X 10^10 tonnes coal)
= 1.833318 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 1995 to 1999 inclusive was 312,340,520 / 5 barrels per day. The corresponding carbon output is:
312,340,520 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.3431985 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 1995 to 1999 inclusive was about 29,640,680 / 5 barrels per day. The corresponding carbon output is:
29,640,680 barrels / 5 day X 365.25 days/year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .127554976 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 1995 to 1999 inclusive, as obtained by summing the producers outputs was:
404,737.67 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
404,737.67 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
= 40.473767 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes
= 582.227786 X 10^7 tonnes carbon
=.582227786 X 10^10 tonnes carbon
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release rate of fossil carbon obtained by summing the 1995 to 1999 contributions from coal, oil, natural gas liquids and natural gas is:
(1.833318 + 1.3431985 +.127554976 + .582227786) X 10^10 tonnes carbon
= 3.886299262 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1995 to 1999 inclusive was:
(44 / 12) X 3.886299262 X 10^10 tonnes carbon
= 14.249764 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the 5 year period from 1995 to 2000 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 360.80 ppmv to 369.52 ppmv. This is an annual atmospheric carbon increase as compared to the historic value was:
(369.52 - 360.80) / (275) = .03170909

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.03170909 X 220.89 X 10^10 tonnes CO2
= 7.0042211 X 10^10 tonnes CO2

The value of To for 1997 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(363.71 / 275) - 1] X 5 / [(14.249764 / 220.89) year^-1 - .03170909 year^-1]
= [.312]X 5 / [.03280159 year^-1]
= 49.17167 years in 1997

2000 to 2005 DATA

WORLD COAL PRODUCTION:
During 2000 to 2004 inclusive the total world coal production was 27,218.597 million short tons. Converting this figure into metric tonnes gives:
27,218.597 X 10^6 tons X 2000lb / ton X 1 tonne / 2202 lb
= 24,721.7048 X 10^6 tonnes
= 2.47217 X 10^10 tonnes/year
The corresponding carbon mass that entered the atmosphere in 2000 to 2004 inclusive was about:
(0.8 tonne carbon / tonne coal) X (2.47217 X 10^10 tonnes coal)
= 1.9777364 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 2000 to 2004 inclusive was 334,882,770 / 5 barrels per day. The corresponding carbon output is:
334,882,770 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.4411263 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquids production in 2000 to 2004 inclusive was 34,654,850 / 5 barrels per day. The corresponding annual carbon output is:
34,654,850 barrels / 5 day X 365.25 days/year X 5 year X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .1491328 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 2000 to 2004 inclusive, as obtained by summing the producers outputs was:
455,576.4 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
455,576.4 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
= 45.55764 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes
= 655.360888 X 10^7 tonnes carbon
=.655361 X 10^10 tonnes carbon
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release of fossil carbon obtained by summing the 2000 to 2004 inclusive contributions from coal, oil, natural gas liquids and natural gas is:
(1.9777364 + 1.4411263 +.1491328 + .655361) X 10^10 tonnes carbon
= 4.2233565 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 2000 to 2004 inclusive was:
(44 / 12) X 4.2233565 X 10^10 tonnes carbon dioxide
= 15.48564 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the five year period from 2000 to 2005 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 369.52 ppmv to 379.80 ppmv. This is a atmospheric carbon dioxide increase as compared to the historic value of:
(379.80 - 369.52) / (275) = .037381818

The corresponding number of tonnes of CO2 retained by the atmosphere is:
.037381818 X 220.89 X 10^10 tonnes CO2
= 8.2572698 X 10^10 tonnes CO2

The value of To for the year 2002 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(373.22 / 275) - 1] X 5 / [(15.48564 / 220.89) year^-1 - .037381818 year^-1]
= [.357163636] X 5 / [.0327238455 year^-1]
= 54.57238 years in 2002

2005 t0 2010 DATA

WORLD COAL PRODUCTION:
During the year 2005 to 2009 inclusive the total world coal production was 35,385.699 million short tons. Converting this figure into metric tonnes gives:
35,385.699 X 10^6 tons /year X 2000lb / ton X 1 tonne / 2202 lb
= 32,139.59946 X 10^6 tonnes
= 3.213959946 X 10^10 tonnes.
The corresponding carbon mass that entered the atmosphere in 2005 - 2009 was about:
(0.8 tonne carbon / tonne coal) X (3.21396 X 10^10 tonnes coal)
= 2.571168 X 10^10 tonnes carbon.

WORLD OIL PRODUCTION:
The world crude oil production in 2005 to 2009 inclusive was about 358,141,430 / 5 barrels per day. The corresponding carbon output is:
(358,141,430 / 5) barrels / day X 365.25 days/year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 1.541217 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to oil production is used to produce asphalt. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD NATURAL GAS LIQUID PRODUCTION:
The world natural gas liquid production in 2005 to 2009 inclusive was about 39,750,000 / 5 barrels per day?????. The corresponding carbon output is:
39,750,000 barrels / 5 day X 365.25 days / year X 5 years X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .171059 X 10^10 tonne carbon
Not all of this carbon goes into the atmosphere because part of the carbon related to natural gas liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially flared natural gas.

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 2005 to 2009 inclusive, as obtained by summing the producers outputs was:
517384.12 X 10^9 cubic feet.
The corresponding amount of carbon released to the atmosphere was:
517,384.12 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
= 51.738412 X 10^13 X 28.328 X (1 / 22.4) X (273/288) X 16 X 10^-6 X .75 tonnes / year
= 744.273 X 10^7 tonnes carbon
=.744273 X 10^10 tonnes carbon / year
Almost all of this fossil carbon enters the atmosphere.

TOTAL FOSSIL CARBON RELEASE:
Thus the total release of fossil carbon during the period 2005 to 2009 inclusive obtained by summing the contributions from coal, oil, natural gas liquids and natural gas is:
(2.57117 + 1.54122 +.17106 + .74427) X 10^10 tonnes carbon
= 5.02772 X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 2005 to 2009 inclusive was:
(44 / 12) X 5.02772 X 10^10 tonnes carbon
= 18.43497 X 10^10 tonnes CO2

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE:
During the five year period from 2005 to 2010 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 379.80 ppmv to 389.78 ppmv. This is an atmospheric carbon increase as compared to the historic value of:
(389.78 - 379.80) / (275) = .0362909

The corresponding number of tonnes of CO2 retained by the atmosphere is:
.0362909 X 220.89 X 10^10 tonnes CO2
= 8.0162989 X 10^10 tonnes CO2

The value of To is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(383.76 / 275) - 1] X 5 / [(18.43497 / 220.89) year^-1 - .0362909 year^-1]
= [1.97745454] / [.04716679 year^-1]
= 41.9247 years in 2007

YEARTo
198248.53 years
198747.72 years
199238.58 years
199749.17 years
200254.57 years
200741.92 years

TRENDS IN To:
The high values of To of 48.53 years in 1982 and 47.72 years in 1987 are consistent with flaring of unmetered natural gas that naturally occurs along with oil and for which during the 1980s there was no easily accessible market. Once this flared natural gas was metered the calculated value of To fell to 38.58 years as shown in 1992.

The increase in To from 38.58 years in 1992 to 49.17 years in 1997 and on to 54.57 years in 2002 is consistent with the ongoing depletion of the supply of exposed metal carbonates in the oceans.

The decrease in To from 54.57 years in 2002 to 41.92 years in 2007 is consistent with melting of the Arctic Ocean ice which increased the open ocean area.

Note that at this time the shortage of exposed metal carbonates is strongly suspected but is not conclusively proven strictly from measurement of To. However, this shortage of metal carbonates is starting to show in ocean pH measurements. In view of the difficulty of stopping use of fossil fuels it may already be too late to prevent a global extinction.

SEQUESTERING FOSSIL CARBON DIOXIDE:
The experimental data indicates that long term sequestration of fossil CO2 is practically impossible because over time the fossil CO2 combines with water and CaCO3 and leaks out via (HCO3)- ions diffusion through ground water. If these (HCO3)- ions get into the ocean or ground water they present an ongoing threat because they will liberate part of the CO2 if the water is warmed.

Long term sequestration of CO2 is only theoretically possible if the containment rock is a volcanic pure metal silicate such as CaSiO3. Suitable natural containment vaults in pure volcanic rock are few and far between.

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 silicate 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.

The proponents of land based CO2 sequestration have totally failed to address the issue of why natural gas (methane,CH4) naturally occurs with minimal CO2. Natural anaerobic biochemical processes that produce CH4 also produce CO2. The simple explaination is that the CO2 was originally produced but leaked out over time due do the solubility of CO2 in hard ground water.

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.

GLOSSARY OF TERMS

This web page last updated July 22, 2012.

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