XYLENE POWER LTD.

CARBON DIOXIDE

ATMOSPHERIC CONCENTRATION

By Charles Rhodes, P.Eng., Ph.D.

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 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 massive combustion or 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 or that will be caused by a change in average ocean temperature.

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

Carbon dioxide in the atmosphere dissolves in both rain water and open ocean water.

At present, the CO2 in solution near the ocean surface 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 solubility product for this metal bicarbonate solution is highly temperature dependent. 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)

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 (ice microcrystals, 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 the rock 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 ~ 280 ppmv, 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.

At steady state 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 and precipitation.

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 causing a transient CO2 pressure. 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 560 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 due to formation of fossil fuels and carbonate rock, is impractical.

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

It is shown that the half life of excess carbon dioxide in the atmosphere was about 10 years. Failure to act immediately to sufficiently reduce carbon dioxide emissions will have substantial adverse effects for at least the next 40 years (4 CO2 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 increased temperatures will cause melting of ice and hence a reduction in the planetarynd albedo from about 0.30 to about 0.10. The decrease in planetary albedo will lead to further heat absorption and an increase in emission temperature of about 17.5 degrees C.

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. As the average ocean temperature increases, the ocean will less readily absorb CO2 gas and the half-life of excess atmospheric CO2 will increase. Due to the rising water temperature the oceans will then become a net CO2 source rather than a net CO2 sink until a new steady state balance is established. The temperature at which this new balance occurs may be 12 degrees C to 14 degrees C higher than at present.

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 multiple major new nuclear plants as well as major transmission lines:
a) to northern Ontario to access wind power,
b) to Manitoba and Quebec to access Hydro Power and
c) 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 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 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 and an increase in the ocean-atmosphere total carbon dioxide content that will be with us causing atmospheric instability for as long as mankind inhabits the Earth.
 

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 280 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:
(280 /1,000,000) X (44 / 28.84) X .5265 X 10^19 kg
= 224.91 x 10^13 kg
= 224.91 X 10^10 tonnes
 

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 280 ppmv the mass of carbon in the atmosphere was:
.273 X 224.91 X 10^10 tonnes = 61.401 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.
When this web page was first drafted about 2004 it was believed that the rate of release of fossil carbon to the atmosphere could be calculated by summing the carbon contributions from reported coal, oil and natural gas production. However, the problem with that methodology is that the input data is consistently too low because there are several major CO2 flows to the atmosphere that are not included in the input data.
 

FOSSIL CARBON DATA PROBLEMS:
The amount of fossil carbon that that is oxidized per year is approximately equal to the amount of fossil carbon that is extracted from the earth per year. However, that amount of fossil carbon production that is reported in government statistics is the amount of fossil carbon for which the government received tax or royalty revenue. I first became aware of this major discrepency in 2015 when I compared electricity generated to the amount of coal supposedly used to generate it and came to the conclusion that in some countries coal production is hugely under reported. I came to the conclusion that as much as 60% of the fossil carbon that is extracted from the ground is being oxidized without appearing on reported government coal, oil and natural gas production statistics.

There are several major CO2 production routes that are not captured by government coal, oil and natural gas production statistics.
1. Fossil carbon that is burned on the production site as part of the extraction process. In the case of tar sand and heavy oil production this fuel is largely used to generate steam to separate oil from sand. In the case of conventional oil wells natural gas that occurs along with the oil is often flared off because the cost of recovering that gas and piping it to a market exceeds its immediate market value. In neither case is the combusted fossil carbon part of the reported fossil fuel production.

2. Petroleum as extracted from the ground before being metered goes through a basic refining process to separate the petroleum into asphalt, tar, resin feedstocks and lighter fractions to serve as feedstocks for production of liquid hydrocarbon fuels. The asphalt, tar and resin feedstock streams are usually not subject to tax or royalty and hence are not captured by coal, oil and natural gas production statistics. The asphalt and tar finds their way onto roads, driveways, sealants and shingles where they slowly oxidize adding to the atmospheric CO2. The resin feedstock finds its way into a wide variety of items such as plastics and vehicle tires that eventually wind up in municipal waste streams. These waste streams are either intentionally burned or naturally decompose over time in a shallow land fill to form methane and CO2. That methane is burned or eventually naturally oxidizes. Hence most of the carbon in the waste stream eventually becomes CO2 in the atmosphere.

3. The government statistics only capture coal, oil and natural gas that is legally sold to an arms length third party. If a single organization mines coal and burns it to make electricity the government tax revenue statistics do not capture that CO2 emission because there was no sale of coal to a third party. The same is true for integrated oil and natural gas producers who sell electricity.

4. The government statistics only capture sales, not trades. For example a coal producer may need a lot of electricity to run a coal mine. If the coal producer trades coal for electricity that coal production is not captured on government statistics.

5. Coal is not a uniform product and it is difficult to meter accurately. It can be measured either by weight or by volume (railway cars full). The problem with weight is assessing the carbon content per tonne which can easily vary by a factor of two. The problem with volume is that railway cars are not of uniform size and are not uniformly filled. Since the parties dealing with coal are aware that the government is seeking a royalty or tax they will almost always adjust coal quality or coal volume estimates to minimize payment obligations to the government. The result is massive coal consumption under reporting.

6. In places where there is either no government legislation or the government is corrupt or the legislation is not effectively enforced fossil fuels are extracted and exported but are not reported on government production statistics.
 

WORLD COAL PRODUCTION:
During the year 2019 the total world coal production, obtained by summing the productions from the major producers was;
8.13 billion tonnes
= .813 X 10^10 tonnes/year
The corresponding carbon mass that entered the atmosphere in 2019 was about:
0.8 X .813 X 10^10 tonnes / year = .6504 X 10^10 tonnes carbon / year.

The average thermal power liberated by world combustion of coal during 2019 was about:
.813 X 10^10 tonnes coal / year X 32,494 X 10^6 J / tonne coal X 1 year / 8766 hour X 1 hour / 3600 s
= 8.371 X 10^12 watts
 

WORLD OIL PRODUCTION:
The world oil production in 2019 as obtained by summing producers outputs was about 35 billion barrels / year. The corresponding annual carbon output is:
35 X 10^9 barrels /year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 0.412 X 10^10 tonne carbon / year
Not all of this carbon immediately goes into the atmosphere because a small fraction of the carbon related to oil production is used to produce asphalt, which may take as much as 50 years to oxidize into CO2.

The thermal power liberated by world combustion of oil is about:
35 billion barrels / year X (5.8 X 10^6 BTU / barrel) X 1055.06 J / BTU X 1 year / 8766 hour x 1 hour / 3600 s
= 6.786 X 10^12 watts
 

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 carbon / 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.

The thermal power liberated by world combustion of natural gas liquids in 2004 is about:
7,393,210 barrels / day X 5.8 X 10^6 BTU / barrel X 1055.06 J / BTU X 1 day / 24 hour x 1 hour / 3600 s
= 0.5236 X 10^12 watts
 

WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 2019, as obtained by summing the producers outputs was:
4100 billion m^3 / year.
The corresponding amount of carbon released to the atmosphere was:
4100 X 10^9 m^3 /year 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
= 4.1 X 10^15 lit / year X (1 mole / 22.4 lit) X (273/288) X 16 g / mole X 10^-6 tonne / gm X .75
= 2.082 X 10^9 tonnes carbon / year
=0.2082 X 10^10 tonnes carbon / year
Almost all of this carbon enters the atmosphere.

The averaqge thermal power liberated by world combustion of natural gas in 2019 was:
4100 X 10^9 m^3 / year X 1000 ft^3 / 28.328 m^3 X 1000 BTU / ft^3 X 1055.06 J / BTU X 1 year / 8766 hour X 1 hour / 3600 s
= 4.839 X 10^12 Watts
 

WORLD AVERAGE FOSSIL FUEL THERMAL POWER PRODUCTION IN 2019:
[8.371 + 6.786 + 0.5236 + 4.839] X 10^12 Wt
= 20.52 X 10^12 Wt
= 20.52 X 10^3 GWt
 

WORLD AVERAGE FOSSIL FUEL THERMAL POWER PER PERSON:
The world average fossil fuel thermal power per person in 2019 was about:
20.52 X 10^12 Wt / 7.8 X 10^9 people
= 2.63 kW / person

By comparison in Canada and the USA the average fossil fuel thermal power per person is about 9 kWt and the average electrical power per person is about 1.2 kWe. In the Province of Ontario the average thermal power per person is about 7 kWt per person but the Canadian average is higher, in large part due to energy intensive fossil fuel resource extraction in the province of Alberta.
 

WORLD NUCLEAR ENERGY PRODUCTION:
The world nuclear electric capacity in 2004 is about 372,751 MWe.
Assume an average capacity factor of about 0.9.
Then the average nuclear electric power in 2004 was about:
0.9 (372,751 MWe) = 335,476 MWe
= 375.476 GWe

Assume that the average thermal to electricity conversion efficiency is 0.33
Then the total heat emitted by nuclear reactions in 2004 was:
372,751 MWe X 0.9 X 1 MWt / 0.33 MWe
= 1,006,428 MWt
= 1006 GWt

Thus on an average thermal power basis the installed nuclear capacity is only about 5% of the installed fossil fuel capacity.
 

WORLD THERMAL POWER PRODUCTION BY COMBUSTION OF FOSSIL FUELS AND BY NUCLEAR REACTORS:
Total world thermal power production by combustion of fossil fuels and by nuclear reactors is:
20.52 X 10^12 Wt + 1.006 X 10^12 Wt
= 21.52 X 10^12 Wt

When this power is averaged over the Earth's surface area As = 509.55 X 10^12 m^2 the average impact is:
21.52 X 10^12 watts / 509.55 X 10^12 m^2
= 0.0422 watts / m^2
 

TOTAL FOSSIL CARBON RELEASE RATE:
Thus the total release rate of fossil carbon obtained by summing the 2019 contributions from coal, oil and natural gas is:
(.6504 + .412 + .03179 + .2082) X 10^10 tonnes / year = 1.302 X 10^10 tonnes /year

This amount must be increased by a factor Fx where Fx > 1 to capture all the other fossil carbon that is released but not metered.

The corresponding rate of production of fossil carbon dioxide in 2019 was:
Fb = Fx (44 / 12) X 1.302 X 10^10 tonnes / year
= 4.774 X 10^10 Fx tonnes / year

The corresponding per capita annual production of fossil carbon dioxide in 2019 for the entire world was:
(4.774 X 10^10 Fx tonnes / year) / (7.8 X 10^9 persons) = 6.12 Fx tonnes / person-year

The claimed 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 claimed Canadian per capita greenhouse gas production rate was about (3.83 / Fx) 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 / 280) X 224.91 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 560 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) / 280 ppmv) X (224.91 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 average atmospheric carbon dioxide concentration. The atmospheric carbon dioxide concentration near fossil fuelled power stations and over cities is much higher than this average.
 

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 280 ppmv. 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 both precipitation and spacecraft 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 ~ 1.0

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 microscopic ice crystals or 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 heat absorption rate which sets the ocean evaporation rate. Hence, subject to a minor correction for Fs, the natural carbon dioxide release rate due to ocean evaporation can be determined from the known ocean bicarbonate concentration, the incident solar energy flux and the latent heat of vaporization of water.

At steady state conditions the rate of emission of CO2 from the ocean equals the rate of absorption of CO2 by the ocean. The rate of absorption is proportional to the atmospheric CO2 partial pressure.

In preindustrial times the rate of emission of CO2 balanced the rate of absorption of CO2. This balance held the atmospheric carbon dioxide concentration at about 280 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 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 transient carbon dioxide concentration in the atmosphere must increase from its long term steady state value of 280 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 trap the Earth in a warm state that leads to complete melting of all land borne glaciers, including the Greenland and the Antarctic glaciers. The result would be a 70 m sea level rise. Eventually after several hundreds of thousands of years plant photosynthesis and related fossil carbon sequestration would reduce the atmospheric CO2 concentration.
 

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 during the 20th century.
 

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 plus the dissolved CO2 gas concentration.

In the absence of sunlight the rate at which the CO2 molecules flow from the ocean to the atmosphere is proportional to the CO2 gas pressure in the ocean. This issue is referred to as Charles Law.

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. Hence, the rate at which the ocean absorbs CO2 molecules from the atmosphere is proportional to the CO2 partual pressure in the atmosphere.

At steady state the fluxes of CO2 into and out of the atmosphere are in balance.
 

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:
224.91 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 / 224.91 X 10^10 tonnes = 32.76
 

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 atmospheric CO2 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:
Conservation of CO2 mass requires that the mass M of carbon dioxide in the atmosphere follow the general differential equation:
dM / dT = F + Fh + Fv + Ev Kc Fs - Kd M
where:
T = time
F = mass flow of carbon dioxide to the atmosphere from oxidation of fossil carbon
Fh = mass flow of carbon dioxide into the atmosphere due to spontaneous oxidation of naturally produced CH4 in the atmosphere
Fv = mass flow of carbon dioxide to the atmosphere from land borne volcanic action
Fl = mass flow of carbon dioxide to the atmosphere from Charles Law
Ev = ocean evaporation rate in m^3 / year
Kc = mass of carbon dioxide per m^3 of ocean water stored in calcium bicarbonate solution
Kc = Ks Ps
where:
Ks = temperature dependent solubility of CO2 in sea water Ps = steady state CO2 atmospheric partial pressure 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.
Md = mass of CO2 in atmosphere due to Charles law
Nominally:
Kd M = Fh + Fv + Fl + Ev Kc Fs

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

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

MEANING OF To:
Define To by:
To = (1 / Kd)
= Ma / (Fha + Fva +Fla + Ev Kc Fs)
= Average residency time of non-equilibrium CO2 molecules in the Earth's atmosphere.

Generally (Fh + Fv) is negligibly small giving:
To = Ma / (Fla + Ev Kc Fs)
= Ma / (Fla + Ev Ks Ps Fs)

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

Assume that:
(Fhb - Fha + Fvb - Fva + Flb - Fla) = 0

Then:
d(M / Ma)/ dT = [Fb / Ma] + Kd - [(Kd M) / Ma]

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

Prove this solution:
d(M / Ma)/ dT = [(Fb / Ma) EXP [-Kd (T - Ta)]
= Kd { [(Fb / Kd Ma) + 1] - (M / Ma)}
= (Fb / Ma) + Kd - Kd M / Ma
which proves the trial solution.

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 for (Mb / Ma) to come within 5% of its ultimate value.

Recall that:
d(M / Ma)/ dT = (Fb / Ma) + Kd - Kd M / Ma
or
Fb = dM / dT + Kd [M - Ma]
= dM / dT + [(M - Ma) / To]

This equation can be numerically evaluated.

From C-14 concentration decay data:
To = 16 years

From 2003 to 2005 the average rate of increase in the atmospheric CO2 concentration was:
(dM / dT) = 2.015 ppm / year

From 2003 to 2005 the average value of atmospheric CO2 concentration was:
M = (379.80 ppmv + 375.77 ppmv) / 2
= 377.785 ppmv

Hence:
Fb = (dM / dT) + [(M - Ma) / To]
= {2.015 ppm / year + [(377.785 ppmv - 280 ppmv) / 16 years]}{224.91 X 10^10 tonnes / 280 ppmv}
= 6.527 X 10^10 tonnes / year

By comparison the world CO2 emissions calculated from published coal, oil and natural gas production in 2004 was:
3.391 X 10^10 Fx tonnes / year

Hence:
Fx = (6.527 X 10^10 tonnes / year) / (3.391 X 10^10 tonnes / year)
= 1.925

Thus the unmetered fossil CO2 emissions to the atmosphere are almost as large as the metered fossil CO2 emissions.

The differential equation can be numerically evaluated using published data for the period 1980 to 2010. The Ma values correspond to an atmospheric CO2 concentration of 280 ppmv. Then (M / Ma) values are easily obtained from measured atmospheric CO2 concentration data as a fuction of time for Mauna Loa. The metered 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.
 

IN THE NEAR FUTURE:
Assume that Fb is held constant. 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.

Numerical evaluation of (Mc / Ma) in 2004 gives:
(Mc / Ma) = [((Fb To) / Ma) + 1]
= [((6.527 X 10^10 tonnes CO2 / year X 16 years) / 224.91 X 10^10 tonnes CO2) + 1]
= 1.464
Thus if CO2 emissions were held at the 2004 level, and if To remains constant, the global CO2 concentration would stabilize at:
1.464 X 280 ppmv = 410.01 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]

From the web page titled: CARBON DIOXIDE RETENTION TIME

The term (Ma /To) is given by:
(Ma / To) = (224.91 X 10^10 tonnes) /(15.966 years)
= 14.0868 X 10^10 tonnes / year

If the atmospheric carbon dioxide concentration is to be stabilized at 560 ppmv:
(Mc / Ma) = 560 ppmv / 280 ppmv = 2
and
Fb = (Ma / To)
= 14.0868 X 10^10 tonnes / year
It has been shown that in order to prevent the atmospheric carbon dioxide concentration measured at Mauna Loa exceeding 560 ppmv the world wide total rate of emissions of fossil carbon to the atmosphere must be kept below 14.0868 X 10^10 tonnes CO2 per year, which is:
(14.0868 X 10^10 tonnes / year) / (6.527 X 10^10 tonnes / year)
= 2.158 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 / 280 = 1.2643
and
Fb = (Ma / To)[(Mc/Ma)-1]
= 14.0868 X 10^10 tonnes / year X (1.2643 - 1)
=3.723 X 10^10 tonnes / year

As a fraction of the 2004 emissions this amount is:
(3.723 X 10^10 tonnes CO2) / (6.527 X 10^10 tonnes / year) = 0.5704 = 57%

On a world wide per capita basis the corresponding fossil CO2 emission rate is:
(6.527 X 10^10 tonnes / year) / 6.6 X 10^9 persons = 9.889 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 57% 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, China 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 Fx tonnes / person-year) = 24 (1.925) tonnes / person-year
= 46.2 tonnes / person-year
to about 9.889 tonnes / person-year
or 4.67 fold.

However, the problem with that approach is the 1990 level is still a runaway warming condition, there are numerous small nations where no fossil CO2 emission reduction is possible, and at a 4.67 fold CO2 emission reduction it would take a infinitely long time just to get to the 1990 CO2 emission level. A more realistic CO2 emission reduction for preventing thermal runaway is 10 fold.
 

THE PHYSICAL ORIGIN OF To:
From the web page titled: CARBON DIOXIDE RETENTION TIME the value of To = 15.966 years was obtained by analysis of the experimentally measured atmospheric C-14 concentration decay rate 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 / (Fla + 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 total 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
= 0.981 X 10^15 m^3 / year
 

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 = 0.981 X 10^15 m^3 / year

Ev Kc Fs = 0.981 X 10^15 m^3 water / year) X Kc Fs
= [(.981 X 10^15 m^3 water/ year)(.055 kg CO2 / m^3 H2O) X (1 tonne CO2 / 1000 kg CO2) X Fs]
= (5.3955 X 10^10 tonne CO2 / year) Fs
 

FIND MASS FLOW Fl OF CO2 INTO THE ATMOSPHERE DUE TO CHARLES LAW:
Charles Law retains a partial pressure of CO2 over the ocean even if there is no ocean evaporation. Charles Law is in effect the CO2 flux out of the ocean due to CO2 molecules randomly coming out of water solution.

Recall that:
To = Ma / (Fla + Ev Kc Fs)

Recall that:
To = 15.966 years
Ma = 224.91 X 10^10 tonnes CO2
Ev Kc = 5.3955 X 10^10 tonnes / year

However:
0 < Fs < 1.0

Hence:
0 < Ev Kc Fs < 5.3955 X 10^10 tonnes / year

Hence:
Fla = (Ma / To) - Ev Kc Fs
or
[(Ma / To) - Ev Kc] < Fla < (Ma / To)
or
[(224.91 X 10^10 tonnes CO2 / 15.966 years) - (5.3955 X 10^10 tonnes / year)] < Fla < (224.91 X 10^10 tonnes CO2 / 15.966 years)
or
8.691 X 10^10 tonnes CO2 / year < Fla < 14.066 X 10^10 tonnes CO2 / year

Note that the CO2 flux injection Fla into the atmosphere due to Charles Law is larger than the CO2 flux injection into the atmosphere due to ocean evaporation.
 

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 AS INDICATED BY GOVERNMENTAL RECORDS:
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 1980:
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 1980:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 1980:
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
 

WORLD DRY NATURAL GAS PRODUCTION 1980:
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 1980:
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

This amount must be increased by the factor Fx = 1.925 to account for unmetered fossil carbon extracted from the ground.

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

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE 1980:
During the two year period from 1979 to 1981 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 336.85 ppmv to 339.93 ppmv. This is an annual atmospheric carbon increase as compared to the historic value of:
(339.93 - 336.85) / (2 years X 280) = .0055 / year
= .55 % / annum

The corresponding number of tonnes of CO2 retained by the atmosphere per annum is:
.0055 / year X 224.91 X 10^10 tonnes CO2
= 1.237005 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]
= [(338.69 / 280) - 1] / [(2.280686462 Fx / 224.91) year^-1 - .0055 year^-1]
= [.209607143] / [.01402 year^-1]
= 14.95 years in 1980.

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 1984 DATA

WORLD COAL PRODUCTION 1980 TO 1984:
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 1980 TO 1984:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 1980 TO 1984:
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
 

WORLD DRY NATURAL GAS PRODUCTION 1980 TO 1984:
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 1980 TO 1984:
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:
Fx (1.45016436 + 1.188401071 +.0784516542 + .3947784757) X 10^10 tonnes carbon
= 3.111795561 Fx X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1980 to 1984 inclusive was:
(44 / 12) X 3.111795561 Fx X 10^10 tonnes carbon
= 11.40991706 Fx X 10^10 tonnes CO2
 

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE 1980 - 1985:
During the 5 year period from 1980 to 1985 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 338.69 ppmv to 345.90 ppmv. This atmospheric carbon increase as compared to the historic value was:
(345.90 - 338.69) / (280) = .02575

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.02575 X 224.91 X 10^10 tonnes CO2
= 5.7914325 X 10^10 tonnes CO2

The measured value of To for 1982 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(341.13 / 280) - 1] X 5 / [(11.40991706 Fx / 224.91) year^-1 - .02575 year^-1]
= [(341.13 / 280) - 1] X 5 / [(11.40991706 (1.925) / 224.91) year^-1 - .02575 year^-1]
= [1.091607143 / [.071907 year^-1]
= 15.18 years in 1982
 

1985 to 1990 DATA

WORLD COAL PRODUCTION 1985 TO 1989:
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 1985 TO 1989:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 1985 TO 1989:
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
 

WORLD DRY NATURAL GAS PRODUCTION 1985 TO 1989:
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
 

TOTAL FOSSIL CARBON RELEASE 1985 TO 1989:
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) Fx X 10^10 tonnes carbon
= 3.522524354 Fx X 10^10 tonnes carbon

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

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE 1985 - 1990:
During the 5 year period from 1985 to 1989 inclusive the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 345.90 ppmv to 354.19 ppmv. This atmospheric carbon increase as compared to the historic value was:
(354.19 - 345.90) / (280) = .0296071429

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0296071429 X 224.91 X 10^10 tonnes CO2
= 6.6589425 X 10^10 tonnes CO2

The value of To for 1987 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(348.93 / 280) - 1] X 5 / [(12.91592263 Fx / 224.91) year^-1 - .0296071429 year^-1]
= [.246178571]X 5] / [.0809399 year^-1]
= 15.207 years in 1987
 

1990 to 1995 DATA

WORLD COAL PRODUCTION 1990 TO 1994:
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 1990 TO 1994:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 1990 TO 1994:
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
 

WORLD DRY NATURAL GAS PRODUCTION 1990 TO 1994:
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
 

TOTAL FOSSIL CARBON RELEASE 1990 TO 1994:
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) Fx X 10^10 tonnes carbon
= 3.723516677 Fx X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1990 to 1994 inclusive was:
(44 / 12) X 3.723516677 Fx X 10^10 tonnes carbon
= 13.65289448 Fx 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 354.19 ppmv to 360.88 ppmv. This is an annual atmospheric carbon increase as compared to the historic value was:
(360.88 - 354.19) / (280) = .0238928571

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0238928571 X 224.91 X 10^10 tonnes CO2
= 5.3737425 X 10^10 tonnes CO2

The value of To for 1992 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(356.37 / 280) - 1] X 5 / [(13.65289448 Fx / 224.91) year^-1 - .0238928571 year^-1]
= [.27275]X 5 / [.0929648 year^-1]
= 14.669 years in 1992
 

1995 t0 2000 DATA

WORLD COAL PRODUCTION 1995 TO 1999:
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 1995 TO 1999:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 1995 TO 1999:
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
 

WORLD DRY NATURAL GAS PRODUCTION 1995 TO 1999:
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 1995 TO 1999:
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) Fx X 10^10 tonnes carbon
= 3.886299262 Fx X 10^10 tonnes carbon

The corresponding production of fossil carbon dioxide in 1995 to 1999 inclusive was:
(44 / 12) X 3.886299262 Fx X 10^10 tonnes carbon
= 14.249764 Fx 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 360.88 ppmv to 369.14 ppmv. This is an annual atmospheric carbon increase as compared to the historic value was:
(369.48 - 360.88) / (280) = .0307142857

The corresponding number of tonnes of CO2 retained by the atmosphere was:
.0307142857 X 224.91 X 10^10 tonnes CO2
= 6.690795 X 10^10 tonnes CO2

The value of To for 1997 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(363.76 / 280) - 1] X 5 / [(14.249764 Fx / 224.91) year^-1 - .0307142857 year^-1]
= [.299142857]X 5 / [.0912491 year^-1]
= 16.39 years in 1997
 

2000 to 2005 DATA

WORLD COAL PRODUCTION 2000 TO 2004:
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 2000 TO 2004:
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
 

WORLD NATURAL GAS LIQUID PRODUCTION 2000 TO 2004:
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
 

WORLD DRY NATURAL GAS PRODUCTION 2000 TO 2004:
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
 

TOTAL FOSSIL CARBON RELEASE 2000 TO 2004:
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) Fx X 10^10 tonnes carbon
= 4.2233565 Fx 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 Fx X 10^10 tonnes CO2
 

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE 2000 TO 2005:
During the five year period from 2000 to 2005 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 369.48 ppmv to 379.67 ppmv. This is a atmospheric carbon dioxide increase as compared to the historic value of:
(379.67 - 369.48) / (280) = .0363928571

The corresponding number of tonnes of CO2 retained by the atmosphere is:
.0363928571 X 224.91 X 10^10 tonnes CO2
= 8.1851175 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]
= [(373.10 / 280) - 1] X 5 / [(15.48564 Fx / 224.91) year^-1 - .0363928571 year^-1]
= [(373.10 / 280) - 1] X 5 / [(15.48564 (1.925) / 224.91) year^-1 - .0363928571 year^-1]
= [.3325] X 5 / [.0961484 year^-1]
= 17.29 years in 2002
 

2005 t0 2010 DATA

WORLD COAL PRODUCTION 2005 TO 2009:
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 2005 TO 2009:
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 2005 TO 2009:
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 2005 TO 2009:
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 2005 TO 2009:
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) Fx X 10^10 tonnes carbon
= 5.02772 Fx X 10^10 tonnes carbon

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

MEASURED ATMOSPHERIC CARBON DIOXIDE CONCENTRATION INCREASE 2005 TO 2010:
During the five year period from 2005 to 2010 the atmospheric carbon dioxide concentration measured at Mauna Loa increased from 379.80 ppmv to 389.85 ppmv. This is an atmospheric carbon increase as compared to the historic value of:
(389.85 - 379.80) / (280) = .0358928571

The corresponding number of tonnes of CO2 retained by the atmosphere is:
.0358928571 X 224.91 X 10^10 tonnes CO2
= 8.0726625 X 10^10 tonnes CO2

The value of To in 2007 is given by:
To = [(M / Ma) - 1] / [(Fb / Ma) - d(M / Ma) / dT]
= [(383.76 / 280) - 1] X 5 / [(18.43497 Fx / 224.91) year^-1 - .0358928571 year^-1]
= [(383.76 / 280) - 1] X 5 / [(18.43497 (1.925) / 224.91) year^-1 - .0358928571 year^-1]
= [1.852857143] / [.1218916668 year^-1]
= 15.20 years in 2007
 

SUMMARY TABLE:
The average residency time To of non-equilibrium CO2 molecules in Earth's atmosphere is given by:

YEAR	To
1980	14.95 years
1982	15.18 years
1987	15.21 years
1992	14.67 years
1997	16.39 years
2002	17.29 years
2007	15.20 years

This table effectively says that if there is a step increase in atmospheric CO2 concentration after about 15 years a sufficient fraction of these excess CO2 molecules will have diffused into the oceans to bring the ocean-atmosphere CO2 system to equilibrium. Viewed another way, the concentration of CO2 in the ocean lags the concentration of CO2 in the atmosphere by about 15 years.

Viewed another way, if we could today stop all production of new fossil CO2 molecules, the atmospheric CO2 concentration would decay to where it was about 15 years ago. That atmospheric-ocean CO2 concentration would then be almost fixed for thousands of years.
 

CO2 SEQUESTRATION:
also known as Carbon Capture and Storage (CCS)

The concept of CCS is to find a geology consisting of a layer of impervious top rock, usually a layer of metal silicate which covers a thick field of metal oxides such as CaO and MgO. This geology might arise from original formation of a thick metal silicate layer by volcanic action followed by millions of years of subsurface exposure of the underlying rock to water and carbon dioxide that converts the underlying rock to metal carbonates plus SiO2, followed by mild heating that drives off the CO2 leaving metal oxides behind. Then if CO2 is pressurized to about 1000 psi to make it liquid and then injected into the underlying rock, the CO2 should chemically combine with the underlying rock resulting in formation of lime stone.

CCS has become a lame excuse used by fossil fuel companies for extraction of more fossil carbon.
 

BASIC PHYSICS PREVENTS SUCCESS OF CCS:
The concept of CCS is to extract petroleum from the ground, refine it into oil, burn the oil, capture the resulting CO2, liquify that CO2 and put the liquid CO2 back in the ground at a depleted oil field. However, there is fundamental problem. The density of petroleum ia about equal to that of water which is about 1000 kg / m^3. Petroleum consists of chains of CH2. The weight of carbon contained in 1 m^3 of petroleum is about:
(12 / 14) X 1000 kg = 857 kg.

The density of liquid CO2 is about 1100 kg / m^3. CO2 consists of one carbon atom and two oxygen atoms. The weight of carbon in 1 m^3 of liquid CO2 is:
1100 kg X 12 / (12 + 2(16)) = 314 kg

Thus, even with otherwise perfect CCS, if liquid CO2 is to replace liquid petroleum only:
(314 / 857) X 100% = 36.6% of the CO2 can be so stored.

With respect to conventional oil there is usually a large bubble of overhead methane that when removed can provide additional liquidd storage volume. However, that extra liquid storage volume may not exist in a fracked oil and gas field. Thus the storage volume available for CCS is simply not sufficient to support continuing production of liquid hysrocarbons.
 

CCS IMPLEMENTATION:
CO2 sequestration involves:
Geological exploration to find a depleted oil field with sufficient liquid containment volume;
Capping of existing relevant boreholes;
Preparation of suitable injection bore holes;
CO2 purification;
CO2 pressurization to about 1000 psia = 6.8 MPa;
Pipeline transport of CO2 to contemplated injection boreholes;
Preliminary injection;
CO2 absorption test;
CO2 leakage test;
Ongoing CO2 injection

Practical implementation of CCS has been demonstrated at a small scale but CO2 containment seems to consistently fail when CCS is implemented at a large scale. This author believes that the reason for these containment failures is that any failure in the above sequence of steps results in a failure of the whole.

CO2 sequestration is inherently limited by the finite supply of suitable CO2 storage sites.

If the geology is less than ideal long term sequestration of fossil CO2 is practically impossible because over time the stored gaseous CO2 will combine with ground water and CaCO3 to become Ca(HCO3)2 which will diffuse out and become part of the ocean-atmosphere pool of CO2.

Long term sequestration of CO2 is only theoretically possible if the cap rock is formed from a volcanic pure metal silicate such as CaSiO3. Suitable natural containment vaults in pure volcanic rock are few and far between.
The rock suitability is also a function of the rock porosity. If the rock is not sufficiently porous there is insufficient contact area between the rock and the CO2 gas/liquid. If the rock is too porous pressurized CO2 tends to leak out of storage both vertically and horizontally. It is difficult to investigate porosity because every exploratory borehole becomes a source of future CO2 leakage. CO2 has been used for enhancing oil extraction, but the demonstrated CO2 containment times are decades, not millennia.
 

PROHIBITION OF CARBON DIOXIDE SEQUESTRATION:
Refer to chemistry reference relating to chemical reactions between water, CO2 and CaCO3.
The concept of sequestration of carbon dioxide sounds nice in theory but such sequestration is both unreliable and inherently dangerous. If concentrated carbon dioxide gas escapes into the atmosphere it is locally toxic. Volcanic CO2 emissions have killed many people in the past.

If the geology is favorable, carbon dioxide (CO2) injected deep underground at a low temperature will eventually react with available mineral metal oxides such as CaO or MgO or a mineral metal silicate such as CaSiO3 to form a stable carbonate compound such as limestone (CaCO3).
A rapid reaction path is:
CaO + H2O = Ca(OH)2
Ca(OH)2 + CO2 = CaCO3 + H2O

A slower reaction path is:
CO2 + H2O = H2CO3
H2CO3 + CaSiO3 = CaCO3 + H2SiO3
H2SiO3 = H2O + SiO2

The absorption of CO2 by CaO an MgO to form carbonates occurs relatively quickly, but the absorption of CO2 by silicates is very slow (microns per year). The net CO2 absorption rate is also dependent on the rock porosity. If the rock is too tight the CO2 will escape before the rock chemically absorbs it. If the rock is too porous the sequestered CO2 will leak out laterally, often via diffusion through water solution. The mere act of drilling boreholes to check on the extent of rock suitability for CO2 sequestration renders the rock unsuitable for CO2 sequestration due to long term CO2 leakage via the exploratory boreholes. These challenges make carbon dioxide sequestration unsuitable for large scale implementation.

When CO2 dissolves in water the resulting weak carbonic acid (H2CO3) will react with the metal carbonate (CaCO3) to form highly water soluble metal bicarbonate [Ca(HCO3)2].
H2CO3 + CaCO3 = Ca(HCO3)2
This water soluble bicarbonate becomes part of the ocean-atmosphere pool of CO2. The CO2 in that pool is in equilibrium with and readily rejoins the atmosphere over about a 15 year period.

The CO2 sequestration process is usually limited by the limited natural availability of MgO, CaO, Mg(OH)2 or Ca(OH)2 or by the rate of the reaction:
H2CO3 + CaSiO3 = CaCO3 + H2O + SiO2
This silicate reaction is extremely slow. The natural rate of corrosion of silicate rock (CaSiO3) by weak carbonic acid (H2CO3) is typically 1 um to 5 um per year. Objects fabricated from granite (mixed silicates) by humans exhibit little corrosion after more than 2000 years. Major limestone deposits took several hundred million years to form from silicate rock after cessation of volcanic heating. Addition of volcanic heat makes the sequestration chemical reactions run backward releasing the trapped CO2 to the atmosphere.

For example, many farmers draw ground water from wells for irrigation. If the water in these wells contains dissolved bicarbonate [Ca(HCO3)2], the contained carbon dioxide will be released to the atmosphere when the water is used for irrigation.
Ca(HCO3)2 + heat = CaCO3 + CO2 + H2O (evaporation)

In addition, in places such as depleted oil fields that might be geologically suitable for Carbon Capture and Storage (CCS) there are often many existing uncapped boreholes that will easily allow CO2 at a pressure of
1000 psi ~ 6.8 MPa
to escape.
Hence sequestration of carbon dioxide should be prohibited. If a large body of compressed CO2 starts leaking 50 years in the future, who is going to pay the remediation costs?

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 component of anaerobic decomposition either leaked out of underground deposits much faster than methane or was absorbed by formation of carbonate rock (limestone) and water soluble Ca(HCO3)2.

This observation indicates that underground CO2 sequestration is primarily a time delay mechanism rather than a permanent storage mechanism and that long term large scale permanent sequestration of CO2 under ground is virtually impossible due to diffusion of dissolved calcium bicarbonate through ground water and other compressed CO2 leakage mechanisms.
 

DETAILS OF CCS PROBLEMS:
The proponents of CO2 sequestration have totally failed to address the issue of why natural gas (methane or CH4) usually occurs with minimal CO2. Natural anaerobic biochemical processes that produce CH4 also produce a nearly equal amount of CO2. The simple explanation is that the CO2 that was originally produced has leaked out over time due to formation of water soluble Ca(HCO3)2. The Ca(HCO3)2 diffuses through ground water to surface water where, due to a lower CO2 partial pressure, the CO2 is gradually released to the atmosphere like CO2 being emitted from an uncapped soda drink.

Another major problem with CO2 sequestration is existing inadequately capped oil and gas wells. In the Province of Alberta only a small fraction of the existing oil and gas wells and related boreholes have seals sufficient for long term containment of high pressure CO2 gas. The total number of boreholes by category to be addressed is almost 500,000.

According to an article by Alex Boyd published in the Toronto Star on February 20, 2023, in Alberta and Saskatchewan there are over 10,000 orphaned wells, there are 7,400 wells that are abandoned but not fully orphaned and there are 225,000 wells that are inactive but whose future is uncertain. These numbers do not include active boreholes and boreholes for which there are no government records. The cost of cleaning up each orphaned well is about $100,000.

The issue is that for Carbon Capture and Storage (CCS) to work as intended each well must be permanently sealed against a CO2 back pressure of about 1000 psi. Any well in the CCS storage zone that leaks CO2, however slowly, will eventually make that entire CCS project nonfunctional.

The fossil fuel industry, consisting of Canadian Natural, Cenovus, Conoco Phillips, Imperial, Meg Energy and Suncor, via the website PathwaysAlliance.ca is running a propaganda campaign to promote CCS. From this author's perspective this campaign is not founded in fact and is nothing but a lame excuse for burning more fossil fuels. Due to the large number existing undocumented and poorly sealed boreholes, the probability of CCS in Alberta and Saskatchewan actually achieving large scale permanent CO2 storage is remote.

Here is a foul language video https://www.youtube.com/watch?v=MSZgoFyuHC8 from Australia that accurately summarizes some of the problems actually experienced with Australian attempts at large scale CO2 capture and storage.

An additional problem with CO2 sequestration is its ongoing threat to public safety. The CO2 sequestration process involves compressing CO2 to a pressure of over 1000 psi to make it liquid at ambient temperature. That liquid is then injected into a depleted oil field. However, that liquid will continuously exert a 68 bar internal pressure on the field's borehole caps. If a borehole cap blows off or if someone unwittingly drills a new borehole into the CO2 containment space CO2 will escape very rapidly, likely killing anyone in the vicinity of the borehole who is not wearing a self contained air supply. Compressed CO2 accidents have occurred in the past that have killed hundreds of people. At high concentrations CO2 is toxic and asphyxiates victims. The proponents of CO2 capture and storage almost never mention this danger that will persist for centuries into the future.

COMMENT BY CHARLES W FORSBERG:
May 22, 2023

If you look at most failed CCS projects, it is the separation of the CO2 at 10% concentration from the stack gas. Its low concentration CO2 at one atmosphere where need to clean up the stack gas before CO2 removal. Massive volumes of gas. Most of these are amine solution systems for CO2 removal—where need to avoid various impurities from stack gas that degrade the amines or cause other problems. This is a cyclic process where small impurities can build up in the amine solution. Sequestration is the easy part of the process.

What it says is that CCS is relatively low cost where the process chemistry yields a relatively pure CO2 stream—particularly at pressure. That implies a massive cost / technology difference between CCS with power plants versus: fermentation, conversion of natural gas to hydrogen with byproduct CO2 and removal of CO2 from natural gas production wells.
 

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 has existed underground and under the sea for many 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 submerged in water or buried deep enough that air 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. Mining and 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 air 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 from the volatile gases 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.
 

CARBON SEQUESTRATION 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 hydrocarbons are no longer viable fuels for primary power generation. Like it or not, humans will have to convert from fossil hydrocarbons to other 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 and oceans, causing a permanent increase in air conditioning load, a permanent decrease in agricultural output, a permanent increase in storm violence and a permanent increase in sea level. Fundamentally combustion of fossil hydrocarbons decreases Earth's ratio of weakly bound carbon to carbon dioxide that natural processes took over 500 million years to attain.

From a religious perspective humans are rapidly destroying the Garden of Eden.

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This web page last updated November 13, 2023.