GB2447513A - Atmospheric carbon dioxide removal - Google Patents

Abstract

Carbon dioxide is permanently and economically removed from the atmosphere on a huge scale by adding powdered limestone (calcium carbonate, CaCO3) or dolomite, CaMg(CO3)2) to the ocean so it reaches a depth where it can dissolve 5. Dissolved limestone returns to the surface at 7 in upwelling current 6. The dissolved limestone will increase the alkalinity of the ocean and encourages the ocean to dissolve more carbon dioxide to maintain an equilibrium. Preferably the material may be formed into a slurry with water and discharged in the ocean such that the plume drops to a depth where carbonate ion concentration is below the solubility limit for calcium carbonate. The solubility of the limestone may be enhanced by ocean fertilization.

Description

Atmospheric Carbon Dioxide Removal This invention relates to the

prevention of global warming.

Background

Because of the impact of emissions of carbon dioxide (C02) associated with burning fossil fuel on global temperatures, there is interest in technology to remove the gas from the atmosphere economically. A prize of $25 million has been offered by Sir Richard Branson for technology capable of removing one thousand million tonnes of CO2 per annum from the atmosphere for ten years. Various carbon capture technologies have been developed for large point sources (eg power stations). At great expense it might be possible to extend these to home heating applications by for example piping flue gas from (or oxygen to and carbon dioxide from) the home, alongside the gas supply line. Perhaps motor vehicles could even be fitted with liquid oxygen and carbon dioxide tanks to allow CO2 condensed from compressed exhaust gas to be stored for return to the petrol station, and ultimate underground disposal.

These options for dealing with small scale carbon dioxide emissions are likely to be very expensive and moreover could not be extended to cover aircraft emissions or gas hobs etc. and would be difficult to enforce worldwide. The scheme proposed here is not only relatively inexpensive but also easy to monitor and enforce and has the further advantage of alleviating the increase in ocean acidity which is stunting the growth of many forms of sea life, including for example coral. A further advantage of removing carbon dioxide from the atmosphere, over curtailing its emission, is that the technique can be applied retrospectively and on a very large scale.

Proposal According to the present invention, carbon dioxide is removed from the atmosphere by dumping limestone (CaCO3) and/or dolomite (CaMg(C03)2) into the ocean in a location that ensures a worthwhile proportion dissolves.

The basic chemistry is the reaction of carbon dioxide with water to form carbonic acid, followed by the reaction of carbonic acid with carbonate to form bicarbonate, which is the predominant form of carbon in the ocean.

CO2 + H20 H2C03 CaCO3 + H2C03 Ca(HCO3)2 Dolomite has a similar effect to limestone as a source of cations and carbonate ions but is more effective per tonne, because magnesium has a lower atomic weight than calcium.

Other basic compounds, such as for example magnesium oxide (MgO), will also react with carbonic acid, but limestone and dolomite are preferred because of their cost and availability.

Impact The oceans already contain two hundred thousand billion tonnes of dissolved carbonate and bicarbonate ions and even greater quantities of calcium and magnesium ions.

Dissolving I extra mole of calcium or magnesium carbonate in the ocean results in the removal of 0.78 moles of carbon dioxide from the atmosphere, as it equilibrates (refer example 2). Because water from the depths is laden with carbon dioxide from respiration and decay, the immediate effect on the atmosphere of dissolving limestone may be from reduced release of carbon dioxide when the water upwells to the surface, rather than actual absorption. As it equilibrates with the atmosphere at the prevailing local surface conditions, the ocean annually absorbs and releases fifteen times as much carbon dioxide as comes from burning fossil fuel.

Over 10% of the earth's land area is limestone, dolomite or combinations thereof There is about one hundred thousand times as much carbonate in this form as there is carbon dioxide in the atmosphere on a molar basis. There is twenty thousand times as much as there is carbon in all the fossil fuel remaining underground. Availability of limestone is never going to be an issue.

Removing a billion tonnes a year of carbon dioxide from the atmosphere for six hundred years would (other things being equal) remove half of all the carbon dioxide produced to date from burning fossil fuel, but increase the ocean carbon content by only 0.9% and the calcium content by only 0.1%.

Over the last one hundred million years the carbonate ion concentration of the ocean is thought to have increased fourfold (refer History of carbonate ion concentration over the last 100 million years by Toby Tyrrell and Richard E Zeebe published by Pergamon).

This was associated with a 30% increase in combined calcium and magnesium ion concentration and a collapse of atmospheric carbon dioxide from over 1500 ppm (parts per million by volume).

Perhaps just in time, man has reversed the trend in atmospheric carbon dioxide concentration and delayed or even prevented our return back into the ice age and widespread glaciation, which would have been many times more destructive than global warming. We should not overlook this great achievement.

Solubility Only dissolved calcium carbonate takes part in the reaction with carbon dioxide. The oceans are already supersaturated in calcium carbonate in the upper layer, but below what is called the calcite compensation depth (roughly 4.5 kilometres down) virtually all the calcium carbonate dissolves. Even at much shallower depths, very substantial additional quantities could dissolve. The surface supersaturation is caused by photosynthesis, which consumes carbon dioxide and thereby increases carbonate ion concentration at the expense of bicarbonate ions. This increases the calcium ion times carbonate ion concentration multiple way above the solubility limit, preventing additional calcium carbonate from dissolving. Fortunately it does not lead to significant precipitation from solution in the time-scale of the ocean circulation, except as skeletal material in organisms.

Magnesium carbonate solubility in the ocean may not be constrained by supersaturation, but because of the intimate collocation of calcium and magnesium in the structure of dolomite, it is likely that dissolving the magnesium carbonate portion from dolomite in water saturated with calcium carbonate would be extremely slow. Furthermore the associated calcium carbonate could be wasted.

Some of the dead organic matter from the ocean surface layer sinks to deeper levels where the soft parts decompose and put carbon dioxide back. This, together with the higher pressure, increases calcium carbonate solubility there. Substantial amounts of calcium carbonate from the skeletal remains of dead marine life also sink and dissolve every year. It has been estimated that approximately 90% of the calcium carbonate precipitated by organisms in the upper layer of the oceans dissolves in the deep ocean.

38% of the ocean floor is abyssal clay, which occurs where virtually all the sinking calcium carbonate skeletal remains have been dissolved (i.e. below the calcite compensation depth).

The quantity of limestone required to remove 1 billion tonnes of carbon dioxide spread overjust five percent of the area of abyssal clay would be only 0.16 mm deep, even if none dissolved. The current rate of sedimentation on the abyssal clay is only about 1 mm every thousand years so it is unlikely that the limestone would be covered before it had a chance to dissolve.

Economics Limestone (CaCO3) is already quarried and ground to powder in large quantities. In the UK in 2004, nine million tonnes of limestone were produced and sold for industrial and agricultural purposes at an average price of 1 7/tonne (refer Mineral Planning Factsheet issued by the Office of the Deputy Prime Minister). A further seventy-five million tonnes of limestone were used for construction and cement manufacture. Twelve million tonnes of dolomite (CaMg(CO3)2) were used in the UK mainly by the construction industry. To put these tonnages in context, UK carbon dioxide emissions are five hundred and eighty million tonnes per annum and worldwide emissions are twenty seven thousand million tonnes per year.

To remove one thousand million tonnes of carbon dioxide with a molar efficiency of 78% would require 2.9 billion tonnes of limestone. On a pro rata share with carbon dioxide emissions, the UK limestone requirement would be 63 million tonnes per annum, which would appear to be reasonably practical and unlikely to have a serious adverse visual impact, bearing in mind the current scale of the industry and its low profile.

Prior to 2003 rates for dry cargo such as grain in vessels of sixty to seventy thousand tonnes were relatively stable and typically about $1 2/te US Gulf to the EU. Refer Ocean Freight Rates -Dry Bulk Cargoes -Monday August 21, 2006 published by HGCA (Home-Grown Cereals Authority)'. More recently shipping rates have increased dramatically perhaps due to demand for raw materials in China. Hopefully in the medium term using much larger ships, rates comparable to those prior to 2003 will again prevail.

At recent exchange rates this is about 6/tonne.

If one assumes that the delivered cost to the ocean by super-tanker from coastal quarries is comparable to the current small-scale local lorry delivered cost offl7/tonne, the cost would be 51/tonne of carbon dioxide removed from the atmosphere. This is equivalent to 12p/litre of petrol, O.90p/KWH of natural gas (compared to a recent domestic gas bill at 2.64p/KWI-I) or 160/tonne of oil burned (compared to a recent crude price of229/te or $61.25/barrel).

If initially the scale of the enterprise were limited to Richard Branson's I billion tonnes/year, but the cost spread as a levy on all fossil fuel, it would be a mere 6/te of oil or 0.4p/litre of petrol.

Persistence Over time, calcium carbonate deposits out in the shallower water due to the activity of corals and other sea life. Calcium has a residence time (ocean content divided by dissolved supply from rivers) of nearly a million years, compared to about twelve million years for magnesium and over a hundred and fifty thousand years for carbonate and bicarbonate combined. This latter residence time is indicative of the sort of timescale for which the carbon dioxide removed from the atmosphere could be held in the ocean.

Figures for dissolved minerals in total river flow and for ocean composition are taken from Why is the Ocean Salty?' by Herbert Swenson, US Geological Survey Publication.

If the natural rate of sedimentation of calcium carbonate is unchanged by limestone dumping, the extra carbon dioxide will be retained permanently. But if the deep ocean dissolved carbonate ion concentration rises, a smaller proportion of the skeletal calcium carbonate raining down from the surface layer will dissolve and more will be lost as sediment.

Intuitively one might have expected that removing dissolved carbonate from the ocean as solid calcium carbonate would enable the ocean to dissolve more carbon dioxide from the atmosphere as carbonate, but in fact the reverse is true. The ionic chemistry involved is, however, well established and well known. It is its application as proposed here that is novel.

Because of the recent increase in atmospheric carbon dioxide, the rate of loss of calcium carbonate to sediment will already have been significantly reduced, or will be when the recently downwelied surface water spreads through the ocean depths.

The carbon content of the atmosphere is only 2% of that in the ocean. The key to keeping this percentage down and to keeping the added calcium carbonate in solution is to balance addition of carbon dioxide from fossil fuel emissions with addition of calcium carbonate through limestone dumping, such that the ocean carbonate ion concentration is unchanged.

Other environmental effects By adding limestone to the ocean we would only be returning it to where it had come from millions of years before. The specification would ensure that oils, toxic waste etc. were absent from the material used, but there would inevitably be some other minerals associated with the limestone. The typical specification for industrial limestone is >97% calcium carbonate. The other 3% of 2.9 billion tonnes is still nearly 90 million tonnes.

To limit the local impact on sea life, which is concentrated in the top one hundred metres or so where the light can penetrate, it would be possible to introduce the limestone as a slurry below the surface layer via a pipe. The addition method proposed below, however, would anyway mean that little if any of the injected material remained in the surface layer. This is unfortunate because the impurities could well have been beneficial in their own right.

In particular iron has been successfully tested as a fertiliser in certain ocean areas. Only tiny amounts are needed in theory to make a big difference; the total dissolved iron inventory of the oceans is only about 50 million tonnes (cf phosphate, the other limiting nutrient, at nearly 300 billion tonnes). The problem with trying to add iron is its very low solubility. The rivers already supply 30 million tonnes a year of dissolved iron. It is not the supply that is limited, hut the availability of the organic ligands, produced by living organisms, that maintain the iron in solution in the alkaline ocean water.

Ocean fertilisation and limestone addition are complementary in a very fundamental way.

The annual scale on which limestone can be dissolved in the deep ocean depends on the quantity of biomass that decays there. The long-term retention by the ocean of additional carbon captured in biomass depends on the addition of limestone. The oceans might absorb a vast quantity of extra carbon dioxide but it would be released back into the atmosphere within a few hundred years unless it was balanced with a vast quantity of extra calcium or magnesium carbonate.

Potential scale of operation There is thirteen times as much fossil fuel still in the ground as has been burnt already.

Absorbing all the carbon dioxide from burning this remaining fuel would require ocean calcium concentration to be raised by just 2%. Dissolved ocean carbon content would increase by 19% (refer example 4). The atmospheric carbon dioxide concentration would also have to be allowed to rise to balance this and avoid increased calcium carbonate loss through ocean sedimentation, but only to 420 ppm from 380 ppm today.

The multiple of calcium and carbonate ion concentration at the ocean surface, which is important for marine life skeletal growth, would increase back to 100% of pre-industrial levels compared to 78% today.

Using the same arguments and calculation methods as above the atmosphere would eventually settle out at roughly 420 ppm carbon dioxide without intervention, if nothing else changed, due to input of dissolved limestone and dolomite from the rivers. But this would take 27,000 years even if all net deposition of skeletal calcium carbonate in the ocean stopped in the meantime.

The annual capacity of the deep ocean to dissolve added limestone is limited by the annual availability of carbon dioxide from decaying biomass. Without ocean fertilisation (refer example 3) the maximum extra carbon dioxide that could be absorbed from the atmosphere using limestone addition would be about 10 billion tonne/year in the long term (ie in the few hundred years it will Lake to circulate the deep ocean). This is only 39% of current carbon dioxide emissions from burning fossil fuel. At this rate it would take 930 years to add enough limestone to balance carbon dioxide from all the fossil fuel remaining underground, as in example 4.

Because of cooling and increased salinity the surface water is drawn down (downwelling) in parts of the ocean. Elsewhere wind patterns encourage the deep waters to rise. In most areas the density gradient of the oceans inhibits such exchange.

In the short term, because the water upwelling today downwclled when atmospheric carbon dioxide concentrations were much lower, the maximum extra calcium carbonate it can dissolve is less. The estimated carbon dioxide removal is currently limited to 3.8 billion tonnes/year (refer example 2).

In essence for every mole of extra carbon dioxide created at depth by sinking decaying biomass about 0.88 extra moles of limestone can be dissolved (refer example 8), and for every extra mole of limestone dissolved an extra 0.78 moles of carbon dioxide are retained permanently. Calcium carbonate dissolving from sinking skeletal remains backs out dissolving limestone on a mole for mole basis. This biological calcium carbonate does nothing for carbon dioxide retention because it is all reabsorbed from the surface ocean into skeletons before it can impact the capacity of the downwelling polar waters to retain carbon dioxide and move it to the deep ocean.

The long term maximum carbon dioxide removal rate quoted above (10.4 billion tonnes/year) is based on a carbon rain (from soft tissue and skeletons) of 9.4 giga-tonnes per year net of sedimentation. (Refer Exploring the Dynamics of Earth Systems, a guide to constructing and experimenting with computer models of Earth systems using STELLA, Dave Bice, Dept. of Geology, Carleton College, Northfield, MN 55057. The Met Office have a very similar value, 9.8 giga-tonnes, on their website: Hadley Centre, The carbon cycle: a simple explanation) Using recent analyses of total dissolved inorganic carbon (DIC) and pre-industrial predictions, together with an assumption about where the water downwells and upwells, the ocean turnover is calculated. Using this turnover and analyses of alkalinity it is estimated that about 1.2 of the 9.4 giga-tonnes rains down as counter-productive skeletal calcium carbonate (refer example 1 and 2). Using this same turnover and current deep ocean analyses to determine the maximum dissolvable limestone dump, gives the quoted short-term carbon dioxide removal rate of 3.8 billion tonnes per year.

The downwelling water only sinks because it is denser than the icy cold water below. The deep water cannot be easily or quickly warmed up because warm, less dense, water cannot downwell. Consequently, regardless of temperatures elsewhere in the ocean surface layer, the downwelling water temperature will be constant and low. It is the solubility of carbon dioxide in this downwelling water that affects the concentration in the deep ocean. Because the surface layer that can be warmed by global warming is confined to the top few hundred metres, the reduced solubility of carbon dioxide as temperatures rise there is of relatively less significance. A 5 C rise in average ocean surface temperature might expel about as much carbon dioxide as man produces in eighteen years (refer example 9).

Effect of downwelling flow rate and fertilisation On the other hand, global warming may well reduce the flow rate of downwelling water.

Simplistically, less surface layer water can be cooled to deep ocean temperatures if the planet is warmer. In addition, for many years there will be a downward trend in surface layer salinity, over and above the seasonal swings, due to melting ice.

If there were no downwetling, and hence no corresponding upwelling, the deep ocean carbon content would rise year on year as dead organic matter sank there and decayed. As the deep ocean water returns to the surface it brings this carbon back with it. The standing carbon concentration in the deep ocean is a balance between what sinks down and what flows up. If the downwelling and hence upwelling flow rate halved and atmospheric carbon dioxide concentration were unchanged and the rain of dead organisms remained the same (see example 10), the deep ocean carbon content would eventually increase by close to 1200 giga-tonnes of carbon. This is nearly four times as much as has been released by burning fossil fuel to date.

Fertilising the ocean to double productivity everywhere would have the same long-term impact as halving the downwelling flow rate, but the equilibrium would be approached more quickly. This elevation in deep ocean carbon content, however, would account for only 30% of the fossil fuel remaining underground and would persist only while the fertilisation continued.

Other things being equal, the annual quantity of limestone that could be dissolved would increase a little in the long run as the downwelling flow reduced. This is because the effect of increased deep ocean dissolved carbon concentration on calcium carbonate solubility would more than offset the effect of the reduced ocean circulation. In the circumstances, however, what with the long-term prospect of mopping up all that extra carbon dioxide and the probability of re-dissolving some of the calcium carbonate sediment from the sea floor to add to the impact, we might not bother.

If the circulation halved, the loss of recirculated nutrient would probably reduce the harvest of organic remains sinking to the depths. If both circulation and harvest halved, there would be no long-term change in deep ocean carbon inventory, but the amount of limestone that could be dissolved each year would be halved.

Dumping locations The average deep ocean water takes hundreds of years to resurface. The dumping areas should preferably be selected just upstream of where the deep water upwells in order to feel the effect within a reasonable time.

There is a thermo-haline ocean circulation with downwelling near both poles and upwelling mainly near the Antarctic (S. Rahmstorf: Thermohaline Ocean Circulation. In: Encyclopedia of Quatemary Sciences, Edited by S. A. Elias. Elsevier, Amsterdam 2006.).

There may perhaps also be some upwelling in the Pacific and Indian Ocean. Fortunately, the calculated deep ocean turnover and the amount of limestone that can be dissolved per torme of water change with the measured concentration of dissolved carbon in opposite directions. In terms of calculating the potential maximum scale of operation, picking the location where the water upwells and the depth from which it comes are therefore less important than they could have been.

For the purpose of the calculations the oceans were assumed to downwell equally at each Pole and upwell near the Antarctic. If instead 90% of downwelling occurred near the North Pole the short-term annual maximum carbon dioxide removal using limestone would be reduced by 22%. If 90% of downwelling were near the South Pole, removal would increase by 37%. The proportion downwelling at each pole is not therefore critical to the success of the concept, refer example 11.

In the short term, assuming equal upflow from every depth, the calculated maximum annual carbon dioxide removal with all upwelling in the Antarctic is 76% of the calculated value with all upwelling in the North Pacific and 121% of the value with all upwelling in the South Pacific. The Indian Ocean is expected to be similar to the North Pacific but data on variation of alkalinity and dissolved inorganic carbon (DIC) with depth within the deep Indian Ocean were not to hand. Again the assumption on what proportion of the upwelling happens in what location is not critical to the concept of limestone addition. For all further calculations all limestone addition has been assumed to happen near the Antarctic.

Because measured DIC near the Antarctic is not a strong function of depth below about 700 metres, the calculated total upflow does not depend on the depth from which it is assumed to occur. Average calculated deep ocean residence time is 333 years.

On the other hand the calculated solubility of limestone does depend on depth. The calculated short-term maximum carbon dioxide removal rate varies significantly with the depth from which the water is assumed to upwell. But it will exceed Sir Richard Branson's billion tonne per year target so long as at least a twentieth of the upwelling water comes from each of the three lowest depths (3000 metres, 4000 metres and 5000 metres). Longer term when the water currently downwelling at the poles (with its higher carbon content) upwells, the maximum removal rate would be nearly 4 billion tonnes per year even if all the water upwelled from only l000m down. The depth at which raining soft tissue decomposes and skeletal calcium carbonate dissolves is assumed to remain the same. This estimate is based on the current variation of measured alkalinity and DIC with depth, which reflects decomposition and dissolving over the last few hundred years.

When we actually begin to dump limestone into the ocean it is anticipated that the issue of analysis and water flow and destination will be examined in more detail to decide on dumping location, dosage and depth. The addition method proposed below should allow limestone slurry added near the ocean surface to be distributed at the depth of choice.

With fine enough particles it might be possible to dissolve enough limestone at each depth to approach calcium carbonate saturation and hence the maximum carbon dioxide removal rate.

I lowever, the approach to saturation will reduce the rate at which the natural local rain of calcium carbonate can dissolve. So even if all the added limestone dissolved at the targeted depth some of the natural rain could be displaced to dissolve at lower depths or even form sediment. Hopefully the local rain will only be a small proportion of that dissolving during the journey from the downwelling zone.

In the implementation proposals below a method for taking account of the delay between dosing and upwelling (which may well vary with depth even in a single location) is suggested. This method will also allow the loss of extra calcium carbonate into sediment to be balanced with other issues affecting the timing of the benefit or cost of the addition.

Maximum limestone addition is greater at great depth but the very deep water may take much longer to reach the surface. The method allows these aspects to be compared properly.

Particle Size The limestone and/or dolomite should preferably be ground to powder to control the speed of descent, and provide a large and accessible surface area in order to make it dissolve more quickly.

A single 5 micron particle of limestone would take about twelve years to descend to the calcite compensation depth but a slurry of particles would descend in a milky cloud, like a column of cold salty water in a downwelling zone, or the plume of hot gas from a chimney. The depth to which the milky cloud descends is dominated by buoyancy effects, although the speed of the ship and the rate of discharge have some impact. Even quite tiny density gradients with depth in the ocean can counteract the weight of the limestone as the milky plume entrains more and more of the surrounding lower density water that it sinks through, refer example 6.

In this example with a one million tonne limestone tanker discharging its load over two days while travelling at 9mlsec relative to the ocean water, the milky plume reaches a depth ofjust less than 1200 metres after 45 minutes, and stays there. After 12 hours the limestone dilution is calculated to be about 37 microgram mole/kg but at this stage dilution might be controlled by external turbulence which is not modelled. Reducing ship speed to half a metre per second and discharge time to 12 hours drops the plume down to about 3200m. Because the discharge is locally much bigger in this case it is diluted more slowly and therefore contains relatively less of the less dense water from the shallower depths it has fallen through.

To reach down to say 4.5 kilometres would require a 1,300 metre extension pipe. With a uniform ocean density gradient as assumed here the depth of discharge is simply added onto the plume penetration.

These numbers were generated using a density gradient (ignoring the effect of pressure) of 0.221 kg/m3 over 5000 metres (ie about 0.02%, equivalent to a temperature change of about 30 C at temperatures around two degrees centigrade. Reducing the density gradient by a factor of 10 drops the plume depth for the first case from just less than 1 200m to about 2500m. Raising it by a factor often reduces the depth in the second case from about 3200 metres to just over 1300 metres. With no density gradient the plume reaches 5000m and a limestone dilution to about 12 microgram moles/kg after 6 hours under the first set of conditions.

The calculation method employed is a very simple one and therefore onlyapproximate, but the inference that the momentum at discharge is swamped by the accumulating momentum due to buoyancy (force equals rate of change of momentum) is sound. For this reason the inclination to the vertical of the discharge and the initial velocity are relatively unimportant. If the discharge nozzle is kept horizontal, as in the first example, but the velocity is raised from 3.1 metres/sec to 28 metres/sec, the depth at which the plume settles is about 20 metres less, because more of the less dense surface water is entrained at the higher velocity. If the nozzle is pointed directly downwards rather than horizontally but still at the very high velocity the plume deepens back by about 20 metres.

in the first example the limestone was discharged as a 10% slurry in seawater but the dilution was down to 1% eleven seconds later and after sinking only 16 metres, so the initial slurry concentration is not very important as long as it flows easily.

It should be possible to monitor the milky cloud path and dilution (J)erhaps by measuring the underwater opacity with a suitable dangled probe, perhaps even in real time) providing information that could be used to modify the depth of the extension pipe etc. This procedure would no doubt be more accurate than trying to predict the cloud behaviour from old data on the variation of salinity, temperature and turbulence with depth.

After the milky plume reaches its stable depth within a few hours, the individual particles will continue to descend relative to the water around them, but for small particles this happens over a much longer timescale.

in 1966 Peterson measured the rate at which 15mm polished optical grade calcite spheres dissolved at various depths in the ocean south of Hawaii. The results are reproduced in Oceanography 540 Pages by Russell E. McDuff arid G. Ross Heath. The alkalinity and DIC at the locations where the polished spheres were placed were not reproduced, if indeed they were measured. Assuming that dissolving rate per unit surface area is proportional to the difference between the actual bulk ocean carbonate concentration and the saturation value at that depth, Peterson's results are not a good match with the water analyses for the deep North Pacific that are used for other calculations herein. The South Pacific analyses are a closer match but still not good. The solubility driving force at 5000 metres is large and about the same for all locations, so this has been used, together with Peterson's data, to estimate the ratio of dissolving rate to driving force for all calculations.

A 5 micron sphere of polished optical grade calcite would take 1.8 years to dissolve at 5000 metres in the Antarctic Ocean (refer example 7). Natural limestone even when ground to 5 microns may have an effective surface area per unit weight that is several times greater than a spherical particle due to shape, internal pore structure arid roughness.

Limestone particles ground to I to 2 mm have been reported to have a surface to weight ratio of 0.3 to 0.5m2/grm, similar to a 5 micron sphere with no porosity (refer Arsenic Removal from Drinking Water by Limestone-based Material Davis, A; Webb, C; Dixon, D; Sorensen, J; Dawadi, S). This is 270 times what would be expected for a 1.5mm sphere. Very crude calculations suggest, however, that diffusion of dissolved carbonate from within a 1.5mm particle would be slow perhaps giving a dissolving time of nearly twenty years at 5000 metres assuming no change in bulk carbonate concentration (ie at low dosage).

The same crude diffusion calculations suggest that a 100 micron particle with 0.4m2/grm internal area would dissolve in about 2 years, which would be fine, but such particles would descend even as individuals at 400 metres per day. Ideally settling time would be the same or greater than the dissolving time so that the dissolved calcium carbonate could be distributed throughout the lower layers of the ocean.

As the scale of annual limestone addition approaches the solubility limit, the dissolving rate is reduced. At say 80% of the short-term maximum addition rate, the dissolving time for an extra 5 micron particle (with 0.4m2/grm internal area) would be over 7 years, during which time it would sink through nearly 1000 metres. A 2 micron particle would take 4 years to dissolve as it sank through just under 90 metres. A 10 micron particle would take 10 years to dissolve as it sank through 5300 metres. Although smaller particles are quicker to dissolve and easier to target at specific bodies of water, grinding cost increases.

Implementation It is envisaged that a scientific panel would identify the areas of ocean to be dosed, the dosage and the depth, ensuring that there was a large excess of acreage over that required.

The acreage would then be auctioned off routinely to the companies that entered the limestone dumping business. These companies would purchase their limestone supplies on the open market to a specification (including particle size) approved by the scientific panel. The companies would then proceed to their dumping area and discharge the cargo.

It is expected that some acreage would be free of charge but that competition for the areas closest to the cheapest limestone sources and giving the quickest benefits would ensure a premium at auction. This income would fund the scientific panel and the enforcement commission.

The enforcement commission would monitor the limestone dumpers to make sure they dumped the declared quantity of the correct material in the right place at the right depth.

It is suggested that a fuel levy would in principle be collected at both the oil well or coal mine and the refinery or power station etc. Multinational oil companies have proved very efficient at collecting both production and sales taxes with little smuggling or fraud. At each stage of the fuel's journey a certificate of levy paid would be required such that if the producer had not paid, the shipper would have to, and if neither had paid, the refiner would have to. A small surcharge for payment later down the supply chain would motivate all concerned to pay at the point of production.

The certificates would be in the form of a computer record held by the enforcement commission identifying all the elements in the supply chain for a particular batch of fuel.

Because all the intermediaries would have to balance fuel in and fuel out, it would be difficult to avoid the levy on internationally traded fuel. If the enforcement commission felt that some states were using some fuel internally without paying the levy, they could increase the levy on imported or exported fuel for that state. A similar remedy would apply for any states that chose not to support the scheme at all. In principle though, the levy would be a fixed amount per tonne of contained carbon.

The levy would not be paid with money but by placing a contract with one of the limestone dumping companies for the appropriate quantity to be dumped. It is envisaged that the enforcement commission would run a trading exchange for this purpose so that all the oil companies and limestone dumpers would need to do would be to buy and sell generic contracts.

The ratio of dissolvable limestone to carbon for the levy would be fixed by international agreement. Carbon dioxide capture contracts would also be traded on this same exchange as an alternative to limestone dumping. Perhaps dumping acreage would also be traded there. Credits (at the same fraction of the carbon content as was levied on the crude oil) could be given for high carbon fractions from the refinery that were not burnt, such as bitumen used for roads (if this could be shown to be permanently non-polluting).

In this way all fuels and all carbon dioxide removal schemes would be treated equally.

Market forces would then drive us towards the most economic combination of limestone dumping, renewable energy, nuclear power, carbon dioxide capture and energy saving, within the constraint of the agreed limestone to carbon ratio. The political messiness around the Kyoto Protocol or carbon trading (such as who owns the right to pollute in the first place) would be avoided. The only political decision to be made would be what proportion of worldwide carbon dioxide emissions from fossil fuel to recover each year, within the practical limits determined by the scientific panel.

There are easily calculated economic trade-offs between paying something now and paying more later. This allows dumps with different limestone utilisation and different delays before the dosed water upwells to be compared meaningfully. It might be preferred to get an immediate effect from limestone dumped in twenty years time than the same effect delayed for twenty years from limestone dumped now. For example, if the discount rate were 3% per year after allowing for inflation, even if due to poor utilisation 80% more limestone had to be dumped in twenty years time, that would still be marginally preferred economically. Environmentally there would be no difference.

(Effectively the money required to pay for the dump in twenty years time could be sitting in the bank earning interest for twenty years). Similarly a limestone dump added in 100 years time that then had an immediate effect would be more worthwhile than a much smaller one added now having the same effect but taking 100 years to surface, even if only 5.3% of the former dissolved but all the latter did.

Saving the planet is always going to be worthwhile whatever the cost. What constitutes a worthwhile proportion of the added limestone to dissolve depends on the alternative options for providing the same benefit at the same time. There are large areas of the ocean over the continental shelves where no extra limestone will dissolve and any addition will be lost to sediment. Dumping limestone there is outside the scope of this invention.

The limestone dumper could sell future contracts for effect with various dates to cover the dump he was about to make, or indeed dumps he had made or planned to make in the distant future. The scientific panel would determine the dates and quantity of carbon dioxide absorption expected to result from his dump.

Trading futures would not only allow options having the same effect at the same time (including carbon dioxide capture) to be valued equally but would also permit an instant start to the scheme. This would impact immediately on the demand for alternative energy and energy saving. If oil producers were allowed to fulfil their current obligations by purchasing say fifteen year dumping futures this could provide capital for the dumper's supertankers or power station carbon dioxide capture. Some input from the scientific panel would be needed to set a practically feasible delay between producing the fuel and feeling the effect of the related limestone dump.

Figure 1 is a diagram of the scheme. It is illustrative only and certainly not to scale. It shows a vertical cross section of the ocean. 1 is a coastal quarry where limestone is excavated and loaded onto ship 2. Ship 2 transports the limestone to ocean area 3 where it slurries its cargo in seawater and pumps it into the ocean. 4 is the calcite compensation depth below which no limestone remains undissolved. 5 is the zone where the dumped limestone dissolves. 6 is an upwelling ocean current that carries the dissolved calcium carbonate to the surface at area 7 where the water equilibrates with the air reducing the amount of carbon dioxide in the atmosphere.

Chemistry Model A simple spreadsheet model of the carbonate chemistry of the ocean was used.

In the model:- 1. Equilibrium atmospheric carbon dioxide concentration in ppm (parts per million by volume) is proportional to ocean surface carbonic acid concentration in microgram moles/kg.

[H2C03} = CO2 x (0.05867 -0.001668 x (Temperature C-4.85)) The values for the constants are taken from Walker, J.C.G., 1991,Numerical Adventures with Geochemical Cycles, Oxford University Press, 192 p. as reported in Exploring the Dynamics of Earth Systems a guide to constructing and experimenting with computer models of Earth systems using STELLA. Dave Bice, Dept. of Geology, Carleton College, Northfield, MN 55057. The constants are also in principle functions of salinity but salinity is not varied.

2. Carbonic acid concentration is in equilibrium with hydrogen ion concentration and bicarbonate ion concentration (all in moles/kg) such that: Log([H1]x [HCO3/[H2CO3])=6.0004-0.03279xTemp. C3 33 5/(Temp. C+273.15) This is based on a salinity of 35 and the formulae reproduced at:-www.geo.uu.nh/ResearchlGeochemistryfkb [KnowledgebooklH2CO3dissociation.pdf on the website of the Faculty of Geosciences at Utrecht University. In principle the constants will vary with pressure but no data were to hand so no sensitivity is included in the model.

3. Bicarbonate ion concentration is in equilibrium with carbonate ion and carbonic acid concentration such that: [CO] = [HCO3]x[HCO3] x (0.0005 75+0.0000060x(Temperature C-4.85)/[H2C03] The constants are from the same source as for 1 above. Again in principle they are also functions of pressure but no data were to hand.

4. The multiple of hydrogen and hydroxide ion concentrations in mole/kg is given by ln({1{'J x [01-F]) = 113.04 -13145/(Temp. C+273.15) -17.44 x ln(Temp. C+273.15) This is based on a salinity of 35 and the formulae in:-www. geo. uu.nllResearch/Geochemistry/kb/KnowledgebooklH2Odissociation.pdf.

5. Boric acid is present in the ocean as a fixed proportion of the salinity. Some of it dissociates into borate ion and hydrogen ion. At a salinity of 35 the boric acid and borate together are 410.6 microgram moles per kilogram. The extent of dissociation is defined by:- {B(OH)4] 2.864 x ici x [B(OH)3] / [I{] Concentrations are in moles/litre. The constant was taken from Advanced Aquarist's Online Magazine 2003. No temperature or pressure sensitivities were given 6. The total dissolved inorganic carbon (DIC) concentration is the sum of carbonic acid, bicarbonate ion and carbonate ion concentrations and is a measurable quantity.

7. Alkalinity is also measurable and is equal to the extra hydrogen ions needed to neutralise the negative charge on all the weakly acidic anions. These are mostly the species mentioned above. The contribution from phosphate is ignored because concentration is low. The contribution from silicates is ignored because little of the silica is ionised. The effect of including these species would have been to enhance limestone solubility at depth using the measured alkalinity.

As total negative and positive charge must always balance and the concentration of all other ionic species is assumed to be constant, alkalinity must go up by 2 microgram moles/kg whenever [Ca] or [Mg} go up by 1 microgram mole/kg. In other words the balance of carbonate, bicarbonate and carbonic acid within the constraint of the total DIC, together with the borate, hydroxide and hydrogen ion concentrations shift to match the extra positive charge.

Approximately:-Alkalinity -DIC = [COfl -[H2C03] + [B(OH)4] In the ocean, alkalinity and DIC are similar large numbers while carbonate, carbonic acid and borate are similar small numbers. This makes the key parameters (carbonate concentration for limestone solubility and carbonic acid concentration for atmospheric carbon dioxide concentration) very sensitive to changes in the other parameters.

Example I

Calcium ion concentration is fairly constant so the multiple of calcium ion and carbonate ion concentration, which determines limestone solubility, is approximately proportional to the carbonate ion concentration. The saturation carbonate ion concentrations for calcite at various depths are taken from a graph prepared by David Archer, University of Chicago, and reproduced in Oceanography 540 Pages by Russell E. McDuff and G. Ross Heath. The values are shown in table 1 below.

Table I _________________ Depth km C03 micromolefkg ________ 54 2 63 3 73 4 87 102 Table 2 below shows the model results for various conditions. All concentrations in this, and all other tables below, are in microgram moles per kg except for atmospheric carbon dioxide, which is in parts per million by volume (ppm).

The first six lines use actual data for alkalinity and DIC at various depths in the Antarctic to calculate the other parameters. The data are from Holmen, K., 1992, The Global Carbon Cycle, in, Butcher, S., Charison, R., Orians, G., and Wolfe, G., (eds.), Global Biogeochemical Cycles, London, Academic Press, p. 23 7-262 as reported in Exploring the I'--amics of Earth Systems a guide to constructing and experimenting with computer mon. of Earth systems using STELLA. Dave Bice, Dept. of Geology, Carleton College, Northfield, MN 55057. The calcium ion concentrations are based on the value of 10475 microgram moles/kg average for the ocean and a typical alkalinity of 2305 microgram moles/kg. A deep Ocean temperature of 2 C is used throughout and is also applied to downwelling water.

Table 2 _____ _____ _____ ______ _____ _____ _________ __________ Depth m Ca HC03 C03 H2C03 CO2 DIC Alkalinity Org Carbon CaCO3 0 10500 2063 91 26 410 2180 2354 1000 10500 2149 63 41 642 2253 2355 164 20 2000 10504 2152 65 40 632 2257 2362 164 23 3000 10507 2156 65 40 625 2261 2368 165 26 4000 10509 2155 67 39 611 2261 2372 163 28 5000 10509 2148 69 37 584 2254 2372 156 28 0 10500 1998 113 20 310 2131 2354 Antarctic preindustrial 0 10462 1862 133 15 230 2009 2278 Arctic preindustrial 1000 10500 2149 63 41 642 2253 2355 Max Limestone 2000 10504 2152 65 40 632 2257 2362 Max Limestone 3000 10525 2171 73 36 566 2280 2406 Max Limestone 4000 10555 2189 87 31 483 2307 2464 Max Limestone 5000 10578 2196 102 26 417 2324 2511 Max Limestone The next two lines take measured alkalinity and calculate what the downwelling water might have been like in pre-industrial times with the same alkalinity. This is the water that became the deep water in the top lines. At the modelled 2 C temperature, today's measured Antarctic surface water DIC corresponds to an equilibrium atmospheric carbon dioxide concentration of 410 ppm, which exceeds the actual atmospheric concentration; perhaps because it has mixed with water upwelling from the depths. Otherwise one might expect that water drifting in from warmer climes would be on the lean side of equilibrium with the atmosphere and would be absorbing carbon dioxide at the surface as it cools.

The Arctic downwelling water is assumed to have an alkalinity the same as in the North Atlantic and to acquire a DIC corresponding to a 50 ppm approach to equilibrium. For pre-industrial times (at 280 ppm compared to today's 380 ppm) this gives 230 ppm. The Antarctic equilibrium concentration is also assumed to be 100 ppm lower than today and a new DIC calculated accordingly.

The CaCO3 column shows the amount of calcium carbonate that needed to rain down to each depth to raise the alkalinity from that in the downwelling preindustrial water (with equal downflow at each pole) to that measured at depth today. The Org Carbon shows the amount of soft tissue that needed to rain down and decay to give the observed build up in DIC at the various depths.

In the last 5 lines limestone is dissolved at each depth in the waters from the top of the table, until they are saturated. Down to 2000 metres there is no change because no additional calcium carbonate can dissolve.

Example 2

In table 3 below, the first line shows the composition the water would have had after upwelling and crossing the ocean surface but just before downwelling again, if no limestone had been added. The input equilibrium carbon dioxide composition in ppm is the arithmetic average of the Arctic and Antarctic values from example 1, but with the ppm added back on to allow for today's higher atmospheric concentration.

Table 3 ____ _____ ____ _____ ____ _____ ___________ _______ Depth m Ca HC03 C03 H2C03 CO2 DIC years CO2 tonnes/a C02/lime.

all 10481 2009 96 23 370 2128 ______ _____________ ________ 1000 10481 2009 96 23 370 2128 325 0 0.0% 2000 10481 2009 96 23 370 2128 332 0 0.0% 3000 10499 2040 99 23 370 2162 339 2,631,358,179 77.7% 4000 10527 2084 103 23 370 2210 339 6,461,317,260 77.6% 5000 10550 2122 107 23 370 2252 327 10,105,937,018 77.5% For each depth the numbers are calculated as if all the ocean circulation upwelled from that depth. The water was followed till it downwelled again. Because the carbon and calcium carbonate rain are considered not to vary with time, the gain when the water is at depth exactly balances the loss as it flows back across the surface, for the no limestone addition case in the first row. The concentrations in the downwelling water when no limestone is added are therefore the same regardless of the depth the water was considered to be at before it upwelled.

The bottom five rows show the composition of the water with limestone dissolved in it, after upwelling and crossing the ocean surface but just before it downwells again. The upwelling water flow is calculated from the assumed carbon rain of 9.4 giga-tonnes of carbon per year, and the gain in DIC (in microgram moles per kilogram) from when the water downwclled in preindustrial times, till when it is about to upwell. The latter DIC value is based on current measurements at depth.

For this example the downwelling flow was assumed to be divided equally between the two poles. Because the DIC analyses are similar at every depth, especially in the Antarctic Ocean, the calculated flow is about the same (ie about 130 million tonnes/second) regardless of the depth it is assumed to have come from. The residence times in table 3 are calculated as if all the upflow came from the depth in question via the whole volume of all the oceans, using a value of 1.39 x 1018 tonnes for the weight of the oceans. The actual residence times can be less than this if a part of the ocean is bypassed but they cannot be more unless some of the flow is upwelling elsewhere or from a different depth. If thc flow were divided equally between all five depths and the volume of the ocean that had been swept by flow from each depth was a fifth of the total volume of all the oceans, the residence times would be the same as given in the table.

The 1000 and 2000 metre depths are the same as when no limestone was added because none could dissolve there. The carbon associated with the added limestone at each lower depth is subtracted from the gain in DIC (compared to the no limestone case). This net gain in concentration is then multiplied by the downflow of water.

These net extra moles are carried to the deep ocean. An equal extra quantity of carbon dioxide can then be generated from fossil fuel and released without increasing atmospheric concentration.

The overall total extra carbon dioxide removed from the atmosphere (and the amount of limestone that could be dissolved) depends on the fraction of deep ocean circulation upwelling from each depth. If a fifth came from each depth we would use the average of the numbers in table 3 ie 3.8 billion tonnes/year. If all the flow came from the top 2000 metres no extra carbon dioxide would be removed. The billion tonne target would be met if at least 5.2% of the flow came from each of the lower 3 depths. 1,000,000,000 = 5.2% of (2,631,358,179 + 6,461,317,260 + 10,105,937,018).

Example 3

In this example the water currently downwelling with its much higher carbon content has reached the limestone addition zone. It started at the poles with a composition like the first row in table 3 but DIC and calcium content have increased due to the rain of biomass during the water's passage across the ocean. The first 5 rows of table 4 below show the waterjust before the limestone is added. Note the lower carbonate (allowing more limestone to be dissolved) and higher DIC compared to the current Antarctic analyses in

table 2.

After being saturated with limestone at every depth the water flows up and across the ocean surface as in example 2. The ocean circulation is assumed to be the same but the quantity of carbon dioxide removed is much increased particularly for shallower depths.

Table 4 ______ _____ ____ ______ ____________ ________ _________ Depth m Ca C03 CO2 DIC B(OH)4 CO2 tonnes/a C02/lime.

Deep 1000 10500 45 950 2312 58 ____________ ________ Antarctic long 2000 10504 46 933 2316 59 ___________ _______ term just 3000 10507 47 923 2320 60 ____________ ________ before adding 4 10509 48 900 2320 61 _____________ ________ limestone 5000 10509 50 2313 63 ____________ ________ ___________ Source m _____ Downwelling 1000 10507 100 370 2176 116 3,900,492,027 77.7% water after 2000 10529 104 370 2214 117 6,889,869,477 77.6% limestone 3000 10551 107 370 2254 119 9,857,491,950 77.5% addition 4000 10579 112 370 2303 121 13,700,003,090 77.4% _________ 5000 10602 116 3702344 122 17,622,055,647 77.3% The borate ion concentration in microgram moles per kilogram is included for illustrative purposes. The annual carbon dioxide removal rate assuming equal flow at each depth

Example 4

Table 5 below shows the model results when all the fossil fuel still in the ground (containing 4000 giga-tonnes of carbon) is burnt. Sufficient limestone is added to remove most of it from the atmosphere while leaving the deep ocean carbonate ion calcium ion concentration multiple unchanged, so that there is no increase in calcium carbonate loss rate to sediment. Note the similarity between the carbonate concentrations and those shown in Table 2. As in Table 2 the Arctic equilibrium carbon dioxide concentration is ppm below atmospheric and the Antarctic 30 ppm above. The values in Table 5 therefore correspond to an atmospheric concentration ofjust 420 ppm Table 5 ________ ______ ______ ____ _____ _________ _____________________ Depth m Ca C03 CO2 DIC C02/lime.

Downwelling Arctic water 0 10665 126 370 2455 0% Downwelling Antarctic water 0 10703 114 450 2561 0% Upwelling Antarctic water 1000 10704 62 932 2692 115% Upwelling Antarctic water 2000 10707 63 918 2696 115% Upwelling Antarctic water 3000 10710 64 909 2700 115% Upwelling Antarctic water 4000 10712 66 889 2700 115% Upwelling Antarctic water 5000 10712 68 853 2693 115%

Example 5

This example looks at the results for an addition of limestone that gives the same driving force for dissolving at every depth, that is the same value for the maximum soluble carbonate concentration less the actual carbonate concentration. The carbonate concentrations before limestone addition are calculated from the current Antarctic analyses (and are as shown in table 2). The numbers after limestone addition would give rise to 80% of the maximum carbon dioxide removal, assuming equal upflow from every depth.

Table 6 _____ __________ _____ _____ Depth Ca C03 Delta C03 DIC H4 0H 1000 10500 63 -9.3 2253 0.012 0.50 2000 10504 65 -1.3 2257 0.012 0.51 3000 10515 69 4.2 2270 0.011 0.54 4000 10546 83 4.2 2298 0.010 0.64 5000 10570 97 4.2 2315 0.008 0.75

Example 6

This example considers the behaviour of a cloud of small limestone particles in the ocean.

A turbulent momentum jet emerging from a nozzle has an approximately constant angle of divergence of 20 degrees, and entrains surrounding fluid such that at any distance from the nozzle:-Total Flow = 0.32 x Initial Flow x Distance/Nozzle Diameter Equation I This formula is given in Perry's Chemical Engineering Handbook 6th Edition' on page 22. I have modified this equation slightly so that Total Flow is equal to Initial Flow at zero Distance. The entrainment rate would be expected to be some function of the velocity of the jet relative to the surrounding fluid and to be proportional to the circumferential area of the growing jet across which entrainment can take place.

Conservation of momentum must apply in the absence of other forces, such that the mass of material in the jet times its velocity is maintained for all distances. The jet is slowed down by entraining the surrounding still fluid.

Equation 1 is replicated by:-I. Consider a portion of the jet formed during a short time step. 2. The length of that portion at any downstream point velocity x time

step 3. The area for entrainment = Jet circumference x portion length 4. The rate of entrainment = 0.08 x velocity x area for entrainment 5. The next volume flow = previous flow + rate of entrainment x time step 6. The mass entrained is known because the density of the entrained fluid is known.

7. By conservation of momentum: The next velocity = previous velocity x the previous mass/the next mass 8. The next circumference is known (assuming a circular jet cross-section) because the velocity and hence portion length is known, and the volume is known.

The jet properties can thus be calculated time step by time step. The jet angle is constant with distance but with the entrainment coefficient of 0.08 (which is exactly equivalent to the 0.32 of the original formula) the jet angle comes out at 18 degrees. Presumably there is some fuzziness at the edge of the jet.

To model the milky cloud this same entrainment coefficient is used but the effect of buoyancy forces are added into the momentum conservation step. Force equals rate of change of momentum. Both horizontal and vertical momentum are calculated at each step.

The velocity used to calculate the rate of entrainment is the velocity of the cloud relative to the ocean water. The velocity used to calculate the circumferential area of the cloud is the velocity of the cloud relative to the source (or ship in this instance).

The plot below shows the plume centre line path for a 1,000,000 tonne limestone tanker discharging its load horizontally backwards as a 10% slurry in surface water through a 3metre nozzle at the surface, whilst travelling at 9 mlsec relative to the ocean water. The Ocean has a linear density gradient going from 1027.835 kg/rn3 at the surface to 1028.056 kg/rn3 at 5000 metres (ignoring the effect of pressure). The penetration depth is very clearly defined. The bouncing is probably an artefact of the oversimplified representation of the plume, in that the velocity is everywhere the same across a radial cross-section. In reality the plume would probably not have a circular cross-section but would be flattened out vertically by the density gradient thus adding to the area for entrainment.

Ocean turbulence will also add to entrainment and indeed become dominant as time passes. If one supposes that the ocean turbulence is related to entrainment through the same coefficient and some characteristic velocity, it can be added into the model. With a characteristic velocity of say 0.1 metres/sec the plume settles out just over 1000 metres down. Such a velocity would be sufficient to circumnavigate the globe in twelve years, which feels a bit strong for the deep ocean. Indeed if it were valid to extend the method to account for the penetration of temperature (by turbulence and entrainment from the ocean top layer) to say l000m down over 300 years, using the same entrainment coefficient would suggest a characteristic velocity of only 5mm/hour.

Plume Centre-line Depth 0 I F -200 -1-00 -200----300---400.---0 E-600 ____ Distance from Ship km

Example 7

This example considers the impact of particle size on settling and dissolving rate.

Settling velocities can be calculated as a function of particle diameter, particle density, ocean density and viscosity. The equations are given in Perry's Chemical Engineering Handbook 6th Edition on page 5-63'. A density of 2610 kglm3 is used for limestone based on Reade Advanced Materials 2006'. Settling velocity is a complicated function of diameter, but for Reynolds number (velocity x diameter x water density/water viscosity) less than 0.1, Stokes law applies. In our case Reynolds number falls below 0.1 for particles less than 70 microns. Settling velocity for such particles at 2 C in seawater ignoring the effect of pressure on density and viscosity is given by:-Settling velocity in metres/second = 489558 x (diameter in metres)2 One reference (see earlier) gave the internal surface area for I to 2 mm particles as 0.3 to 0.5m2/grm. A value of 0.4 m2/grrn is used for these calculations. The external area of the particles (assuming they are spherical) is added to this internal area.

Values for seawater at 2 C (but ignoring the effect of pressure on viscosity) have been substituted into a formula for diffusion given in Perry 3-286, giving:-Diffusion coefficient = 0.0000791 /(molar volume of carbonate) 6 No data on carbonate molar volume were to hand so a wild approximation was made that it has the same density as water, making it 60 cm3/grammole. Of much greater significance is the lack of data to hand on the internal porosity and the tortuosity of the pores in limestone. No doubt internal area and porosity vary anyway from quarry to quarry and probably also within each lump of rock. A bold assumption has therefore been made that the pores are straight and radial and that their cross-sectional area is 3.7% of the external area of the spherical particle. This value is simply the density difference between the value of 2610 kglm3 for limestone (see above) and the value of 271 1 kglm3 given for calcite in Perry. Aragonite, a less common form of calcium carbonate in limestone, is significantly denser.

The diffusion flux of dissolved carbonate ions in microgram moles/secondlcm2 of pore cross-section (for a guessed penetration) is then very loosely given by:- (Diffusion coefficient) x (Concentration difference ocean to saturation)/(penetration) The calcium ions must of course diffuse at the same time, but much larger concentration gradients can be sustained without affecting the solubility multiple significantly.

An internal dissolving flux through the cross-sectional area of the pores is also calculated.

This is based on the extent of internal area that is within the penetration depth (assuming it is uniformly distributed), and a dissolving rate assuming that bulk ocean carbonate concentration applies within the particle. A crude penetration depth is then found that makes the two fluxes equal.

Without internal area the rate of diameter loss for a given dissolving rate in mg/cm2/year would be constant. Abandoning any residual rigor, this is assumed also to apply when there is internal area, regardless of the reality of widening pores, reduced density within the penetration zone etc. In other words the diameter of the particle decreases as if all the material were dissolved at the surface at a rate per unit area the same as at the start.

Peterson measured a dissolving rate of 0.4 mg/cm2/year at 5000 metres depth. This is assumed to be associated with a 5000 metre ocean carbonate concentration of 66 microgram moles/kg, as calculated for the North Pacific, and a carbonate solubility limit of 102 microgram moles/kg. This gives a dissolving rate of 0.01 12 mg/cm2/year per microgram mole/kg, which is used in all calculations. Particle lives are simply calculated from the linear rate of loss of diameter that resuhs from the assumed constant particle density.

As the particle dissolves, its diameter and settling velocity decrease. For particles of less than 70 microns the settling velocity is integrated over the life of the particle to give the depth through which they settle.

Table 7 below gives the results of the calculations. Delia CO3 conc. is the difference between the carbonate ion concentration in the ocean and the saturation value in microgram moles/kilogram. The first three columns are based on Antarctic carbonate ion concentration at 5000 metres, calculated from current analyses. The last three use the concentration for 80% of maximum limestone addition as in Table 6.

Table 7 _________ _____ _________ _______ ______ ______ _____ Diameter micron 5 1500 100 5 2 10 Internal area m2/grm 0 0.4 0.4 0.4 0.4 0.4 Delta C03 cone. micromlkg 32.2 32.2 32.2 4.2 4.2 4.2 Initial sink rate rn/year 386 5.8E+06 1.5E+05 386 62 1544 Penetration micron 2.5 26.2 40.2 2.5 1.0 5.0 Internal/External area % 0% 2645% 1727% 87% 35% 174% Diameter loss micron/a 2.8 75.6 50.3 0.7 0.5 1.0 Life years 1.8 19.9 2.0 7.5 4.2 10.3 Integrated sink depth metres 234 _________ _______ 967 86 5278

Example 8

In this example the figures in example 3 were recalculated assuming that an extra 25% of soft tissue carbon rains down but no extra skeletal calcium carbonate.

Table 8 ________ _____ _____ _______ __________ _________ _____ ________ Depth m Ca C03 PlC alkalinity Carbon rain Extra Ca/Extra C Deep 1000 10527 54 2338 2408 164 _____________ Antarctic long 2000 10552 63 2364 2458 --164 _____________ term just after 3000 10577 73 2390 2509 165 _____________ adding max. 4000 10607 87 2418 2568 163 _____________ limestone 5000 10630 102 2434 2616 156 _________ ____ Asabovewith 1000 10562 54 2415 2480 205 87.2% 25% extra 2000 10588 63 2441 2531 205 87.8% softtissue 3000 10614 73 2468 2582 207 88.3% carbon rain 4000 10643 87 2495 2641 204 88.7% __________ 5000 10665 102 2508 2685 195 89.0%

Example 9

In this example the amount of carbon dioxide expelled from the upper ocean layer by a rise in temperature is calculated. The first line shows the calculated temperature needed to match the current North Atlantic surface analysis, assuming it is in equilibrium with the atmosphere at 380 ppm carbon dioxide. This temperature is then raised in two steps of 2.5 C and re-equilibrated with the atmosphere. Delta C is the resulting change in the value of dissolved inorganic carbon (DIC) in microgram moles/kg.

The warming effect of the surface appears to be largely confined to the upper 1000 metres of the oceans, as does the reduction in D1C associated with photosynthesis in the top 100 metres. It therefore seems reasonable to consider the top 500 metres as being in equilibrium with the atmosphere at the surface temperature and the next 500 metres being the same as the deep ocean, as this gives the same total DIC in the top 1000 metres as a linear profile from deep ocean to surface conditions. On this basis and applying the change to the entire ocean area (362,000,000 km2) the carbon content of the ocean is reduced by 130 giga-tonnes by a temperature increase of 5 C. This is about eighteen times current annual emissions from burning fossil fuel.

Table 9

Temp C Ca C03 CO2 DIC Alkalinity Delta C NorthAtlantic surface 18.71 10462 162 380 2000 2278 0 analysis, temperature effect 21.21 10462 179 380 1974 2278 -26 23.71 10462 199 380 1942 2278 -58

Example 10

In this example the downwelling flow is halved but the rain of carbon and calcium in dead organisms is unchanged. The midway calcium concentrations are as before (ie an average of downwelling and upwelling value, before limestone addition, as given in table 3 and 4). The loss of calcium carbonate concentration as the surface water flows from the midway point to the downwelling zones is the same as the average rain given in table 2.

On the entire journey from upwell to downwell zone the loss would be twice this value.

The DIC value for the downwell is based on the average equilibrium carbon dioxide concentration at the downwell zones as in example 2 and relates to an actual atmospheric concentration of 380 ppm. Delta DIC is the increase in midway dissolved inorganic carbon concentration compared to the original midway value (calculated from table 3 and 4) before the downflow was halved.

Table 10 Depth m Ca C03 CO2 DIC Delta DIC Downwell 0 10468 94 370 2106 -22 Midway 1000 10490 45 926 2290 69 2000 10492 45 930 2294 71 3000 10494 45 938 2298 73 4000 10495 46 926 2298 73 _____________ 5000 10495 48 883 2291 70 The change in ocean carbon inventory of 1194 giga-tonnes is calculated by multiplying the ocean mass by the average midway Delta DIC.

Example 11

In this example the proportion of water downwelling in the Arctic is varied from the 50% of example 2 to 10% and 90% with the balance downwelling in the Antarctic.

Table 11 ____ ____________ ________ 10% Arctic downwelling _____ ____ ____________ ________ depth m Ca HC03 C03 H2C03 CO2 DIC ___ _________ ______ all 10496 2052 92 26 402 2170 No limestone added ________ _______ _______ _______ _____ _______ _____ -years CO2 te/a CO2flime.

1000 10496 2052 92 26 402 2170 239 ___________ ________ 2000 10496 2052 92 26 402 2170 246 ____________ ________ 3000 10515 2083 95 26 402 2203 253 3,578,370,821 78.7% 4000 10542 2128 99 26 402 2252 253 8,787,213,643 78.6% 5000 10565 2166 103 26 402 2294 240 13,925,511,711 78.6% ______ 90 % Arctic downwelling _____ -____ _____________ _________ all 10465 1964 100 21 338 2086 Nolimestoneadded _______ ______ _______ ______ _____ ______ _____ -years CO2 te/a CO2flime.

1000 10465 1964 100 21 338 2086 412 ____________ ________ 2000 10465 1964 100 21 338 2086 419 ____________ ________ 3000 10484 1994 103 21 338 2119 426 2,065,570,041 76.6% 4000 10511 2038 108 21 338 2167 426 5,071,697,299 76.5% 5000 10535 2075 112 21 338 2209 413 7,871,283,369 76.4%

Example 12

In this example the impact of limestone addition if upwelling is not in the Antarctic is assessed, assuming all the uptiow is from the depth and location shown for the particular row. The downflow composition is as given in the middle rows of table 2 (i.e. pre-industrial). The conditions with no limestone added are based on measured DIC and alkalinity. The conditions in the bottom ten rows relate to water upwelling from the depth shown, after it has crossed the oceans and is about to downwell again. The carbon dioxide removal rate is based on a comparison with downwelling water if no limestone was added as in example 2. The residence time in years is calculated as in example 2. To the extent that the actual measured residence time of deep water at these locations is greater than the value in table 12, some of the circulation must be upwelling elsewhere.

The average carbon dioxide removal rate indicated would be somewhat greater than example 2 if upwelling occurs in the North Pacific and less if it occurs in the South Pacific. But the differences are not large enough to be critical for the concept.

Table 12 _______ ______ _____ ________ _____ _______ _____ _____________ ________ Depth m Ca C03 CO2 DIC alkalinity years CO2 te/a North 1000 10523 38 1191 2388 2400 565 No Limestone Pacific 2000 10544 50 922 2390 2443 568 Added 3000 10545 56 799 2370 2445 533 4000 10541 62 704 2343 2437 485 _______ 5000 10537 66 657 2325 2429 453 _____________ South 1000 10503 63 652 2260 2360 338 No Limestone Pacific 2000 10534 65 664 2320 2422 444 Added 3000 10534 68 627 2312 2423 430 4000 10525 69 609 2290 2404 391 _______ 5000 10520 67 622 2284 2394 380 _____________ North 1000 10532 104 370 2219 2418 565 4,297,186,655 Pacific 2000 10518 102 370 2195 2391 568 3,128,435,986 3000 10523 103 370 2204 2401 533 3,785,701,434 4000 10538 105 370 2231 2431 485 5,629,316,595 _______ 5000 10559 108 370 2268 2474 453 8,256,753,964 South 1000 10481 96 370 2128 2316 338 0 Pacific 2000 10481 96 370 2128 2316 444 0 3000 10493 98 370 2150 2340 430 1,327,683,067 4000 10522 102 370 2203 2399 391 5,065,341,499 ______ 5000 10556 108 370 2263 2467 380 9,418,490,113

Claims (13)

1. Claims 1. A process by which carbon dioxide is removed from the

   atmosphere by dumping limestone (CaCO3) and/or dolomite (CaMg(C03)2) into the ocean in a location that ensures a worthwhile proportion dissolves.
2. 2. A process as in claim I in which at least 5% of the added material is expected to dissolve.
3. 3. A process as in claim I or 2 in which the material to be added is ground to a size of 1.5mm diameter or less.
4. 4. A process as in claim I or 2 in which the material is ground to a size of 0.1mm diameter or less.
5. 5. A process as in claim br 2 in which the material is ground to a size of less than 0.0 1mm diameter.
6. 6. A process as in claim br 2 in which the material is ground to a size of 0.005mm diameter or less.
7. 7. A process as in any of the above claims in which the material is slurried in water and discharged into the ocean in such a way that the plume drops to a depth where the carbonate ion concentration is below the solubility limit for calcium carbonate.
8. 8. A process as in any of the above claims where the material is added less than twenty years upstream of a zone where the deep water upwells.
9. 9. Enhancing the solubility of limestone added according to any of the above claims by ocean fertilisation.
10. 10. Providing the expectation of an increase in marine surface calcium, magnesium or carbonate ion concentration, compared to what it would have been, by operating a process as described in any of the above claims.
11. 11. Providing the expectation of a reduction in the atmospheric carbon dioxide concentration, compared to what it would have been, by operating a process as described in any of the above claims.
12. 12. Providing the expectation of a reduction in average outdoor temperatures, compared to what they would have been, by operating a process in international waters as described in any of the above claims.
13. 13. Being engaged to perform a process as in any of the above claims.