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GLOSSARY OF TERMS
FOSSIL CARBON EMISSIONS IN CANADA:
It is widely recognized that the largest sources of fossil carbon dioxide emissions to the atmosphere in Canada are vehicles, coal fueled electricity generators and natural gas fueled tar sands extraction plants. However, there are also substantial fossil carbon dioxide emissions to the atmosphere from processing of metal ores, from space and water heating systems, from concrete production and from long term degradation of asphalt, plastic resins and synthetic rubber.
FOSSIL CARBON TAX:
The concept of a fossil carbon tax is to impose a surcharge on fossil carbon extracted from the ground to discourage its use. The revenue from this surcharge should be applied to replacement of existing fossil carbon dependent systems with new systems that use biocarbon or that otherwise avoid use of fossil carbon.
A fossil carbon tax should be applied at the point where the carbon is removed from the ground. Otherwise there are many ways to avoid the tax. For example, there are processes that use CO2 emissions from coal fueled electricity generators to produce liquid hydrocarbons. These processes reduce dependence on foreign oil but do not prevent carbon emissions to the atmosphere because somewhere downstream from the process the liquid hydrocarbons that are produced eventually convert to CO2.
The logic of a fossil carbon tax in the electricity sector is to increase the cost of electricity generated by combustion of fossil fuels to the point where the same amount of electricity can be obtained less expensively from non-fossil fuel sources. Then natural economic forces will cause fossil fuel electricity generation to be replaced by cost effective non-fossil fuel electricity generation.
COST OF ENERGY FROM NON-FOSSIL FUEL ELECTRICITY GENERATION:
At the present time fossil fuelled electricity generators provide controllable power for load following. Hydraulic electricity generators with storage dams provide comparable flexibility, but the usefulness of hydraulic generators is gradually being compromised by global warming, which reduces the average river flow in the late summer when electricity is most needed.
In principle a coal fuelled electricity generator could be directly replaced by a nuclear electricity generator with the same peak power output capacity. However, in terms of both thermal efficiency and equipment working life it is better to base load nuclear generators and to use energy storage for load following.
In areas with consistently high wind speed, wind turbines in combination with energy storage can economically compete with nuclear generators. Wind generators provide unconstrained power at a direct cost of about $.14 / kWe-h. However, the wind generator power output as a function of time does not match the loads' power requirement as a function of time. It is necessary to introduce a combination of energy storage, generation constraint and load control in order to match the electricity production rate to the electricity consumption rate. The cost of these additional measures increases the average cost of non-fossil fuel electricity to about $0.29 / kWe-h. The cost of transmission/distribution is additional.
PROPOSED FOSSIL CARBON TAX:
The analysis set out herein shows that a fossil carbon tax of about $200 per emitted CO2 tonne ($55.55 / carbon tonne) is required to cause the cost of coal fueled electricity generation to exceed the cost of non-fossil fuel electricity generation. A lesser fossil carbon tax simply will not achieve the desired result.
IMPACT OF A FOSSIL CARBON TAX ON COMBUSTION OF COAL:
In Canada, as elsewhere in the world, a lot of electricity is produced by combustion of coal. Coal is extremely cheap. Coal is dug out of the ground from an open pit mine using a large backhoe, dumped onto an earth mover, dumped into a railway car, dumped onto a storage pile and then carried by conveyor into a boiler. The labor content is very small. The cost is primarily amortization of the mechanical equipment. The IESO website indicates that, with government guaranteed debt financing, the average cost of electricity generated from combustion of coal is about:
$.048 / kWe-h.
Consider the additional cost of generating electricity from coal if coal is subject to a fossil carbon tax of $200 / tonne CO2. The thermal energy from coal comes from combustion of carbon. The thermal energy released by combustion of carbon to form carbon dioxide gas at 25 degrees C is 94.26 kcal / mole CO2 (National Bureau of Standards Circ. 500 (1950)). Converting this figure into more convenient units gives:
(94.26 kcal / mole) X (4180 J / kcal) X (1 mole / .044 kg CO2) = 8.9547 X 10^6 J / kg CO2
Using conventional equipment this heat can be converted into electricity with a conversion efficiency of about 33%, so the resulting electricity output is:
8.9547 X 10^6 J / kg CO2 X (.33 We-s / J) X 1 kWe / 1000 We X 1 h / 3600 s
= .8208 kWe-h / kg CO2
The effect of a $200 / CO2 tonne carbon tax is to increase the cost of electricity obtained by combustion of coal by about:
($200 / 1000 kg CO2) / (.8208 kWe-h / kg CO2) = $.244 / kWe-h.
The IESO advises that in 2007 about 18% of the Ontario provincial electricity produced came from coal. Hence the effect of a $200 / tonne CO2 fossil carbon emissions tax on coal combustion is to increase the average Hourly Ontario Electricity Price (HOEP) by:
.18 X $.244 / kWe-h = $.044 / kWe-h.
Similarly, data published by the IESO indicates that the effect of a $200 / tonne CO2 fossil carbon tax on oil and natural gas combustion is to increase the average HOEP by about:
,08 X $.12 / kWe-h = $.0096 / kWe-h
Hence the total effect of a $200 / tonne CO2 fossil carbon tax is to increase the HOEP by about:
$.044 / kWe-h + $.0096 / kWe-h = $.054 / kWe-h
With a fossil carbon tax of $200 / CO2 tonne the projected cost of energy obtained from combustion of coal is about:
$.048 / kWe-h + $.244 / kWe-h = $.292 / kWe-h
plus transmission/distribution cost.
Note that the proposed fossil carbon tax of $200 / CO2 tonne is still not quite enough to make coal fuelled electricity generation more expensive than non-fossil fuel electricity generation. However, it is anticipated that as coal fuelled generation diminishes its economies of scale will diminish causing the cost of energy from coal to increase.
The time frame necessary to effect a conversion from coal to new nuclear is thought to be about ten years. This author strongly recommends that for electricity generation Ontario goes immediately to a fossil carbon tax of $200 / CO2 tonne in order to rapidly repay the existing electricity stranded debt principal, thus enabling Ontario government guarantees of financing for at least part of the Ontario Power Authority's Integrated Power System Plan (OPA IPSP). The fossil carbon tax on the transportation and heating sectors should be brought in more slowly because application of a fossil carbon tax to those sectors will cause an increase in electricity load, requiring additional generation and transmission capacity that presently does not exist.
OTHER COST CONSEQUENCES OF A FOSSIL CARBON TAX:
The following sections consider the effect of a $200 / emitted CO2 tonne fossil carbon tax on gasoline fuelled transportation, fuel oil heating, natural gas heating and plug-in hybrid vehicles. It is assumed that all fossil carbon used will be taxed at the same rate per unit mass of fossil carbon consumed. The dominant resulting greenhouse gas is carbon dioxide.
COST OF GASOLINE AND FUEL OIL WITHOUT FOSSIL CARBON TAX:
It is assumed herein that the retail price of liquid hydrocarbons without fossil carbon or sales tax is about $1.00 / lit. In early 2011 this assumption was very close to reality. This assumption allows the result to be easily corrected using the actual retail price of liquid hydrocarbon fuels.
COST OF HEAT FROM FUEL OIL:
Assume that the thermal energy content of number 2 fuel oil is 38.2 MJ / L. Assume that for heat production the fuel oil is burned at 85% efficiency. Then the cost for heat obtained by combustion of fuel oil without fossil carbon tax is:
(1 L fuel oil / (38.2 MJ X .85)) X (1 MJ / 10^6 J) X ($1.00 / L) X (1J / Wt-s) X (1000 Wt / kWt) X (3600 s / h)
= $.111 / kWt-h + GST
COST OF ENERGY FROM GASOLINE:
It is assumed herein that the mass density of gasoline is .73722 kg / L. This density actually varies slightly for different gasoline blends.
It is assumed herein that the thermal energy content of gasoline is 45 MJ / kg. This thermal energy content actually varies depending on the fuel blend.
Assume that 30% of the chemical energy in gasoline converts to mechanical energy. Then the cost of energy obtained by combustion of gasoline without fossil carbon emissions tax is given by:
(1 kg gasoline / (45 MJ X .30)) X (1 MJ / 10^6 J) X (1 L / .73722 kg gasoline) X ($1.00 / L) X (1J / We-s) X (1000 We / kWe) X (3600 s / h)
= $.362 / kWe-h
IMPACT OF FOSSIL CARBON TAX ON GASOLINE AND FUEL OIL:
It is further assumed herein that to a good approximation gasoline and fuel oil consist of hydrocarbon chain molecules configured such that on average for every carbon atom there are 2 hydrogen atoms. The atomic weight of carbon is taken as 12 and the atomic weight of hydrogen is taken as 1. Hence the carbon content of gasoline or fuel oil is about:
.73722 kg / L X (12 / 14) = .632 kg C / L
The atomic weight of oxygen is about 16, so the molecular weight of carbon dioxide is about:
(12 + 2(16)) = 44.
Hence the mass of carbon dioxide produced by burning a litre of gasoline or fuel oil is about:
(44 / 12) X .632 kg C / L = 2.317 kg CO2 / L
Hence a tax of $200 / emitted CO2 tonne corresponds to a tax on gasoline or fuel oil of:
(2.317 kg CO2 / L) X ($200 / tonne CO2) X (1 tonne CO2/ 1000 kg CO2) = $.464 / L.
Consider the impact of a fossil carbon tax of $200 / tonne CO2 on the cost of heat obtained by burning fuel oil. Assume that the thermal energy content of the fuel oil is 38.2 MJ / L. Assume that for heat production the fuel can be burned at 85% efficiency. Then the extra cost for heat obtained from combustion of fuel oil caused by a fossil carbon tax of $200 / emitted CO2 tonne is given by:
(1 L fuel oil / (38.2 MJ X .85)) X (1 MJ / 10^6 J) X (2.317 kg CO2 / L fuel oil) X ($200 / tonne CO2) X (1 tonne / 1000 kg) X (1 J / Wt-s) X (1000 Wt / kWt) X (3600 s / h)
= $.0512 / kWt-h
Thus with a $200 / tonne fossil carbon tax the cost of heat from fuel oil is:
$.111 / kWt-h + $.0512 / kWt-h = $.1622 / kWt-h + GST
Consider the impact of a fossil carbon tax of $200 / CO2 tonne on the cost of energy obtained from gasoline. Assume that the thermal energy content of the gasoline is 45 MJ / kg. Assume that for energy production the gasoline can be burned at 30% efficiency. Then the extra cost of energy obtained from combustion of gasoline caused by a fossil carbon tax of $200 / CO2 tonne is given by:
(1 kg gasoline / (45 MJ X .30)) X (1 L gasoline / .73722 kg gasoline) X (1 MJ / 10^6 J) X (2.317 kg CO2 / L gasoline) X ($200 / tonne CO2) X (1 tonne / 1000 kg) X (1J / We-s) X (1000 We / kWe) X (3600 s / h)
= $.1676 / kWe-h
Thus with a $200 / CO2 tonne fossil carbon tax the cost of energy from gasoline is:
$.362 / kWe-h + $.1676 / kWe-h = $.5296 / kWe-h
PLUG-IN HYBRID VEHICLES:
These figures are very important in the economics of plug-in hybrid vehicles. In order for plug-in hybrid vehicles to make economic sense the cost of electricity from non-fossil fuel sources must be much less than the cost of a kWe-h of mechanical energy derived from liquid fossil fuels. Since the combined energy storage and recovery efficiency of a battery-inverter system is only about 75%, it is essential that the vehicle owner be able to purchase electricity for battery charging at an average price, including transmission and distribution, that is much less than:
.75 X $.5296 / kWe = $.3972 / kWe
However, it was shown herein that the average cost of new non-fossil fuel energy is about $.29 / kWe-h plus transmission and distribution costs. Hence, for hybrid vehicles to make economic sense the vehicle batteries must usually be charged with less expensive off-peak electricity.
IMPACT ON COST OF HEAT FROM NATURAL GAS:
Natural gas is primarily methane (CH4). The practical recoverable heat from combustion of natural gas is about:
10.4 kWt-h / m^3 NG X .85 = 8.84 kWt-h / m^3 NG.
The retail price of natural gas in Ontario is typically about $.43 / m^3. Hence the cost of heat from natural gas without fossil carbon tax is about:
($.43 / m^3) X (1 m^3 / 8.84 kWt-h) = $.0486 / kWt-h
The mass density of natural gas is about:
(1 mole / 22.4 L NG) X (273.15 K / 288.15 K) X (16 X 10^-3 kg / mole) X (1000 L NG/ m^3 NG)
= .677 kg / m^3 NG
The carbon content of natural gas is about:
(12 / 16) X .677 kg / m^3 NG = .50775 kg C / m^3 NG
and the corresponding CO2 production is:
(44 / 12) X .50775 kg / m^3 NG = 1.8617 kg CO2 / m^3 NG
Thus the effect of a fossil carbon tax of $200 /CO2 tonne is to increase the cost of natural gas by about:
(1.8617 kg CO2 / m^3 NG) X ($200 / 1000 kg CO2 = $.372 / m^3 NG + GST
In terms of cost per unit of recoverable heat output, the corresponding cost increase is:
($.372 / m^3 NG) / (8.84 kWt-h / m^3) = $.04212 / kWt-h
Hence, with a fossil carbon tax of $200 /CO2 tonne the cost of heat from natural gas becomes:
$.0486 / kWt-h + $.04212 = $.09072 / kWt-h + GST
This amount which includes a fossil carbon tax of $200 / CO2 tonne is still less than the amount that rural Ontario residents are presently paying for oil heating with no fossil carbon tax.
In order to meet the long term CO2 reduction targets it is necessary that the average cost of heat derived from electricity be below the average cost of heat from natural gas. To meet this objective, with an electric heat pump having an average COP of 4.0, the average retail price of electricity, including transmission/distribution costs, must be constrained to less than:
(4 kWt / kWe) X $.09072 / kWth = $.389 / kWe-h
Hence, even with a $200 / CO2 tonne fossil carbon tax, the cost of natural gas will have to increase substantially before large scale conversion from natural gas to electric ground source heat pumps will occur.
A fossil carbon tax of about $200 / emitted tonne CO2 is required to close coal fuelled electricity generation and to substantially reduce CO2 emissions in the transportation and oil heating sectors. Even with this fossil carbon tax, large scale natural gas to electric heat pump conversions will not occur until the cost of natural gas increases. In the near term a $200 / CO2 tonne fossil carbon tax on electricity generation could be implemented by the Ontario Energy Board (OEB). The proceeds of this tax could be used to reduce the existing electricity system debt.
GLOSSARY OF TERMS
This web page last updated Octobet 11, 2014
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