Gasoline and diesel fuel: Carbon pricing and heating values

Gasoline and diesel fuel:
Carbon pricing and heating values

Introduction

Shortly after New Year’s Day 2017 a radio news item noted that the Province of Ontario’s newly introduced cap and trade¹ system for carbon pricing would result in higher pump prices for gasoline and diesel fuel. The increase for diesel fuel would be greater on a per litre basis. Why is this? It is because diesel fuel produces more carbon dioxide on a per litre basis. Diesel fuel also produces more heat energy on a per litre basis when burned. These facts provide teachers with a lead-in to some stoichiometry and thermochemistry calculations, as well as to the concept of carbon pricing. These engineering topics will provide several opportunities for unit conversion exercises.

According to the US Energy Information Administration: “About 19.64 pounds of carbon dioxide (CO₂) are produced from burning a gallon (US) of gasoline that does not contain ethanol. About 22.38 pounds of CO₂ are produced from burning a gallon of diesel fuel.”² (See Question 1.)

Gasoline¹ and diesel fuel¹ are complex mixtures of hydrocarbons, mainly alkanes, and additives. The actual composition of a fuel can vary widely, due to feedstock variability, refinery capability, supply and demand factors, climate and seasonality. For this reason, statements about ‘gasoline’ or ‘diesel fuel’ properties must be understood as average or typical values only.

Data from Wikipedia article diesel fuel - the information as of 2010.

The table data shows that diesel and gasoline are very close in heating value (energy content) on a mass basis. This is because the carbon content of diesel and gasoline are very similar; although gasoline alkanes range from C₄ to C₁₂, while diesel alkanes range from C₁₀ to C₁₅. The carbon percentage of octane (C₈H₁₈), a stand-in for gasoline, and hexadecane (C₁₆H₃₄), a stand-in for diesel, are 84.2% and 85.0% respectively. The amount of carbon dioxide produced from gasoline and diesel and therefore the carbon pricing, are also both very similar on a mass basis. However, the straight chain higher C-number liquid alkanes in diesel pack more densely than the branched chain lower C-number alkanes in gasoline. The difference in liquid densities is some 11%. Diesel produces 11% more heat energy and 11% more carbon dioxide than gasoline on a volume basis. Using the data in the table, one can calculate that diesel produces 2.627 kg of carbon dioxide per litre burned, and gasoline 2.361 kg/L (see Question 2). Transport fuels are pumped, measured and carbon priced by volume, and fuel efficiency is measured using volume units as mpg or L/100 km. For this reason, the carbon price of diesel at the pump will be about 11% greater than that of gasoline. It is interesting to note that diesel engines have an advantage of 11% in fuel efficiency before any other performance factors are considered.

Carbon pricing in Canada

The Province of British Columbia has a carbon tax that is unambiguous at $30 (Canadian) per tonne of CO2 or equivalent emission.3 At this level, gasoline users pay $0.0667/L and diesel fuel users $0.0767/L. British Columbia mandates that gasoline must contain at least 5% ethanol by volume and diesel fuel must contain at least 4% biodiesel or other biologically sourced substances.⁴ These components are sustainable, and are not subject to the carbon pricing. (See Question 3.) Under Ontario’s cap and trade, pricing is not so straightforward, and the actual retail price increases are not yet clear. One estimate for the pricing in Ontario suggests retail users will be paying an extra $0.0427/L for gasoline and $0.0544/L for diesel fuel.⁵

Carbon dioxide production: stoichiometry 

It would be overly complex to do stoichiometry for a real gasoline or diesel fuel mixture, but we can model the fuels in a simple manner using iso-octane to represent gasoline and cetane to represent diesel fuel. The hydrocarbon iso-octane (2,2,4-trimethylpentane¹) is a superb alkane fuel for engines. The hydrocarbon cetane¹ (hexadecane or n-hexadecane) is an excellent fuel for diesel engines.

“2,2,4-Trimethylpentane, also known as isooctane or iso-octane, is an organic compound with the formula (CH₃)₃CCH₂CH(CH₃)₂. It is one of several isomers of octane (C₈H₁₈). This particular isomer is the standard 100 point on the octane rating scale (the zero point is n-heptane). It is an important component of gasoline, frequently used in relatively large proportions to increase the knock resistance of the fuel.

“Strictly speaking, if the standard meaning of ‘iso’ is followed, the name isooctane should be reserved for the isomer 2-methylheptane. However, 2,2,4-trimethylpentane is by far the most important isomer of octane and so, historically, it has ended up with this name.

“Engine knocking is an unwanted process that can occur during combustion in internal combustion engines. Graham Edgar in 1926 added different amounts of n-heptane and 2,2,4-trimethylpentane to gasoline, and discovered that the knocking stopped when 2,2,4-trimethylpentane was added. This was the origin of the octane rating scale. Test motors using 2,2,4-trimethylpentane gave a certain performance which was standardized as 100 octane. The same test motors, run in the same fashion, using heptane, gave a performance which was standardized as 0 octane. All other compounds and blends of compounds then were graded against these two standards and assigned octane numbers.” (Quotes from the Wikipedia article 2,2,4-trimethylpentane.)

“Cetane number, Cetane rating or CN is an indicator of the combustion speed of diesel fuel and compression needed for ignition. It is an inverse of the similar octane rating for gasoline. The CN is an important factor in determining the quality of diesel fuel, but not the only one; other measurements of diesel's quality include (but are not limited to) energy content, density, lubricity, cold-flow properties and sulphur content.” (Quote from the Wikipedia article cetane number.)

According to Wikipedia, the density of iso-octane is 0.692 g/mL, and the density of cetane is 0.770 g/mL. Take the mass of a litre of iso-octane as 692 g, and the mass of a litre of cetane as 770 g. The relevant chemical equations, mass and liquid volume relationships are:

2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O
228.5 g iso-octane → 704.2 g carbon dioxide
1 g iso-octane → 3.08 g carbon dioxide
1 L iso-octane → 2131 g carbon dioxide

2C₁₆H₃₄ + 49O₂ → 32CO₂  +  34H₂O
452.9 g cetane → 1408 g carbon dioxide 
1 g cetane → 3.11 g carbon dioxide
1 L cetane → 2395 g carbon dioxide

From these values, the ratio of carbon dioxide production for one litre of diesel fuel to one litre of gasoline is calculated to be 2395/2131 = 1.12 (12% greater). Reference 2 gives values measured for real samples, where the ratio is 22.38/19.64 = 1.14 (14% greater). The Province of British Columbia’s carbon pricing suggests the ratio is 0.0767/0.0667 = 1.15 (15% greater).

Heating values and thermochemical calculations

Heating values for fuels are generally measured empirically, especially for mixed fuels such as gasoline and diesel fuel. We can model the heating values by using standard heats of combustion¹ for iso-octane and cetane. Engineers distinguish between higher heating value (HHV)¹ and lower heating value (LHV)¹ of a fuel. HHV corresponds to the standard heat of combustion where the product water is condensed to its liquid state. This will be the case for a high efficiency condensing home furnace, for example. For automotive engines, LHV is the heating value where the product water is a gas. In the two calculation strings below, LHV differs from HHV by subtracting the energy required to vaporize 18 and 34 mol of water respectively (40.65 kJ/mol).¹ The standard heats of combustion of iso-octane and cetane are –5461 kJ/mol and -10.70 MJ/mol respectively.

2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O(l) (HHV = 10.9 MJ)
2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O(g) (LHV = 10.2 MJ)
228.5 g iso-octane → 10.2 MJ
1 g iso-octane → 44.6 kJ
1 L iso-octane → 30.9 MJ

2C₁₆H₃₄ + 49O₂ → 32CO₂ + 34H₂O(l) (HHV = 21.4 MJ)
2C₁₆H₃₄ + 49O₂ → 32CO₂ + 34H₂O(g) (LHV = 20.0 MJ)
452.9 g cetane  → 20.0 MJ
1 g cetane → 44.2 kJ
1 L cetane → 34.0 MJ

These values are about 4% and 6% respectively lower than those quoted for gasoline and diesel fuel in Wikipedia. The empirical values given in Wikipedia suggest that diesel fuel delivers about 1% more energy per litre than does gasoline. This is one of the factors that make diesel engines more fuel efficient than gasoline engines.

Questions for students

1. Convert the values in the second paragraph of the Introduction from pounds and US gallons to kg and L units. (Answers: 2.354 kg/L; 2.682 kg/L) 
2. The Wikipedia article alkane contains a table with the formulas and densities of the straight-chain or n-alkanes. The twelve n-alkanes from pentane (C₅) to hexadecane (C₁₆) are liquids of increasing density at 20 °C. Tabulate the names, formulas and densities.

• Add two columns: g carbon/L and g CO₂ produced/L
• Calculate and fill in the required entry values.

(Challenge: program a spreadsheet or write a program in some other application to calculate these values.)
(Answers for pentane: 521 g C/L; 1910 g CO₂/L.) 
 

3.  In British Columbia, gasoline contains 5% sustainable ethanol, and  diesel fuel contains 4% sustainable ‘biodiesel’. These are not subject to carbon pricing. Use your answers to Question 1 above but reduced by 5% and 4% respectively, and the Province of British Columbia’s carbon prices per litre of gasoline and diesel fuel, $0.0667 and $0.0767 respectively, to calculate the implied prices per tonne (1000 kg) of carbon dioxide for the two fuels. (Answers: $29.83/tonne; 29.79/tonne. The values should be $30 per tonne. The average fuel compositions in British Columbia may be different from those of Reference 2.)

4.  Using the values calculated above in this article, calculate the value of g CO₂/MJ for each of iso-octane and cetane. Compare these values to those for gasoline and diesel fuel given in Wikipedia. (Answers: 69.0 and 70.4 g/MJ compared to 73.38 and 73.25 g/MJ respectively.)

References

1. www.wikipedia.org for: Cap and Trade; gasoline; diesel fuel; alkane; 2,2,4-trimethylpentane; cetane; octane number; cetane number; heat of combustion; properties of water.
2. US Energy Information Administration: www.eia.gov/tools/faqs/faq.cfm?id=307&t=9.
3. Province of British Columbia, Ministry of Finance, How the Carbon Tax Works: www.fin.gov.bc.ca/tbs/tp/climate/A4.htm.
4. Clean Energy Canada, Biofuels in Canada, March 2016, Table 1 page 5 and Table 2 page 6: http://cleanenergycanada.org/wp-content/uploads/2016/03/FINAL-Report-Biofuel-Policy-Review-March-2016.pdf.
5. Dowler Karn, What You Need to Know About Ontario’s New Cap and Trade Program: http://dowlerkarn.com/capandtrade/.