Calculations Used in Carbon Footprint Calculator
Written By: Jeremy Caves
Car Emissions:
Car emissions are calculated by dividing the miles driven by the fuel efficiency of the vehicle. This number is then multiplied by the CO2 emissions coefficient, 19.36 lbs CO2/gallon[1] of gasoline, and then divided by 2204.6 lbs/metric ton to obtain the tonnes of CO2 emitted from car travel (Equation 1).
Equation 1
Airplane Emissions:
The total number of passenger revenue miles sold by U.S. airlines, 809,728,364,758 miles[2], is divided by the total gallons of jet fuel purchased by United States based carriers, 19,285,575,892 gallons[3]. Both of these numbers include domestic and international travel by U.S. airlines in 2006. The result of this calculation is the fuel efficiency per passenger, 41.986 passenger miles/gallon, and is averaged over all flights operated by U.S. carriers. Because airplanes use significantly more fuel during takeoff, this number is an overestimation for short flights, but an underestimation of fuel efficiency for long flights.
The total number of miles flown is divided by the above fuel efficiency per passenger and multiplied by 20.88 lbs CO2/gallon[4], the CO2 emissions coefficient for jet fuel. This number is then multiplied by 2.7, the Radiative Forcing Index (RFI), which is a measure of the global warming impact from greenhouse gases other than carbon dioxide[5]. Airplanes emit both nitrous oxides (NOx) and water vapor (contrails) high in the troposphere, both of which are greenhouse gases. Thus, the RFI accounts for the global warming potential of airplane emissions due to gases other than CO2. Finally, this number, in pounds of CO2, is divided by 2204.6 lbs/metric ton to obtain CO2 emissions in tonnes (Equation 2).
Equation 2
Electricity:
Several numbers were important in developing the calculations of CO2 emissions due to electricity use; these are detailed in Table 2.
Rice Central Plant Heat Rate
The calculation of the Central Plant’s heat rate is not straightforward and depends largely upon which combination of boilers, generators, and chillers are in use. According to Doug Wells, the Central Plant has a heat rate of 13.3MMBtu/Mwh. However, this measurement excludes steam production, which is produced by the generators as a by-product of electricity production. To determine how much natural gas is used to produce steam, one of the boilers is operated to determine the ratio of natural gas input to steam output. The quantity of natural gas used to produce an equivalent amount of steam as during generator operation is then “credited” to the generator. However, the generators run at a lower efficiency than the boilers (in terms of steam production), and this must be accounted for when “crediting” the generators. In addition, each of the boilers operates at a different efficiency, and the Solar and Ruston generators vary by more than 15% in their efficiency, complicating these calculations[6]. Ultimately, accounting for steam production results in a 3-5 MMBtu/Mwh decrease in the Central Plant’s heat rate. Thus, we chose a fairly conservative value, 10 MMBtu/Mwh, as the Central Plant’s heat rate for use in our calculator. We relied heavily on communications with Mark Gardner and usage of his “Plant Lineup Scenario 1” model, produced in the early part of this decade, for this information.
Rice Central Plant CO2 Emissions Coefficient
The Central Plant emits 27411.7188 tonnes of CO2 annually[7]. This number is derived from computer models and simulations of generator operations which predict the total amount of CO2 released for a given amount of natural gas. Given that Rice purchased 494,327MMBtus last year[8], the Central Plant emits 122.25 lbs CO2/MMBtu, and, with a heat rate of 10 MMBtu/Mwh, the CO2 emissions coefficient is 1.22 lbs CO2/Kwh (Equation 3)
Equation 3
Calculation of Reliant Energy’s CO2 Emissions Coefficient
Reliant Energy uses a fuel mix of 42% lignite, 43% natural gas, 9% nuclear, 1% renewable, and 5% other production means to produce the electricity that Rice purchases[9],[10]. This electricity is slightly dirtier than the Texas average; where 100 is an indexed value corresponding to the average CO2 emissions for electricity production in Texas, Reliant emits CO2 at a 109 value[11]. The average CO2 emissions coefficient for Texas electric power, averaged over the years 1998-2000, is 1.46 lbs CO2/Kwh[12]. Increasing the state average by 9%, to model Reliant’s slightly dirtier energy production, yields a CO2 emissions coefficient of 1.59 lbs CO2/Kwh (Equation 4). We used 1.6 lbs CO2/Kwh in our calculator to match the calculations of Dr. K. Zygourakis.
Equation 4
where 109/100 is a ratio of Reliant’s CO2 emissions to the Texas state average for electricity production (indexed to 100).
CO2 Emissions Due to Appliance Use
Table 3 lists constants used for appliance electricity consumption. Equation 5 was used to calculate the CO2 emissions from each appliance.
Equation 5
In Equation 5, “electricity consumption” is the daily consumption by the given appliance, “use(suite/individual)” is the number of people using that appliance (1 for an individual; 2, 3, 4, or 5 for suite use), and “1.486 lbs CO2/Kwh” is the weighted carbon emissions coefficient for Rice electricity (assuming 30% is generated at the Central Plant and 70% is purchased from Reliant). Note that, for blow-dryers, electricity consumption was measured on a weekly basis; that is, instead of scaling up use by 365 days, use was scaled up by 52 weeks, given that many women only blow-dry their hair several times per week and not on a daily basis.
CO2 Emissions Due to Air-Conditioning
We assumed that 30% of Rice’s electricity consumption was used for air-conditioning and that, of this fraction, 20% was used to air-condition the colleges. These assumptions were supplied to us by Richard Johnson, who himself assumed that all of the Central Plant’s electricity production was being used for air-conditioning, amounting to approximately 30% of Rice’s electricity consumption. As a result, per-capita electricity consumption among on-campus students is 2,854Kwh (Equation 6).
Equation 6
Facilities, Engineering, and Planning (FE&P) uses 76º as the baseline temperature for air-conditioning; any extra degree of cooling increases electricity use by 4%. Conversations with Mark Gardner, FE&P Energy Manager, and Doug Wells, Director of the Central Plant, indicated that these two figures are standard “rules-of-thumb” and were obtained from engineering textbooks or websites. For our calculator, we assumed that, if a student set his or her thermostat at 76º, he or she would be using 2,854 Kwh for air-conditioning. For every extra degree of cooling, the calculator increases the electricity consumption by 4%; similarly, for every degree higher than 76º to which the thermostat is set (such as 78º or 80º), the calculator decreases the electricity consumption by 4%. For instance, a student who sets his thermostat at 70º would use 3,539Kwh of electricity for air-conditioning (Equation 7).
Equation 7
where “thermostat setting” is the temperature at which the thermostat is set and “electricity consumption” is the total electricity used, by that student, to keep his or her room at that thermostat setting.
Finally, the total CO2 emissions due to air-conditioning is calculated using Equation 8.
Equation 8
CO2 Emissions Due to Steam Use
The colleges used 34.771 million pounds of steam during 2006[13]. In our calculator, we converted pounds of steam into kilowatt-hours, finding that each student uses 1,655.76Kwh of steam (Equation 9). This is an unnecessary conversion which requires using the heat rate, an uncertain figure, and future versions of the calculator should only convert heat rate into equivalent values of Btus.
Equation 9
where 100lbs steam/therm and 10therms/MMBtu are standard conversions[14].
This number is subsequently converted to CO2 emissions using Equation 10.
Equation 10
For every extra degree of heating, an additional 4% energy is needed; however, steam is used for both hot water and heating, and we lacked data which broke down what percentage of steam was destined for which end-use. Thus, we kept this figure constant for every student.
CO2 Emissions Due to Commons/Servery Electricity Consumption
This calculation is quite crude due to a lack of data. The colleges use 10,335.795Mwh of electricity (approximately 10% of the Rice’s electricity consumption)[15]; however, even if every student used every appliance we measured (listed in Table 3) every day of the year, these appliances would only account for 1,717.727Mwh of college electricity consumption (Equation 11). Clearly, a large amount of electricity is being used by servery equipment, common areas, and possibly ceiling lights in dorm rooms (which we did not measure). Since appliance electricity consumption is included in the total college electricity consumption, it is necessary to subtract appliance electricity consumption from total college electricity consumption in order to approximately gauge the total amount of electricity consumed due to commons/serveries (see Equation 12). To do this, we assumed that every student used every appliance we measured every single day of the year and subtracted this total from the college electricity total to obtain an estimate of commons/servery electricity use. While this assumption is almost certainly incorrect, it does avoid counting appliance electricity use twice.
Equation 11
where the above, decimal figures are drawn from Table ???.
Equation 12
Thus, common areas and serveries draw 8,618.039Mwh of electricity, which, divided among 2100 students is 4,103Kwh/student. This figure is then used to determine the CO2 emissions due to common areas and servery electricity consumption (Equation 13).
Equation 13
Green Energy CO2 Emissions:
At the very end, the calculator determines how much CO2 one would emit if Rice purchased green energy. It assumes all domestic energy use (electricity, heating, and cooling) would be produced via green energy. This total is calculated using Equation 14.
Equation 14
where “Total CO2 Emissions” equals the sum of air travel, car travel, and domestic energy CO2 emissions and “Domestic Energy CO2 Emissions” equals the sum of appliance, cooling, steam use, and common areas/servery CO2 emissions.
[1] Office of Policy and International Affairs. Technical Guidelines: Voluntary Reporting of Greenhouse Gases (1605(b)) Program. United States Department of Energy; March 2006.
[2] TranStats. “Revenue Passenger Miles by Unique Carrier for 2006.” Bureau of Transportation Statistics; 2006.
[3] “Airline Fuel Cost and Consumption (1977-2007).” Bureau of Transportation Statistics; 2007.
[4] Office of Policy and International Affairs. Technical Guidelines: Voluntary Reporting of Greenhouse Gases (1605(b)) Program. United States Department of Energy; March 2006.
[5] “Executive Summary.” Aviation and the Global Atmosphere. Intergovernmental Panel on Climate Change; 1999.
[6] Mark Gardner, FE&P Energy Manager (personal communication)
[7] Doug Wells, Director of Central Plant (personal communication)
[8] Ibid.
[9] Eric Valentine, Energy Manager, FE&P (personal communication)
[10] “Electricity Facts: Reliant Energy Residential Services—12 Month OneRate Secure Plan.” Powertochoose.org. February 2007.
[11] Ibid.
[12] Energy Information Administration. Updated State-level Greenhouse Gas Emission Coefficients for Electricity Generation 1998-2000. United States Department of Energy. April 2002.
[13] Mark Gardner, FE&P Energy Manager (personal communication)
[14] “Rules of Thumb.” A.B. Young Companies. A website hosted by A.B. Young Companies, a heating and cooling engineering firm, listing standard conversions for steam and chilled water.
[15] Mark Gardner, FE&P Energy Manager (personal communication)