### Intro

This page summarizes the calculations used by the Biodiesel Buddy smartphone app, to calculate net CO2 impacts of using biodiesel, gasoline, or petroleum diesel fuels. These comparisons are conducted solely on the net carbon criterion, not on cost, or any other factor.

### Raw Data

From the EPA (2005), the carbon emissions from

 1 US gallon of gasoline 19.4 lbs 1 US gallon of petro-diesel 22.2 lbs

From Oak Ridge National Laboratory, the energy content of fuels are (in MJ/liter)

 Gasoline 32 Diesel 36.4 Biodiesel 33.3

From the DOE (2009) and the Union of Concerned Scientists (2004), diesel engines enable cars to travel approximately 30% farther on a gallon of fuel, than comparable gasoline models.

From the Department of Agriculture 2009 and 2011, the life cycle energy efficiency of fuels are

 Gasoline 0.805 Diesel 0.843 Biodiesel 5.54

The life cycle energy efficiency refers to the amount of energy (i.e. Joules or BTU) available via combustion of the fuel produced with 1.0 units of fuel input. The 1.0 units of fuel input are assumed to be (dirty) fossil fuels. For example, if it takes 0.195 units of fossil fuel energy to drill for, refine, and transport oil, to make gasoline, and you get 0.805 units of usable gasoline energy out of the process, you arrive at the 0.805 energy ratio for gasoline.

```   Efficiency = (energy out) / (energy consumed)
0.805 = 0.805 / (0.805 + 0.195)
```
Note that for biodiesel, the ratio is greater than 1.0. Using 1.0 units of fossil fuels, you can produce 5.54 units of usable biodiesel energy. This is possible, of course, because the extra energy is provided (for free) by the sun, converted by the plant feedstock during photosynthesis. The biodiesel energy, unlike gas or diesel energy, is not counted as energy consumed. This is because the biofuel is not producing any net atmospheric carbon dioxide at all. Every molecule of CO2 produced in the burning of biodiesel was CO2 that was already in the atmosphere, and was absorbed by the plant feedstock grown to make the fuel. Only the fossil fuel used to farm, process, and distribute the biodiesel counts as dirty energy consumed (1.0 units in for each 5.54 units out).

There is much debate about which factors should be considered in the total "energy consumed" calculation. This will not be addressed in detail here. Suffice it to say that the same (USDA) source has been used for life cycle energy efficiency statistics for all three fuels compared, in an attempt to keep the comparison as legitimate as possible.

Of note is also that the aforementioned energy efficiencies for gas and diesel are getting worse with time (as oil becomes harder to find and extract), and better with time for biofuels (as farming becomes more efficient). As biofuels begin to be made with crops not grown to the quality standards needed for edible food crops, this efficiency should go even higher. Nevertheless, this calculation is conducted with the historical data provided in the USDA report.

### Derivation

First, we calculate the amount of CO2 used to "produce" 1 gallon of biodiesel. It would not be a valid comparison to compare this amount of CO2 to the amount of CO2 produced by a gallon of gas, or a gallon of diesel. To make the comparison valid, we will calculate all CO2 emissions relative to the amount of energy that exists in one gallon of biodiesel. The energy in one gallon of biodiesel is

```  Ebd = (energy per liter) * (liters per gallon)
= (33.3 MJ / liter) * (3.785 liter / gallon)
= 126 MJ
```
Based on the energy efficiencies, in order to produce 126 MJ of biodiesel energy, we must input fossil fuel energy with a ratio of 5.54 : 1
```  Ein = Ebd / 5.54
= 22.75 MJ
```
We will assume that the fossil fuel energy used to produce biodiesel was petro-diesel. Most farm and trucking equipment runs on petro-diesel. Thus, in order to consume 22.75 MJ of input energy, the volume of diesel used was
```  Vd = Ein / (energy per volume for diesel)
= (22.75 MJ) / (36.4 MJ / liter)
= 0.625 liters
= 0.165 gallons
```
The CO2 emissions from 0.165 gallons of diesel, per the EPA data, are
```  CO2 = (CO2 / gallon) * 0.165 gallons
= (22.2 lbs / gallon) * (0.165 gallons)
= 3.66 lbs
```
So, using 1 gallon of biodiesel creates 3.66 lbs of atmospheric CO2, solely as a result of the fossil fuels used to produce and distribute the fuel.

Next, we calculate the amount of CO2 produced by an equivalent amount of diesel energy. To get 126 MJ of usable energy from diesel, we must actually consume

```  Vd = [E / (energy per liter)]
= (126 MJ / 0.843) / (36.4 MJ / liter)
= 4.106 liter
= 1.085 gallon

CO2 = Vd * (CO2 / gallon)
= (1.085 gallon) * (22.2 lbs / gallon)
= 24.1 lbs
```
So, an alternative to using 1 gallon of biodiesel is to burn petrodiesel, producing 24.1 lbs of atmospheric CO2. So, compared to diesel, using a gallon of biodiesel saves 24.1 - 3.66 = 20.4 lbs of CO2.

Finally, we calculate the amount of CO2 produced by an equivalent amount of gasoline. To get 126 MJ of usable energy from gas, we must actually consume

```  Vg = [E / (energy per liter)]
= (126 MJ / 0.805) / (32.0 MJ / liter)
= 4.89 liter
= 1.292 gallon
```
However, comparing solely on the equivalent energy content is not valid, because gas and diesel are burned in different types of engines (but biodiesel and diesel are burned in the same type of engine). Diesel cycle engines have higher energy efficiencies than gasoline (aka Otto cycle) engines, so we must multiply the volume of gas required by the difference in engine efficiency. Per the data above, diesel engines are about 30% more efficient (per gallon). However, this efficiency is due to both the engine's thermodynamic efficiency, and the higher energy content per gallon of diesel vs. gas. We have already accounted for the energy content of gas in the previous calculation, so we must not double-count that factor. The total diesel vs. gas efficiency ratio is the product of two factors:
```  Rd-vs-g = 1.30
= Rengine * Rfuel

Rengine = 1.30 / (36.4 / 32.0)
= 1.14
```
So, about half of the improved fuel economy of diesel vehicles is due to the more energetic fuel, and half is due to the engine design itself. Thus, we multiply the volume of gas needed by the ratio of engine efficiencies to yield
```  CO2 = Vg * (CO2 / gallon)
= [1.14 * (1.292 gallon)] * (19.4 lbs / gallon)
= 28.65 lbs
```
Therefore, a second alternative to using a gallon of biodiesel is to burn gasoline, producing 28.65 lbs of atmospheric CO2.

### Results

These data are the final values used in the Biodiesel Buddy CO2 savings calculation

 Gasoline 28.65 lbs Diesel 24.10 lbs Biodiesel 3.66 lbs

All values are expressed as CO2 generated by using the amount of fuel equivalent to 1 gallon of biodiesel, accounting for engine efficiencies.

```  Vh = [1.14 * (1.292 gallon)] * 0.7 Copyright ©2003-2012 Enscand, Inc. All Rights Reserved Modified February 21, 2012 Privacy Security Environment