The emission of fuel vapors into the atmosphere from underground storage tanks at filling stations is a common occurrence in many parts the world. The conditions of the vapor in the tanks vary significantly over a 24 hour period such that evaporation and excess air ingestion during the refueling process can cause tank over pressurization and subsequent emissions. At other times during a 24 hour cycle, pressures can fall below atmospheric pressure. The state of California has recognized this emissions problem and has enacted regulations to address it. Due to these low-emission environmental requirements in California, solutions must be implemented that do not entail release of these vapors into the atmosphere. One solution requires that the vapors fill a balloon during the appropriate times. However, the size of the balloon at typical inflation rates requires a significant amount of physical space (approximately 1000-2000 liters), which may not necessarily be available at filling stations in urban areas. Veeder-Root has a patent pending for a system to compress the vapors that are released to a 10:1 ratio, store this compressed vapor in a small storage tank, and then return the vapors to the original underground fuel tank when the conditions are thermodynamically appropriate (see Figure 1 for the schematic representation of this system). The limitation of the compressor, however, is that the compression phase must take place below the ignition temperature of the vapor. For a 10:1 compression ratio, however, the adiabatic temperature rise of a vapor would be above the ignition temperature. Mathematical modeling is necessary here to estimate the performance of the compressor, and to suggest paths in design for improvement. This report starts with a mathematical formulation of an ideal compressor, and uses the anticipated geometry of the compressor to state a simplified set of partial differential equations. The adiabatic case is then considered, assuming that the temporary storage tank is kept at a constant temperature. Next, the heat transfer from the compression chamber through the compressor walls is incorporated into the model. Finally, we consider the case near the valve wall, which is subject to the maximum temperature rise over the estimated 10,000 cycles that will be necessary for the process to occur. We find that for adiabatic conditions, there is a hot spot close to the wall where the vapor temperature can exceed the wall temperature. Lastly, we discuss the implications of our analysis, and its limitations
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