Relationship between auto-ignition temperature with pressure and fuel Experimentally it appears that increase in pressure, fuel concentration, and chain length causes AIT to decrease until a minimum where even further increase in these parameters increases the AIT. Additionally, it seems that AIT is lowered by increasing the vessel volume. 

From the last page of this paper:


  Semenoff's equation seems to indicate that it is possible to lower the AIT to arbitrarily low values by increasing the pressure. But the higher the total pressure of the fuel/air mixture, the higher is also the partial pressure of the fuel required to reach the most critical fuel concentration. At some temperature, the required partial pressure will become equal to the fuel vapor pressure. At even higher pressures and lower temperatures, it is impossible to reach the critical fuel concentration, and the depression of the AIT is expected to stop. A similar mechanism has been employed to explain the reincrease of the standard AIT with chain length for very long chain molecules /5/.


Edit: Article title is Autoignition Temperature for Mixtures of Flammable Liquids at Elevated Pressures by Brandes, Hirsh, and Stolz

1) From this, it seems that pressure and fuel concentration effects are related. Is the critical fuel concentration related to the equivalence ratio and the ability to reach this equivalence ratio based on the saturation pressure of the fuel?

2) I do not get the relation between the above explanation and the last sentence regarding re-increase of AIT for longer chain molecules?

3) I'm not sure why larger volumes leads to lower AIT as stated in ASTM E659 Appendix X2.
1) One could argue that yes. All other things being equal, larger molecules will clearly have lower vapor pressures at the same temperature so it is reasonable that there is a limit at which the fuel-air mixture is too lean to support autoignition.

2) After reading the paper I can only conclude that they are referring to the above idea that autoignition temperatures increase for larger compounds due to the need to increase the vapor pressure to reach an appropriate fuel concentration that supports autoignition.

3) Larger volumes have lower surface-area-to-volume ratios. The lower surface area means a the walls of a vessel play less of a role in the combustion chemistry leading to a lower AIT. These surface effects are detailed by Babrauskas with references to those who have observed this.
 

Babrauskas, V.
 of Fire Protection Engineers, S. (Ed.)
 Ignition Handbook 
 Fire Science Publishers, 
2003