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What would cause such a vast amount of plants and animals to be buried rapidly enough to produce the carbon for this oil?
Who said it had to be rapid? What you are forgetting is that oil does not stay where it is formed. Instead it perculates down into the ground, often taking up the spaces between particles in sedimentary rock (such as oil shales). An oil "well" is not a vast, open cavern filled with hydrocarbons, but an area of porous material that holds oil under pressure. Once that pressure is released then the oil shoots to the surface.
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I have heard the creationist argument that since oil resevoirs exist in permiable rock at such high pressures, they must be young or else the pressures would have dissipated over the millions of years. What is the uniformitarian explanation?
My geologic knowledge is pretty shaky, but if I remember correctly the oil wells are surrounded by rock that holds the oil in so that it can't escape. Think of it as mud kept in a cement ditch. The pressure can't escape because there is nowhere for it to escape to.
The rest I will have to read up on, or leave it for the local geology experts (eg Bill Berkland). Like I said, don't take my word as gospel (pardon the pun).