However, the volume of the pyramid that is full of oil is much less than the volume of the pyramid that is full of water.  Let's assume that we drill horizontal wells into our oil leg and let's assume that we can produce the field at a relatively high rate until the water hits the horizontal wells.  Let's assume a moderately strong water drive that is augmented by water injection into the water leg, in order to maintain a fairly constant pressure as the oil is withdrawn.

Initially, the oil column would thin at a fairly low rate because the lower portions of the oil column are being depleted first.  However, if we look at the oil column in terms of 100' intervals, the volume of each successively higher 100' interval is less than the 100' interval below it.   (Key point.)

So, as we continue to produce the field at a fairly constant rate, the rate of thinning in the oil column accelerates dramatically.  

If you throw in a gas cap, this is grossly simplified explanation of what is happening in the two largest oil fields in the world, Ghawar and Gantarell, accounting for almost 10% of world crude + condensate production.  (Note that Cantarell has had a pretty sophisticated nitrogen injection program.)

In any case, you can see how the fields would have the appearance of robust production right up to the point at which production starts crashing.