Is the bottom of the reservoir flat? I thought that oil had migrated thru porous rock from below and become trapped under a curved inpermiable layer. In such case i think that the bottom should be flat and the top curved. The cross sections show both the bottom and the top curved. Is the oil pushed towards the middle or upwards and towards the middle so that the bottom is still flat?

No, that is not correct. When the sediment was deposited many millions of years ago, everything was flat, as flat as the bottom of the shallow sea anyway. Geological activity deep in the earth has since buckled and curved everything. Nothing is flat anymore, certainly not the bottom bottom of the reservoir. The bottom of the reservoir, with a few exceptions, should resemble the top of the reservoir. It is an anticline. An anticline resembles a mountain beneath the surface with all sediment layers curved.

And the oil does not push up from below the middle of the reservoir. The oil, which originally came from source rock below the reservoir rock, rose up through cracks and fissures to the reservoir rock. The oil settled to the top of the anticline. The oilcame from a much larger and likely thinner area but settled at the very top of the anticline.

Ron Patterson

Like this? from top to bottom:

Seal Rock with no permeability
Reservoir Rock with preferably high permeability
... Rock with very low or no permeability
Source rock Where the oil comes from
Rock bottom Non sedimentary rock

I have looked at everything again and noticed something important. The simulations for 'Ain Dar in the figures show that the areas of oil are getting smaller and thinner.
If the areas are long but narrow i guess the area of the remaining cross sections not to close to the ends could be approximated with a triangle. The volume for each section could then be calculated by multiplying with the distance halfway to the next section.

l Distance halfway from section before to halfway to section after
w Width of cross section
h Height of cross section
v Volume
c Constant

Formula for the correlation between height and width: h=c*w this is crucial, but is it approximately correct?

Formula for the volume:
v=l*(w*h)/2=[substitution h=c*w]=l*(w*c*w)/2=l/2*c*w^2
This is a quadratic function which means that the remaining volume is proportional to the width w in square. If the width is multiplied by 2 the volume gets 4 times higher!!

If the length and width is approximately equal the function becomes qubic and multiplying the width with 2 will make the volume 8 times larger.