Page 157 - Fundamentals of Reservoir Engineering

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 96

zero lateral strain on the sample. This pressure is continually adjusted so that any
change in vertical thickness of the sample ∆h is uniformly related to the measured
water expelled from the porous rock.

If such an experiment were performed on an uncompacted sample of sand and the
compaction ∆h/h plotted as a function of the applied vertical stress which, considering
the fluid pressure is maintained at one atmosphere, is equivalent to the grain pressure,
then the result would be as shown in fig. 3.11 (b). The slope of this curve, at any point,
is
∆ h / ∆ p = c ≈ c φ refer equ. (1.37)
h b f

The characteristic shape of this compaction curve is intuitively what one would expect.
At low grain pressures the compressibility of the uncompacted sample is very high
since it is relatively easy to effect a closer packing of the grains at this stage. As the
grain pressure increases, however, it becomes progressively more difficult to compact
the sample further and the compressibility decreases. What is clear from such an
experiment is that the bulk or pore compressibility of a reservoir is not constant but will
continually change as fluids are withdrawn and the grain pressure increases.

Under normal hydrostatic conditions, since both the overburden and water pressures
increase linearly with depth, then so too does the grain pressure which is the difference
between the two. Thus a reservoir whose initial condition corresponds to point A will
normally be buried at shallow depth, while a reservoir corresponding to point B will be
buried deeper.

Compaction drive is the expulsion of reservoir fluids due to the dynamic reduction of
the pore volume and will only be significant as a drive mechanism if the pore
compressibility c f is large. It therefore follows that such a drive mechanism will normally
only provide a significant increase in the primary hydrocarbon recovery in shallow
12
reservoirs. In parts of the Bachaquero field, Venezuela, as reported by Merle, et al ,
the compaction drive mechanism accounts for more than 50% of total oil recovery. This
large reservoir dips between 1000−4000 ft. and has uniaxial compressibilities in excess
-6
of 100 × 10 /psi.
If the mechanics of reservoir compaction were as simple as described above, it would
appear possible to derive a relationship between uniaxial compressibility and depth, for
various types of typical reservoir rock, in an attempt to apply such a correlation
universally. Unfortunately, the process of compaction is frequently irreversible which in
turn implies that in-situ compressibility cannot be estimated in such a simple manner.

If the reservoir rock consists of well cemented grains in a rigid rock frame then the
compaction, over a limited pressure range, will be approximately elastic and reversible.
In loose unconsolidated sands, however, compaction is both inelastic and irreversible
since upon each reloading cycle on such a sample, in a repeated loading experiment in
a triaxial cell, it is possible for the individual grains to be packed in a different
configuration than on the previous cycle and, in addition, some of the grains can suffer
permanent mechanical deformation due to crushing. The effect of this inelastic