Page 159 - Fundamentals of Reservoir Engineering

MATERIAL BALANCE APPLIED TO OIL RESERVOIRS 98

Compaction, and its associated effect of surface subsidence, will be much more
pronounced for shallow, unconsolidated reservoirs than for the deeper, more
competent sands. It is therefore necessary to experimentally determine the
compressibility of shallow reservoir sands in order to estimate to what degree
compaction will enhance the hydrocarbon recovery, and also, to enable the prediction
of the resulting surface subsidence, which can cause serious problems if the surface
13
location of the field is adjacent to the sea or a lake .

Unfortunately, the deformation of unconsolidated sands is usually inelastic and this in
turn leads to complications in relating laboratory measured compressibilities to the in-
situ values in the reservoir. The nature of the problem can be appreciated by referring
again to fig. 3.12. Suppose that both the grain and fluid pressures in a reservoir are
normal so that under initial conditions the reservoir is at point B on the compaction
curve. The process of cutting a core and raising it to the surface will cause unloading,
which for a rock which deforms inelastically, will place the core at point C′, which lies
off the normal compaction curve. During the re-loading the horizontal path B−C′ is not
reversed, instead there is a mechanical hysteresis effect which means that the true
compaction curve is not re-joined until point D, where p D > p B. As a result, the
laboratory measured compressibility, determined as the slope of the line C′−D at
pressure p B, will be somewhat lower than the in-situ value, which is the slope of the
normal curve at p B. Thus, initial values of the in-situ compressibility are difficult to
determine and usually require estimation by back extrapolation of laboratory values
obtained for grain pressures in excess of p D.

The above description of the various complications in estimating in-situ, uniaxial
compressibility has been applied for the extreme case of a perfectly inelastic reservoir
rock. Generally rock samples are neither perfectly elastic or inelastic but somewhere in
between. Nevertheless, the same qualitative arguments apply and it is therefore not
always meaningful to merely estimate in-situ compressibilities by reference to
published charts for typical sandstones and limestones.

REFERENCES

1) Schilthuis, R.J., 1936. Active Oil and Reservoir Energy. Trans.,
AIME, 118: 33-52.

2) Amyx, J.W., Bass, D.M., and Whiting, R.L., 1960. Petroleum Reservoir
Engineering - Physical Properties. McGraw-Hill: 448-472.

3) McCain, W.D., 1973. The Properties of Petroleum Fluids. Petroleum Publishing
Company, Tulsa: 268-305.

4) Havlena, D. and Odeh, A.S., 1963. The Material Balance as an Equation of a
Straight Line. J.Pet.Tech. August: 896-900. Trans., AIME, 228.

5) Havlena, D. and Odeh, A.S., 1964. The Material Balance as an Equation of a
Straight Line. Part II - Field Cases. J.Pet.Tech. July: 815-822. Trans., AIME.,
231.