Constitutive rock equation in the
Upper Adriatic basin from in situ compaction measurements
D. Bau', G. Gambolati, P. Teatini Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
EXTENDED ABSTRACT
The vertical compressibility cM of gas/oil bearing formations is of great
importance to reliably predict land subsidence over depleted fields.
Traditionally cM is obtained in laboratory from oedometer and triaxial tests
carried out on rock samples taken at depth of burial from exploratory boreholes.
It is well recognized that laboratory experiments lead to substantial errors,
in particular to an overestimate of the actual sediment compressibility by a
factor of two or more. This is mainly due to the disturbance experienced by the core
samples in their way from the field to the laboratory. A different technique referred
to as the marker technique has recently been developed and implemented by
Schlumberger and Western Atlas to make in situ compaction measurements of the
stressed reservoir sediments. The marker technique is based on monitoring the
distance between small radioactive bullets, called markers, shot at a regular
distance of 10.5 m into the depleted levels generally from an unproductive well.
The measurement is performed by a rod carrying two couples of gamma-ray detectors
10.5 m apart which is slowly raised from the borehole bottom and record the
count rate peaks when the detectors are right opposite the markers. Each peak
is fitted with a modified Gaussian function to locate the marker position.
An in situ estimate of cM may be obtained
relating the shortening of the distance between two adjacent markers to the pore
pressure decline occurred during the monitored time interval.
The marker technique is currently used in two
deep boreholes drilled in productive Lower Pleistocene sandy formations
underlying the Northern Adriatic Sea and located offshore the
Italian cities of Cattolica and Ravenna, respectively.
Available in situ measurements span the time intervals 1992-1994-1996.
The cM values thus derived are statistically
processed to reduce the influence of operational and instrumental errors.
The method of the moving weighted average is used over clustered depth intervals
from a same borehole.
To reduce the estimation variance as much as possible and
preserve at the same time the natural variability of cM with the vertical
effective (grain to grain) stress σz,
and hence depth z, a cluster size of
5 is adopted. The above moving average are regressed in a double log-log plot
by a linear straight line of cM vs σz.
By the use of known
relationships between cM and rock porosity Φ, and
σz and Φ the
behavior of the in situ average cM vs z can also be determined.
Comparison of the in situ cM profile and the
lab cM profile obtained from
oedometer tests on rock samples taken from holes scattered through the Northern
Adriatic basin shows
that the cM derived from the markers is between 4 and 6 times smaller than the
corresponding lab values in the depth interval between 1000 and 4000 m, i.e. the
depth of burial of the vast majority of the Northern Adriatic gas fields.
The constitutive laws displayed in the Figure represent the most realistic
cM estimates to date and are to be recommended for use in the numerical
prediction of the Italian coastland settlement which is expected to occur
because of gas production from the Northern Adriatic basin.
Constitutive relationships cM vs σz for the
Northern Adriatic basin.
