Отправлено: 11.03.16 06:02. Заголовок: Interval inversion approach for an improved interpretation of well logs

Interval inversion approach for an improved interpretation of well logs
Mihбly Dobrуka1
, Norbert Pйter Szabу2
, Jуzsef Tуth3
, and Pйter Vass3

GEOPHYSICS, VOL. 81, NO. 2 (MARCH-APRIL 2016); P. D163–D175, 12 FIGS., 3 TABLES.


ABSTRACT
The quality analysis of well-logging inversion results has always
been an important part of formation evaluation. The precise
calculation of hydrocarbon reserves requires the most accurate
possible estimation of porosity, water saturation, and shale and
rock-matrix volumes. The local inversion method conventionally
used to predict the above model parameters depth by depth represents
a marginally overdetermined inverse problem, which is
rather sensitive to the uncertainty of observed data and limited
in estimation accuracy. To reduce the harmful effect of data noise
on the estimated model, we have suggested the interval inversion
method, in which an increase of the overdetermination ratio allows
a more accurate solution of the well-logging inverse problem.
The interval inversion method inverts the data set of a longer
depth interval to predict the vertical distributions of petrophysical
parameters in a joint inversion procedure. In formulating the forward
problem, we have extended the validity of probe response
functions to a greater depth interval assuming the petrophysical
parameters are depth dependent, and then we expanded the model
parameters into a series using the Legendre polynomials as basis
functions for modeling inhomogeneous formations. We solved
the inverse problem for a much smaller number of expansion coefficients
than data to derive the petrophysical parameters in a
stable overdetermined inversion procedure. The added advantage
of the interval inversion method is that the layer thicknesses and
suitably chosen zone parameters can be estimated automatically
by the inversion procedure to refine the results of inverse and forward
modeling. We have defined depth-dependent model covariance
and correlation matrices to compare the quality of the local
and interval inversion results. A detailed study using well logs
measured from a Hungarian gas-bearing unconsolidated formation
revealed that the greatly overdetermined interval inversion
procedure can be effectively used in reducing the estimation errors
in shaly sand formations, which may refine significantly the
results of reserve calculation.