Summary
Many problems in reservoir characterization require the formulation and
solution of an inverse problem. The definition of the inverse problem is the
prediction of reservoir properties from measurements made on the reservoir. The
most familiar example of an inverse problem is well-log interpretation. Well
logging involves the acquisition of various kinds of data for the purpose of
predicting reservoir properties of the earth formations near the borehole.
Conventional inverse methods used in the industry today typically involve
the constrained minimization of a weighted sum of the squared deviations
between a set of measurements and a forward-model equation or equations. The
forward-model equations are either empirically or theoretically derived
equations. These equations relate the reservoir property to be predicted (e.g.,
saturation, permeability) to measurements (e.g., resistivity, T2 distributions,
porosity). Adjustable parameters in the forward-model equations are determined
using a "calibration database" of laboratory measurements made on a suite of
representative samples. This traditional methodology suffers from fundamental
limitations that stem from the fact that reservoir rocks and fluids are too
complex to be described accurately by the simple idealized equations that are
used today as forward models. Additionally, the forward models contain
adjustable parameters that can vary over a wide range, thereby leading to
additional inaccuracies in reservoir properties.
Our paper discusses a new model-independent inversion method that overcomes
the limitations and inaccuracies of the conventional method. The new inversion
method predicts reservoir properties without the need to use idealized model
equations or to solve minimization problems. The new method divides the
calibration database into input measurements (i.e., used for the predictions)
and output measurements (i.e., the reservoir properties to be predicted). The
outputs are mapped to the inputs using model-independent mapping functions
constructed from Gaussian radial-basis functions (RBFs). The RBF mapping
functions are accurate representations of the functional relationship between
the database inputs and outputs. The coefficients of the mapping function can
be determined uniquely using the database. Once the coefficients are
determined, there are no adjustable parameters.
The new method is applicable to a wide variety of reservoir-characterization
problems. The construction of the mapping functions is presented in detail. We
apply the method to a challenging problem in nuclear well logging: accurate
predictions of formation thermal neutron-capture cross sections (sigma) from
well-logging data. Logs of formation ∑ predicted using the conventional
regression method and using the new method are compared and discussed.
© 2012. Society of Petroleum Engineers
View full textPDF
(
5,069 KB
)
History
- Original manuscript received:
23 December 2011
- Meeting paper published:
31 October 2011
- Revised manuscript received:
8 March 2012
- Manuscript approved:
10 April 2012
- Published online:
30 June 2012
- Version of record:
7 August 2012
View Cart
