Отправлено: 22.05.11 07:14. Заголовок: Validation of Input and Output Parameters for Realistic Evaluation of Open Hole Logs Through Inverse

6th International Conference & Exposition on Petroleum Geophysics “Kolkata 2006”
(797)
Validation of Input and Output Parameters for Realistic Evaluation of Open Hole Logs Through Inverse Modeling

Lalaji Yadav*, Narayan Singh Rawat, Aloke Kr Bhanja and Kamaleshwar Rai

KDMIPE ONGC Dehradun


Introduction
Solving the simultaneous system of logging tool
response equations through statistical approach by using
weighted least square minimization technique performs
inversion of open hole logs. It involves minimization of the
objective function i.e. summation of square of errors between
the measured and constructed logs by incorporating the total
uncertainties on tools, parameters and response equations.
Global minimum for objective function is ensured only for
a particular combination of input and output parameters.
However, theoretically same value of objective function can
be achieved with infinite number of combinations of input /
output parameters, even with uniquely determined system
of equations i.e. equal number of unknowns and equations.
Hence, validation of input/ output parameters becomes
essential part of log data processing / interpretation with
greater degree of authenticity, similar to calibration of
logging tools prior to recording of logs.
Standard log response parameters for almost all
type and group of known minerals are generally well
published and available along with inverse modeling
packages. These parameters cannot be directly used for
inversion of logs, as formations in nature cannot be modeled
with limited number of pure mineral constituents. Actually,
lumping of the group of minerals is done to keep the number
of minerals less than or equal to the available number of
Summary
Inversion of open hole logs is performed by solving the simultaneous system of logging tool response equations
through statistical approach by using weighted least square minimization technique. It involves minimization of the objective
function i.e. summation of square of errors between the measured and constructed logs by incorporating the total uncertainties
on tools, parameters and response equations. Global minimum for objective function is ensured for a particular combination of
input and output parameters. However, theoretically same value of objective function can be achieved with infinite number of
combinations of input / output parameters, even with uniquely determined system of equations. Imposition of geological and
geophysical constraints on the solutions brings it to a finite but still too large to fix it for a unique set of parameters. Further,
imposition of constraints from core measurements viz. porosity, mineral volumes and grain density and production testing
results on input/output parameters, makes the parameters selection easier and more realistic in a particular geological setting.
Hence, validation of input/output parameters becomes essential part of log data processing / interpretation with greater degree
of authenticity, similar to calibration of logging tools prior to recording / presentation of logs.
All the inverse modeling packages are to be treated as weighted least square solver of approximate linear/nonlinear
simultaneous tool response equations with geological and geophysical constraints imposed on the solutions and provide no
means for model selection and verification. Validation of I/O parameters is to be ensured by its calibration against known
lithologies like clean sand, limestone or shale/clay zones if available. Otherwise, log response parameters for the respective
component has to be derived from partial effects seen on the log by using linear extrapolation technique on cross plots where
log responses of the different constituents are defined as vertices of a multidimensional polygon defined by the number of
available log measurements. Multidimensional polygon is visualized by generating cross plots for all the possible subsets/
planes viz. four log measurements will have six planes / cross plots. Vertices of the rock components are kept same on the entire
cross plots.

http://www.spgindia.org/conference/6thconf_kolkata06/23.pdf