Page 193 - Machine Learning for Subsurface Characterization

Dimensionality reduction and clustering techniques Chapter 6 167

Though the formulation shown in Eq. (6.5) is simple, calculating the
incorporated parameters from well logs is a challenge.

4.2.1 Step 1: NMR decomposition using factor analysis
Wireline NMR T2 distribution (Fig. 6.5, Track 1) is an overall response of all
the fluid phases/components filling a range of pore sizes, such that the T2
signature of a fluid phase overlaps with those from other phases/components.
The NMR T2 distribution used in this study are T2 amplitudes measured at 64
discrete T2 times in the range of 0.3 ms to 3000 ms. In other words, the T2
distribution has been discretized into 64 T2 bins. The mix of constituent
signals masks the information related to the relative volumes and pore sets
occupied by various fluid phases in the pore. Volume fractions of various
fluid phases in Eq. (6.5) are obtained by decomposing the NMR T2
distribution into the contributions of individual fluid phases/components,
which in our study are oil and water. The proposed decomposition assumes
fluid phases possess distinct properties and occupy different sets of pore
spaces. We implement Jain et al.’s [32] factor analysis to decompose the
subsurface NMR-T2 distribution responses acquired in the shale formation.
Factor analysis is a statistical method to extract unobserved latent variables,
so it can only be applied to formations that share similar formation
characteristics. Factor analysis describes variability among several observed,
correlated variables in terms of a potentially lower number of unobserved
variables called factors. Hence, it serves as a dimensionality reduction
technique. For example, the variations in the 64 bins of NMR T2 distribution
mainly reflect the variations in unobserved (underlying) variables/factors,
such as bound water, bound oil, free water, and free oil.
Much like cluster analysis that involves grouping similar samples into clusters,
factor analysis involves grouping similar features into fewer constructed features.
The purpose of factor analysis is to explain observed features/variables (in our
study, the measurements for the 64 bins of NMR T2 distribution) in terms of a
much smaller number of variables called factors. These factors represent
underlying concepts that cannot be adequately measured by the original
variables. Factor analysis simplifies data. We are implementing an exploratory
factor analysis to compute the underlying factors that influence the NMR T2
distribution response measured over 64 discrete bins without setting any
predefined structure to the outcome. Factor analysis involves factor extraction
followed by factor rotation. Factor extraction involves making a choice about
the type of model as well as the number of factors to extract. Factor rotation
comes after the factors are extracted, with the goal of achieving simple structure
in order to improve interpretability. Factor analysis is applied to units with
relatively similar pore structures. In our study the upper and lower shales are
remarkably similar. The middle shale is associated with lower TOC and larger
pore sizes. Consequently, factor analysis is jointly applied to the upper and
lower shales and separately on the middle shale. Five factors were identified in
the upper and lower shales, and eight factors were identified in the middle
sections (Fig. 6.4). Each factor represents a fluid phase occupying a set of pores.