Page 105 - Machine Learning for Subsurface Characterization

Shallow neural networks and classification methods Chapter 3 87

original NMR T 2 distribution to test the robustness of the predicted NMR T 2 .
The first ANN model being the better performing predictive model, as com-
pared with the second ANN. In this section, we focus on the first ANN model.
Petrophysical validation of the first model is demonstrated by comparing ϕ N
and T 2,gm derived from the original NMR T 2 distribution with those derived
from the ANN-based predictions of T 2 distribution. ϕ N is the sum of all ampli-
tudes (values) of the 64 bins of a T 2 distribution at a single depth. T 2,gm is the
64th root of the product of the 64 discretized T 2 amplitudes at a single depth.
Details of the calculation procedures are in Appendix D. Schlumberger-Doll
Research (SDR) model is a popular model for the estimation of permeability
based on ϕ N and T 2,gm , which is expressed as
4

k SDR ¼ C T 2 ϕ ¼ C T 2,gm ϕ 2 2 (3.11)
2,gm N N
where k SDR is the permeability computed using the SDR model and C is a con-
2
stant. We derived the SDR-model term, T 2,gm ϕ N , in Eq. (3.11) using the orig-
inal and predicted NMR T 2 distribution and then compare them to test the
accuracy of the ANN-based predictions of NMR T 2 for purposes of permeability
estimation based on the SDR model. Comparison results are presented in
Fig. 3.10. Table 3.2 indicates that the ANN-based predictions of NMR T 2
can be reliably used to compute the three reservoir parameters of interest with
good accuracy.
Fig. 3.C1 can serve as another petrophysical validation of the ANN-based T 2
synthesis model because it indicates lithology, chlorite content, sonic travel
time logs, isolated porosity, rock consolidation, clay content, fluid saturations,
and porosity to be important for the NMR T 2 synthesis. The importance of fea-
tures as shown in Fig. 3.C1 is consistent with physical dependence of NMR logs
response on pore size, mineralogy, fluid distribution, and bound fluids.

3.7 ANN-based predictions of NMR T 2 distribution for various depth
intervals
Prediction accuracy is the lowest in the MS formation (Table 3.3). The grain size
in MS ranges from poorly sorted siltstone to moderately well sorted sandstone.
Varying grain size and depositional texture in MS result in more complex pore
size distribution that deteriorates the correlations between the feature logs and
NMR T 2 distribution in MS. Features in MS tend to have unusually high coeffi-
cients of variation (Fig. 3.A2). Furthermore, prediction accuracy in CR1 is lower
than those in CR2, CR3, and CR4 formations (Table 3.3). Although all intervals
of CR have relatively similar lithology and mineral composition, CR1 is the thin-
nest, and CR4 is the thickest among the four (Fig. 3.2). The difference of thick-
ness of intervals and the resulting limited training data led to the differences in the
prediction accuracies in the various CR intervals. Features in CR1 tend to have
unusually high coefficients of variation as compared with CR2, CR3, and CR4
intervals (Fig. 3.A2). Prediction accuracy is the highest in CR4 because CR4
is a thick interval with predominance of dolosiltite. Simple grain size and