Rock Classification Using Multivariate Analysis of Measurement While Drilling Data: Towards a Better Sampling Strategy
Abstract
:1. Introduction
2. Background
3. Materials and Methods
3.1. Data
3.2. PreProcessing MWD Data
3.3. Hidden Markov Models
 Most likely sequence of rock classes given all MWD data: $\widehat{\mathit{X}}=\mathrm{argmax}\left[P\left(\mathit{X}\right\mathit{Y})\right]$.
 Estimation of model parameters $\mathit{P}$, $\mathit{\pi}$, ${\mathit{\mu}}_{k}$ for $k=1,\dots ,d$, and $\mathbf{\Sigma}$.
3.4. Rock Class Prediction
3.5. Parameter Estimation—EM Algorithm
3.6. Workflow Summary
Algorithm 1 Workflow. 

4. Results
4.1. Identifying the Best HMM for Rock Classification
 Even though fluctuations due to rod change are eliminated in the preprocessing, feed pressure and percussion pressure are showing trends in approximately every 3.5 m depth (see Figure 8). This variation is also visible in dampening pressure with less intensity. In Figure 9, one can see that MAP_{all}, MAP_{no Flushair} and MAP_{PD} are showing trends in approximately every 3.5 m depth. Because of this possible misclassification we are not considering MAP_{all}, MAP_{no Flushair} and MAP_{PD} for further analysis.
 The penetration rate depends on the pressures and the rock characteristics. In theory, a model with more variables will give better results. So MAP_{P} is also not considering further.
4.2. Precision and Characteristics of Predicted Classes
5. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
MWD  Measurement while drilling 
HMM  Hidden Markov Models 
MSUS  Magnetic Susceptibility 
SGAM  Spectral gamma 
Appendix A. ForwardBackward Algorithm
Appendix B. Parameter Updates in EM Algorithm
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MWD  193918  193921  19417 

Penetration rate (m/s)  2.20(0.22)  2.11(0.28)  1.88(0.31) 
Percussion pressure (Bar)  189.67(5.97)  189.35(5.50)  188.39(6.56) 
feed pressure (Bar)  87.69(3.95)  87.95(3.51)  87.34(4.55) 
Flush air pressure (Bar)  8.36(0.90)  8.12(0.50)  6.77(0.52) 
Rotation pressure (Bar)  56.28(2.83)  53.36(3.35)  54.17(3.65) 
Dampening pressure (Bar)  69.68(3.81)  70.44(3.32)  68.22(3.83) 
Class  Pen Rate  Rot Press  Damp Ress  MSUS  TGAM  Assigned Class 

Class118  2.2  57.7  67.5  −0.1  16.6  Pure Marble 
Class218  2.2  55.4  71.7  0  40.7  Pure Marble 
Class318  2.3  61.8  59.2  1.2  46.7  Fracture/small intrusion 
Class121  2.1  51.4  70.4  −0.1  22.2  Pure Marble 
Class221  2.3  55.8  71.3  0.5  20.1  Pure Marble 
Class321  1.6  58.2  67.6  8.9  116.5  Hard Intrusion 
Class17  1.7  51.8  69.0  0.3  43.5  Pure Marble 
Class27  1.9  56.5  68.6  0.5  71.5  Impure Marble 
Class37  2.5  60.7  63.3  0.9  90.8  Fracture 
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Vezhapparambu, V.S.; Eidsvik, J.; Ellefmo, S.L. Rock Classification Using Multivariate Analysis of Measurement While Drilling Data: Towards a Better Sampling Strategy. Minerals 2018, 8, 384. https://doi.org/10.3390/min8090384
Vezhapparambu VS, Eidsvik J, Ellefmo SL. Rock Classification Using Multivariate Analysis of Measurement While Drilling Data: Towards a Better Sampling Strategy. Minerals. 2018; 8(9):384. https://doi.org/10.3390/min8090384
Chicago/Turabian StyleVezhapparambu, Veena S., Jo Eidsvik, and Steinar L. Ellefmo. 2018. "Rock Classification Using Multivariate Analysis of Measurement While Drilling Data: Towards a Better Sampling Strategy" Minerals 8, no. 9: 384. https://doi.org/10.3390/min8090384