# A machine learning approach to predict drilling rate using petrophysical and mud logging data

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## Abstract

Predicting the drilling rate of penetration (ROP) is one approach to optimizing drilling performance. However, as ROP behavior is unique to specific geological conditions its application is not straightforward. Moreover, ROP is typically affected by various operational factors (e.g. bit type, weight-on-bit, rotation rate, etc.) as well as the geological characteristics of the rocks being penetrated. This makes ROP prediction an intricate and multi-faceted problem. Here we compare data mining methods with several machine learning algorithms to evaluate their accuracy and effectiveness in predicting ROP. The algorithms considered are: artificial neural networks (ANN) applying a multi-layer perceptron (MLP); ANN applying a radial basis function (RBF); support vector regression (SVR), and an hybrid MLP trained using a particle swarm optimization algorithm (MLP-PSO). Data preparation prior to executing the algorithms involves applying a Savitzky–Golay (SG) smoothing filter to remove noise from petrophysical well-logs and drilling data from the mud-logs. A genetic algorithm is applied to tune the machine learning algorithms by identifying and ranking the most influential input variables on ROP. This tuning routine identified and selected eight input variables which have the greatest impact on ROP. These are: weight on bit, bit rotational speed, pump flow rate, pump pressure, pore pressure, gamma ray, density log and sonic wave velocity. Results showed that the machine learning algorithms evaluated all predicted ROP accurately. Their performance was improved when applied to filtered data rather than raw well-log data. The MLP-PSO model as a hybrid ANN demonstrated superior accuracy and effectiveness compared to the other ROP-prediction algorithms evaluated, but its performance is rivalled by the SVR model.

## Keywords

Rate of penetration Data mining Machine-learning predictions ROP variables Feature selection ranking Data filtering## Nomenclature

*WOB*Weight on bit

*BRS*Bit rotation speed

*BFR*Bit flow rate

*PP*Pump pressure

*MW*Mud weight

*GR*Gamma ray

*T*_{s}Sonic shear velocity

*T*_{p}Sonic compressional velocity

*P*_{p}Pore pressure

*NP*Neutron porosity

*DT*Decision tree

*RF*Random forest

*MLP*Multi-layer perception

*RBF*Radial- basis function

*SVR*Support vector regression

*PSO*Particle swarm optimization

*x*Input variable value

*W*Weight matrix

*b*Bias vector

*N*Number of clusters

*M*Number of input and output variables

*δ*Slack variable

*ε*Error- monitoring parameter

*a*Lagrange multiplier

*K*Kernel function

*c*_{i}Center of RBF unit i

*RMSE*Root mean square error

*PI*Performance index

*VAF*Variance account for

## Notes

## Supplementary material

## References

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