Application of artificial neural network to predict the rate of penetration for S-shape well profile

Abstract

The rate of penetration (ROP) is defined as the required speed to break the drilled rock by the bit action. The existing established models for estimating the rate of penetration include the basic mathematical correlation that have many limitations. The objective of this paper is to implement an artificial neural network (ANN) technique to predict the rate of penetration for the S-shape well profile from the surface drilling data. The data used to build the ANN model is based on real field data of more than 7900 data points obtained from two wells. The data from well A and B was used to train and test an ANN model, while 4000 unseen data points from well C were used for validation. More than 30 sensitivity analyses were performed and the results showed that ANN-ROP model has a high performance with an average correlation coefficient of around 0.93 and a root mean square error (RMSE) of 6.2%. The best ANN parameter combination was with 1 layer, 29 neurons, tan-sigmoid as the transfer function, and trainlm as the training function. The model was then validated by the data from well C which was unseen by the model during the training and testing stage with a correlation coefficient of 0.92 and an RMSE of 6.7%. To enable ROP prediction in real time, an empirical correlation was developed based on the optimized ANN model weights and biases.

Appendices

Appendix 1

The table below summarizes multiple published ROP models including ones that were developed empirically or using artificial intelligence techniques.

Table 8 Summary of previous ROP models

Appendix 2

The governing factors for selection of the optimum parameters were the correlation coefficient (R) and the root mean square error (RMSE) which are defined by the following equations, respectively:

$$ R=\sqrt{1-\frac{\sum_{\mathrm{i}}^N{\left({y}_{\mathrm{i}\mathrm{act}}-{y}_{\mathrm{i}\mathrm{pred}}\right)}^2}{\sum_{\mathrm{i}}^N{\left({y}_{\mathrm{i}\mathrm{act}}\right)}^2-\frac{\sum_{\mathrm{i}}^N{\left({y}_{\mathrm{i}\mathrm{pred}}\right)}^2}{N}}} $$

(B1)

$$ RMSE=\sqrt{\sum_{i=1}^N\frac{{\left({y}_{\mathrm{iact}}-{y}_{\mathrm{ipred}}\right)}^2}{N}} $$

(B2)

where y_iact is the actual value, y_ipred is the predicted value, and N is the number of data points. Higher accuracy and better performance of prediction are indicated by higher values of R and lower values of RMSE.