Newly Developed Correlations to Predict the Rheological Parameters of High-Bentonite Drilling Fluid Using Neural Networks
Abstract
:1. Introduction
1.1. High-Bentonite Mud (HBM)
1.2. Drilling Fluid Rheology
1.3. Predicting the Rheological Properties of Drilling Fluid While Drilling
2. Methodology
2.1. Experimental Work
2.2. Implementation of Artificial Neural Network (ANN) to Predict HBM Rheology
2.2.1. Data Description
2.2.2. Quality Check and Data Filtration
2.2.3. Model Development
- –
- Number of hidden layers (ranges from one to four layers)
- –
- Number of neurons in each layer (range 5: 30 neurons for each layer)
- –
- Transfer functions (tansig, logsig, elliotsig, radbas, satlin, purelin, tribas, hardlim)
- –
- Training algorithm (trainlm, trainrp, traingd, traingda, trainbr, trainc)
- –
- Learning rate (ranges from 0.01 to 0.9)
3. Results and Discussion
3.1. Yield Point Prediction
3.2. Plastic Viscosity Prediction
3.3. Apparent Viscosity Prediction
3.4. Apparent Viscosity Model Validation
4. Conclusions
- The new ANN models can predict the rheological parameters (PV, YP, and AV) for HBM while drilling based on MD and FV with high accuracy (R-value was greater than 0.90 and AAPE was less than 6%).
- The optimized models were developed using a network of a single hidden layer with 20 neurons processed by Levenberg-Marquardt algorithm. The optimum training rate was 0.12 for developing the ANN models. Tan-sigmoidal was used as a transfer function to get the best results with the linear function as an activation function for the output layer.
- The developed ANN-based empirical equations provide a practical way to estimate the rheological parameters of HBM directly without requiring any special programs or compilers.
- The developed ANN-based model for the apparent viscosity outperformed the previously published correlations.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
HBM | High-bentonite mud |
MD | Mud density |
FV | Marsh funnel viscosity |
Yp | yield point |
PV | Plastic viscosity |
AV | Apparent viscosity |
ECD | Equivalent circulating density |
AAPE | Average absolute percentage error |
R | Correlation coefficient |
tansig | Hyperbolic tangent sigmoid transfer function |
logsig | Log-sigmoid transfer function |
elliotsig | Elliot symmetric sigmoid transfer function |
radbas | Radial basis transfer function |
purelin | Linear transfer function |
Tribas | Triangular basis transfer function |
hardlim | Hard-limit transfer function |
satlin | Saturating linear transfer function |
trainlm | Levenberg-Marquardt backpropagation |
trainrp | Resilient backpropagation |
trainbr | Bayesian regularization |
trainc | Cyclical order incremental update |
traingda | Gradient descent with adaptive learning rule backpropagation |
traingd | Gradient descent backpropagation |
Appendix A
Appendix B
i | |||||
---|---|---|---|---|---|
j = 1 | j = 2 | ||||
1 | −6.438 | −1.722 | −0.976 | 5.256 | −0.646 |
2 | −3.871 | −5.183 | −1.309 | 5.189 | |
3 | 1.196 | 8.918 | 1.450 | −4.763 | |
4 | 5.324 | 3.405 | −0.843 | −5.262 | |
5 | −4.281 | −3.710 | 0.938 | 5.971 | |
6 | −0.898 | 8.725 | −1.511 | −4.598 | |
7 | −6.191 | 0.259 | 0.783 | 3.726 | |
8 | −6.592 | −0.724 | 0.333 | 0.379 | |
9 | 7.256 | 1.198 | 0.466 | −1.105 | |
10 | 5.796 | 1.522 | 0.252 | 3.285 | |
11 | 5.534 | −1.909 | −0.561 | 3.017 | |
12 | −5.377 | −10.789 | −0.131 | −4.180 | |
13 | −0.876 | −10.431 | −0.192 | 0.002 | |
14 | 5.633 | −2.006 | −1.256 | 3.742 | |
15 | 5.424 | −3.472 | 0.839 | 3.876 | |
16 | 5.851 | −7.147 | 0.596 | 3.011 | |
17 | −4.425 | 2.739 | −0.628 | −5.963 | |
18 | −9.930 | −3.096 | 0.126 | −1.936 | |
19 | −5.837 | 12.148 | 0.667 | −5.094 | |
20 | −9.246 | 1.508 | −0.581 | −5.767 |
i | |||||
---|---|---|---|---|---|
j = 1 | j = 2 | ||||
1 | 3.457 | 4.020 | 0.190 | −7.611 | 0.811 |
2 | −5.002 | 3.575 | 1.172 | 6.281 | |
3 | −5.545 | −3.368 | −0.390 | 5.267 | |
4 | −6.538 | −1.564 | −0.718 | 2.211 | |
5 | 5.248 | −2.050 | −0.798 | −4.631 | |
6 | −2.253 | 3.617 | −0.827 | 3.458 | |
7 | −3.930 | 6.908 | 0.134 | 2.085 | |
8 | −9.102 | 5.892 | 0.675 | 3.095 | |
9 | −1.800 | −7.060 | 0.258 | −2.057 | |
10 | −1.567 | 4.346 | 0.584 | −3.198 | |
11 | 10.680 | −7.060 | −0.188 | 1.384 | |
12 | 2.985 | −0.144 | 0.230 | −0.355 | |
13 | −3.206 | 1.819 | −0.608 | 0.834 | |
14 | −1.983 | −0.408 | 0.274 | −0.381 | |
15 | −5.065 | 1.269 | −0.124 | −2.345 | |
16 | −0.031 | −9.201 | 0.150 | −4.596 | |
17 | −4.567 | −5.151 | −0.424 | −2.586 | |
18 | 6.310 | 0.927 | −1.990 | 6.763 | |
19 | 2.492 | 5.563 | 0.158 | 6.596 | |
20 | −6.164 | 0.435 | −1.146 | −5.166 |
i | |||||
---|---|---|---|---|---|
j = 1 | j = 2 | ||||
1 | 7.678 | −2.892 | 0.384 | −4.868 | −0.365 |
2 | 3.632 | −5.384 | −1.561 | −6.839 | |
3 | 4.647 | 4.557 | 0.499 | −2.401 | |
4 | −5.234 | −2.113 | −0.325 | 5.115 | |
5 | 6.199 | 0.612 | 0.510 | −4.399 | |
6 | −6.369 | 3.674 | 1.956 | 2.124 | |
7 | −2.347 | 5.874 | −0.911 | −2.496 | |
8 | 0.733 | −6.371 | 1.034 | −5.309 | |
9 | −8.594 | 3.012 | −1.277 | 1.524 | |
10 | 1.460 | −3.995 | −1.316 | 1.886 | |
11 | 7.201 | −9.123 | −0.219 | −0.057 | |
12 | 7.542 | 6.624 | −0.229 | −1.789 | |
13 | −1.736 | −7.167 | 0.574 | −1.700 | |
14 | −2.995 | −0.354 | 0.103 | −10.009 | |
15 | 5.760 | 3.549 | 0.693 | 2.579 | |
16 | −8.152 | 0.364 | 0.029 | −2.345 | |
17 | −2.961 | 5.941 | 0.593 | 1.817 | |
18 | 0.420 | 7.370 | −0.733 | 3.554 | |
19 | −8.938 | −2.516 | −0.356 | −6.634 | |
20 | −4.404 | −1.935 | −0.346 | −9.442 |
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Additive | Range/Unit | Uses |
---|---|---|
Bentonite | 40–50 lb/bbl | Viscosifier Fluid loss control |
Enviro-thin | 1–3 lb/bbl | Dispersant Shear strength reduce/deflocculant |
Caustic Soda (NaOH) | 0.2–0.5 lb/bbl | pH adjustment |
Starch | 1–3 lb/bbl | Fluid loss control |
Bactcide | 0.01–0.03 gal/bbl | Antibacterial/Biocide |
Item | Quantity | Unit |
---|---|---|
Water | 340 | g |
Bentonite | 40 | g |
Caustic Soda | 0.5 | g |
Dispersant | 3 | g |
Starch | 3 | g |
Statistical Quantity | MD | FV | PV | Yp | AV |
---|---|---|---|---|---|
Mean | 67.6 | 85.4 | 25.2 | 30.3 | 40.3 |
Median | 68.0 | 82.0 | 25.0 | 30.0 | 40.0 |
Mode | 68.0 | 85.0 | 25.0 | 26.0 | 40.0 |
Range | 9.0 | 105.0 | 45.0 | 26.0 | 56.0 |
Minimum | 64.0 | 45.0 | 11.0 | 20.0 | 23.0 |
Maximum | 73.0 | 150.0 | 56.0 | 46.0 | 79.0 |
Standard Deviation | 1.4 | 19.6 | 8.0 | 5.3 | 9.5 |
Kurtosis | 6.2 | 1.1 | 1.7 | 0.8 | 2.0 |
Skewness | 1.5 | 1.0 | 0.9 | 0.7 | 0.9 |
No. | MD (lb/ft3) | FV (s) | PV (cP) | Yp (lb/100 ft2) | AV (cP) |
---|---|---|---|---|---|
1 | 68 | 60 | 11 | 28 | 25 |
2 | 64 | 135 | 13 | 20 | 23 |
3 | 69 | 80 | 12 | 27 | 25.5 |
4 | 73 | 70 | 15 | 30 | 30 |
5 | 67 | 75 | 16 | 22 | 27 |
6 | 68 | 59 | 11 | 27 | 24.5 |
7 | 69 | 85 | 40 | 25 | 52.5 |
8 | 66 | 150 | 45 | 40 | 65 |
9 | 68 | 110 | 31 | 31 | 46.5 |
10 | 67 | 90 | 31 | 36 | 49 |
11 | 68.5 | 76 | 29 | 28 | 43 |
12 | 67 | 105 | 29 | 36 | 47 |
13 | 73 | 108 | 40 | 28 | 54 |
14 | 67 | 92 | 40 | 36 | 58 |
15 | 68.5 | 75 | 32 | 26 | 45 |
Property | Range | Unit | Remarks |
---|---|---|---|
Mud weight | 67 | lb/ft3 | Mud balance measurement |
Marsh Funnel Viscosity | 75–120 | s | Qualitative measurement |
pH | 9.5–10.5 | Alkalinity measurement | |
Initial Gel Strength | 15–27 | lb/100 ft2 | 10-senocd rheometer measurement |
10-min Gel Strength | 25–75 | lb/100 ft2 | 10-min rheometer measurement |
30-min Gel Strength | 26–80 | lb/100 ft2 | 30-min rheometer measurement |
Yield Point | 25–50 | lb/100 ft2 | Rheometer measurement |
Plastic Viscosity | 10–60 | cP | Rheometer measurement |
Filtrate Volume | 8–10 | cm3/30 min | Filter Press measurement |
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Gowida, A.; Elkatatny, S.; Abdelgawad, K.; Gajbhiye, R. Newly Developed Correlations to Predict the Rheological Parameters of High-Bentonite Drilling Fluid Using Neural Networks. Sensors 2020, 20, 2787. https://doi.org/10.3390/s20102787
Gowida A, Elkatatny S, Abdelgawad K, Gajbhiye R. Newly Developed Correlations to Predict the Rheological Parameters of High-Bentonite Drilling Fluid Using Neural Networks. Sensors. 2020; 20(10):2787. https://doi.org/10.3390/s20102787
Chicago/Turabian StyleGowida, Ahmed, Salaheldin Elkatatny, Khaled Abdelgawad, and Rahul Gajbhiye. 2020. "Newly Developed Correlations to Predict the Rheological Parameters of High-Bentonite Drilling Fluid Using Neural Networks" Sensors 20, no. 10: 2787. https://doi.org/10.3390/s20102787
APA StyleGowida, A., Elkatatny, S., Abdelgawad, K., & Gajbhiye, R. (2020). Newly Developed Correlations to Predict the Rheological Parameters of High-Bentonite Drilling Fluid Using Neural Networks. Sensors, 20(10), 2787. https://doi.org/10.3390/s20102787