#
Data-Driven Framework to Predict the Rheological Properties of CaCl_{2} Brine-Based Drill-in Fluid Using Artificial Neural Network

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## Abstract

**:**

## 1. Introduction

#### 1.1. Drilling Fluid Rheology

_{2}brine-based drilling fluid depending on frequent measurements of $MW$ and $MF$. The real-time measurements of these parameters are very helpful for identifying the efficiency of the hole cleaning, optimizing the drilling fluid hydraulics, equivalent circulating density calculations and swab and surge pressure determination.

#### 1.2. Artificial Neural Network (ANN)

## 2. Methodology

#### 2.1. Data Description

_{2}brine-based drill-in fluid (515 field data for actual mud samples) is listed in Table 1, including $\left(MW,MF,PV,\mathrm{and}{Y}_{p}\right)$. The drilling fluid samples are collected after the mud was cleaned from the cuttings by using the shale shaker $MW$ and $MF$ are measured in the field using a mud balance and Marsh funnel, respectively. The rheometer is used for measuring the rheology of the mud, namely $PV,\mathrm{and}{Y}_{p}$ at atmospheric pressure and ${120}^{o}F$. The collected data have a wide range as follows: $MW$ ranges from 43 to 119 $Ib/f{t}^{3}$, $MF$ ranges from 26 to 135 $s/quart$, $PV$ ranges from 10 to 54 cP, and ${Y}_{P}$ ranges from 8 to 41 $Ib/100f{t}^{2}$. Figure 1 shows that $MW$ has R of 0.36 and 0.76 with ${Y}_{P}$ and $PV$ respectively while $MF$ has R of 0.86 with ${Y}_{P}$ and 0.36 with $PV$.

#### 2.2. Development of ANN Models

- –
- Input layer: It contains input features which are $MW$ and $MF$.
- –
- (One) Hidden layer: It contains the optimized number of neurons which was found to be 20 neurons.
- –
- Output layer: It contains the output parameters, which are ($PV,{Y}_{P},AV,n$ and $k$ individually).

## 3. Results and Discussion

#### 3.1. Yield Point (${Y}_{P}$) Model

#### 3.2. Apparent Viscosity ($AV$) Model

#### 3.3. Plastic Viscosity ($PV$) Model

#### 3.4. Prediction Power Law Model Parameters (n and k)

#### 3.5. Validation of the Apparent Viscosity ($AV$) Model vs the Models in the Literature

## 4. The Value of Predicting the Drilling Fluid Rheology in Real-Time

## 5. Conclusions

_{2}brine-based drill-in fluid in a real-time (15–20 min) including ($PV,{Y}_{P},AV,n$ and $k$) using 515 field data measurements of $MW$ and $MF$ in ratios 70:30 for training and validating the ANN models respectively. Accordingly, the following conclusions can be drawn:

- (1)
- The new ANN models can predict the rheological parameters $\left(PV,{Y}_{p},AV,n,andk\right)$ in real time based on $MW$ and $MF$ with high accuracy (R was greater than 0.97 and AAPE was less than 6.1%).
- (2)
- The optimization process for the ANN models showed that the optimized parameters yielding the highest accuracy and the lowest error were 20 neurons for only one hidden layer, the Levenberg-Marquardt algorithm of learning rate 0.12. The activation function linking the input and hidden layers was the tan-sigmoidal function, while a linear function was used for linking the hidden and output layers.
- (3)
- The extracted correlations from the developed ANN models provide the ability to estimate the rheological properties of CaCL
_{2}brine-based mud directly without the need to run the models. - (4)
- These models are very helpful in the calculations of rig hydraulics, surge and swab pressures, and ECD.
- (5)
- The developed correlations can help in predicting several drilling problems by providing the ability for real-time monitoring of the hole cleaning performance, and detecting any abnormal changes in the normal trends to avoid interrupting problems like sticking. As a result, this will save on the drilling cost, and it optimizes the drilling operation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The relative importance of $MW$ and $MF$ with the rheological properties (${Y}_{P}$ and $PV$) of CaCL

_{2}brine-based mud in terms of the correlation coefficient, R.

$\mathit{M}\mathit{W},\mathit{I}\mathit{b}/\mathit{f}{\mathit{t}}^{3}$ | $\mathit{M}\mathit{F},\mathit{s}/\mathit{q}\mathit{u}\mathit{a}\mathit{r}\mathit{t}$ | $\mathit{P}\mathit{V},\mathit{c}\mathit{P}$ | ${\mathit{Y}}_{\mathit{P}},\mathit{I}\mathit{b}/100\mathit{f}{\mathit{t}}^{2}$ |
---|---|---|---|

78 | 62 | 8 | 21 |

80 | 45 | 8 | 22 |

88 | 62 | 12 | 18 |

73 | 50 | 11 | 20 |

65 | 48 | 11 | 21 |

75 | 44 | 12 | 20 |

Parameter | $\mathit{M}\mathit{W},\mathit{I}\mathit{b}/\mathit{f}{\mathit{t}}^{3}$ | $\mathit{M}\mathit{F},\mathit{s}/\mathit{q}\mathit{u}\mathit{a}\mathit{r}\mathit{t}$ | $\mathit{P}\mathit{V},\mathit{c}\mathit{P}$ | ${\mathit{Y}}_{\mathit{P}},\mathit{I}\mathit{b}/100\mathit{f}{\mathit{t}}^{2}$ |
---|---|---|---|---|

Min. | 43 | 26 | 10 | 8 |

Max. | 119 | 135 | 54 | 41 |

Mean | 85.45 | 56.33 | 22.59 | 25.88 |

Mode | 76 | 109 | 44 | 33 |

Range | 72 | 50 | 19 | 24 |

Skewness | 0.50 | 1.43 | 1.29 | 0.83 |

Neural Network Parameter | Types and Range |
---|---|

Training Algorithm | Levenberg Marquardt |

Number of neurons | 20 |

Number of hidden layer(s) | 1 |

Learning rate | 0.12 |

The hidden layer transfer function | Tan-sigmoidal |

The outer layer transfer function | Pure-linear |

Training ratio | 70% |

Testing ratio | 30% |

Neuron Index | Input Layer Weights | Hidden Layer Weights | Input Layer Biases | Output Layer Bias | |
---|---|---|---|---|---|

$i$ | ${w}_{{1}_{i,1}}$ | ${w}_{{1}_{i,2}}$ | ${w}_{2,i}$ | ${b}_{1,i}$ | ${b}_{2}$ |

1 | −4.251 | 5.585 | −0.950 | 5.530 | −0.508 |

2 | −0.709 | −6.857 | −0.155 | 4.936 | - |

3 | 2.631 | 5.539 | 0.168 | −4.752 | - |

4 | −0.743 | 6.411 | 1.005 | 3.899 | - |

5 | −4.986 | 5.903 | −0.932 | 3.661 | - |

6 | −5.203 | −0.250 | −1.022 | 3.135 | - |

7 | 4.859 | 4.645 | −0.410 | −2.792 | - |

8 | −1.185 | −6.192 | 0.721 | 2.879 | - |

9 | 4.188 | −3.646 | −1.697 | −3.015 | - |

10 | 3.238 | −5.080 | 0.297 | −0.585 | - |

11 | 0.708 | −7.849 | −0.380 | 0.213 | - |

12 | −4.893 | −9.220 | −0.428 | −1.489 | - |

13 | 2.227 | −6.971 | −1.173 | 2.051 | - |

14 | 3.101 | 5.504 | −1.046 | 1.840 | - |

15 | −6.059 | −1.558 | −0.030 | −3.063 | - |

16 | −5.020 | 3.702 | −0.902 | −3.873 | - |

17 | 2.892 | 5.503 | −0.260 | 4.287 | - |

18 | −0.736 | −5.668 | 0.190 | −5.818 | - |

19 | 4.290 | −4.592 | 0.639 | 5.571 | - |

20 | −4.290 | 4.570 | −0.686 | −6.252 | - |

Neuron Index | Input Layer Weights | Hidden Layer Weights | Input Layer Biases | Output Layer Bias | |
---|---|---|---|---|---|

$i$ | ${w}_{{1}_{i,1}}$ | ${w}_{{1}_{i,2}}$ | ${w}_{2,i}$ | ${b}_{1,i}$ | ${b}_{2}$ |

1 | 2.960 | 7.136 | −0.950 | −5.667 | 1.535 |

2 | −5.586 | −7.703 | −0.155 | 2.751 | - |

3 | 4.037 | 5.355 | 0.168 | −1.886 | - |

4 | −3.362 | 3.743 | 1.005 | 2.292 | - |

5 | 6.295 | −5.066 | −0.932 | −8.110 | - |

6 | 0.406 | 7.091 | −1.022 | 6.492 | - |

7 | −10.26 | −8.654 | −0.410 | −0.995 | - |

8 | −0.572 | −9.022 | 0.721 | −0.909 | - |

9 | −7.565 | 4.329 | −1.697 | 4.884 | - |

10 | −4.256 | 3.855 | 0.297 | 2.094 | - |

11 | 6.458 | 1.765 | −0.380 | 1.786 | - |

12 | 4.537 | −4.152 | −0.428 | 1.324 | - |

13 | −5.410 | 3.103 | −1.173 | −2.553 | - |

14 | −4.859 | −2.202 | −1.046 | −1.924 | - |

15 | −7.190 | 1.704 | −0.030 | −4.783 | - |

16 | 2.196 | −5.993 | −0.902 | 2.408 | - |

17 | −0.576 | 6.113 | −0.260 | −4.569 | - |

18 | −2.889 | −4.782 | 0.190 | −4.645 | - |

19 | −3.799 | −7.588 | 0.639 | −2.337 | - |

20 | −3.877 | 4.861 | −0.686 | −6.301 | - |

Neuron Index | Input Layer Weights | Hidden Layer Weights | Input Layer Biases | Output Layer Bias | |
---|---|---|---|---|---|

$i$ | ${w}_{{1}_{i,1}}$ | ${w}_{{1}_{i,2}}$ | ${w}_{2,i}$ | ${b}_{1,i}$ | ${b}_{2}$ |

1 | −3.740 | 4.001 | 1.983 | 9.616 | −1.831 |

2 | −3.304 | −5.296 | −1.243 | −5.482 | - |

3 | −11.57 | −3.788 | 3.380 | 7.537 | - |

4 | −6.403 | −2.376 | −4.833 | 4.301 | - |

5 | 1.308 | 7.156 | −0.307 | 2.069 | - |

6 | 0.457 | −12.03 | 1.182 | 1.413 | - |

7 | −3.684 | 10.384 | −0.141 | 3.236 | - |

8 | 1.511 | −3.887 | 1.414 | −3.601 | - |

9 | −7.490 | −1.848 | 1.788 | 6.460 | - |

10 | −5.945 | −6.028 | −0.985 | 5.412 | - |

11 | 2.211 | −1.365 | −1.087 | −1.030 | - |

12 | 6.136 | −3.409 | 1.093 | 3.100 | - |

13 | −0.450 | −2.759 | 0.560 | 1.993 | - |

14 | 15.104 | 15.336 | 0.612 | 1.763 | - |

15 | 8.423 | 2.774 | 0.501 | 7.032 | - |

16 | −6.361 | −2.459 | −0.544 | −1.495 | - |

17 | −5.252 | 5.003 | 1.075 | −1.282 | - |

18 | −4.470 | −4.547 | 1.533 | −5.938 | - |

19 | −3.457 | 6.210 | 1.761 | −2.930 | - |

20 | 3.769 | −5.543 | 1.014 | 5.828 | - |

Neuron Index | Input Layer Weights | Hidden Layer Weights | Input Layer Biases | Output Layer Bias | |
---|---|---|---|---|---|

$i$ | ${w}_{{1}_{i,1}}$ | ${w}_{{1}_{i,2}}$ | ${w}_{2,i}$ | ${b}_{1,i}$ | ${b}_{2}$ |

1 | 11.343 | −1.862 | −0.798 | −9.530 | −0.867 |

2 | 2.093 | −7.313 | −1.517 | −7.827 | - |

3 | −0.197 | 7.842 | −0.937 | 5.778 | - |

4 | 6.518 | −3.319 | 2.163 | −5.132 | - |

5 | 4.967 | 1.743 | −1.977 | −3.641 | - |

6 | −5.643 | −4.788 | 0.789 | 2.501 | - |

7 | 7.452 | −2.491 | 1.194 | −1.205 | - |

8 | −8.873 | 1.168 | 1.495 | 0.426 | - |

9 | −3.821 | 0.042 | −8.516 | 2.781 | - |

10 | −4.896 | 1.759 | 6.460 | 3.734 | - |

11 | −6.355 | −8.089 | 0.160 | −0.850 | - |

12 | −12.05 | 3.917 | −1.539 | −1.785 | - |

13 | 9.180 | −0.935 | −2.199 | 2.377 | - |

14 | 2.500 | −6.815 | −2.203 | 3.462 | - |

15 | −3.105 | 4.973 | −0.752 | −3.526 | - |

16 | −4.068 | 4.687 | −1.196 | −3.731 | - |

17 | 8.037 | 9.291 | 0.592 | 9.212 | - |

18 | 6.726 | 5.979 | 0.963 | 3.974 | - |

19 | 4.042 | −5.058 | 1.376 | 5.431 | - |

20 | 4.585 | −3.606 | −0.777 | 6.701 | - |

Neuron Index | Input Layer Weights | Hidden Layer Weights | Input Layer Biases | Output Layer Bias | |
---|---|---|---|---|---|

$i$ | ${w}_{{1}_{i,1}}$ | ${w}_{{1}_{i,2}}$ | ${w}_{2,i}$ | ${b}_{1,i}$ | ${b}_{2}$ |

1 | −6.753 | −1.103 | 1.041 | −9.530 | −0.106 |

2 | 8.434 | 3.590 | −2.501 | −7.827 | - |

3 | −5.541 | 2.870 | 0.111 | 5.778 | - |

4 | −2.502 | −4.938 | −0.160 | −5.132 | - |

5 | 1.257 | −4.551 | 0.671 | −3.641 | - |

6 | −6.886 | 0.157 | 0.523 | 2.501 | - |

7 | 2.427 | −3.904 | 1.129 | −1.205 | - |

8 | 3.711 | −4.231 | −0.680 | 0.426 | - |

9 | −4.383 | −2.456 | −4.228 | 2.781 | - |

10 | 3.781 | 2.628 | 0.781 | 3.734 | - |

11 | 4.197 | −0.920 | −0.658 | −0.850 | - |

12 | −5.986 | 7.171 | −0.378 | −1.785 | - |

13 | 5.429 | 4.213 | −2.285 | 2.377 | - |

14 | 3.700 | −7.289 | −1.825 | 3.462 | - |

15 | 4.037 | 3.723 | 2.991 | −3.526 | - |

16 | 5.432 | 2.211 | −1.677 | −3.731 | - |

17 | 7.672 | −3.691 | 5.346 | 9.212 | - |

18 | −1.757 | 6.114 | 2.971 | 3.974 | - |

19 | 2.719 | 2.906 | 2.767 | 5.431 | - |

20 | −7.991 | −2.637 | 1.733 | 6.701 | - |

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**MDPI and ACS Style**

Gowida, A.; Elkatatny, S.; Ramadan, E.; Abdulraheem, A.
Data-Driven Framework to Predict the Rheological Properties of CaCl_{2} Brine-Based Drill-in Fluid Using Artificial Neural Network. *Energies* **2019**, *12*, 1880.
https://doi.org/10.3390/en12101880

**AMA Style**

Gowida A, Elkatatny S, Ramadan E, Abdulraheem A.
Data-Driven Framework to Predict the Rheological Properties of CaCl_{2} Brine-Based Drill-in Fluid Using Artificial Neural Network. *Energies*. 2019; 12(10):1880.
https://doi.org/10.3390/en12101880

**Chicago/Turabian Style**

Gowida, Ahmed, Salaheldin Elkatatny, Emad Ramadan, and Abdulazeez Abdulraheem.
2019. "Data-Driven Framework to Predict the Rheological Properties of CaCl_{2} Brine-Based Drill-in Fluid Using Artificial Neural Network" *Energies* 12, no. 10: 1880.
https://doi.org/10.3390/en12101880