# Physics-Based Swab and Surge Simulations and the Machine Learning Modeling of Field Telemetry Swab Datasets

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Swab Surge Modeling

#### 2.1. Physics-Based Modeling

^{TM}[19]) to evaluate the swab and surge behaviors in vertical and horizontal well profiles filled with different drilling fluids. Here, the experimental simulation setup is presented.

#### 2.1.1. Pore and Fracture Gradient

#### 2.1.2. Experimental Well Construction and Well Trajectory

^{TM}software was used to construct the experimental well [19].

#### 2.1.3. Fluid Models

#### Fluid PVT Models

#### Rheology Models

^{TM}software [19]. These were Bingham plastic (BP), power law (PL), and Robertson–Stiff (RS) models for the evaluation of swab and surge simulations.

#### 2.1.4. Drilling Fluids

**Figure 3.**Fluid 1 viscometer data measured at 20 °C [25].

**Figure 4.**Fluid 2 viscometer data measured at 20 °C [26].

#### 2.2. Machine Learning Modeling

^{2}) and mean square error. All the ML models and the model’s accuracy performance analysis were simulated using Python Built-in Libraries. Therefore, only brief descriptions of both models, their concepts, and how they work are presented.

#### 2.2.1. Polynomial Regression

_{w}), the polynomial mapping function can be written as:

_{0}, β

_{1}, and β

_{2}are the curve fitting parameters to be determined by the least sum square error method.

#### 2.2.2. Multivariate Regression

_{1}, x

_{2}, x

_{3}… x

_{n}) to predict the target variable, y (ECD). The multiple linear regression model is the linear combination of the weighted features, and is written as (Anderson T.W., 2003) [28]:

_{0}is the y-intercept (value of y when all other independent variables are set to 0), β

_{1}is the regression coefficient of the first independent variable x

_{1}, β

_{n}is the regression coefficient of the last independent variable x

_{n}, and ε is the model error (how much variation there is in our estimate of y). The regression coefficients were determined by the least square error method.

#### 2.2.3. Random Forest

#### 2.2.4. Artificial Neural Network

#### 2.2.5. LightGBM

#### 2.2.6. XGBoost

#### 2.2.7. LSTM

#### 2.3. Model Accuracy Evaluation

^{2}), as recommended by Montgomery (2019) [36].

#### 2.3.1. Mean Square Error (MSE)

#### 2.3.2. Regression Coefficient (R^{2})

#### 2.4. Description of Tripping-Out Data

## 3. Results

#### 3.1. Physics-Based Simulation Results

#### 3.1.1. Result 1

#### 3.1.2. Result 2

#### 3.2. Machine-Learning-Based Modeling Result

#### 3.2.1. Result 1—Simulated and Laboratory-Based Data Model

_{c}). The variation in well pressure due to tripping speeds, obtained from Equation (11), is given as follows:

_{0}, β

_{1}, and β

_{2}are the curve fitting parameters, determined from the green or blue datasets.

_{0}, β

_{1}, and β

_{2}); the results are presented in Table 9. Both models showed higher R

^{2}correlation values. However, it is essential to note that polynomial-based modeling was only applied for swab and surge field data or laboratory data if the pressure variations behaved as polynomials when the tripping speeds varied.

^{2}values of 0.999 and 0.999, respectively. Moreover, the other statistical parameter also shows that the model perfectly predicted the synthetic dataset. Physics models generate data without including noise; the ML model prediction demonstrates the trustworthiness of the method.

^{2}values of the training and testing datasets showed strong correlations: 0.999 and 0.999, respectively. The MSE values indicate that the RF method accurately predicted the simulated data.

#### 3.2.2. Result 2—Field-Data-Based Machine Learning

^{2}score and a minimum mean sum square error. The results demonstrate the potential application of machine learning modeling for the swab and surge field dataset.

## 4. Discussion

- The model’s predictions were inconsistent compared with each other.
- As the flow rates increased to approximately 200–300 lpm, surging speeds in the deviated well filled with 90:10 OBM showed an increasing trend, whereas in 80:20 OBM, the surging speed showed a decreasing trend. On the other hand, in both fluid systems, the surging speeds decreased when the flow rate increased above 300 lpm. Even though the trends in surge speeds for the three models’ predictions seemed similar, the values were quite different.
- Regarding rheology fluid descriptions, the RS model showed a lower error deviation. However, the swab and surge percentile deviation from the BP was lower than the RS with PL. The swab and surge predictions with the three models varied in the different well trajectories filled with fluids of different densities and viscosities.
- It was difficult to conclude the accuracy of the hydraulics model prediction based on how the model accurately described the fluid rheological properties.

## 5. Conclusions

- Deviations of swab surge model predictions from each model are inconsistent.
- Physics-based models generally require model calibration based on accurately measured data.
- The reviewed physics models do not consider all operational parameters, constraints, fluid properties, and non-uniform eccentricity. Moreover, it is difficult to quantify these parameters precisely in a drilling well.
- Data-driven-based modeling predicts both training and unseen test data with higher accuracy.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) Example of swabbing and surging effects in the 2.0 sg 80:20 OBM filled in a deviated well. (

**b**) Example of swabbing and surging effects in the 2.0 sg 90:10 OBM filled in adeviated well.

**Figure 9.**Swabbing comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 10.**Surging comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 11.**Swabbing comparisons of 1.96 sg 80:20 and 90:10 OBMs filled in deviated and inclined wells.

**Figure 12.**Surging comparisons of 1.96 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 13.**(

**a**) Example of swabbing and surging effects of 2.0 sg 80:20 OBM filled in a deviated well. (

**b**) Example of swabbing and surging effects of 2.0 sg 90:10 OBM filled in a deviated well.

**Figure 14.**Swabbing comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 15.**Surging comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 16.**Swabbing comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 17.**Surging comparisons of 2.0 sg 80:20 and 90:10 OBMs filled in deviated and vertical wells.

**Figure 18.**Drillbench-software-simulated surging pressure as a function of tripping speed up to the fracture point.

**Figure 19.**Experimental surge pressure gradient vs. tripping speed data [7].

**Figure 22.**(

**a**) Scatter plot of 70% training tripping-out data vs. ANN model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. ANN model prediction.

**Figure 23.**(

**a**) Scatter plot of 70% training tripping-out data vs. RF model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. RF model prediction.

**Figure 24.**(

**a**) Scatter plot of 70% training tripping-out data vs. LightGBM model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. LightGBM model prediction.

**Figure 25.**(

**a**) Scatter plot of 70% training tripping-out data vs. XGBoost model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. XGBoost model prediction.

**Figure 26.**(

**a**) Scatter plot of 70% training tripping-out data vs. LSTM model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. LSTM model prediction.

**Figure 27.**(

**a**) Scatter plot of 70% training tripping-out data vs. multivariable model prediction. (

**b**) Scatter plot of 30% test tripping-out data vs. multivariable model prediction.

**Table 1.**The 80:20 OBM rheological parameters derived from Figure 3.

Rheology Models | Parameters | % Error | |
---|---|---|---|

Bingham Plastic (BP) | YS [lbf/100sqft] | 6.061 | 13.2 |

PV [cP] | 40.314 | ||

Power Law (PL) | n [ ] | 0.546 | 13.6 |

k [lbfs^{n}/100sqft] | 1.656 | ||

Robertson–Stiff (RS) | A [lbfs^{n}/100sqft] | 0.262 | 1.5 |

B [ ] | 0.838 | ||

C [s^{−1}] | 26.670 |

**Table 2.**The 90:10 OBM rheological parameters derived from Figure 3.

Rheology Models | Parameters | % Error | |
---|---|---|---|

Bingham Plastic (BP) | YS [lbf/100sqft] | 4.843 | 21.9 |

PV [cP] | 29.82 | ||

Power Law (PL) | n [ ] | 0.570 | 12.2 |

k [lbfs^{n}/100sqft] | 1.080 | ||

Robertson–Stiff (RS) | A [lbfs^{n}/100sqft] | 0.179 | 2.1 |

B [ ] | 0.855 | ||

C [s^{−1}] | 24.418 |

**Table 3.**The 80:20 OBM rheological parameters derived from Figure 4.

Rheology Models | Parameters | % Error | |
---|---|---|---|

Bingham Plastic (BP) | YS [lbf/100sqft] | 8.690 | 11.1 |

PV [cP] | 33.13 | ||

Power Law (PL) | n [ ] | 0.435 | 12.2 |

k [lbfs^{n}/100sqft] | 3.005 | ||

Robertson–Stiff (RS) | A [lbfs^{n}/100sqft] | 0.404 | 2.3 |

B [ ] | 0.751 | ||

C [s^{−1}] | 40.48 |

**Table 4.**The 90:10 OBM rheological parameters derived from Figure 4.

Rheology Models | Parameters | % Error | |
---|---|---|---|

Bingham Plastic (BP) | YS [lbf/100sqft] | 1.724 | 13.6 |

PV [cP] | 30.26 | ||

Power Law (PL) | n [ ] | 0.720 | 7.7 |

k [lbfs^{n}/100sqft] | 0.384 | ||

Robertson–Stiff (RS) | A[lbfs^{n}/100sqft] | 0.138 | 5.6 |

B [ ] | 0.884 | ||

C [s^{−1}] | 8.890 |

OBM/Well/Density | Swabbing | Surging | ||
---|---|---|---|---|

% BP to PL Change | % BP to RS Change | % BP to PL Change | % BP to RS Change | |

90:10 Inclined 2.0 sg | 3.63 | 5.12 | 17.58 | 4.66 |

80:20 Inclined 2.0 sg | 13.11 | 0.82 | 25.86 | −1.15 |

90:10 Vertical 2.0 sg | 1.97 | 4.82 | −3.06 | −2.97 |

80:20 Vertical 2.0 sg | 12.39 | 0.72 | −1.15 | −0.40 |

OBM/Well/Density | Swabbing | Surging | ||
---|---|---|---|---|

% BP to PL Change | % BP to RS Change | % BP to PL Change | % BP to RS Change | |

90:10 Inclined 1.96 sg | 0.14 | −1.58 | −3.09 | −2.84 |

80:20 Inclined 1.96 sg | 2.73 | −2.10 | 1.34 | −0.15 |

90:10 Vertical 1.96 sg | 1.16 | −1.60 | −2.36 | −2.80 |

80:20 Vertical 1.96 sg | −0.61 | −3.53 | −1.49 | −0.23 |

OBM/Well/Density | Swabbing | Surging | ||
---|---|---|---|---|

% BP to PL Change | % BP to RS Change | % BP to PL Change | % BP to RS Change | |

90:10 Inclined 2.0 sg | −4.77 | 0.30 | 9.28 | −0.70 |

80:20 Inclined 2.0 sg | 14.00 | 0.00 | 18.83 | −0.65 |

90:10 Vertical 2.0 sg | 1.97 | 4.82 | −3.06 | −2.97 |

80:20 Vertical 2.0 sg | 13.12 | −0.50 | −0.76 | 0.30 |

OBM/Well/Density | Swabbing | Surging | ||
---|---|---|---|---|

% BP to PL Change | % BP to RS Change | % BP to PL Change | % BP to RS Change | |

90:10 Inclined 1.96 sg | −9.89 | −2.42 | −4.55 | 0.14 |

80:20 Inclined 1.96 sg | −3.21 | −0.99 | 0.68 | −0.51 |

90:10 Vertical 1.96 sg | −7.34 | −2.73 | −2.96 | 0.05 |

80:20 Vertical 1.96 sg | −6.05 | −0.33 | −1.24 | −0.79 |

Data | ${\mathsf{\beta}}_{2}$ | ${\mathsf{\beta}}_{1}$ | ${\mathsf{\beta}}_{0}$ | R^{2} |
---|---|---|---|---|

Figure 19 [7] | −0.1675 | 0.4851 | 0.0452 | 0.9992 |

Figure 18 [PL] | −9 × 10^{−10} | 1 × 10^{−5} | 1.9954 | 0.9965 |

Figure 18 [RS] | −4 × 10^{−10} | 1 × 10^{−5} | 1.9941 | 0.9997 |

ML Models | Dataset | Model Performance Accuracy | |
---|---|---|---|

MSE | R^{2} | ||

ANN | Training | 2.63 × 10^{−9} | 0.999 |

Testing | 2.35 × 10^{−9} | 0.999 | |

RF | Training | 2.58 × 10^{−8} | 0.999 |

Testing | 5.84 × 10^{−9} | 0.999 |

ML Model Algorithms | Dataset | Model Performance Accuracy | |
---|---|---|---|

MSE | R^{2} | ||

ANN | Training | 2.94 × 10^{−5} | 0.7921 |

Testing | 3.43 × 10^{−5} | 0.7836 | |

RF | Training | 1.95 × 10^{−6} | 0.9879 |

Testing | 1.45 × 10^{−5} | 0.8921 | |

LightGBM | Training | 1.05 × 10^{−5} | 0.9256 |

Testing | 1.88 × 10^{−5} | 0.8884 | |

XGBoost | Training | 7.01 × 10^{−6} | 0.9504 |

Testing | 1.52 × 10^{−5} | 0.9098 | |

LSTM | Training | 3.60 × 10^{−5} | 0.7449 |

Testing | 4.56 × 10^{−5} | 0.7299 | |

Multivariable | Training | 3.87 × 10^{−5} | 0.7264 |

Testing | 4.86 × 10^{−5} | 0.7120 |

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## Share and Cite

**MDPI and ACS Style**

Mohammad, A.; Belayneh, M.; Davidrajuh, R.
Physics-Based Swab and Surge Simulations and the Machine Learning Modeling of Field Telemetry Swab Datasets. *Appl. Sci.* **2023**, *13*, 10252.
https://doi.org/10.3390/app131810252

**AMA Style**

Mohammad A, Belayneh M, Davidrajuh R.
Physics-Based Swab and Surge Simulations and the Machine Learning Modeling of Field Telemetry Swab Datasets. *Applied Sciences*. 2023; 13(18):10252.
https://doi.org/10.3390/app131810252

**Chicago/Turabian Style**

Mohammad, Amir, Mesfin Belayneh, and Reggie Davidrajuh.
2023. "Physics-Based Swab and Surge Simulations and the Machine Learning Modeling of Field Telemetry Swab Datasets" *Applied Sciences* 13, no. 18: 10252.
https://doi.org/10.3390/app131810252