# Application of Digitalization in Real-Time Analysis of Drilling Dynamics Using Along-String Measurement (ASM) Data along Wired Pipes

^{*}

## Abstract

**:**

## 1. Introduction

References | Rock Name | Bulk Density | Porosity | $\mathit{UCS}$ | Poisson’s Ratio | Young Modulus |
---|---|---|---|---|---|---|

(gr/cc) | (%) | (kpsi) | (Mpsi) | |||

Rajabov et al. [7] | Carthage Marble | 2.63 | 1–2 | 9–12 | 0.27 | 4–5 |

Torrey Buff Sandstone | 2.54 | 7.9 | 9–11 | 0.22 | 1.5–1.6 | |

Mancos Shale | 2.47 | 16 | 5–7 | 0.2 | 4.6 | |

Glowka [2,3] | Berea Sandsone | - | - | 7.1 | - | - |

Sierra White Granite | - | - | 21.5 | - | - | |

Tennessee Marble | - | - | 17.8 | - | - | |

(Holton Limestone) | ||||||

Akbari et al. [11,12] | Carthage Marble | - | - | 14.48 | - | - |

Richard et al. [44] | Fontenoille Sandstone | - | - | 13.775 | - | - |

Moka Limestone | - | - | 9.425 | - | - | |

Lens Limestone | - | - | 4.35 | - | - | |

Voges Sandstone | - | 20 | 2.32 | - | - | |

Nurabup Sandstone | - | 41 | 1.16 | - | ||

MC Field Sandstone | - | 24.5 | 1.015 | - | - | |

Majidi et al. [45] | Indiana Limestone | - | 11–16 | 7 | - | - |

Carthage Marble | - | 1–2 | 9–11.7 | - | - | |

Tensile Strength (kpsi) | ||||||

Wang et al. [16] | Shale | - | - | 9.764 | 0.81 | |

Marble | - | - | 12.294 | 0.90 | ||

Granite | - | - | 13.656 | 1.017 | ||

Limestone | - | - | 15.013 | 1.141 |

## 2. Cutter–Rock Interaction Modeling

#### 2.1. Experimental Data

#### 2.2. Methodology and Calculations

#### 2.2.1. Regression Analysis

**Table 5.**Proposed basis regression functions based on experimental observations for ${F}_{a}$ and ${F}_{c}$.

Parameter | Basis Function | Multiplier Bounds | Related References |
---|---|---|---|

Back-Rake Angle $\left(\theta \right)$ | ${e}^{{\lambda}_{1}sin\left(\theta \right)}$ | ${\lambda}_{1}\ge 0.5$ | [7,15,16,47] |

Cutting Area $\left({A}_{cut}\right)$ | ${A}_{cut}^{{\lambda}_{2}}$ | $0.4\le {\lambda}_{2}\le 0.9$ | [2,3,7,11,15,16,45,46] |

Wear Flat Area $\left({A}_{wear}\right)$ | ${e}^{{\lambda}_{3}{\left({A}_{wear}\right)}^{{\lambda}_{4}}}$ | $0.1\le {\lambda}_{3}\le 0.3$ | [2,3,48] |

$0.1\le {\lambda}_{4}\le 1.0$ | |||

Rock Drillability $\left(K\right)$ | ${K}^{{\lambda}_{5}}$ | $1.0\le {\lambda}_{5}\le 4.0$ | [16] |

Differential Pressure $(\Delta P)$ | ${e}^{{\lambda}_{6}{(\Delta P)}^{{\lambda}_{7}}}$ | $0.2\le {\lambda}_{6}\le 1.4$ | [1,7,8,11,12,46] |

$0.1\le {\lambda}_{7}\le 0.4$ | |||

Cutter Wear Height $\left({h}_{w}\right)$ | ${e}^{{\lambda}_{8}\left(\frac{{h}_{w}}{OD\phantom{\rule{0.166667em}{0ex}}cos\left(\theta \right)}\right)}$ | $1.0\le {\lambda}_{6}\le 2.0$ | [2,3,48] |

#### 2.2.2. Regression Techniques

## 3. Drilling Dynamics Modeling

#### 3.1. Bit Models

#### 3.2. Specific Energy Analysis

#### 3.3. Data Analytic Approach

- Since all cutters that are located at the same radial distance (from the axis of the bit) have the same design characteristics, their traces can be summed up into a single cutter equivalent.
- The cleaning action of the hydraulic system is efficient enough to remove all cuttings ahead of cutters and cuttings do not adversely affecting drilling performance.
- Assuming homogeneity of the rock all over the bottom of the hole; therefore, the drillability value would be constant and would apply to all equivalent cutters.

- Geometrical modeling of the PDC bit as equivalent cutter and blade.
- Recording of drilling parameters mainly the torque and the weight on the bit, rate of penetration (ROP) using along-string measurement system.
- Updating cutter status and calculate normal and cutting forces, specific energy and the torque at the cutters.
- Estimate torque at the bit and comparing it to the torque delivered to the drill string at the surface to monitor drill string dynamics for possible drilling problems.

## 4. Results and Discussion

#### 4.1. Mathematical Modeling

#### 4.2. Drill Bit and String Dynamics

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PDC | Polycrystalline diamond compact |

ASM | Along-string measurement |

EMS | Enhanced measurement system |

TDS | Top drive system |

SE | Specific energy |

MSE | Mechanical specific energy |

DS | Drilling strength |

GA | Genetic algorithm |

RLS | Recursive least square |

ROP | Rate of penetration |

NCS | Norwegian continental shelf |

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**Figure 3.**Scatter plot of experimental and estimated values by K-fold cross validation during training of the deep learning network.

**Figure 4.**Geometrical parameters of a single cutter defined as back-rake ($\theta $) and side-rake ($\varphi $) angles.

**Figure 5.**Sample PDC bit and the equivalent blade representation of the cutters; r, z, and w indicate the coordinate axis in radial, normal, and tangential directions, respectively; C is the bit profile curve; n is the normal direction to the bit profile and $\sigma $ is the angle between normal to the bit profile and bit axis.

**Figure 6.**(

**a**) Traces of all cutters on a vertical plane. (

**b**) Equivalent blade produced by traces of cutters involved in drilling depth, d, in one revolution and discretization of equivalent blade into equivalent rectangular cutters. (

**c**) Spatial position of cutters in two successive revolutions.

**Figure 7.**(

**a**) The framework of equivalent rectangular cutters formed by the overlapping of complete or partial circular cutters and (

**b**) schematic of an equivalent cutter composed of several partial cutters.

**Figure 8.**Graphical representation of specific energy and drilling strength. Marker data are calculated based on drilling measurement data utilized in this study, and solid lines are tangent to these data to build cutting and friction lines.

**Figure 10.**Schematic of wear height and wear flat area of a blunt cutter. The hatched area indicates the worn section of the cutter.

**Figure 11.**Scatter plot of experimental data and the calculated values by the regression methods for normal force.

**Figure 12.**Scatter plot of experimental data and the calculated values by the regression methods for cutting force.

**Figure 13.**Normal distribution of normal force concluded from experimental data and the results of regression by non-linear regression and deep learning methods.

**Figure 14.**Normal distribution of cutting force concluded from experimental data and the results of regression by non-linear regression and deep learning methods.

**Figure 15.**Specific energy (

**left**) and torque (

**right**) plots for bit run number 1 for three equivalent cutters; i.e., 1, 5, and 9.

**Figure 16.**Specific energy (

**left**) and torque (

**right**) plots for the bit run number 2 for three equivalent cutters; i.e., 1, 5, and 9.

**Figure 19.**Specific energy for the drilled interval in bit run number 1. Each plot is for a specific equivalent cutter which is written as legend.

**Figure 20.**Specific energy for the drilled interval in bit run number 2. Each plot is for a specific equivalent cutter which is written as legend.

**Figure 21.**Torque at bit and torque delivered to the drill string at the surface for bit run number 1.

**Figure 22.**Torque at bit and toque delivered to the drill string at the surface for bit run number 2.

**Table 2.**Summary of experimental data implemented in regression: ${F}_{a}$, normal force, ${F}_{c}$, cutting force.

References | No. of Data in | Cutter | Cutter Size | Back-Rake | $\mathbf{\Delta}\mathit{P}$ |
---|---|---|---|---|---|

${\mathit{F}}_{\mathit{n}},\phantom{\rule{0.166667em}{0ex}}{\mathit{F}}_{\mathit{c}}$ | Condition | (mm) | Angle (°) | (psi) | |

Rajabov et al. [7] | 40, 117 | New | 13 | 10, 20, 30, 40 | 0, 250, 500 |

Glowka [2,3] | 403, 403 | New, Dull | 12.7, 19 | 20 | 0 |

Akbari et. al. [11,12] | 64, 67 | New | 13, 16 | 20 | 450 |

Richard et al. [44] | 0, 50 | New | 13, 19 | 15 | 0 |

Majidi et al. [45] | 54, 54 | New | 13 | 15 | 0, 50, 150, 250 |

Wang et al. [16] | 93, 88 | New | 13 | 5, 10, 15, 20, 25 | 0 |

**Table 3.**Statistical summary of experimental data employed in regression of ${F}_{a}$ (Number of observations 654).

Variable | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|

Normal Force (N) | 2124.7 | 1957.33 | 59.16 | 7893.36 |

Cutter Diameter (mm) | - | - | 12.7 | 19.05 |

Cutting Area (mm^{2}) | 9.19 | 8.08 | 0.1 | 49.5 |

Wear Flat Area (mm^{2}) | 10.78 | 10.58 | 0 | 25.8 |

Back-Rake Angle (deg) | - | - | 5 | 40 |

Cutter Wear Height (mm) | 0.68 | 0.65 | 0 | 1.69 |

Rock Drillability, K | 5.46 | 0.94 | 3.2 | 7.78 |

(dimensionless) | ||||

Differential Pressure (psi) | 52.67 | 136.81 | 0 | 450 |

**Table 4.**Statistical summary of experimental data employed in regression of ${F}_{c}$ (Number of observations 779).

Variable | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|

Cutting Force (N) | 1382.48 | 1224.54 | 11.41 | 5747.19 |

Cutter Diameter (mm) | - | - | 12.7 | 19.05 |

Cutting Area (mm^{2}) | 8.53 | 7.56 | 0.11 | 37.92 |

Wear Flat Area (mm^{2}) | 9.05 | 10.47 | 0 | 25.8 |

Back-Rake Angle (deg) | - | - | 5 | 40 |

Cutter Wear Height (mm) | 0.57 | 0.65 | 0 | 1.69 |

Rock Drillability, K | 5.36 | 1.07 | 3.2 | 7.78 |

(dimensionless) | ||||

Differential Pressure (psi) | 78.32 | 156.88 | 0 | 500 |

Source | SS | df | MS | F–Factor |
---|---|---|---|---|

Regression (${F}_{c}$) | 745.727 | 6 | 149.145 | 505.576 |

Residual | 228.083 | 772 | 0.295 | |

Total | 973.810 | 778 | 1.251 |

Source | SS | df | MS | F–Factor |
---|---|---|---|---|

Regression (${F}_{a}$) | 4736.6 | 6 | 789.434 | 1652.53 |

Residual | 309.08 | 647 | 0.4771 | |

Total | 5045.68 | 653 | 7.7269 |

Cutting Force (${\mathit{F}}_{\mathit{c}}$) | Coef. | Std. Err. | t-Stat | p-Value | 95% Confidence Interval | |
---|---|---|---|---|---|---|

${\beta}_{0}$ | 0.2469 | 0.1821 | 1.3558 | 0.004 | 0.1632 | 0.8782 |

${\beta}_{1}$ | 0.5237 | 0.0216 | 24.2453 | 0.001 | 0.5 | 0.7370 |

${\beta}_{2}$ | 0.7454 | 0.0562 | 13.2633 | 0.0 | 0.6013 | 0.8347 |

${\beta}_{3}*$ | 0.1 | — | — | — | — | — |

${\beta}_{4}**$ | 0.6432 | — | — | — | — | — |

${\beta}_{5}$ | 2.6821 | 0.0947 | 28.3220 | 0.0 | 2.4564 | 2.8283 |

${\beta}_{6}$ | 0.5173 | 0.0387 | 13.3669 | 0.0 | 0.3789 | 0.5310 |

${\beta}_{7}***$ | 0.4 | — | — | — | — | — |

${\beta}_{8}*$ | 1.0 | — | — | — | — | — |

Cutting Force (${\mathit{F}}_{\mathit{a}}$) | Coef. | Std. Err. | t-Stat | p-Value | 95% Confidence Interval | |
---|---|---|---|---|---|---|

${\alpha}_{0}$ | 0.0 | — | — | — | — | — |

${\alpha}_{1}$ | 1.2826 | 0.3836 | 3.34 | 0.001 | 0.5294 | 2.0358 |

${\alpha}_{2}$ | 0.4524 | 0.0288 | 15.7083 | 0.0 | 0.4308 | 0.4776 |

${\alpha}_{3}*$ | 0.1 | — | — | — | — | — |

${\alpha}_{4}**$ | 0.7055 | — | — | — | — | — |

${\alpha}_{5}$ | 3.2531 | 0.0714 | 45.5616 | 0.0 | 3.0342 | 3.5148 |

${\alpha}_{6}$ | 0.2958 | 0.0603 | 4.9054 | 0.002 | 0.2 | 0.3044 |

${\alpha}_{7}***$ | 0.4 | — | — | — | — | — |

${\alpha}_{8}*$ | 1.0 | — | — | — | — | — |

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**MDPI and ACS Style**

Gomar, M.; Elahifar, B. Application of Digitalization in Real-Time Analysis of Drilling Dynamics Using Along-String Measurement (ASM) Data along Wired Pipes. *Energies* **2022**, *15*, 8930.
https://doi.org/10.3390/en15238930

**AMA Style**

Gomar M, Elahifar B. Application of Digitalization in Real-Time Analysis of Drilling Dynamics Using Along-String Measurement (ASM) Data along Wired Pipes. *Energies*. 2022; 15(23):8930.
https://doi.org/10.3390/en15238930

**Chicago/Turabian Style**

Gomar, Mostafa, and Behzad Elahifar. 2022. "Application of Digitalization in Real-Time Analysis of Drilling Dynamics Using Along-String Measurement (ASM) Data along Wired Pipes" *Energies* 15, no. 23: 8930.
https://doi.org/10.3390/en15238930