# Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Oil Drilling Rig under Study: Description and Operations

- DRILLING: the drill string is slowly lowered into the wellbore while the top-drive provides the drill bit with the torque to drill. When the drilling depth equals the drill string length, the drill string is blocked into the wellbore while the top-drive and hook block alone are raised to attach two more drill pipes and resume drilling.
- TRIP OUT: the top-drive and hook block are raised to pull out of the hole (POOH) the drill string. When a double stand of drill pipes comes out of the wellbore, it is removed from the top-drive and hook block, which then are lowered to lift the remaining drill string.
- CASING: a joint of two casing pipes is lowered into the wellbore; then, the top-drive and hook block are raised to pick up another joint and repeat the operation. When the casing pipes into the wellbore reach the bottom of the wellbore, they are cemented.
- TRIP IN: the drill string is run into the hole (RIH), starting from the drill collars, which are thicker than the drill pipes to provide the weight on the bit (WOB). When a double stand of drill collars or drill pipes is completely lowered into the wellbore, the top-drive and hook block are raised to pick up another double stand and repeat the operation until the drill string occupies the whole wellbore length. Then, the drilling phase can restart.

#### 2.2. Parametric Model for Power-Split Transmissions: A Modular Procedure for the Design

- 5.
- IDENTIFICATION OF THE OVERALL SPEED AND POWER RATIOS: the operations of the ICE and the output load are defined to assess the overall speed ratio $\tau $ and the overall power ratio $\eta $:

- 6.
- MECHANICAL POINTS SELECTION AND ELECTRIC MACHINES’ POWER SIZE: the power flows of the electric machines (${P}_{i}$ and ${P}_{o}$) are ruled only by the mechanical points:

- 7.
- DESIGN CHART AND PLANETARY GEARING SYNTHESIS: the nodal ratios rule the so-called characteristic functions, defined as the speed ratio between two generic TPM branches when the third one is motionless to the same speed ratio when the third shaft is moving:

- 8.
- CORRESPONDING SPEED RATIOS SELECTION: the corresponding speed ratios rule the speed and torque ratios at the PSU ports along with the nodal ratios. Indeed, the MG I and MG O speeds are:

- 9.
- ORDINARY GEARING SYNTHESIS: after selecting both nodal and corresponding speed ratios, the PSU kinematics is fully characterized. The OGs on each TPM branch must be synthesized to ensure that the kinematic constraints are satisfied during PG synchronism, as demonstrated in [22]. Therefore, the fixed ratios of the OGs belonging to the same TPM are ruled by the following equations:

## 3. Results

#### 3.1. First Solution: 403-kW ICE

#### 3.1.1. Identification of the Overall Speed and Power Ratios

#### 3.1.2. Mechanical Points Selection and Electric Machines’ Power Size

#### 3.1.3. Design Chart and Planetary Gearing Synthesis

#### 3.1.4. Corresponding Speed Ratios Selection

#### 3.1.5. Ordinary Gearing Synthesis

#### 3.2. Second Solution: Downsized ICE

#### 3.2.1. Identification of the Overall Speed and Power Ratios

#### 3.2.2. Mechanical Points Selection and Electric Machines’ Power Size

#### 3.2.3. Design Chart and Planetary Gearing Synthesis

#### 3.2.4. Corresponding Speed Ratios Selection

#### 3.2.5. Ordinary Gearing Synthesis

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Krithika, V.; Subramani, C. A Comprehensive Review on Choice of Hybrid Vehicles and Power Converters, Control Strategies for Hybrid Electric Vehicles. Int. J. Energy Res.
**2018**, 42, 1789–1812. [Google Scholar] [CrossRef] - Tran, D.D.; Vafaeipour, M.; El Baghdadi, M.; Barrero, R.; Van Mierlo, J.; Hegazy, O. Thorough State-of-the-Art Analysis of Electric and Hybrid Vehicle Powertrains: Topologies and Integrated Energy Management Strategies. Renew. Sustain. Energy Rev.
**2020**, 119, 109596. [Google Scholar] [CrossRef] - Zhuang, W.; Li (Eben), S.; Zhang, X.; Kum, D.; Song, Z.; Yin, G.; Ju, F. A Survey of Powertrain Configuration Studies on Hybrid Electric Vehicles. Appl. Energy
**2020**, 262, 114553. [Google Scholar] [CrossRef] - Capata, R. Preliminary Analysis of a New Power Train Concept for a City Hybrid Vehicle. Designs
**2021**, 5, 19. [Google Scholar] [CrossRef] - Karimi, D.; Behi, H.; Van Mierlo, J.; Berecibar, M. Advanced Thermal Management Systems for High-Power Lithium-Ion Capacitors: A Comprehensive Review. Designs
**2022**, 6, 53. [Google Scholar] [CrossRef] - Wang, L.; Cui, Y.; Zhang, F.; Li, G. Architectures of Planetary Hybrid Powertrain System: Review, Classification and Comparison. Energies
**2020**, 13, 329. [Google Scholar] [CrossRef] - İnce, E.; Güler, M.A. On the Advantages of the New Power-Split Infinitely Variable Transmission over Conventional Mechanical Transmissions Based on Fuel Consumption Analysis. J. Clean. Prod.
**2020**, 244, 118795. [Google Scholar] [CrossRef] - Zeng, X.; Wang, J. Analysis and Design of the Power-Split Device for Hybrid Systems; Springer: Singapore, 2017; ISBN 9789811042720. [Google Scholar]
- Zhao, Z.; Tang, P.; Li, H. Generation, Screening, and Optimization of Powertrain Configurations for Power-Split Hybrid Electric Vehicle: A Comprehensive Overview. IEEE Trans. Transp. Electrif.
**2022**, 8, 325–344. [Google Scholar] [CrossRef] - Buchsbaum, F.; Freudenstein, F. Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms. J. Mech.
**1970**, 5, 357–392. [Google Scholar] [CrossRef] - Gomà Ayats, J.R.; Diego-Ayala, U.; Minguella Canela, J.; Fenollosa, F.; Vivancos, J. Hypergraphs for the Analysis of Complex Mechanisms Comprising Planetary Gear Trains and Other Variable or Fixed Transmissions. Mech. Mach. Theory
**2012**, 51, 217–229. [Google Scholar] [CrossRef] - Pei, H.; Hu, X.; Yang, Y.; Tang, X.; Hou, C.; Cao, D. Configuration Optimization for Improving Fuel Efficiency of Power Split Hybrid Powertrains with a Single Planetary Gear. Appl. Energy
**2018**, 214, 103–116. [Google Scholar] [CrossRef] - Pei, H.; Hu, X.; Yang, Y.; Peng, H.; Hu, L.; Lin, X. Designing Multi-Mode Power Split Hybrid Electric Vehicles Using the Hierarchical Topological Graph Theory. IEEE Trans. Veh. Technol.
**2020**, 69, 7159–7171. [Google Scholar] [CrossRef] - Shanmukhasundaram, V.R.; Rao, Y.V.D.; Regalla, S.P. Enumeration of Displacement Graphs of Epicyclic Gear Train from a given Rotation Graph Using Concept of Building of Kinematic Units. Mech. Mach. Theory
**2019**, 134, 393–424. [Google Scholar] [CrossRef] - Du, M.; Yang, L. A Basis for the Computer-Aided Design of the Topological Structure of Planetary Gear Trains. Mech. Mach. Theory
**2020**, 145, 103690. [Google Scholar] [CrossRef] - Zhou, X.; Qin, D.; Rotella, D.; Cammalleri, M. Hybrid Electric Vehicle Powertrain Design: Construction of Topologies and Initial Design Schemes. In Advances in Italian Mechanism Science; Springer International Publishing: Cham, Switzerland, 2019; Volume 68, pp. 49–60. [Google Scholar]
- Ngo, H.T.; Yan, H. Sen Configuration Synthesis of Parallel Hybrid Transmissions. Mech. Mach. Theory
**2016**, 97, 51–71. [Google Scholar] [CrossRef] - Zhang, X.; Li, C.T.; Kum, D.; Peng, H. Prius + and Volt -: Configuration Analysis of Power-Split Hybrid Vehicles with a Single Planetary Gear. IEEE Trans. Veh. Technol.
**2012**, 61, 3544–3552. [Google Scholar] [CrossRef] - Wang, W.; Song, R.; Guo, M.; Liu, S. Analysis on Compound-Split Configuration of Power-Split Hybrid Electric Vehicle. Mech. Mach. Theory
**2014**, 78, 272–288. [Google Scholar] [CrossRef] - Ke, T.; Ding, H.; Gong, C.; Geng, M. Configuration Synthesis of Nine-Speed Automatic Transmissions Based on Structural Decomposition. Mech. Mach. Theory
**2021**, 164, 104421. [Google Scholar] [CrossRef] - Chen, H.; Li, L.; Lange, A.; Küçükay, F. Innovative Dedicated Hybrid Transmission Concepts in the Next Generation of Hybrid Powertrains. SAE Int. J. Altern. Powertrains
**2019**, 8, 75–88. [Google Scholar] [CrossRef] - Cammalleri, M.; Rotella, D. Functional Design of Power-Split CVTs: An Uncoupled Hierarchical Optimized Model. Mech. Mach. Theory
**2017**, 116, 294–309. [Google Scholar] [CrossRef] - Rotella, D.; Cammalleri, M.; Qin, D.; Zhou, X. A Simple Method for the Design of Hybrid Electric Power-Split Cvts: A Case Study. In Advances in Italian Mechanism Science; Springer International Publishing: Cham, Switzerland, 2019; Volume 68, pp. 70–79. [Google Scholar]
- Cammalleri, M.; Castellano, A. Analysis of Hybrid Vehicle Transmissions with Any Number of Modes and Planetary Gearing: Kinematics, Power Flows, Mechanical Power Losses. Mech. Mach. Theory
**2021**, 162, 104350. [Google Scholar] [CrossRef] - Rotella, D.; Cammalleri, M. Power Losses in Power-Split CVTs: A Fast Black-Box Approximate Method. Mech. Mach. Theory
**2018**, 128, 528–543. [Google Scholar] [CrossRef] - Castellano, A.; Cammalleri, M. Global Efficiency of Power-Split Hybrid Electric Powertrain. In Mechanisms and Machine Science, Proceedings of the I4SDG Workshop 2021, I4SDG 2021, Online, 25–26 November 2021; Quaglia, G., Gasparetto, A., Petuya, V., Carbone, G., Eds.; Springer: Cham, Switzerland, 2022; Volume 108, pp. 502–511. ISBN 9783030873820. [Google Scholar]
- Castellano, A.; Cammalleri, M. Optimal Operation of Power-Split Hybrid Electric Powertrain: Comparison between Two Performance Indices. Int. J. Mech. Control
**2022**, 23, 3–14. [Google Scholar] - Castellano, A.; Cammalleri, M. Power Losses Minimization for Optimal Operating Maps in Power-Split Hevs: A Case Study on the Chevrolet Volt. Appl. Sci.
**2021**, 11, 7779. [Google Scholar] [CrossRef] - Lyons, W.C.; Plisga, G.J.; Lorenz, M.D.B.T. Standard Handbook of Petroleum and Natural Gas Engineering; Gulf Professional Publishing: Houston, TX, USA, 2016; ISBN 9780123838469. [Google Scholar]
- Ismail, A.; Moustafa, W. New Hybrid Drill Bit with Innovative Technology Improves Drilling Efficiency in Challenging Jordanian Drilling Project. Soc. Pet. Eng. SPE Saudi Arab. Sect. Tech. Symp. Exhib.
**2014**. [Google Scholar] [CrossRef] - Yadav, P.; Kumar, R.; Panda, S.K.; Chang, C.S. An Improved Harmony Search Algorithm for Optimal Scheduling of the Diesel Generators in Oil Rig Platforms. Energy Convers. Manag.
**2011**, 52, 893–902. [Google Scholar] [CrossRef] - Pavković, D.; Sedić, A.; Guzović, Z. Oil Drilling Rig Diesel Power-Plant Fuel Efficiency Improvement Potentials through Rule-Based Generator Scheduling and Utilization of Battery Energy Storage System. Energy Convers. Manag.
**2016**, 121, 194–211. [Google Scholar] [CrossRef] - Chupin, E.; Frolov, K.; Korzhavin, M.; Zhdaneev, O. Energy Storage Systems for Drilling Rigs. J. Pet. Explor. Prod. Technol.
**2022**, 12, 341–350. [Google Scholar] [CrossRef] - Bilgin, M.; Donen, J.; Scaini, V.; Snijder, M. World’s First Hybrid Drilling Rig. In Proceedings of the SPE/IADC Drilling Conference and Exhibition, Galveston, TX, USA, 3–5 March 2020. [Google Scholar] [CrossRef]
- Lujun, Z. An Energy-Saving Oil Drilling Rig for Recovering Potential Energy and Decreasing Motor Power. Energy Convers. Manag.
**2011**, 52, 359–365. [Google Scholar] [CrossRef] - Dai, X.; Wei, K.; Zhang, X. Analysis of the Peak Load Leveling Mode of a Hybrid Power System with Flywheel Energy Storage in Oil Drilling Rig. Energies
**2019**, 12, 606. [Google Scholar] [CrossRef] [Green Version] - Lupașcu (Oprea), A.-M.; Ionescu, V.-M.; Potârniche, I.; Năvrăpescu, V.; Săpunaru, A.-A. Increase of Energy Efficiency of Electrically Driven Drilling Installations by Valorising the Braking Regime of the Draw Works upon Descending the Pipe Line. EMERG Energy. Environ. Effic. Resour. Glob.
**2020**, 6, 33–40. [Google Scholar] [CrossRef] - Hamada, A.T.; Orhan, M.F. An Overview of Regenerative Braking Systems. J. Energy Storage
**2022**, 52, 105033. [Google Scholar] [CrossRef] - Drillmec Mobile Rigs. Available online: https://www.drillmec.com/en/onshore/mobile-rigs (accessed on 14 May 2022).
- Rotella, D.; Cammalleri, M. Direct Analysis of Power-Split CVTs: A Unified Method. Mech. Mach. Theory
**2018**, 121, 116–127. [Google Scholar] [CrossRef]

**Figure 1.**Drillmec MR-8000 hoisting system and drawworks prime movers before and after hybridization. Red arrows show the PSU power positive sign.

**Figure 5.**Scheme of a three-port mechanism with one PG (rounded-corner square) and three OGs (rhombi) realizing the k

_{j}fixed ratio.

**Figure 6.**PSU overall speed and power ratios for the simulated drilling with ICE working at 1400 rpm and 2080 Nm.

**Figure 7.**Design chart for PG synthesis and selected layout with ICE working at 1400 rpm and 2080 Nm.

**Figure 8.**Functional layout of the output-split transmission designed for ICE working at 1400 rpm and 2080 Nm. The shown OGs arrangement corresponds to the first row of Table 6.

**Figure 9.**PSU overall speed and power ratios for the simulated drilling with ICE working at 1400 rpm and 1045 Nm.

**Figure 10.**Design chart for PG synthesis and selected layout with ICE working at 1400 rpm and 1045 Nm.

**Figure 11.**Functional layout of the input-split transmission designed for ICE working at 1400 rpm and 1045 Nm.

Phase | Hook Speed [m/s] |
---|---|

Drilling | 0.002 |

Trip out/in | −0.2/0.2 |

Casing | 0.1 |

Unladen lowering/raising | 0.8/−0.8 |

Weight of top-drive and hook block | 16.5 t |

WOB | 5 t |

Buoyancy factor | 0.8 |

Drill collar and drill pipe length | 9.5 m |

Drill collars specific weight | 225 kg/m |

Drill pipes specific weight | 33 kg/m |

Casing pipe length | 7.5 m |

Casing pipe specific weight (up to 500 m) | 160 kg/m |

Casing pipe specific weight (up to 1500 m) | 90 kg/m |

Casing pipe specific weight (up to 2500 m) | 60 kg/m |

Casing pipe specific weight (up to 3000 m) | 40 kg/m |

Drilling | Trip Out | Casing | Trip In | Hook + Top-Drive Up | Hook + Top-Drive Down |
---|---|---|---|---|---|

0.0017 | −0.17 | 0.085 | 0.17 | −0.68 | 0.68 |

**Table 4.**MG I and MG O extreme operations for each drilling subphase with ICE working at 1400 rpm and 2080 Nm. MG I torque values exceeding the maximum torque of 4775 Nm are bolded.

Drilling Subphase | $\mathit{\tau}$ | $\mathit{\eta}$ | ${\mathit{\omega}}_{\mathit{i}}\left[\mathbf{rpm}\right]$ | ${\mathit{T}}_{\mathit{i}}\left[\mathbf{Nm}\right]$ | ${\mathit{\omega}}_{\mathit{o}}\left[\mathbf{rpm}\right]$ | ${\mathit{T}}_{\mathit{o}}\left[\mathbf{Nm}\right]$ |
---|---|---|---|---|---|---|

Drilling | 0.0017 | −0.0078 | −116.6 | −9788 | 3500 | $-$1165 |

Drilling | 0.0017 | −0.0011 | −116.6 | −1391 | 3500 | $-$879.4 |

Casing | 0.085 | $-$0.64 | 0 | −15,550 | 3500 | $-$1361 |

Casing | 0.085 | −0.065 | 0 | −1595 | 3500 | $-$886.3 |

Trip out | −0.17 | 0.16 | −356.7 | −1937 | 3500 | $-$898.0 |

Trip out | −0.17 | 1.05 | −356.7 | −12,820 | 3500 | $-$1268 |

Trip in | 0.17 | −0.92 | 118.9 | $-$11,300 | 3500 | $-$1216 |

Trip in | 0.17 | −0.16 | 118.9 | $-$1937 | 3500 | $-$898.0 |

Hook + top-drive up | −0.68 | 0.503 | −1070 | $-$1539 | 3500 | $-$884.4 |

Hook + top-drive down | 0.68 | −0.503 | 832.4 | $-$1539 | 3500 | $-$884.4 |

Drilling Subphase | $\mathit{\tau}$ | $\mathit{\eta}$ | ${\mathit{\omega}}_{\mathit{M}\mathit{G}\mathit{I}}\text{}\left[\mathbf{rpm}\right]$ | ${\mathit{T}}_{\mathit{M}\mathit{G}\mathit{I}}\text{}\left[\mathbf{Nm}\right]$ |
---|---|---|---|---|

Drilling | 0.0017 | −0.0078 | 435.8 | 2619 |

Drilling | 0.0017 | −0.0011 | 435.8 | 372.3 |

Casing | 0.085 | $-$0.64 | 0 | 4162 |

Casing | 0.085 | −0.065 | 0 | 426.7 |

Trip out | −0.17 | 0.16 | 1333 | 518.3 |

Trip out | −0.17 | 1.05 | 1333 | 3430 |

Trip in | 0.17 | −0.92 | −444.4 | 3023 |

Trip in | 0.17 | −0.16 | −444.4 | 518.3 |

Hook + top-drive up | −0.68 | 0.503 | 4000 | 411.7 |

Hook + top-drive down | 0.68 | −0.503 | −3111 | 411.7 |

${k}_{in}$ | ${k}_{out}$ | ${k}_{i}^{*}$ | ${k}_{o}$ |

1 | −0.170 | 0.952 | 2.50 |

$-$5.89 | 1 | −5.61 | −14.7 |

1.05 | −0.178 | 1 | 2.63 |

0.400 | −0.0680 | 0.381 | 1 |

**Table 7.**MG I and MG O extreme operations for each drilling subphase with ICE working at 1400 rpm and 1045 Nm. MG O torque values exceeding the maximum torque of 3008 Nm are bolded.

Drilling Subphase | $\mathit{\tau}$ | $\mathit{\eta}$ | ${\mathit{\omega}}_{\mathit{i}}\left[\mathbf{rpm}\right]$ | ${\mathit{T}}_{\mathit{i}}\left[\mathbf{Nm}\right]$ | ${\mathit{\omega}}_{\mathit{o}}\left[\mathbf{rpm}\right]$ | ${\mathit{T}}_{\mathit{o}}\left[\mathbf{Nm}\right]$ |
---|---|---|---|---|---|---|

Drilling | 0.0017 | −0.0078 | −1951 | 752 | −9.72 | 1962 |

Drilling | 0.0017 | −0.0011 | −1951 | 752 | −9.72 | −35.04 |

Casing | 0.085 | −0.64 | −2190 | 752 | −500.0 | 3333 |

Casing | 0.085 | −0.065 | −2190 | 752 | −500.0 | 13.31 |

Trip out | −0.17 | 0.16 | −1460 | 752 | 1000 | 94.81 |

Trip out | −0.17 | 1.05 | −1460 | 752 | 1000 | 2682 |

Trip in | 0.17 | −0.92 | −2433 | 752 | −1000 | 2321 |

Trip in | 0.17 | −0.16 | −2433 | 752 | −1000 | 94.81 |

Hook + top-drive up | −0.68 | 0.503 | 0 | 752 | 4000 | $0$ |

Hook + top-drive down | 0.68 | −0.503 | −3893 | 752 | −4000 | 0 |

${\mathit{k}}_{\mathit{i}\mathit{n}}$ | ${\mathit{k}}_{\mathit{o}\mathit{u}\mathit{t}}$ | ${\mathit{k}}_{\mathit{i}}$ | ${\mathit{k}}_{\mathit{o}}$ |
---|---|---|---|

1 | −0.170 | −1.04 | 0.714 |

−5.89 | 1 | 6.14 | −4.20 |

−0.959 | 0.163 | 1 | −0.685 |

1.40 | −0.238 | −1.46 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Castellano, A.; Leone, D.; Cammalleri, M.
Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig. *Designs* **2022**, *6*, 74.
https://doi.org/10.3390/designs6050074

**AMA Style**

Castellano A, Leone D, Cammalleri M.
Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig. *Designs*. 2022; 6(5):74.
https://doi.org/10.3390/designs6050074

**Chicago/Turabian Style**

Castellano, Antonella, Daniele Leone, and Marco Cammalleri.
2022. "Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig" *Designs* 6, no. 5: 74.
https://doi.org/10.3390/designs6050074