Research Papers

Control of Down-Hole Drilling Process Using a Computationally Efficient Dynamic Programming Method

[+] Author and Article Information
Chong Ke

Department of Mechanical Engineering,
College of Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: mkxxz314@tamu.edu

Xingyong Song

Department of Engineering Technology and
Industrial Distribution;
Department of Mechanical Engineering,
Texas A&M University,
College of Engineering,
College Station, TX 77843;
e-mail: songxy@tamu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 23, 2017; final manuscript received March 20, 2018; published online May 22, 2018. Assoc. Editor: Mahdi Shahbakhti.

J. Dyn. Sys., Meas., Control 140(10), 101010 (May 22, 2018) (10 pages) Paper No: DS-17-1318; doi: 10.1115/1.4039787 History: Received June 23, 2017; Revised March 20, 2018

The unconventional down-hole resources such as shale oil and gas have gradually become a critical form of energy supply thanks to the recent petroleum technology advancement. Its economically viable and reliable production highly depends on the proper operation and control of the down-hole drilling system. The trend of deeper drilling in a complex environment requires a more effective and reliable control optimization scheme, either for predrilling planning or for online optimal control. Given the nonlinear nature of the drilling system, such an optimal control is not trivial. In this paper, we present a method based on dynamic programming (DP) that can lead to a computationally efficient drilling control optimization. A drilling dynamics model that can enable this method is first constructed, and the DP algorithm is customized so that much improved computational efficiency can be achieved compared with using standard DP. A higher-order dynamics model is then used to validate the effectiveness of the optimized control, and the control robustness is also evaluated by adding perturbations to the model. The results verify that the proposed approach is effective and efficient to solve the down-hole drilling control optimization problem.

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Fig. 1

Schematic diagram of the down-hole drilling system

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Fig. 2

Axial-torsional coupled model for the down-hole drilling system [10,19]

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Fig. 3

Comparison between model using time-delay based depth of cut and that with the approximated depth of cut

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Fig. 4

Conventional DP state space gridding

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Fig. 5

Computationally efficient DP state space gridding

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Fig. 6

Forward model versus partially inverse model. The partially inverse model needs much less sampling rate compared with forward model.

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Fig. 7

Model accuracy of partially invertible model and forward model versus sampling rate

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Fig. 8

Controlled bit velocities using optimized control inputs from DP

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Fig. 9

Bit axial velocity over varied parameter ϵ with computationally efficient DP optimized inputs

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Fig. 10

Bit axial velocity over varied parameter ϵ with robust DP optimized inputs

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Fig. 11

Bit axial speed over three perturbed ϵ (50%, 150%, and 200% perturbation) with computationally efficient DP optimized inputs

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Fig. 12

Bit axial speed over three perturbed ϵ (50%, 150%, and 200% perturbation) with robust DP optimized inputs

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Fig. 13

Computational expense of two DP approaches



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