Article Contents

2022, Volume 15, Issue 6: 1547-1560. Doi: 10.3934/dcdss.2022007

This issue Previous Article Null controllability for semilinear heat equation with dynamic boundary conditions Next Article Well-posedness and stability for semilinear wave-type equations with time delay

Stability analysis of pressure and penetration rate in rotary drilling system

Rhouma Mlayeh^,

LIM laboratory, Polytechnic School of Tunisia, BP 743, 2078 La Marsa, Tunisia

^*Corresponding author: Rhouma Mlayeh
^*Corresponding author: Rhouma Mlayeh

Received: August 2021

Revised: October 2021

Early access: January 2022

Published: June 2022

Abstract / Introduction Full Text(HTML) Figure(8) / Table(1) Related Papers Cited by

Abstract

The purpose of this paper is to stabilize the annular pressure profile throughout the well bore continuously while drilling. A new nonlinear dynamical system is developed and a controller is designed to stabilize the annular pressure and achieve asymptotic tracking by applying feedback control of the main pumps. Hence, the paper studies the control design for the well known Managed Pressure Drilling system (MPD). MPD provides a closed loop drilling process in which pore pressure, formation fracture pressure, and bottomhole pressure are balanced and managed at surface. Although, responses must provide a solution for critical downhole pressures to preserve drilling efficiency and safety. Our MPD scheme is elaborated in reference to a nontrivial backstepping control procedure, and the effectiveness of the proposed control laws is shown by simulations.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. MPD in Rotary Drilling System

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Figure 2. Stabilization of the state $ y $

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Figure 3. Stabilization of the pressure $ P_2 $

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Figure 4. Stabilization of the penetration rate of the bit $ v $

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Figure 5. Stabilization of the rotation velocity of the drill string $ \Omega $

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Figure 6. Stabilization of the the flow rate from the tool $ q_{bit} $

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Figure 7. Stabilization of the control law $ u_1 $

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Figure 8. Stabilization of the control law $ u_4 $

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Table 1. Different physical parameters

Variable	Value
$L$	$2000~m$
$I$	$0.095~kg.m$
$\rho_1 = \rho_3$	$1250~kg. m^{-3}$
$M$	$8300~kg.m^{-4}$
$\beta_1 = \beta_3$	$24750~bar$
$V_0$	$110~ m^3$
$g$	$9.81~ m s^{-2}$
$S$	$\pi\times(0.25)^2~ m^2$
$c_d$	$0.61$
$T_a$	$0.003. 10^6~ \frac{bar. s^2}{m^6}$

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