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Stability analysis of pressure and penetration rate in rotary drilling system

  • *Corresponding author: Rhouma Mlayeh

    *Corresponding author: Rhouma Mlayeh
Abstract Full Text(HTML) Figure(8) / Table(1) Related Papers Cited by
  • 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.

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


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  • Figure 1.  MPD in Rotary Drilling System

    Figure 2.  Stabilization of the state $ y $

    Figure 3.  Stabilization of the pressure $ P_2 $

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

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

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

    Figure 7.  Stabilization of the control law $ u_1 $

    Figure 8.  Stabilization of the control law $ u_4 $

    Table 1.  Different physical parameters

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