Pressure Control for Offshore Managed Pressure Drilling (MPD): Analysis, Design, and Experimental Validation
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Deepwater offshore drilling operations are among the most complex activities. For example in regions such as the Gulf of Mexico, wells are drilled in water depths of up to 3 kilometers, drilling depths can exceed 6 kilometers, and geologic formation pressures can exceed 1400 bar. In offshore wells safe drilling and completion operations can be difficult due to narrow margins between pore pressure and fracture pressures. Moreover multiple zones of uncertain pore pressures and fracture pressures in reservoir formation makes drilling operation even more challenging. To avoid fracturing, collapse of the well, or influx of fluids from the reservoir surrounding the well, it is crucial to control the pressure in the open part of the well within a certain operating window. One method to regulate bottom-hole pressure is Managed Pressure Drilling (MPD). In Constant Bottom-hole Pressure (CBHP) MPD, the annulus is sealed and the drilling fluid exits through a controlled choke, allowing for faster and more precise control of the annular pressure. In automatic MPD systems, the choke is controlled by an automatic control system which manages the annular well pressure to be within specified upper (fracture pressure) and lower (pore pressure) bounds. In the North Sea environment, a large number of subsea wells are drilled from floating rigs. In this case, there would be the extra challenging factor of severe vertical motion (heave) of the rig in harsh weather, typically more than 3m up and down with a 10 - 20 seconds period. When drilling from a floating rig, the rig moves vertically with the waves. While drilling with weight on bit (WOB), a heave compensation system is in operation that isolates the drill string from the heave motion of the rig. As drilling proceeds, the drill string needs to be extended with new sections, referred to as pipe connection. Thus, every couple of hours or so, drilling is stopped to add a new segment of about 27 meters to the drill string. During connections, the pump is stopped and the drill-string is disconnected from the heave compensation mechanism and put into slips rigidly connected to the rig. The drill string then moves vertically with the heave motion of the floating rig, and acts like a piston on the drilling fluid in the well. The heave motion in this case can result in severe pressure fluctuations (surge and swab pressures) in the bottom of the well. Pressure changes have been observed to be beyond the standard limits for pressure regulation accuracy in MPD. The goal of this thesis is mainly to develop control design methodologies for regulating bottom-hole pressure (BHP) in offshore drilling operations. In essence extending control over BHP to the pipe connections scenario when the rig pumps are off and the drilling string is moving vertically. Two different lines of research are presented, which will be discussed in the sequel. This thesis comprises two parts. First part gives an introduction to MPD, and discusses briefly variants of MPD. Next common equipment and technology components in MPD are discussed. Then different estimation and control techniques proposed in the literature are reviewed thoroughly. Variety of estimation and control techniques have been applied in different scenarios in drilling operations. The majority of the control methods are based on PID and Model Predictive Control (MPC). While estimation techniques are mostly based on Kalman filters and Lyapunov techniques. Then an introduction to the connection scenario and down-hole pressure fluctuations (surge and swab) caused by the heave motion of floating drilling rig is given. Methods for modeling and prediction of surge and swab pressures are reviewed and different techniques proposed for compensating their effect in MPD and Under-Balanced Drilling operations (UBD) are discussed. An introduction to MPD-Heave lab at NTNU and a comparison with industrial scale MPD systems are given. Contributions are stated in detail. In the second part selected conference and journal papers are presented. In the first paper a simplified nonlinear dynamic model based on mass and momentum balances for managed pressure drilling (MPD) is presented. The sources of uncertainty in drilling operations is discussed and two parameters for calibrating the hydraulic model against uncertainties in the viscosity of mud, temperature distribution in the well, frictional pressure losses, the geometry of the well, and bulk modulus are considered. The key uncertain model parameters and the bottom-hole pressure are simultaneously estimated using joint unscented Kalman filter based on only available top-side pump and choke pressure measurements. The performance of the algorithm is tested for the case of normal drilling operations and connection operations, in which there is no flow through the drill-string and borehole pressure reduces significantly. The results of simulations show accurate estimation of the bottom-hole pressure and uncertain parameters during both transient and steady-state drilling operations. In the second paper a model describing the flow and pressure fluctuations in the bore-hole due to drill-string movement has been presented. It consists of a pair of coupled nonlinear partial differential equations modelling the distributed pressure and flow in the well, and a simple oscillator for the disturbance. Considering only top-side flow and pressure as measurements, it is shown that the model can be represented by a linear time invariant finite-dimensional system with output delay. This result is achieved by linearization and de-coupling using Riemann invariants. An infinite-dimensional observer is designed that estimates the disturbance, and the estimate is used in a controller that rejects the effect of the disturbance on the down-hole pressure. A model reduction technique based on the Laguerre series representation of the transfer function is used to derive a simple, rational, transfer function for the controller. The performance of the full-order and reduced-order controllers are compared in simulations, which show satisfactory attenuation of the heave disturbance for both controllers. In the third paper the results of the previous paper are extended by incorporating friction partially into the model and considering the heave disturbance to be a superposition of multiple sine waves. In the fourth paper, the output regulation problem for an offshore deep-water managed pressure drilling system subject to periodic disturbances is addressed. The disturbance is caused by the heave motion of the floating drilling rig during pipe connections and the objective is to maintain a constant pressure at the bottom of the well. The controller for the heave disturbance attenuation consists of three cascaded parts: First, a nonlinear inversion element is applied to invert nonlinearity of choke. Second, an adaptive compensator is designed based on internal model, and certainty equivalence principles for asymptotic rejection of time-varying heave disturbance. Third, an output feedback controller is synthesized using LMIs for providing stability and improving transient performance of closed-loop system. Robust stability of closed-loop time-varying system is analyzed using edge theorem. Simulation results of the combined adaptive output regulator are presented, which show satisfactory set-point tracking and attenuation of the heave disturbance. In the fifth paper, a modified L1 adaptive controller is applied to handling heave disturbances in MPD. It presents a modification to L1 adaptive control that allows for disturbances entering at the plant output. By incorporating the disturbance at the output into the reference model, it is shown that the L1 adaptive control structure can be left unchanged while the original transient performance bounds are preserved. It is further shown that rejection of the output disturbance can be taken care of entirely in the filter design step of L1 adaptive control using the internal model principle. A systematic filter design procedure based on LMIs is provided, that requires only one tuning parameter to be adjusted by the designer. While satisfying asymptotic robust regulation constraints, it guarantees a desired level of performance measured in terms of peak value of output signal subject to a peak value constraint on the control signal. The control design is applied for disturbance attenuation and set-point tracking in the so-called heave problem in oil well drilling, and successfully tested in a medium size experimental test facility containing a 900m long well. The results demonstrate that the proposed regulator efficiently regulates the down-hole pressure to the desired set-point, with significant attenuation of unmatched periodic disturbances. Finally in the last chapter, the conclusions and future work directions are offered.