Modeling and Control of Heave- Induced Pressure Oscillations in Offshore Drilling
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This thesis addresses the topic of heave-induced pressure fluctuations in offshore drilling from floating platforms. Such pressure oscillations occur during drill string connections when the drill string is rigidly attached to and moves with the heaving platform. Depending on the pressure margins of the formation, well geometry, drilling mud properties and wave conditions, these pressure oscillations can violate safety margins, resulting in costly downtime while waiting for calmer weather. The contributions of the thesis fall into two main categories. First, it addresses the modeling of heave-induced pressure oscillations in order to facilitate assessment of their severity and to identify situations in which heave threatens safety margins, and when drilling can continue safely. Second, it addresses the problem of attenuating the pressure oscillations by control in order to extend the window of drillability. Actuation is considered both in form of controlling the opening of the topside choke, which requires no or little additional instrumentation compared to standard managed pressure drilling, and by controlling the flow through the drill bit in the case when circulation is maintained during connections. The controller design using topside actuation is approached via the substantially more general mathematical problem of boundary control of semilinear hyperbolic systems. The thesis is a collection of papers that are organized into 4 chapters. Following an introduction in Chapter 1, Chapter 2 contains two papers on the modeling, simulation and assessment of heave-induced pressure oscillations. In the modeling part, emphasis is given on friction modeling in drilling muds with Herschel-Bulkley rheology. The system behavior is analyzed in simulations, and the use of the simulator as a decision support tool is discussed. The next three chapters focus on control. Chapter 3 contains a paper on the boundary control of 2 × 2 semilinear hyperbolic systems. The method exploits the system dynamics on the characteristic lines along which the actuation and measurement propagate, respectively, and achieves global stabilization, estimation of the distributed state, and tracking at an arbitrary location in the domain in minimum time. As this paper is written in a mathematically general form, the method is applicable to the control of various forms of flow and transport, including the mud dynamics in the annulus during heave, flow through pipelines or open water channels, and traffic flow. Chapter 4 deals with rejecting heave-induced pressure oscillations by control. The focus is mostly on control from topside by controlling the opening of the choke at the outlet of the annulus in managed pressure drilling. Two papers deal with the controller design for a model of the annular mud dynamics with linear and nonlinear friction, using a backstepping design and the controller design from Chapter 3, respectively. The controller performance in both the linear and nonlinear case is further analyzed in two different papers. The sensitivity with respect to uncertainty in downhole parameters, unmodeled dynamics and actuation errors is investigated. Moreover, the papers investigate fundamental limitations related to the fact that only the topside boundary of the well is actuated, several kilometers from the well bottom where pressure control is required. Due to the delay, the control laws require a prediction of the heave motion. Therefore, due to the stochastic nature of waves, inevitable errors in the heave prediction affect performance. Furthermore, even if good pressure control is achieved at one location, control from topside creates a particular pressure amplitude profile in the well, leading to significant pressure oscillations in other parts of the well. Finally, performance is compared to simpler strategies, such as keeping the choke opening or choke pressure constant. A fifth paper present a different approach using continuous circulation, with actuation in form of controlling the flow through the bit rather than the topside choke. This approach avoids the distance between sensors and actuator and the well bottom, which simplifies the controller design, eliminates the need for heave predictions, and generally makes performance less sensitive to uncertainty in downhole parameters. However, control in this form creates large oscillations in the differential pressure over the bottom hole assembly (BHA) that can amplify the BHA motion. The controllers are designed to avoid exciting this potentially destabilizing mechanism. Chapter 5 contains two variations of the method for boundary control of semilinear hyperbolic systems introduced in Chapter 3. First, the method is generalized to systems consisting of a series interconnection of 2×2 semilinear hyperbolic systems with actuation and sensing at the boundary of one of the subsystems, leading to a cascade-like structure. This system structure occurs when the bit is not at the well bottom, with two subsystem modeling the mud in the annulus and mud below the bit, respectively, that are coupled at the drill bit. Second, the methodology is applied for control and state estimation of systems with sensing and actuation at both boundaries of the domain, achieving faster control and state estimation compared to one-sided control, and enabling tracking at up to two locations in the domain.