Glenn-Ole Kaasa

Switched Control for Pressure Regulation and Kick Attenuation in a Managed Pressure Drilling System

This paper presents a switched control scheme for regulation of the annular pressure in a well during drilling. The main feature is automatic kick attenuation while drilling reservoir sections. A simple mathematical model is presented that captures the dominant phenomena of the drilling system and forms the basis for observer and control design. A switched pressure control algorithm for feedback control of the choke valve opening and the back-pressure pump is proposed, and asymptotic stability properties are established. Kick attenuation is guaranteed for a set of reservoir models, including the most common ones. As part of the control scheme, novel observers for estimation of the flow rate through the bit and kick detection are developed. Simulation results obtained with a high fidelity drilling simulator are presented to demonstrate the effectiveness of the proposed switched control scheme.

Adaptive observer design for the bottomhole pressure of a managed pressure drilling system

In this paper a reduced order observer that adapts to unknown friction and density, and estimates the bottomhole pressure in a well during drilling, is presented. The design is based on a newly developed third order nonlinear model with a nonlinear output equation containing a product between an unknown parameter and unmeasured state. Based on a Lyapunov approach the pressure estimate is shown to converge to the true pressure under reasonable conditions. Application of the observer to real data from a North Sea oil well demonstrates promising behaviour.

Drilling seeking automatic control solutions

Abstract This paper addresses control challenges within drilling for the oil and gas industry. Drilling has not been modernized as much as other industries and there is still a great potential for automatic control. Heavy machinery is used to handle pipes and other equipment topside and in and out of the hole. These machines can be controlled remotely with a joystick. Very advanced tools are being used downhole several km away from the rig and these are often controlled remotely. Mud pulse telemetry with low bandwidth is used to communicate with downhole equipment. Drilling involves certain risks and mistakes may have disastrous consequences both for people and economically, e.g. a blow-out. Safety is therefore always the most important issue, and new solutions must be robust and fault tolerant. Extensive testing is required before being used in an actual drilling operation. Managed pressure drilling is a relative new method for drilling challenging wells with narrow margins requiring precise pressure control. Nonlinear model based control solutions and observers have been developed for this technology. This is addressed in this paper together with experimental results. In addition an overview of some other interesting challenges is given.

Parameter estimation and compensation in systems with nonlinearly parameterized perturbations

We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions, for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.

Adaptive Redesign of Nonlinear Observers

To estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers. In this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented. The redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties. To enable parameter adaption, a new type of update law is derived using Lyapunov analysis and a nonlinear coordinate transformation. The uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states, and still achieves convergence of the state estimate without requiring persistent excitation. Two examples are presented that demonstrate these properties.

Experimental disturbance rejection on a full-scale drilling rig

Abstract Drilling operations in oil and gas industry increasingly require accurate control of the pressure in the well. In managed pressure drilling operations, the pressure is controlled by choking the flow of the drilling fluid out of the well. This pressure control system needs to handle various disturbances. In particular, vertical movement of the drill string, which occurs in several operational procedures, causes severe pressure variations. In this paper we present two nonlinear control algorithms that handle such disturbances due to vertical motion of the drill string. Performance of both algorithms has been tested on a full-scale drilling rig. These experimental results demonstrate applicability and limitations of the proposed solutions and indicate directions for further theoretical research and practical developments in this field.

Brief paper: Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.

Pressure regulation with kick attenuation in a managed pressure drilling system

This paper presents a switched control scheme for regulation of the annular pressure in a well during drilling. The main feature is automatic kick attenuation while drilling reservoir sections. A simple mathematical model is presented that captures the dominant phenomena of the drilling system and forms the basis for observer and control design. A switched pressure control algorithm for feedback control of the choke valve opening and the back-pressure pump is proposed, and asymptotic stability properties are established. Kick attenuation is guaranteed for a set of reservoir models, including the most common ones. As part of the control scheme, novel observers for estimation of the flow rate through the bit and kick/loss detection are developed. Simulation results obtained with a high fidelity drilling simulator are presented to demonstrate the effectiveness of the proposed switched control scheme.

Adaptive output feedback control of a managed pressure drilling system

This paper presents a nonlinear observer-based control scheme to stabilize the annular pressure profile throughout the well bore continuously while drilling. A simple mechanistic model is presented that captures the dominant phenomena of the drilling system and forms the basis for model-based observer and control design. A new nonlinear adaptive observer is developed for state estimations. A new adaptive controller is designed to stabilize the annular pressure and achieve asymptotic tracking by applying feedback control of the choke valve opening and the main pumps.

A constructive speed observer design for general Euler-Lagrange systems

Astolfi, Ortega, and Venkatraman (2010) recently proved the existence of a globally exponentially convergent speed observer for general Euler-Lagrange systems. Key to their result, is a function defined by certain integrals which cannot be solved a priori, and may not have explicit analytic solutions. In this paper, this obstacle to a constructive design is removed and equations that solve the speed observer problem are given in closed form. The design is further simplified by removing up to one third of the observer states used in Astolfi et al. (2010). With the significant reduction in complexity, the new observer is easily applied to estimate the angular velocities in a Furuta pendulum example.