Agus Hasan

Boundary observer design for hyperbolic PDE-ODE cascade systems

The paper presents an observer design for a class of hyperbolic PDE-ODE cascade systems with a boundary measurement. The cascade systems consist of coupled PDEs, featuring one rightward and one leftward convecting first-order transport PDEs, and a set of ODEs, which enter the PDEs through the left boundary of the systems. The design, which is based on the Volterra integral transformation, relies only on a single sensor at the right boundary of the system. The observer consists of a copy of the plant plus output injection terms both in the PDEs and the ODEs. The observer is constructed in a collocated setup, which means both sensing and actuation are located at the same boundary. The observer gains are computed analytically by solving Goursat-type PDEs in terms of Bessel function of the first kind. The observer design is tested against a field scale flow-loop test experiment in Stavanger by Statoil Oil Company. The results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling.

Flow control of fluids through porous media

This paper discusses flow control of fluids through porous media, specifically related to its application in petroleum science. The flow of fluids is described by the Boussinesq equation with mixed boundary conditions; a Neumann boundary condition describes no flow at the outer boundary of the porous media and a nonlinear boundary condition describes the interaction between the porous media and the source potential. In many ways, the source potential can be controlled. This leads to a boundary control problem of the Boussinesq equation. The problem can be analyzed by the Lyapunov method. Numerical examples are performed to provide a clear understanding of the concept of boundary control for these fluid flow systems.

Disturbance attenuation of n + 1 coupled hyperbolic PDEs

In this paper, we present a state-feedback and a state-observer for disturbance attenuation problems for a class of n + 1 coupled linear hyperbolic partial differential equations. The disturbance and the sensing are located at the left boundary of the system while the actuation is located at the right boundary of the system (anti-collocated setup). The designs are based on the backstepping method and rely on boundary measurement only. The feedback control law is found by utilizing the fact that the closed-form solution of the equivalent target system can be obtained. Furthermore, by defining a modified L2-norm, we show the observer is exponentially stable. A numerical example inspired from an oil well drilling problem is presented to validate the results.

Well rate control design for gas coning problems

This paper presents a method which uses boundary control to increase the oil production in the subcritical phase of a thin oil rim reservoir which is drained via horizontal wells. The problem of finding an optimal well rate is considered using the backstepping method. The feedback control law is constructed explicitly and together with a reservoir-well simulator are used to generate a time varying production plan. The simulation result shows that the performance of the active control law is much better than conventional production strategies using constant oil rates until gas breakthrough.

Adaptive boundary control and observer of linear hyperbolic systems with application to managed pressure drilling

Managed Pressure Drilling (MPD) is an advanced pressurecontrol method that is used to precisely control the annular pressure throughout the wellbore in an oil well drilling. Because downhole measurements are unreliable due to slow sampling, transmission delay, and loss of communication for low or noflow conditions, the challenge is to accurately estimate the flow and pressure along the annulus and the unknown in/out flux at the bottom of the well using only topside measurements. This paper describes the development of an adaptive control and observer for such problems that models the transport phenomenon as a 2 2 linear hyperbolic system. The adaptive design, which relies only on the measurements taken at the right boundary, is based on the backstepping method. The design is tested using data from a field scale flow-loop test conducted in Stavanger, Norway by the Statoil oil company. The results show that the observer converges to the actual value and that the update law accurately estimates the unknown parameter.

Moving horizon estimation in managed pressure drilling using distributed models

This paper presents a moving horizon estimation (MHE) approach for estimating flow and pressure inside the annulus during managed pressure drilling (MPD). MPD is an advanced pressure control method that is used to precisely control the annular pressure throughout the wellbore in oil well drilling. The MPD model, which is a hyperbolic-type partial differential equation (PDE), is a hydraulic model based on basic fluid dynamics. Using an early lumping approach, the model yields a high-dimensional system of an ordinary differential equation (ODE). We show the adjoint-based method combined with a line search algorithm can solve the MHE dynamic optimization problem efficiently. The estimator is tested using data from a field scale flow-loop test conducted in Stavanger, Norway by the oil company Statoil.

Boundary control for a class of pseudo-parabolic differential equations

Abstract The boundary stabilization problem for a class of linear and nonlinear pseudo-parabolic differential equations is considered. The proposed control laws are used to achieve global exponential stability for the linear system and semi-global exponential stability for the nonlinear system in the H 1 -sense. An H 2 bound of the solution for the nonlinear system is also derived. A numerical example is included to illustrate the application of the proposed control laws.

Well Testing by Sinusoidal Stimulation

A new approach to testing of oil and gas wells by means of sinusoidal oscillations in flow and pressure instead of the traditional buildup test is proposed in this article. This approach allows faster testing and simultaneous testing of several wells, with no need for a dedicated test header; it can also be adjusted to strike an appropriate compromise between measurement precision and production loss. This study details various operating issues such as generation of input signals, choice of test frequencies, applicability, and interpretation of results. To demonstrate the method, both a synthetic test and several field tests are presented.

Output-feedback stabilization of the Korteweg-de Vries equation

The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and actuators are located at different boundaries (anti collocated set-up) using backstepping method. The feedback control law and the output injection gains are developed from the backstepping method for the linear KdV equation. The novelty of this paper is the nonlinear observer for the KdV equation. Furthermore, proof of stability is based on construction of a strict Lyapunov functional which includes the observer states. A numerical simulation is presented to validate the result.

Modeling, Simulation, and Optimal Control of Oil Production under Gas Coning Conditions

Gas coning is a tendency of the gas to impel the oil downward in an inverse cone contour toward the well perforations. Once the gas reaches the well, gas production will dominate the well flow and the oil production will hence significantly decrease. From an economical and operational standpoint this condition is undesirable since the gas price is much lower than the oil price, and the gas handling capacity often is a constraint. Therefore, there is an incentive to maximize oil production up until gas breakthrough. In this paper, the gas coning process in a gas oil reservoir completed with a single horizontal well is analytically modeled, simulated, and analyzed applying a nonlinear control approach. The model which describes the interaction between the well and the reservoir may be cast into a boundary control problem of the porous media equation with two boundary conditions; a Neumann boundary condition describing no flow at the outer boundary of the reservoir, and a nonlinear boundary condition describing the well production rate. A well rate controller for the boundary control problem is designed using the Lyapunov method. The controller holds some formal performance guarantees and requires information on the gas oil contact at the well heel only. Further, the controller has a tuning parameter which can be used to maximize a suitable performance measure. The controller is evaluated using a detailed ECLIPSE simulator of a gas coning reservoir. Simulation results show significant improvement of production profit of the proposed method compared to a conventional method which usually uses a constant rate up until gas breakthrough. Introduction Optimization of the trade-off between oil and gas production is an important issue in reservoir management. The use of secondary recovery techniques such as gas lift and waterflooding, and EOR techniques such as surfactant injection has been proven successful to increase the oil production significantly. Those techniques are now supported by the growing application of smart well technologies. A smart well is usually equipped with several valves that can be regulated over the time of production. Questions regarding how to operate these valves can be partially answered using optimal control theory, in particular when it is combined with the adjoint method; see [1], [2], and [3]. Adjoint based optimization can also be used to determine optimal well placement [4] and for history matching [5]. Optimal control theory combined with data assimilation form a closed-loop reservoir management. A comprehensive summary of the closed loop reservoir management concept may be found in [6]. Although providing solutions in a relatively short time in an efficient way, the adjoint method is difficult to implement. This is because one needs access to reservoir simulator code and implements the algorithm there. An alternative way which can be done is by creating a mathematical model which is simpler but can be used to explain the same physical process. This model will then be referred to as a proxy model and serves as a representative of a complex model which is usually contained in a reservoir simulator. A proxy model may be derived from the basic principle of physics such as mass conservation and Darcy law. Since the proxy model is simpler than the high-fidelity model, a proxy model is certainly easier than working with the actual one. Therefore, instead of using the full model, in this paper a proxy model will be used for design and analysis purposes. Further, the results will be tested using a complex reservoir dynamics which is usually contained in a tested and well known reservoir