Ulf Jakob F. Aarsnes

Control-Oriented Drift-Flux Modeling of Single and Two-Phase Flow for Drilling

We present a simplified drift-flux model for gas-liquid flow in pipes. The model is able to handle single and two-phase flow thanks to a particular choice of empirical slip law. A presented implicit numerical scheme can be used to rapidly solve the equations with good accuracy. Besides, it remains simple enough to be amenable to mathematical and control-oriented analysis. In particular, we present an analysis of the steady-states of the model that yields important considerations for drilling practitioners. This includes the identification of 4 distinct operating regimes of the system, and a discussion on the occurrence of slugging in underbalanced drilling.Copyright

Fit-for-Purpose Modeling for Automation of Underbalanced Drilling Operations

Automation has the potential to improve efficiency, precision, and safety of pressure and flow control during underbalanced drilling (UBD). In addition, advanced estimation theory can be used to extract more information from existing measurements to increase knowledge of the downhole conditions during operation. An essential part of an advanced (model based) pressure control system is the hydraulic model. Even with high- bandwidth distributed downhole measurements, a calibrated hydraulic model is required to ensure robustness, e.g. to sensor loss, and obtain real time estimates of unmeasured quantities and reservoir characteristics. In UBD operations, in contrast to Managed-Pressure-Drilling (MPD) operations, the flow in the annulus is inherently a multiphase gas liquid flow, which severely complicates the modelling. Much effort has been put into developing multiphase flow models, however, to date; most of these are very complex, requires extensive configuration and are not well suited for real-time applications. Consequently, a major gap with respect to automation of UBD is the lack of a fit-for-purpose model capable of reproducing the main dynamics of the multiphase flow in the annulus, while being sufficiently robust and suitable for real-time applications. In this work, we present recent advances on the development of a simplified fit-for-purpose model of the distributed gas- liquid dynamics, suited for advanced control of UBD operations. Using an automated calibration procedure, the model is shown to retain accuracy in a realistic case study. It is also shown that its reduced complexity enables real time coupling with measurements to obtain estimates of unmeasured quantities such as gas distribution and perform reservoir characterization

A SIMPLIFIED GAS-LIQUID FLOW MODEL FOR KICK MITIGATION AND CONTROL DURING DRILLING OPERATIONS

Real-time estimation of annular pressure profile and formation pressure is crucial for the execution and planning of a well control operation, especially when drilling formations with narrow pore and fracture pressure margins. A simple transient multi-phase simulator, capable of accurately representing gas and liquid dynamics while minimizing complexity and computational requirements, is highly desirable for real-time kick mitigation and control applications. Such a simulator is presented here in the form of a coupled ODE-PDE model composed of a first order ODE and a first order hyperbolic PDE. This model is shown to retain the dominating two-phase dynamics encountered during gas kick incidents. As a particular application, we demonstrate the use of the model in design of switched control algorithms for kick handling in a Managed Pressure Drilling setting. A Recursive Least Squares algorithm is employed for estimation of unknown model parameters.Copyright

A Methodology for Classifying Operating Regimes in Underbalanced-Drilling Operations

This paper proposes an extension to an existing operating-envelope technique used for underbalanced drilling (UBD) to enhance control of bottomhole pressure and inflow parameters. With the use of an implementation of the drift-flux model (DFM) with boundary conditions typically encountered in underbalanced operations (UBO), a steady-state analysis of the system is performed. Through this analysis, four distinct operating regimes are identified, and the behavior in each of them is investigated through steady-state calculations and transient simulations. In particular, the analysis reveals that a section of the operating envelope previously believed to be unstable/transient is, in fact, stable/steady when a fixed choke opening is used as an independent variable in place of a fixed wellhead pressure (WHP). This results in the steady-state operating envelope being extended, and gives an increased understanding of the well behavior encountered in UBO toward enabling the introduction of automated control. Finally, we investigate the mechanism behind severe slugging in UBO and argue that the cause is different from that of the slugging encountered in production and multiphase transport.

Review of two-phase flow models for control and estimation

Abstract Most model-based control and estimation techniques put limitations on the structure and complexity of the models to which they are applied. This has motivated the development of simplified models of gas-liquid two-phase flow for control and estimation applications. This paper reviews the literature for such models with a focus on applications from the field of drilling. The models are categorized in terms of complexity and the physical interpretation of the simplifications employed. A simulation study is used to evaluate their ability to qualitatively represent dynamics of 3 different gas-liquid scenarios encountered in drilling, based on which conclusions are drawn.

State and Parameter Estimation of a Drift-Flux Model for Underbalanced Drilling Operations

We consider a drift-flux model (DFM) describing multiphase (gas–liquid) flow during drilling. The DFM uses a specific slip law, which allows for transition between single and two phase flows. With this model, we design unscented Kalman filter (UKF) and extended Kalman filter (EKF) for the estimation of unmeasured state, production, and slip parameters using real-time measurements of the bottom-hole pressure, outlet pressure, and outlet flow rate. The OLGA high-fidelity simulator is used to create two scenarios from underbalanced drilling on which the estimators are tested: a pipe connection scenario and a scenario with a changing production index (PI). A performance comparison reveals that both UKF and EKF are capable of identifying the PIs of gas and oil from the reservoir into the well with acceptable accuracy, while the UKF is more accurate than the EKF. Robustness of the UKF and EKF for the pipe connection scenario is studied in case of uncertainties and errors in the reservoir and well parameters of the model. It is found that these methods are very sensitive to errors in the reservoir pore pressure value. However, they are robust in the presence of error in the liquid density value of the model.