March 2012 SPE Drilling & Completion 127 Simplified Hydraulics Model Used for Intelligent Estimation of Downhole Pressure for a Managed-Pressure-Drilling Control System Glenn-Ole Kaasa, Statoil and Norwegian University of Science and Technology, and Øyvind Nistad Stamnes, Lars Imsland, and Ole Morten Aamo, Norwegian University of Science and Technology Copyright © 2012 Society of Petroleum Engineers This paper (SPE 143097) was accepted for presentation at the SPE/IADC Managed Pressure Drilling and Underbalanced Operations Conference & Exhibition, Denver, 5–6 April 2011, and revised for publication. Original manuscript received for review 26 April 2011. Revised manuscript received for review 11 October 2011. Paper peer approved 4 November 2011. Summary An essential part of an automated managed-pressure-drilling (MPD) control system is the hydraulics model, which, in many cases, is the limiting factor for achievable accuracy of the system. Much effort, therefore, has been put into developing advanced hydraulics models that capture all aspects of the drilling-fluid hydraulics. However, a main drawback is the resulting complex- ity of these models, which require expert knowledge to set up and calibrate, making it a high-end solution. In practice, much of the complexity does not contribute to improvement of the overall accuracy of the pressure estimate simply because conditions in the well change during MPD opera- tions and there are not enough measurements to keep all of the parameters of an advanced model calibrated. We will demonstrate that a simplified hydraulics model based on basic fluid dynamics is able to capture the dominating hydrau- lics of an MPD system. Furthermore, we will demonstrate that, by applying algorithms for online parameter estimation similar to those used in advanced control systems in the automotive and aerospace industry, the model can be calibrated automatically by use of existing measurements to achieve a level of accuracy com- parable with that of a calibrated advanced hydraulics model. The results are demonstrated using field data from MPD operations in the North Sea and dedicated experiments obtained at a full-scale drilling rig in Stavanger. Introduction The main objective of MPD is accurate control of the annular downhole pressure during drilling operations. The basic principle of MPD is to apply additional backpressure to control the down- hole pressure and compensate for annular-pressure fluctuations. In a standard MPD setup, a rotating control device seals the top of the annulus and the flow of mud from the well is controlled by a choke manifold to apply a desired backpressure. A backflow pump is usually installed to boost the flow through the choke, enabling control of the backpressure also in the case of no flow from the mud pumps. A description of the standard setup of an automated MPD system can be found in van Riet et al. (2003), for example. In an automated MPD system, the automation of the choke manifold is performed by a control system usually consisting of two main parts: a hydraulics model that estimates the downhole pressure in real time and yields a desired choke pressure according to a desired downhole pressure set point and a feedback control algorithm that automates the choke manifold to maintain the desired choke pressure. A schematic of this configuration of an automated MPD system is shown in Fig.1. In many cases, the hydraulics model is the limiting factor for achievable accuracy of the MPD system. Much effort, therefore, has been put into developing advanced hydraulics models in order to capture all aspects of the drilling hydraulics (Rommetveit and Vefring 1991; Petersen et al. 1998, 2001, 2008a; Lage et al. 1999; Lage and Time 2000; Bjørkevoll et al. 2000, 2003). These models are able to reproduce a wide range of drilling-specific effects to an impressingly high degree of detail. Real-time versions of these models have also been used in MPD operations—both offline and online [see, for example, Eck-Olsen et al. (2005) and Bjørkevoll et al. (2008, 2010)]. For any simulation model, however, the overall accuracy is limited by the least accurate term. Typically, several parameters are both uncertain and slowly changing, such as the friction coef- ficients along the well, the amount of gas dissolved in the mud, or external boundary conditions such as the unmeasured reservoir temperature. Calibration, thus, is a vital part of any real-time hydraulics model in order to predict the downhole pressure with high accuracy. In practice, the calibration of a hydraulics model must be based on available topside measurements and measure- ments at the drill bit, such as pressure-while-drilling (PWD) data. These data contain insufficient information to calibrate properly all of the physical parameters of an advanced hydraulics model. Hence, as the conditions downhole in the well are typically inho- mogeneous and uncertain caused by changes during an MPD operation, without additional distributed measurements along the well available for calibration, much of the sophisticated detail of an advanced model does not contribute to improve the overall accuracy of the downhole pressure. Motivation Several aspects motivate the use of simpler hydraulics models in an MPD control system. Three important factors are summarized and discussed in the following paragraphs: • Bandwidth of the control system • Robustness of the implemented algorithm • Online calibration of the hydraulics model A control system is only able to compensate for changes that are slower than a particular frequency range, referred to as the bandwidth of the closed-loop control system. Typically, the achievable bandwidth of an MPD system is determined by the dynamic response of the choke actuator and the sampling fre- quency of the control system. The system is inherently incapable of compensating changes that occur at frequencies higher than this limit. Consequently, a control system behaves like a low-pass filter in the sense that it is not able to compensate high-frequency dynamics. Furthermore, if the bandwidth of the control system is pushed closer to the physical limit in an attempt to compensate for high-frequency changes, the stability margins of the system are reduced, making the system less robust to disturbances. Because the hydraulics model provides the pressure set point as input to the control system, it is undesirable that the model contain high- frequency dynamics simply because the control system is not able to accommodate fast changes in the pressure set point. A primary concern in a failure-critical control system such as MPD is the complexity and robustness of the implemented algorithm. (By “failure-critical,” we mean that a failure may have