Nonlinear Moving Horizon Observer for Estimation of States and Parameters in Under-balanced Drilling Operations

It is not possible to directly measure the total mass of gas and liquid in the annulus and geological properties of the reservoir during petroleum exploration and production drilling. Therefore, these parameters and states must be estimated by online estimators with proper measurements. This paper describes a nonlinear Moving Horizon Observer to estimate the annular mass of gas and liquid, and production constants of gas and liquid from the reservoir into the well during Under-Balanced Drilling with measuring the choke pressure and the bottom-hole pressure. This observer algorithm based on a low-order lumped model is evaluated against Joint Unscented Kalman filter for two different simulations with low and high measurement noise covariance. The results show that both algorithms are capable of identifying the production constants of gas and liquid from the reservoir into the well, while the nonlinear Moving Horizon Observer achieves better performance than the Unscented Kalman filter. NOMENCLATURE UBD Under-balanced drilling. UKF Unscented Kalman filter LOL Low-order lumped model. ∗Address all correspondence to this author. INTRODUCTION In recent years there has been increasing interest in UnderBalanced Drilling (UBD). UBD has the potential to both decrease drilling problems and improve hydrocarbon recovery. In conventional (over-balanced) drilling, or Managed Pressure Drilling (MPD), the pressure of the well must be kept greater than pressure of reservoir to prevent influx from entering the well. But in an UBD operation, the hydrostatic pressure in the circulating downhole fluid system must be kept greater than pressure of collapse and less than pressure of reservoir pcoll(t,x)< pwell(t,x)< pres(t,x) (1) at all times t and positions x. Since hydrostatic pressure in the circulating downhole fluid system is intentionally lower than the reservoir formation pressure, influx fluids (oil, free gas, water) from the reservoir are mixed with rock cuttings and drilling fluid (“mud”) in the annulus. Therefore, modeling of the UBD operation should be considered as multiphase flow. Different aspects of modeling relevant for UBD have been studied in the literature [1–4]. Estimation and control design in MPD has been investigated by several researchers [5–12]. However, due to the complexity of multi-phase flow dynamics in UBD operations, there are few studies on estimation and control of UBD operations [1, 13–16]. Nygaard et al. [13] compared and evaluated the performance of Proceedings of the ASME 2014 Dynamic Systems and Control Conference DSCC2014 October 22-24, 2014, San Antonio, TX, USA