State and Parameter Estimation for a Gas-Liquid Cylindrical Cyclone

Abstract

The development and production of hydrocarbons from oil and gas discoveries in deep water require costefficient compact separation technology. However, the small operational volume of compact separators make them highly sensitive to changes in flow rate and composition. Therefore, measurements of critical variables are crucial for providing operators with the necessary insight, as well as enabling the use of advanced controllers to efficiently control such separators. Available measurements are, however, often limited due to high investment cost or lack of suitable sensor technology. Estimators (soft sensors) can alleviate this problem. The gasliquid cylindrical cyclone is a type of compact separator recently considered for subsea application. Several advanced controllers have recently been derived for this separator, but estimators are needed for implementation in subsea applications. Therefore, in this paper, we develop and study the performance of the UKF and MHE estimators providing state feedback to a linear MPC.

Nonlinear State and Parameter Estimation for a Gas-Liquid Cylindrical Cyclone

“…A comparison of the performance of the UKF in this paper to that in [11] reveals that the oscillations are significantly increased. This increase is due to the increased sampling time between correction step resulting in an increased prediction step from ∆t s to ∆t y .…”

“…The estimators are based on the same transformed state-space model as the MPC and uses the available measurements of the inlet conditions w in and β in , the level h L , the pressure p G and the two outlet gas mass fractions β LL and β WG to estimate the transformed states x. The estimation model was derived in [11] and is included in this section for completeness.…”

“…The mean state estimatex k =x + k is provided as state feedback to the MPC. The frequency of the UKF is changed from that used in [11] to that of the NMHE to operate the UKF at the same frequency as the MPC and the sensors providing measurements, i.e., changed from executing each ∆t s second to each ∆t y second where ∆t y is the sampling time of the observations. This also enables a fairer comparison between the UKF and NMHE.…”

“…In [8], a Model Predictive Controller (MPC) using state feedback from an EKF was proposed, but the EKF gave low robustness and assumed knowledge of two unmeasured states. Therefore, [11] investigated the performance of an UKF and a linear MHE using a nonlinear measurement model based on measured states. However, although the linear MHE achieved good estimates of the directly and indirectly measured states, it was only able of accurately predicting one of the two unknown parameters.…”

“…In this paper, we derive an NMHE to achieve improved accuracy of the unknown parameters and extend the UKF based on [11] so that both operate at the same frequencies equal to that of the sensors providing measurements. The simplified estimation model derived in [11], consisting of four states (two directly and two indirectly measured) and two unknown parameters, is applied by both estimators. The measurements are inverted prior to running the estimators to have a linear relationship between the estimates and measurements.…”