State and parameter estimation for a Gas-Liquid Cylindrical Cyclone SUBPRO SUBSEA PRODUCTION AND PROCESSING State and parameter estimation for a Gas-Liquid Cylindrical Cyclone Torstein Thode Kristoffersen and Christian Holden

Subsea compact separation SUBPRO Subsea compact separation Offshore oil and gas production Current status New discoveries Subsea compact gas-liquid separation reducing the number of flowlines and topside processing capacity providing cost-efficient hydrate management enabling single-phase boosting enabling long range gas compression Today, most of the developed oil and gas discoveries are in shallow waters in areas near to shore, while new oil and gas discoveries are in deep waters in remote areas. Subsea processing is an enabling technology for the development of these new fields and for increased oil and gas recovery of mature fields. Subsea gas-liquid compact separation is a key component of subsea processing for several reasons, including: - reducing the number of flowlines and topside processing capacity - providing cost-efficient hydrate management - enabling single-phase boosting for overcoming high hydrostatic pressure in deep waters - enabling long range gas compression from subsea to shore Foto: Statoil ASA

Gas-Liquid Cylindrical Cyclones (GLCC) SUBPRO Gas-Liquid Cylindrical Cyclones (GLCC) The Gas-Liquid Cylindrical Cyclone separator, in short GLCC, is a type of compact gas-liquid separator suited for subsea separation. The inlet gas-liquid flow enters tangentially into the separator. The tangential inlet combined with the high velocity creates large centrifugal forces that separates the gas from the liquid due to the density difference. The gas moves towards the center creating a gas core, while the liquid is forced towards the wall creating a falling liquid film that accumulates at the bottom establishing a liquid level. The gas leaves at the top and the liquid at the bottom. Since the gas contains some droplets it is called wet gas (WG) and since the liquid contains some bubbles it is called light liquid (LL). The performance of the GLCC separator depends on several variables and therefore, multiple sensors are required to provide operators and controllers with information to achieve efficient operation. In this presentation we consider this separator equipped with level measurement, pressure measurement, measurement of the gas mass fraction in the WG and measurement of the gas mass fraction in the LL. The two later indirectly measure the purity of the main separator volumes.

Challenges Equipment located at the seabed SUBPRO Challenges Equipment located at the seabed Limited and costly maintenance interventions Sensor requirements Sensors quality and availability limitations prone to failures low data quality limited number of sensors A major challenge with subsea processing is that the equipment is located at the seabed and is not easily available for maintenance. Maintenance interventions are limited and costly as they require good weather conditions and expensive lifting or subsea intervention vessels. Sensors should therefore be robust and reliable to withstand the harsh environment on the seabed and operate for long times without failures. However, sensors quality and availability are limited as sensors are: - prone to failures - sensor data quality is often low due to indirect sensing and/or low sampling frequency - and the number of sensors are often limited due to too expensive sensors and/or due to lack of suitable sensor technology.

Soft sensors (estimators) Cost-efficient alternative to physical sensors Principle Types of soft-sensors stochastic estimators deterministic estimators Soft-sensors, or estimators, are a cost-efficient alternative to physical sensors. Soft-sensors are based on the principle that a unmeasured state or parameter can be filtered from a limited set of measured states using a mathematical model of the plant and available measurements. Estimators are characterized as either stochastic and deterministic estimators. - stochastic estimators models the initial state and estimates as random variables and use a stochastic estimation model for prediction - deterministic estimators models the initial state and estimates as deterministic variables and use a deterministic model for prediction

Research status of GLCC separators SUBPRO Research status of GLCC separators Extensive research on control of GLCC separators non-model based using few measurements model based using several measurements Little research on estimation of GLCC separators Extended Kalman Filter (EKF) Adaptive estimation The GLCC separator has been subject to extensive research on control. The proposed controllers typically separates into two groups. - The first group of proposed controllers typically require no model of the plant and only use feedback and a few measurements to control the plant, e.g., PI, gain-scheduling - The other group of proposed controllers typically require a model of the plant and use feedback and several measurements to control the plant, e.g., MPC, feedback linearizing controllers, However, the GLCC separator has been subject to little research on estimation. As of my knowledge there has only been two attempts on estimation of unmeasured parameters for the GLCC separators. The first attempt used a - EKF for estimation of unmeasured parameters in a parameterized model of the plant. However, this method assumed full-state knowledge including knowledge of realistically unmeasured states. - adaptive estimation of unmeasured parameters in a feedback linearizing controller. However, this method does not accurate estimate parameters that could be used in any other predictive manner.

Scope of this presentation Comparison of a stochastic and a deterministic estimator Unscented Kalman Filter (UKF) Linear Moving Horizon Estimator (MHE) Realistic measurements Discrete-time estimation execution at discrete-time Different frequency for estimation and prediction This presentation compares a stochastic and a deterministic estimator in simulations. The stochastic estimator is the UKF and the deterministic estimator is the linear MHE. In contrast to the previous work on estimation, we will use a set of realistic measurements resulting in a nonlinear observation model. The estimators execute at discrete-time with frequency equal to that of the sampling of the measurements. However, the fast dynamics of the system necessitates a much faster sampling resulting in different frequencies for the estimation and prediction.

Estimator design Objective Prediction model Observation model The objective of the estimator is to determine approximate values of the states and parameters with minimum error mean (bias) and variance. The dynamic model of the GLCC separator is nonlinear involving several parameters. However, only four measurements are available resulting in limited observability. Therefore, the dynamic model is simplified and parameterized with two unknown parameters to enable estimation of the system. Moreover, using realistic measurements of the liquid level, gas pressure and the gas mass fractions for each outlet results in a nonlinear observation model. Therefore, to have a linear relationship between the estimated states and the measurements, the measurements are inverted prior to execution of the estimation algorithms.

Closed-loop system

Unscented Kalman Filter (UKF) Principle Estimation procedure sigma points eq two steps Frequencies The UKF is based on the principles that an approximation of the estimates based on average of a set of transformed points is more correct than an estimate of the random variable properties estimates based on transformation of a single point. The estimation procedure of the UKF is similar to the Kalman filter with exception of that the random variable properties are based on set of points rather than a single point. - the set of points are called sigma points are chosen deterministically based on the following equation. - the estimation is done in a two step procedure. In the first step, each sigma points, calculated from the previous time a posteriori estimate, is time-propagated to the current time and then the a priori estimate of the mean and covariance are calculated from these sigma points. The subsequent step calculates a new set of sigma points from the current time a priori estimate and transforms it to measurement space. The mean of these transformed points is calculated and used with the current time measurement to correct the a priori estimate giving the a posteriori estimate In our system, the sampling rate of the measurement is much slower than that of the dynamics. Therefore, the prediction and correction step operates with different frequencies. The discrete-time UKF executes at the same frequency as the sampling of the measurements, so that the prediction step needs to integrate over a time step equal to that of the time sampling of the measurements.

Linear Moving Horizon Estimator (MHE) Principle Optimal Estimation Problem (OEP) Estimation procedure linearize around previous estimate (aut) substitute past observations into OEP solve OEP to obtain the current discrete-time estimate repeat at next sampling instant qpOASES Frequencies The principle of the MHE is to solve an Optimal Estimation Problem using observations of measurements and inputs on a finite moving time window in the past to estimate the discrete-time estimates on a time horizon stretching from the past to the current time. The estimation procedure consists of first linearizing around the previous time estimate to get the Jacobians describing the dynamics. Next the past observations are substituted into the OEP before it is then solved to obtain the current time estimate. At the next sampling instant, the procedure is repeated. As with the UKF, the MHE operates with to different sampling frequencies for the states and observations.

Configuration Tuning Simulation scenario Measurement noise covariance matrices Simulation scenario changing inlet conditions (flow rate and composition) Measurement noise The covariance of the estimation algorithms are tuned until satisfactory performance were achieved. The estimation performance of both estimators were then analyzed in separate, but equal simulations where the inlet conditions changed every 3 minutes between a low, intermediate and high inlet flow. All measurements used by the estimators were added zero-mean Gaussian white noise with the following statistical properties. (std dev.= A*mu_z)

Simulation results Here the simulation results for the UKF and MHE. As the figures indicate, the UKF achieves better performance with smaller measurement variance and no bias of the unknown parameters.

Estimation evaluation To objectively evaluate the estimator performances, the statistical properties of all estimates for both the UKF and the MHE are calculated and listed in this table. As you can see in the estimates of the level, impurities in the liquid, and the second unknown parameters there are small differences, while for the estimates of the impurities in the gas and the second unknown parameter is better estimated by the UKF. Only the UKF achieves an unbiased estimate of the second unknown parameter. However, the pressure is better estimated by the MHE with smaller bias and error variance.

Control and system evaluation The control and system performance are objectively evaluated using RMS values for the control and system error. As you can see, there are small differences, but the UKF achieves better level control, while the MHE achieves better pressure control. The same is observed for the system performance.

Conclusions Comparison between a discrete-time UKF and MHE Evaluated based on statistical properties UKF performed better than linear MHE UKF uses nonlinear estimation model MHE uses linear estimation model Uncertain estimation model pressure dynamics largely described by unknown parameters creating significant oscillations This this presentation we have compared the performance between a discrete-time nonlinear UKF and a discrete-time linear MHE. Their performance were evaluated based on statistical properties of the estimates. The UKF performed better than the MHE. The UKF generally achieves estimates with smaller bias and error variance and is the only estimator to accurately estimate both unknown parameters without bias. This is not suppressing as the UKF uses a nonlinear estimation model and accounts for the noise and uses a nonlinear model, while the MHE uses a linearized estimation model and does not consider the noise and uses a linear model. The estimators use a uncertain estimation model. The pressure dynamics are largely described by unknown parameters that oscillates and are likely to created the significant pressure oscillations. The performance of the MHE is likely to improve using a nonlinear estimation model, e.g., unbiased estimate of the first unknown parameter. Thus, development of a nonlinear MHE is future work.