Soft Sensing for Gas-Lift Wells

Abstract

Abstract This paper considers the use of extended Kalman Filtering as a soft-sensing technique for gas-lift wells. This technique is deployed for the estimation of dynamic variables that are not directly measured. Possible applications are the estimation of flow rates from pressure measurements or the estimation of parameters of a drift-flux model. By means of simulation examples different configurations of sensor systems are analyzed. The estimation of drift-flux model parameters is demonstrated on real data from a laboratory set-up. Introduction The smart well paradigm involves the instrumentation of wells with sensors and actuators, which can be used for monitoring and control purposes. From a monitoring point of view, the use of sensors that measure different properties at several locations is preferred. However, because of practical and economical reasons such demands are unrealistic. Some measurements, like pressure measurements, are more readily available than others (e.g. oil flow rate). To have access to the unmeasured variables, the concept of soft sensing is used in this paper: the unmeasured dynamic variables are estimated from the measured ones by fitting a model to the measurements using extended Kalman Filtering [6]. In this paper a gas-lift well is considered. Possible applications of soft sensing for gas-lift wells are the estimation of gas and oil flow rates from pressure measurements and the parameter estimation for models that describe the multiphase flow phenomena. The use of soft sensing for well operations has been described in e.g. [9], [10]. In [9], [10] ensemble Kalman Filtering is used as the soft sensing algorithm, whereas in this paper extended Kalman Filtering is used. The main difference between these two algorithms is the prediction of the state-covariance matrix: ensemble Kalman filtering uses an ensemble of nonlinear state predictions to construct the predicted state-covariance matrix, whereas extended Kalman Filtering uses a locally linearized model to predict the state-covariance matrix. For models that are moderately nonlinear, in the sense that the change of the dynamics is small within two subsequent sampling times, extended Kalman filtering works well since in such cases the linear approximation between two sampling times is accurate. For highly nonlinear models this approximation is no longer accurate, and the use of an ensemble of nonlinear predictions may improve the predicted state covariance matrix [4]. However, the nonlinearity of the gas-lift model considered in this paper proved to be modest in the investigated operating region, which justifies the use of local linearizations. According to [9] a disadvantage of the extended Kalman Filter is the large computational demand of the numerical linearizations, which require a number of model evaluations that is of the same order as the number of state variables. However, in the ensemble Kalman Filter in [9] and [10] the number of nonlinear model predictions is set to 100, which is also of the same order as the number of state variables (159 in [10]: a discretization of 20 meters for a 1000 meter well results in 50 sections and each section consists of 3 states, additionally 9 states are used for the estimation of model parameters). Drawing the ensemble members randomly from a distribution introduces a stochastical component in the prediction of the state-covariance matrix of an ensemble Kalman Filter. This stochastic dependency on the random realization of the ensemble can be circumvented by choosing the realizations as suggested in [4] and [5], but this results in a number of ensemble members that is twice the number of state variables. Thus with respect to the computational load the extended Kalman Filter may be preferred over the ensemble Kalman Filter in the case of the application for gas-lift wells. The organization of the paper is as follows: first brief descriptions are given of both the model for the gas-lift well and of the extended Kalman Filter. Next, different measurement configurations are analyzed by means of simulations: the use of pressure measurements along the tubing, and the use of topside measurements from the annulus and the tubing. These configurations can be used for the on-line estimation of the gas and oil flow rates in the tubing, acting as a multiphase-flow soft-sensor. Besides, unknown model parameters can be estimated on-line in order to keep the model on track. For the estimation of unknown parameters of a drift-flux model, the soft sensor is tested on experimental data from a laboratory set-up.