Stochastic Nodal Analysis

Abstract

A petroleum production system is generally modelled based on the concept of nodal analysis, where the entire system is broken down into discrete elements such as near-well bore, tubing, surface choke and flow line. Operating flow rates and pressures can be estimated with a nodal analysis procedure by calculation of the intersection of performance curves. Input parameters in nodal analysis of production systems are considered deterministic, however, some of these parameters are better represented as distributions. In this report, the ensemble-based data assimilation methods “ensemble Kalman filter” (EnKF) and “particle filter” (PF) are applied to steady-state models of a production system for tuning of uncertain model parameters during the test separator phase. The performance of the EnKF and the PF is tested with the use of twin experiments. The calibrated model parameters of the choke, tubing and the near-well bore elements with EnKF and PF can be used to create an ensemble of performance curves leading to an ensemble of operating flow rates and pressures. The foreseen next step is to use the posterior distributions of model parameters as inputs for soft sensing of flow rates during semi-steady-state production for a single phase oil reservoir, where the oil rate and reservoir pressure are considered as unknown parameters. In the twin experiments as used in this thesis, a total number of three steady-state pressure drop measurements was used to estimate a total of six independent parameters which constitutes an ill-posed problem, resulting in non-unique parameter estimates. It is recommended to alleviate this issue by either reducing the number of parameters or by using multiple separator tests at different flow rates.