Parameter estimation and statistical analysis of limit cycle models using a local optimization algorithm: applications for simplified well models of slugging oil systems

This paper presents a new methodology for parameter estimation of models with limit cycle and Hopf bifurcation. By calculating average cycle values for the process signal, a convex objective function can be produced using a maximum likelihood approach. This methodology allows for the proper statistical analysis of the results and the usage of local optimization algorithms for fast and efficient estimation. A case study is presented for a simplified well model of slugging oil systems, for which parameter estimation is crucial to correctly represent any system of interest. Two other objective functions from the literature are compared through Particle Swarm Optimization. The proposed method outperformed those of previous works as determined by a rigorous statistical assessment.