This paper addresses the problem of reproducing oscillations generated by the well-known slugging phenomenon in multiphase flow. Reported investigations show how to determine the parameters of a recently proposed ordinary differential equations system, so that it captures the characteristics of actually observed slugging oscillations. A tuning procedure based on the mathematical properties of the model is presented. It is then applied to a test case consisting of a real oil well located in the North Sea. An observer using only topside measurements allows asymptotic reconstruction of critical variables such as the downhole pressure.