The three phase separator is an important unit in oil and gas production facilities to separate gas, water and condensate from the fluid (raw gas) generated from gas wells. A dynamic model of the three phase separator is essential for process optimization and control design. Since first principles modelling of the three phase separator is complex, a data based model (Wavelet Network based Nonlinear AutoRegressive eXogenous model (WN-NARX)) is used to capture the dynamics of the process. As most of the terms in the WN-NARX expansion are redundant, this identification problem is over parameterized. In order to handle this issue, a sparsity constraint on the parameter vector is considered and sparse estimation algorithms such as Orthogonal Matching Pursuit (OMP) and Least Angle Regression (LAR) are used for identification of the WA-NARX model. The application of these sparse estimation methods for identification of an industrial three phase separator process is demonstrated. © 2019 IEEE.