Analytical Modeling of Wax Plug Transportation during Pipeline Pigging Using a Foam Pig

In our previous article (Gao et al. 2020), a mathematical model including elastic and yield components but not viscous component was developed to predict the wax plug transportation force. In this work, an analytical model was developed to calculate the wax plug transportation force, and the viscous component was introduced into the analytical model to capture some of the time effects. In this analytical model, the viscoelastic behavior of the wax deposit was characterized by a three-parameter model, formulated by adding an additional spring element to the Kelvin-Voight model. The Laplace transformation was used to solve the model. According to the calculated results of the analytical model, the transportation force of the wax plug was observed to slightly increase with time and then tended to level off. To obtain a parameter in the model and verify the model, the pigging experiments were conducted using foam pigs. During the pigging process of the foam pig, the wax plug transportation force in a five-phase wax removal profile was determined by taking the steady wax breaking force from the resistive force of the wax layer. Moreover, the linear increase of the wax plug transportation force per unit contact area with the shear strength of the wax layer was found, as described by the functional relationship in the analytical model. The interfacial lubrication coefficient calculated from the experimental data based on the analytical model is between the coefficient for diesel-prepared deposits and coefficient for oil-A-prepared deposits. Experimental verification results show that the average relative error of the model is 12.47%. Field implication was proposed to illustrate the application of the model and the formation condition of the wax blockage.