Mathematical formulation and numerical modeling of wax deposition in pipelines from enthalpy–porosity approach and irreversible thermodynamics

In the last 10 years, there have been a number of studies in modeling of the deposition processes in flowlines. Most of these models: (1) assume empirical or semi-empirical correlations to predict the pressure drop and temperature profile, (2) ignore the radial convection flow in the layer composed of the two-phase wax and oil (that is the gel layer), and (3) use Fick’s law to describe the diffusion flux of species towards the wall by using the chain rule to relate concentration gradient to temperature gradient. In this work, a rigorous mathematical model for the prediction of wax deposition in pipelines is presented for laminar flow. The transient deposition of each component is calculated from the solution of the coupled momentum, energy and, species balance equations, and a thermodynamic wax precipitation model at the local level. An enthalpy formulation based on a fixed-grid approach is used to approximate the convection flow in the gel layer. We do not use the chain rule to relate composition gradient to temperature gradient in Fick’s law to avoid violating the laws of irreversible thermodynamics. Our diffusion flux expression includes molecular diffusion (concentration gradient is driving force) and thermal diffusion (temperature gradient is driving force) with appropriate diffusion coefficients. This work also includes the description of the numerical solution of the governing equations. Numerical results and features of wax deposition as well as model verification with experimental data are presented in a separate paper.