An aging theory-based mathematic model for estimating the wax content of wax deposits using the Fick's second law

In this study, a mathematic model is proposed for estimating the wax content of wax deposits. The proposed model was built based on the diffusion of wax molecules and counter-diffusion of oil molecules and described using the Fick's second law, allowing for the stacking fraction and orientational order of precipitated wax crystals and the tortuosity of diffusion path of de-waxed oil molecules during the counter-diffusion. The calculated results were verified by comparing with the flow-loop wax deposition experimental results. Dependence of radial position, deposition duration, bulk temperature, and wall temperature were investigated. These factors significantly affected the wax content during wax deposition. Good agreements were observed between the predictions and experimental results. The variation trends of wax content affected by various aspects are consistent with the existing studies.