Modeling of Wax Deposition in Pipelines from Irreversible Thermodynamics

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Abstract Wax deposition in flowline of some crude oils and gas condensates in offshore is a serious problem. Deposition often reduces flow capacity and may block the line and reduce flow rate and increase the production cost substantially. In the last ten years, there have been a number of studies in modeling the deposition processes. All these models assume that the Fick's law of diffusion adequately describes the mass diffusion flux of wax-forming species from the oil or gas phase towards the wall. Wax deposition in flowlines is the result of radial temperature gradient and subsequent diffusion mass flux of species in the radial direction. However, the diffusion mass flux of species in the radial direction cannot be described by the Fick's law of diffusion. In this work, we first write the expression for diffusion flux in terms of: 1) molecular diffusion, and 2) thermal diffusion. Thermodynamics of irreversible processes is used to model the diffusion flux at non-isothermal conditions. We avoid the use of chain rule to relate composition gradient to temperature gradient. We also include the radial convective velocity in problem formulation for the laminar flow for the first time. In our formulation, both the mass balance and energy balance are written for a multicomponent two-phase solid-liquid mixture. A control volume method is used to solve the coupled problem of mass, momentum, and energy balances. A numerical example for a binary mixture shows that at long times, of the order of several days and longer, both molecular and thermal diffusion affect the hardening of the layer in which the wax forms.