Mathematical models for waxy crude oils

In this paper we review a series of mathematical models formulated for the flow of waxy crude oils, that is, of mineral oils with a high content of paraffinic hydrocarbons ( with the generic name of waxes) which may be dissolved or segregated as solid crystals at sufficiently low temperatures. The flow takes place in a laboratory test loop. The crystals have a tendency to form aggregates, producing a gel-like structure. The resulting product can be modeled as a Bingham fluid, but its rheological parameters ( yield stress and viscosity) depend on the amount and state of the segregated phase, whose evolution is in turn influenced by the flow. Of course temperature plays a key role. Wax can form a solid deposit at the pipe wall, reducing the pipe radius and this phenomenon is also taken into account. The models presented have a different degree of complexity, depending on which phenomena they include. In presenting each of them we discuss their expected range of validity.