Wax diffusivity under given thermal gradient: a mathematical model

Abstract

In this paper we describe how to obtain wax diffusivity and solubility in a saturated crude oil using the measurements of solid wax deposit in the experimental apparatus known as cold finger. Assuming that migration of dissolved wax is primarily driven by thermal gradients, mathematical models are derived relating the deposit growth rate to the above mentioned quantities. We will investigate the case in which the oil is not agitated. The stirred case is studied in part II. Comparisons with available experimental data are performed and possible sources of errors are discussed.

Solvent Dewaxing of Heavy Crude Oil with Methyl Ethyl Ketone

“…This can be explained by the fact that due to a greater temperature difference, a longer amount of time is required for the mixture to reach thermal equilibrium. This translates to a greater crystallisation time, allowing a greater amount of wax crystals to form [13]. In addition to this, the greater temperature gradient which the mixture is exposed to further encourages the formation of new crystals or nucleation, which enables a greater rate of formation of the wax crystals [13].…”

A Survey on Mathematical Modelling of Deposition in Waxy Crude Oils

“…As the dissolved wax reaches the cold finger surface it precipitates, forming a layer of deposit that is subsequently collected and weighed. In [7], [8] two mathematical models for the cold finger apparatus have been proposed, distinguishing between two different situations : (i) the oil is immobile (ii) the solution is stirred.…”

“…The main scope is to determine predictive formulas for the wax deposit and to use them for deducing the values of wax solubility c s and liquid wax diffusivity D. In [7] it has been shown that for typical temperature ranges of cold finger experiments wax solubility can be considered as a linear function of temperature. Therefore we write…”

“…It must be kept in mind that normally the deposit grows not as a thick solid layer, but rather as a gel structure with a large inclusion of liquid oil. Therefore it is important to perform suitable corrections to the mass collected over the cold finger to obtain the real content of solid wax (see [7] to see how to quantify this correction).…”

“…A device that is used to this end and that exploits the phenomenon of wax deposition is the so-called cold finger, which can be static or agitated by impellers. The theoretical basis of such a device has been investigated in [7], [8] and will be described in Section 4.…”