Modelling wax diffusion in crude oils: The cold finger device

Abstract

In this paper we show how to obtain wax diffusivity and solubility in crude oils from deposition measurements in the cold finger device with stirring. We present a mathematical model in which the physical quantities are assumed to be space-independent in the bulk region of the device, because of agitation. Comparison with available laboratory results is provided, showing that the wax diffusivity values obtained in simulations are in agreement with data of field experiments.

Badanie wpływu ciśnienia i temperatury na proces wytrącania parafin w ropie naftowej

“…Walec jest stopniowo ochładzany i gdy temperatura spadnie poniżej WAT, rozpoczyna się osadzanie parafiny na jego powierzchni. Metoda ta obarczona jest błędem, gdyż zaobserwowanie parafiny możliwe jest dopiero, gdy utworzy ona odpowiednio grubą powłokę [2,13].…”

Wax Segregation in Oils: A Multiscale Problem

“…This fact can be modelled introducing a second free boundary x = σ(t) where σ(t) represent the thickness of the deposit or assuming that such thickness is negligible and that the wax reaching x = 0 simply leaves the system; this corresponds to replacing the third condition in (26) by G x (0, t) = 0. This approach (with or without the free boundary σ(t)) has been used to interpret the data of the cold finger experiment (see [14]); in [27] the difference of heat between the mixture and the deposit has been also taken into account.…”

“…Under these assumptions, we will consider a one-dimensional geometry having in mind the interpretation of experiments done on commercial oils with a laboratory device called "cold finger" where a steady thermal gradient is applied between two co-axial cylinders kept at constant temperatures T 1 and T 2 and the gap between the two cylinders is filled by oil with given wax concentration c * . Of course at least one of the two thermostats is maintained at a temperature below T CL (c * ) ( [14], [15]). Just to simplify notation, we refer here to plane (rather than cylindrical) symmetry, and for the same reason we will assume that T CL depends linearly on concentration in the range of interest, so that…”

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.…”

“…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.…”