Some Mathematical Problems in Oil Pipelining
Mario Primicerio
When a crude oil containing a relevant amount of heavy components (paraffin, asphaltene, waxes) is transported in pipelines and radial thermal gradients appear, then a solid deposit can be formed at the pipe wall, thus reducing the efficiency of transport.
The aim of this talk is to provide a general description of the mathematical models used to describe the phenomenon and to discuss them in the framework of a multiscale approach.
The main phenomena that are involved are:
a) Fluid motion.
b) Thermal convection and conduction.
c) Crystallization.
d) Convection and diffusion of wax.
Concerning c), it is known that at temperatures below WAT (wax appearance temperature) wax is present both in the form of dissolved phase and as a crystallized phase suspended in the oil. Different scenarios can be considered, depending on the specific kinetics that is assumed to describe the process of dissolution/segregation, including the limit case of instantaneous thermodynamical equilibrium. In addition, the possibility of the formation of a gel-like structure should also be taken into account as well as the phenomenon of ageing of the gel.
Special cases are considered and discussed in connection with an experimental device (the so-called cold finger) designed to determine the wax diffusivity. The corresponding mathematical models are presented and the results of numerical simulation are compared with the experimental results.
The mathematical analysis of the models will also be summarized and some well-posedness results will be reported. The possibility that the wax deposit influences the thermal (and velocity) field is also taken into account.