Page 177 - Handbook Of Multiphase Flow Assurance

Paraffin wax 173

the cutting of wax from the pipe wall and the pushing of wax cuttings ahead of the scraper.
The wax cutting force had been measured at the University of Tulsa. The same laboratory
provided an estimate of the amount of wax removed by a scraper. Typically 30–50% of wax is
removed in one scraping run when softer polymer cup scrapers are used. The rest of the wax
is smeared on the pipe wall. Subsequent scraper runs remove additional amounts of wax.
When more rigid K-disk scrapers are used, the wax removal may increase to 50–60% per run.

Comprehensive modeling
Models of wax deposition reproduce and model physical processes which occur in a pipe
during the process of n-paraffins diffusion to and inclusion in the solid deposit on a pipe wall.
Wax deposition is driven by diffusion of heavy normal paraffins to the cold surface.
Diffusion is caused by the difference in concentration of normal paraffin molecules dissolved
in the bulk of oil at high temperature and near the cold surface where these molecules come
out of solution as crystals. The straight chain normal paraffin molecules are more easily orga-
nized into regular crystal structures than the branched isomer paraffins. This affects their ten-
dency to crystallize and their solubility in hydrocarbon liquids. As some paraffin molecules
precipitate, their concentration in liquid decreases, and other molecules diffuse from liquid
to take their place.
When there is no difference in temperature, there is no driving force for normal paraffin
molecules to diffuse, and no wax deposition on a surface occurs. Nonetheless, when there is
a uniform cooling of fluid, without flow, the normal paraffins still precipitate as crystals and
usually settle at the bottom of the fluid because solids are usually denser than liquid from
which they form (except aqueous solids such as ice or hydrate).
The rate of diffusion of normal paraffins to the cold surface limits the growth rate of a wax
crystal in a deposit.
Similar to settling mobility of particles, diffusion of solids in liquid may be estimated by
Stokes-Einstein equation. Einstein's equation (1905) comes from the solute diffusion coeffi-
cient, derived from Stokes's law for a sphere of diameter D moving in a liquid, and van't
Hoff's law for the osmotic pressure:
Diffusion Coefficient_particle = k × T/(3 × π × viscosity_fluid × D)
where k = 1.381 × 10 −23 J/K, the Boltzmann constant.
However, the Einstein relation is only valid for small values of particle concentrations.
Dissolved particle movement due to collisions with other molecules can be estimated from
the same equation as:

( position position _ 0 ) ( time time_ 0 ) =× / 3kT ( ×× viscosityfluiid× )
2
−
−
π
_
/
D
Hayduk and Minhas (1980) method for evaluating diffusion coefficients in hydrocarbon
fluids fit laboratory data better than other correlations. That's why this diffusion correlation
may be preferred for use in wax deposition modeling.
As oil cools down, heavier n-paraffins become less soluble in oil, and partly precipitate out
of oil as solid crystals. In order to evaluate the amount of paraffins dissolved in oil at vari-
ous conditions, the solubility correlations were developed. Several recent solubility correla-
tions for waxy paraffins in hydrocarbons have been developed such as Won (1986), Erickson