Incipient wax−oil gel deposits form in crude oil transport pipelines when long-chain n-paraffins
precipitate at the cold interior surface of the pipe wall. The kinetics of paraffin gel formation
was studied using model fluids consisting of monodisperse and polydisperse n-paraffin
components dissolved in petroleum mineral oil. Classical homogeneous nucleation theory was
applied to investigate the supersaturation conditions necessary for crystal formation. Differential
scanning calorimetry was used to monitor paraffin crystallization rates and to provide solid-phase fraction measurements. Gelation occurs when growing n-paraffin crystals interlock and
form a volume-spanning crystal network which entrains the remaining liquid oil among the
crystals. Paraffin wax−oil gels exhibit a mechanical response to an imposed oscillatory stress,
which is characterized by the elastic storage modulus G‘ being greater in magnitude than the
viscous loss modulus, G‘ ‘. Low-temperature rheological gels can form from model fluids with
n-paraffin contents as low as 0.5 wt %. Images of wax−oil gel morphologies were obtained using
a cross-polarized microscope fitted with a z-drive and indicated crystal lengths of ∼10−20 μm.
A microstructural gelation model based on percolation theory was introduced to provide
predictions of gel formation conditions among randomly oriented paraffin crystals. The structural
model provides correlations of crystal morphologies and solid fractions at the percolation threshold
condition. Comparison of the initial wax contents required for gelation of monodisperse and
polydisperse n-paraffin wax indicates that sharp crystal edges and ordered crystal faces hinder
the paraffin crystal−crystal “anchoring” interactions which result in mechanical gelation.
Analytic approximations for percolation points in two-dimensional and threedimensional particulate arrays have been reported for only a very few, simple particle geometries. Here, an analytical approach is presented to determine the percolative properties (i.e. statistical cluster properties) of permeable ellipsoids of revolution. We generalize a series expansion technique, previously used by other authors to study arrays of spheres and cubes. Our analytic solutions are compared with Monte Carlo simulation results, and show good agreement at low particle aspect ratio. At higher aspect ratios, the analytic approximation becomes even more computationally intensive than direct simulation of a number of realizations. Additional simulation results, and simplified, closed-form bounding expressions for percolation thresholds are also presented. Limitations and applications of the asymptotic expressions are discussed in the context of materials design and design of sensor arrays.
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