(305a) A Model of Wax Deposition Accounting for Deposit Aging

Wax
deposition usually occurs in pipelines when temperature in the near wall region
drops below a so-called Wax Appearance Temperature (WAT). Precipitation of wax
particles from a fluid (the lower the temperature, the higher the particle
concentration) causes a corresponding deficiency of wax molecules in a fluid.
The wax molecule gradient leads to a diffusive flux towards the wall causing
the deposit layer formation. The wax deposit layer, growing over time, may
cause a significant reduction in a pipe cross-section and a flow rate
respectively. Eventually, the deposit may almost entirely obstruct the pipe
cross-section; therefore, under field conditions, the deposit layer formed on
the pipe wall is usually removed mechanically (by pigging). The pigging
procedure is applied periodically and its frequency depends on a deposit growth
rate forecast. To properly schedule a wax removal procedure, an accurate
modeling of the deposition phenomenon is needed.

A
model of wax deposition in oil-transport pipelines is developed. A deposit
layer is modeled as a porous medium with variable porosity that decreases due
to wax molecular diffusion across the layer. A deposit porosity reduction with
time is called aging. Wax solids are assumed to be in a thermodynamic
equilibrium with a hydrocarbon fluid. It is also assumed that the wax molecular
diffusivity through the porous layer is obeyed to the Archie law. Thermal
conductivities of the solid wax and the hydrocarbon fluid, composing the
deposit layer, are assumed to be different. An increase in the deposit thermal
conductivity due to aging is taken into account. The deposit removal rate due
to viscous friction between fluid flow and the layer surface is assumed to be a
function of both the local deposit layer thickness and the shear stress at the
deposit surface. An equation of the deposit layer growth is obtained in an
analytical form. A model performance is illustrated by calculations of wax
deposition in a flow loop (e.g., see Fig.1). The developed model is
computationally expensive for modeling wax deposition in long transport
pipelines. A simplified (engineering) deposition model, based on an analysis of
numerical results obtained using the full model, is also developed. The
simplified model excellently reproduces the numerical results obtained by the
original model. An engineering model performance is illustrated by numerical
calculations of wax deposition in a long oil transport pipeline (e.g., see
Fig.2).

Fig.1
Evolution of the porosity distribution across the deposit layer with time for
the two different values of the Archie's law exponent

z=y/d, y is the coordinate across the
deposit layer,  d is the layer thickness, D_p is the pipe
diameter, U is the mean flow velocity, k_sr
is the shear?removal model parameter, n is the Archie's law exponent

Fig.2 Distributions
of the average layer porosity along a pipeline (the axis x) for the two different
values of the Archie's law exponent and for the different deposition durations