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Calculating Deposit Formation in the Pipelining of Waxy Crude Oils

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Abstract

Wax deposition from a waxy crude oil is modelled in turbulent flow in a pipeline. Molecular diffusion in a thin boundary layer near the pipe wall is taken as the only mechanism responsible for deposition. The model takes into account the ablation, which is a flow-related phenomenon that limits the growth of the deposit. The effect of desaturation of the oil is analyzed as well. Two field cases are presented in which the numerical implementation of the model is in agreement with the experimental data.

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Abbreviations

r :

Radial coordinate

z :

Longitudinal coordinate

L :

Length of the pipeline

R :

Pipe radius

R T :

Radius of the region where temperature is independent from r

R m :

Radius of the turbulent core

\({\nu}\) :

Radius of the deposition front

\({\sigma_{\rm d}}\) :

Thickness of the deposit

\({\sigma_{\rm T}}\) :

Thermal boundary layer thickness

\({\sigma_{\rm m}}\) :

Momentum boundary layer thickness

\({\theta_{\rm T}}\) :

Ratio \({R_{\rm T}/\nu}\)

\({\theta_{\rm m}}\) :

Ratio \({R_{\rm m}/\nu}\)

\({\varepsilon_{\rm T}}\) :

\({1-\theta_{\rm T}}\)

\({\varepsilon_{\rm m}}\) :

\({1-\theta_{\rm m}}\)

V :

Velocity of the turbulent core

η:

Viscosity

Q :

Volumetric flow rate

ΔP :

Pressure gradient

\({\tau}\) :

Shear stress acting on the turbulent core

\({\rho}\) :

Density

f :

Friction factor

χ:

Surface roughness

Re :

Reynolds number

T :

Temperature in the thermal boundary layer

T c :

Temperature in the region 0 ≤ r ≤ R T

T e :

Temperature of the surroundings

T w :

Temperature at the pipe wall

T o :

Temperature of the oil at the inlet

T cloud :

Cloud point

c :

Specific heat

k :

Heat conductivity

h :

Heat transfer coefficient

α:

\({k/(\rho c)}\)

μ:

k/(h R)

z f :

Longitudinal coordinate after which deposition starts

z des :

Longitudinal coordinate after which the turbulent core becomes unsaturated

z e :

Longitudinal coordinate after which deposition ceases

z s :

Longitudinal coordinate after which deposition ceases because of desaturation

M tot :

Total mass of deposit (oil included)

M exp :

Mass of recovered material

D :

Wax diffusivity

C s(T):

Solubility

G :

Segregated wax concentration

c :

Dissolved wax concentration

\({\beta}\) :

Derivative of solubility w.r.t. temperature

\({\psi}\) :

Solid wax fraction of the deposit

A :

Ablation coefficient

\({\overrightarrow{j}_{\rm wax}}\) :

Dissolved wax mass flux

\({\overrightarrow{j}_{\rm dep}}\) :

Total mass flux

\({j_{\rm abl}}\) :

Ablation rate per unit surface

\({\overrightarrow{e}_{\rm r}}\) :

Unit radial vector

\({\overrightarrow{e}_{\rm z}}\) :

Unit longitudinal vector

\({\overrightarrow{n}}\) :

Unit normal to the deposition front

\({t_{\rm a}}\) :

Characteristic consolidation time

\({t_{\rm o}}\) :

Characteristic deposition time.

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Authors and Affiliations

  1. EniTecnologie, Via F. Maritano 26, 20097, San Donato Milanese (MI), Italy

    S. Correra & D. Merino-Garcia

  2. Dipartimento di Matematica, “U. Dini” University of Florence, Viale Morgagni 67/a, 50134, Firenze, Italy

    A. Fasano & L. Fusi

Authors
  1. S. Correra
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  2. A. Fasano
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  3. L. Fusi
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  4. D. Merino-Garcia
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Corresponding author

Correspondence to A. Fasano.

Additional information

Work performed in the framework of the cooperation between EniTecnologie (Milan) and I2T3 (Florence).

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Correra, S., Fasano, A., Fusi, L. et al. Calculating Deposit Formation in the Pipelining of Waxy Crude Oils. Meccanica 42, 149–165 (2007). https://doi.org/10.1007/s11012-006-9028-4

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  • DOI: https://doi.org/10.1007/s11012-006-9028-4

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