Page 178 - Handbook Of Multiphase Flow Assurance

174 5. Flow restrictions and blockages in operations

et al. (1993), Pedersen (1995), Lira-Galeana et al. (1996), Coutinho et al. (2001), and Escobar-
Remolina et al. (2009). The relative comparison (Huang et al., 2015) of precipitated wax of
some of the above solubility models shows that the Erickson model predicts on average more
precipitated wax and is more conservative than the Coutinho method. Both models allow
tuning to WAT.
The solubility models evaluate the solid-liquid equilibrium for each component (such as
f
f
n-C 30 ) as function of the heat of fusion ΔH i and the melting point T i .
exp (
f
f
S
/
RT
S / X = (γ i L /γ i ) ( ∆ H / )(1 − T T ))
i
i
i
i
S
L
γ i and γ i are activity coefficients of component i in liquid and solid phases. The melting
point for normal paraffins depends on the molecular weight.
f
T = 374 50 02617 MW − 20172/ MW i
.
+
.
i
i
In comprehensive models the multiphase or single phase flow model which calculates hy-
draulic frictional and hydrostatic pressure drops is coupled through time with heat transfer
from oil to surroundings and with mass transfer which calculates the radial diffusion of wax
components in crude oil as a function of pressure and temperature. This coupling is done
for several sections of the pipeline. Changes in composition of oil are tracked from section to
section. Two-dimensional models keep track of both longitudinal and radial distribution in
wax components. Circumferential variation in properties is commonly ignored because heat
transfer is calculated axisymmetrically.
An overview of wax deposition laboratory measurements and modeling methods was pre-
sented by Theyab (2017).
The models allow to evaluate the rate, location and amount of wax deposited on a cold
surface such as well tubing or pipe wall.
There are commercial wax deposition models, proprietary in-house models developed by
operator companies, and university research models some of which were in part derived
from the proprietary company models. A comparison of field data and commercial models'
predictions was presented by Giacchetta et al. (2017).
Waxy gels
In normal production, wax deposits contain some solid wax crystals and some liquid occluded
within the porous wax matrix. Solids content in a deposit usually ranges from 10 to 50 vol%.
Waxy gels form when the whole bulk of fluid converts, upon cooling, into a solid-like
material. In a waxy gel, the amount of wax is sufficient to form a network of solid crystals
interconnected so that it behaves like a solid. Solid content in a gel typically ranges from 3 to
10 vol%. The pores are occupied by liquid.
Both wax deposit and wax gel have the same structure. Waxy oils which can form a gel,
contain enough normal paraffins to build a network of crystals in the whole volume of the
liquid after cooling. The oils which form a deposit do not have enough normal paraffins to
fill the whole volume with crystals after cooling, but gradually build the deposit on the pipe
or a well tubing wall.