B41oa oil and Gas Processing Section a flow Assurance Heriot-Watt University

 
Mathematical Modelling of Wax 
A mathematical model is a more cost-effective method for estimating wax 
phase equilibrium. The models developed in the early years are very simple 
with regard to components and commonly include only one solvent compound 
and only one solute (Holder et al., 1965). 

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TOPIC 3: Wax Deposition 
 
 
 
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NIVERSITY B41OA December 2018 v3 
Several thermodynamic models have been presented in the literature for 
predicting wax phase boundary. Some of the more cited models are reviewed 
below. 
Won
 
(1986, 1989) presented a wax model as an early effort to use a 
thermodynamic approach for predicting wax phase boundary: 
•
The Soave-Redlich-Kwong (SRK) EoS was used for vapour-liquid 
equilibrium (VLE) calculations. 
•
A modified regular solution approach was employed for solid-liquid 
equilibrium (SLE) calculations, where activity coefficients were 
calculated using solubility parameters of individual components. 
•
The critical temperature, critical pressure and acentric factor were 
estimated using correlations suggested by Spencer and Daubert 
(1973) and Lee-Kesler (1975), respectively. 
•
The fusion temperature and heat of fusion were correlated to molecular 
weight using experimental data – this was predominantly for pure n-
paraffins with odd carbon numbers. 
In 1989, Won modified the model: 
•
He used an approach that combined the modified regular solution with 
Flory-Huggins equation for calculating the activity coefficients in the 
liquid phase. 
•
The wax model proposed by Won was validated against cloud point 
temperatures measured for synthetic fuels, diesel fuels and North Sea 
gas condensates. 
•
This model was adopted by many other researchers, sometimes 
without any modifications, for developing their own wax models. 
However, there are several major shortcomings in the model proposed by Won 
and these limit its capability and reliability when used to predict the wax phase 
boundary: 
1. Two different approaches are applied to the liquid phase for VLE and 
SLE, i.e., an EoS is used for VLE, while an activity coefficient model is 
applied to SLE – this often leads to inconsistent liquid phase 
description and calculation convergence problems. 
2. Next, the modified regular solution approach used for describing wax 
solids does not vary greatly from the ideal solid solution approach; this 
is due to the similarity of the solubility parameters for n-paraffins. Both 
approaches lead to overestimated wax phase boundary. 
3. The model cannot provide reliable predictions on wax phase boundary 
at high-pressure conditions – this is because it ignores the effect of 
pressure on wax formation. 
4. Finally this model is based on WAT data, which are not reliable for 
tuning and/or validating a model. 
 

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TOPIC 3: Wax Deposition 
 
 
 
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NIVERSITY B41OA December 2018 v3 
Hansen et al. (1988) presented a wax model as follows: 
•
It uses the SRK EoS for VLE calculations. 
•
For SLE calculations, the ideal solid solution approach was applied to 
the solid phase, and a polymer solution approach was applied to the 
liquid phase. 
•
Parameters required in the polymer solution approach were determined 
by fitting measured cloud point temperatures for 13 North Sea crude 
oils. 
•
It was, therefore, not surprising that the model-predicted WAT values 
were in good agreement with measured data, since the North Sea 
WAT data was used to tune the model parameters. 
Pedersen et al. (1991a, 1991b) presented a wax model as follows: 
•
They modified the model proposed by Won. 
•
The modified regular solution approach was applied to both the liquid 
and solid phases. 
•
Fusion properties and heat capacity for pure compounds were tuned to 
fit the measured wax precipitation data for North Sea oils. 
•
This model was validated using experimental WAT data for North Sea 
oils. 
•
Pedersen (1995) modified the model in that a cubic equation of state 
was used for consistent description of the liquid phase in both VLE and 
SLE calculations. 
•
The ideal solid solution approach was applied to the solid phase. 
•
Fusion properties were calculated using correlations suggested by 
Won. 
•
The wax model proposed by Pedersen et al. uses doubtful values of 
fusion properties and heat capacity. 
•
The approaches used for describing wax solids in the model proposed 
by Pedersen et al. i.e., the approaches of regular solid solution and 
ideal solid solution, led to an overestimated wax phase boundary. 
•
These models are based on WAT data. 
 
Erickson (1993) presented a wax model as follows: 
•
He proposed a modification of the model proposed by Won. 
•
The ideal solution approach was applied to SLE calculations. 
•
Heat of fusion for pure compounds was tuned against experimental 
SLE data for binary mixtures. 
•
The proposed model was validated against experimental WAT data for 
crude oil and condensate samples. 
•
The model proposed by Erickson et al. has similar limitations as the 
model proposed by Won.